A new math

[btiffin]

Hello,

I was pondering placing this in Off-topic, but I thinks it's technical enough for a General Discussion, and I went to Waterloo back in the day, and the only CS degree was BMath so ...

Ok. I'm pondering quantum physics today. I need someone with some extraordinary skills in Mathematics.

We currently see the number line as a one dimensional ± straight line passing off into infinity at both ends. What if the Natural numbers aren't one dimensional? I want to figure out the math that would be required to allow the number line to twist in on itself such that 0 and ±∞ are actually in the same position. I envision a slow twist, somewhat like a mobius twist. The number line, while appearing single dimensional, will require a second (at least) dimension to allow for this twist space.

Any takers?

It is part of a theory I ponder that links the 10 dimensions (maybe 11, giving the 10 the extra dimension required to allow for this theoretical twist) required for some quantum particle theory to fold down to the 5 we kind of know of (I'm going on the theory of Quantum Holograms for this). It seems like a not quite reachable brain experiment, but I get a gut feel that it makes sense. The start and end of the Universe are the same point in space/time/hologram. The smallest small is a direct reflection of the biggest big. I don't think it will be an easy to grasp symmetrical twist, but perhaps exponential. Perhaps circular, perhaps not.

Linking gravity and force particles with matter and mass particles may be hidden in the message of this twist (I think ... but I can't get hold of the thread that will let me reject this idea as completely bogus, or something with potential).

Thanks for letting me vent off some brain waves.

Cheers

[Tony]

btiffin @ Thu Sep 18, 2008 12:54 am wrote:

We currently see the number line as a one dimensional ? straight line

Except that the "number line" is actually a two dimensional plane, if you consider the complex numbers. I'm not sure if you took those into the account already.

[btiffin]

Kind of. I want to get my head around the possibilities for the Natural numbers first. This may well be a bogus thought experiment, but I think it is worth the ponder. Then add to the complexity of the model, if it has any legs.

I delved a little into the complication of the fact that the Real ∞ between 0 and 1 being larger than the Integer ∞ at the end of the number line, but again ... until I get a yea/nay in my head, I'd like to keep it as simple as possible. It already has me thinking in circles. But the ∞R > ∞N truth gives me extra urge to pursue this path as I feel it is related.

And yes, I like your brand of thinking ... this it totally outside the box (that is inside the box).

Cheers
Edit; added an extra thought.

[Zeroth]

Well, one issue with having the smallest small linked to the largest large number, implies a limit on Natural numbers. This would counter several proven basic discrete mathematical theories, which rely on the fact that natural numbers are countably infinite. These theories then form the basis for several other theories, for one, cryptography, for another language theory. These theories are then applied in the real to great success. In essence, its like studying everything you know about aerodynamics, then coming to the conclusion that Bees cannot fly; they fly, so obviously something is wrong with what you know about aerodynamics.

I hate to be a buzzkill, but I don't think this thought experiment works. Quantum physics/mechanics defies thought experiments. It is so mind-numbingly different from common sense that it reportedly angered Einstein on several occasions. And that is the real difficulty for coming up with the GUT(Grand Unifying Theory). No one has been able to come up with a testable theory that explains why quantum physics works the way it does, and how this works on the macro scale that General and Special Relativity work. Of course, the closest is some versions of String Theory, which will be tested in a few weeks with the LHC.(I've looked at the physics, and for the LHC to destroy the world with black holes would invalidate a large number of theories, an immense number of observations, and completely invalidate Special Relativity. And in addition, these quack claims are coming from a guy that believes if you rubbed your feet on the carpet enough, your finger would blow up from static charge.)