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bloodsheen
ChemChaplin



Registered: 09/24/08
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Re: Found this pretty good explanation for how large Graham's number is [Re: realfuzzhead]
#20112413 - 06/11/14 12:02 AM (9 years, 8 months ago) |
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realfuzzhead said:
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bloodsheen said: Again not being a buzzkill on purpose. My math jizz days are just over.
My final loss of mathimatical innocence occured when I truly grasped the concept that all measured, non quantized, figures are ALWAYS estimates because all figures must round eventually. So the universe CANNOT be explained with a perfect equation because numbers are too abstract to describe the perfection of the innumerable forces in the universe. Let me say that again. NUMBERS are TOO ABSTRACT to describe why the universe truly works
This is a pretty interesting concept and if you thought of this all on your own that is pretty impressive because it's actually a pretty well studied concept. Basically, the real number line is infinite, but there are not an infinite number of possible different computer programs out there to calculate all of these numbers. A computer program can only have as many variations as the message space of its bits. So if a computer program is 3 bits long, you can have the following programs
000, 001, 010, 011, 100, 101, 110, 111
Since there are 8 possible ways to arrange 3 bits, there can only be 8 possible numbers this program can calculate (probably less because some might repeat and some might be nonsense). In general, the upper bound on the size of the message space of a computer program with n bits is 2n.
Since there are only so many bits available at are disposal ( we can only go so far into the universe before we cross a barrier where information cannot travel back to earth because the universe is expanding fast than our signal can get back ), this means there are only a finite number of computer programs that once can make. A finite number of computer programs can only compute a finite amount of numbers. Since there are an infinite number of real numbers, an infinite amount of them cannot be calculated.
tl;dr there is an infinity of numbers we cannot physically calculate
I actually lost some sleep over this. It occured to me while I was taking Physical Chemistry and was considering the effect of gravity on my desk from mars. And Pluto and so on. I went into my profs office to discuss this and he reminded me that at a certain point the quantum probability of an event happening to my desk would make a concrete number impossible to measure due to the Schrodinger paradox.
Literally on that day I stopped caring about math
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A cautious young fellow named Lodge / Had seat belts installed in his Dodge. / When his date was strapped in / He committed a sin / Without even leaving the garage. That's clever, isn't it?-A boy and his dog
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realfuzzhead



Registered: 03/03/10
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Re: Found this pretty good explanation for how large Graham's number is [Re: Shroomslip]
#20112418 - 06/11/14 12:05 AM (9 years, 8 months ago) |
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It's like this
Lets say we have some number x
x = 1,000,000,000,000,000,000,000,000,000,000.......,000,000,000,000
Where there are 1 million (1,000,000) zeros total
now lets say D1 = the number of digits in x
D1 = 1,000,000
Because x has a million digits, D1 is a million.
Now lets say we have a number D2 = the number of digits in D1
D1 = 1,000,000 - this has 7 digits total
D2 = 7, because D1 has 7 digits.
Now see what we just did, we took a number x that is larger than the number of atoms in the universe, and in two steps we brought it down to 7. Now imagine repeating this process on a number trillions of trillions of trillions of times, and still ending up with a number that is larger than the number of atoms in our universe.
That is how this image tries to explain Grahams number
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realfuzzhead



Registered: 03/03/10
Posts: 10,783
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Re: Found this pretty good explanation for how large Graham's number is [Re: bloodsheen]
#20112430 - 06/11/14 12:08 AM (9 years, 8 months ago) |
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I don't think that's a reason to stop caring about math though, look how far we have come in spite of the fact that an infinity of numbers are non calculable and thus will never be exposed by humans. There's no reason to think that mathematics is futile just because of this fact. And it also doesn't apply to equations. If you get an equations correct that symbolically defines one quantity in terms of another it doesn't matter that you can't calculate the actual solution, we can approach the solution to whatever precision we desire. Either way we have a symbolic method of dealing with the incalculable number in question and thus aren't really limited all that much.
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Shroomslip
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Re: Found this pretty good explanation for how large Graham's number is [Re: realfuzzhead] 1
#20112434 - 06/11/14 12:10 AM (9 years, 8 months ago) |
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Quote:
realfuzzhead said: It's like this
Lets say we have some number x
x = 1,000,000,000,000,000,000,000,000,000,000.......,000,000,000,000
Where there are 1 million (1,000,000) zeros total
now lets say D1 = the number of digits in x
D1 = 1,000,000
Because x has a million digits, D1 is a million.
Now lets say we have a number D2 = the number of digits in D1
D1 = 1,000,000 - this has 7 digits total
D2 = 7, because D1 has 7 digits.
Now see what we just did, we took a number x that is larger than the number of atoms in the universe, and in two steps we brought it down to 7. Now imagine repeating this process on a number trillions of trillions of trillions of times, and still ending up with a number that is larger than the number of atoms in our universe.
That is how this image tries to explain Grahams number
Well shit, that's a lot easier to understand.
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With my face against the floor I can’t see who knocked me out of the way. I don’t want to get back up but I have to so it might as well be today. Nothing appeals to me no one feels like me, I’m too busy being calm to disappear. I’m in no shape to be alone contrary to the shit that you might hear. You can't wake up, this is not a dream. You're part of a machine, you are not a human being With your face all made up, living on a screen. Low on self esteem, so you run on gasoline
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bloodsheen
ChemChaplin



Registered: 09/24/08
Posts: 7,659
Last seen: 4 years, 1 month
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Re: Found this pretty good explanation for how large Graham's number is [Re: realfuzzhead]
#20112453 - 06/11/14 12:21 AM (9 years, 8 months ago) |
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Quote:
Shroomslip said:
Quote:
realfuzzhead said: It's like this
Lets say we have some number x
x = 1,000,000,000,000,000,000,000,000,000,000.......,000,000,000,000
Where there are 1 million (1,000,000) zeros total
now lets say D1 = the number of digits in x
D1 = 1,000,000
Because x has a million digits, D1 is a million.
Now lets say we have a number D2 = the number of digits in D1
D1 = 1,000,000 - this has 7 digits total
D2 = 7, because D1 has 7 digits.
Now see what we just did, we took a number x that is larger than the number of atoms in the universe, and in two steps we brought it down to 7. Now imagine repeating this process on a number trillions of trillions of trillions of times, and still ending up with a number that is larger than the number of atoms in our universe.
That is how this image tries to explain Grahams number
Well shit, that's a lot easier to understand.
Yea this is the non-math douches way to explain it lol
Quote:
realfuzzhead said: I don't think that's a reason to stop caring about math though, look how far we have come in spite of the fact that an infinity of numbers are non calculable and thus will never be exposed by humans. There's no reason to think that mathematics is futile just because of this fact. And it also doesn't apply to equations. If you get an equations correct that symbolically defines one quantity in terms of another it doesn't matter that you can't calculate the actual solution, we can approach the solution to whatever precision we desire. Either way we have a symbolic method of dealing with the incalculable number in question and thus aren't really limited all that much.
I just was no longer interested. I had come to the brink of my ability to grasp the math I was learning and began to see how a logical religion/philosophy could arise. But in one day of high imaginings (oh yea forgot to say I was baked) I essentially disproved the supposed infallibility of math.
Not to say its dumb or useless just...overrated
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A cautious young fellow named Lodge / Had seat belts installed in his Dodge. / When his date was strapped in / He committed a sin / Without even leaving the garage. That's clever, isn't it?-A boy and his dog
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