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I agree that most physicists believe that an external reality exists. I agree that physical theories aim to describe how it works. But I disagree that it foll
by n4r9 11y ago
I agree that most physicists believe that an external reality exists.
I agree that physical theories aim to describe how it works.
But I disagree that it follows that our physical reality has a mathematical structure. My objections are:
- There is no compelling reason to think that "purely abstract" mathematics any less anthropocentric than human language;
- Even if mathematics transcends humanity, there is no compelling reason to think that there is a single overarching mathematical structure of the universe, despite being able to predict the outcomes of our interactions to greater and greater accuracy as our physical theories develop.
It may be that Tegmark addresses these points in his "full strength" version, but given the way he glosses over these hidden assumptions in this paper, I'm not inclined to dig in and find out.
- tlb 11y agoTegmark is explicit about his assumptions elsewhere. For an overview, see https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis https://en.wikipedia.org/wiki/Mathematical_universe_hypothes.... Indeed, it's not the only productive line of thinking in physics.
- kazinator 11y agoTegmark believes (pardon me if I have this wrong) that all conceivable realities exist that can be described by equations, not only this reality. The reality we have access to is the one in whose equations we are ourselves locked up, so to speak. I'm basically with Tegmark. For one thing, what has physics ever come up with but equations, and improved equations to replace those, and so on? Everything so far has been math. So, going forward, either everything in physics will always be rooted in math, or else some "non-math stuff" has to be discovered. (The very idea of "non math stuff" being at the root of reality seems absurd.) What kind of thing would that be? I think if we discover the ultimate equations then that's all there will be: those equations, and mysterious constants embedded in them that just are. The only explanation for those constants will be the anthropic principle: if those constants were different, we wouldn't be here to contemplate why they are, and in some other universe there are beings completely different from us also wondering why their constants and equations are they way they are.)
- animefan 11y agoFor reference, the poorly named "standard model" which is the quantum theory of all forces except gravity, cannot really be called equations in the usual sense. This is because the kind of mathematical model that would describe the standard model (nonperturbative QFT) can't currently be done rigorously. It can only be done for simpler models in lower dimensions. The standard model is a very complex sort of approximation to a theory that is assumed to exist. This might be a mere detail to some but to me it is a sign that physics is complex in all kinds of ways, and can't really be described as "choosing the right equations". Even if you think that this is what physics is fundamentally, I think you would have to admit that it wasn't possible to describe what the meaning of "equation" was before qft was developed, and the same may be true about future theories that unify the standard model and gravity.
- effie 11y ago> For one thing, what has physics ever come up with but equations, and improved equations to replace those, and so on? Observations of nature and rational explanation of those in terms of old but also new concepts. Equations are just one of technical artifacts to help us think in a precise way. If we had computers sooner, there might have been physics without differential equations.
- kazinator 11y agoWhat observations are made in physics experiments which don't end up expressed as a cluster of floating-point numbers?