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beero1000
Veteran Member
I'd say that the 
non-computable numbers fit the bill.
non-computable numbers fit the bill.
Kharakov
Quantum Hot Dog
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 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.
Bomb#20
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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
Bomb#20
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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.
Kharakov
Quantum Hot Dog
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
I'm looking for a basic mathematical operation that indicates a consciousness engaged in the operation because natural law prevents it from happening.
Kharakov
Quantum Hot Dog
Think classical scale.
Kharakov
Quantum Hot Dog
Ahh, but primes are naturally selected for in certain scenarios, so one would have to pick something other than primes to indicate consciousness did the selection:
https://en.wikipedia.org/wiki/Prime_number#Prime_numbers_in_nature
If someone encoded primes into certain DNA sequences, a metaphysical naturalist would claim that the primes just come up because of evolutionary adaptions that at one time favored primes being selected, using the obvious example of cicadas.
ryan
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A thought must exist for every possible pattern that we think of. And let us assume that for every thought there is a physical representation in the form of a process. If there is no dual nature to mind and body, then our thoughts are just samples of the universe; therefor, all thoughts must exist in nature.
However, if there is a interacting duality or a duality that does not interact between mind and body, then I have no idea.
However, if there is a interacting duality or a duality that does not interact between mind and body, then I have no idea.
beero1000
Veteran Member
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?
Kharakov
Quantum Hot Dog
Ok. Derailed, maybe split this portion off to whatever philosophy subforum is most appropriate, or let the thread run its course until someone injects a math question?
As to the math portion of the question, I'm satisfied that in accordance with relativistic scale physics, instantaneous reflections across a plane do not occur in nature. Is this acceptable to everyone else (the math portion)?
As to the math portion of the question, I'm satisfied that in accordance with relativistic scale physics, instantaneous reflections across a plane do not occur in nature. Is this acceptable to everyone else (the math portion)?
ryan
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Here's one, the Banach–Tarski paradox . So far, it is not known to be physically possible but is mathematically true.
Kharakov
Quantum Hot Dog
I'm interested in an actual accepted proof that certain geometric transformations would not occur in nature (at a classical level) without a conscious agent, with the base assumption of general and special relativity.
Kharakov
Quantum Hot Dog
1-2+3-4+5...
What's the sum?
1-2+3-4+5-6... != 0+1-2+3-4+5...
To keep it tight, one must use the same number of terms for a partial summation. Here's one version of it:
1-2+3-4+5...
__1-2+3-4...
__1-2+3-4...
___ 1-2+3...
It equals 1 when we don't use the same amount of terms for the different series. We can divide it by 4 and say it is 1/4th.
Here's how it should look (same number of terms to keep it tight, otherwise we can arbitrarily pick the amount of terms for each series):
1-2+3-4+5...
__1-2+3-4+5....
__1-2+3-4+5....
___ 1-2+3-4+5....
After 5 terms, the summation is 12. After 6, it is -12....
Of course, if we're being crazy, and skipping terms when we want because they do have the "same" lack of defined amount of terms, we can add in 2 times the series:
3s= 1 +(3 -8 +5) +(7 -16 +9) + (11 -24 +13) + (15 -32 + 17)....
s= 1/3
It's shocking that for 4* the series you get 1/4th, ehh?
4s = 1 + a whole lot of nothing: (-2+6-4) +(5-12+7) + (-8+18-10) + (11-24+13)....
s=1/4th..
Guess what... 5 series = 1/5th. By analytic continuation, the series itself is equal to 1.
What's the sum?
1-2+3-4+5-6... != 0+1-2+3-4+5...
To keep it tight, one must use the same number of terms for a partial summation. Here's one version of it:
1-2+3-4+5...
__1-2+3-4...
__1-2+3-4...
___ 1-2+3...
It equals 1 when we don't use the same amount of terms for the different series. We can divide it by 4 and say it is 1/4th.
Here's how it should look (same number of terms to keep it tight, otherwise we can arbitrarily pick the amount of terms for each series):
1-2+3-4+5...
__1-2+3-4+5....
__1-2+3-4+5....
___ 1-2+3-4+5....
After 5 terms, the summation is 12. After 6, it is -12....
Of course, if we're being crazy, and skipping terms when we want because they do have the "same" lack of defined amount of terms, we can add in 2 times the series:
Code:
s=1-2+3-4+5-6+7-8+9-10+11-12+13...
2s= 2 -4 +6 -8 +10 -12 +....3s= 1 +(3 -8 +5) +(7 -16 +9) + (11 -24 +13) + (15 -32 + 17)....
s= 1/3
It's shocking that for 4* the series you get 1/4th, ehh?
Code:
s=1-2+3-4+5-6+7-8+9-10+11-12+13...
3s= +3 -6 +9 -12......s=1/4th..
Guess what... 5 series = 1/5th. By analytic continuation, the series itself is equal to 1.
George S
Veteran Member
Yes that 1/4 plays a role in finding that the sum of 1+2+3+4+5... is -1/12.
I do have a conundrum, though. 2 is just 0+1+1, in number theory. 0 and the successor function s is where we begin.. 1 is s(0), 2 is s(s(0)), +1 is notation for s. A number is the depth of the stack of s(s(s(...(0)...))).
+1 and -1 add or remove one layer of number, changing the number by 1. +0 and -0 are "no change" operators. Using 1 instead of s(0) saves a scribe a lot of ink. And when we use exponential notation the fact of that number being, in the number-theoretical sense, merely a mental stack of that depth.
0+1 is shorthand for s(0)
0+2 is shorthand for s(s(0))
0+1+1 is a longer hand for s(s(0))
0+1+1+0 is even longer for s(s(0))
0+1 is named 1
0 +1+1 is called 2
0+2 is called 3
0 +1+1+1 is 3 as well
0+1+1+1+1+1+1+1... is named infinity.
Program 0 +1+1+1+1+1+1+1+1+1... = infinity
s=0
n=1
Do while 1=1
...s=s+n
...n=0+n
End Do
print s.
End Program
a 1 bit change and the program becomes
Program 0 +1+2+3+4+... = -1/12 This one is necessary for physics.
s=0
n=1
Do while 1=1
... s=s+n
... n=1+n
End Do
print s
End Program
Change one add to a subtract and we get
Program 0 +1-1+1-1+1-1+1-1+... = 1/2 The Grandi series, of course.
s=0
n=1
Do while 1=1
...s=s+n
...n=1-n
End Do
print s
End Program
Introducing multiply
Program 0 +1*1+2*2+3*3+... = 0 works in "renormalization" of physics (sum of squares of natural numbers)
s=0
n=1
Do while 1=1
... s=s+n*n
... n=1+n
End Do
print s
End Program
Introduce the division operator and double n at each step instead of merely count.
Program 0 +1/1+1/2+1/4+... = 2
s=0
n=1
Do while 1=1
... s=s+1/n
... n=n+n
End Do
print s
End Program
I do have a conundrum, though. 2 is just 0+1+1, in number theory. 0 and the successor function s is where we begin.. 1 is s(0), 2 is s(s(0)), +1 is notation for s. A number is the depth of the stack of s(s(s(...(0)...))).
+1 and -1 add or remove one layer of number, changing the number by 1. +0 and -0 are "no change" operators. Using 1 instead of s(0) saves a scribe a lot of ink. And when we use exponential notation the fact of that number being, in the number-theoretical sense, merely a mental stack of that depth.
0+1 is shorthand for s(0)
0+2 is shorthand for s(s(0))
0+1+1 is a longer hand for s(s(0))
0+1+1+0 is even longer for s(s(0))
0+1 is named 1
0 +1+1 is called 2
0+2 is called 3
0 +1+1+1 is 3 as well
0+1+1+1+1+1+1+1... is named infinity.
Program 0 +1+1+1+1+1+1+1+1+1... = infinity
s=0
n=1
Do while 1=1
...s=s+n
...n=0+n
End Do
print s.
End Program
a 1 bit change and the program becomes
Program 0 +1+2+3+4+... = -1/12 This one is necessary for physics.
s=0
n=1
Do while 1=1
... s=s+n
... n=1+n
End Do
print s
End Program
Change one add to a subtract and we get
Program 0 +1-1+1-1+1-1+1-1+... = 1/2 The Grandi series, of course.
s=0
n=1
Do while 1=1
...s=s+n
...n=1-n
End Do
print s
End Program
Introducing multiply
Program 0 +1*1+2*2+3*3+... = 0 works in "renormalization" of physics (sum of squares of natural numbers)
s=0
n=1
Do while 1=1
... s=s+n*n
... n=1+n
End Do
print s
End Program
Introduce the division operator and double n at each step instead of merely count.
Program 0 +1/1+1/2+1/4+... = 2
s=0
n=1
Do while 1=1
... s=s+1/n
... n=n+n
End Do
print s
End Program
Kharakov
Quantum Hot Dog
Yup. They used the method I used to get the values 1/3, 1/4, 1/5, etc.. for 1-2+3-4+5....
s=1+2+3+4+5...
-4s = -4 - 8 -12...
-3s = 1-2+3-4+5...
In other words, you can get any answer by that method.
1-2+3-4+5... = 1/3 or 1/4 or 1/5 or...
1+2+3+4+5... = -1/9 or -1/12 or -1/15...
Don't really care that the Riemann zeta function allows a analytic continuation for it which gives -1/12. Just because someone uses some sketchy math to fudge something, doesn't mean its right.
beero1000
Veteran Member
The divergent series are the invention of the devil, and it is a shame to base on them any demonstration whatsoever. 
Have any of you ever checked out http://math.stackexchange.com? Makes me cross-eyed.
I was good at math in high-school, but I look at that site and go.. damn.
I was good at math in high-school, but I look at that site and go.. damn.