exponential change

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exponential change

Postby TerraFrost » Fri Nov 07, 2003 3:46 am

well... i've been reading the age of spiritual machines, as per one of my CS classes, and, despite just finishing the first chapter, i have a few quirks with it...

a lot of people like to say that change occurs at an exponential rate. either it exponentially speeds up or it exponentially slows down. consider the "evolution" of technology. it may have taken us hundreds of thousands of years (or tens of thousands - i'm not sure how long humans are thought to have lived) for us to develop fire, but in this past century alone, we've developed video / audio playback devices, fusion, computers, photography, cars, airplanes, the light bulb, etc.

additionally, consider the "evolution" of evolution. it took billions of years for the universe to create a single cellular organism, but only took tens of thousands of years for it to create man.

finally, consider the "evolution" of the universe. in the first few seconds after the universe is said to have began, we had change on a huge scale. gravity is said to have come about in the first 10^(-43) seconds. 10^(-34) seconds into the big bang, electrons were created, as were other forces (gravity, the strong force, and the electroweak force). 10^(-6) seconds into the big bang, the electroweak force was split into two sep. forces - the electromagnetic force and the weak force. a bunch of other changes occured that the book, the age of spiritual machines, mentions, but i won't bother to mention them here. sufficide to say, the period between these events slowed down. now, it may well take billions of years for events such as these to happen.

so anyways, that's the basic premise for why people say change occurs at an exponential rate, be it increasing or decreasing.

however, one small point that the author (ray kurzweil) forgot to consider... not all change is equal. reducing the size of the transistor by a micron, for example, is *not* as profound as the initial development of the transistor. likewise, i would argue that the birth of man is not as important on the grand scheme of things as the birth of single cellular life was. similarily, the birth of single cellular life was not as important as the creation of the universe was.

so anyways, what i would argue, as an alternative to ray kurzweil's view, is that, while, with time, the importance of each progresive change decreases, the importance of all the changes at any given time, put together, should be equal to the importance of the first change - that is, the birth of the universe. ie. the importance of overall change is constant, but individual change is going to necessarily be less important.

something ray kurzweil likes to mention is the second law of thermodynamics (which i'll start another thread about). i believe the above theory works much better with this law than the theory of exponential change that kurzweil does present (he calls it the law of time and chaos).
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Postby TerraFrost » Mon Nov 10, 2003 7:32 am

bah - i said i'd start a new thread about the second law of thermodynamics, but i'll just explain how my proposed law works quite nicely with the second law of thermodynamics, and in doing so, hopefully explain that law, as well :)

the second law of thermodynamics states that things in disorder tend towards disorder. as an example of this, consider the throwing of a glass at a wall. the resultant pieces of that glass, one would expect, would fall randomly on the floor. if you were to pick up all those pieces, and throw them back at the wall, one would quite reasonably expect them not to fall randomly on top of each other, reforming a glass, randomly.

however, while the overall system may tend towards disorder, there can be, and indeed, should be some order within that system. the order that would result from a shattered glass may be hard to spot, so here's another example. say you are randomly generating an infinitly long sequence of numbers. within that random sequence, there *should* be atleast one occurance of exactly ten consecutive numbers. to calculate the exact probabilities with finite sequences, you'd have to use combinations and permutations, and i don't like those, so i won't, heh. but sufficide to say, there should be some order within a system of disorder. lack of any order would suggest that the system wasn't really random.

so, the theory of change presented above tends towards disorder, however, within that disorder, there can be some highly ordered changes.
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Postby slayerchange » Mon Nov 10, 2003 2:50 pm

Actually, change accurs at an exponential rate , is not seems true. But every change can be expressed as an exponential function , might be more true.

:) ,and second law of thermodynamics implies "We Will Die " :( . puhhahahha. Andit also implies, our bones will be destroyed, and we will be nothing but a small partical that creates the chaos in the universe , after 1000 years :)).
As an old cheat says:
" It is a good day to die " :)
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