Nature vs. Maths

[BeardofPants]

Because many plants exhibit the sequence. The fern is the perfect example.



More stuff here.

[Haradrim]

But BoP are the ferns perfect down to the very last decimal point. I dont think so. THe odds a re phenomenal.

[Jonathan]

To quote the website BoP posted:

Starting from any leaf on a plant, a spiral is traced in an anti- clockwise direction from leaf to leaf. Upon reaching a leaf directly above the first, the number of leaves and turns around the stem within the spiral are constant, irrespective of the starting point.

I believe most ferns exhibits the Fibonacci sequence perfectly. The question if they are "perfect down to the very last decimal point" is irrelevant, since there are just natural numbers in the sequence. One leaf, two leaves etc.

Interesting site, BoP.

[Beren3000]

Originally Posted by Jonathan

The question if they are "perfect down to the very last decimal point" is irrelevant,

With all due respect, I guess that's the very question we're discussing here. We want to see if Mathematical perfection can exist. If there's an error of a billionth of a billionth of a millimetere, that still doesn't count as perfection.

Originally Posted by Insidious Rex

Its called chaos. And it IS math.

I don't know much about the theory of chaos, but I don't think that it can't be applied in any case where there is an apparent randomness. Consider human behaviour, for instance. How can THAT be modelled with numbers and predicted mathematically. Another example: get two rabbits together in a cage so that they copulate. Can you predict each time the female gives birth how many rabbits she's gonna give birth to?

Originally Posted by Jonathan

I believe nature is ruled by mathematics though.

According to Fat Middle's (and my) point of view, the opposite is true. If maths are a set of laws to model and describe nature, then nature rules maths.

Originally Posted by Janny

you do find mathematical perfections, such as fibonacci numbers in plants

True, you do find the Fibonacci numbers in plants. But can you predict, given a certain plant, which number of the Fibonacci sequence its leaves or flower petals are gonna have? If you can't, then perfect order is still not established.
Another example, consider an egg hatching. If nature were mathematically perfect, all the eggs that have ever hatched and ever would hatch should have the same shape after hatching (i.e. the same parts broken, the same ridges, etc...) which, of course, is not the case.

[BeardofPants]

Yeeess, certainly is an interesting site.

*BoP makes a note to read links more thoroughly before posting.

Still, had the pertinent information that I needed at the time.

Better linky-pooh here.

[Jonathan]

Originally Posted by Beren3000

With all due respect, I guess that's the very question we're discussing here. We want to see if Mathematical perfection can exist. If there's an error of a billionth of a billionth of a millimetere, that still doesn't count as perfection.

When talking about the number of leaves that a fern has, the leaves size down to the last attometre is irrelevant.

Originally Posted by Beren3000

I don't know much about the theory of chaos, but I don't think that it can't be applied in any case where there is an apparent randomness. Consider human behaviour, for instance. How can THAT be modelled with numbers and predicted mathematically. Another example: get two rabbits together in a cage so that they copulate. Can you predict each time the female gives birth how many rabbits she's gonna give birth to?

Eh, isn't that what chaos is about? Chaos makes predictions impossible. And no, you can't apply chaos theory to every case of apparent randomness. Mainly because chaos and randomness are two different things.

Originally Posted by Beren3000

Another example, consider an egg hatching. If nature were mathematically perfect, all the eggs that have ever hatched and ever would hatch should have the same shape after hatching (i.e. the same parts broken, the same ridges, etc...) which, of course, is not the case.

I don't see how unidentical eggs is proof of nature's mathematical imperfection.

Thanks for the linky-poohs, BoP. I feel oddly enlightened

[Haradrim]

Beren- Chaos theroy is a form of mathematics saying that you cant predict things. It instead shows all different possibilities and while sometimes we think something may be 50 50 chaos theroy shows us that actually a coin flip is not 50/50 it is actually I think 50.05/50 for heads because its slightly weightier. Thats chaos theroy. nothing is perfect and therefore nothing can truly be predicted because there are an infinite amount of variables.

and Jonathon we are discussing down to the last atometre so in fact it is not irrevelant.

[Jonathan]

Originally Posted by Haradrim

and Jonathon we are discussing down to the last atometre so in fact it is not irrevelant.

Not if you're looking for perfect circles or lines, but the Fibonacci sequence has little to do with such things.

[Haradrim]

I think it would have great importance to a line (cause you need to make sure that it never vears off to the left or rigth and especially for a circle because you need to make sure every degree, angle, curve, and all that whatnot are the same.

[Fat middle]

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.

Chaos is a way of modelling our thought (mathematical thought) to match nature.

Today, not "every known phenomenon can ultimately be expressed in numbers", but as maths develop they may be able to express better the natural phenomena.

Nature follows its laws, we try and model our thought to understand them. But our thought is only a representation of the world, not the world itself. World is first.

[Haradrim]

Thanks Fat Middle. Every time you post here you sum up what I have been trying to say very nicely. Thanks

[Fat middle]

You're welcome Thanks for the compliments.

[Beren3000]

Originally Posted by Jonathan

When talking about the number of leaves that a fern has, the leaves size down to the last attometre is irrelevant.

I see your point, now!

Originally Posted by Jonathan

I don't see how unidentical eggs is proof of nature's mathematical imperfection.

Well, if nature were mathematically perfect, then we should be able to predict the shape of the broken egg shell down to each ridge. Maybe we shouldn't have identicall egg-shells (my mistake in phrasing), it's just that there's now way (at least that I know of) to predict its shape so that each egg hatching is a unique event. This was meant to emphasise my point that there would always be that element of spontaneity in nature that can never be represented by maths.

Originally Posted by Haradrim

Beren- Chaos theroy is a form of mathematics saying that you cant predict things. It instead shows all different possibilities and while sometimes we think something may be 50 50 chaos theroy shows us that actually a coin flip is not 50/50 it is actually I think 50.05/50 for heads because its slightly weightier. Thats chaos theroy. nothing is perfect and therefore nothing can truly be predicted because there are an infinite amount of variables.

I didn't know that, thanks for an enlightening post!

[Insidious Rex]

Originally Posted by Beren3000

I don't know much about the theory of chaos, but I don't think that it can't be applied in any case where there is an apparent randomness. Consider human behaviour, for instance. How can THAT be modelled with numbers and predicted mathematically. Another example: get two rabbits together in a cage so that they copulate. Can you predict each time the female gives birth how many rabbits she's gonna give birth to?

chaos theory is a form of mathematics used to make some predictions about extremely complex events. Its used every day in predicting things like traffic patterns and weather and yes it can even predict human behavior quite well. if you are asking can math anticipate EVERY conceivable action in the universe well potentially it could. If we had all the variables. And super computers powerful enough to do that kind of number crunching. and who knows maybe somewhere the complete life and every event down to the quantum level of our universe has been predicted and logged somewhere. maybe we are just living out these mathematical predictions as we sit here. im supposed to be writing this and you are supposed to be thinking I don’t think hes right… *twilight zone music*

Another example, consider an egg hatching. If nature were mathematically perfect, all the eggs that have ever hatched and ever would hatch should have the same shape after hatching (i.e. the same parts broken, the same ridges, etc...) which, of course, is not the case.

lets start by figuring out what you mean by “mathematically perfect.” Because im not sure if that really has any meaning. Nature is what nature is. And it follows laws of mathematics but no it doesn’t always end in nice round numbers or have (or need) perfect shapes. And keep in mind there a billion billion billion variables that go into just how one egg will hatch. Its an almost infinitely complex math problem but a math problem none the less. The way an egg shell will break WILL follow a certain pattern but of course not be the same each and every time. But you WILL see a bell curve if you plot many many different egg hatchings. And that alone should show us that nature (well at least egg hatching) has a pretty clear element of predictability. If it was as you say simply random then it would have to follow a PERFECTLY random pattern. And any miniscule variation in the randomness would show us that there is in fact some specific predictable pattern going on there.

[Beren3000]

Originally Posted by Insidious Rex

And it follows laws of mathematics but no it doesn’t always end in nice round numbers or have (or need) perfect shapes.

My point exactly! Since measurement and interpretation of nature doesn't produce round numbers, then shouldn't nature be considered "imperfect" from the POV of maths? Or (as I said earlier), since nature is the origin and math the copy, shouldn't our current maths system be considered imperfect from the POV of nature?

Originally Posted by Insidious Rex

But you WILL see a bell curve if you plot many many different egg hatchings.

I'm not following, sorry but statistics isn't exactly my strongest point in maths

[Insidious Rex]

Originally Posted by Beren3000

My point exactly! Since measurement and interpretation of nature doesn't produce round numbers, then shouldn't nature be considered "imperfect" from the POV of maths? Or (as I said earlier), since nature is the origin and math the copy, shouldn't our current maths system be considered imperfect from the POV of nature?

well why do you consider non round numbers to be imperfect exactly? 5 has no more intrinsic value in nature then 5.893872983787837283798... But you DO have constants in nature. speed of light, planks constant, an electronvolt, avogadros number, etc. Because of the nature of our universe these constants are always the same.

I'm not following, sorry but statistics isn't exactly my strongest point in maths

well lets say you were a scientist that studied birds and you spent 10 years recording how the egg of one particular species hatched. you would plot maybe on the location of the break in the egg shell or something. well you would find that as more and more recordings were made that you had a distribution that looked something like a hill. tall in the middle and short on either end. the ends represent the extremes, that is the scenarios that dont often happen but SOMETIMES do. the middle hill represents the usual outcome. how the egg USUALLY is broken. therefore you conclude there is a certiain degree of predictability in how this specific species breaks out of its shell. you could even measure it by measuring the height of your bell curve if you will. you would, on the other hand, NEVER see a perfectly straight distribution because egg hatching is not in fact a perfectly random activity in nature. even the slightest micro blip one way or the other would show that there is some kind of predictiable pattern involved.

[Rían]

Originally Posted by Beren3000

I don't know much about the theory of chaos, but I don't think that it can't be applied in any case where there is an apparent randomness. Consider human behaviour, for instance. How can THAT be modelled with numbers and predicted mathematically.

It CAN'T.

Unless of course you wish to use numbers like this:

"what do you think he'll choose to do with his free will?
1 - he'll walk; 2 - he'll run; 3 - he'll take the bus; 4 - other"


I must say that every time I read the title of this thread, I just bust out laughing! I get this mental picture of a gigantic banner with "TONITE'S TOP MATCH - Nature Vs. Maths!" and these two wrestlers in an area, and if Maths wins, Nature implodes, and if Nature wins, Maths turns into complete and utter nonsense!

(you may now return to your regularly scheduled discussion)

[Rían]

Originally Posted by Haradrim

... and while sometimes we think something may be 50 50 chaos theroy shows us that actually a coin flip is not 50/50 it is actually I think 50.05/50 for heads because its slightly weightier.

*goes out looking for some poor ignorant sucker to flip coins with ... *

EDIT - shouldn't it be 50.05/49.95?

Beren - a bell-shaped curve is a very common distribution of a set of numbers that you get from measuring natural events, so called because the graph looks like -- a bell

FM - I agree with you

[BeardofPants]

Doesn't that rather depend on what country the 50 cent coin comes from..... *squints suspiciously*

[Jonathan]

Actually it does, especially Belgian euro coins more often land heads up

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