origami: art or mathematics?

[HankSimon]

>>>I'm saying that Mathematics is by definition not a science.

Please elaborate. What objective proof can you craft that the field of Mathematics is not self-consistent, reproducible, falsifiable, and follows a set of rules and principles, which can be derived?

:-0

- Hank Simon

[Pop pop]

depending how you use origami for math or science

[dinogami]

I guess I'm not clear on why this is even a discussion. Just because an artist doesn't use math or science consciously when creating art doesn't mean that there isn't math or science involved, or that cannot be applied to it after the fact. Similarly, just because an artist does apply math or science while creating art doesn't diminish the artistic aspect; it simply augments it in a unique way.

For the record, math is simply a means of expressing fundamental aspects of the universe that can be used and applied in scientific endeavors; they are not two separate things, though there are, um, slightly different perspectives...

[img]http://imgs.xkcd.com/comics/purity.png[/img]

[the modern einstein]

hahahaha.
Maybe adam shouldn't have started this. It's niggling me how he just opposes everyone else and everything they propose. This is just heading away from origami by the second and has turned more into a debate about the relationships between science and maths.
oh, and I've changed the title, so you can't argue over whether I should have used maths or science anymore.

[Pop pop]

its ok i just take as a debate

[LeafPiece]

I agree this is getting off topic, but...

I'm not saying they're unrelated, I'm saying that Mathematics is by definition not a science.

*cough* 1. ( functioning as singular ) a group of related sciences, including algebra, geometry, and calculus, concerned with the study of number, quantity, shape, and space and their interrelationships by using a specialized notation

[C14: mathematik (n), via Latin from Greek (adj), from mathēma a science, mathēmatikos (adj); related to manthanein to learn]

Taken directly from World English Dictionary. What is your definition of a definition???

I understand the point though. It just depends on the math. Do I consider 2 + 2 = 4 science? Not really. But the scientific method is nearly impossible without mathematics.

the movie Between the Fold says it a science of art and the art of science

I just saw that on PBS recently! I was enthralled, although I think that quote sounds better than it is. The more I think about it, the more I feel as though it doesn't offer any insight into the matter .

[ahudson]

So basically you consider mathematics (or specifically geometry) a science, even though it technically speaking isn't²; just like in Origami, there is no empirical evidence gathered for the purpose of hypothesis testing.

Robert Lang is a physicist; does that make all of his work scientific?
Eric Joisel was an artist; does that mean he could not possibly conduct a scientific experiment?
I am an Economist; does that mean that I make wild assumptions about Origami and that people confuse my work with that of businessmen or think that what I do makes absolutely no sense? I certainly hope not!

On the contrary, a lot of people use the scientific method when they're designing origami. You come up with a creasepattern based on previous theoretical knowledge, then follow an experimental method (folding the model) to determine the validity of the hypothesis; then analyze the results, and figure out why it worked (or didn't). A good designer will also conduct more formal experiments to figure out how to use new technical ideas.

And if the experiment was successful, we publish a record of it in the form of instructions, and our work gets peer-reviewed by other folders who replicate our experiments by folding the model from diagrams, or independently verify the results by constructing another experiment that uses the same theoretical ideas.

That's not to say that everyone is going about origami in a scientific way, but I think some of us are.

[malachi]

To take this conversation in a different direction, does the categorization of origami/paper folding change your practice of it? If so, how?

[the modern einstein]

It changes your view of what your origami should be, the final result of your folds and how you should achieve technical folding or design a model. treating it as a work of art means that there is less limits to what you can achieve, or what you can fold. treating it as a work of mathematical accuracy means that the model will go according to restrictions you place on it, and become a work of accurate reproduction, that in itself is a work of art.

[malachi]

Please speak for yourself, not for me. Thanks.

[Adam]

*cough* 1. ( functioning as singular ) a group of related sciences, including algebra, geometry, and calculus, concerned with the study of number, quantity, shape, and space and their interrelationships by using a specialized notation

[C14: mathematik (n), via Latin from Greek (adj), from mathēma a science, mathēmatikos (adj); related to manthanein to learn]

Dictionaries are not some form of absolute truth; if I'd want to, I could probably find a dictionary definition that does not state that Mathematics is a science. Furthermore, the word Economics comes from "Oikos" and "Nomos", meaning "House" and "Law" respectively; does that mean I study law at home..?

Mathematics is a system that was consciously created by mankind; do we then truly discover new things, as we do in the natural sciences?

-snip-

Ah, but we can apply this method to practically everything we do in daily life. I'm taking a break at the moment and I'm hypothesising that once I go home I'll grab a butter waffle and some "hati & ampela penyet" as my dinner [Hypothesis stage]. In a few hours I'll be able to observe whether I got these two meals [Data collection/Experiment]. Afterwards, I'll be able to analyse the results to see whether my hypothesis was correct.
Ergo, going home and grabbing dinner on the way is science.²


²Technically, this would fall under Economics; but then again, is Economics truly a science?

[dinogami]

Mathematics is a system that was consciously created by mankind; do we then truly discover new things, as we do in the natural sciences?

>>>SIGH<<< Mathematics is a language used to express (and predict) natural phenomena that exist independent of human existence or awareness. If there were no humans, the concepts expressed with mathematics would still exist -- in fact, they've existed for 13 or so billion years before there ever were people and did just fine without ever being expressed. That humans have the ability to comprehend them and find a means of expressing them in no way affects them (unless you're a solipsist).

Yes, we discover things with math all the time, just as we do in science. But in order to be discovered, the things discovered must already exist. We simply use language -- be it words, numbers, or other symbols -- to express those concepts. Discovery does not equal creation.

[Adam]

snip

>>>> SIGH <<<< If Mathematics is a language then by definition it is created by humans; just like any other language on this planet. Could you, by the way, give me an example of how -1 exists in nature? Maybe an anti-apple?

The difference between the natural sciences and mathematics is that we created the system we're exploring: We are the ones who defined concepts like addition/subtraction, integration, differentiation, etcetera, whereas in the natural sciences we observe phenomena that have somehow come into existence following laws and axioms that were not invented by mankind.

[dinogami]

If Mathematics is a language then by definition it is created by humans; just like any other language on this planet.

Correct. But just because humans invented the words "bird" and "run" does not mean that they invented birds and running -- those things exist without humans (or anyone else) there to observe them (again, unless you're a solipsist). We invented the symbols "2," "4," "+," and "=," but that says nothing about the fact that 2+2=4 (that two objects added to two objects produces a total of four objects). There are eight (or nine, if you like Pluto) planets in our Solar System, and there have been for 4.6 billion years. After 4.6 billion years, some humans invented the symbol "8" that can be applied to this concept, but that quantity of planets were there before there were humans; there simply wasn't anyone/anything capable of expressing it symbolically.

>Could you, by the way, give me an example of how -1 exists in nature? Maybe an anti-apple?

Not all numbers necessarily represent quanta! (Though for all I know there is a logical negative quantity.) Negative numbers are needed to express more complex relationships between other quanta (in, for example, the quadratic formula, which expresses (but does not invent!) the relationship between quanta. But just because humans need them to express those relationships does not mean that humans invented those relationships -- the relationships are part of the nature of the universe, just as the relationship of a circle's diameter and circumference exists independently of humans applying the symbol pi (or the symbols 3.1415925...) to that relationship.

The difference between the natural sciences and mathematics is that we created the system we're exploring: We are the ones who defined concepts like addition/subtraction, integration, differentiation, etcetera, whereas in the natural sciences we observe phenomena that have somehow come into existence following laws and axioms that were not invented by mankind.

Yes, we created mathematics. But we did not create the concepts that mathematics is used to explore.

I'm afraid I simply do not understand your position. The fundamental advances humans have made as a species have been made because of increased understanding of the nature of the universe and inventing (!) ways to exploit those in our favor. Math has been integral to that because we have learned to see deeper and more extensive relationships between naturally occurring phenomena -- again, we did not invent those phenomena; we simply learned about them using the language of mathematics that we did invent. You seem to be saying that humans can (should?) abandon mathematics altogether just because it is wholly artificial, and that somehow science can continue to function without mathematics. Science (which is a process, not an entity), I suppose, might be able to survive, just as it would survive if we abandoned any other form of language, but the lack of ability to communicate to others would grind us to a halt, if not start us on a backward slide.

So if math is entirely invented, then how is it that different cultures, using different series of symbols, independently arrived at similar conclusions about fundamental principles from each other? This alone should indicate that there are fundamental principles about the universe that exist independently of humans but that humans have learned to explore using the language(s) of mathematics.

[Adam]

It would seem that my point has not come across as I had intended, so sorry for making you type up that long post (even though we almost seem to share the same view). What I am trying to say is that Mathematics is an insanely useful tool and that modern life would be impossible without it, but it simply doesn't fall into the category of science. This does not mean that it's worth less than subjects that do fall in that category; it's simply different.

Would you consider a study of language to be science (-please don't involve the Latin origins of the word 'science' in this)? I would not, but that certainly doesn't make language any less useful. Cooking isn't a science either, due to for instance the lack of [perfectly] controlled experiments, but I can't imagine living in a world where nobody knows how to cook; I wouldn't be able to enjoy that lovely butter waffle (the one I mentioned earlier) and the 'seafood hor fun' I ate earlier today.

In short, Mathematics is extremely useful and probably necessary to be able to advance as a civilisation, but it is not a science in itself; it makes science possible.