Some comments on information theory

  • Thread starter Thread starter Cleopatre VII
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I hope ya'll don't mind my participation in this thread. I'm not very much educated formally in mathematics but the topic is very interesting to me.

John Napier was a Scottish Laird. So is there useful information in the romance novels about logarithms? About the time he "invented" logarithms people began making slide rules. A few months ago for some reason I became interested in and purchased an antique slide rule. A K&E that had been owned by a naval engineer who likely was involved in work with rocketry and space vehicles.
 
dennis said:
I hope ya'll don't mind my participation in this thread. I'm not very much educated formally in mathematics but the topic is very interesting to me.

John Napier was a Scottish Laird. So is there useful information in the romance novels about logarithms? About the time he "invented" logarithms people began making slide rules. A few months ago for some reason I became interested in and purchased an antique slide rule. A K&E that had been owned by a naval engineer who likely was involved in work with rocketry and space vehicles.
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I was using a slide rule when I was studying physics and analyzing results of experiments. Like that by K&E. I hated it. Then computers came. At first I was appaled by the thought of using something artificial instead of my own head. Then I became enthusiastic about them. Yesterday I was talking to Laura about how lazy I became because of relying on computers to do the boring calculations for me. With computers we do not to so many calculations in our heads Many circuits in our brains deteriorated because we don't use them any more. Is that good or bad? Today, for instance' I was using Mathematica and Reduce symbolic computer programs and got the results that it would take me months to calculate them by hand using pen and paper and relying on my own calculating powers.

Returning to order and chaos and entropy. Perhaps the issues is that many many different piles of pieces of the puzzle we perceive jutas "piles" that we do not distinguish one from the other, while the fully assembled picture can be done so in only one way? But that is subjective, not objective. And subjective is not "for a person". It is for the whole "society", perhaps for the whole "species". To what extent our DNA is responsible for the way we perceive and interpret the world? Are all "the laws of physics" subjective in this sense? But then is there also an objective description? Gurdjieff was thinking about that as well and came to a rather bizarre view of the world expressed in his Beelzebub's Tales. C's present us with a similar bizarre view. But how to make it scientific?
 
ark said:
Returning to order and chaos and entropy. Perhaps the issues is that many many different piles of pieces of the puzzle we perceive jutas "piles" that we do not distinguish one from the other, while the fully assembled picture can be done so in only one way? But that is subjective, not objective. And subjective is not "for a person". It is for the whole "society", perhaps for the whole "species". To what extent our DNA is responsible for the way we perceive and interpret the world? Are all "the laws of physics" subjective in this sense? But then is there also an objective description?
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I have "resonated" strongly with this and perhaps the explanation is on that path.

Today there are 6,582 people registered in this Forum.

The "consensus" and the way of "seeing" life for these people is so different that ...

"Elementary" concepts here are totally unacceptable to billions.
 
The objective description would be the real world happenings that are demonstrations of the mathematical theories. Examine everything, even mundane events/things and compare them to the academic mathematical concepts. You can see correlations and relationships. Try an experiment, ask a question of the universe and then go the grocery store or the museum or the train station, or just go about your normal business. If you are receptive to the idea that an answer or example (usually also containing even more questions) can come to you in this way and are observant but not expecting anything particular, interesting things begin to happen. At first its kind of frightening, then it gets to be easier and even highly playful.

However, most people would probably call this the operational definition of insanity.
 
dennis said:
The objective description would be the real world happenings that are demonstrations of the mathematical theories. Examine everything, even mundane events/things and compare them to the academic mathematical concepts. You can see correlations and relationships. Try an experiment, ask a question of the universe and then go the grocery store or the museum or the train station, or just go about your normal business. If you are receptive to the idea that an answer or example (usually also containing even more questions) can come to you in this way and are observant but not expecting anything particular, interesting things begin to happen. At first its kind of frightening, then it gets to be easier and even highly playful.

However, most people would probably call this the operational definition of insanity.
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I am afraid almost everybody does exactly what you have described. And nevertheless there are no breakthroughs. And, as far as I know, Einstein or Dirac were not visiting the grocery stores. A bath, though, may be of help, as the story about Archimedes tells us, and as I have experienced myself several times. But apparently my baths did not last long enough, or the water was not right, for a major breakthrough
 
ark said:
We have already learned from previous posts that the probability of arranging the pieces exactly as in the first picture is the same as probability of arranging them as in the second picture. If so, why do we consider the second picture as "order" and the first one as "chaos"? This I would like to see explained. Is there more than just probability in the concepts of entropy and information? Or one should be very careful when applying probabilities? And why does Nature care about probabilities? Are they objective? Or are they subjective? And if they are subjective, why they seem to work nevertheless?
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I think we consider the second picture as "order" because it is the only arrangement which matches the intent of the creator of the puzzle. Maybe this is where there is "bridge" to consciousness. The creator has imagined a puzzle and has decided to give it a physical manifestation. The puzzle can be altered or destroyed, but its original, non-material meaning remains intact and can be reproduced by its creator (or anyone who has access to the puzzle's corresponding thought pattern).

If we tried to replicate the first picture using the same pieces in a different place, we would need a very detailed instructions manual, i.e. order. By using very precise measurements, the first picture would then be laboriously replicated and people would proudly claim the end result as "order", even though it would be indistinguishable from the chaotically-generated version.

It seems that there is order in chaos (pattern forms "out of nowhere") and chaos in order (pattern is unique).
It is easy to generate a chaotic situation, but it is very difficult to generate/replay a particular chaotic situation.
 
Dear readers! Thank you very much for such a lively discussion!

I myself am thinking about one more issue in the context of entropy. Are mathematical proofs really timeless and always timeless?

And if I mix blue and red and want to prove that the two colours will separate again after purple, how can I prove it? I can give you formulas, I can give you a theory, but it's just a model. What about physics? Does this require empirical evidence? What if this empiricism requires infinity in time? So how could I argue entropy mathematically? I can give formulas, definitions, theorems... But I will never empirically prove that by mixing colours endlessly, I will finally get red and blue. Never or ever (putting it poetically)... So what about entropy? Theoretical models fail without empirical confirmation.

And in it all, Poincaré's theorem about returning. But when will this comeback occur? The proof seems to take time. It is indeed timeless, but it is not physics. It's pure mathematics. And time may be short. One human life is extremely short compared to the time we need. And we need this time. So many issues take time! And nothing else. Only time. You could give anything for time. Except for time...
 
And one more observation. Backed by some experience that is not great, but still. The science we practice does not only require dedication. It requires love.

When you love, you can go beyond what you've ever dreamed of. When you are not in love (for example, you don't love time!), you can only do what the world in which you currently are allows you to do. So you can create, but when you create, you only compose from the constituent elements of this world. You are not going to do anything new. You will not come up with anything that transcends anything that exists. You will not do it without loving. Never.

Does our Universe not deserve love? I think that deserves it. And getting to know the Universe? Is it not the most beautiful journey of our hearts and souls?
 
Cleopatre VII said:
Dear readers! Thank you very much for such a lively discussion!

I myself am thinking about one more issue in the context of entropy. Are mathematical proofs really timeless and always timeless?

And if I mix blue and red and want to prove that the two colours will separate again after purple, how can I prove it? I can give you formulas, I can give you a theory, but it's just a model. What about physics? Does this require empirical evidence? What if this empiricism requires infinity in time? So how could I argue entropy mathematically? I can give formulas, definitions, theorems... But I will never empirically prove that by mixing colours endlessly, I will finally get red and blue. Never or ever (putting it poetically)... So what about entropy? Theoretical models fail without empirical confirmation.

And in it all, Poincaré's theorem about returning. But when will this comeback occur? The proof seems to take time. It is indeed timeless, but it is not physics. It's pure mathematics. And time may be short. One human life is extremely short compared to the time we need. And we need this time. So many issues take time! And nothing else. Only time. You could give anything for time. Except for time...
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Sounds related to Ark's mentioning of the arrow of time and knowledge. 4D STS (in the context of alien abduction) supposedly can get the environment to respond to thought more than we can (going well against entropy and the arrow of time). More knowledge perhaps but supposedly it's also eventually limited by wishful thinking for the self which kind of relates to what you said about "love" too aka kind of more knowledge.
 
I think any elucidation on the questions of consciousness, gravity, information, time, etc. (mathematically speaking) probably needs to start with foundations and fundamentals. If we start from somewhere that is already complicated we will probably need to reverse engineer to apply it all the way back to foundations and fundamentals. If these things don't appear in the foundations and fundamentals I have a difficult time in seeing how they progress to the more complicated.

That being said I have posted something a couple of years ago that begins with the foundations and fundamentals per se. In fact, I thought about it for months and finally got the courage to post it back in June of 2019. It never garnered a response, so I pretty much assumed that if it was viewed or read that it was probably just more self illusion and nonsense on my part and not of value.

Some recent coincidences have made me re-think that. There is a possibility that it was never noticed. It still could be nonsense and self illusion. I will mention it once again in case it does have anything of value. Maybe it can just contribute to thinking about the roots of mathematics itself in simpler terms.

The Ark two hats session with Joyeaeia of 18 May 2019, spurred me on to make the first post. The latest session with Gloriaea in excelsis along with this thread and a couple coincident threads, has made me decide to mention it once again.

The original posting was in the thread 'Hidden Secrets of all existence in Prime Numbers?'
Hidden Secrets of all existence in Prime Numbers?

In short, I came up with a product over the primes over the rationals with a real valued variable in the exponents of each prime power series that my limited 12th grade education cannot find whether it even exists in the available literature. That is probably due to my American 12 grade education. The C's did tell us that the secrets of all existence dwell within the rationals.

Anyway, in it I think it satisfies many of the sessions descriptions of what we are supposed to be looking for.
Gravity, consciousness, the synchronous relationship between consciousness and gravity, 'Both times 2 is your square, my dear. In other words, perfect balance.', 'the reals begin to reveal their perfectly squared nature to you', and other clues also. Since I posted it two or so years ago I have also come to see the possibility that it also may have the two loops of the cylinder, one that is 'Included, but not inclusive' and a second one that is even larger and does encompass the whole perfectly square structure.

The attached pdf to the above mentioned thread.
https://cassiopaea.org/forum/attachments/biverse-pdf.30495/

I am sorry if this is seen as a hijacking of this current thread and I apologize if my thoughts have already been assessed as nonsense or if it ends up being just nonsense.
 
christx11 said:
I am sorry if this is seen as a hijacking of this current thread and I apologize if my thoughts have already been assessed as nonsense or if it ends up being just nonsense.
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The problem is with your presentation of the results. In mathematics we have definitions and theorems and proofs. Can you condense your results in a theorem, clearly stated, and a proof, clearly written? Then perhaps it will be readable.
 
I am going to jump back into this classroom since it is so fascinating and seems to be a place where many disciplines and realms of conception seem to be merging and bouncing off each other.

I have a BS in BS, but no formal advanced training in anything beyond that. I might even have a Doctorate in BS, but I haven’t bothered to fake the degree certificate. BTW, my favorite class in college was non-Euclidian geometry which pretty much blew my mind and I will try to make some kind of positive contribution with that at the end of this post.

#1. I agree, we have no idea what consciousness is, and yet I think we have it. There is a high degree of possibility that we all at least have some modicum of consciousness or we wouldn’t be here discussing these things

#2. As for nature observing herself, are we humans not equal to or a part of nature or a subset thereof? To think of ‘us’ as outside nature is ummm… not quite right. (even if our containers are GMO’s)

#3. I see math as a language or a set of paints to try to describe phenomena / events / processes.

#4. Observation is only one kind of Causation.

I walked out of this class earlier for a reason: What is the point to information theory if it is only good under “normal” circumstances? Because, IMO, we have entered a period of abnormality or ‘special” circumstances. So, how and why do special circumstances come about that change the rules of the game? And how does one account for this in the models?

And that brings me back to non-Euclidean Geometry. What if there are TWO (or more) mathematics with different laws that apply in different circumstances AND/OR different realms? Isn’t this a huge problem? Falling prey to looking for the one-size-fits-all solution?

4D math and physical laws are not equal to 3D math and physical laws (I assume) AND since the two realms may be blending on some level which may or may not be perceivable or definable, well, that is one big can of wormholes.

Bonus Material:

Nothing doesn’t exist.

We can’t really think consciousness, we can only be conscious.
(sounds like something a fake guru high on mushrooms or a Werner Erhard type might say)

All parallel lines meet at the vanishing point.
 
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