Do numbers exist in nature or are they human contructs?

[rainbow]

God made numbers when they created the Universe.

[pErvinalia]

I think your logic is silly. If even 'high powered' scientists are baffled I would have thought it was a deeply profound question.

It is, and it's a fascinating thing to consider. I can't remember what side I fell on the last handful of times I debated this. My bones are telling me that, no, they don't exist in nature. But when I look out the window, I see unities. Straight away I'm seeing numbers. But was that instinctual and therefore possibly instinctual to a lot of animals? Or is this something that I've learned from other humans when I was growing up? I really don't know.

[pErvinalia]

In my opinion, numbers, and all the relationships between them, exist independently of human discovery.

The ratio between the radius and the circumference of the circle, 2 times Pi, exists in the universe whether some clever ancient Greeks described the phenomenon or not.

Intelligent aliens would recognise exactly the same irrational number, whatever language they used to describe it.

Cicadas can count to prime numbers. The Fibonacci sequence is exhibited in sunflower seed-heads. The gravitational constant, Avogadro's number, Planck's constant, and c or rather, the mathematical relationships between them and which they represent) exist with or without human knowledge and would be discovered by any species investigating the universe.

Sure, but that doesn't mean that numbers "exist". All that means necessarily is that there are physical laws of the universe that dictate how certain things form.

[pErvinalia]

Humans constructed numbers and numerals but not math. They discovered math.

Yeah, I almost think that a better question would be: Does mathematics exist in nature? That one too has been debated over and over. Not sure where high power (albeit energy efficient) scientists fall on that one...

edit: oh I see I've already had a crack at that in Audley's thread.. http://rationalia.com/forum/viewtopic.p ... 9#p1450789

[pErvinalia]

Oh, it seems I don't think numbers exist: http://rationalia.com/forum/viewtopic.p ... 9#p1450826

Thank god for the forum acting as my off-site brain backup storage.

[FBM]

Mathematics would have to exist in nature insofar as human consciousness exists in nature, as does everything else I know of. Maybe a better phrasing of the question would be, 'Do numbers exist outside human consciousness?'

[JimC]

Mathematics would have to exist in nature insofar as human consciousness exists in nature, as does everything else I know of. Maybe a better phrasing of the question would be, 'Do numbers exist outside human consciousness?'

That question could be applied to anything in the observable world - does sand exist, other than in human consciousness labelling certain grades of finely divided minerals as belonging to the category "sand"?

I return to an earlier observation. A hillside has five trees. The opposite hillside has 5 rocks. To an observer, the two sets of different objects have a common property.

I assert that, sans observer, the 2 sets of objects would still share that common property of "fiveness"

[FBM]

That seems to be leaning towards a reification fallacy. Sand, trees and rocks can be analyzed into their component molecules and atoms, etc. What is the (material/energetic) substance of "five" or "fiveness"?

[JimC]

That seems to be leaning towards a reification fallacy. Sand, trees and rocks can be analyzed into their component molecules and atoms, etc. What is the (material/energetic) substance of "five" or "fiveness"?

It is a generalisable property of any set of objects. If we go through a process of counting, it is easy to see that 2 sets of different objects may have one property in common, if the counting process ends at an identical point in each set. So, it may not have a "substance", but it gives a very consistent comparison of sets - they are either the same in the count, or they are not.

I said earlier that numbers and their logical relationships have a form of existence that differs from the existence of a pebble, or a photon of light. What makes me confident about its existence being more than subjective is that disparate human cultures may have very different experiences of many aspects of the material world or the nature of "reality", but confronted with 7 sheep, and 7 jugs, they will agree that they are commonly enumerated.

[pErvinalia]

Isn't there a tribe somewhere that only counts up to three? Or is that an urban myth?

[JimC]

Isn't there a tribe somewhere that only counts up to three? Or is that an urban myth?

Valley girls?

[FBM]

Edit: @ Jim:

OK, but there are more than one common element there. One being that all of those people agreeing are humans. Therefore, the "sevenness" has not been shown to be other than a shared subjective, abstract constructed in the human mind. I do agree, however, that whatever numbers are, they do exist in nature simply because human consciousness is also included as a natural process. I'm very ambivalent about the whole concept of qualia.

Anyway, this business about the reality of abstract entities has been done to death with no clear conclusion on the horizon: http://plato.stanford.edu/entries/abstract-objects/

[mistermack]

I think numbers definitely exist in nature.
If humans didn't exist, a hydrogen atom would still have one proton, and one electron. Any other combination wouldn't behave in the same way.
And a hydrogen molecule would always have two hydrogen atoms, bonded together. Otherwise, it wouldn't be a hydrogen molecule, it would be something else, and behave as something else.

You can go right through the periodic table, and the same thing happens. Different numbers mean different elements and different isotopes.

If humans had never evolved, helium would still be different from hydrogen. So the numbers must exist, because they make a difference. Or perhaps, because they DESCRIBE a difference. Or because they ARE the difference.

[klr]

Apparently, crows can count up to 3. Maybe 1,2 and 3 are corvid constructs, and humans made up the rest.

http://www.scientificamerican.com/artic ... y-to-count

I think we all knew that monkeys outperform the average college student....

Don't get me started ...

[rainbow]

Isn't there a tribe somewhere that only counts up to three? Or is that an urban myth?

Valley girls?

Libertarians?