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.

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It helps to be able to count to four.

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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.

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Touche’ granama.

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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.

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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.

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Do mathematicians have a thick corpus callosum?

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gw. Even though I am not a mathematician I would like to think I had one.

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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.

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I’ve heard Tony McManus has such a qualification.

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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.

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No truth in art? Haha, I see this going in circles 🙂

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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

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Of course there is no truth in art. The question of truth is the one and only thing that sets science and art apart

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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.

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Keats wasn’t a scientist, he didn’t know what he was talking about.

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Lets not start by using examples of how you write music down, that is completely irrelevant

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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.

🙂

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A good diddley musician is also a good composer, by definition. The way you mess with tunes when you play them is composing

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So…poets don’t know what they’re talking about because they aren’t scientists?

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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

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I meant that poets don’t know waht they are talking about when they talk about truth

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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.

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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

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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.

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But at the far creative end of mathematics you can re-write the rules, or invent new ones, and see what happens.

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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.

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I almost had an unfortunate bladder response.

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I’m terrible at math. Mebbe I’m a terrible musician too…?
At least I don’t play bodhran!

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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

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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.

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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.

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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.

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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.

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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.

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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.

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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

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that would be "ability in the test" obviously.

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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. 🙂

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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 ;)

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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.

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And for the coup de grace -
how many bodhranistas here consider they are good at maths, and maybe languages as well?

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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.

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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.

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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.

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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.

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Sudoko, sudoku, whatever - it gives me a heedick as they say.

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Opinion or research, c.g.?

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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.

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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,,,,

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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.

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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!

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Jim, do you think you have an aptitude for learning other languages?
What does your friend lecture in at Trinity College.

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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. 🙂

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Looks like it is fair to say he would be handy with maths, Jim.

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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.

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Do you like sudoku, wolfbird.

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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.

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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.

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in maths tou have to follow rules but music lets you bee free to do what you want

chick xx

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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???

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"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.

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My

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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.
🙂

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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.

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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.

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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.

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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…

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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?

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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.

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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."

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"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.

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

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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 😉

Re: Do mathemeticians make the best musicians?

am I the only one to be getting a headache ?

Re: Do mathemeticians make the best musicians?

1+1=1?

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

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.

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

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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.

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).

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.

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*

Didn’t Einstein flunk math?

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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

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.

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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!

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.

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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

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 ? )

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.

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.

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.

Re: Do mathemeticians make the best musicians?

I guess I know as much as I need to know now, Screetch, thanks 🙂

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.

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 🙂

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.

Re: Do mathemeticians make the best musicians?

"I think the thread’s question IS actually a bit ambiguous", that should be.

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.

Re: Do mathemeticians make the best musicians?

But doesn’t that assume that mathematical ability is hereditary?

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.

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?

Re: Do mathemeticians make the best musicians?

Mehere, I’m in the same boat - just double your numbers!

Re: Do mathemeticians make the best musicians?

im a matamatician and i can play any instrument so there you have it

Re: Do mathemeticians make the best musicians?

mathematician’s can’t spell! lol

Re: Do mathemeticians make the best musicians?

sorry - couldn’t resist! 😉

Re: Do mathemeticians make the best musicians?

Just like crysania, I’m entirely dyslexic when it comes to maht.

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.

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."

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?

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.

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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.

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.

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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.

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.

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.

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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.

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.

Re: Do mathemeticians make the best musicians?

Y’all are gettin’ way too esoterical for me.

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.)

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.

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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.

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.

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.

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

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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 ? 😉

Re: Do mathemeticians make the best musicians?

Negative numbers DO exist. I see them in my bank statement all the time…

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)

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.

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.

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.

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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.

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.

Re: Do mathemeticians make the best musicians?

of course we do.

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…

Re: Do mathemeticians make the best musicians?

the notation has absolutly nothing whatsoever to do with it

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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 .

Re: Do mathemeticians make the best musicians?

The comments on this thread are multiplying exponentially (or is that "geometrically"?)

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.

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.)

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.

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.

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.

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‘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.

Re: Do mathemeticians make the best musicians?

How many musicians, or mathematicians for that matter, CAN DO THAT, and sound like a cat, indeed.

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.

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.

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!

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.

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.

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.

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.

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.

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……

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.

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.

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.

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.

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.

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 ?

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 ?

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.

Re: Do mathemeticians make the best musicians?

"for hundreds of years"

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.

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.

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

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 question the rigour of the *mathematics* used, albeit it most certainly calls in to question ideas of human "Intuition". I stress that the experiments are *repeatable* in order to avoid any nonsensical post-modernist suggestions that, because experiments that defy so-called common sense, or intuition, can be constructed, then all perceptions are equally valid.

I am of course perfectly aware that the axioms of mathematics are held to be self-evident on the basis of intuition, but it nevertheless does appear to be the case that mathematical analogies hold true for the the physical world - whatever the hell *that* might actually be. If I may stray in to the realm of pure conjecture, I am quite prepared to admit of the possibility that the human brain might exhibit quantum characteristics, and that there may be something to the Eastern concept of the fundamental unity, or connectedness, of observer and observed. Like Babbage, I would give a lot to come back in a few hundred years & see what people think then……

To return to the baseline question re whether mathematicians make the best musicians - well - judging from the quality of the contributions to this discussion, it would seem to me that there is certainly an overlap of interest. My own view is that there is probably a statistically significant correlation between musical & mathematical aptitude, but this does not exclude tone-deaf mathematicians and superb musicians with little mathematical talent. I rather suspect that the former is more common than the latter.

Re: Do mathemeticians make the best musicians?

Amazing how frequently Schroedinger’s dead/alive cat turns up on this site 🙂

"An intriguing alternative, called the many-minds view, has been advanced by David Z. Albert, a physicist-turned- philosopher at Columbia University, and Barry Loewer, a philosopher from Rutgers University. Each observer, they explain, or " sentient physical system," is associated with an infinite set of minds, which experience different possible outcomes of any quantum measurement. The array of choices embedded in the Schrödinger equation corresponds to the myriad experiences undergone by these minds rather than to an infinitude of universes. The concept may sound far-fetched, but it is no more radical, Albert argues, than the many histories theory or even the Copenhagen interpretation itself."

Re: Do mathemeticians make the best musicians?

Would account for a lot…

I don’t recommend that anyone actually try, but an experiment to test the validity of the Many Worlds theory can be found at

http://space.mit.edu/home/tegmark/everett_guardian.html

Mind you, it is not clear to me why, if the subject of the experiment is supposed to retain consciousness, s/he is not aware of parallel consciousnesses - so, if the experiment holds veracity, there may be substance to Wolfbird’s above.

At this stage, several of my parallel consciousnesses start to hurt……

Re: Do mathemeticians make the best musicians?

Mind-boggling stuff, Sean. I wonder if there is a connection to zen meditation. To get to the final stages and penetrate as far as it is possible to go, you have to let go of everything, (what Dogen calls ‘jumping from the top of the hundred foot pole’) which is really no different to death, because no trace of anything remains. No observer, no observed. It’s only difficult to do because the ego clings to existence and wants to resist oblivion. It is profoundly mysterious, because although it’s possible to have the experience and then return to the everyday world, nobody actually has the experience, in the sense that all features and characteristics of self and being are left behind.

I’ve read a twist on the experiment you linked to above. To test whether God plays dice, replace the wretched cat with a convicted murderer and then with an innocent child, to see if there’s any moral influence on collapsing the probability wave.

Yes, my parallel consciousnesses are feeling the strain too, but its fun to think about.

Re: Do mathemeticians make the best musicians?

Applied mathematics in the physical world consists of models which, as accurately as we can measure, describe various phenomena. These are mechanistic tools. You set up the problem and you turn the crank. “Pure” mathematics consists essentially of logical statements (if A, then B) which are true or false, regardless of whether they model anything in the physical world. Mathematics doesn’t say “B is true”. It says “if A is true, then B is true”. A and B don’t have to exist in the physical world - or any other world, past, present or future - in order for the statement “if A, then B,” to be true.

Re: Do mathemeticians make the best musicians?

Nicely & succinctly put, Bob.

Re: Do mathemeticians make the best musicians?

On 1 of the waltzes, Ookpik. we play AAB AB A.
It is so nice to come back to the 1st part.

Posted by .

Re: Do mathemeticians make the best musicians?

& when I die, if there is I God, I will want some pretty damn’ convincing explanations as to

Why relativity ?
Why quantum mechanics ?
Why turbulence ?
Why Godel ?
Why wasn’t I born rich and irresistible to young ladies ?

Re: Do mathemeticians make the best musicians?

I meant *a* God, not *I* God.

(Lord - if ye’re listening - that was a typo, not a Freudian slip. Honest)

Re: Do mathemeticians make the most unexpectedly verbose musicians?

Interesting reading.

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Re: Do mathemeticians make the best musicians?

"Interesting reading."

You must be a geek, Bren! 🙂

Re: Do mathemeticians make the best musicians?

Evolutionary psychology provides plausible explanations as to why you’d want to be born rich and irresistible to young ladies, Sean. Can’t help with the other 4. More seriously, my definition of ‘God’ ( a troublesome word if ever there was one ) might be along the lines of ‘everything you’ll ever know and experience’, so the questioner and the questions are included….Why any of it ? is a tough question. Why is there something rather than nothing whatsoever ? How’d you frame that question in pure mathematics ?

Re: Do mathemeticians make the best musicians?

“if A is true, then B is true”. So, Bob, if I wanted to argue that pure maths is socially constructed… there’s you and your brilliant mind, and you work out a fantastic logical proof that B must be true. But then, you’re the only fella that knows that. You’ve got to convince your colleagues and the wider community, which is a social process…you might be right, but nobody else can understand you, so the proof lies in the archives gathering dust…whilst everyone carries on believing what they learned at school…

Re: Do mathemeticians make the best musicians?

God - I’d be a Laplace man - "Je n’avais pas besoin de cette hypothèse"

Why something rather than nothing ? That’s the province of *applied* mathematics. Cosmology does not yet have an answer.

Evolutionary psychology - Sure - explains why I *want* to be - not why I’m *not* 🙁

Re Bren being a geek - Maybe he his - But look at his profile. Ye get interested in the oddest things when ye spend half yer life in hotel rooms.

I’m a geek. I even know how computers work.

Re: Do mathemeticians make the best musicians?

"explains why I *want* to be - not why I’m *not*"

Maybe you were too wicked in your previous incarnations, Sean, just be grateful you weren’t reincarnated as a dung beetle 🙂

Re: Do mathemeticians make the best musicians?

Wolfbird -

Re yours to Bob - Might I respectfully suggest that there is a difference between whether something *is* actually true, and whether or not any corpus of individuals (including peer-reviewing mathematicians) *believe* it true ? Mathematicians have often found errors in other mathematicians’ claimed proofs.

To go back to Fermat - either there *is* a counter-instance which disproves the conjecture, or there is not. There is no room for ambiguity - the conjecture is either true or false, & this is unaffected by whether people believe it true or false. Actually - to take up the point of the first para - Wiles had to enhance his original proof in the wake of flaws found by peer reviewers.

Re: Do mathemeticians make the best musicians?

Absolutely fascinating philosophical point, Sean…Just because everyone alive believed something to be true, it may not actually be true…

Yes, I read that bit about Wiles gap in his proof. It must have been an exciting episode for all concerned. And also the intriguing mystery of Fermat’s original supposed proof, which some believe must have been impossible at that time.

Re: Do mathemeticians make the best musicians?

Hans Eysenck - late professor of psychology at London - "If a proposition is absurd, the fact that many people subscribe to it does not make it less absurd".

When I was Lead Og Fionn, I used to argue with people. Maturing years brought the realisation that most people believe things that they want to believe for emotional reasons, rather than things that are sustained by evidence. I never argue religion, or homeopathy, or astrology or anything similar with anyone - The riposte is always "Well - It works for me".

Re: Do mathemeticians make the best musicians?

I tend to argue with myself, trying to take into account the various ideas I’ve come across from diverse sources. Re the Laplace quote, I wanted to test the hypothesis. That was a long time ago.
There’s a zen quote ‘Those who speak do not know, those who know do not speak’, because when you get right down to it, there’s not much that can be said. Sure, we know some stuff.

"It might be thought that knowledge might be defined as belief which is in agreement with the facts. The trouble is that no one knows what a belief is, no one knows what a fact is, and no one knows what sort of agreement between them would make a belief true." Bertrand Russell.

Re: Do mathemeticians make the best musicians?

But let me bring this back to music - I know rationally that when I play, it is I causing the sounds to emanate.

But I have a powerful emotional feeling that the rhythm is out there, & I’m only tapping in to it - like tapping in to an energy field - I am sure I am not alone when I state that I live for the times when the ghost takes over my playing, and I just sit back and listen. The ghost can do things that I could never do.

Re: Do mathemeticians make the best musicians?

Yes, I’m familiar with that wonderful experience of being carried away or losing oneself in the music….I can offer a suggestion. I think that music and dance are very ancient, maybe partly courtship display which might go right back to the earliest birds, reptiles, even insects. Partly social bonding, which social animals do. So, the effects of rhythm and sound go quite deep into our biology, like the heart beat that the growing baby is attuned to. All the stuff being discussed on this page is cerebral, the higher mind that we require as an executive function, especially in this modern soceity which is so incredibly complex. We’re a long way from sitting around in a bunch of huts, preparing food, making pottery by hand, listening to the birds.
I think we have to switch of that executive agency for a while to gat deeper into playing and listening. Will CPT mentioned some reference to that idea, a few weeks back, about going into the dreamy space. I think it’s called hypnapompic and hypnagogic reverie, the mental state between wakefulness and sleep, in the morning and evening (or tother way around).
It’s probably got something to do with alpha, delta, beta, theta brainwaves. Sometimes a bit of music can just grab your complete attention and it’s as if time stopped, and sometimes when playing it’s as if the instrument is doing it by itself, but as soon as you start noticing that and analyzing, the higher mind is back, and the magic vanishes.

Re: Do mathemeticians make the best musicians?

Wolfbird, I don’t mean to take away from the great discussion you and Sean are having, but I wanted to respond to your question, "it’s impossible to prove that, isn’t it?" (regarding the falling tree). That depends on what you define proof to be. The only "proofs" I’m aware of are logical or mathematical. Everything else is really a misuse of the word. For example, one can "prove" their legal case in court, despite the fact that they may be lying. Science does not really deal in proof, it deals with prediction. We can predict that a falling tree will make a sound without an observer due to the mountain of empirical data regarding sound and how it is produced. This might all sound mundane, but my point is that non-verifiable propositions are worthless to argue about. If the proposition can neither be shown (to everyone’s satisfaction) to be true nor untrue, but 100% of the physical evidence says it will go one way, which would you ascribe to? Especially when the counter view rests solely on the basis of an interesting thought experiment and nothing more.

Philosophy and metaphysics are certainly interesting, and have contributed much to the fields of ethics and other social studies, but when it comes to the physical world I’ll stick with empirical science.

Why are we here to observe the universe at all? Or why there is something rather than nothing? In my opinion it really doesn’t matter. We are, or we wouldn’t be having this discussion. Any hypotheses for a reason behind it all (or a meaning of life, thanks Monty Python) are completely untestable. So they might be fun to argue about, but I don’t see the point unless I’m bored and I need something to argue about over a pint.

If, however, the search for an answer enriches your life or teaches you something valuable about yourself, then that’s great. Keep at it and maybe others can learn something about the human experience too - that seems to be the point of philosophy to me. But too often those discussions stray into the domain of the physical sciences, where they need to take a backseat rather than try to drive the search for scientific knowledge.

Oh yeah, we’re on a music board. So maybe I should mention I’m listening to Altan right now. 🙂

Re: Do mathemeticians make the best musicians?

Scott, I very much disagree with your view, which seems much to narrow. The way I see it, philosophy comes before science. It’s a shame scientists don’t know more about philosophy, it would help them in many ways to better understand what they’re own subject is - e.g. Popper, Kuhn, Feyerabend,etc.. There is already loads of philosophical assumptions and preconceptions implicit in the way you outline science and your conception of what philosophy is. Way I see it, science was once a noble endeavour to understand more, but in recent times it’s changed. Most ‘scientists’ are just technicians who serve power. A government or corporation says ‘we want a new bomb, (or a new flavour of toothpaste or a new way to poison bugs), here’s the money lads, off you go and see what you can do’. That’s not the same quest that Galileo and Faraday and Darwin and Bohr were on.
You say that ‘proof’, other than in the mathematical sense, is a misuse, but it could be argued that mathematical term is only a more specialist strict technical definition of the common term. But that’s another vast area, how meaning is encoded in language, and the problems that arise when the same word can have dozens of different meanings. There are very many people who take your position, that questions like ‘why is there anything?’ etc. cannot be answered or tested and are therefore pointless, and that the only serious pursuit is restricted to the physical sciences. IMO, that position is obsolete. It rests upon the thought of people like Comte, and the Enlightenment project which imagined that if we measured everything, everything would be eventually explained, and there is only material ‘stuff’, everything else is woo woo hokum. All the established certainties were upturned by Einstein and then Quantum physics. I refuse to be packaged into a science v. religion camp, or a science v. the arts camp, or whatever; that’s what the education system typically produces. My position is closer to someone like Aldous Huxley; everything is interesting, everything is worth checking out, nothing should be accepted just because someone says ‘that’s what you’re supposed to think’. For me, the conundrum about the tree falling silently is beautiful, because it makes my mind consider things in new ways, different ways, and makes me curious about the conclusions that other thinkers have come to, like Bishop Berkeley. Dr. Johnson refuted Berkeley by kicking a rock. I find that delightful. As I said way up the page, the trouble with science is that it can only deal with stuff it can measure. For most humans, those things are not the most important. For most people love is important, laughter is important, it’s the craic that’s important.

Re: Do mathemeticians make the best musicians?

Your view seems very anthropocentric to me. There is far more to the universe than just humans, and all of it is just material stuff. Science is the only thing that can tell us anything reliable about this vast universe - all the other disciplines are confined to the relatively small world of humans. It certainly is a fascinating world, but it’s not everything.

But I wouldn’t want to tell you how to live your life, so enjoy it however you need to. If that means putting philosophy above everything else, I don’t have a problem with it. It’s just a friendly discussion.

Re: Do mathemeticians make the best musicians?

Hi again, Scott. Yes, just a friendly discussion 🙂, an attempt to communicate, and I suppose we just have to do the best job we can with what we have. Which is just this little box of text and words with all their limitations and muddles….

I seem to have given you are wildly mistaken impression, somehow. I am at the opposite end of the spectrum of views from anthropocentric. I’m not even ecocentric. I’ll give you the URL to my old website when I find it, and you’ll have a better picture. I don’t think of myself as any more important than the trees and birds here.

But your next statement "all of it is just material stuff" is bizarre. How do you know ? You professed previously, and again now, your high regard for science. Do you think science has now understood everything ? Nothing left to understand ? And if you understood what science has actually established via quantum mechanics, you’d realize that science no longer claims that "it is just material stuff" …

I mean, is consciousness ‘material stuff’ ?, or superpositioned particles ? I mean, wtf is ‘material stuff’ that can be in two places at the same time ? because, well, there are folks who can explain it all far better than I can….e.g.

http://www.fortunecity.com/emachines/e11/86/index2.html

Try Roger Penrose or Danah Zohar or John Wheeler or any of the folks there who are far better equipped to make the case than I am, and I don’t think any of them will agree with you that all there is is material stuff. What we have is some awesome mystery that nobody understands. The idea of material stuff is left over from the time when people still thought atoms were like billiard balls.

Look Scott, " Science is the only thing that can tell us anything reliable about this vast universe" is fine, as a statement. But you really don’t grasp what philosophy actually is. For one thing, it’s about how we think, how we frame questions, which questions are valid and which are not. You’re already doing philosophy when you make statements like the above, you just have not realized that yet. It’s not something separate in a weird little box all on it’s own. The very word from which ‘physics’ comes, begins with a philosopher, Heraclitus, who wanted to think about ‘emerging nature’.

Oh yes, my old website…try here ‘a little bit of taoism’ about half way down if you’re interested

http://www.geocities.com/dao_house/basics.html

Re: Do mathemeticians make the best musicians?

Well, is the universe just energy and matter or isn’t it? That’s what I mean by it’s all material. There’s a huge difference between acknowledging the veracity of quantum mechanics and saying that there must also be something supernatural out there. You’re getting a little hung up over my choice of the word "material." I studied astronautical engineering in university (with some classes in astrophysics and cosmology) so I’m at least somewhat familiar with the cutting edge of physics research.

Science will never understand everything, and any proper scientist would never make such a claim anyway. It’s been claimed before, and of course those who made such statements were shown to be incorrect. But I think science is the best way to explore how the universe works. Philosophy is a great tool for examining our own existence as humans, and how we acquire knowledge, but it can’t be used to theorize about how evolution works, how black holes are formed, or how long the sun is going to be around.

While the earliest philosophers predated the scientific method, and helped establish a proper way to ask questions, that has all been internalized by the physical sciences. It’s a part of the basic structure of science today.

I did sell philosophy short by not acknowledging its earlier contributions, but I really do think its importance (in its own context and not in concert with any other discipline) has diminished today.

But I’m still enjoying this discussion, and I agree with you that it is a philosophic one!

Re: Do mathemeticians make the best musicians?

Well, thanks for your thoughts, Scott ; and that’s a stimulating question to begin with.

‘just energy and matter’ versus ‘something supernatural’….

"….lay in the beginning a distinct explication of what is meant by ‘thing’, ‘reality’, ‘existence’ : for in vain shall we dispute concerning the real existence of things, or pretend to any knowledge thereof, so long as we have not fixed the meaning of those words." George Berkeley, 1710

That’s the problem we have here, Scott. We can go round and round in circles for years arguing, simply because our understanding and definitions of the terms are different.

I’d say that, by definition, everything and anything in the Universe is ‘natural’. The opposite of natural, for me, would be artificial, or manmade, something like a rocket or the Great Pyramid. So, (although of course I know the dictionary definition) supernatural doesn’t seem like a useful or required term.

If supernatural is used as a label, as commonly occurs, to categorise all the stuff that science doesn’t accept, (e.g ghosts, miracles, ESP, angels, a Creator, and so on), that strikes me as more like prejudice springing from an ideology (scientism) than authentic science at it’s best.

So we end up with the ludicrous slanging matches between literalist fundamentalist Creationists (who claim to speak for God and religion, when they are merely a fanatical fringe) and they’re mirror image, e.g. Richard Dawkins (whose limited comprehension of what religion actually is means he’s forever bashing strawmen he’s invented). IMHO, that battle is a fruitless farce. Both sides use what should be interesting and important stuff to study, as ammunition to throw at each other in a power struggle. It’s boring.

The way I see it, the project of science, stemming from ancient Greeks up until the present, was to try and study aspects of what we find around us in an orderly and objective fashion. I have no problem with that. It seems an eminently sensible worthwhile approach. We want to know what we’re actually dealing with here. We don’t want no mumbo jumbo. Let’s have a close look and see what we actually find, record it, measure it, label it. The empirical method. Philosophy goes hand in hand with that project from the start. It’s verbal mathematics, if you like. It says, ‘we don’t know what we’re studying but nevermind, call it X and continue and maybe we’ll get somewhere’.

We never will know whether we’ve understood 90 percent of what is laying out there, or merely one percent. All science can ever say is that it’s got one little patch pretty well sussed, on a provisional basis. So it should be a very humble procedure, full of wonder at the peculiar stuff that turns up, e.g. the DNA double helix, which is no more, or less, astonishing than Pythgoras’s discoveries, or a Heliocentric solar system. It’s ALL downright miraculous and bizarre…

Where I part company with science (or rather, scientism, as an ideology) is when it sees itself as the be all and end all, when it stops being a humble enquiry into the nature of things and gets hubristic, seeking to displace all other belief systems. This kind of thing has happened throughout history. Particular ideologies decide that they hold the only ‘truth’ and seek to dominate and eradicate all competitors, e.g. what happened to Christianity when Constantine coopted it as the official religion of the Roman Empire.

We are some sort of evolved animal, some sort of fancy social primate. As such, we have needs, as biological creatures. We need food, water, shelter and so on. But we also have much more subtle and sophisticated needs, for example, to discuss stuff that interests us, to share gossip and ideas. One of our fundamental needs is for some sort of spiritual or philosophical or religious belief system that can orientate us, regarding ethics, and the meaning of death, the way to celebrate marriage and birth, how to deal with grief and suffering, all kinds of very human experiences like that.

It’s all very well for strong high-minded individuals like Laplace or Voltaire or Dawkins or whoever, to be macho and insist they no need for anything except rational thought. The great mass of humanity just aren’t in that league and don’t want to be.

Personally, I’d see it as being a lot healthier to be believe in astrology and angels than be obsessed with gambling, explosions, pornography and serial killers.

Sorry that this has drifted into some sort of sermonising, and away from mathematics and music….I’ve got a brain that wants to go in every direction at the same time. Must be a quantum thing. 🙂 Einstein said ‘Reality is an illusion, albeit a persistent one’ 🙂 I must attend to other things in my personal reality here.

Re: Do mathemeticians make the best musicians?

O body swayed to music, O brightening glance,
How can we know the dancer from the dance?

- W.B Yeats

Re: Do mathemeticians make the best musicians?

Ah, yes. Seems to me that if you have a belief system, - like say, the Bible or Euclidean geometry or 19th. C. Enlightenment science, - all belief systems have certain implicit or explicit foundational assumptions that everything that follows after is built upon.

If something new turns up that kicks away the foundation, then the whole edifice requires radical reappraisal. Einstein did it for Euclidean geometry, Darwin and geological studies did it for Genesis, and Quantum theory has done it for science.

I mean, I have no way to judge which, if any, of the several interpretations of Schroedinger’s collapse of the probability wave is correct, if any. But all the ones on offer make the world appear a lot weirder than anyone could ever have expected.

As I understand it, John Wheeler thought that it was consciousness, (of the observer of the experiment) that collapsed the probability wave. So, you can imagine walking around looking at things, but those things only become real at the instant you become conscious of their existence.

Others suggest that it’s a matter of scale. What is true for minute particles, photons and neutrons, isn’t relevant to large structures like ourselves, consisting of billions of atoms. But from what I can gather, the probability wave effect still holds good up to the size of an amoeba. Just that the amoebae would take about three years to go through the slots.

And so maybe quantum effects are relevant on the everyday scale of humans and tables and chairs ?
Roger Penrose seems to suggest that the micro tubules in brain cells would be subject to quantum effects. But then who am I to venture an opinion ? The opinion I do have is that we are due for a paradigm shift. At one time everyone in Europe believed in divine intervention in everyday affairs. To question the orthodoxy could get you burned alive or incarcerated for life. I think the Lisbon earthquake had a big influence, because people began to ask why all those innocent people got killed ? How could there be an omnipotent deity who seemed to have a grudge against the Portugese ?

But that sort of dilemma is only a problem for the Abrahamic Faiths. Hindus, Buddhists, Taoists, and others have a very different conception as to the nature of the deity.

Most scientist know a lot about a very specific area, and not much else. They argue against religion as if it was still Galileo against the Catholic Church , as if that was the only religion, or even the only Christian religion. There have been, and still are, thousands and thousands of different conceptions of Divinity.

Personally, I prefer zen buddhism out of all others, because it’s unique. It’s a sort of ‘anti-religion religion’, a methodology for getting free from all belief systems including, finally, it’s own.