Infinite Possibilities in Life, or NOT!

[alexander]

This is something that has I have myself pondered, and just yesterday, my friend Pete(dellcom) actually pointed me back in this direction, so I decided to post.

 

You will see how the following goes with CS (more so then with philosophy or anything else).

 

So, have you ever wondered if there is a limit to life, is there any one number that can encompass anything and everything that can possibly happen? Yes, i know how philosophical this actually sounds, but to the point.

 

Say that everything, or every eventthat can ever happen can be encompassed in a picture; picture paints a 1000 words, movies are pictures with music, etc. And say we choose the picture to be an 800 by 600 in size. It seems that the possibilities are endless, but are they? A picture of 800 by 600 in 24 bit color, a bit can represent 2 values, therefore 2^24 is the total amount of color combinations for any pixel. Now factor in a field 800 pixels wide and 600 pixels high. So the total amount of possible combinations of colored pixels in the field of 800x600 can be expressed as [math](2^{24})^{800*600}=(2^{24})^{480000}=2^{11520000}[/math]

(anyone have bc and a lot of time, maybe i do, we will see how long its gonna take...)

 

Basically however, this encompasses any picture of any event anyone can ever possibly take in any dimension, on any planet, anywhere, of any planet or organism, and any video that can be taken of any possible phenomena in 800x600 resolution... Interesting to think about it, isn't it.

 

(btw if anyone decides to move this post to another part of the forum, please, at least ask me before doing so, there is reasons why i posted it here, in CS over philosophy or math/physics)

[alexander]

came out to be a 3 meg text file

 

be sensible, i only have 6gb transfer /month, and i had to host it on my box, for time savings....

 

you can view the answer file:

http://linuxconversions.com/infty.txt

[alexander]

in short its [math]3.5485*10^{3518864}[/math]

[Buffy]

(btw if anyone decides to move this post to another part of the forum, please, at least ask me before doing so, there is reasons why i posted it here, in CS over philosophy or math/physics)

As long as you stick to binary exponents, it belongs in CS...

 

The Power of 2, :eek_big:

Buffy

[alexander]

how about representing the power in Hex? :)

[dellcom]

Ok i was just about to post my file alex, but i see you beat me to it. Now the trick is can we write software that will do object recognition to only store images that are not composed of static (which will save a significant amout of space). The best way i can think of is do you in stages. The first stage look for one group of objects, for instence coke cans, then people, then ..... The images could then be tagged with their contents so the database could be easily searchable. The trick is getting the software, the massive amount of disk space, and computing power to pull this off.

 

 

maybe we should call google...

 

and the accuall number is 3.548534*10^(3,569,864 bytes) not counting the slashes in the file (i took them out)

 

--pete

[Jay-qu]

Very cool alex ;) reminds me of the way I think sometimes

 

So if this is a video, running at 24fps for 2mins... :)

[Buffy]

how about representing the power in Hex? :)

That's perfectly fine, but decimal is not onto the group binary or hex...

 

Abstractly,

Buffy

[alexander]

oopsie, first of all a typo in my previous post, its to the power of 3518864 (i just thought of something else)

 

so now why is dellcom wrong (no offense Pete ;) ):

 

execute:

#wc -c infty.txt

3569863 infty.txt

but if you cat the file, you will see that every single line is delimited by a \ at the end of it, so we need to know how many slashes we need to count out of the total # of characters

#wc -l infty.txt

50999 infty.txt

now

#tail infty.txt

last line does not end on a slash therefore

3569863 - (50999 - 1)

to get the total number of digits in the answer

you can even bc it

# echo '3569863 - (50999 - 1)' | bc

3518865

 

so that is the total amount of digits in the answer, now to the exponent part

first line of the file reads:

#grep -m1 '^' infty.txt

35485347568249036055446802957154058824287799932924395201661061923085\

 

and you determine to use 3548534, ok, so, 3.548535 first of all because there is a seven after it, then there is the 10^power to consider.

 

[math]1_12_23_34_45_5 = 1.2_13_24_35_4 * 10^{\underline{4}}[/math]

similarly if we have 3518865 total places then we need to subtract one to make it the correct exponent of 10 for our use, so the final answer should be:

[math]3.548535*10^{3518864}[/math]

 

i mean, check my math, pretty sure that i'm right :)

[CraigD]

Alexander appears to be engaging in the venerable pastime of musing on how easily everything can be mapped to fairly manageable integers. If Neil Stephenson’s Baroque Cycle books are anywhere close to an accurate depiction of real history, folk like Leibniz have mused similarly for at least the last 300 years.

 

An interesting consequence of this sort of thinking is that, given enough time, you can generate any of whatever you’ve mapped to integers through a simple process of incrementing, beginning with zero. To use Alexander’s example, starting with 0 as a completely black image, we could begin counting 1, 2, 3, etc, eventually reaching an 800x600 rendering of, say, the Mona Lisa, or a family picnic of bug-eyed aliens actually occurring on a planet in another galaxy (though we would likely never know that it was an accurate depiction of a real event, not fanciful) - a variation on the infinite monkey theorem one might term “a large number of perfectly systematic monkeys”. ;)

 

My favorite part of “The Emperor's New Mind” (As much a must read for math and computer heads as GEB, never mind the tentative quantum mysticism) is where Penrose applies this thinking to the program tapes of a Universal Turing machine of his invention (conveniently, one using a 2-symbol, binary alphabet), noting that every possible computer program can be found by counting from 0 by 1, and actually proceeds to count the first several million or billion, noting the first integers that correspond to programs one might consider “interesting”. This process would, in principle, eventually produce a program that would simulate in perfect detail this thread, down to the clock tick that each of us post our exact text.

 

:) A question that really, truly, deeply, profoundly intrigues me is if there exists one of these UTM tape integers corresponding to a program that, for example, produces the complete works of Shakespeare, where the length (bits) of the integer is dramatically less than the length of the complete works of Shakespeare after they have been compressed by a good, non-lossy algorithm. This thought rounds on the idea inspiring one of my first hypography threads, 3203, a variation on the compression challenge (AKA “Mike Goldman’s $5,000 compression challenge”) – a short thread of mine one might accurately describe as “the thread that time forgot” :eek:

[alexander]

hey craig,

i used to know a guy, who's friend wrote a perl script that was a poem or haiku generator, that he used to pass his english class. It was fairly intuitive, but used a database of verbs and adjectives that it combined in different ways to make these haiku. Apparently it was good too, but i never got my hands on the script, and then he went to jail for something :)

[alexander]

Case and point i guess, there is most likely a division of google that is working on a content generator, an algorithm that will generate custom news articles for google news page, based on a basic outline of the event, on a per-user basis. Now, i have no way of confirming that ofcourse, but i believe there is... But think about the implications of a piece of code like that, changes the world of news like GUI changed OSes...

[CraigD]

in short its [math]3.5485*10^{3518864}[/math]

Following a quick check, I believe there’s something very off with this approximation.

 

[math]2^{24*800*600} = 2^{11520000} = 10^{\frac{\log 2}{\log 10}11520000} \dot= 10^{3467865.55}[/math] a number much smaller than [math]3.5485*10^{3518864}[/math]

 

Am I missing something? How did you calculate your number, alexander? :QuestionM

 

When I get home, I’ll see if I can write all 3-ish MBs of the exact decimal value of [math]2^{11520000}[/math] to a file. The last digit will be 6 ;)

[alexander]

i use GNU arbitrary point calculator called bc

i am pretty user that i'm not running out of any of the limits....

#bc
limits
BC_BASE_MAX     = 2147483647
BC_DIM_MAX      = 65535
BC_SCALE_MAX    = 2147483647
BC_STRING_MAX   = 2147483647
MAX Exponent    = 2147483647
Number of vars  = 32767

i may be wrong i guess

but it seems unlikely that a power of 2 will be = to anything ending with a 0, therefore the .55 is a round up, and in a number with precision over a million places, those places may mean that difference that you are seeing...

 

let me rerun your math.... its not that simple

[alexander]

can someone with a desktop run this? (fast one at that, preferably dual core or dual dualcore with at least 2 gigs of ram, preferably 64 bit too.... it will eat up hours probably)

 

cat "scale=5000000;10^((l(2)/l(10))*11520000)" > test
cat test | bc -l > infty_craig.txt

[alexander]

oh also tail the end of it, you will probably have 3,000,000 zeros after the point... or so

[alexander]

prolly wanna write a script to delete all the zeros after the .