(March 1, 2012 at 1:31 am)Categories+Sheaves Wrote: Thank you for going into that.
Not much more to add here. I'm a fan of that empty set theory, you're not. But if you ever do write this stuff out/formalize it more, I would like to take a look at it.
As much as a ramble on in forums, I'm actually a horrible author. I've started to write a book on this topic more times that I care to count. I still have those old manuscripts. I'm never happy with them and I keep starting the book over again. I'm currently not working on it at all. I'd really rather produce a lecture video series and present it that way instead. I don't have the equipment to do that at the moment.
I also have extreme ADHD which causes me to be easily distracted into other things. I'm one of those people who has so many pokers in the fire that I've put the fire out. (ha ha)
I've been thinking a lot about Planck's Constant and how it most likely is like Pi. As a mathematician, I'm sure you're fully aware that Pi is a constant that is entirely dependent upon flat space. In other words, the value of Pi changes if you change the geometry from Euclidean to spherical or hyperbolic. The value of Pi is actually a property of flat space.
It's not some magical 'number'. It's just a quantitative property of flat space.
I've become increasingly aware the the same thing is true of Planck's Constant. It's very much like Pi. It's value is dependent upon the curvature of space. I'm not sure if physicists are actually aware of this. In some ways they might be, but in other ways I don't think they have fully grasped the significance of this. Especially in terms of unifying General Relativity and Quantum Mechanics.
When General Relativity and Quantum Mechanics actually 'meet' in a significant way there is necessarily always an extremely warpage of spacetime involved. Thus, not only is the value of Pi going to change dramatically, but so will the value of Planck's Constant. And other constants as well.
The mystery of what's going on in a blackhole, for example, baffles the scientists because all known physics seems to break down. However, so does the fabric of spacetime.
In fact, since time itself slows down at an increasing rate as the curvature of spacetime becomes more intense, this means that time, inside a black hole also slows down to a near standstill.
In fact, here's something to think about.
If you fell into a black hole by the time you reached the supposed singularity the entire universe will have ended.
In other words during your seemingly short trip (from your perspective) falling into the black hole, the universe exterior to the black hole will have aged almost infinitely.
So by the time you 'hit bottom' (if there is such a thing) then the universe external to the black hole would be infinitely old.
Here's another interesting thought.
Realizing the truth of what I have just observed above, and adding to that Stephen Hawking's theory that black holes will eventually "evaporate away" given enough time (through Hawking radiation), then, if you fell into a black hole, but the time you got to the singularity the universe would have aged infinitely. And thus the very black hole that you had fallen into will have evaporated by the time you reach the singularity!
Wow!
I mean, seriously. Stop and think about that for a moment.
This basically means that everything that falls toward the singularity of a black hole can ultimately never reach that singularity because by the time they get there (due to time dilation) the black hole will have evaporated completely.
Thus in a sense, it's meaningless to even speak about there being a singularity at the center of black hole because by the time anything reaches it, the universe will be over and the black hole will have evaporated completely.
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Ok, well I warned you that I have severe ADHD, so perhaps now you can see how I go off on tangents so easily.
But that's they way I am. I try to address a particular subject and end up going off in every imaginable direction except where I had planned as my destination.
So if I ever succeed in writing a completed book, that will be a miracle and I'll have to return to Christianity and start believing in Gods that speak from clouds again I guess. (ha ha)
Christian - A moron who believes that an all-benevolent God can simultaneously be a hateful jealous male-chauvinistic pig.
Wiccan - The epitome of cerebral evolution having mastered the magical powers of the universe and is in eternal harmony with the mind of God.
Atheist - An ill-defined term that means something different to everyone who uses it.
~~~~~
Luke 23:34 Then said Jesus, Father, forgive them; for they know not what they do.
Clearly Jesus (a fictitious character or otherwise) will forgive people if they merely know not what they do
For the Bible Tells us so!
Wiccan - The epitome of cerebral evolution having mastered the magical powers of the universe and is in eternal harmony with the mind of God.
Atheist - An ill-defined term that means something different to everyone who uses it.
~~~~~
Luke 23:34 Then said Jesus, Father, forgive them; for they know not what they do.
Clearly Jesus (a fictitious character or otherwise) will forgive people if they merely know not what they do
For the Bible Tells us so!