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The Conservation of Information...

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Re: The Conservation of Information...

Postby Whateverman » Mon May 31, 2010 5:14 pm

I've just thought of something: doesn't the amount of information associated with a system increase with time? I can take a snapshot of a ball bouncing in a room and have a certain amount of information, but there'd be more if I could explain how the ball got to its current state (how fast was moving a second ago, where it came from, which parts of the room it hit, etc). It'd be like a video of a potted plant; the image doesn't change much, but the amount of film increases as camera keeps rolling.

Does conservation of information only apply to 3 dimensional (timeless) systems?
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Re: The Conservation of Information...

Postby ExPatMatt » Wed Jun 02, 2010 3:13 pm

Whateverman wrote:Since we can only be aware of information when we have symbols to identify and express it with, any system could have an infinite amount of information, as there'd be an infinite number of ways of expressing the patterns it contains.


Information is only definable/quantifiable when it can be deciphered? So information becomes a subjective thing?

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Re: The Conservation of Information...

Postby Whateverman » Wed Jun 02, 2010 3:44 pm

ExPatMatt wrote:
Whateverman wrote:Since we can only be aware of information when we have symbols to identify and express it with, any system could have an infinite amount of information, as there'd be an infinite number of ways of expressing the patterns it contains.


Information is only definable/quantifiable when it can be deciphered? So information becomes a subjective thing?

I think so, yes.

"Information" must exist in the form of a pattern; something which can be decoded to provide understanding. Cognitivie scientists have long-known that the human brain is wired for pattern recognition, such that we even tend to find them where they do not exist. There are plenty of references on this, but I'm gonna hafta leave it up to you to do further searching.

Information can exist regardless of our abilities to recognize it, but until we have the symbology with which it can be detected, it remains "hidden". A string of characters can be interpreted to mean multiple things, so how do we qualify & quantify the amount of information it contains? The interpretation of Scripture is a good example - how many meanings can be attached to a single passage? What if there are languages yet to be invented which derive other novel meanings?

The real problem here, one which everyone except the fundies recognize, is that "information" isn't defined very well. The ratio of a circle's radius to its area is 3.141593... in base 10 numerology. The ratio is different in binary; it happens to be 10.11111110111111011001... What's the base 10 value of pi, written in binary, but interpreted in base 3 numerology? I think it's 12.220121110022 (<-- I don't know where the decimal point belongs!)

A string of characters can be interpreted differently, and the interpretations do not have to agree. While this doesn't mean (practically) that every string can have an "infinite" number of meanings, it certainly implies that meaning must be linked specifically with the method used to derive it.

And this means that the amount and kind of information in a thing is relative. Perhaps subjective too.
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Re: The Conservation of Information...

Postby rhiggs » Wed Jun 02, 2010 6:37 pm

I'm probably missing something, but here's my take on it...

Since different people can glean different information from the exact same source, this means that the very existence of information is subjective. It is fallacious to say that 'the information is there, you're just not seeing it', because that would leave open the possibility that there is additional information present which nobody has seen, and hence refutes the notion that there is a quantifiable amount of information in the first place. There could always be more information. Thus, it is impossible to assign a tangible value to the amount of information in any system at any time, and so it is also impossible to definitively state whether it has increased or not - the amount of information might have increased for one observer but decreased for another.

Example: Two men watch a library and all its original contents (no other copies) burn to the ground. The first man observes a loss of information as hundreds of thousands of original books are incinerated. Most people would probably agree with this man. However, the second man, who is not interested in literature, observes an increase in information because he is an arsonist and has thus gained plenty of information from the experience. Who is to say that more information was lost than gained? What if 2 arsonists gleaned information from the fire? Would that mean that twice as much information was gained? If so, what if a billion arsonists were watching? By increasing the amount of arsonists watching, at some point in theoretical space more information would have been gained than lost. The same can be demonstrated the opposite way too, meaning information is subjective and can't be quantified or said to have definitively increased or decreased.
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Re: The Conservation of Information...

Postby E-lad » Wed Jun 02, 2010 6:43 pm

Very interesting, Rhiggs. Very intersting, indeed.
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Re: The Conservation of Information...

Postby Hugo » Wed Jun 09, 2010 4:13 pm

Very interesting yes. I had never thought of information being subjective but it is so obviously the case.

I think this can be used the other way around to explain why DNA is NOT information per se. The atoms that form the DNA cannot be interpreted differently by the organism because they are not interpreted at all, they just bound chemically with other atoms. The process constantly evolve and might not work the same in a million years as it did a million year ago, but that's not in any way similar to the different interpretation of '0xFFFFFFFF' for example...
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