I don't think there's any more maths in music than there is in anything else. That's something the Ancient Greeks believed and it continues to this day. Galileo thought the planets revolved in harmonic proportions and Newton listed seven colours of the rainbow to match the diatonic scale. But I don't think it's true at all. Music possibl…
I don't think there's any more maths in music than there is in anything else. That's something the Ancient Greeks believed and it continues to this day. Galileo thought the planets revolved in harmonic proportions and Newton listed seven colours of the rainbow to match the diatonic scale. But I don't think it's true at all. Music possibly originates in our need to learn through sound, like birds. What is more mysterious is why do we hear tones in cycles but see along a linear spectrum.
Thank you so much for saying that. The maths/music thing is something that just seems to be accepted, I'm so pleased to find someone who agrees with me. I can see the beauty in maths too and there are obvious mathematical properties in music: the relationship between frequencies and pitch and the rhythmical divisions. However, what gives rhythm its power and what makes great drummers, their ‘feel’, isn't strictly mathematical. Drummers anticipate (play ahead of), lay back (play behind) or play dead on the beat depending on the feel. It's something that's not taught in classical training but all the great musicians have it and it can be learnt. For me, personally, it was learning to play reggae, which uses all three simultaneously (whereas most other genres of music use one at a time).
BTW, there was an interesting series on the BBC by Hannah Fry, a mathematician, in which she explores the question whether mathematics is a fundamental property of the universe, i.e. discovered, or invented. I tend to the former view as did she, ultimately.
LOL, mathematicians are all platonists but I'm not. Maths was invented, a brilliant invention to be sure. It's humans exploring patterns, and sometimes they invent patterns that decades later turn out to help them understand things they never suspected. That's why they think it's discovered. But sometimes they invent patterns that have no correlation in the world either, but the pattern is just as valid. I think that maths is a mental construct that helps us with our limited minds to make sense of the physical world, and it works brilliantly. But it's a human invention, like language and music and chess. Incidentally, maths, music and chess are three activities a child prodigy can be as good as the best adult.
I agree with much of what you say including that that a lot of maths is invented, e.g. set and group theory, which I was particularly interested in. That contradicts my earlier contention that maths is discovered but I would also say that the universe exhibits certain mathematical properties that seem inherent (to me at least, although I wouldn't go as far as Tegmark and say that the universe is a mathematical object in and of itself) and it's in that sense that I consider maths to be discovered: right angled triangles had the properties of Pythagoras's theorem before he discovered/invented it; the ratio of a circle's radius to its circumference had the same value before it was calculated/discovered and called pi; on the other hand, I would say propositional calculus (the formal name for (mathematical) logic) is purely invented; calculus is more difficult. I think it lies somewhere between discovered and invented: the properties of curves it describes existed before Newton's & Leibniz's techniques to calculate them. One argument to support that it was discovered is the synchronicity between Newton and Leibniz although, equally, it could have been a consequence of previous mathematical inventions, an idea whose time had come (but isn't that a Platonist concept, an idea whose ‘time has come’?). I just find it interesting that that happens as often as it does. BTW, Hannah Fry initially thought as you do, that mathematics is an invention. She changed her mind in the course of making her programme but I guess it's more accurate to say that I think it has elements of both. The properties of objects that mathematics describes are inherent but the techniques are invented.
Anyway, thank you so much for taking the time to reply to me and for supplying the title of your book, The Illustrated Story of Pan. It's an intriguing title, I look forward to reading it 🙏🏼.
Pythagoras got "his" theorum from the Babylonians. Calculus is just an approximation. Either way, the reason why I think mathematics can never be the language of the universe, and neither physics too, is that both are blind to two great components of the universe: life and consciousness. The physical sciences are wonderful for explaining and manipulating inanimate matter, but know absolutely nothing about life and consciousness. Leibnitz himself said so, when he said if he could go into a mind as big as a windmill and observe how it worked when that giant was happy, he would still know nothing about happiness.
I struggle to not be Platonist but there are some aspects of mathematics that is difficult to not find transcendental. Take complex numbers for instance. It was centuries before i was found to apply to anything in the real world, or n infinities, but now they are vital to modern science and technology. I find the more I learn about the history of mathematics the more difficult it is to cling to non-Platonism. I still cling but only with my fingernails and teeth.
When music filled my world and defined my identity it wasn't at etheral, it was down and dirty: Zeppelin, Stevie Wonder, Stones, James Brown, Bob Marley.
I don't think there's any more maths in music than there is in anything else. That's something the Ancient Greeks believed and it continues to this day. Galileo thought the planets revolved in harmonic proportions and Newton listed seven colours of the rainbow to match the diatonic scale. But I don't think it's true at all. Music possibly originates in our need to learn through sound, like birds. What is more mysterious is why do we hear tones in cycles but see along a linear spectrum.
Thank you so much for saying that. The maths/music thing is something that just seems to be accepted, I'm so pleased to find someone who agrees with me. I can see the beauty in maths too and there are obvious mathematical properties in music: the relationship between frequencies and pitch and the rhythmical divisions. However, what gives rhythm its power and what makes great drummers, their ‘feel’, isn't strictly mathematical. Drummers anticipate (play ahead of), lay back (play behind) or play dead on the beat depending on the feel. It's something that's not taught in classical training but all the great musicians have it and it can be learnt. For me, personally, it was learning to play reggae, which uses all three simultaneously (whereas most other genres of music use one at a time).
BTW, there was an interesting series on the BBC by Hannah Fry, a mathematician, in which she explores the question whether mathematics is a fundamental property of the universe, i.e. discovered, or invented. I tend to the former view as did she, ultimately.
LOL, mathematicians are all platonists but I'm not. Maths was invented, a brilliant invention to be sure. It's humans exploring patterns, and sometimes they invent patterns that decades later turn out to help them understand things they never suspected. That's why they think it's discovered. But sometimes they invent patterns that have no correlation in the world either, but the pattern is just as valid. I think that maths is a mental construct that helps us with our limited minds to make sense of the physical world, and it works brilliantly. But it's a human invention, like language and music and chess. Incidentally, maths, music and chess are three activities a child prodigy can be as good as the best adult.
I agree with much of what you say including that that a lot of maths is invented, e.g. set and group theory, which I was particularly interested in. That contradicts my earlier contention that maths is discovered but I would also say that the universe exhibits certain mathematical properties that seem inherent (to me at least, although I wouldn't go as far as Tegmark and say that the universe is a mathematical object in and of itself) and it's in that sense that I consider maths to be discovered: right angled triangles had the properties of Pythagoras's theorem before he discovered/invented it; the ratio of a circle's radius to its circumference had the same value before it was calculated/discovered and called pi; on the other hand, I would say propositional calculus (the formal name for (mathematical) logic) is purely invented; calculus is more difficult. I think it lies somewhere between discovered and invented: the properties of curves it describes existed before Newton's & Leibniz's techniques to calculate them. One argument to support that it was discovered is the synchronicity between Newton and Leibniz although, equally, it could have been a consequence of previous mathematical inventions, an idea whose time had come (but isn't that a Platonist concept, an idea whose ‘time has come’?). I just find it interesting that that happens as often as it does. BTW, Hannah Fry initially thought as you do, that mathematics is an invention. She changed her mind in the course of making her programme but I guess it's more accurate to say that I think it has elements of both. The properties of objects that mathematics describes are inherent but the techniques are invented.
Anyway, thank you so much for taking the time to reply to me and for supplying the title of your book, The Illustrated Story of Pan. It's an intriguing title, I look forward to reading it 🙏🏼.
Pythagoras got "his" theorum from the Babylonians. Calculus is just an approximation. Either way, the reason why I think mathematics can never be the language of the universe, and neither physics too, is that both are blind to two great components of the universe: life and consciousness. The physical sciences are wonderful for explaining and manipulating inanimate matter, but know absolutely nothing about life and consciousness. Leibnitz himself said so, when he said if he could go into a mind as big as a windmill and observe how it worked when that giant was happy, he would still know nothing about happiness.
I struggle to not be Platonist but there are some aspects of mathematics that is difficult to not find transcendental. Take complex numbers for instance. It was centuries before i was found to apply to anything in the real world, or n infinities, but now they are vital to modern science and technology. I find the more I learn about the history of mathematics the more difficult it is to cling to non-Platonism. I still cling but only with my fingernails and teeth.
When music filled my world and defined my identity it wasn't at etheral, it was down and dirty: Zeppelin, Stevie Wonder, Stones, James Brown, Bob Marley.
LOL. I guess we all do.
Discovered