The Mystery of Mathematics

[Polednice]

The fact that the orderly language of mathematics is capable of describing our universe, and the fact that our brains are powerful enough to invent and utilise mathematical concepts, is often considered a compelling example of why the universe must require a designer. This is one of the more tempting theological arguments, but I'd like you to consider some points against it, and show me where I may be making wrong steps.

 

Essentially, I think this view is an entirely hubristic one. It seems to rest on the unwarranted (and probably unacknowledged) assumption that the human intellect is a superior one, and that the mathematics it uses is intrinsically good. It seems perfectly reasonable to think, however, that despite the wonderful efficacy of mathematics, there could be intelligences far superior to our own elsewhere in the universe with even better, even more efficient systems to understand the universe. To think that ours is special and indicative of a designer appears to place human intellect on a pedestal we can't be sure it deserves.

 

Also, it seems that the awe felt at the fact mathematics works is a little entangled. Rather than viewing consciousness as arising from the world and then, at some point, suddenly, mystically capable of understanding the world through mathematics, is it not more logical to imagine that a universe based on the laws this one features, if it gives rise to consciousness, would necessarily give rise to a consciousness equipped to understand its laws? We are able to understand things mathematically because we evolved to understand our environment in order to survive and reproduce more effectively in it. If we were in some other universe with other laws, we would have evolved a completely different system, maybe a much more chaotic one to suit a more chaotic environment, and we would be marvelling at the wonderful way that our devised language of physics fits reality so well.

 

I can't remember who first described the image, but I think it's similar to the caricature that a puddle one day forms in a small hole in the ground, and it thinks to itself, "My! This hole is perfectly suited to my shape! I surely can only conclude that this hole was designed with me in mind." I don't think there must be a special reason why maths fits - instead, it was a necessary consequence of our evolution, and we can't draw conclusions from our aesthetic sense that mathematics is wonderful when, in fact, it could be an unnecessarily complicated system for all we know.

[immortal]

I don't have any expertise on mathematics and I don't know whether mathematicians invent it or just discover it and mathematicians like Godel was a strong platonist.

 

Kurt Godel said "I don't believe in natural science" and also "Either mathematics is too big for the human mind or the human mind is more than a machine".

[Moontanman]

There are brains larger and more complex than human brains on the earth, whether or not they think mathematically is not obvious but I think it can be inferred. Whales use sonar to "see" their surroundings, they have huge complex brains, they are social animals, I think this is a prerequisite for math but I wonder if it's the same thing as we call math. Do whales think about complex math problems? Probably not, and neither did we until we invented writing, even then it took a quite a while before we came up with a system to understand math beyond 1 2 3 and many.

 

I think our culture is both a result of math and the cause of math. Having a big complex powerful brain is not enough, you have to have the ability to write down symbols connected with your thoughts and the reality around you.

 

Communicating is not enough either, elephants have a complex language, they communicate, they have a large brain, they have a manipulative organ they can use to effect their will on the environment, they even have a sense of their own mortality, they too are social animals, but they lack written symbols. I think this is significant, I'm not sure where the ability to not only think symbolically but to transfer those symbols to a physical manifestation outside the body comes from but elephants don't seem to have it even though they do have a hand of sorts.

 

What I am trying to say is that I'm not sure that brain size or social systems or intelligence has anything to do with math, possibly it is something if not unique to humans it is at least hard to define why we have it but it is for sure not something that comes about due to brain size or social pressure or being able to manipulate the world around us. Math may not in fact be necessary to have a civilization but it might be an emergent property of a complex society.

 

edit: I think the concept of 0 has a lot to do with our understanding of math. Is complex math possible with Roman numerals?

Edited May 27, 2012 by Moontanman

[John Cuthber]

 

 

 

I can't remember who first described the image, but I think it's similar to the caricature that a puddle one day forms in a small hole in the ground, and it thinks to itself, "My! This hole is perfectly suited to my shape! I surely can only conclude that this hole was designed with me in mind." I don't think there must be a special reason why maths fits - instead, it was a necessary consequence of our evolution, and we can't draw conclusions from our aesthetic sense that mathematics is wonderful when, in fact, it could be an unnecessarily complicated system for all we know.

 

I believe it was Douglas Adams.

(Slightly belated "happy towel day!")

http://en.wikipedia.org/wiki/Towel_Day

Edited May 27, 2012 by John Cuthber

[rigney]

Other than basics, math has never been a strong point with me. But it's good to know there are those out there with exceptional skills when math is needed. Other than social studies, there isn't a single field I can think of where math isn't use to its fullest. In kingdoms outside the human element, math seems necessity to both plants and animals. Things such as, a spider designing its web, bees building a honeycomb, or ants laying out tunnel systems and maternity wards. It's hard to believe that math in some fashion doesn't go into the design of a morel mushroom, axis of a leaf or petals on a flower of any kind. Saw the following and thought it may be interesting in how brain power might be used.

http://en.wikipedia.org/wiki/List_of_animals_by_number_of_neurons

 

Steven Weinberg, a most profound Physicist also said: I'd guess that if we were to see the hand of the designer anywhere, it would be in the fundamental principles, the final laws of nature, the book of rules that govern all natural phenomena. We don't know the final laws yet, but as far as we have been able to see, they are utterly impersonal and quite without any special role for life. There is no life force. As Richard Feynman has said, when you look at the universe and understand its laws, 'the theory that it is all arranged as a stage for God to watch man's struggle for good and evil seems inadequate.'

Edited May 27, 2012 by rigney

[md65536]

The fact that the orderly language of mathematics is capable of describing our universe, and the fact that our brains are powerful enough to invent and utilise mathematical concepts, is often considered a compelling example of why the universe must require a designer.

That's a logical non sequiter, and I don't think you need to come up with good counter points to argue against it. Though I do partially agree with some of your points.

 

Can you say for certain whether mathematics are invented, or discovered? I think it's a little of both.

The properties of many mathematical concepts are based on properties found in nature (eg. similar to systems where 1+1=2, if you put one object together with another they remain the equivalent of 2 objects rather than merging into 1 equivalent to either of the originals). The "mystery" of mathematics and the universe might be their consistency. Like with Douglas Adams' "puddle" example: If we lived in a universe where things were different, we might have a different set of maths with completely different sets of rules. If we lived in a universe without consistency, nothing might exist that could contemplate it.

 

It should not be surprising that systems invented or discovered based on observing and contemplating the real universe, should have similar sets of properties to the real universe. The "there must be a designer" arguments seem to come from a lack of understanding and imagination. Certainly hubris plays a part, such as in "I can answer any question, and I can't think of any alternative to there being a designer, therefore that must be the case."