Yes. Without a doubt. Unless they haven't taken graduate level complex analysis, or they don't understand Galois Theory very well. Then they're crap.
Which doesn't mean the good ones don't sometimes get lost as to whether this is the first or second time through the tune. Counting to 2 is usually left to the graduate students.
I don't think a flare for analysis sets mathematicians apart. There are two ways you can do maths, the first is to be thorough and patient, the second is to be wreckless first and thorough later. The wreckless part requires intuition
But my distionary has intuition as "direct perception of truth, fact, etc., independent of any reasoning process" But there is no truth in art.
I think being good at math is more closely connected with being a good composer than just a good instrumentalist, which really just requires good memory, rhythm and coordination and not so much the logical aspects needed to put together really nice tunes. The way music is written is very mathematical--notated music is dressed-up graphs with the notes being functions of time, although music notation is very different and more elaborate than that used in math so the two don't look too alike. Tunes are just big piecewise functions really.
For Western Art Music, I'd say being mathematically inclined is a big help, especially when one has continually to sight read complex rhythms. Also, the classical musician has to play notes of the same duration (without the swing) and that's something us trad heads aint great at.
Folk music to me is more about intuition and for that, being mathematically inclinded may even get in the way....
Intuition is not the right word. An example of intuition is where a poker player bets on a hand with a feeling it's gonna win. He could do the complex probability maths, but instead he has intuition. This is not how music works. You choose how to play a phrase based on some spurious think in you head somewhere that is pure creativity. There is no subconscious thought of probability that it will work, just pure invention
Mathmeticians=good technicians, music robots, perhaps, not good musicians. Capturing the feeling, the phrasing, making the magic happen through the music is more artistic than technical. My cousin could play all the right notes for all the great guitar heros like Van Halen, Hendrix, etc, but he knew he couldn't really make music; so he went and made a killing on Wall Street as a hedge fund manager (still is) and is the richest man I know, but still a lousy musician.
poems and musical phrases aren't equations that have to balance. The best poems and musical phrases are the once that don't quite balance, and are all the more inexplicably good for it
But in math there are set rules that you must follow to get the solution. In music you can bend the rules and change note values as long as you stay with the fairly loose parameters of the rhythm. Also, the rules used when writing music are often broken. Im math this would lead to a mis-solved problem. If you subtract before you divide, the answer will be different.
I think it might be backwards. Musicians make better math students. At least that's what the St Louis Symphony said on some flyers for their community music programs. They said there was proof that kids that played instruments score better in math.
I would venture, there are different "types" of musicians. Some are more technically skilled, i.e., in terms of being able to transcribe from one key to another without thinking about it, or being able to place extemporaneous variation.. Some are more intuitive in other areas, and their playing might be more appealing in some ways to listeners if they are emotionally intuitive -- but perhaps they are not so good at playing spontaneous variations. People with certain kinds of mathematical intuitive ability tend to juggle patterns very rapidly, in their brains.
Some have a balance of mathematical-type intuitive ability and other kinds of inuitiveness (more language-oriented and emotional). They might have "the whole package."
Long answer to follow. It has much more to do with the ear you're born with. Your ear affects everything from how you speak to how you play music. By ear I mean how well your brain can distinguish pitch without referring to an additional reference.
My wife is an excellent mathematician, but has less of an ear for pitch than I do. What this means in practical terms is fairly profound. She can explain to me how counterpoint works, along with other aspects of music theory, and can sight read music and play it on the piano. However, I can pick up tunes purely by ear despite having little knowledge of theory.
I can also speak with almost any accent after I hear enough of it. My wife's French accent sucks, while mine is pretty damn good, to the point that French people can understand what I say even though she has the superior French vocabulary. Knowing the words is not very useful in conversation if you can't pronounce them properly. I think your ear has a great bearing on your ability to speak with a different accent.
Still, people with a lesser ear can appreciate music to the same degree as those more fortunate in the area of pitch recognition. My wife will correctly point out that I can't sing certain songs with the same feeling as the originals. Even though I can sing in key and she might not, she can tell when the actual quality of my performance is not up to snuff.
So it's a bit of a wash I suppose. For the record, I have an engineering degree but never got above a "C" in college math classes. I suck at math. But I'm lucky to have an above-average ear for pitch. I'm okay with that.
I do think there's a connection. I've met people who were skilled in both; they could be show-offs, to be honest, but some of that lay I think in the fact that they couldn't conceive how other people weren't able to think as nimbly as they could, in mathematical and musical matters and no doubt other things besides - these were bright people.
At school I dreaded maths and wasn't just no good at it, I found it entirely incomprehensible once I was past learning my tables. I was told my life had no prospects if I didn't pass Maths O-Level, certainly none of going to University. I passed the O-Level by doing a fraudulent subject called New Maths, which was explained to me (adequately) in about ten, fifteen minutes by a fellow-pupil after I'd spent about a year and a half failing to understand it in class. I went to university, and found the place full of people with no Maths O-Level.
Thanks for the article. I'm a huge fan of science conducted with proper empirical evidence, yet this didn't seem to jibe with my own experience.
I've been exposed to classical music since I was very young. It's about 90% of the music I listened to for the first 15 years of my life. I also would seem to have good "spatial temporal" reasoning based on the article's definition. So why do I suck at math? My teachers were pretty good, and fairly patient. I think it has been a failing within myself.
Again, I think musical ability has got more to do with the link between our ear and our brain than anything else.
To add to my last comment: and that's hardly quantifiable, which is why people seek other explanations for a link between math and music. Specious reasoning in my opinion.
Maybe, if the article is anything to go by, that you might have done better by listening to Mozart only - and bodhrans!
Personally, I have a feeling that the link being made between math and music mightn't be the best link. We always used what is called the Modern Language Aptitude Test (for want of anything else) to get some empirical indicator of people's ability for shorthand, which is essentially an aural skill - and a language, just like any other language. There was a high correlation between ability in the best and ability in shorthand - it wasn't written in stone, but an indicator. Some of the best successes were by people who didn't go well at the exam at all.
What is recognised (anedotally) in that industry though is that people who are skilled musicians, especially pianists (and probably harpists) for that matter, but including melody instruments of course, had a particularly high aptitude for learning shorthand i.e. learning a new language.
It would be interesting to see whether there is a correlation between people who are good at maths and whether they score highly on the MLAT test. Maybe music is processed and acquired by the brain in a similar way to that in which language and shorthand is acquired.
Maybe music is a form of language - at least according to how we process the learning of it - whether we know what that process is or not.
I was pretty much the worst mathematician in my form back when I did my A-levels. I was so bad that I was the only one in a course of 20 who wouldn't have to take the oral examination since it wouldn't have changed anything to my mark. Anyway, I did get my A-levels and while I'm not uber great at music, I'm certainly not as bad as my mark in mathematics.
Bingo! There IS a link between language and music, as I alluded to earlier. The military/DoD has a test called the "Denfense Language Aptitude Battery" or DLAB. It doesn't test your ability in any one language, but rather your capability to learn new ones. I scored well enough in the DLAB to request whatever I wanted to learn from Persian to Tagalog to Mandarin. Of course I got French since I admitted to taking three years of it in high school LOL but it's considered an 'easy' language compared to most others.
Language and music are most definitely related. The link between math and music is tenuous at best. Re. Mozart: I heard "Eine Kleine Nachtmusik" at least ten years before I had to take calculus! Didn't help much ;)
what we also noticed was the fairly stunning statistical incidence of people who were trained in classical music (we noticed piano mainly), who were also fluent in other languages, not just (on their observation) because they had received training in them, but because they felt they had a natural aptitude for language. It is almost a universal response.
So, I was wondering how many people here, who play ITM and/or other music also think they have a natural ability for or do speak languages other than their first language.
As a corollary, perhaps, I wonder what proportion of those players (the language speakers) also consider they are good at math.
Well, you were probably typing when I posted my last response, but there's one reply. I am good at music and other languages and sub-par at math. One qualification though: I am better at learning pronunciation of other languages than their grammar. Perhaps that directly correlates to the fact that I can recognize pitch but not explain how it fits into a mode.
I think that pronunciation acquisition is an aural skill an additional subset of language acquisition. Sure we can learn how to read and speak a language, but pronunciation is something that seems to come more naturally to some people than others. It seems to be a nuance that some people can pick up on earlier than others? Maybe playing music has a similar dichotomy - one can play music technically well, but maybe without the nuance of message than may come from particular emphasis on rhythm, emotion, etc, - maybe those things equate to 'pronunciation' in music - including ITM of course - and in particular. We can all speak a language, but not many of us are poets.
My hunch is that the linguists, and the speakers of other languages from natural aptitude probably make the "best" musicians. This of course doesn't exclude good mathematicians, nor does it necessarily follow that the speakers would be musicians, but I wonder about the statistical correlation.
Your own experience, Scott, seems to be consistent with that hypothesis.
And I'll first, just for the record - my wife is a 'natural' bodhran player - didn't learn anything, just picked it up and off you go - very very good. She's also a strong mathematician and sudoko fan, for goodness sake. I can't think of a more exquisite torture than flickin' sudoko. Her brother is also a serious maths/engineering person - designs pacemakers (there's the rhythm connection, eh), and stuff like that. He's probably a fair rocket scientist as well.
1. Maths has nothing to do with the ability to do arithmetic. Alan Turing, possibly one of the greatest mathematicians of the last century, couldn't even be trusted to add up the scores in card games.
2. Real mathematicians are inventive rule breakers. "I wonder what would happen if I . . . " Fortunately if it goes wrong all you get is a messy bit of paper or a really boring pattern on the computer screen. This is not true when chemists just wonder what would happen if they added this to that.
3. The ability to recognize patterns is important in both maths and music. It's what makes both playing by ear and reading at sight possible.
4. Mathematicians are very lazy. That part of maths which is not driven by the desire to see what happens if . . . is driven by the desire to find an easy way to do something.
5. Many 'arts' people despise maths without having the faintest idea what they are talking about. 'I was always hopeless at maths' they say proudly, as though it's some badge of honour.
The ability to recognise patterns is also important so that you don't get run over crossing the road, c.g., or being able to pick the likely winner of a horse race.
Humans are pattern-recognising beings, it isn't just confined to maths and music.
I dont think it means quite alot - I read also the creative and -
Mathematical + Languages sides of the the Brain are in two different places - But theres me who Never passed a Maths
Test in his Life - Last nearly always - Though that dose'nt
count for much- But a friend who was worse than maths than
me {saying something} Was a Cracker Banjo player.. And
another friend who is a Lecturer at Trinity College Dublin,
Is also a great banjo now fiddle player,,Both could hold notes/tunes in their heads after hearing the tune just a couple of times,,Maybe this Juxtaposition {like that word} .Dose not
really matter at all...
jim,,,,
I'm reasonable at maths, music and languages, not great at any of them but able to see what is needed!
If I really understand the maths of traffic flow patterns, I might be able to predict the traffic (you'd have to factor in the psychology of road users, though). If I had enough information about the horse, jockeys, course going etc etc I could probably predict what would win. Lack of data, not inherent fault of the method, Plus, in the case of racing, Really Large Gentlemen who would like to tell you that the bookmaker Isn't Happy about you winning so much.
A BA (Hons) in maths, and you say you are (only) reasonable at maths, c.g? I would think you would have quite enough stats from that to pick the winner of a horse race!
Great link, Jim. I'm definitely a clockwise/right-brainer for the most part, but can see the direction go anticlockwise if I don't think about it too much.
I suppose that's better than being a 'no brainer', so it is a comfort to me.
That's a statement i cannot agree with. It depends what you mean by 'truth'. You seem to be saying that mathematics, and/or science produces 'truth', whilst art does not.
I think there are at least two kind of 'truths'. 'One plus one equals two', could claim to be a scientific truth. 'I love you', could claim to be a human truth. When you get down to the kernel of both, they are just stories we tell ourselves, just electro-chemical neural activity.
Science doesn't claim to establish truth. Science proposes hypotheses and theories which can be tested by measured data. I assume that we have been living on the same planet for thousands of years, but science has seen it as being in a Ptolemaic, a Copernican, a Newtonian, an Einsteinian Universe, as one theory superseded its predescessor and was accepted as being of greater explanatory power. Now we've got String Theory and M-Theory, that propose that we are actually living in an 11 dimensional Multiverse....where that leaves 'truth', I really don't know.
Even the claim that 'one and one equals two' cannot be proven in an ultimate sense. See Godel's Theorem.
Whilst scientific method seems to be the best way available to us when we try and understand existence, the big drawback is that it only deals with what can be measured, so elusive qualities like beauty and soul are beyond it's remit. But for most people, all the stuff that makes life worth living is in the un-measurable domain, and that's why the truths of art, music, poetry, literature, etc, matter, because they can convey truths about the human condition.
Look at the Palaeolithic cave paintings. They tell us something about those people who could observe and depict the 'true' qualities of animals as well as any artists ever.
I have a foot in both camps. If I want an operation for cancer, I want a scientifically trained surgeon who knows what a milligram is, please, not a poet. But if I'm in a lousy mood, I like to listen to something like 'The fair haired boy', played by a musician with the sensitivity and depth of character to express profound human emotions, and I don't care whether he or she can count a handful of beans.
Never tried it, Duijera Dubh. From the rumours I heard, it seemed like Rubik's Cube or the card game Patience or Crossword puzzles, and I already have far too many more exciting and intriguing matters to keep myself rewarded.
Science doesn't find the "truth" so much as it constructs models -- often mathematical ones -- that describe a natural phenomenon. The models are "true" so long as they work but if data is found that doesn't fit the paradigm, scientists (over a period of time) end up modifying the paradigm.
Perhaps another explanation of the math-music link is in part a self-fulfilling prophecy. The theory that people who are good at math are also good at music has been around for a while. Is there actual evidence showing a physiological connection between a person's mathematical and musical abilities? Unlikely, as maths and music are both heavily influenced by social factors and other variables, to such an extent that I don't think you ever can empirically prove they are linked. Too many intervening variables in the way to be able to make a good argument. However, there is quite a lot of research showing the power of suggestion. If you hear that mathematical and musical abilities are linked and you happen to be good at math and like it, you can take up music believing you can be good at it, which greatly increases the likelihood that you will be.
While math factors into music in terms of understanding how rhythm and chords work, I would say that there are multiple ways to familiarize oneself with rhythmic and chordal structures. There are people who intuitively understand it, brilliant musicians who don't know a thing about music theory. If you have more of an analytic approach to music theory, I don't think it is necessarily linked to maths alone, but rather any analytic ability to understand and better yet create structures and patterns.
Music, math, language, are not LINKED, they are different representations of the same thing.
(I really don't know how else to say it)
As a former music teacher in US public schools, I saw the "research' being strutted about, saying music helped kids score better in math, etc... But I always felt that they were missing the point. Music IS math, music IS language. As for those test scores: Did the kid whose parents saw to it that an instrument was procured, the kid practiced, did they not also oversee other homework? Did those kids also follow through with other things?
I just know that I don't need "research" to tell me what I know to be true. Phythagorus wanted to measure "music" and that's how we got math.
MY brother was in the area of Knoxville, and Oakridge, TN for awhile (nuclear power something), huge concentration of scientists, mathematicians live and work in the area. In his spare time, he part of an opera chorus there. The arts/music scene there was/is filled with very good musicians that have dayjobs in the math and science fields. One guy was a concert classical guitarist in Europe before becoming a top nuclear physicist.
Does it make the statement, " If your good at maths you'll be good at music! " true or not? There are too many other things to factor in. Maybe that thing they are good at (math, music, languages) is the way they express that deep understanding of "it" (that thing that music, math, and language represent). Maybe some people can express that deep understanding of "it" in a variety of ways.
Early in the morning here, I haven't had my coffee yet, no one else is up. can ya tell???
"Science doesn't find the "truth" so much as it constructs models -- often mathematical ones -- that describe a natural phenomenon. The models are "true" so long as they work but if data is found that doesn't fit the paradigm, scientists (over a period of time) end up modifying the paradigm."
I don't disagree, Silver Spear.
(Kuhn was good on that stuff, but I like Feyerabend even better.) And what you have said here is a model (in your brain) of what science is. It's one of the generally agreed models, taught and shared in our culture.
Seems to me that what culture is, (e.g., English or Irish or Japanese), is bunch of such commonly shared models, indoctrinated by the previous generation.
I would argue though that a model commonly used to describe science is one describe a narrative of going from ignorance to enlightenment, towards a greater understanding of "truth." Michael's above comment about truth setting science and art apart seems to be partaking in that narrative, which I contend doesn't accurately describe what science does.
In fact, you can make the argument that "truth" itself is a construction.
I meant to add in my last post that the interesting questions then are how culture is constructed. Post modernism isn't as cutting edge as it used to be and it's taken for granted in a lot of fields that yes, knowledge and culture are indeed socially constructed. Most of the work done now by people who take that relativist position is researching the mechanisms by which that happens.
Yeah, Silver Spear', I think it's better to speak of 'claims to truth' made in whatever context.
I see the major distinction between Science and the rest, is that scientific 'truths' are supposed to be supported by an argument resting upon empirical evidence, rather similar to the Law, where a prosecution case requires evidence. You can't just say anything you want.
Whereas in the Arts, anybody can do anything they like. If it resonates with an audience, maybe they'll recognize some new 'truth' about themselves or their situation and adjust their socially-constructed preconceptions.
but, are artists really just saying anything they want, or are they saying truth, and that is why it resonates? Yes, on the surface, that in art one can just say anything, but really, in the heart of the artist, is it "just anything" or is it truth based on the evidence of themselves?
going for the coffee now...
One plus one only equals two under certain circumstances.
Do the statements 'I like this work of art' and 'This work of art is good' mean the same thing?
'In maths you have to follow the rules . . . ' Certain 'rules' apply to all of us. Like the Law of Gravity. We don't 'follow' them, in the sense that we follow a rule that tells us to stop when traffic signals are are on red. Mathematics is a way of describing reality. Or unreality.
I think that is what distinguishes the great or highly regarded artists from the ones that are quickly forgotten. I mean, anybody who paints or sculpts or writes an opera can think they are producing important wonderful stuff to change the world. But if most people think it's crap it'll soon disappear. Whereas there's plays like Antigone that still have influence after a couple of thousand years, because they resonate, they reflect something that we know is true about humans and the way the behave.
Silver Spear wrote : "...knowledge and culture are indeed socially constructed. Most of the work done now by people who take that relativist position is researching the mechanisms by which that happens."
Seems to me that one of the mechanisms is compulsory education. Here's a quote from Forbes magazine, from
"The techniques of brainwashing developed in totalitarian countries are routinely used in psychological conditioning programs imposed on school children. These include emotional shock and desensitization, psychological isolation from sources of support, stripping away defenses, manipulative cross-examination of the individual’s underlying moral values by psychological rather than rational means. These techniques are not confined to separate courses or programs...they are not isolated idiosyncracies of particular teachers. They are products of numerous books and other educational materials in programs packaged by organizations that sell such curricula to administrators and teach the techniques to teachers. Some packages even include instructions on how to deal with parents and others who object. Stripping away psychological defenses can be done through assignments to keep diaries to be discussed in group sessions, and through role-playing assignments, both techniques used in the original brainwashing programs in China under Mao."
"Even the claim that 'one and one equals two' cannot be proven in an ultimate sense. See Godel's Theorem."
Godel's theorem says nothing even remotely like that. In fact, it only applies to formal deductive systems that ARE strong enough to prove a certain collection of facts about arithmetic.
If you read carefully the first paragraph of the modernized translation of Godel's original paper (the link at the top of the miskatonic page), it makes this very clear:
"The development of mathematics towards greater exactness has, as is well-known, lead to formalization of large areas of it such that you can carry out proofs by following a few mechanical rules. The most comprehensive current formal systems are the system of Principia Mathematica (PM) on the one hand, the Zermelo-Fraenkelian axiom-system of set theory on the other hand. These two systems are so far developed that you can formalize in them all proof methods that are currently in use in mathematics, i.e. you can reduce these proof methods to a few axioms and deduction rules. Therefore,
the conclusion seems plausible that these deduction rules are sufficient to decide all mathematical questions expressible in those systems. We will show that this is not true, but that there are even relatively easy problems in the theory of ordinary whole numbers that can not be decided from the axioms. This is not due to the nature of these systems, but it is true for a very wide class of formal systems, which in particular includes all
those that you get by adding a finite number of axioms to the above mentioned systems, provided the additional axioms don’t make false theorems provable. "
For the first known (1982, 51 years after Godel's paper) example of a meaningful fact about arithmetic (as opposed to a fact about arithmetic arising from the technical details of Godel's proof) that can't be proven in the modern replacement for PM (Peano Arithmetic), see http://en.wikipedia.org/wiki/Goodstein's_theorem . That gives an indication of the kind of complexity that's necessary to construct unprovable statements. The difference between that and 1+1=2 is colossal.
I'll bet it would be possible to employ a small army of mathematical logicians to debunk all of the mis-applications of Godel's theorem made by people who don't understand what it says.
I'm happy with my understanding of Godel's Theorem, GaryAMartin, so I'm not going to argue with you about it here, because it'll go on forever and I'm not in the premier league of mathematicians. No doubt there are lots websites where myriads of mathematicians are haggling over the topic just as folks like to haggle over Frankie Gavin on this site
To say that mathematicians make the best musicians implies to me that the music is a science when it obviously is not. Yes there is a scientific mathematical aspect but such views ignore the role of art and feelings and opinion on what sounds good.
Thank goodness for that other wise we would all sound and play the (insert the name of the perfect instrument) the same way, it’s the interpretation , the art that makes the difference
Computers work using binary system, zeroes and ones. If I remember, Leibniz invented it and got idea from the Tao te Ching, a divination system using long and short sticks.
As I understand it, binary counting can do anything that conventional arithmetic with more familiar numerals can do.
Duijera Dubh -- A case in point -- in support of the post half-way back on this thread on correlation between music and shorthand.
It works for me. I went into medical transcription because I already had very good shorthand skills which had gotten me most of my jobs. I learned Gregg shorthand in high school. I started studying on a court reporting machine and got up to about 90 words a minute -- using standard American shorthand machine (court reporting language) with some used textbooks.
When I became a medical transcriptionist - right from the start I knew I would invent my own keyboard shorthand to get speed, and that's what I did.
I invented a form of truncated "Pigeon English -- top-heavy in medical terminology and drug names." I hear it in my head when I transcribe.
Likewise, I have been learning the IrTrad by ear since I started. After long long years of playing and listening, I'm also really beginning to get a strong grasp on the stylistic aspects that require fine-tuned listening, like how to combine bowing with ornaments to get the music to sound like i was born in an Irish household. Acute listening skills and language ability (translated into shorthand) have allowed me to actually make a reasonable per-hour salary in transcription (which many would-be transcriptionists cannot do).
I'm NOT at all good at mathematical formulations when they get abstract. The more abstract they get, the less good I am. But this seems to have nothing to do with my ability to HEAR when I begin to get a sense of phrasing that makes a reel sound like a reel. I would correlate this to working on developing a good speaking accent for a foreign language. Learning the structure of a language, like verb conjugation, is one thing. Speaking a language is entirely another.
You might do a decent job of speaking a foreign language with 5 years of intense study, but it might take you another 5 or 10 years to be able to speak that foreign language so you get the "native" inflexion, pronounciation and understanding of the idiom.
Actually, wolfbird, you're really describing a bit-wise logical operation, not binary arithmetic. There are different ways to use bits and they don't always represent the same thing.
What you are describing is a bit-wise OR operation:
There are specific techniques for performing multiplication, division, etc. using binary digits, and logical operations like the above get used in the process. But you can't say that 1+1 = 1 is true in binary without giving a context, because the bits can represent different things.
Yestedray I was speaking with my musician friend who teaches algebra. He is a special ed teacher. It is always a challenge to find a way to make math interesting to his students. It is extremely stressful.
I cannot recall any music teacher who has expressed the frustration (with music instruction) he does (with math instruction). Math & music have some things in common. But why do so many people love music (in all its' forms) yet so many despise math (in all its' forms)?
Back to your question . . . I have some friends who are excellent mathematicians & excellent musicians. What they have for each ~ is Passion! They can do one, or the other, for hours.
I starting teaching myself on the keyboard pretty much anything I heard when I was five years old. I excelled at the concert flute for eight years without any private lessons, taught myself the oboe, stand-up bass, and piano; also taught myself Irish woodwinds (and I'm good at all these things too!); have no problems reading different clefs and transposing music...and I am probably the worst mathematician ever to walk the planet. The thought of math sends my stomach all a-flutter and makes me feel cold and nervous. I feel completely lost without a calculator when it comes to dealing with numbers. I barely passed math in high school, but always got 100% in music classes.
I've even had people who know of/have witnessed my music ability muse aloud that I must be great at math, to which my response is usually laughter and a shake of the head.
Maybe math and music abilities are interchangeable in some cases, but definitely not in mine!
=D
Apparently, musicians do. People are not born with a thick CC, but through the exercise of playing music it gets thicker.
If mathematicians don't, this says to me that musicians use their brain differently than our math oriented friends. That a mathematician is also a good musician would then only be a coincidence of two different interests coming together in a single person.
As someone who is a classically trained clarinetist, composer, and music theorist, plus a whistle and bodhran player, I can say that being good at music does not mean one is good at math. I can't do math to save my life -- I'm entirely dyslexic when it comes to math!
Is there anyone else with a PH.D. in mathematics here? It never did much good for my playin' -- in fact -- the best years of my musical development were spent studying Galois Cohomology and such. Fifteen years as a mathematics professor didn't help much with my playin' either -- department politics can do in even the best of reels.
Not exactly. And not like that. It depends on the computer.
There are two basic ways to represent binary numbers in computers: big-endian and little-endian, depending on whether the most significant bit is at the top of the memory address or at the bottom (depends on the architecture of the system). Most desktop computers are little-endian, so two would be 01. In a big-endian system, it would be 10.
But it's nothing like "1 + 1 = 0 + 1 × 10"
It's like this: each bit increases in value by a power of 2, starting with the first bit at one (assuming little-endian). So eight bits would have these values:
1 2 4 8 16 32 64 128
You represent a number by turning on the bits that add up to what you need. Notice that the second bit has a value of 2, so to represent two it's:
0100000
The trailing zeros are insignificant in a little-endian system so you can write it 01.
You can represent any number between 1 and 128 with eight bits, this way. For instance, 42 is (32 + 8 + 2) so turn on the 32, 8 and 2 bits:
Okay, Screetch, you seem to have a grand grasp of the subject. So, how does this relate to burning CDs, etc, when the term 16 or 24 or 32 bit turns up ?
(Didn't you have to have a major surgery thing earlier this year ? How did that go ? )
My first surgery is May 12, still coming up. But thanks for asking.
I'm not sure what you mean about burning CD. CD drive have ratings like 16x, 32x, etc., but that's about the speed that it can read/write. Basically you can represent any number in binary, if you have enough bits.
But to represent big numbers you need lots of bits and if you write out the numbers in binary they get really long very fast. It's not very practical to write down binary numbers of any size, so even when a programmer needs to write down binary numbers they use hexadecimal or octal instead, to make the numbers shorter.
I didn't mean the CD read/write speed. I meant the sampling when recording sound, which can be 8,16, 24, 32. I find it slightly confusing when the same word 'bit' turns up there, and also in the machine code you're talking about.
Oh, in sampling the bit depth is how much information is being stored in each cycle. A bit is a basic unit of computer memory, so the more bits you are using the larger the storage area you have for each sample, so the more information you can store.
The sample rate is how often a snapshot is taken of the sound, while the bit depth is how much information gets stored for each snapshot. So the higher the bit depth, the more accurate each sample is.
Basically, a higher bit depth means a more detailed and accurate snapshot of the sound.
Linda, you had your work cut out trying to learn those old machine shorthand theories. Very cumbersome.
Good work you made them work in your favour anyway.
Looks like from the reports so far that the consensus is that being a good musician isn't the prerequisite for being the "best" musician - if that is what the thread title is actually asking.
Well, I really think that being a good musician is mostly just sticking to it. Musicianship is really something like 10% aptitude and 90% work.
So even if being good at math, language, or anything else is an advantage in learning, I doubt that it would really make a good predictor of whether or not someone becomes a good musician.
A better predictor would be obsessive personality traits
I guess they are talking about aptitudes, screetch.
Sure aptitude counts for nothing if one doesn't work at whatever the pursuit is. Given all equals in relation to quantum of practice and dedication, aptitude might well be an indicator of the degree of musical skill acquired, or how quickly that skill was acquired.
I don't think the thread's question is actually a bit ambiguous.
The ambiguity of the title of this thread ...
Taking one interpretation, one answer would be to do a study of a number of "best musicians" (however one defines that term) and see what proportion have at least one mathematician in their parents - I think you'd have to define a mathematician as being someone who's studied the subject to at least degree level; and then compare with a similarly-sized population of non-musicians to see if there is a statistically significant difference to the proportion of mathematicians in the parentage of the non-musicians.
No, not necessarily. There could perhaps be a genetic component (I'm not qualified to comment on that); it could also be a case of the child being exposed to the culture of mathematics from an early age. The study I outlined in my previous post (possibly partly tongue-in-cheek - I don't know) would do no more than establish the level of a statistical correlation, if it exists. The interpretation of the correlation would be a far different matter: a correlation does not necessarily imply a causal relationship.
Some earlier posts have alluded to the link between hard work and becoming good at something, but whether that's what the original post meant or whether we're talking about 'aptitude' is hard to pin down.
Maybe it's hard to separate aptitude from actual ability gained through perseverance. If you enjoy something and have a good work ethic, you'll probably achieve a higher level of competence than someone who may have a natural gift but lacks the desire to work at it.
Perhaps so many of us are bad at math because we simply didn't like it, and thus didn't apply ourselves. On the other hand, we find music enjoyable and will gladly work hard at it to get where we want to be.
I think c.g is spot on with those five points above. People who’ve never lived in the world of higher mathematics tend to think of math in terms of advanced computation and following complex recipes for solving problems. While there’s a bit of truth (heh) to that in the world of applied math (engineering, statistical analysis, etc.), people who are good at pure mathematics explore the parts of their brain-mind that deal in abstraction, intuition, potentialities. Charts, graphs, numbers, etc. appear after the intuitive reflection as a means of translating insight into something that can be communicated to another human.
And wyogal has a great point: “Music, math, language, are not LINKED, they are different representations of the same thing.” Except I would say that they *can* be representations of the same thing.
It’s not “mathematical skills” that are valuable to a musician. It’s having the kind of awareness that can visit the intuitive/imaginative regions of the brain-mind and return with a good tune. Or a good way to represent infinity.
But, to answer the question, no. Mathematicians don't make the *best* musicians. If they did, they wouldn't be wasting their time being mathematicians, would they?
I think an important difference between mathematical thinking and musical thinking is "reason" - both the noun and the verb.
A mathematician is consumed with reason. What is the reason such and such happens? Reasoned argument. The reason such and such is not proof. I did it this way because ... etc.
Reason to the musician is an irrelevance. Why does it go that way? I dunno. Why did you do that? No reason.
That’s true, Michael, but there’s also the non-rational part of mathematical “thinking” where you conceptualize the problem in your rational mind and then turn it over to the not-quite-conscious, free-running mind.
I went as far as a few years of graduate school in math before I burned out. I had to work really hard at the applied courses, but I seemed to have a knack for the more abstract topics. It wasn’t anything I earned through hard work or preparation. It felt almost literally like turning the problem over to sub-conscious elves who would work up a solution and send back “images” that I could translate into logic.
When I improvise music, it feels like it’s coming from the same psychic neighborhood, if not the same block or house. But, in that case, there’s usually no rational translation stage. It just goes straight to the fingers.
Damn, this stuff is hard to verbalize! Maybe we’re dancing about neurons.
I know what you mean, there is a certain zen thing when understanding calculus, for example. A bit like when a tune inexplicably falls under your fingers. But it's what you do with it that really counts. Calculus, beautiful as it is, is merely a problem solving tool, and I just don't see music that way.
Well Bob, mathematicians might still choose to stick with math even if they're great musicians too. There is certainly beauty in math, even if I can only see it in the more abstract concepts and not the numbers themselves. Both math and music improve our lives, just in greatly different ways.
I've heard music justified with reason before, not that I followed it. I had a disagreement about Rimsky-Korsakov once. I just like his compositions, though I can't put my finger on the why, but the counter argument was based on music theory and overuse of some conventions that the person felt made Rimsky-Korsakov less enjoyable.
There are similar arguments here all the time about Irish music. "I don't like this because of ___" "This band is better because they use ____" And so on. I don't enjoy those arguments, or trying to rationalize why I like certain music and not other kinds, but I understand why people debate it.
"Damn, this stuff is hard to verbalize!" said Bob Himself...
The way I see it, words are like a Set, (in the Godel's Theorem Set Theory sense). They're like a system of formal logic. So, if you look up a word and search for meaning, in the dictionary, you get the definition in several more words, so you then have to look up the definitions of those words, and on and on ad infinitum, until you get back to the start.
So, you can enclose the whole English language, the whole dictionary, inside brackets and consider it as as Set, and to make real sense of big questions like 'life', or 'what am I ?', you have to get outside the Set.
For example, musical notes or colours cannot be described with words. If you want to explain to a blind person what orange is, you can say it's in between yellow and red. Then you have to explain those...and there's never an end, because the symbolic description using alphabetical symbols is always a signpost, not the place itself.
You get to the point that Russell and Whitehead reached with their Principia Mathematica, and Wittgenstein's 'Of those things of which we cannot speak, we must remain silent'. You want to understand existence but thought and language comes up against some impenetrable limitation.
Personally, I found that situation frustrating. If words are just an overlay which we spread over reality to describe and label it, then how can one get closer to the real ? Stories and poems and parables and paintings and music can sometimes express and convey deeper truths than can literal language.
My personal way forward was found in buddhist meditation. Someone here mentioned the zen garden recently. Gazing at a mossy rock for hours, days, months. You switch of thought and the intellect, because that cannot provide the answer. So what remains ? Feelings and sensations. So when those have been explored, they are cast off. You keep stripping away, until there's nothing. Just a mossy rock and an observer of the mossy rock. And then those too, those two, vanish, and there's no observer, no rock. There's just the 'is-ness' of existence. It surely sounds very weird and nonsensical to most people, but the amazing thing is that it's totally liberating. All the stuff that most people on the planet find so hard to cope with every day of their lives, is transcended. Best thing I ever found. It can't be explained or described, but it can be experienced.
But you "can" explain to a blind person what orange is. For two interconnected reasons: language is clever, and so are people. A blind person is well able to understand the concept of eyes converting different frequencies of electromagnetic waves into brain waves. They can understand the physics of it, and through the power of analogy - you could say silk is yellow and velvet is red, and orange is in between - they can grasp the aesthetics of it also.
Language is not a self contained set because with it, it is possible to reference anything.
So michael, how do you explain to a 3-Dimensional being (well 4, actually, including time), so that they can understand, that gravity is actually the curving of space-time, or to a macroscopic being that photons are both waves and particles?
Are you absolutely sure a blind person could visualise the colour orange, beyond grasping the theory, cos I'm not.
Michael, this is drifting away from the points I was attempting to make above, but it's an interesting area to discuss....I'm not saying that language ( English, for example, but Chinese or Sanskrit or any other, could be considered) is an *exact* parallel to a mathematical set, just that it can be viewed in a similar sense. Language consists of verbal units, each one of which is defined by other units. But the word 'orange' is not the colour orange. I don't want to get us tangled up in semiotics, but there's that tremendous difference between the word 'swimming' and the sensual experience and physical activity of being immersed in the cold sea. Even the most gifted writer can only hint, with words, at what raw experience is like. The language system, with all it's grammar and syntax and etymology can be internally logical and consistent, but it's always set apart, separate, from the real world, in the same sense as a map and the actual territory. The blind from birth person, if educated and intelligent, can probably build up an adequate conception of colours, but it would, I assume, be in some personal analogue they construct in their mind's eye, as you suggested, rather than the raw experience of orange that the sighted individual has.
BTW, I'm not saying anything *against* language, just that there are areas where it cannot enter. That's one reason why astrophysicists and the like can only talk about their ideas using abstruse mathematics.
You've nailed it there wolf.
Bob, for example, a negative number doesn't actually exist. It's just an abstraction. You can't actually *get* minus three shakey eggs (shame, though.)
Yes, there is a world of difference between the word swimming and actually swimming. But the most gifted writer manipulates your memories and imagination with his descriptions to invoke much more that mere words, and yet all done with mere words.
A blind person cannot directly experience colour any more than we can never directly experience the make up of an atom, yet we know it exists. It is described to us with analogy and mathematics. And we are even powerful enough to experience and have a level of understanding of stuff that does not and cannot ever exist. The square root of minus one, for example.
Yes, words are fantastic and can convey tremendous, powerful imagery...for example, Donal Og
"It is late last night the dog was speaking of you;
the snipe was speaking of you in her deep marsh.
It is you are the lonely bird through the woods;
and that you may be without a mate until you find me."
And words and mathematics can tell us about notions that we cannot actually experience, and we can create abstractions and play around with those too. But (if I can remember it ) the point that I wanted to make, the description of the world is not the real world. That might seem obvious and trite, but everybody (almost) I've known lives 'in the description', not the real thing. It's like looking at a photo or google earth as compared to standing in the actual place with the wind in your face. We are so good at labelling everything, we forget, it's just a convenient trick, and we get trapped inside it. Does that make any sense to anybody ? I know I'm not alone, because Dogen spoke about it in his Mountains and Rivers sutra.
The way I abstract some elements of mathematics - field theory is one - feels intuitively similar to the way I abstract music. I can't articulate it any better than that.
As has been alluded to by other contributors, what distinguishes good mathematicians is a feeling for deep structure. I think good musicians have a similar faculty. Anecdotally, it does seem to me that the two often, but do not always overlap.
Mathematics is appallingly taught in schools - often by people who do not really understand it. There are lots of people going round who are, unbeknownst to themselves, good natural mathematicians.
I can certainly agree about the appalling standard of maths teaching, but I think it goes for all subjects really. IMO, all knowledge is intrinsically interesting if it's taught in a way that brings it to life, but bad education ruins them for most students. That's why I found 'The underground history of american education' absolutely fascinating. A lot of it also applies to UK education. It's no accident that the education system is so dismal. It's never been designed to make knowledge and learning exciting, to produce well-educated individuals. It's been designed as a tool for social control and to produce people who cannot think for themselves. I've met so many people who spent ten years and more in school, yet cannot read or write at a basic level. I'm sure you're right, Sean Lead Liath, most people could learn maths to a high level if they had it explained properly and were shown how thrilling it can be. It's sad.
They're LEy lines, Michael, and I don't believe they have a reality, other than in some folks imagination. Does that make them like square root of minus one ?
No problem, Scott, just refuse to pay 'em. After all, banks create money to loan out of thin air and then expect the rest of us to work to earn money to pay them back. If they get troublesome, just tell them you've got some missing time from your life, due to alien abduction, and someone must have used your credit card without authorization. Most Americans seem to have suffered alien abduction at some point, so it should stand up, if you get some decent legal representation.
Negative numbers and square roots of negative numbers are as real as positive numbers [Oh boy, now the terminology is wrapping around itself! Square roots of negative numbers are called "imaginary" numbers, as distinct from "real" numbers. But since we're just being silly, I'll keep going.] We can use them all to represent values of things in the real world. Surely, some folks here are familiar with the use of complex variables in electronics. But, sorry, I've lost track of what all this has to do with music and mathematicians.
Stupid banks...don't get me started on the fuzziness between investment banks and commercial banks playing with our money.
I agree that people could learn math to a higher level if it was made interesting and taught well. I was fortunate that I at least had math teachers who got me to the point where I could begin to understand some of the physics that I really enjoyed. The concepts were always more fun to me than working out specific examples.
Maybe that's why I like music so much, and it has to do with the underlying constructs, as alluded to earlier. I'm bad at the finer points of music theory, like I have difficulty working out complex calculations, but I tend to get the gist of it all. The bigger picture if you will.
I know it's a little separate from pure mathematics, but the field of physics also has a lot to offer to musicians. Some of the papers I've read about what makes a violin produce sound, psychoacoustics, and the like are very fascinating. Physics can be just a tool sometimes, but I think it can also enhance one's enjoyment of music if you are so inclined. Just as it enhances our understanding and wonder for the natural world.
In my experience (at the undergrad level anyway), physics majors do a lot freakier math than the pure mathematics kids. Physics takes math and ties it into knots.
When I think of math, and associated fields like physics, engineering, chemistry... the brain function that most comes to mind is problem-solving. Math is not so much about the structure and patterns and rules (just as writers do far far more than worry about grammar), as it is figuring out how to model a system properly.
Music is not about problem-solving. I think to be one of "the best" musicians probably requires a deep lifelong emotional connection (obsession maybe?) with your genre, and also really really really really really really good motor skills.
In other words, I think video gamers make the best musicians.
I wouldn't say that music is about problem-solving, but there are problems to solve when playing or composing (including improvising) music.
How do you get from one note or chord to another in a certain number of beats so that it sounds good? So that it fits on a particular instrument? So that it doesn't clash with what others are playing? So that it's different from the last 20 times you did it?
Where can you sneak in a breath without disrupting the rhythm, phrasing, and melody line?
What fingering allows you to get the right notes with the desired speed and phrasing? What is the desired phrasing?
Do I need to modify the ending of one tune or the pickup to another to get them to work well in a set, and if so, how?
What tuning on a guitar, banjo, dulcimer, lute, etc. works best for a particular piece of music?
Some of these things get solved in real time (or reel time) without consciously thinking them through; others require a more concerted effort; but either way it's problem solving that would tend to appeal to the mathematically inclined.
Music notation is a kind of mathematical modelling - if you think about it - using abstract symbols to represent a physical system.
In fact - you could draw the analogy further - in the case of ITM music notation is actually only ever an approximate representation of the physical system.
The discussion keeps coming around to functional mathematical skills applied to playing music and I think that misses the mark. The mathematical/computational skills needed in playing music are fairly trivial. I don’t see where Isaac Newton or Bertrand Russell would have any advantage over my dad, with his seventh-grade education, in that respect. My feeling is that the more interesting link between mathematicians and musicians is that the Mathematical Mind and the Musical Mind share a fair amount of psychic real estate, particularly in areas where intuitive things happen – things that seem to be largely independent of learned skills. It’s not about using tools and following rules.
My son is a natural musician and has been from very early days. [At the age of about eighteen months, he had an argument with his mother over whether a piece of music on the radio was Bach or Monteverdi. And he was right.] But eighth-grade algebra was painful for him and, years after school, he still has trouble with simple arithmetic. Yet he once asked me what calculus was about and, when I gave him an introductory lesson on integral calculus (which involved discussion about approaching infinity), he grasped it easily and thought it was cool.
I think the overlap does have something to do with, for lack of a better word, beauty. The visceral appreciation of the way various elements can come together into a harmonious whole. I know that’s not an original thought, but it’s where I arrive when I think about this stuff for a while.
Michael, I don't understand the thinking behind your claim that the examples you offer are not models, because the way I see it, they are obviously models. They are mental analogs invented by the Babylonians or Sumerians (or some folks from that era) as a way of representing sacks of grain or clay pots or soldiers. They then got abstracted so that the symbols and the system can be applied universally, as a means of counting, measuring, and constructing more complex models.
I am also hesitant to accept the claim to see them as absolute, because numbers get kinda weird when it comes to the quantum level and postulated infinite number of universes where the laws of physics may vary. But, on our everyday scale, at a practical level, 4 + 4 = 8 seems very useful as an absolute. But it's still just a story you're telling yourself, information received and encoded in brain tissue, one component of the complex of cultural conditioning that we share, (like 'a,e,i,o,u,' are components of the language modelling system.)
Sometimes, when I have been trying to figure out the proper fingering to play a tune, I wil start with the end of the tune because I know which finger I need to use to play the last note. Then I start to figure out the fingering backward from the last note.
Sometimes I have had to use a similiar technique with math problems when the instructor told us what the solution is supposed to be. Then it was the responsibility of myself and the other students to figure out how to get from the original problem to the solution.
When I took Music Acoustics in college to fulfill the requirement that I must take at least one physics course for my degree, I was glad that I had already taken two or three semesters of algebra because it helped me understand the mathematical reasoning behind the physics.
I suspect that one of the main reasons that my wife is having so much trouble with the Pre-Algebra Skills class that she is taking in college right now were apathetic and uncaring math teachers when she was a little girl in elementary school.
My seventy-nine year old father can still do math problems in his head that I need pencil and paper to solve. However, he has a bachelor's degree in geography and a master's in meteorology. My mother only got as far as a bachelor's degree in music education and she did struggle with math in college. My mother was a music teacher who taught me how to play the piano. On the other hand, though, my father doesn't play any instruments but he was a lot of help with math when I was in school.
wolfbird, 'a,e,i,o,u' are just sounds. My cat makes most of them.
4 + 4 = 8 is not a model, just as playing scale exercises is not making music. Imagine a music curriculum that consists of 6 years of scales before being allowed to play a tune. Imagine a writing curriculum that consists of years of grammar and spelling before being let loose to write a story.
That's the problem with math education: someone decided that 9th graders should spend a year factoring polynomials, 10th graders should spend half a year computing derivatives. Worthless. A calculator does these.
Estimate how many people in Zone B will buy our product, based on current sales and demographics in Zone A. Find the radius and incline of a highway curve such that a truck doesn't fly off the road. Design a 1000 acre irrigation system, tell me drawdown of the water table, the most efficient pipe diameters and flow scheme, the horsepower of the pumps, the total cost. Tell me when the sun is going to run out of hydrogen and start burning helium. Those are models.
To say that math and music are similar because "they both use a structure of abstract symbols" completely misses the point of both activities. I could possibly buy the argument of the Musical Mind having a lot of psychic overlap with the Mathematical Mind (if either exist), but I wouldn't believe it without good evidence.
'a,e,i,o,u' are just sounds. My cat makes most of them. (silver bow)
Yes, and all in the same breath too - How many musicians, or mathematicians for that matter, and sound like a cat.
Cats obviously make better mathematicans. Why can't you guys see that.
"wolfbird, 'a,e,i,o,u' are just sounds. My cat makes most of them."
silver bow, you seem to be missing a few points here.
Contrary to what you wrote above, a, e, i, o, u, are NOT sounds.
I'm looking at them here on my computer screen at this moment. They are shapes (made of pixels), and are completely silent. Before they reached the screen they were electronic pulses in the telephone line and binary machine code.
The same goes for 4 + 4 = 8.
Because I am literate and numerate, and share the conventions of the culture I've grown up in, I know the concepts that these shapes represent, and know the appropriate conversion procedure which transposes these symbols to vocalised sounds.
I maintain that they are models, albeit very simple, or constituents of a modelling system, be it mathematics or language.
Lots of music is math, but then a lot of everything in life is math, one big complex equation, some say. Rhythm is clearly math based, and the fact that tunes are based on standard repeating patterns of 2s, 3s, 8s, 16s is one of the things that makes this music accessible. And pitches and harmonies are clearly math based.
But like a lot of things, you don't need to understand and calculate the math as long as you can feel it, lots of people use math without realize it just by feeling the relationships and acting accordingly.
And like all art, athough there are features of music you can map out, the true beauty of it defies description!
I think you've got it the wrong way round, AlBrown, when you say rhythm, pitch, harmony, is math based. Surely, people were singing and dancing and playing instruments long before anybody began thinking about counting and inventing equations, and seems from Pythagoras that it might be more accurate to say that maths is music based.
Whan you state that the mathematical equations you render are not models, you raise an interesting point. Most mathematicians would hold that mathematics is *discovered* rather than *developed*. Any rigorous notation will suffice for the expression of mathematical truths in the absolute. The simple arithmetic truths you illustrate are good examples. We'll leave Godel & Church / Turing out of matters for the moment.
Matters become a little more complex when mathematics are applied to physical systems. Newton's laws, or Maxwell's equations, or the equations of relativity, describe *how* various particles and fields interact. They do not actually tell us very much about *what* the particles and fields actually *are* - if indeed that question makes any sense at all.
It is in this sense that I averred that musical notation is similar to mathematics, in that musical notation is a set of abstract symbols that define pitch and duration in time of - ultimately - vibrations of air.
Not wishing to speak for Michael, of course, but seems obvious to me that 'discovered rather than developed' is too crude, because someone must have first discovered, - e.g. Pythagoras noticing how the note produced by a plucked string varies with the measurable length, - and then developed, leading to further discoveries and further developments, up until the present time.
"Discovered' in the sense that the truths are held to be "Out there" as it were - independent of human perception or experience. Thus, that which Pythagoras discovered re the mathematical properties of pitch & string length was true before him, & remains true after him. Similarly, harmonics were always there - in precisely the mathematical relationships the analysis of which Fourier demonstrated.
The "Developmental" view - that mathematics is an artefact of human perception or societal conditioning - is on occasion heard from post-modern sociologists.
I'll attempt to explain the way I see it. There's the primate mammal we call Homo sapiens, and it evolves a brain which is capable of some sort of symbolic representation of meaning. Maybe, 'that's the way home' or 'that's my mother'. Then, some smart fella scratches a mark on a stone every time the full moon comes around. And then we get to Pythagoras.
The Moon, the properties of strings, and everything else, was always there, before and since. But the mathematical stuff (and also language) is to do with our brains, something that we overlay, or project out onto, the raw reality.
It is astounding, almost miraculous, that starting from simple correspondences between making three marks with a charcoal stick and say, three sheep, we end up with statistics and Fourier transforms and all the rest.
It's equally amazing that the alphabet can lead to all the world's great literature.
The way I see it, these things are cultural, the accumulated result of thousands of brains passing on insights. They can tell us a lot of useful and interesting things, about ourselves, about the world, about the Universe we find ourselves existing in.
We possibly agree about much of this stuff. The main point that bugs me, that I've been trying to put across, is that we fall into the trap of believing that our symbolic representations of reality, are the actual reality. I think that's a massive mistake. We've labelled and measured and counted. But nothing is explained, at the deeper level, of *what is it ? why is it ?*....fundamental, primary questions which are surely valid ( little children think so, anyway) even if they are impossible to answer in a satisfactory way.
Well, Begod, sure ye learn something new ever day. I was wondering who "Michael" is. Now I see it. I had "Llig Leachim" down for a character from some obscure part of the Fiannaíocht or the Ruadhraíocht - vauge associations with something along the lines of an Old Irish rendition of Fear Lag an Leath-cheim or suchlike......
...& mathematicians are supposed to be good at pattern recognition......
I do agree with much of that which you say - cf my ref above to the fact that mathematical representations of physical phenomena do not tell us much about *what* the physical phenomena are.
I do nevertheless hold that mathematics is not merely a matter of perception - to wit - a human development. Our *insights* to mathematics were developed, but the mathematics itself was always there. If matters were otherwise, then I do not think that mathematics would be much use as a predictive tool in the physical sciences - which it clearly is.
Anyone who doubts the above is cordially invited to stand underneath a thermonuclear device prior to detonation.
Ha,ha, Llig is maybe more Welsh sounding than Irish....anyway, fascinating points, Sean.
I probably part company with you that 'mathematics was always there', (although I'm open to being convinced), but your examples, that it provides predictive power, don't do it for me.
Seems to me that using maths to predict that radioactive fissile material would produce a chain reaction and nuclear explosion, is, philosophically, little different to using triangulation to accurately map the landscape as surveyors do.
I don't deny that mathematics is fantastic, e.g. nuclear particles or black holes can be predicted from mathematical models, and, lo and behold, you look in the likely place, and there they are. But, for me, the stuff was there, and our maths merely a means, like using a mirror to look around a blind corner.
IMO, the models are in our minds. The relationship between the model and the modelled is hard to understand. If I remember, there are half a dozen philosophical schools of thought to choose from, and none of them are very easy to understand or totally convincing, especially as the deeper folks probe into quantum physics and astrophysics, the more bizarre it seems to get.
I agree with you with regard to applied mathematics - mathematics is a descriptive analogy - and, as I have alluded to previously, does not tell us very much about *what* the phenomena it models actually are.
Pure mathematics differs. Fermat's last theorem was true before Fermat described it & before Wiles proved it. I do not believe that the truth it describes is a human construct.
Okay, Sean, I'll have to concede that I'm out of my depth when it comes to Fermat's last theorem and it's proof, but I'm willing to learn.
From what I do understand, I'd see the distinction between applied and pure maths as roughly comparable to factual writing, which is attached in some way to our everyday world, and fictional literature, such as science fiction, which can construct alternative realities as wonderful as the author's imagination can extend to.
In the first category I'd put, say, 'The variety of life', by Colin Tudge, which attempts to be a catalogue of all creatures that have ever lived, or a geographic Atlas. In the second category I'd put Tolkien's 'Lord of the rings' or Asimov's 'Foundation' trilogy.
I just took Fermat's last as an example. It is very simple. It states that there are no numbers that meet the criterion
a^n + b^n = c^n for n greater than 2, and a,b,c non-zero.
(The equation would of course represent the familiar Pythagoras theorm if n were equal to 2).
My point is that Fermat's last theorem was always true, and always will be, and would have been true even if humankind had never evolved. It is an eternal mathematical truth, not a human construct.
Okay. It tells us about numbers. The numbers are in our heads.
You don't find a 3, 4, 5, Pythagorean triangle laying there in the natural landscape. If you do find one, it's because somebody made it. Artifice. A product of human culture. Sure, numbers do all kinds of weird and wonderful things. I don't know why that happens to be so. But I'm very suspicious of your claim that they have some kind of existence independent of human intellect (if that's a correct understanding of your position ? )
I mean, to take it back to music. The sounds or noises can be an entirely natural phenomena. We investigate and find regularities that we can represent with numbers, or dots, or ABCs. But these are our invention, maps we draw to help navigate the raw territory. Or are you saying that pure maths is quite unlike that ?
Um, I just see a weakness in my own argument here. It's true that there aren't perfect right angles in nature, of if they occur its random chance. But there's plenty of Fibonacci series, Golden Mean, spirals and ellipses and cones and stuff, and when I think about it, ratio is intrinsic to natural forms of many kinds.
But I think what happened is that, for a lot of folks, early writing was ideographic, the symbol was linked to the image (of a bird, pot, ox, etc. ) and the Greeks were the first to take the Phoenician alphabet and make abstract, in the sense that pure maths is abstracted from applied maths. When you do that, when you take the step of separating a symbolic form from it's original referent, then you can play with it in all sorts of novel ways, very much as we have discovered more recently, with digital electronic gadgets that can give everyone access to jpegs and mp3s.
You say Sean, that Fermat's last theorem is an eternal truth. But what does that mean ? Where was it, 20 million years ago ? How can something be 'true' without a human mind to acknowledge the veracity ? Obviously, it doesn't have to be Fermat's, it could be the expansion coefficient of copper, or even one plus one equals two. These are things that humans have established, fixed rocks in the landscape, so to speak. But I still think that they are epiphenomena that arise from our mapping of the territory.
Certainly, the mathematics has an elegance and beauty, with all sorts of quirky puzzles, like pi, that upset the pattern. But then, the same can be said of Bach's music. Does that also have some independent existence ?
Looks as if we're on the verge of discussing whether a falling tree in a forest makes a sound if there's no creature out there to hear it.
Literature was of course around for a long time before writing was invented. Homer's Iliad and Odyssey were being recited (declaimed, perhaps) to the public for hundreds of years and passed on by word of mouth and human memory or hundreds of years before they were committed at an early opportunity to the written version we have today. The Druids, however, deliberately did not commit their corpus of learning to the written form, even though writing was available at that time, with the result that we now know very little about their learning. But Virgil's Aeneid was written down before it was recited to Virgil's audience. This procedure continues to the present day. However, ITM and other folk musics have redressed the balance in that they are still passed on aurally and by memory.
Yes, lazyhound, the falling tree also crossed my mind. And also Bishop Berkeley's idea, that there's really nothing at all 'out there', it's all in our heads....isn't the internet incredible ? I just googled 'social construction of pure mathematics' and it got me 1,430000 pages to read...should keep me quiet for the rest of my life
I see the sort of literature you're talking about, 'pre-literature', as somehow more natural. It's kind of noises we make, and facial expressions and impersonating characters, all the charm and magic of a good story teller, and presumably traces back to the sounds that many creatures make to communicate. Once writing comes along, we've moved into a new area.
I'm coming down firmly in Sean's camp here. Wolfbird, here's a question: if we did not exist, would the universe still exist? I think how you answer that question says much about your world view. By the way, I'm not saying there is a right or wrong answer, just that this can turn into a philosophical or metaphysical discussion. Maybe it already has
The "tree falling in a forest with no one around" question deserves some clarification. If no one is there to hear it, does it make a sound? No, if you define sound as what our ears perceive based on vibrations in air. But the vibrations will still be produced by the falling tree, regardless of the presence or absence of an observer.
Sean is saying that this is true for pure math as well, and I agree. It does not matter how we represent numbers, or what symbols we choose to use to write equations. There is a foundation beneath it all that was here before us and will be here after it.
I doubt there has been enough research to determine exactly why humans like music, but as with math I'm sure there are some underlying physical principles that are fairly simple. The best musicians intuitively tap into these, but unlike math there are some decidedly human factors. If our biology was significantly different we would probably make much different music, or maybe none at all.
However, the physical laws that determine what happens when a string vibrates would still hold true even if there were no people to make a string vibrate.
Yes, Scott, but I'd say that all questions, if you really dig down, are philosophical and metaphysical matters...
It might seem reasonable to assume, for common sense practical purposes, that the sound of the falling tree is produced even if there's no human to hear. Point is, it's impossible to prove that, isn't it ? I don't think I agree with you or Sean, at this stage, but I need to study some more, because there's a number of different positions on offer. My personal metaphysical or philosophical position is zen buddhist, but that doesn't mean I agree with all zen buddhists or that there is only one clear zen buddhist position. I found this page which seems to be a reasonable summary of recent thinking, so I'm going to start there and see where it takes me.
Berkeley's one about the tree is a special case of solipsism. I'm not aware that there is any rigorous way to refute solipsism, but, as a stance, it seems rather sterile to me.
Along with most other mathematicians, I would hold that there are truths which are independent of human experience. Pure mathematics is a corpus of these. Pythagorean triplets exist in the domain of pure mathematics. The veracity of the statement -"There is an infinite number of solutions to the equation a^n+b^n=c^n for n=2" does not depend on the fact that, in plane geometry, right-angled triangles can be formed using sides the lengths of which define Pythagorean triplets. We do not actually live in a plane geometry universe - our universe is curvilinear - so Pythagoras theorem, as it may be applied, will never be fully accurate. I stress again, though, the relationship of the *numbers* is independent of the application to plane geometry.
With regard to physical phenomena, though, I think we need to be careful. Repeatable experiments the results of which are at variance with common sense can be performed. A simple one is described well at http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/quantum.html - which also provides a good introduction to quantum weirdness. Note however that none of this calls in to questio
Do mathemeticians make the best musicians?
Do mathemeticians make the best musicians?
A statement I once heard and it stayed with me: " If your good at maths you'll be good at music! " Over to you for comment.
# Posted on April 18th 2008 by chuneboi slim
Re: Do mathemeticians make the best musicians?
It helps to be able to count to four.
# Posted on April 18th 2008 by granama
Re: Do mathemeticians make the best musicians?
I've heard that before. I think the idea is that music has a lot of mathematical aspects to it.
But I think that it's missing the point, as playing music is more about intuition and expression than analytic thinking.
Mathematicians probably make great music theorists. But I haven't met many dedicated musicians who have math degrees.
# Posted on April 18th 2008 by Screetch
Re: Do mathemeticians make the best musicians?
Touche' granama.
# Posted on April 19th 2008 by chuneboi slim
Re: Do mathemeticians make the best musicians?
Yes. Without a doubt. Unless they haven't taken graduate level complex analysis, or they don't understand Galois Theory very well. Then they're crap.
Which doesn't mean the good ones don't sometimes get lost as to whether this is the first or second time through the tune. Counting to 2 is usually left to the graduate students.
# Posted on April 19th 2008 by ayedbl
Re: Do mathemeticians make the best musicians?
sorry screetch but you miss the point. To be good at maths takes much more than analytic thinking. It takes a large slice of intuition also.
# Posted on April 19th 2008 by llig leahcim
Re: Do mathemeticians make the best musicians?
Do mathematicians have a thick corpus callosum?
# Posted on April 19th 2008 by gw
Re: Do mathemeticians make the best musicians?
gw. Even though I am not a mathematician I would like to think I had one.
# Posted on April 19th 2008 by chuneboi slim
Re: Do mathemeticians make the best musicians?
Yeah, I know llig, there's plenty of creativity and intuition involved in being good at math. I'm not trying to deny that.
But there's plenty of that in many disciplines; that isn't unique to mathematics. It's the analytic part that most sets the math people apart.
# Posted on April 19th 2008 by Screetch
Re: Do mathemeticians make the best musicians?
I've heard Tony McManus has such a qualification.
# Posted on April 19th 2008 by chuneboi slim
Re: Do mathemeticians make the best musicians?
I don't think a flare for analysis sets mathematicians apart. There are two ways you can do maths, the first is to be thorough and patient, the second is to be wreckless first and thorough later. The wreckless part requires intuition
But my distionary has intuition as "direct perception of truth, fact, etc., independent of any reasoning process" But there is no truth in art.
# Posted on April 19th 2008 by llig leahcim
Re: Do mathemeticians make the best musicians?
No truth in art? Haha, I see this going in circles
# Posted on April 19th 2008 by Screetch
Re: Do mathemeticians make the best musicians?
Had to look it up, couldn't remember the exact words:
"Beauty is truth, truth beauty.
That is all ye know on Earth, and all ye need to know"
--John Keats
# Posted on April 19th 2008 by Screetch
Re: Do mathemeticians make the best musicians?
Of course there is no truth in art. The question of truth is the one and only thing that sets science and art apart
# Posted on April 19th 2008 by llig leahcim
Re: Do mathemeticians make the best musicians?
I think being good at math is more closely connected with being a good composer than just a good instrumentalist, which really just requires good memory, rhythm and coordination and not so much the logical aspects needed to put together really nice tunes. The way music is written is very mathematical--notated music is dressed-up graphs with the notes being functions of time, although music notation is very different and more elaborate than that used in math so the two don't look too alike. Tunes are just big piecewise functions really.
# Posted on April 19th 2008 by Whiddler
Re: Do mathemeticians make the best musicians?
Keats wasn't a scientist, he didn't know what he was talking about.
# Posted on April 19th 2008 by llig leahcim
Re: Do mathemeticians make the best musicians?
Lets not start by using examples of how you write music down, that is completely irrelevant
# Posted on April 19th 2008 by llig leahcim
Re: Do mathemeticians make the best musicians?
For Western Art Music, I'd say being mathematically inclined is a big help, especially when one has continually to sight read complex rhythms. Also, the classical musician has to play notes of the same duration (without the swing) and that's something us trad heads aint great at.
Folk music to me is more about intuition and for that, being mathematically inclinded may even get in the way....
So that's my penny; (1 and 1/5th cents) worth.
# Posted on April 19th 2008 by martin t
Re: Do mathemeticians make the best musicians?
A good diddley musician is also a good composer, by definition. The way you mess with tunes when you play them is composing
# Posted on April 19th 2008 by llig leahcim
Re: Do mathemeticians make the best musicians?
So...poets don't know what they're talking about because they aren't scientists?
# Posted on April 19th 2008 by Screetch
Re: Do mathemeticians make the best musicians?
Intuition is not the right word. An example of intuition is where a poker player bets on a hand with a feeling it's gonna win. He could do the complex probability maths, but instead he has intuition. This is not how music works. You choose how to play a phrase based on some spurious think in you head somewhere that is pure creativity. There is no subconscious thought of probability that it will work, just pure invention
# Posted on April 19th 2008 by llig leahcim
Re: Do mathemeticians make the best musicians?
I meant that poets don't know waht they are talking about when they talk about truth
# Posted on April 19th 2008 by llig leahcim
Re: Do mathemeticians make the best musicians?
Mathmeticians=good technicians, music robots, perhaps, not good musicians. Capturing the feeling, the phrasing, making the magic happen through the music is more artistic than technical. My cousin could play all the right notes for all the great guitar heros like Van Halen, Hendrix, etc, but he knew he couldn't really make music; so he went and made a killing on Wall Street as a hedge fund manager (still is) and is the richest man I know, but still a lousy musician.
# Posted on April 19th 2008 by InSearchofCraic
Re: Do mathemeticians make the best musicians?
poems and musical phrases aren't equations that have to balance. The best poems and musical phrases are the once that don't quite balance, and are all the more inexplicably good for it
# Posted on April 19th 2008 by llig leahcim
Re: Do mathemeticians make the best musicians?
But in math there are set rules that you must follow to get the solution. In music you can bend the rules and change note values as long as you stay with the fairly loose parameters of the rhythm. Also, the rules used when writing music are often broken. Im math this would lead to a mis-solved problem. If you subtract before you divide, the answer will be different.
# Posted on April 19th 2008 by rob_handel
Re: Do mathematicians make the best musicians?
But at the far creative end of mathematics you can re-write the rules, or invent new ones, and see what happens.
# Posted on April 19th 2008 by lazyhound
Re: Do mathemeticians make the best musicians?
I think it might be backwards. Musicians make better math students. At least that's what the St Louis Symphony said on some flyers for their community music programs. They said there was proof that kids that played instruments score better in math.
# Posted on April 19th 2008 by nofrets
Re: Do mathemeticians make the best musicians?
I almost had an unfortunate bladder response.
# Posted on April 19th 2008 by Sir Dungsmere
Re: Do mathemeticians make the best musicians?
I'm terrible at math. Mebbe I'm a terrible musician too...?
At least I don't play bodhran!
# Posted on April 19th 2008 by rob_handel
Re: Do mathemeticians make the best musicians?
I would venture, there are different "types" of musicians. Some are more technically skilled, i.e., in terms of being able to transcribe from one key to another without thinking about it, or being able to place extemporaneous variation.. Some are more intuitive in other areas, and their playing might be more appealing in some ways to listeners if they are emotionally intuitive -- but perhaps they are not so good at playing spontaneous variations. People with certain kinds of mathematical intuitive ability tend to juggle patterns very rapidly, in their brains.
Some have a balance of mathematical-type intuitive ability and other kinds of inuitiveness (more language-oriented and emotional). They might have "the whole package."
Linda
# Posted on April 19th 2008 by Fid42
Re: Do mathemeticians make the best musicians?
Both math and music require a lot of patience to learn properly. Beyond that, I don't see much similarity.
I think music is just the type of talent a math nerd is more likely to be proud of rather than say, a sport. Correlation isn't causation.
# Posted on April 19th 2008 by silver bow
Re: Do mathemeticians make the best musicians?
Short answer, no.
Long answer to follow. It has much more to do with the ear you're born with. Your ear affects everything from how you speak to how you play music. By ear I mean how well your brain can distinguish pitch without referring to an additional reference.
My wife is an excellent mathematician, but has less of an ear for pitch than I do. What this means in practical terms is fairly profound. She can explain to me how counterpoint works, along with other aspects of music theory, and can sight read music and play it on the piano. However, I can pick up tunes purely by ear despite having little knowledge of theory.
I can also speak with almost any accent after I hear enough of it. My wife's French accent sucks, while mine is pretty damn good, to the point that French people can understand what I say even though she has the superior French vocabulary. Knowing the words is not very useful in conversation if you can't pronounce them properly. I think your ear has a great bearing on your ability to speak with a different accent.
Still, people with a lesser ear can appreciate music to the same degree as those more fortunate in the area of pitch recognition. My wife will correctly point out that I can't sing certain songs with the same feeling as the originals. Even though I can sing in key and she might not, she can tell when the actual quality of my performance is not up to snuff.
So it's a bit of a wash I suppose. For the record, I have an engineering degree but never got above a "C" in college math classes. I suck at math. But I'm lucky to have an above-average ear for pitch. I'm okay with that.
# Posted on April 19th 2008 by Scott Esch
Re: Do mathemeticians make the best musicians?
I do think there's a connection. I've met people who were skilled in both; they could be show-offs, to be honest, but some of that lay I think in the fact that they couldn't conceive how other people weren't able to think as nimbly as they could, in mathematical and musical matters and no doubt other things besides - these were bright people.
At school I dreaded maths and wasn't just no good at it, I found it entirely incomprehensible once I was past learning my tables. I was told my life had no prospects if I didn't pass Maths O-Level, certainly none of going to University. I passed the O-Level by doing a fraudulent subject called New Maths, which was explained to me (adequately) in about ten, fifteen minutes by a fellow-pupil after I'd spent about a year and a half failing to understand it in class. I went to university, and found the place full of people with no Maths O-Level.
# Posted on April 19th 2008 by nicholas
Re: Do mathemeticians make the best musicians?
The answer to this is SOOO obvious people...
1: Didn't Seamus Ennis have a BCS in applied mathematics?
2: Kevin Burke wrote the fouriers Series.... didn't he?
and 3: as EVERYONE knows.. Tommy Peoples invented the fibonacci sequence AND Pi
Case closed.
# Posted on April 19th 2008 by session savage
Re: Do mathemeticians make the best musicians?
Perhaps check out some research:
http://serendip.brynmawr.edu/exchange/node/1869
Maybe bodhranistas are the best mathematicians after all.
# Posted on April 19th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
Thanks for the article. I'm a huge fan of science conducted with proper empirical evidence, yet this didn't seem to jibe with my own experience.
I've been exposed to classical music since I was very young. It's about 90% of the music I listened to for the first 15 years of my life. I also would seem to have good "spatial temporal" reasoning based on the article's definition. So why do I suck at math? My teachers were pretty good, and fairly patient. I think it has been a failing within myself.
Again, I think musical ability has got more to do with the link between our ear and our brain than anything else.
# Posted on April 19th 2008 by Scott Esch
Re: Do mathemeticians make the best musicians?
To add to my last comment: and that's hardly quantifiable, which is why people seek other explanations for a link between math and music. Specious reasoning in my opinion.
# Posted on April 19th 2008 by Scott Esch
Re: Do mathemeticians make the best musicians?
Maybe, if the article is anything to go by, that you might have done better by listening to Mozart only - and bodhrans!
Personally, I have a feeling that the link being made between math and music mightn't be the best link. We always used what is called the Modern Language Aptitude Test (for want of anything else) to get some empirical indicator of people's ability for shorthand, which is essentially an aural skill - and a language, just like any other language. There was a high correlation between ability in the best and ability in shorthand - it wasn't written in stone, but an indicator. Some of the best successes were by people who didn't go well at the exam at all.
What is recognised (anedotally) in that industry though is that people who are skilled musicians, especially pianists (and probably harpists) for that matter, but including melody instruments of course, had a particularly high aptitude for learning shorthand i.e. learning a new language.
It would be interesting to see whether there is a correlation between people who are good at maths and whether they score highly on the MLAT test. Maybe music is processed and acquired by the brain in a similar way to that in which language and shorthand is acquired.
Maybe music is a form of language - at least according to how we process the learning of it - whether we know what that process is or not.
http://en.wikipedia.org/wiki/Modern_Language_Aptitude_Test
# Posted on April 19th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
that would be "ability in the test" obviously.
# Posted on April 19th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
I was pretty much the worst mathematician in my form back when I did my A-levels. I was so bad that I was the only one in a course of 20 who wouldn't have to take the oral examination since it wouldn't have changed anything to my mark. Anyway, I did get my A-levels and while I'm not uber great at music, I'm certainly not as bad as my mark in mathematics.
# Posted on April 19th 2008 by s.g.
Re: Do mathemeticians make the best musicians?
Bingo! There IS a link between language and music, as I alluded to earlier. The military/DoD has a test called the "Denfense Language Aptitude Battery" or DLAB. It doesn't test your ability in any one language, but rather your capability to learn new ones. I scored well enough in the DLAB to request whatever I wanted to learn from Persian to Tagalog to Mandarin. Of course I got French since I admitted to taking three years of it in high school LOL
but it's considered an 'easy' language compared to most others.
Language and music are most definitely related. The link between math and music is tenuous at best. Re. Mozart: I heard "Eine Kleine Nachtmusik" at least ten years before I had to take calculus! Didn't help much ;)
# Posted on April 19th 2008 by Scott Esch
Re: Do mathemeticians make the best musicians?
what we also noticed was the fairly stunning statistical incidence of people who were trained in classical music (we noticed piano mainly), who were also fluent in other languages, not just (on their observation) because they had received training in them, but because they felt they had a natural aptitude for language. It is almost a universal response.
So, I was wondering how many people here, who play ITM and/or other music also think they have a natural ability for or do speak languages other than their first language.
As a corollary, perhaps, I wonder what proportion of those players (the language speakers) also consider they are good at math.
# Posted on April 19th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
And for the coup de grace -
how many bodhranistas here consider they are good at maths, and maybe languages as well?
# Posted on April 19th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
Well, you were probably typing when I posted my last response, but there's one reply. I am good at music and other languages and sub-par at math. One qualification though: I am better at learning pronunciation of other languages than their grammar. Perhaps that directly correlates to the fact that I can recognize pitch but not explain how it fits into a mode.
# Posted on April 19th 2008 by Scott Esch
Re: Do mathemeticians make the best musicians?
I think that pronunciation acquisition is an aural skill an additional subset of language acquisition. Sure we can learn how to read and speak a language, but pronunciation is something that seems to come more naturally to some people than others. It seems to be a nuance that some people can pick up on earlier than others? Maybe playing music has a similar dichotomy - one can play music technically well, but maybe without the nuance of message than may come from particular emphasis on rhythm, emotion, etc, - maybe those things equate to 'pronunciation' in music - including ITM of course - and in particular. We can all speak a language, but not many of us are poets.
My hunch is that the linguists, and the speakers of other languages from natural aptitude probably make the "best" musicians. This of course doesn't exclude good mathematicians, nor does it necessarily follow that the speakers would be musicians, but I wonder about the statistical correlation.
Your own experience, Scott, seems to be consistent with that hypothesis.
# Posted on April 19th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
And I'll first, just for the record - my wife is a 'natural' bodhran player - didn't learn anything, just picked it up and off you go - very very good. She's also a strong mathematician and sudoko fan, for goodness sake. I can't think of a more exquisite torture than flickin' sudoko. Her brother is also a serious maths/engineering person - designs pacemakers (there's the rhythm connection, eh), and stuff like that. He's probably a fair rocket scientist as well.
# Posted on April 19th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
1. Maths has nothing to do with the ability to do arithmetic. Alan Turing, possibly one of the greatest mathematicians of the last century, couldn't even be trusted to add up the scores in card games.
2. Real mathematicians are inventive rule breakers. "I wonder what would happen if I . . . " Fortunately if it goes wrong all you get is a messy bit of paper or a really boring pattern on the computer screen. This is not true when chemists just wonder what would happen if they added this to that.
3. The ability to recognize patterns is important in both maths and music. It's what makes both playing by ear and reading at sight possible.
4. Mathematicians are very lazy. That part of maths which is not driven by the desire to see what happens if . . . is driven by the desire to find an easy way to do something.
5. Many 'arts' people despise maths without having the faintest idea what they are talking about. 'I was always hopeless at maths' they say proudly, as though it's some badge of honour.
# Posted on April 19th 2008 by c.g.
Re: Do mathemeticians make the best musicians?
Sudoko, sudoku, whatever - it gives me a heedick as they say.
# Posted on April 19th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
Opinion or research, c.g.?
# Posted on April 19th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
The ability to recognise patterns is also important so that you don't get run over crossing the road, c.g., or being able to pick the likely winner of a horse race.
Humans are pattern-recognising beings, it isn't just confined to maths and music.
# Posted on April 19th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
I dont think it means quite alot - I read also the creative and -
Mathematical + Languages sides of the the Brain are in two different places - But theres me who Never passed a Maths
Test in his Life - Last nearly always - Though that dose'nt
count for much- But a friend who was worse than maths than
me {saying something} Was a Cracker Banjo player.. And
another friend who is a Lecturer at Trinity College Dublin,
Is also a great banjo now fiddle player,,Both could hold notes/tunes in their heads after hearing the tune just a couple of times,,Maybe this Juxtaposition {like that word} .Dose not
really matter at all...
jim,,,,
# Posted on April 19th 2008 by FIDDLE4
Re: Do mathemeticians make the best musicians?
B.A. (Hons) in maths, Duijera Dubh.
I'm reasonable at maths, music and languages, not great at any of them but able to see what is needed!
If I really understand the maths of traffic flow patterns, I might be able to predict the traffic (you'd have to factor in the psychology of road users, though). If I had enough information about the horse, jockeys, course going etc etc I could probably predict what would win. Lack of data, not inherent fault of the method, Plus, in the case of racing, Really Large Gentlemen who would like to tell you that the bookmaker Isn't Happy about you winning so much.
# Posted on April 19th 2008 by c.g.
Re: Do mathemeticians make the best musicians?
Go study this a while and youll see=
http://www.news.com.au/perthnow/story/0,21598,22492511-5005375,00.html
jim,,
# Posted on April 19th 2008 by FIDDLE4
Re: Do mathemeticians make the best musicians?
Really large gentlemen in patterned suits maybe.
A BA (Hons) in maths, and you say you are (only) reasonable at maths, c.g? I would think you would have quite enough stats from that to pick the winner of a horse race!
# Posted on April 19th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
Jim, do you think you have an aptitude for learning other languages?
What does your friend lecture in at Trinity College.
# Posted on April 19th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
Great link, Jim. I'm definitely a clockwise/right-brainer for the most part, but can see the direction go anticlockwise if I don't think about it too much.
I suppose that's better than being a 'no brainer', so it is a comfort to me.
# Posted on April 19th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
Duijera Dubh
My great friend from way back - Is well knowen in ITM.
Dermi Diamond-to me , This to others =
http://www.dcu.ie/chemistry/biographies/dermot_diamond.shtml
jim,,,
# Posted on April 19th 2008 by FIDDLE4
Re: Do mathemeticians make the best musicians?
Looks like it is fair to say he would be handy with maths, Jim.
# Posted on April 19th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
Llig wrote : "there is no truth in art"
That's a statement i cannot agree with. It depends what you mean by 'truth'. You seem to be saying that mathematics, and/or science produces 'truth', whilst art does not.
I think there are at least two kind of 'truths'. 'One plus one equals two', could claim to be a scientific truth. 'I love you', could claim to be a human truth. When you get down to the kernel of both, they are just stories we tell ourselves, just electro-chemical neural activity.
Science doesn't claim to establish truth. Science proposes hypotheses and theories which can be tested by measured data. I assume that we have been living on the same planet for thousands of years, but science has seen it as being in a Ptolemaic, a Copernican, a Newtonian, an Einsteinian Universe, as one theory superseded its predescessor and was accepted as being of greater explanatory power. Now we've got String Theory and M-Theory, that propose that we are actually living in an 11 dimensional Multiverse....where that leaves 'truth', I really don't know.
Even the claim that 'one and one equals two' cannot be proven in an ultimate sense. See Godel's Theorem.
http://www.miskatonic.org/godel.html
Whilst scientific method seems to be the best way available to us when we try and understand existence, the big drawback is that it only deals with what can be measured, so elusive qualities like beauty and soul are beyond it's remit. But for most people, all the stuff that makes life worth living is in the un-measurable domain, and that's why the truths of art, music, poetry, literature, etc, matter, because they can convey truths about the human condition.
Look at the Palaeolithic cave paintings. They tell us something about those people who could observe and depict the 'true' qualities of animals as well as any artists ever.
I have a foot in both camps. If I want an operation for cancer, I want a scientifically trained surgeon who knows what a milligram is, please, not a poet. But if I'm in a lousy mood, I like to listen to something like 'The fair haired boy', played by a musician with the sensitivity and depth of character to express profound human emotions, and I don't care whether he or she can count a handful of beans.
# Posted on April 19th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
Do you like sudoku, wolfbird.
# Posted on April 19th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
Never tried it, Duijera Dubh. From the rumours I heard, it seemed like Rubik's Cube or the card game Patience or Crossword puzzles, and I already have far too many more exciting and intriguing matters to keep myself rewarded.
# Posted on April 19th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
Science doesn't find the "truth" so much as it constructs models -- often mathematical ones -- that describe a natural phenomenon. The models are "true" so long as they work but if data is found that doesn't fit the paradigm, scientists (over a period of time) end up modifying the paradigm.
Perhaps another explanation of the math-music link is in part a self-fulfilling prophecy. The theory that people who are good at math are also good at music has been around for a while. Is there actual evidence showing a physiological connection between a person's mathematical and musical abilities? Unlikely, as maths and music are both heavily influenced by social factors and other variables, to such an extent that I don't think you ever can empirically prove they are linked. Too many intervening variables in the way to be able to make a good argument. However, there is quite a lot of research showing the power of suggestion. If you hear that mathematical and musical abilities are linked and you happen to be good at math and like it, you can take up music believing you can be good at it, which greatly increases the likelihood that you will be.
While math factors into music in terms of understanding how rhythm and chords work, I would say that there are multiple ways to familiarize oneself with rhythmic and chordal structures. There are people who intuitively understand it, brilliant musicians who don't know a thing about music theory. If you have more of an analytic approach to music theory, I don't think it is necessarily linked to maths alone, but rather any analytic ability to understand and better yet create structures and patterns.
# Posted on April 19th 2008 by TheSilverSpear
Re: Do mathemeticians make the best musicians?
in maths tou have to follow rules but music lets you bee free to do what you want
chick xx
# Posted on April 19th 2008 by music chicken
Re: Do mathemeticians make the best musicians?
Music, math, language, are not LINKED, they are different representations of the same thing.
(I really don't know how else to say it)
As a former music teacher in US public schools, I saw the "research' being strutted about, saying music helped kids score better in math, etc... But I always felt that they were missing the point. Music IS math, music IS language. As for those test scores: Did the kid whose parents saw to it that an instrument was procured, the kid practiced, did they not also oversee other homework? Did those kids also follow through with other things?
I just know that I don't need "research" to tell me what I know to be true. Phythagorus wanted to measure "music" and that's how we got math.
MY brother was in the area of Knoxville, and Oakridge, TN for awhile (nuclear power something), huge concentration of scientists, mathematicians live and work in the area. In his spare time, he part of an opera chorus there. The arts/music scene there was/is filled with very good musicians that have dayjobs in the math and science fields. One guy was a concert classical guitarist in Europe before becoming a top nuclear physicist.
Does it make the statement, " If your good at maths you'll be good at music! " true or not? There are too many other things to factor in. Maybe that thing they are good at (math, music, languages) is the way they express that deep understanding of "it" (that thing that music, math, and language represent). Maybe some people can express that deep understanding of "it" in a variety of ways.
Early in the morning here, I haven't had my coffee yet, no one else is up. can ya tell???
# Posted on April 19th 2008 by wyogal
Re: Do mathemeticians make the best musicians?
"Science doesn't find the "truth" so much as it constructs models -- often mathematical ones -- that describe a natural phenomenon. The models are "true" so long as they work but if data is found that doesn't fit the paradigm, scientists (over a period of time) end up modifying the paradigm."
I don't disagree, Silver Spear.
(Kuhn was good on that stuff, but I like Feyerabend even better.) And what you have said here is a model (in your brain) of what science is. It's one of the generally agreed models, taught and shared in our culture.
Seems to me that what culture is, (e.g., English or Irish or Japanese), is bunch of such commonly shared models, indoctrinated by the previous generation.
# Posted on April 19th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
My
# Posted on April 19th 2008 by wyogal
Re: Do mathemeticians make the best musicians?
Wyogal, 'early in the morning here, ...can ya tell?'
Yup.
Stir in another spoon of coffee, wyo.
Wolfbird - top your's up with more hot water, mate.
# Posted on April 19th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
I was lazily paraphrasing Kuhn.
I would argue though that a model commonly used to describe science is one describe a narrative of going from ignorance to enlightenment, towards a greater understanding of "truth." Michael's above comment about truth setting science and art apart seems to be partaking in that narrative, which I contend doesn't accurately describe what science does.
In fact, you can make the argument that "truth" itself is a construction.
# Posted on April 19th 2008 by TheSilverSpear
Re: Do mathemeticians make the best musicians?
I meant to add in my last post that the interesting questions then are how culture is constructed. Post modernism isn't as cutting edge as it used to be and it's taken for granted in a lot of fields that yes, knowledge and culture are indeed socially constructed. Most of the work done now by people who take that relativist position is researching the mechanisms by which that happens.
# Posted on April 19th 2008 by TheSilverSpear
Re: Do mathemeticians make the best musicians?
Yeah, Silver Spear', I think it's better to speak of 'claims to truth' made in whatever context.
I see the major distinction between Science and the rest, is that scientific 'truths' are supposed to be supported by an argument resting upon empirical evidence, rather similar to the Law, where a prosecution case requires evidence. You can't just say anything you want.
Whereas in the Arts, anybody can do anything they like. If it resonates with an audience, maybe they'll recognize some new 'truth' about themselves or their situation and adjust their socially-constructed preconceptions.
# Posted on April 19th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
but, are artists really just saying anything they want, or are they saying truth, and that is why it resonates? Yes, on the surface, that in art one can just say anything, but really, in the heart of the artist, is it "just anything" or is it truth based on the evidence of themselves?
going for the coffee now...
# Posted on April 19th 2008 by wyogal
Re: Do mathemeticians make the best musicians?
One plus one only equals two under certain circumstances.
Do the statements 'I like this work of art' and 'This work of art is good' mean the same thing?
'In maths you have to follow the rules . . . ' Certain 'rules' apply to all of us. Like the Law of Gravity. We don't 'follow' them, in the sense that we follow a rule that tells us to stop when traffic signals are are on red. Mathematics is a way of describing reality. Or unreality.
Where else could I find discussions like this?
# Posted on April 19th 2008 by c.g.
Re: Do mathemeticians make the best musicians?
I think that is what distinguishes the great or highly regarded artists from the ones that are quickly forgotten. I mean, anybody who paints or sculpts or writes an opera can think they are producing important wonderful stuff to change the world. But if most people think it's crap it'll soon disappear. Whereas there's plays like Antigone that still have influence after a couple of thousand years, because they resonate, they reflect something that we know is true about humans and the way the behave.
# Posted on April 19th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
Silver Spear wrote : "...knowledge and culture are indeed socially constructed. Most of the work done now by people who take that relativist position is researching the mechanisms by which that happens."
Seems to me that one of the mechanisms is compulsory education. Here's a quote from Forbes magazine, from
http://www.johntaylorgatto.com/chapters/13l.htm
"The techniques of brainwashing developed in totalitarian countries are routinely used in psychological conditioning programs imposed on school children. These include emotional shock and desensitization, psychological isolation from sources of support, stripping away defenses, manipulative cross-examination of the individual’s underlying moral values by psychological rather than rational means. These techniques are not confined to separate courses or programs...they are not isolated idiosyncracies of particular teachers. They are products of numerous books and other educational materials in programs packaged by organizations that sell such curricula to administrators and teach the techniques to teachers. Some packages even include instructions on how to deal with parents and others who object. Stripping away psychological defenses can be done through assignments to keep diaries to be discussed in group sessions, and through role-playing assignments, both techniques used in the original brainwashing programs in China under Mao."
# Posted on April 19th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
"Even the claim that 'one and one equals two' cannot be proven in an ultimate sense. See Godel's Theorem."
Godel's theorem says nothing even remotely like that. In fact, it only applies to formal deductive systems that ARE strong enough to prove a certain collection of facts about arithmetic.
If you read carefully the first paragraph of the modernized translation of Godel's original paper (the link at the top of the miskatonic page), it makes this very clear:
"The development of mathematics towards greater exactness has, as is well-known, lead to formalization of large areas of it such that you can carry out proofs by following a few mechanical rules. The most comprehensive current formal systems are the system of Principia Mathematica (PM) on the one hand, the Zermelo-Fraenkelian axiom-system of set theory on the other hand. These two systems are so far developed that you can formalize in them all proof methods that are currently in use in mathematics, i.e. you can reduce these proof methods to a few axioms and deduction rules. Therefore,
the conclusion seems plausible that these deduction rules are sufficient to decide all mathematical questions expressible in those systems. We will show that this is not true, but that there are even relatively easy problems in the theory of ordinary whole numbers that can not be decided from the axioms. This is not due to the nature of these systems, but it is true for a very wide class of formal systems, which in particular includes all
those that you get by adding a finite number of axioms to the above mentioned systems, provided the additional axioms don’t make false theorems provable. "
For the first known (1982, 51 years after Godel's paper) example of a meaningful fact about arithmetic (as opposed to a fact about arithmetic arising from the technical details of Godel's proof) that can't be proven in the modern replacement for PM (Peano Arithmetic), see http://en.wikipedia.org/wiki/Goodstein's_theorem . That gives an indication of the kind of complexity that's necessary to construct unprovable statements. The difference between that and 1+1=2 is colossal.
I'll bet it would be possible to employ a small army of mathematical logicians to debunk all of the mis-applications of Godel's theorem made by people who don't understand what it says.
# Posted on April 19th 2008 by GaryAMartin
Re: Do mathemeticians make the best musicians?
0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 1
It's logical, internally consistent and it makes your computer work
# Posted on April 19th 2008 by c.g.
Re: Do mathemeticians make the best musicians?
I'm happy with my understanding of Godel's Theorem, GaryAMartin, so I'm not going to argue with you about it here, because it'll go on forever and I'm not in the premier league of mathematicians. No doubt there are lots websites where myriads of mathematicians are haggling over the topic just as folks like to haggle over Frankie Gavin on this site
# Posted on April 19th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
am I the only one to be getting a headache ?
# Posted on April 19th 2008 by bazouki dave and the real tooty flutey
Re: Do mathemeticians make the best musicians?
1+1=1?
# Posted on April 19th 2008 by Whiddler
To say that mathematicians make the best musicians implies to me that the music is a science when it obviously is not. Yes there is a scientific mathematical aspect but such views ignore the role of art and feelings and opinion on what sounds good.
Thank goodness for that other wise we would all sound and play the (insert the name of the perfect instrument) the same way, it’s the interpretation , the art that makes the difference
# Posted on April 19th 2008 by bazouki dave and the real tooty flutey
Re: Do mathemeticians make the best musicians?
1+1=1?
Computers work using binary system, zeroes and ones. If I remember, Leibniz invented it and got idea from the Tao te Ching, a divination system using long and short sticks.
As I understand it, binary counting can do anything that conventional arithmetic with more familiar numerals can do.
# Posted on April 19th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
Duijera Dubh -- A case in point -- in support of the post half-way back on this thread on correlation between music and shorthand.
It works for me. I went into medical transcription because I already had very good shorthand skills which had gotten me most of my jobs. I learned Gregg shorthand in high school. I started studying on a court reporting machine and got up to about 90 words a minute -- using standard American shorthand machine (court reporting language) with some used textbooks.
When I became a medical transcriptionist - right from the start I knew I would invent my own keyboard shorthand to get speed, and that's what I did.
I invented a form of truncated "Pigeon English -- top-heavy in medical terminology and drug names." I hear it in my head when I transcribe.
Likewise, I have been learning the IrTrad by ear since I started. After long long years of playing and listening, I'm also really beginning to get a strong grasp on the stylistic aspects that require fine-tuned listening, like how to combine bowing with ornaments to get the music to sound like i was born in an Irish household. Acute listening skills and language ability (translated into shorthand) have allowed me to actually make a reasonable per-hour salary in transcription (which many would-be transcriptionists cannot do).
I'm NOT at all good at mathematical formulations when they get abstract. The more abstract they get, the less good I am. But this seems to have nothing to do with my ability to HEAR when I begin to get a sense of phrasing that makes a reel sound like a reel. I would correlate this to working on developing a good speaking accent for a foreign language. Learning the structure of a language, like verb conjugation, is one thing. Speaking a language is entirely another.
You might do a decent job of speaking a foreign language with 5 years of intense study, but it might take you another 5 or 10 years to be able to speak that foreign language so you get the "native" inflexion, pronounciation and understanding of the idiom.
Linda
# Posted on April 19th 2008 by Fid42
Re: Do mathemeticians make the best musicians?
Actually, wolfbird, you're really describing a bit-wise logical operation, not binary arithmetic. There are different ways to use bits and they don't always represent the same thing.
What you are describing is a bit-wise OR operation:
false + false = false
true + false = true
false + true = true
true + true = true
There are specific techniques for performing multiplication, division, etc. using binary digits, and logical operations like the above get used in the process. But you can't say that 1+1 = 1 is true in binary without giving a context, because the bits can represent different things.
# Posted on April 19th 2008 by Screetch
Re: Do mathemeticians make the best musicians?
Oh, and actually, if you're talking addition in binary, it's 1+1 = 01 (the leading zero is significant).
# Posted on April 19th 2008 by Screetch
Re: Do mathemeticians make the best musicians?
Yestedray I was speaking with my musician friend who teaches algebra. He is a special ed teacher. It is always a challenge to find a way to make math interesting to his students. It is extremely stressful.
I cannot recall any music teacher who has expressed the frustration (with music instruction) he does (with math instruction). Math & music have some things in common. But why do so many people love music (in all its' forms) yet so many despise math (in all its' forms)?
Back to your question . . . I have some friends who are excellent mathematicians & excellent musicians. What they have for each ~ is Passion! They can do one, or the other, for hours.
# Posted on April 19th 2008 by Random_notes
*
Didn't Einstein flunk math?
# Posted on April 19th 2008 by Random_notes
Re: Do mathemeticians make the best musicians?
I starting teaching myself on the keyboard pretty much anything I heard when I was five years old. I excelled at the concert flute for eight years without any private lessons, taught myself the oboe, stand-up bass, and piano; also taught myself Irish woodwinds (and I'm good at all these things too!); have no problems reading different clefs and transposing music...and I am probably the worst mathematician ever to walk the planet. The thought of math sends my stomach all a-flutter and makes me feel cold and nervous. I feel completely lost without a calculator when it comes to dealing with numbers. I barely passed math in high school, but always got 100% in music classes.
I've even had people who know of/have witnessed my music ability muse aloud that I must be great at math, to which my response is usually laughter and a shake of the head.
Maybe math and music abilities are interchangeable in some cases, but definitely not in mine!
=D
# Posted on April 19th 2008 by Tasia
Re: Do mathemeticians make the best musicians?
No one has answered my question:
Do mathematicians have a thick corpus callosum?
Apparently, musicians do. People are not born with a thick CC, but through the exercise of playing music it gets thicker.
If mathematicians don't, this says to me that musicians use their brain differently than our math oriented friends. That a mathematician is also a good musician would then only be a coincidence of two different interests coming together in a single person.
And doesn't 1 + 1 = 10 in binary?
1 + 1 = 0 + 1 × 10
Binary 10 = 2
Therefore 1 + 1 = 2 whether it's binary or not.
...
# Posted on April 19th 2008 by gw
Re: Do mathemeticians make the best musicians?
As someone who is a classically trained clarinetist, composer, and music theorist, plus a whistle and bodhran player, I can say that being good at music does not mean one is good at math. I can't do math to save my life -- I'm entirely dyslexic when it comes to math!
# Posted on April 19th 2008 by Crysania
Re: Do mathemeticians make the best musicians?
Is there anyone else with a PH.D. in mathematics here? It never did much good for my playin' -- in fact -- the best years of my musical development were spent studying Galois Cohomology and such. Fifteen years as a mathematics professor didn't help much with my playin' either -- department politics can do in even the best of reels.
# Posted on April 19th 2008 by Eliot
Re: Do mathemeticians make the best musicians?
"And doesn't 1 + 1 = 10 in binary?
1 + 1 = 0 + 1 × 10
Binary 10 = 2"
---------------------------
Not exactly. And not like that. It depends on the computer.
There are two basic ways to represent binary numbers in computers: big-endian and little-endian, depending on whether the most significant bit is at the top of the memory address or at the bottom (depends on the architecture of the system). Most desktop computers are little-endian, so two would be 01. In a big-endian system, it would be 10.
But it's nothing like "1 + 1 = 0 + 1 × 10"
It's like this: each bit increases in value by a power of 2, starting with the first bit at one (assuming little-endian). So eight bits would have these values:
1 2 4 8 16 32 64 128
You represent a number by turning on the bits that add up to what you need. Notice that the second bit has a value of 2, so to represent two it's:
0100000
The trailing zeros are insignificant in a little-endian system so you can write it 01.
You can represent any number between 1 and 128 with eight bits, this way. For instance, 42 is (32 + 8 + 2) so turn on the 32, 8 and 2 bits:
01010100, or 010101
# Posted on April 19th 2008 by Screetch
Re: Do mathemeticians make the best musicians?
Okay, Screetch, you seem to have a grand grasp of the subject. So, how does this relate to burning CDs, etc, when the term 16 or 24 or 32 bit turns up ?
(Didn't you have to have a major surgery thing earlier this year ? How did that go ? )
# Posted on April 19th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
My first surgery is May 12, still coming up. But thanks for asking.
I'm not sure what you mean about burning CD. CD drive have ratings like 16x, 32x, etc., but that's about the speed that it can read/write. Basically you can represent any number in binary, if you have enough bits.
But to represent big numbers you need lots of bits and if you write out the numbers in binary they get really long very fast. It's not very practical to write down binary numbers of any size, so even when a programmer needs to write down binary numbers they use hexadecimal or octal instead, to make the numbers shorter.
# Posted on April 19th 2008 by Screetch
Re: Do mathemeticians make the best musicians?
I didn't mean the CD read/write speed. I meant the sampling when recording sound, which can be 8,16, 24, 32. I find it slightly confusing when the same word 'bit' turns up there, and also in the machine code you're talking about.
# Posted on April 19th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
Oh, in sampling the bit depth is how much information is being stored in each cycle. A bit is a basic unit of computer memory, so the more bits you are using the larger the storage area you have for each sample, so the more information you can store.
The sample rate is how often a snapshot is taken of the sound, while the bit depth is how much information gets stored for each snapshot. So the higher the bit depth, the more accurate each sample is.
Basically, a higher bit depth means a more detailed and accurate snapshot of the sound.
# Posted on April 19th 2008 by Screetch
Re: Do mathemeticians make the best musicians?
I guess I know as much as I need to know now, Screetch, thanks
# Posted on April 19th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
Linda, you had your work cut out trying to learn those old machine shorthand theories. Very cumbersome.
Good work you made them work in your favour anyway.
Looks like from the reports so far that the consensus is that being a good musician isn't the prerequisite for being the "best" musician - if that is what the thread title is actually asking.
# Posted on April 20th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
Well, I really think that being a good musician is mostly just sticking to it. Musicianship is really something like 10% aptitude and 90% work.
So even if being good at math, language, or anything else is an advantage in learning, I doubt that it would really make a good predictor of whether or not someone becomes a good musician.
A better predictor would be obsessive personality traits
# Posted on April 20th 2008 by Screetch
Re: Do mathemeticians make the best musicians?
I guess they are talking about aptitudes, screetch.
Sure aptitude counts for nothing if one doesn't work at whatever the pursuit is. Given all equals in relation to quantum of practice and dedication, aptitude might well be an indicator of the degree of musical skill acquired, or how quickly that skill was acquired.
I don't think the thread's question is actually a bit ambiguous.
# Posted on April 20th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
"I think the thread's question IS actually a bit ambiguous", that should be.
# Posted on April 20th 2008 by Duijera Dubh
Re: Do mathematicians make the best musicians?
The ambiguity of the title of this thread ...
Taking one interpretation, one answer would be to do a study of a number of "best musicians" (however one defines that term) and see what proportion have at least one mathematician in their parents - I think you'd have to define a mathematician as being someone who's studied the subject to at least degree level; and then compare with a similarly-sized population of non-musicians to see if there is a statistically significant difference to the proportion of mathematicians in the parentage of the non-musicians.
# Posted on April 20th 2008 by lazyhound
Re: Do mathemeticians make the best musicians?
But doesn't that assume that mathematical ability is hereditary?
# Posted on April 20th 2008 by Screetch
Re: Do mathemaicians make the best musicians?
No, not necessarily. There could perhaps be a genetic component (I'm not qualified to comment on that); it could also be a case of the child being exposed to the culture of mathematics from an early age. The study I outlined in my previous post (possibly partly tongue-in-cheek - I don't know) would do no more than establish the level of a statistical correlation, if it exists. The interpretation of the correlation would be a far different matter: a correlation does not necessarily imply a causal relationship.
# Posted on April 20th 2008 by lazyhound
Re: Do mathemeticians make the best musicians?
I studied maths at university (20+ years ago); does that mean there is hope for my music (4+ years of playing?
# Posted on April 20th 2008 by mehere
Re: Do mathemeticians make the best musicians?
Mehere, I'm in the same boat - just double your numbers!
# Posted on April 20th 2008 by lazyhound
Re: Do mathemeticians make the best musicians?
im a matamatician and i can play any instrument so there you have it
# Posted on April 20th 2008 by Pat Duff
Re: Do mathemeticians make the best musicians?
mathematician's can't spell! lol
# Posted on April 20th 2008 by jamascc
Re: Do mathemeticians make the best musicians?
sorry - couldn't resist!
# Posted on April 20th 2008 by jamascc
Re: Do mathemeticians make the best musicians?
Just like crysania, I'm entirely dyslexic when it comes to maht.
# Posted on April 20th 2008 by Steve Shaw
Re: Do mathemeticians make the best musicians?
Some earlier posts have alluded to the link between hard work and becoming good at something, but whether that's what the original post meant or whether we're talking about 'aptitude' is hard to pin down.
Maybe it's hard to separate aptitude from actual ability gained through perseverance. If you enjoy something and have a good work ethic, you'll probably achieve a higher level of competence than someone who may have a natural gift but lacks the desire to work at it.
Perhaps so many of us are bad at math because we simply didn't like it, and thus didn't apply ourselves. On the other hand, we find music enjoyable and will gladly work hard at it to get where we want to be.
# Posted on April 21st 2008 by Scott Esch
Re: Do mathemeticians make the best musicians?
Forgot to add, the slogan of our local gym is "Hard work beats talent when talent isn't willing to work hard."
# Posted on April 21st 2008 by Scott Esch
Re: Do mathemeticians make the best musicians?
I think c.g is spot on with those five points above. People who’ve never lived in the world of higher mathematics tend to think of math in terms of advanced computation and following complex recipes for solving problems. While there’s a bit of truth (heh) to that in the world of applied math (engineering, statistical analysis, etc.), people who are good at pure mathematics explore the parts of their brain-mind that deal in abstraction, intuition, potentialities. Charts, graphs, numbers, etc. appear after the intuitive reflection as a means of translating insight into something that can be communicated to another human.
And wyogal has a great point: “Music, math, language, are not LINKED, they are different representations of the same thing.” Except I would say that they *can* be representations of the same thing.
It’s not “mathematical skills” that are valuable to a musician. It’s having the kind of awareness that can visit the intuitive/imaginative regions of the brain-mind and return with a good tune. Or a good way to represent infinity.
But, to answer the question, no. Mathematicians don't make the *best* musicians. If they did, they wouldn't be wasting their time being mathematicians, would they?
# Posted on April 21st 2008 by Bob himself
Re: Do mathemeticians make the best musicians?
I think an important difference between mathematical thinking and musical thinking is "reason" - both the noun and the verb.
A mathematician is consumed with reason. What is the reason such and such happens? Reasoned argument. The reason such and such is not proof. I did it this way because ... etc.
Reason to the musician is an irrelevance. Why does it go that way? I dunno. Why did you do that? No reason.
# Posted on April 21st 2008 by llig leahcim
Re: Do mathemeticians make the best musicians?
That’s true, Michael, but there’s also the non-rational part of mathematical “thinking” where you conceptualize the problem in your rational mind and then turn it over to the not-quite-conscious, free-running mind.
I went as far as a few years of graduate school in math before I burned out. I had to work really hard at the applied courses, but I seemed to have a knack for the more abstract topics. It wasn’t anything I earned through hard work or preparation. It felt almost literally like turning the problem over to sub-conscious elves who would work up a solution and send back “images” that I could translate into logic.
When I improvise music, it feels like it’s coming from the same psychic neighborhood, if not the same block or house. But, in that case, there’s usually no rational translation stage. It just goes straight to the fingers.
Damn, this stuff is hard to verbalize! Maybe we’re dancing about neurons.
# Posted on April 21st 2008 by Bob himself
Re: Do mathemeticians make the best musicians?
I know what you mean, there is a certain zen thing when understanding calculus, for example. A bit like when a tune inexplicably falls under your fingers. But it's what you do with it that really counts. Calculus, beautiful as it is, is merely a problem solving tool, and I just don't see music that way.
# Posted on April 21st 2008 by llig leahcim
Re: Do mathemeticians make the best musicians?
Well Bob, mathematicians might still choose to stick with math even if they're great musicians too. There is certainly beauty in math, even if I can only see it in the more abstract concepts and not the numbers themselves. Both math and music improve our lives, just in greatly different ways.
I've heard music justified with reason before, not that I followed it. I had a disagreement about Rimsky-Korsakov once. I just like his compositions, though I can't put my finger on the why, but the counter argument was based on music theory and overuse of some conventions that the person felt made Rimsky-Korsakov less enjoyable.
There are similar arguments here all the time about Irish music. "I don't like this because of ___" "This band is better because they use ____" And so on. I don't enjoy those arguments, or trying to rationalize why I like certain music and not other kinds, but I understand why people debate it.
# Posted on April 22nd 2008 by Scott Esch
Re: Do mathemeticians make the best musicians?
"Damn, this stuff is hard to verbalize!" said Bob Himself...
The way I see it, words are like a Set, (in the Godel's Theorem Set Theory sense). They're like a system of formal logic. So, if you look up a word and search for meaning, in the dictionary, you get the definition in several more words, so you then have to look up the definitions of those words, and on and on ad infinitum, until you get back to the start.
So, you can enclose the whole English language, the whole dictionary, inside brackets and consider it as as Set, and to make real sense of big questions like 'life', or 'what am I ?', you have to get outside the Set.
For example, musical notes or colours cannot be described with words. If you want to explain to a blind person what orange is, you can say it's in between yellow and red. Then you have to explain those...and there's never an end, because the symbolic description using alphabetical symbols is always a signpost, not the place itself.
You get to the point that Russell and Whitehead reached with their Principia Mathematica, and Wittgenstein's 'Of those things of which we cannot speak, we must remain silent'. You want to understand existence but thought and language comes up against some impenetrable limitation.
Personally, I found that situation frustrating. If words are just an overlay which we spread over reality to describe and label it, then how can one get closer to the real ? Stories and poems and parables and paintings and music can sometimes express and convey deeper truths than can literal language.
My personal way forward was found in buddhist meditation. Someone here mentioned the zen garden recently. Gazing at a mossy rock for hours, days, months. You switch of thought and the intellect, because that cannot provide the answer. So what remains ? Feelings and sensations. So when those have been explored, they are cast off. You keep stripping away, until there's nothing. Just a mossy rock and an observer of the mossy rock. And then those too, those two, vanish, and there's no observer, no rock. There's just the 'is-ness' of existence. It surely sounds very weird and nonsensical to most people, but the amazing thing is that it's totally liberating. All the stuff that most people on the planet find so hard to cope with every day of their lives, is transcended. Best thing I ever found. It can't be explained or described, but it can be experienced.
# Posted on April 22nd 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
But you "can" explain to a blind person what orange is. For two interconnected reasons: language is clever, and so are people. A blind person is well able to understand the concept of eyes converting different frequencies of electromagnetic waves into brain waves. They can understand the physics of it, and through the power of analogy - you could say silk is yellow and velvet is red, and orange is in between - they can grasp the aesthetics of it also.
Language is not a self contained set because with it, it is possible to reference anything.
# Posted on April 22nd 2008 by llig leahcim
Re: Do mathemeticians make the best musicians?
So michael, how do you explain to a 3-Dimensional being (well 4, actually, including time), so that they can understand, that gravity is actually the curving of space-time, or to a macroscopic being that photons are both waves and particles?
Are you absolutely sure a blind person could visualise the colour orange, beyond grasping the theory, cos I'm not.
# Posted on April 22nd 2008 by Key Maniac Lad
Re: Do mathemeticians make the best musicians?
Michael, this is drifting away from the points I was attempting to make above, but it's an interesting area to discuss....I'm not saying that language ( English, for example, but Chinese or Sanskrit or any other, could be considered) is an *exact* parallel to a mathematical set, just that it can be viewed in a similar sense. Language consists of verbal units, each one of which is defined by other units. But the word 'orange' is not the colour orange. I don't want to get us tangled up in semiotics, but there's that tremendous difference between the word 'swimming' and the sensual experience and physical activity of being immersed in the cold sea. Even the most gifted writer can only hint, with words, at what raw experience is like. The language system, with all it's grammar and syntax and etymology can be internally logical and consistent, but it's always set apart, separate, from the real world, in the same sense as a map and the actual territory. The blind from birth person, if educated and intelligent, can probably build up an adequate conception of colours, but it would, I assume, be in some personal analogue they construct in their mind's eye, as you suggested, rather than the raw experience of orange that the sighted individual has.
BTW, I'm not saying anything *against* language, just that there are areas where it cannot enter. That's one reason why astrophysicists and the like can only talk about their ideas using abstruse mathematics.
# Posted on April 22nd 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
Y’all are gettin’ way too esoterical for me.
# Posted on April 22nd 2008 by Bob himself
Re: Do mathemeticians make the best musicians?
You've nailed it there wolf.
Bob, for example, a negative number doesn't actually exist. It's just an abstraction. You can't actually *get* minus three shakey eggs (shame, though.)
# Posted on April 22nd 2008 by Key Maniac Lad
Re: Do mathemeticians make the best musicians?
Yes, there is a world of difference between the word swimming and actually swimming. But the most gifted writer manipulates your memories and imagination with his descriptions to invoke much more that mere words, and yet all done with mere words.
A blind person cannot directly experience colour any more than we can never directly experience the make up of an atom, yet we know it exists. It is described to us with analogy and mathematics. And we are even powerful enough to experience and have a level of understanding of stuff that does not and cannot ever exist. The square root of minus one, for example.
# Posted on April 22nd 2008 by llig leahcim
Re: Do mathemeticians make the best musicians?
Yes, words are fantastic and can convey tremendous, powerful imagery...for example, Donal Og
"It is late last night the dog was speaking of you;
the snipe was speaking of you in her deep marsh.
It is you are the lonely bird through the woods;
and that you may be without a mate until you find me."
And words and mathematics can tell us about notions that we cannot actually experience, and we can create abstractions and play around with those too. But (if I can remember it
) the point that I wanted to make, the description of the world is not the real world. That might seem obvious and trite, but everybody (almost) I've known lives 'in the description', not the real thing. It's like looking at a photo or google earth as compared to standing in the actual place with the wind in your face. We are so good at labelling everything, we forget, it's just a convenient trick, and we get trapped inside it. Does that make any sense to anybody ? I know I'm not alone, because Dogen spoke about it in his Mountains and Rivers sutra.
# Posted on April 22nd 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
The way I abstract some elements of mathematics - field theory is one - feels intuitively similar to the way I abstract music. I can't articulate it any better than that.
As has been alluded to by other contributors, what distinguishes good mathematicians is a feeling for deep structure. I think good musicians have a similar faculty. Anecdotally, it does seem to me that the two often, but do not always overlap.
Mathematics is appallingly taught in schools - often by people who do not really understand it. There are lots of people going round who are, unbeknownst to themselves, good natural mathematicians.
# Posted on April 22nd 2008 by Sean Lead Liath
Re: Do mathemeticians make the best musicians?
I can certainly agree about the appalling standard of maths teaching, but I think it goes for all subjects really. IMO, all knowledge is intrinsically interesting if it's taught in a way that brings it to life, but bad education ruins them for most students. That's why I found 'The underground history of american education' absolutely fascinating. A lot of it also applies to UK education. It's no accident that the education system is so dismal. It's never been designed to make knowledge and learning exciting, to produce well-educated individuals. It's been designed as a tool for social control and to produce people who cannot think for themselves. I've met so many people who spent ten years and more in school, yet cannot read or write at a basic level. I'm sure you're right, Sean Lead Liath, most people could learn maths to a high level if they had it explained properly and were shown how thrilling it can be. It's sad.
# Posted on April 23rd 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
Blimey, put that colander on your head. No, better still, wrap it in tin foil and go to sleep with your bed at right angles to a lay line
# Posted on April 23rd 2008 by llig leahcim
Re: Do mathemeticians make the best musicians?
They're LEy lines, Michael, and I don't believe they have a reality, other than in some folks imagination. Does that make them like square root of minus one ?
# Posted on April 23rd 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
Negative numbers DO exist. I see them in my bank statement all the time...
# Posted on April 23rd 2008 by Scott Esch
Re: Do mathemeticians make the best musicians?
No problem, Scott, just refuse to pay 'em. After all, banks create money to loan out of thin air and then expect the rest of us to work to earn money to pay them back. If they get troublesome, just tell them you've got some missing time from your life, due to alien abduction, and someone must have used your credit card without authorization. Most Americans seem to have suffered alien abduction at some point, so it should stand up, if you get some decent legal representation.
http://www.youtube.com/watch?v=QkeOUzKRzLY
(just kidding)
# Posted on April 23rd 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
Negative numbers and square roots of negative numbers are as real as positive numbers [Oh boy, now the terminology is wrapping around itself! Square roots of negative numbers are called "imaginary" numbers, as distinct from "real" numbers. But since we're just being silly, I'll keep going.] We can use them all to represent values of things in the real world. Surely, some folks here are familiar with the use of complex variables in electronics. But, sorry, I've lost track of what all this has to do with music and mathematicians.
# Posted on April 23rd 2008 by Bob himself
Re: Do mathemeticians make the best musicians?
Stupid banks...don't get me started on the fuzziness between investment banks and commercial banks playing with our money.
I agree that people could learn math to a higher level if it was made interesting and taught well. I was fortunate that I at least had math teachers who got me to the point where I could begin to understand some of the physics that I really enjoyed. The concepts were always more fun to me than working out specific examples.
Maybe that's why I like music so much, and it has to do with the underlying constructs, as alluded to earlier. I'm bad at the finer points of music theory, like I have difficulty working out complex calculations, but I tend to get the gist of it all. The bigger picture if you will.
I know it's a little separate from pure mathematics, but the field of physics also has a lot to offer to musicians. Some of the papers I've read about what makes a violin produce sound, psychoacoustics, and the like are very fascinating. Physics can be just a tool sometimes, but I think it can also enhance one's enjoyment of music if you are so inclined. Just as it enhances our understanding and wonder for the natural world.
# Posted on April 23rd 2008 by Scott Esch
Re: Do mathemeticians make the best musicians?
In my experience (at the undergrad level anyway), physics majors do a lot freakier math than the pure mathematics kids. Physics takes math and ties it into knots.
When I think of math, and associated fields like physics, engineering, chemistry... the brain function that most comes to mind is problem-solving. Math is not so much about the structure and patterns and rules (just as writers do far far more than worry about grammar), as it is figuring out how to model a system properly.
Music is not about problem-solving. I think to be one of "the best" musicians probably requires a deep lifelong emotional connection (obsession maybe?) with your genre, and also really really really really really really good motor skills.
In other words, I think video gamers make the best musicians.
# Posted on April 23rd 2008 by silver bow
Re: Do mathemeticians make the best musicians?
I wouldn't say that music is about problem-solving, but there are problems to solve when playing or composing (including improvising) music.
How do you get from one note or chord to another in a certain number of beats so that it sounds good? So that it fits on a particular instrument? So that it doesn't clash with what others are playing? So that it's different from the last 20 times you did it?
Where can you sneak in a breath without disrupting the rhythm, phrasing, and melody line?
What fingering allows you to get the right notes with the desired speed and phrasing? What is the desired phrasing?
Do I need to modify the ending of one tune or the pickup to another to get them to work well in a set, and if so, how?
What tuning on a guitar, banjo, dulcimer, lute, etc. works best for a particular piece of music?
Some of these things get solved in real time (or reel time) without consciously thinking them through; others require a more concerted effort; but either way it's problem solving that would tend to appeal to the mathematically inclined.
# Posted on April 23rd 2008 by GaryAMartin
Re: Do mathemeticians make the best musicians?
Music notation is a kind of mathematical modelling - if you think about it - using abstract symbols to represent a physical system.
In fact - you could draw the analogy further - in the case of ITM music notation is actually only ever an approximate representation of the physical system.
# Posted on April 23rd 2008 by Sean Lead Liath
Re: Do mathemeticians make the best musicians?
of course we do.
# Posted on April 23rd 2008 by geoffwright
Re: Do mathemeticians make the best musicians?
Are we divided on this?
Seems that it all adds up.
All together now, medium slow foxtrot: ONE, TWO, THREE, FOUR...
# Posted on April 23rd 2008 by Krick Stahlschwanz
Re: Do mathemeticians make the best musicians?
the notation has absolutly nothing whatsoever to do with it
# Posted on April 23rd 2008 by llig leahcim
Re: Do mathemeticians make the best musicians?
4+4=8 is an absolute.
And so is IV+IV=VIII.
It doesn't mattter how you write it, what convention you use.
100+100=1000
these are not models
# Posted on April 23rd 2008 by llig leahcim
Re: Do mathemeticians make the best musicians?
The comments on this thread are multiplying exponentially (or is that "geometrically"?)
# Posted on April 23rd 2008 by fauxcelt
Re: Do mathemeticians make the best musicians?
The discussion keeps coming around to functional mathematical skills applied to playing music and I think that misses the mark. The mathematical/computational skills needed in playing music are fairly trivial. I don’t see where Isaac Newton or Bertrand Russell would have any advantage over my dad, with his seventh-grade education, in that respect. My feeling is that the more interesting link between mathematicians and musicians is that the Mathematical Mind and the Musical Mind share a fair amount of psychic real estate, particularly in areas where intuitive things happen – things that seem to be largely independent of learned skills. It’s not about using tools and following rules.
My son is a natural musician and has been from very early days. [At the age of about eighteen months, he had an argument with his mother over whether a piece of music on the radio was Bach or Monteverdi. And he was right.] But eighth-grade algebra was painful for him and, years after school, he still has trouble with simple arithmetic. Yet he once asked me what calculus was about and, when I gave him an introductory lesson on integral calculus (which involved discussion about approaching infinity), he grasped it easily and thought it was cool.
I think the overlap does have something to do with, for lack of a better word, beauty. The visceral appreciation of the way various elements can come together into a harmonious whole. I know that’s not an original thought, but it’s where I arrive when I think about this stuff for a while.
# Posted on April 23rd 2008 by Bob himself
Re: Do mathemeticians make the best musicians?
Michael, I don't understand the thinking behind your claim that the examples you offer are not models, because the way I see it, they are obviously models. They are mental analogs invented by the Babylonians or Sumerians (or some folks from that era) as a way of representing sacks of grain or clay pots or soldiers. They then got abstracted so that the symbols and the system can be applied universally, as a means of counting, measuring, and constructing more complex models.
I am also hesitant to accept the claim to see them as absolute, because numbers get kinda weird when it comes to the quantum level and postulated infinite number of universes where the laws of physics may vary. But, on our everyday scale, at a practical level, 4 + 4 = 8 seems very useful as an absolute. But it's still just a story you're telling yourself, information received and encoded in brain tissue, one component of the complex of cultural conditioning that we share, (like 'a,e,i,o,u,' are components of the language modelling system.)
# Posted on April 23rd 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
Sometimes, when I have been trying to figure out the proper fingering to play a tune, I wil start with the end of the tune because I know which finger I need to use to play the last note. Then I start to figure out the fingering backward from the last note.
Sometimes I have had to use a similiar technique with math problems when the instructor told us what the solution is supposed to be. Then it was the responsibility of myself and the other students to figure out how to get from the original problem to the solution.
When I took Music Acoustics in college to fulfill the requirement that I must take at least one physics course for my degree, I was glad that I had already taken two or three semesters of algebra because it helped me understand the mathematical reasoning behind the physics.
I suspect that one of the main reasons that my wife is having so much trouble with the Pre-Algebra Skills class that she is taking in college right now were apathetic and uncaring math teachers when she was a little girl in elementary school.
# Posted on April 23rd 2008 by fauxcelt
Re: Do mathemeticians make the best musicians?
My seventy-nine year old father can still do math problems in his head that I need pencil and paper to solve. However, he has a bachelor's degree in geography and a master's in meteorology. My mother only got as far as a bachelor's degree in music education and she did struggle with math in college. My mother was a music teacher who taught me how to play the piano. On the other hand, though, my father doesn't play any instruments but he was a lot of help with math when I was in school.
# Posted on April 23rd 2008 by fauxcelt
Re: Do mathemeticians make the best musicians?
wolfbird, 'a,e,i,o,u' are just sounds. My cat makes most of them.
4 + 4 = 8 is not a model, just as playing scale exercises is not making music. Imagine a music curriculum that consists of 6 years of scales before being allowed to play a tune. Imagine a writing curriculum that consists of years of grammar and spelling before being let loose to write a story.
That's the problem with math education: someone decided that 9th graders should spend a year factoring polynomials, 10th graders should spend half a year computing derivatives. Worthless. A calculator does these.
Estimate how many people in Zone B will buy our product, based on current sales and demographics in Zone A. Find the radius and incline of a highway curve such that a truck doesn't fly off the road. Design a 1000 acre irrigation system, tell me drawdown of the water table, the most efficient pipe diameters and flow scheme, the horsepower of the pumps, the total cost. Tell me when the sun is going to run out of hydrogen and start burning helium. Those are models.
To say that math and music are similar because "they both use a structure of abstract symbols" completely misses the point of both activities. I could possibly buy the argument of the Musical Mind having a lot of psychic overlap with the Mathematical Mind (if either exist), but I wouldn't believe it without good evidence.
# Posted on April 24th 2008 by silver bow
Re: Do mathemeticians make the best musicians?
'a,e,i,o,u' are just sounds. My cat makes most of them. (silver bow)
Yes, and all in the same breath too - How many musicians, or mathematicians for that matter, and sound like a cat.
Cats obviously make better mathematicans. Why can't you guys see that.
# Posted on April 24th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
How many musicians, or mathematicians for that matter, CAN DO THAT, and sound like a cat, indeed.
# Posted on April 24th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
"wolfbird, 'a,e,i,o,u' are just sounds. My cat makes most of them."
silver bow, you seem to be missing a few points here.
Contrary to what you wrote above, a, e, i, o, u, are NOT sounds.
I'm looking at them here on my computer screen at this moment. They are shapes (made of pixels), and are completely silent. Before they reached the screen they were electronic pulses in the telephone line and binary machine code.
The same goes for 4 + 4 = 8.
Because I am literate and numerate, and share the conventions of the culture I've grown up in, I know the concepts that these shapes represent, and know the appropriate conversion procedure which transposes these symbols to vocalised sounds.
I maintain that they are models, albeit very simple, or constituents of a modelling system, be it mathematics or language.
# Posted on April 24th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
"Cats hath best math" - time yourself and see how many times you can repeat this in one minute, without making mistakes.
It should prove something.
# Posted on April 24th 2008 by Duijera Dubh
Re: Do mathemeticians make the best musicians?
Lots of music is math, but then a lot of everything in life is math, one big complex equation, some say. Rhythm is clearly math based, and the fact that tunes are based on standard repeating patterns of 2s, 3s, 8s, 16s is one of the things that makes this music accessible. And pitches and harmonies are clearly math based.
But like a lot of things, you don't need to understand and calculate the math as long as you can feel it, lots of people use math without realize it just by feeling the relationships and acting accordingly.
And like all art, athough there are features of music you can map out, the true beauty of it defies description!
# Posted on April 24th 2008 by AlBrown
Re: Do mathemeticians make the best musicians?
I think you've got it the wrong way round, AlBrown, when you say rhythm, pitch, harmony, is math based. Surely, people were singing and dancing and playing instruments long before anybody began thinking about counting and inventing equations, and seems from Pythagoras that it might be more accurate to say that maths is music based.
# Posted on April 24th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
llig leachim -
Whan you state that the mathematical equations you render are not models, you raise an interesting point. Most mathematicians would hold that mathematics is *discovered* rather than *developed*. Any rigorous notation will suffice for the expression of mathematical truths in the absolute. The simple arithmetic truths you illustrate are good examples. We'll leave Godel & Church / Turing out of matters for the moment.
Matters become a little more complex when mathematics are applied to physical systems. Newton's laws, or Maxwell's equations, or the equations of relativity, describe *how* various particles and fields interact. They do not actually tell us very much about *what* the particles and fields actually *are* - if indeed that question makes any sense at all.
It is in this sense that I averred that musical notation is similar to mathematics, in that musical notation is a set of abstract symbols that define pitch and duration in time of - ultimately - vibrations of air.
# Posted on April 24th 2008 by Sean Lead Liath
Re: Do mathemeticians make the best musicians?
Not wishing to speak for Michael, of course, but seems obvious to me that 'discovered rather than developed' is too crude, because someone must have first discovered, - e.g. Pythagoras noticing how the note produced by a plucked string varies with the measurable length, - and then developed, leading to further discoveries and further developments, up until the present time.
# Posted on April 24th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
Wolfbird -
"Discovered' in the sense that the truths are held to be "Out there" as it were - independent of human perception or experience. Thus, that which Pythagoras discovered re the mathematical properties of pitch & string length was true before him, & remains true after him. Similarly, harmonics were always there - in precisely the mathematical relationships the analysis of which Fourier demonstrated.
The "Developmental" view - that mathematics is an artefact of human perception or societal conditioning - is on occasion heard from post-modern sociologists.
# Posted on April 24th 2008 by Sean Lead Liath
Re: Do mathemeticians make the best musicians?
Thanks, Sean Lead Liath.
I'll attempt to explain the way I see it. There's the primate mammal we call Homo sapiens, and it evolves a brain which is capable of some sort of symbolic representation of meaning. Maybe, 'that's the way home' or 'that's my mother'. Then, some smart fella scratches a mark on a stone every time the full moon comes around. And then we get to Pythagoras.
The Moon, the properties of strings, and everything else, was always there, before and since. But the mathematical stuff (and also language) is to do with our brains, something that we overlay, or project out onto, the raw reality.
It is astounding, almost miraculous, that starting from simple correspondences between making three marks with a charcoal stick and say, three sheep, we end up with statistics and Fourier transforms and all the rest.
It's equally amazing that the alphabet can lead to all the world's great literature.
The way I see it, these things are cultural, the accumulated result of thousands of brains passing on insights. They can tell us a lot of useful and interesting things, about ourselves, about the world, about the Universe we find ourselves existing in.
We possibly agree about much of this stuff. The main point that bugs me, that I've been trying to put across, is that we fall into the trap of believing that our symbolic representations of reality, are the actual reality. I think that's a massive mistake. We've labelled and measured and counted. But nothing is explained, at the deeper level, of *what is it ? why is it ?*....fundamental, primary questions which are surely valid ( little children think so, anyway) even if they are impossible to answer in a satisfactory way.
# Posted on April 24th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
Well, Begod, sure ye learn something new ever day. I was wondering who "Michael" is. Now I see it. I had "Llig Leachim" down for a character from some obscure part of the Fiannaíocht or the Ruadhraíocht - vauge associations with something along the lines of an Old Irish rendition of Fear Lag an Leath-cheim or suchlike......
...& mathematicians are supposed to be good at pattern recognition......
# Posted on April 24th 2008 by Sean Lead Liath
Re: Do mathemeticians make the best musicians?
Wolfbird -
I do agree with much of that which you say - cf my ref above to the fact that mathematical representations of physical phenomena do not tell us much about *what* the physical phenomena are.
I do nevertheless hold that mathematics is not merely a matter of perception - to wit - a human development. Our *insights* to mathematics were developed, but the mathematics itself was always there. If matters were otherwise, then I do not think that mathematics would be much use as a predictive tool in the physical sciences - which it clearly is.
Anyone who doubts the above is cordially invited to stand underneath a thermonuclear device prior to detonation.
# Posted on April 24th 2008 by Sean Lead Liath
Re: Do mathemeticians make the best musicians?
Ha,ha, Llig is maybe more Welsh sounding than Irish....anyway, fascinating points, Sean.
I probably part company with you that 'mathematics was always there', (although I'm open to being convinced), but your examples, that it provides predictive power, don't do it for me.
Seems to me that using maths to predict that radioactive fissile material would produce a chain reaction and nuclear explosion, is, philosophically, little different to using triangulation to accurately map the landscape as surveyors do.
I don't deny that mathematics is fantastic, e.g. nuclear particles or black holes can be predicted from mathematical models, and, lo and behold, you look in the likely place, and there they are. But, for me, the stuff was there, and our maths merely a means, like using a mirror to look around a blind corner.
IMO, the models are in our minds. The relationship between the model and the modelled is hard to understand. If I remember, there are half a dozen philosophical schools of thought to choose from, and none of them are very easy to understand or totally convincing, especially as the deeper folks probe into quantum physics and astrophysics, the more bizarre it seems to get.
# Posted on April 24th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
Wolfbird -
I agree with you with regard to applied mathematics - mathematics is a descriptive analogy - and, as I have alluded to previously, does not tell us very much about *what* the phenomena it models actually are.
Pure mathematics differs. Fermat's last theorem was true before Fermat described it & before Wiles proved it. I do not believe that the truth it describes is a human construct.
# Posted on April 24th 2008 by Sean Lead Liath
Re: Do mathemeticians make the best musicians?
Okay, Sean, I'll have to concede that I'm out of my depth when it comes to Fermat's last theorem and it's proof, but I'm willing to learn.
From what I do understand, I'd see the distinction between applied and pure maths as roughly comparable to factual writing, which is attached in some way to our everyday world, and fictional literature, such as science fiction, which can construct alternative realities as wonderful as the author's imagination can extend to.
In the first category I'd put, say, 'The variety of life', by Colin Tudge, which attempts to be a catalogue of all creatures that have ever lived, or a geographic Atlas. In the second category I'd put Tolkien's 'Lord of the rings' or Asimov's 'Foundation' trilogy.
# Posted on April 24th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
I just took Fermat's last as an example. It is very simple. It states that there are no numbers that meet the criterion
a^n + b^n = c^n for n greater than 2, and a,b,c non-zero.
(The equation would of course represent the familiar Pythagoras theorm if n were equal to 2).
My point is that Fermat's last theorem was always true, and always will be, and would have been true even if humankind had never evolved. It is an eternal mathematical truth, not a human construct.
# Posted on April 24th 2008 by Sean Lead Liath
Re: Do mathemeticians make the best musicians?
Okay. It tells us about numbers. The numbers are in our heads.
You don't find a 3, 4, 5, Pythagorean triangle laying there in the natural landscape. If you do find one, it's because somebody made it. Artifice. A product of human culture. Sure, numbers do all kinds of weird and wonderful things. I don't know why that happens to be so. But I'm very suspicious of your claim that they have some kind of existence independent of human intellect (if that's a correct understanding of your position ? )
I mean, to take it back to music. The sounds or noises can be an entirely natural phenomena. We investigate and find regularities that we can represent with numbers, or dots, or ABCs. But these are our invention, maps we draw to help navigate the raw territory. Or are you saying that pure maths is quite unlike that ?
# Posted on April 24th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
Um, I just see a weakness in my own argument here. It's true that there aren't perfect right angles in nature, of if they occur its random chance. But there's plenty of Fibonacci series, Golden Mean, spirals and ellipses and cones and stuff, and when I think about it, ratio is intrinsic to natural forms of many kinds.
But I think what happened is that, for a lot of folks, early writing was ideographic, the symbol was linked to the image (of a bird, pot, ox, etc. ) and the Greeks were the first to take the Phoenician alphabet and make abstract, in the sense that pure maths is abstracted from applied maths. When you do that, when you take the step of separating a symbolic form from it's original referent, then you can play with it in all sorts of novel ways, very much as we have discovered more recently, with digital electronic gadgets that can give everyone access to jpegs and mp3s.
You say Sean, that Fermat's last theorem is an eternal truth. But what does that mean ? Where was it, 20 million years ago ? How can something be 'true' without a human mind to acknowledge the veracity ? Obviously, it doesn't have to be Fermat's, it could be the expansion coefficient of copper, or even one plus one equals two. These are things that humans have established, fixed rocks in the landscape, so to speak. But I still think that they are epiphenomena that arise from our mapping of the territory.
Certainly, the mathematics has an elegance and beauty, with all sorts of quirky puzzles, like pi, that upset the pattern. But then, the same can be said of Bach's music. Does that also have some independent existence ?
# Posted on April 25th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
Looks as if we're on the verge of discussing whether a falling tree in a forest makes a sound if there's no creature out there to hear it.
Literature was of course around for a long time before writing was invented. Homer's Iliad and Odyssey were being recited (declaimed, perhaps) to the public for hundreds of years and passed on by word of mouth and human memory or hundreds of years before they were committed at an early opportunity to the written version we have today. The Druids, however, deliberately did not commit their corpus of learning to the written form, even though writing was available at that time, with the result that we now know very little about their learning. But Virgil's Aeneid was written down before it was recited to Virgil's audience. This procedure continues to the present day. However, ITM and other folk musics have redressed the balance in that they are still passed on aurally and by memory.
# Posted on April 25th 2008 by lazyhound
Re: Do mathemeticians make the best musicians?
"for hundreds of years"
# Posted on April 25th 2008 by lazyhound
Re: Do mathemeticians make the best musicians?
Yes, lazyhound, the falling tree also crossed my mind. And also Bishop Berkeley's idea, that there's really nothing at all 'out there', it's all in our heads....isn't the internet incredible ? I just googled 'social construction of pure mathematics' and it got me 1,430000 pages to read...should keep me quiet for the rest of my life
I see the sort of literature you're talking about, 'pre-literature', as somehow more natural. It's kind of noises we make, and facial expressions and impersonating characters, all the charm and magic of a good story teller, and presumably traces back to the sounds that many creatures make to communicate. Once writing comes along, we've moved into a new area.
# Posted on April 25th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
I'm coming down firmly in Sean's camp here. Wolfbird, here's a question: if we did not exist, would the universe still exist? I think how you answer that question says much about your world view. By the way, I'm not saying there is a right or wrong answer, just that this can turn into a philosophical or metaphysical discussion. Maybe it already has
The "tree falling in a forest with no one around" question deserves some clarification. If no one is there to hear it, does it make a sound? No, if you define sound as what our ears perceive based on vibrations in air. But the vibrations will still be produced by the falling tree, regardless of the presence or absence of an observer.
Sean is saying that this is true for pure math as well, and I agree. It does not matter how we represent numbers, or what symbols we choose to use to write equations. There is a foundation beneath it all that was here before us and will be here after it.
I doubt there has been enough research to determine exactly why humans like music, but as with math I'm sure there are some underlying physical principles that are fairly simple. The best musicians intuitively tap into these, but unlike math there are some decidedly human factors. If our biology was significantly different we would probably make much different music, or maybe none at all.
However, the physical laws that determine what happens when a string vibrates would still hold true even if there were no people to make a string vibrate.
# Posted on April 25th 2008 by Scott Esch
Re: Do mathemeticians make the best musicians?
Yes, Scott, but I'd say that all questions, if you really dig down, are philosophical and metaphysical matters...
It might seem reasonable to assume, for common sense practical purposes, that the sound of the falling tree is produced even if there's no human to hear. Point is, it's impossible to prove that, isn't it ? I don't think I agree with you or Sean, at this stage, but I need to study some more, because there's a number of different positions on offer. My personal metaphysical or philosophical position is zen buddhist, but that doesn't mean I agree with all zen buddhists or that there is only one clear zen buddhist position. I found this page which seems to be a reasonable summary of recent thinking, so I'm going to start there and see where it takes me.
http://www.people.ex.ac.uk/PErnest/pome16/perspectives.htm
# Posted on April 25th 2008 by wolfbird
Re: Do mathemeticians make the best musicians?
Berkeley's one about the tree is a special case of solipsism. I'm not aware that there is any rigorous way to refute solipsism, but, as a stance, it seems rather sterile to me.
Along with most other mathematicians, I would hold that there are truths which are independent of human experience. Pure mathematics is a corpus of these. Pythagorean triplets exist in the domain of pure mathematics. The veracity of the statement -"There is an infinite number of solutions to the equation a^n+b^n=c^n for n=2" does not depend on the fact that, in plane geometry, right-angled triangles can be formed using sides the lengths of which define Pythagorean triplets. We do not actually live in a plane geometry universe - our universe is curvilinear - so Pythagoras theorem, as it may be applied, will never be fully accurate. I stress again, though, the relationship of the *numbers* is independent of the application to plane geometry.
With regard to physical phenomena, though, I think we need to be careful. Repeatable experiments the results of which are at variance with common sense can be performed. A simple one is described well at http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/quantum.html - which also provides a good introduction to quantum weirdness. Note however that none of this calls in to questio