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Author Topic:   Objective reality
Son Goku
Inactive Member


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Message 34 of 172 (559409)
05-09-2010 4:34 AM
Reply to: Message 31 by Straggler
05-08-2010 4:09 PM


Junk Maths and a personal opinion
Straggler writes:
Let me ask - Does the number pi exist? Is it only a number that has meaning to the decimal point that we require it to have meaning to? Or does it mean more?
That's a good question. Certainly for most human purposes, we could restrict to some large finite number of decimal places and we'll never need to know any number beyond that precision.
Pi and e and other such irrational numbers are better behaved than most, in the sense that they have a well-defined formula for calculating them. Take the more extreme case of the uncomputable numbers, numbers for which there is no algorithm for computing their digits. In fact virtually all numbers are uncomputable.
The reason we need all these numbers is not because we'll ever use them. The reason is because we need to do calculus. In order for calculus to work in all its glory, you need a number system with a certain collection of axioms. Those same axioms imply the existence of a vast sea of uncomputable numbers.
This is the kind of thing that splits mathematicians on the objective nature of mathematics. An awful lot of mathematicians I have met simply view these numbers as a necessary evil in order to get calculus, that the numbers are just a bunch of formal junk.
As for what I think about mathematics and objective reality, it's a difficult issue. I'm by no means sure of my opinion.
Considering I can easily just write down a set of axioms and explore that system, I don't think every mathematical system has a relation to reality. For example even chess is a formal system with axioms (its rules).
I do think there is something objective about two things:
(a) Some mathematical systems have a very strong relation to reality.
(b) I think that the most subjective part of maths is the axiom system. For example chess, could have had different rules. The most objective part, I think, is the consequences of those rules/axioms. So even though the rules of chess are arbitrary, given those rules the 2006 World championship game, for example, was always (in some sense) possible outcome. It "existed" somewhere in the space of all consequences of those rules.
Although in truth, I don't really know what I'm talking about.
As for objective reality in general, that's an even more difficult question. I'll take a toy model for consideration. Imagine there is a world containing a red box and three beings Alice, Bob and Carl. Also Carl has malfunctioning senses, he perceives the box as yellow. That is the objective truth of this world. I'm not even sure of how the inhabitants would obtain a definition of objective reality in this toy world.

This message is a reply to:
 Message 31 by Straggler, posted 05-08-2010 4:09 PM Straggler has replied

Replies to this message:
 Message 57 by Straggler, posted 05-10-2010 1:20 PM Son Goku has not replied

  
Son Goku
Inactive Member


Message 143 of 172 (560627)
05-16-2010 3:26 PM
Reply to: Message 136 by Straggler
05-16-2010 9:41 AM


Simplicity
I know this is addressed to cavediver, but I'll give it a go.
Straggler writes:
I wanted to ask you about the role of mathematical elegance. As I understand it mathematical/theoretical physicists are often driven by the underlying belief that nature is in some sense mathematically elegant.
I think when physicists say this, they mean something quite different to what a mathematician means. Simply because a lot of physics is not very tidy mathematically.
The best way to describe it would be that we would like to derive physics as the consequence of simple but powerful ideas. Ideas that are quite short to write down mathematically, but contain a wealth of information about the physical world. An example would be Quantum Chromodynamics. If you say you want a theory which is:
1. Quantum
2. Relativistic
3. Makes sense (not self-contradictory)
4. Matches a certain experimental value (one single experiment), by getting a factor of three correct.
Then basically only one theory can possibly obey this. No fixing, no real tuning, no "why wasn't it this, instead of that?". The whole of nuclear physics from three principles and one experimental constraint. That's what we want.
Physics and reality gets more complicated the higher up you go, but at the deepest, lowest levels it is shockingly simple. Abstract and difficult to understand, but simple. As you mentioned, exploring the possibility that we should have simpler and less starting assumptions has lead to advancement.
It's why we have the standard model. In the 1960s particle physics was in a mess, with no way to relate the observations or what they had to do with each other. However by requiring 1-3 above, only one type of theory could possibly be write, "Yang-Mills field theory". All of particle physics is based on this.
If the maths says one thing but empirical reality says another then empirical reality wins (would you agree with that?)
Definitely.
Edited by Son Goku, : Spelling.

This message is a reply to:
 Message 136 by Straggler, posted 05-16-2010 9:41 AM Straggler has replied

Replies to this message:
 Message 148 by Straggler, posted 05-17-2010 10:53 AM Son Goku has not replied

  
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