Physics « Conversational Atheist

On math, chess and God

Sunday, February 14th, 2010

I wrote a previous entry which was based off a comment I sent to a theologian that I’ve been chatting with. He responded to me here.

Theologian RD says: Mathematics maps onto the world but our intuition of which mathematics maps on is not infallible. The problem is with Conversational Atheist’s apparent view that mathematics does not map onto the world at all. That’s the view that needs defending.

Whether mathematics maps onto the world is a very interesting question. Of the infinite number of mathematical models that are able to be constructed, a few map onto the world in very useful ways. If you come up with a mathematical model, the question immediately becomes: DOES your abstract mathematical model map onto the world?

Re-read a section from the comment that prompted this entry:

Conversational Atheist says: However, Einstein, placed in a box before the first experiments in quantum mechanics were done, would never end up CONCLUDING Quantum Mechanics. He might, given infinite time, detail hundreds of thousands of possible physics on small scales [mathematical models] that includes our modern conception of QM, but he would be in no position to choose one from the others with any confidence at all. He might even pick what he thinks is the most beautiful physics at small scales, but what counts is not beauty or arguments, per se, but whether his physics [mathematical model] matches reality. — Emphasis and [mathematical note] added

What counts is whether your mathematical model matches reality. That’s the $64,000,000 question for a physicist. Long ago a person could have come up with the mathematical framework of modern day quantum mechanics by doing math. Lots of math. Now, that person hasn’t done PHYSICS unless he is either consulting data others have taken, or going out and doing experiments himself.

To answer some of your questions raised in the entry itself:

RD: How do we gain knowledge of this realm? That appears very mysterious, indeed somewhat revelatory.

Are you equally perplexed by how we gain knowledge of chess? It doesn’t seem very mysterious to me. We consider the relationships and interactions between entities in chess-space. Are these relationships, rules, interactions all contained in a self-consistent chess-realm similar to the relationships, rules, and interactions in the self-consistent mathematical-realm? Yes. Does this mean that there is a supernatural chess-realm, mathematical-realm, tic-tac-toe-realm, and scrabble-realm? Um… only in the most abused sense of the word “supernatural”. The chess-realm does not exist in any physical way.

Is the pawn, real? Well, you can hold a wooden piece in your hand that people call “pawn”, but then you should realize that you are just holding a representation of a pawn. Does this upset anyone? It shouldn’t.

Is 7 real? Well, you can hold 7 apples in a bag and call it “seven”, but then you should realize that you are just holding a representation of a number. Does this upset anyone? Apparently, yes.

RD: Second, what is the ontological status of this realm?

I’d say that mathematics has the same ontological status as the game of chess.

RD: And if you accept the existence of abstract numbers and their relations which are irreducible to and independent of the physical world, what about other entities like souls, spirit beings, and God? What rational reason does Conversational Atheist have to believe the supernatural realm, like the natural realm, does not far transcend his limited experiences?

If a pawn is irreducible to and independent of the physical world, what about other abstract entities like souls, spirit beings, and God? — Sure. I’d say they have the same status as “real pawns”. Could there be a supernatural pawn out in the “vast supernature of things that I don’t fully comprehend”?

Sure. He might be playing Chinese Checkers with God and the Easter bunny.

But seriously, considerations in the fully abstract might have something to do with external reality — but you have to actually check to have any confidence that your favorite abstract reasoning maps onto external reality in a useful way.

Tags: Philosophy, Philosophy of science, Physics
Posted in Philosophy, Religious Interaction, Theology | 1244No Comments »On+math%2C+chess+and+God2010-02-14+08%3A08%3A23Conversational+Atheist

Gaining knowledge about external reality

Tuesday, February 2nd, 2010

A somewhat more philosophical post than I usually do… I wrote this up during an exchange w/ a theologian differentiating two ways we can gain knowledge.

To a theologian:

Let’s start with mathematical truths — I think that they are true and in a very real sense constitute knowledge. Knowledge about something that is abstract, however. One of the features of abstract subjects, in my view, is that it is quite possible to make real progress in them without new inputs. Euler, an amazing mathematician, placed in a shielded box and given enough time could make real progress in mathematics.

I mean this to contrast methods of inquiry about external reality. When it comes to external reality — how stars work, the rules that govern the motions of the planets, etc., a physicist in a box could make lots and lots of models and guesses and arguments… but, unless he re-analyzes data from before he came into the box, he won’t make progress in physics.

For example, Einstein, with the data of Mercury’s weird orbit and the results from Michelson, could be put in a box, and with enough thinking could come up with General Relativity.

However, Einstein, placed in a box before the first experiments in quantum mechanics were done, would never end up concluding quantum mechanics. He might, given infinite time, detail hundreds of thousands of possible physics on small scales that includes our modern conception of QM, but he would be in no position to choose one from the others with any confidence at all. He might even pick what he thinks is the most beautiful physics at small scales, but what counts is not beauty or arguments, per se, but whether his physics matches reality.

That brings me to what I think is our main point of conflict between our approaches.

I fully acknowledge that progress can be made in all areas of mathematics and much of philosophy from internal reflection and argument without any new data coming into a person’s head. When a person thinks that this abstract knowledge can tell us something specific about external reality, the existence of God for example, they are simply making a category error.

Can theology reason out the attributes of what would be a perfect being? Sure. Can abstract reasoning alone tell us something about external reality? Possibly… although I’m having a hard time thinking of an example where it’s happened before.

Keep thinking about the difference between math and physics. If you wander too far away from direct measurement and experience, you can do a lot of work, and convince yourself of quite a lot… although you won’t learn much about external reality.

I’m not expecting this to be unanimously agreed upon — comments?