
202019 A really thought provoking idea to me is how "much" entropy effects our world. It effects our world so much, it seems to me, that you can really only define time "locally" which respect to a specific point you picked in time. For example, in computer simulations of waves, the form of the wave can be well defined just after the wave starts, but after awhile, this wave looks like all other waves no matter what shape of wave you start out with. This is entropy at work. Henri Bergson spoke of time in a subjective way. It's a way of viewing time more compatible with quantum theory or as some physicists used to refer to it as wave mechanics. This is strikingly obvious when you observe the propagation of waves, especially observing dispersion of waves in time. If you try to model wave propagation using sequences of numbers, then the sequence is only significant in its behavior at the beginning of the sequence. If you then model the sequence as binary tree structure containing information, the most of the model deals with the sequence when the sequence starts. This is inherently dynamical in nature. You can refer to this type of dynamicity as ergodic. You can refer to this type of tree as a prefix tree or trie. This fact of time being actually significant only at certain points in time leads one to think that the "duration" of time is important. I think duration is important only because you "distinguish" experience at points in time. Now, with respect to physics, time is a complimentary aspect of energy. We experience "energy" when our sensory organs feel changes in the energy fields around us. If you try to simulate energy changes in waves on a digital computer, you can use a model which is based very generally on pulses. A good example is computing the energy fields in classical heat distributions using differential equations and Fourier series. Bergson sort of tried to give importance to how time forms a kind of memory of past events. I made this mistake also (I maybe wrong here about Bergson, but time is not "an accumulation"). I'm guessing that Bergson was wrong here. You really cannot experience the "flow" of time in the continuous sense with a ticking wall clock without memory. Bergson refers to memory incorrectly in his temporal accumulation hypothesis. Bergson might have been right if he said temporal events could be correlated, connected or tied together using memory. It's a very subtle point (but I may be wrong). Without memory there would be no way to transfer state information in temporal events. You can't just assume that time carries that much information over a long duration. [3] For awhile, I tried to see how I could extrapolate temporal information over long sequences. I didn't get anywhere. Waves, as dynamic sequences, are ergodic. So I don't think you can build models solely on the nature of time because most of this kind of thinking Bergson makes is meaningless with respect to the physical world. It has significance if you apply this kind of thinking to how humanbeings think. The fact that energy propagation is ergodic leads me to think that time as conceived in relation to Einstein's relativity is really very geometrical ... purely geometrical in which the math of Minkowski works to perfection. The stuff of "waves" happens inside the geometry of spacetime. (I might REALLY be wrong here!) I'm basing this on intuition, but I thought about this alot. So time takes on two views: (1) that of a subjective view like Bergson's and (2) that of on objective view like Einstein's. I think both are correct. The above paragraphs are obviously full of mistakes. It's up to you to work it out also. I expect you to think this through for yourself. It's too important not to think it out for yourself. The treasures here are obvious to me. I greatly admire Satosi Watanabe's work on time. He showed that there are processes in Nature in which you can predict things happening in the future, but not in the past. Entropy or ergodicity determines the flow of time, and retrodiction. This work on prediction and retrodiction [1], reminds me of Bergson's work, but Satosi Watanabe was an incredible mathematician. Professor Watanabe mathematically showed how time is intertwined "within" or emerges from entropy. When I attended his classes, I was just mesmerized with his skill in mathematics. There was no one I've met in person that could do math like he did. Both Bergson and Watanabe were poets. Anyway, retrodiction is an important concept because it shows how entropy works in Nature. Another great work on entropy is Alekandr Khinchin's work in which he brilliantly summarizes what erogodicity is. In his conclusion to his great book [2] he say: The channel we are given is a noisy channel. This means that we cannot determine the sequences of symbols sent at the channel input from the sequences received at the channel output; because of noise, two different sequences at the channel input can give rise to the same sequence at the output. This to me is incredible. I'm sure it is to you also. If not try to understand the above quote by reading it over. It's worth it. The quote above by Khinchin is really, in essence, simple. The math in his book, however, is not so understandable because of its complexity. I think you can read through the stuff on this webpage without formal math training if you're good at using your imagination or intuition. Even if you do know lots of math, you'd still need to use your intuition to understand the world. So if you have questions, just send me an email. The stuff above has multiple levels, and confuses me. Any comments are welcomed.[1] Time and the Probabilistic View of the World, Satosi Watanabe, p. 527, in The Voices of Time, ed. J. T. Fraser., 1966. [2] Alekandr Khinchin, Mathematical Foundations of Information Theory, Dover Publications, Inc. 1957, p. 117. [3] I think Bergson is correct in saying memory needs a connection to time, as in: if time is substance, and memory is form.
