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Monday, April 21, 2008

the mathematical universe

For those still interested in proving the existence of external reality, a programmer recently pointed me to this paper on the mathematical universe hypothesis (MUH). The programmer's very strong (unnecessarily harsh I think) recommendation...
Note that the MUH is not a theory or a position. It is the only formally definable option. Every other option is meaningless gibberish. Therefore, it is FACT.

And by no coincidence, I arrived at this exact conclusion (if a bit fuzzier then) almost a decade ago. My current thinking is much more sophisticated.

I can bootstrap myself starting from solipsism, I make no distinction between models and what they represent, and no distinction between models that all fit the same theory.
...
It gets to where physical reality is defined as whatever minimal theor(ies) will logically explain your subjective experience.

This lets you almost immediately step out from solipsisim by concluding that physical reality is independent from your will. And it resolves paradoxes left, right, front and center.

Like why the universe responds to a mathematical description: because it's made of mathematics. Or why the external reality responds to your will to command it into existence: you never command it!

It also realigns physical reality with major theorems in mathematics. Like the one that says you can't even in theory pick between two dual representations. Or the one where any infinitely expressible language can't be resolved by any finite axiomatic system.

It drives a stake right through the heart of filthy (neo-)Platonism. And it affirms the connection between physics, the study of one reality, and mathematics, the study of all realities.
From Max Tegmark's essay--
The idea that our universe is in some sense mathematical goes back at least to the Pythagoreans, and has been extensively discussed in the literature. Galileo Galilei stated that the Universe is a grand book written in the language of mathematics, and Wigner reflected on the “unreasonable effectiveness of mathematics in the natural sciences”. In this essay, I will push this idea to its extreme and argue that our universe is mathematics in a well-defined sense.

4 comments:

Charlie H said...

I think it is something of a mystery why the universe is so darned mathematical. I generally resist rationalism, but math does give me pause. Richard Feynmann also regarded this as a mystery -- why is it that math is so powerful in describing the physical world? It's been a while, but I remember Kitcher's "The nature of mathematical knowledge" being a good book in this connection.

Mike said...

In his conclusion, the author makes some poignant remarks.

"It is arguably worthwhile to study implications of the MUH even if one subscribes to an alternative viewpoint,
as it forms a logical extreme in a broad spectrum of philosophical interpretations of physics. It is arguably extreme in the sense of being maximally offensive to human vanity.
...
Further deflating our hubris, we have learned that we are not that special either. Darwin taught us that we are animals, Freud taught us that we are irrational, machines now outpower us, and just last year, Deep Fritz outsmarted our Chess champion Vladimir Kramnik. Adding insult to injury, cosmologists have found that we are not even made out of the majority substance. The MUH brings this human demotion to its logical extreme: not only is the Level IV Multiverse larger still, but even the languages, the notions and the common cultural heritage that we have evolved is dismissed as 'baggage', stripped of any fundamental status for describing the ultimate reality."

vince said...

From the physics side, I don't see anything extraordinarily compelling in his article. He throws a lot of physics words around, several formulae, and draws conclusions. Mathematics is remarkable, but I had more fun reading about the heavenly harmonics in Timaeus.

Right up front he admits the biggest criticism. Those who put forward the Copenhagen Interpretation of Quantum Mechanics require something more than mathematics. The math propagates the probable states forward in time, but the actualization of what is observed requires the 'collapse of the wave function into the single observed state. The 'collapse' is not a mathematical formalism. Rather it is the selection of a reality. There is absolutely nothing mathematical about this process.

I think he is no further than Pythagoras.

Mike said...

Thanks for that insight, Vince.

The point of view that interests me most is the one we have as humans and all the terrible messes we make in order to live. But this sort of thing is worth a read once in a while.