Genady

Sublunar point.

Yes, I see now that your question is different. You're right then, the distance to the Moon does not matter. However, you can add the angles only if they are aligned, which they generally are not. Also, the Earth circumference is only important if the point is on the equator, which it generally is not.

The other comments in that thread show the complications in real situation. The answer depends where on Earth is the point above which the Moon is in zenith. No, these calculations are incorrect. The Moon's projection on the Earth surface doesn't move 14.451 degrees per hour. You need to compare linear velocities rather than the angular ones.

This question is the same as to ask, what is the speed of the Moon's shadow on the Earth's surface. This has been discussed here: https://www.scienceforums.net/topic/131698-moon-shadow/ The simple case answer, on the equator, with a back-of-the-envelope calculation was: (https://www.scienceforums.net/topic/131698-moon-shadow/?do=findComment&comment=1240426) The Earth spins from West to East making a full circle in 1 day. The Moon rotates around the Earth from West to East making a full circle in 30 days. OTOH, the radius of the Moon's circle is about 300000 km while the Earth's radius is about 6000 km. This makes the Moon's circle 50 times longer. The Moon makes 50 times longer way in 30 times longer time, i.e., it moves from West to East 50/30 times faster than the Earth surface. Thus, its shadow should move to the East faster than the Earth surface does, hence its shadow on the Earth surface moves to the East.

1. What does happen on the other side of the wheel? 2. Consider the following situation. Assume that the fluid inside the boat is sealed. Heat it up. The pressure inside the boat will rise. Will the boat sink?

Perhaps a better title would be, a rope-timer.

Wouldn't a hair that is more tightly curled offer increased thermal insulation in cold environments? Wouldn't it reduce heat loss from the head in temperate and colder climates? Wouldn't it be advantageous as humans moved out of the Equatorial Africa?

I say, no. Regardless of what happens inside the boat, the Archimede's principle holds.

By what mechanism conserving water and reducing heat allowed for brain growth? Why is it likely?

Correction. I should've said, a bounded TM.

There is a gap in logic between finding that scalp hair reduces the amount of heat gain from solar radiation and stating that scalp hair likely evolved as a way to reduce the amount of heat gain from solar radiation. What is the evidence that it was a crucial adaptation? Isn't it one more "just so" story?

So, if we assume that the observable universe has a limited number of states, then AI is a limited TM. This answers the OP question, correct?

Why is this thread in the mainstream forum?

In the mathematical sense we apply now, yes, they do.

I think that infinite set is an object that exists in mathematics in the same sense as 3. I don't think that (0,1) is said to end.

For example, does a number 3 exist? Does an open interval (0,1) end?

Isn't it already established in a variety of ways that they don't solve problems?

Yes, this is a procedure. What is a resulting pattern?

I see an ambiguity in the question 1 in the concept of "exist." And an ambiguity in the question 2 in the concept of "end." Answers to both questions depend on interpretation of these terms more, or rather than on interpretation of the term "infinity."

You have a rope and a lighter. If you light a rope, it burns about 1 m in 1 hour. However, it does not burn at a uniform rate, e.g., not necessarily 0.5 m in 0.5 hour. Can you measure 0.5 hour? 15 minutes? 20 minutes?

Yep.

There might be. For simplicity, and according to the fact that English is the current language of science communication, I'd limit the discussion to English.

(Inspired by the @mistermack's post above.) ChatGPT could not make the logical step to figure out the following question (and evidently is not familiar with the Chinatown movie) Me: Katherine is Evelyn's sister and daughter. Explain. ChatGPT: It seems there is a contradiction in your statement. If Katherine is both Evelyn's sister and daughter, it implies an inconsistency in the family structure. In traditional family relationships, a sister and a daughter are two distinct roles within a family. Let's examine the possibilities separately: If Katherine is Evelyn's sister: This means Katherine and Evelyn share at least one parent, typically their mother or father. They are siblings and have a common parentage. If Katherine is Evelyn's daughter: This implies that Evelyn is Katherine's mother. In this scenario, Evelyn is the parent, and Katherine is the child. Based on the given information, it is not possible for Katherine to be both Evelyn's sister and daughter. If there is additional context or clarification, please provide it so that I can better assist you.

ChatGPT has handled it very well: In the given scenario, there are two individuals: an Englishman and an American. Let's refer to them as John (the Englishman) and Mark (the American). "The Englishman is the father of the American's son" means that John is the biological father of Mark's child. To further explain the situation, we need to consider a few possibilities: John and Mark are in a same-sex relationship: In this case, they may have used a sperm donor or a surrogate to have a child together. As an Englishman, John would be the biological father, and the child would be their son. John had a previous relationship with a woman and fathered a child: Before being in a relationship with Mark, John might have been in a heterosexual relationship and had a child. Later, he entered a relationship with Mark, who became the child's stepfather or co-parent. Adoption or surrogacy: John and Mark may have adopted a child together or opted for surrogacy, where John is the biological father, and Mark is the legal father. These are just a few possible explanations to illustrate how the Englishman could be the father of the American's son. The specific circumstances would depend on the individuals involved and their personal situation.

AFAIK, Riemann surfaces are not related to the Riemann hypothesis. Greeks were fascinated with numbers philosophically. As opposed to Romans, who built cities. As for the other questions, I'd like to know the answers, too.