Observing natural mathematics from different perspectives

[Write4U]

Just to follow up on my habit of observing natural phenomena from different perspectives.
A long time ago I saw this seemingly simplistic video, that takes the viewer on just a little tour. But after viewing this a few times, some remarkable everyday mathematical truths appeared that I had never even considered.

Give it a try, it's not long.

 

[James R]

I watched it last time you posted it.

Are you advertising, or is there something specific you'd like to discuss?

For instance, what are some of the remarkable everyday mathematical truths you discovered as a result of watching this video?

Why did you post this thread in the Pseudoscience subforum?

 

[C C]

Give it a try, it's not long. Math is the hidden secret to understanding the world

• VIDEO EXCERPTS: You can do it in so many different ways. We can analyze it. We can make up languages for it. And representations are all over mathematics. This is Leibniz's notation from 1675. He invented a language for patterns in nature...
  
  [...] And if I take a bicycle pump and just pump it up, you can see that this is also a little bit like the octahedron. Do you see what I'm doing here? I am changing the perspective every time...
  
  [...] I'm playing around with metaphors. I'm playing around with perspectives and analogies. I'm telling one story in different ways. I'm telling stories. I'm making a narrative; I'm making several narratives. And I think all of these things make understanding possible. I think this actually is the essence of understanding something
  
  [...] You're changing your perspective. You're using your imagination, and you're viewing yourself from the outside. That requires imagination. Mathematics and computer science are the most imaginative art forms ever. And this thing about changing perspectives, should sound a little bit familiar to you, because we do it every day.
  
  And then it's called empathy. When I view the world from your perspective, I have empathy with you. If I really, truly understand what the world looks like from your perspective, I am empathetic. That requires imagination. And that is how we obtain understanding.
  
  And this is all over mathematics and this is all over computer science, and there's a really deep connection between empathy and these sciences...

Yes, patterns (relational structure) and magnitude are abstracted from natural or experienced phenomenal events. Symbolic systems are invented to represent/grapple with those features.

Use of "natural mathematics"[3, 4] in the thread title suggests this maybe being another opener to the classic controversy of is "mathematics an artificial construct", an innate "cognitive faculty" that imposes its pre-settings on perceptual representations/understanding, or a fundamental part of general being.

Ironically, though, if decolonization of mathematics is possible[1] -- or if there is legitimacy to ethnomathematics[2], then the mathematical language of "dead white men" is not universal. And given the snobbish airs of academic hegemony back in the old days, it might not wholly be a leftist conspiracy theory that some mild investment was made in formulating such to be opaque -- i.e., designed to obstruct and oppress the lower classes, marginalized population groups, and non-Western societies.

In that context, Antonsen's "different perspectives" shift from observational POVs to different cultural perspectives involved in interpreting the surroundings of nature. If the Eurocentric representative rendering of the latter is not universal, then that in turn undermines the proposal of the cosmos or whatever being existentially "mathematical"[4] (the Western scheme) in arguably another way than just the usual objections[3].

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[1] Yes, mathematics can be decolonised. Here’s how to begin
https://theconversation.com/yes-mathematics-can-be-decolonised-heres-how-to-begin-65963

Much, though certainly not all, of mathematics was created by dead white men. But maths should and does belong to everybody. Everybody deserves access to its beauty and its power – and everybody should be able to push back when the discipline is used to destroy and oppress.

Pedagogy of the Oppressed
https://en.wikipedia.org/wiki/Pedagogy_of_the_Oppressed

Freire includes a detailed Marxist class analysis in his exploration of the relationship between the colonizer and the colonized.

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[2] Ethnomathematics
https://en.wikipedia.org/wiki/Ethnomathematics

The research of the mathematics of these cultures indicates two, slightly contradictory viewpoints. The first supports the objectivity of mathematics and that it is something discovered not constructed. The studies reveal that all cultures have basic counting, sorting and deciphering methods, and that these have arisen independently in different places around the world. This can be used to argue that these mathematical concepts are being discovered rather than created. However, others emphasize that the usefulness of mathematics is what tends to conceal its cultural constructs. Naturally, it is not surprising that extremely practical concepts such as numbers and counting have arisen in all cultures. The universality of these concepts, however, seems harder to sustain as more and more research reveals practices which are typically mathematical, such as counting, ordering, sorting, measuring and weighing, done in radically different ways...

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[3] Who Says Nature is Mathematical?

Who Says Nature is Mathematical?

This piece wouldn’t have been called ‘Who Says Nature is Mathematical?’ if it weren’t for the many other similar titles which I’d seen…

www.cantorsparadise.com

Strictly speaking, Nature isn’t any “mathematical system of axioms”, and it doesn’t even “include” such a thing. Mathematics is applied to Nature or it is used to describe Nature. Sure, ontic structural realists and other structural realists (in the philosophy of physics) would say that this distinction (i.e., between mathematics and physics) hardly makes sense when it comes to physics generally and it doesn’t make any sense at all when it comes to quantum physics. However, surely there’s still a distinction to be made here.

Similarly, Nature is neither consistent/complete nor inconsistent/incomplete. It’s what’s applied to — or used to describe — Nature that’s (in)complete/(in)consistent. Again, certain physicists and philosophers of science may think that this distinction is hopelessly naive. Yet surely it’s still a distinction worth making.

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[4] Natural Mathematics

Natural Mathematics - exploring nature's mathematical essence

Seashells, snowflakes, plants, ocean waves. Mathematics displays itself in all of these things. This website explores ways in which we can see mathematics all around us.

www.naturalmathematics.com

There are many examples of mathematics in nature: The Fibonacci sequence is a numeric pattern that presents itself in countless species of living organisms. Another is the spiral, which appears in both tiny seashells and entire galaxies. Indeed, the very DNA of our own bodies is organized in a double-helix form, a splendid example of mathematics in nature.

Regrettably, some of the most exciting and thought-provoking areas of mathematics are not conveyed to students through their general education. There is much more to mathematics than tedious equations and dull arithmetic problems. Anyone who can appreciate the magnificence of a crescent moon, the shape of a desert canyon carved by ancient rivers, or waves of tall grass swaying in the wind has already grasped the beauty of mathematics in action.


Natural Mathematics

Natural Mathematics - PhilSci-Archive

philsci-archive.pitt.edu

ABSTRACT

Current approaches to mathematical cognition divide into two major camps. Cognitive studies try to render mathematical intuition—the faculty that gives us immediate and authoritative knowledge of mathematics—respectable on scientific grounds. Cultural studies, on the other hand, regard mathematics as a form of cultural achievement, like literature or architecture.

Both positions have their own shortcomings. While cognitive approaches are limited in scope and fail to account for complex mathematical developments, cultural approaches are short of detailed answers as to what enables us to participate in a common mathematical practice. This situation evinces a need to balance a cognitive perspective on mathematical culture against a cultural perspective on mathematical cognition.

According to current behavioral and neuropsychological evidence, the complex, uniquely human, culture-specific mathematical skills exhibited by human adults rest on a set of psychological and neural mechanisms that (a) are shared by other animals, and (b) emerge early in human development, continue to function throughout the lifespan, and thus are common to infants, children and adults. It has been proposed that these common and evolutionary ancient mechanisms account for humans’ basic “number sense” and form the building blocks for the development of more sophisticated numerical skills.

Indeed, infants leave animals far behind in their numerical sophistication. What boosts this developmental difference? How do human beings acquire mathematical concepts such as the concept of natural number?

First, I specify the representations that are the building blocks for the target concepts. Second, I describe how the target concepts differ from these basic representations. And finally, I characterize the learning mechanisms that enable the construction of the target concepts out of those prior representations.

I argue that the power of the resulting conceptual system derives from the combination and integration of previously distinct representational systems, capitalizing on the human capacity for creating and using external symbols: human beings can only develop their distinct conceptual abilities due to their original embeddedness in both the physical world and, most importantly, in a rich milieu of cultural resources. Thus, an important developmental source of number representations, in addition to the preverbal systems mentioned above, is the representation of numbers within natural language.
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[Write4U]

If the Eurocentric representative rendering of the latter is not universal, then that in turn undermines the proposal of the cosmos or whatever being existentially "mathematical"[4] (the Western scheme) in arguably another way than just the usual objections[3].

Yes, but regardless of the relative perspective, the mathematics don't change, even if the symbolic representations are local, right?

 

[C C]

Yes, but regardless of the relative perspective, the mathematics don't change, even if the symbolic representations are local, right?

Well, that might be the racist Western view, anyway. The politics/morality of the future may complicated with respect to reality, if not very much already.
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[Write4U]

Well, that might be the racist Western view, anyway. The politics/morality of the future may complicated with respect to reality, if not very much already.

But that is exactly what I am arguing against. In science; "A rose is a rose by any other name".

 

[C C]

But that is exactly what I am arguing against. In science; "A rose is a rose by any other name".

Yeah, but (granting we live long enough) we WEIRD folk really will need a manual titled like the one below, to help guide us and explain why the world of tomorrow is upside down...

Sandy Ashbone (from Decolonization of Knowledge For Dummies & Seniors): "Yo mama's science is racist."
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