The relationship between Mathematics, Physics, and Biology

[Yelbir]

Well, I didn't know where to post this rather philosophical stuff, so decided to put it here. But I promise it is related to all sciences mentioned above.

Here is the setting. Whenever we prove something mathematically, we always think that the proof is "eternal", often contrasted with the situation in natural sciences, where you can't really prove anything.

However, nobody ever thinks (as far as I know) about the fact that we are not JUST PROVING, we prove the theorems TO SOMEBODY, namely to a homo sapiens. And the creator of a proof is also a homo sapiens.

So my question is: could it be possible that a non-human mind will not be convinced by our human-to-human arguments?

When we create a physical theory in mathematical terms, we first state several basic postulates. Then we use OUR logic in order to deduce the consequences, which should fit available experimental data and, if possible, try to predict something new using "the laws of nature" we just stated. If the predictions are successful, we say: "The theory seems to be plausible".

Now imagine, that you've shown your basic postulates to a creature with completely different way of thinking. And It says: "NO, whatever you're considering to be a consequence of the postulates DOES NOT seem to be a consequence to me. Moreover, your theory is internally inconsistent and self-contradictory, so your theory DOES NOT predict whatever you thought it's predicting and DOES NOT fit the experimental data."

Now let me stop and put clearly that I completely realize how speculative this whole argument is, if not a pure and useless fantasy.

However, if one accepts the idea as being at least "worth keeping in mind", then one should also inescapably draw the following conclusion:

"There is a possibility that all our physical theories are convincing only for a human being, and make no sense whatsoever for a non-human mind. So it is not impossible that physicists are just a crowd of hairless monkeys, telling each other beautiful fairy tales about the way nature "works". It may be possible, also, that the fact that theories make successful predictions means NOTHING, since the conclusions may work only for us. It is also possible that there can be endless different types of mathematics, depending on the internal structure of a brain of a creature which conceived it. And this means that mathematical proves possesses a property which I will call a "biological relativity', i.e. they make sense only for animals of the same basic "scheme of the brain", so to speak. And that's exactly why mathematical proofs seem so ideal to us - we simply CAN NOT find counter-arguments, due to BIOLOGICAL constraints. The constraints may work in the following manner: the writer accompanies the whole process of creating the theorem and the proof by constant checking of the proof for internal contradictions, and then a brain of essentially THE SAME type (i.e. the brain of the reader) tries to find the contradiction and, obviously, fails. But if it was somebody with a different brain... " etc, etc.

So, overall that's the idea that bothers me already for a very long time. I will appreciate very much if somebody shows me a flaw in my arguments or/and gives me a link, which demonstrates that it is an old and well analyzed philosophical problem and I can simply read about it instead of contemplating and tormenting myself day and night.

Thanks a lot for reading this philosophical c...p. But it really bothers me.

P.S. I am not a native speaker, so I apologize for mistakes.

 

[Crazymechanic]

hey , welcome to PF.

Well I could agree and not agree on everything you basically said.
It's not like mathematics would be flawed , it's rather that mathematics is some language which uses logic as a basic construct and helps us judge how nature works.
Now a alien or any other life form as intelligent or more than us would probably not understand our arguments and reasoning but if they or he would be intelligent enough I believe they would see the logic behind our stuff and the way we organize and deal with it.
Just like a little kid while learning maths and other sciences recognizes some things himself without extra teaching because those things are based on logic assumptions and logic is a common thing among the human species ,in other words there is a certain pattern or way human beings think so not all of them but some could see that pattern without some specific training or learning in that science etc.

But the basic thing that the sun shines without the need to calculate it's mass or that wind blows and doesn't care about where and how strong or that all the things happen in the universe the way they do without our calculations or math , yes I could agree on that in fact I have been thinking about that myself.But going down this route will take us to discussion about the human or limited point of reference of the universe and some absolute universal point of reference , or the concept of God or etc and that will violate the rules and get this thread banned so this is as far as we can walk together here... :)

 

[Yelbir]

Thanks a lot for your reply, Crazymechanic.

 

[micromass]

Sorry, we don't discuss philosophy here.

 

[pmacias]

I find this question and perspective to be very interesting and thought-provoking. It raises important points about the limitations of our understanding and knowledge, and the role that our own biology and cognitive abilities play in shaping our scientific theories and concepts.

Firstly, I would like to address your question about whether a non-human mind could potentially reject our human-to-human arguments and proofs. While it is impossible to definitively answer this question, I believe that it is certainly a possibility. As you mentioned, our understanding and interpretation of theories and proofs are heavily influenced by our own biological and cognitive processes. Therefore, it is possible that a non-human mind with a different biology and cognitive abilities may not be able to understand or accept our human-derived concepts and theories.

This leads to the larger question of the validity and universality of our scientific theories. It is true that our understanding of the natural world is limited by our own biology, and therefore our theories may only make sense to us as humans. However, I believe that the success and predictive power of our theories cannot be ignored. While it is possible that they may not make sense to a non-human mind, the fact that they consistently and accurately predict natural phenomena suggests that they are at least a useful and effective tool for understanding the world around us.

Furthermore, the fact that our theories are constantly evolving and being refined through new evidence and data suggests that they are not simply a product of our biology, but rather a continuous effort to understand and explain the natural world. While we may never be able to fully escape the limitations of our biology, our scientific methods and processes allow us to continuously push the boundaries of our understanding.

In conclusion, while the idea of "biological relativity" in mathematics and science is certainly an intriguing concept, I believe that the success and usefulness of our theories cannot be denied. Our understanding may be limited by our biology, but our continuous pursuit of knowledge and understanding through scientific inquiry is what sets us apart as scientists.