Where Mathematics Come From: How the Embodied Mind Brings Mathematics into Being
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Linguistic Overreach?
Get ready; here’s the headline news: MATHEMATICS IS A HUMAN CONSTRUCTION JUST LIKE LANGUAGE. In fact mathematics is a language and employs the same parts of the human brain and nervous system as any other language. It’s arguably the most precise language we have. But there is no truth to the rumour, first formulated by Plato, that the central elements of mathematics - numbers - have any existence beyond our use of them.
That’s it, ladies and gentlemen. We can rest easy in our beds. Mathematics, it appears, has the same metaphorical structure as any other language. If some alien civilisation has mathematical knowledge, it will resemble ours only to the extent that their bodies and physical environment resemble our own. Sci-fi writers as well as philosophers have got it wrong. Mathematics is in our bodies.
Well, that’s not right either. Mathematics is not in our heads. Like all language, it exists among us when we communicate with each other. We condition each other to recognise and respond to mathematical language. So it only seems to be external to us entirely. But technically speaking, mathematics is more like the Christian God than the pagan god of Plato - it is in us, among us and beyond us, all at the same time.
To some extent this conclusion is passé. Linguists have known about the realities of language for some time. The proposition that mathematics is just a kind of language is hardly revolutionary. So the authors feel compelled to venture out on some thin ice: “To make our discussion of classical mathematics tractable while still showing its depth and richness, we have limited ourselves to one profound and central question: What does Euler's classic equation*... mean?”
This is a very silly question it seems to me. The equation means exactly what it says, no more, no less. Each of its terms is ultimately defined circularly by the other terms, just as in any language. Like the meaning of a Beethoven Symphony or a novel by Jane Austen, its meaning is entirely contained in its expression, or rather in the various interpretations of its expression, which are simply more expressions. To suggest otherwise would be to re-introduce Plato’s religious vision of a realm of eternal forms. Mathematics may be generated by human physiology and its needs but this does not imply that mathematics - including ideas like infinity, imaginary numbers, negative numbers, irrational numbers, etc. - have any definite meaning perceptible to our bodies.
The elements of Euler’s equation may indeed be, as the authors claim, metaphors. But as such the interpretive problem merely has been moved from mathematics to natural language. This is not an advance. It gets us no closer to its meaning other than how it is used by mathematicians. So their discussion of the equation seems seriously off the mark. On the other hand, perhaps it’s just my interpretation that is deficient!
* Euler’s Equation is certainly a profound and profoundly disturbing statement. It summarises the relationship among some of the most important, and on the face of it incommensurable, kinds of mathematical entities. See here for further discussion: https://www.goodreads.com/review/show...
Get ready; here’s the headline news: MATHEMATICS IS A HUMAN CONSTRUCTION JUST LIKE LANGUAGE. In fact mathematics is a language and employs the same parts of the human brain and nervous system as any other language. It’s arguably the most precise language we have. But there is no truth to the rumour, first formulated by Plato, that the central elements of mathematics - numbers - have any existence beyond our use of them.
That’s it, ladies and gentlemen. We can rest easy in our beds. Mathematics, it appears, has the same metaphorical structure as any other language. If some alien civilisation has mathematical knowledge, it will resemble ours only to the extent that their bodies and physical environment resemble our own. Sci-fi writers as well as philosophers have got it wrong. Mathematics is in our bodies.
Well, that’s not right either. Mathematics is not in our heads. Like all language, it exists among us when we communicate with each other. We condition each other to recognise and respond to mathematical language. So it only seems to be external to us entirely. But technically speaking, mathematics is more like the Christian God than the pagan god of Plato - it is in us, among us and beyond us, all at the same time.
To some extent this conclusion is passé. Linguists have known about the realities of language for some time. The proposition that mathematics is just a kind of language is hardly revolutionary. So the authors feel compelled to venture out on some thin ice: “To make our discussion of classical mathematics tractable while still showing its depth and richness, we have limited ourselves to one profound and central question: What does Euler's classic equation*... mean?”
This is a very silly question it seems to me. The equation means exactly what it says, no more, no less. Each of its terms is ultimately defined circularly by the other terms, just as in any language. Like the meaning of a Beethoven Symphony or a novel by Jane Austen, its meaning is entirely contained in its expression, or rather in the various interpretations of its expression, which are simply more expressions. To suggest otherwise would be to re-introduce Plato’s religious vision of a realm of eternal forms. Mathematics may be generated by human physiology and its needs but this does not imply that mathematics - including ideas like infinity, imaginary numbers, negative numbers, irrational numbers, etc. - have any definite meaning perceptible to our bodies.
The elements of Euler’s equation may indeed be, as the authors claim, metaphors. But as such the interpretive problem merely has been moved from mathematics to natural language. This is not an advance. It gets us no closer to its meaning other than how it is used by mathematicians. So their discussion of the equation seems seriously off the mark. On the other hand, perhaps it’s just my interpretation that is deficient!
* Euler’s Equation is certainly a profound and profoundly disturbing statement. It summarises the relationship among some of the most important, and on the face of it incommensurable, kinds of mathematical entities. See here for further discussion: https://www.goodreads.com/review/show...
posted by The Mind of BlackOxford @ July 27, 2020
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