Nature vs. Maths

[Beren3000]

This is a thread for all of you out there; whether you love maths or hate them.
I've always wondered about this topic and I'll divide it into two questions:

1- Is mathematics an invention or a discovery? I mean does it actually exist in nature or is it man's own work?

2- Can perfect mathematics exist in nature? (i.e. does nature have a perfect circle or a perfect straight line, etc...)?

I'm going to post my opinions later after I hear some of you Mooters' opinions.

Speculate away!

[Haradrim]

First off I think Math is in nature but it is not like the way we describe it.
TO me there has to be cuz there are definate constants ie- the golden mean, pi, e, and so on. and I think in nature there can exist a perfect circle or a perfect something it would just be really hard to find. Probably on some distant palnet whos inhabitants have creatyed a perfect-object-shaping machine.

[Jonathan]

Man uses mathematics to describe complicated things in the world we live in. We can make certain things in nature easier for us to grasp if we use maths to simplify what we see.

But perfect mathematics absolutely exists in nature and Man has just invented tools to interpret it. Beren, you have read the Da Vinci code, so you surely know about the Divine Proportion. I guess that is at least some evidence that there is mathematics in nature, though it isn't necessarely perfect mathematics.
I don't know where in nature you can find perfect circles or straight lines, but I'm sure they exist. I'll have to come back to that. I remember reading a scientific article about how nature is the world's best mathematician and I'll see if I can find the magazine I read it in... I believe it had some examples of natural perfect circles etc.

[Beren3000]

Originally Posted by Haradrim

Probably on some distant palnet whos inhabitants have creatyed a perfect-object-shaping machine.

Well the fact that they're produced with MACHINES wouldn't exactly make them NATURAL, would it?

Originally Posted by Jonathan

I don't know where in nature you can find perfect circles or straight lines, but I'm sure they exist.

I wouldn't be so sure; I read some information about The Vitruvian man, Da Vinci's most famous sketch. It talks about how various parts of the body could be divided in the Divine Proportion. But can you actually find a man whose body parts can be divided EXACTLY in the Divine Proportion, to an infinite degree of accuracy? I mean the very fact that the Divine Proportion 1.618..... and pi is 3.141.... the fact that they're not Rational numbers, doesn't that mean that our current system of measurment is not compatible with Nature, that we can't conviently record (accurately) natural events and structures?

P.S. I'd love to see that mag. article if you can supply it

[Haradrim]

well what did you mean by natural. CUz technically since the machine was made of metal and metal came from the earth then isn't the machine natural and since you can probably trace the parts used to make the perfect thingimibobby back to something natural then isnt the whole machine natural and everything it creates natural. Im just being reall stupid, dont pay attention to me.

[Beren3000]

I meant natural as in "present in nature" not made by man. Something that God created and placed in the Universe as is. So a tree would be natural, but a house MADE from that tree's wood wouldn't be natural. Get my point?

[Haradrim]

I know I was just being stupid. So actually now that I think about it could you ever get a pefect object. Now that I think about no for the reasons you have stated. Thanks

[Beren3000]

Ok, do I get it you're on my side now? That no maths existing in nature can be truly perfect. Or, rather more correct, that maths. is not so perfect as to truly model nature?

[Elanor the Fair]

What about tesselations in nature - for example in bee hives and basalt pavements. What about bubbles - these are perfect spheres. What about snowflakes, ice crystals and crystals in rocks such as quartz, amethyst etc. These can have perfectly straight lines and flat planes. What about the perfect cone achieved when the ant lion makes its trap. Spider webs?? Shall I continue???

[Haradrim]

I meant to say that I think Mathematics does exist but that there re no perfect shapes or correlataions but things that are almos tperfect. Which lends its hand to the idea of MAthematics

[Beren3000]

Originally Posted by Elanor the Fair

What about tesselations in nature - for example in bee hives and basalt pavements. What about bubbles - these are perfect spheres. What about snowflakes, ice crystals and crystals in rocks such as quartz, amethyst etc. These can have perfectly straight lines and flat planes. What about the perfect cone achieved when the ant lion makes its trap. Spider webs?? Shall I continue???

How do we know that these shapes are perfect? A bubble isn't that obviously a perfect sphere. I'm not talking about imperfections that can be detected by the human eye. I'm saying that if it came down to taking measures, you won't find that, say a bubble, is a complete sphere even if its almost a sphere, even if it's 99.999999999999999999999999% a perfect sphere; it's still not a 100% perfect sphere. Same goes for the snowflake and the bee-hive.

[Haradrim]

well technically in AMth 9.99999999999999999999999999999999999999999 does mean 10 according to my AMth teacher but I know what you mean.

[Fat middle]

I think that maths are a creation of man, but with a basis in the real world. Sort of a representation of the real world, like arts are.

Perhaps you cannot find in nature perfect euclidean concepts, but sure you can find real maths in the world, the maths of the theory of the big numbers (statistics).

[Haradrim]

yeah Fat Middle you just summed up what Ive been trying to say. GOod job. I agree with him.

[Beren3000]

Originally Posted by Fat Middle

I think that maths are a creation of man, but with a basis in the real world. Sort of a representation of the real world, like arts are.

Yeah, that's kind of my point of view, too. But consider this, do you actually believe you can find perfect mathemtical precision in nature?
Can, say, a certain creature's behaviour be modelled mathematically? I personally don't believe so. I think that however math tries to model nature, no perfect model can ever be achieved; there would always be this element of spontaneity, of randomness in nature. Do you know what I mean?

[Insidious Rex]

Originally Posted by Beren3000

Yeah, that's kind of my point of view, too. But consider this, do you actually believe you can find perfect mathemtical precision in nature?
Can, say, a certain creature's behaviour be modelled mathematically? I personally don't believe so. I think that however math tries to model nature, no perfect model can ever be achieved; there would always be this element of spontaneity, of randomness in nature. Do you know what I mean?

Its called chaos. And it IS math. nature HAS TO follow mathematical laws no matter how complicted. nature resides within this universe therefore it is subject to the same laws as anything else inside this universe. every known phenomenon can ultimately be expressed in numbers.

[Jonathan]

Originally Posted by Haradrim

I meant to say that I think Mathematics does exist but that there re no perfect shapes or correlataions but things that are almos tperfect.

There are perfect shapes. Crystals for example. Of course the bigger a crystal is, the more flaws it will have. But if you look at very small crystal, made up by just a few atoms, you might come across a perfect cube, pentagon etc. depending on what kind of atoms you have.

But considering how gravity and acceleration can distort the space-time continuum, I guess perfect shapes are impossible from a physicist's point of view.

Originally Posted by Insidious Rex

Its called chaos. And it IS math. nature HAS TO follow mathematical laws no matter how complicted. nature resides within this universe therefore it is subject to the same laws as anything else inside this universe. every known phenomenon can ultimately be expressed in numbers.

Yup, chaos is maths. However it's not a fact that nature has to follow mathematical laws, that's just how scientists want it to be. Of course it is very, very likely that every aspect of nature follows certain laws, but still it's impossible to prove definitely. I believe nature is ruled by mathematics though.

[Haradrim]

You are right of course Jonathon.
We can never prove that everything follows certain principles as it is highly likely we will never see anything.

[Janny]

While you may never find the perfect circle in nature, you do find mathematical perfections, such as fibonacci numbers in plants and prime number breeding spans. (ie, two species developing in such a way that they reduce competition by only spawning once ever x many prime number years, eg. two incsects coming out every 13 and 17 years.)

[Haradrim]

I know what the Fibanacci sequence is but how does it realate to plants?