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disprove info theory

Name: Anonopolis 2011-08-29 5:39

Conversation that took place between me and him. This was after a few months of him vaguely mentioning a project he had been working on.

Cameron Kenworthy
But I just disproved Shannon's information THEORY!!! AND YOU ARE THE ONLY PERSON WHO IS SMART ENOUGH TO UNDERSTANTD!

ME:
Hmm
I've never studied the theory before
but I just looked at the Wikipedia article and it doesn't even have a controversial section

MY FRIEND:
It's really simple I'll explain

ME:
proceed

MY FRIEND:
I KNOW!
Shannon states that there is a limit of lossless compression of a message
this is referred to in his equations as H, or entropy rate
He also states that you cannon consistently compress any message do to the fact that the data making up the message is random
In its initial state a message (like a file) has an entropy value, the total amount of information held in each character of the file
for computers it's 1 bit per character (binary duh)
The total entropy for the compressed message is equal to the initial message, therefore the entropy for each character is larger in the compressed message than the inital, but still limited by Shannon's formulas
But imagine being able to generate a seed based on any set of data (fucking impossibly difficult and convoluted I know, but bear with me) that could be used to regenerate the data, each character within that seed would have well past 1000 times Shannon's limit of entropy rate for a standard 15 kB picture!

MY FRIEND:
I refuse to tell you how I did it at this point but I devised a set of algorithms to derive a seed for any data set, from 100 bits to 100 trillion terabytes, therefore I proved that Shannon's source code theorem defining the limit of entropy rate is wrong, which redefines the past 60 years of information theory

MY FRIEND:
and the computer as we know it

ME:
and this seed is... small?

MY FRIEND:
yes, its like a seed for generating a minecraft world, its a few characters that creates a billion

ME:
but the billions it creates is random
er... pseudorandom

MY FRIEND:
yes but it is consistent and defined by the seed
so the seed will generate the same thing every time

ME:
Hmm...
Very interesting
How long does it take to generate the data from a seed?

MY FRIEND:
therefore, if you can go backwards, and start with a billion sized value and then create it's seed you break the entropy limit
exactly the amount of time it takes to make the seed from the data
because you use the inverse of the formulas for decompression that you used for compression

ME:
Genius

MY FRIEND:
*algorithms, not formulas
I KNOW!

ME:
but...
Does it work?
I mean, have you tested those algorithms?

MY FRIEND:
I didn't realize that its exactly what I've been doing for the past 3 months
Yes, it works!
Excuse me for withholding the trillion dollar explanation though
don't worry, I'm writing down all of my smart friends that I will pay their college fees and give them jobs

ME:
That's very benevolent of you

MY FRIEND:
agreed

ME:
Can you show me an example?

MY FRIEND:
Hmmm.... Well, I can compress the film american beauty to 54 bits, and then decompress it

ME:
I think the data compression and decompression would be very slow for a whole movie, wouldn't it?

MY FRIEND:
I could probably get it smaller than that actually
Nope
a blink of an eye

ME:
But...

MY FRIEND:
... maybe two blinks

ME:
But a whole movie would be millions of numbers

MY FRIEND:
billions actually

ME:
the seed would have to do a bunch of calculations to get each number

MY FRIEND:
haha, and therein lies my secret
just think about fractals
And that's all I'

ME:
fractals...

MY FRIEND:
ll give away
Mandelbrot has outdone himself from the grave

ME:
one small pattern, turning into a large uniform one
hmm

MY FRIEND:
exactly

ME:
Ok, I'm just going to look at this logically

MY FRIEND:
go ahead

ME:
There are infinite ammount of possible sets of data

MY FRIEND:
correct, as infinite as its number system that is

ME:
You would need a unique seed for each set

MY FRIEND:
correct
don't worry, there are limits to the seed, but they far exceed (trillions of trillions of trillions of times) Shannon's limits

ME:
That means there are as many seeds as there are sets of data

MY FRIEND:
correct, infinite amounts

ME:
Let's say you wanted to compress the letters "A", and let's just say the seed for that is '1'
then "B" would be '2'

MY FRIEND:
I'm kind of leaving out a key concept here that would make it way simpler for you to understand, sorry about that
but computers cant think in 2

ME:
then "B" would be "10"

MY FRIEND:
2 is the same size as B to a computer

ME:
anyway
yes
yes it is
Compression usually works by shortening of duplicate patterns
But... but... I don't get it!

MY FRIEND:
yes but the only way a computer can read binary is by knowing that all the characters are exactly the same lenght, or else it doesn't know which 1 does what
You will, give me a few months, Dan and I need to pay for legal fees and what not

ME:
Right, thanks
I wouldn't trust me either

MY FRIEND:
I just needed to shit all over Claude E. Shannon's life work ASAP

Name: Anonymous 2011-08-29 12:19

>>7
Therefore, space is obviously discrete. Assuming it is continuous, how would you sample the atom's position?

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