origami: art or mathematics?

LeafPiece · Post by **LeafPiece** » February 1st, 2011, 12:48 am

Adam, I don't think my point has come across as intended, either. When I said "by definition mathematics is a science" I should probably have said it CAN be defined as a science. I posted the dictionary entry to show that it CAN and HAS been defined that way. That is what "by definition" means to me. Obviously dictionaries are not an absolute truth. As you said, I could find dictionaries that don't define it that way. On the other hand, I could find others that do. The point was to offer an authoritative view on the subject since it would have to, at the very least, be a common notion that math is a science. I do not agree or disagree with you, but it is interesting that you have made an equally confident claim that mathematics is not a science. Are we to believe that your opinion is absolute truth instead? I think it is clear by now that this is a philosophical question.

BTW, if it's easy to call mathematics a science, it's even easier to call cooking a science.

@malachi. It doesn't change a bit

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the modern einstein · February 1st, 2011, 3:02 am

maybe I should delete this topic.......

Adam · Post by **Adam** » February 1st, 2011, 3:50 am

LeafPiece wrote:snip

Heh, well my view is of course also not absolute truth, but it is nevertheless interesting to see that there is no common agreement on the exact meaning of 'science' and the value attached to the term, as can be observed in this discussion. I don't really want to involve Karl Popper, Durkheim or other fancy names into this, though, because then it will turn even more off-topic.

the modern einstein: Why would you want to delete this topic? Perhaps it is more appropriate to move it to the off-topic section, but I see no reason for deleting it.

LeafPiece · Post by **LeafPiece** » February 1st, 2011, 4:13 am

I agree with Adam, it would be a shame to delete this topic. We may have inadvertently proven that origami is strictly an art. I know for a fact that origami is an enjoyable activity, and if science and math are this much of a headache, then origami cannot be science and math. And now that we have come full circle, there is also no reason to move it to a different section

.

HankSimon · Post by **HankSimon** » February 1st, 2011, 6:18 pm

I agree for Not deleting. Just because a debate is confident, doesn't make it valid or scientifically correct

...

BTW - I do challenge locating a serious dictionary that does not define math as a science.

Although it is a leap of faith to jump from math to cooking, Gastronomy is the art and science of good eating, and Molecular gastronomy is the study of physical and chemical processes that occur while cooking. Improving the art of cooking through the science of chemistry.

No, this is not quite off-topic, because all good cooks know how to fold eggs!

- Hank Simon

Post by **origami_8** » February 1st, 2011, 10:40 pm

Users can not delete topics only moderators can. The most users can do is delete their own posts what I heavily advice against since this could make the moderators angry on the user, leading to unpredictable results.

the modern einstein · February 2nd, 2011, 1:02 am

I deleted the post at the start of a topic I had created, and it deleted the whole topic, so there may be a bit of a glitch here.

orislater · Post by **orislater** » February 2nd, 2011, 2:39 pm

wait. how do you delete posts?

HopefulFolds · Post by **HopefulFolds** » February 4th, 2011, 4:05 am

People don't understand the complexity of what origami can do until they see some crease patterns.

the modern einstein · February 5th, 2011, 2:12 am

Orislator, you just click edit on your posts, and there should be a button somewhere on the edit page that allows you to delete it, but as I cannot remember exactly where it is, you'll just have to go on that approximation. actually that statement was wrong. I just had a look at the edit page, and there does not seem to be anywhere to delete the post, but I swear I have seen delete links on the edit page for some of my posts.

kevin89 · Post by **kevin89** » February 15th, 2011, 6:52 am

I think origami is both an art and a science, because science can be art. In fact, some of the most beautiful things are very scientific and have lots of math behind them. Even in paintings, there is math behind where our eye goes and what repels and what attracts it.

PaperMaverick · Post by **PaperMaverick** » February 16th, 2011, 10:42 am

I hear a lot of talk about origami and mathematics but I'm not really sure there is a strong "connection" between the two. Certainly, there are angles and patterns which form groups or other mathematical structures but to say that origami is a form of mathematics or that it is rooted in mathematics...well, I don't really see it. To me it seems like people trying to legitimize something which really doesn't need a status boost...the thought being if origami has a mathematical basis it is worthy of serious study or public consideration.

I could see someone taking the fold pattern for a dog and using engineering math to make the legs stronger or maybe using math to figure out how to fold a bridge from a single sheet of paper and have the bridge have certain load bearing properties.

To me, origami like painting, music, etc, is an art and a craft and mathematics happens to come up every once in a while but I certainly can't see any groundbreaking theorems being originated from the fold pattern of a grasshopper or tarantula.

Maybe I'm wrong about all this...tell me otherwise.

dinogami · Post by **dinogami** » February 16th, 2011, 2:32 pm

PaperMaverick wrote:I hear a lot of talk about origami and mathematics but I'm not really sure there is a strong "connection" between the two. Certainly, there are angles and patterns which form groups or other mathematical structures but to say that origami is a form of mathematics or that it is rooted in mathematics...well, I don't really see it.

For a long time, no one saw the connection, and I strongly suspect that most people don't see when first getting into origami. The mathematical connections (I'd hesitate to call them "roots" or "a basis") to origami seem to require a pretty advanced understanding of both origami and math. I'm far from being a mathematician, so I don't pretend to comprehend the maths that go into (or fall out of) origami, but I've been an interested spectator to the development of "mathigami" over the last few decades, and I've had a gander at some of the technical papers that have come out of the subject (for a good, short, though rather complex overview, see here). Origami has helped mathematicians solve some interesting problems, and it has produced some interesting math-related engineering feats (like folding solar panels on satellites). Understanding the underlying geometries of the folds and their relations to one another are incredibly useful in designing models that have specific features in specific places -- certainly, people can and do develop intuitive senses about the same thing, and can invent great models, but that doesn't mean that the geometries involved don't exist, just that they're unrealized, as they were in origami as a whole until, I think, some time in the 1980s.

In short, don't mistake a lack of recognition of math in origami for the absence of math in origami. And I'm also not saying that one must develop any sense of the maths in origami in order to enjoy it -- as I mentioned above, most people get into and start enjoying origami before having any such understanding, and until the 1980s, basically EVERYbody in origami had a great (and artistic) time with it without any such realizations. It's simply that the discovery of mathematical connections in origami added a new level of both application and appreciation for it. It's just not a level that everyone must grasp or appreciate in order to have fun with it!

bethnor · Post by **bethnor** » February 16th, 2011, 4:10 pm

PaperMaverick wrote:I hear a lot of talk about origami and mathematics but I'm not really sure there is a strong "connection" between the two. Certainly, there are angles and patterns which form groups or other mathematical structures but to say that origami is a form of mathematics or that it is rooted in mathematics...well, I don't really see it.

it's interesting that you're folding from origami design secrets but don't see the connection.

part of the reason why lang folds are so difficult is that he uses math to generate the reference points to make the flaps of proper length with the right number of points. out of the many complex turtles out there, his is the only one that i am aware of that asks you to divide the paper into 39ths. how else could he have come up with such an odd (and annoying) number other than using math to design a shell with x and y number of plates.

there is also a connection between math and music, as i'm sure some here are aware. the works of the famous composers are highly mathematical, the intervals between the chords, eighths, fifths, sixths, etc., etc. and when the math is "off" (the notes are not the appropriate distance from one another) the result is discordant. the reason why modern classical music is so difficult to listen to is that it's almost purely mathematical (i.e., there is no melody in the classic sense of the term, you have to "hear" the math, the distance between the chords, intervals, etc., etc.)

kevin89 · Post by **kevin89** » February 17th, 2011, 3:01 am

PaperMaverick wrote:I hear a lot of talk about origami and mathematics but I'm not really sure there is a strong "connection" between the two. Certainly, there are angles and patterns which form groups or other mathematical structures but to say that origami is a form of mathematics or that it is rooted in mathematics...well, I don't really see it. To me it seems like people trying to legitimize something which really doesn't need a status boost...the thought being if origami has a mathematical basis it is worthy of serious study or public consideration.

To me, origami like painting, music, etc, is an art and a craft and mathematics happens to come up every once in a while but I certainly can't see any groundbreaking theorems being originated from the fold pattern of a grasshopper or tarantula.

Maybe I'm wrong about all this...tell me otherwise.

I think the problem is that you've defined "mathematical" by being able to produce groundbreaking theorems, when this isn't the case. What mathematics really is just being very exact and precise, which origami is all about. Also, there are real life applications of origami in the real world: Robert Lang's Treemaker helped develop air bags that unfold easier and faster, along with solar panels that fit into a tiny satellite and unfold easily once in space. Things have been made that fit into a blood vessel and then unfold and keep it open to prevent clogged arteries/veins and to keep the blood moving. So there are applications for it, you just have to look for it, and considering the math behind origami is barely 40 years old, I'm sure there is plenty more to come.

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