Genady

Could you show that calculation here? Perhaps then we can discuss its merits. Maybe there are 1029 different ways of a technological civilization to arise. Probability of each specific one is 10-30, but probability of one of them arising is then 1/10.

How do you know that they are "he"?

I think you could try first converting the polar coordinates to cartesian. Then you could use the existing theory of 3D rotation of cartesian coordinates. Then, convert back from cartesian to polar.

Yes, it is.

If you copy and paste the URL address from your browser, then you are not.

And it is much better in writing than an audio-visual. For me anyway.

Yes, it goes deep ... and into the parts of mechanics with which I'm mostly unfamiliar. The main point is, H does not correspond to an equilibrium state until it reaches the minimum, and thus its decreasing does not correspond to the thermodynamic entropy increase. However, the initial value of H corresponds to an equilibrium state before constraints are removed. The final value of H corresponds to a new equilibrium state, after the decrease of H. This difference between the initial and the final values of H corresponds to a difference in thermodynamic entropy between the two equilibrium states. Thus the inconsistency is removed. Banzai!

I like that the book starts with complex analysis. And I like the no-nonsense style. For comparison, the style of A. Zee's books is repulsive to me.

The textbook, Mathematics for the Physical Sciences by Leslie Copley, which costs $100+ in a hardcover edition, is FREE for Kindle. This was the author's intent. From the Foreword:

Nothing like this has been found in connection with schizophrenia AFAIK: Scientists identify overgrowth of key brain s | EurekAlert!

Math and physics are full of instances when common words from everyday language are used in a new sense. I don't think it is productive to be attached to any one meaning. Natural languages also have such instances, called homonyms. It doesn't generally confuse people using them.

If you are asked to draw an equilateral triangle with the area 1 m^2, will you draw a square?

No, you cannot draw m^2. You can draw a geometric shape, but m^2 is not a geometric shape. You can draw a square. It has various properties such as area, perimeter, sum of angles, etc. These are numbers. You do not draw them.

The book that has been mentioned by @studiot earlier (Lemons, Don S.. A Student's Guide to Entropy) has a paragraph about time-dependent entropy:

Plus 50,000 years that takes the photons from the core to reach the photosphere.

I don't see finding signs of life far away, long time ago would be changing my mindset at all. Surely two data points are better than one.

Even if we find signs of life in our neighbor galaxy, Andromeda, all we'll know that it was there 2.5 million years ago. We'll not have a way to know what happened to it since then and what is there now. We'll still be alone. The vastness of the universe doesn't help in this respect.

To add to these considerations, there can't be "many [stars] far older than our own." Older, yes, but not far older. Our star is 5 billion yo and the universe is 14 billion yo. That is our star's duration takes about 36% of the whole. Plus, it took time after the beginning to accumulate enough "metals" to start making long lived stars and planets. We are perhaps of the average age, not very young.

So, this question is not about their emotions. It is about our emotions.

What a strange question. Of course they do.

An old fable: A Pan Am 727 flight, waiting for start clearance in Munich , overheard the following: Lufthansa (in German): “Ground, what is our start clearance time?” Ground (in English): “If you want an answer you must speak in English.” Lufthansa (in English): “I am a German, flying a German airplane, in Germany . Why must I speak English?” Unknown voice from another plane (in a beautiful British accent): “Because you lost the bloody war!”

Here you are. I'm sure there are more. Word Value Calculator - Sum of Letters Numbers - Online Numerology (dcode.fr)

Hint: Internet search

I don't know of such a program, but do you use Excel?

IMO, the answer to the first question depends on conditions of usage of the memory. In the extreme case when the memory is added but the system is not using it, there is no entropy increase. Regarding the second question, a probability distribution of the memory contents has information entropy. A probability distribution of micro-states of the gas in the box has information entropy as well. This is my understanding. It is interesting to run various scenarios and see how it works.