You mean because they can't arise in nature, period? I expect Kharakov had in mind a pattern that can arise with a conscious agent. It seems to me what would fit the bill is a core dump of a running fully detailed simulation of a human brain.I'd say that the non-computable numbers fit the bill.
Do not occur or could not occur? Big difference. For an object to spontaneously be reflected across the Y-Z plane is no more a violation of known natural law than for all the molecules in the hostess' undergarments to leap one foot simultaneously to the left. In quantum tunneling, all things are possible. The best you'll get is a proof that the expected time you'd probably have to wait before witnessing such an event exceeds the lifetime of the universe.I was thinking more along the lines of geometric transforms that couldn't occur in nature. I don't think there is a mathematical proof that a reflection across an axis cannot occur in nature, so perhaps asking for a proof is a bit over the top, although perhaps there is a proof that according to the current understanding of natural law (that I am aware of), certain transforms do not occur in nature.
I don't think relativity will allow something located at (-1,-1,-1) to be reflected to (1,-1,-1). While we can imagine this reflection happening, or simulate it on a computer, I don't think we will find this type of transform occurring in nature outside of a mind or a simulation.
That's one of the trivial cases.You mean because they can't arise in nature, period? I expect Kharakov had in mind a pattern that can arise with a conscious agent. It seems to me what would fit the bill is a core dump of a running fully detailed simulation of a human brain.I'd say that the non-computable numbers fit the bill.
Think classical scale.Do not occur or could not occur?I was thinking more along the lines of geometric transforms that couldn't occur in nature. I don't think there is a mathematical proof that a reflection across an axis cannot occur in nature, so perhaps asking for a proof is a bit over the top, although perhaps there is a proof that according to the current understanding of natural law (that I am aware of), certain transforms do not occur in nature.
I don't think relativity will allow something located at (-1,-1,-1) to be reflected to (1,-1,-1). While we can imagine this reflection happening, or simulate it on a computer, I don't think we will find this type of transform occurring in nature outside of a mind or a simulation.
A naturally occurring prime number generator seems very farfetched....
I was thinking more along the lines of geometric transforms that couldn't occur in nature. I don't think there is a mathematical proof that a reflection across an axis cannot occur in nature, so perhaps asking for a proof is a bit over the top, although perhaps there is a proof that according to the current understanding of natural law (that I am aware of), certain transforms do not occur in nature.
I don't think relativity will allow something located at (-1,-1,-1) to be reflected to (1,-1,-1). While we can imagine this reflection happening, or simulate it on a computer, I don't think we will find this type of transform occurring in nature outside of a mind or a simulation.
I was thinking more along the lines of geometric transforms that couldn't occur in nature. I don't think there is a mathematical proof that a reflection across an axis cannot occur in nature, so perhaps asking for a proof is a bit over the top, although perhaps there is a proof that according to the current understanding of natural law (that I am aware of), certain transforms do not occur in nature.
I don't think relativity will allow something located at (-1,-1,-1) to be reflected to (1,-1,-1). While we can imagine this reflection happening, or simulate it on a computer, I don't think we will find this type of transform occurring in nature outside of a mind or a simulation.
Wait, is this physics or math? I don't think I completely understand what you mean - why wouldn't reflections be allowed?
If you want something geometric - what about realizing a Klein bottle from it's fundamental polygon in 3-space? Or the existence of any higher-than-reality-dimensional object/transformation?
s=1-2+3-4+5-6+7-8+9-10+11-12+13...
2s= 2 -4 +6 -8 +10 -12 +....
s=1-2+3-4+5-6+7-8+9-10+11-12+13...
3s= +3 -6 +9 -12......
Yup. They used the method I used to get the values 1/3, 1/4, 1/5, etc.. for 1-2+3-4+5....Yes that 1/4 plays a role in finding that the sum of 1+2+3+4+5... is -1/12.