Math and Reality. What is the deep connection?

apeiron

Aha, but complex number magic is all about the irreducibility of dichotomies. It is no surprise at all that you need two dimensions to "number" a system. You must have a local variable and a global variable (such as energy and time, or location and momentum, or even spin and charge now).

Irreducibly orthogonal measurements at the fundamental level are exactly what the systems approach predicts.

QM had to be a theory about complementary properties because systems have no choice but to be organised that way.

ThomasT

I wrote this:

@ rogerl
Ok, so you're not really asking about a deep (reality) connection, which would be meaningless. And you're not asking why mathematics is effective in modelling theoretical/mathematical constructs, which is obvious. Or even why some theoretical/mathematical constructs are difficult to reconcile, which is difficult. What you're asking is how these constructs are translated into the language of instrumental behavior. Is that right?

Then I noticed this:
It's a physically meaningless question, since the only thing we have to compare physical models with is the reality of our sensory experience.

rogerl

How does physical model like general relativity correspond to reality is not a meaningless question. We have instruments like GPS, fermion detectors that interface with them.. it's not just our sensory experience because we don't do the direct detectors. We just interpret it and the results of the instruments correspond to the data which we input into our brain.

nismaratwork

What. The. Hell?

I don't think you understood a word that TT said, adn I surely don't understand your point if there is one.

ThomasT

You want to know how a physical model corresponds to a reality that we can't access. It's a meaningless question. We speculate and make theoretical/mathematical models, and test those models via instrumental behavior amenable to our senses. If the model works, it doesn't mean the model corresponds to some vision of a deep reality. It means the model corresponds to the observed instrumental behavior.

rogerl

I wrote that message with the assumption that we could access the reality that physical instruments couldn't. That is.. i was thinking our mind can access it.. and by contemplating how physical models correspond to reality.. we can use deductions and mind probe to know if the physical model is close to the reality. For example. I was meditating a lot about space and time and what it means to warp and curve. What if our pure mind is interactive with space and time.. then we can view spacetime using our mind's and know how the physical model correspond to it... something like that.

Pythagorean

actually, if you weren't so deluded by the victim role, I was asking questions to get me started in understanding your colorful language. I wasn't aware I insulted you...?

and what exactly was my conclusion?

there seemed to be a lot more in there for a non-reply...

nismaratwork

Whaaaat, the hell is "mind probe"?

Ken G

Yes, that's a fair characterization of our positions. Perhaps it is not that one or the other of us has to be right, but that we are caught in yet another duality-- neither of our positions would make any sense if the other's did not also hold some truth. If the universe was as fundamentally impenetrable as I imagine, then there would be no point in thinking about it in the first place-- that's exactly the stance of the rock, which has given up the effort altogether and so lives in a universe where there is nothing to understand, so nothing is not understood either. Or, if the universe was really our intellectual oyster, just one or two really big ideas away from giving up its deepest secrets (as you might hope, I would not put the words in your mouth), then we have the disastrously appalling possibility of knowing all there is to know, and returning again, thusly, to the same status of the rock. Having nothing left to understand is a lot like having nothing to understand in the first place-- and so instead we find ourselves constantly balanced on the brink of enlightenment, another dynamical equilibrium, between what we do know and what we can know.
And it likes Godel's proof even less, the fundamental divide between what can be certain and what can have meaning. But as you can guess from the above, I view Godel's proof that meaning and truth are fundamentally different as the saving grace, the one Wigner key that doesn't fit, giving us hope that all the other ones that did were not just a completely rigged universe, "losing" to our intellectual advances just to humor us.

ThomasT

Well, that's a whole other question, and since I don't have those powers I can't answer it.

However, when models do correspond to instrumental behavior, then the visions of deep reality that they might provoke can be preserved, for the time being, and maybe tweaked, added to, combined, etc. by theoretical physicists. Wrt most of them, I think it's possible to get a good idea of their thinking processes via their writings.

As for spacetime curvature, I wouldn't ponder that too much. Think in terms of waves and wave complexes, resonances, hierarchies of particulated wave structures, that sort of stuff.
Just a suggestion.

Ken G

I think you may be right about this, and I might add that the key thing that the complex humbers are allowing is an undreamed-of escape from the frozen prison of Parmenides' and Zeno's impossibility of change. Complex numbers are what allow a state to be "stationary" (unchanging in regard to a universe of only that state), and yet also be dynamical (bringing about change when considered as part of a larger system), all at the same time. Perhaps we could say they are what allows a particle to participate in a larger system in a way that does not project onto the internal degrees of freedom of that particle itself.

apeiron

Agreed. What I would add is that I have had to make some radical changes in POV along the way. So I started out as a naive realist and it was a big breakthrough to then get that "everything is just models". Embracing complete doubt is what allows you to turn around and have complete confidence in the fact "now you can model".

Likewise I was first a reductionist, then became completely disillusioned with reductionism. And then in turn found that reductionism was what I also completely believe in because it was a subset (or more correctly, the dichotomous partner) to a fully worked out systems view.

So going all the way over to one side is only worthwhile if you turn round and see now that there is also other side you left behind. To have moved away successfully means that there was definitely the other thing there in the first place.

You will know one of the favourite symbols of what we are talking about here?
http://en.wikipedia.org/wiki/Drawing_Hands

apeiron

Really, I have no idea why I thought that you might have been insulting. It would be out of character.

"Essentially though, what it seems like you're saying is what I've said here before, that mathematics is type of logical clay."

Pythagorean

So I concluded what you sounded like to me, yes. But it's you who chose to make the story end there.

You never confirmed whether semiotics was synonymous with organic logic either.

So the irony of your accusations is that you're the one jumping to conclusions, while I'm still struggling to understand you.

nismaratwork

Yeah, lets sail right past the 'crazy' mind probing, and get on with bickering... wait, what?

Pythagorean

sometimes, to properly probe each other's minds, we have to bicker past the anticipatory language barriers. (probe sent)

nismaratwork

Sometimes people are just bonkers, and believe in magic, and insist on bringing it up (only to be deleted) over and over in the wrong forum.