KJW

Actually, such numbers don't have to be prime, it is sufficient that they are not divisible by either 2 or 3. Also, 1 or 5 (mod 6) implies 1 or 2 (mod 3).

There is no Nobel Prize in Mathematics.

This is a big question. I don't think there are any general answers, with the answer depending on the particular situation. For example, let the two systems be two different points in some abstract space. Then does the measure of difference between the two points depend on the path between them? In thermodynamics, functions of state such as entropy are defined explicitly such that the differences are independent of the path between the initial and final states in state space. By contrast, distances between points in ordinary space or spacetime do depend on the path between them.

As an Australian living in Australia, I watch an Australian TV program called "Planet America", which provides a somewhat humorous view of US politics, though it isn't a comedy. In that show recently, I saw an advertisement from the Democrats appealing to women with Republican husbands to secretly vote for Kamala Harris.

And I will add that it is irrational to be concerned about trace amounts of methanol from the normal consumption of aspartame.

When I was in Year 2 at a regular public school, we were taught matrices, including matrix multiplication. They didn't seem at all useful to a seven-year-old. I didn't encounter them again until senior high school, when their use was revealed. I do not remember when I learnt about negative numbers.

It's been my experience that most people are good. But there are certainly a***holes out there that spoil it for everyone else. It's probably not fair to judge humanity as a whole based on the relatively few a***holes who cause problems. On the other hand, it's wise not to forget that not everyone is a good person and that one needs to keep their wits about them.

You could measure the proper length of a moving object using a ruler that is moving alongside the object, bearing in mind that the object is still moving relative to you, the person doing the measurement.

What has nuclear weapons got to do with travelling to the moon? I would have thought the more appropriate question would be: Was being able to travel to the moon worth the exoneration of Nazi scientists?

Related to this is the problem of determining the molecular formula of a compound from the molecular mass obtained using a high-resolution mass spectrometer.

He probably is if one assumes that what he says is NOT true.

I don't know to what extent it applies to American politics, but in Australia, minor parties and independents can have an exaggerated level of power in the case where the winning party failed to win the majority of seats and must negotiate with the minor parties and independents who won their seats. (Firstly, it must negotiate with the minor parties and independents to actually be the winning party because if no party wins the majority of seats, it is NOT the party that won the most seats that wins government, but the party that gains the majority of seats with support from the minor parties and independents who won their seats. Then once the winning party is in government, it has to negotiate with minor parties and independents on policy.)

Didn't Trump build a wall, or at least part of a wall? He said he was going to build a wall, and make Mexico pay for it.

Did Mexico pay for the border wall?

The proper distance in spacetime between earth now and Alpha Centauri four years from now is somewhat less than the proper distance in spacetime between earth now and Alpha Centauri now. This is length contraction. Because we are talking about proper distances, this is true in all frames of reference. But note that I am not talking about distances between the same pair of points (events) in spacetime. The distances are different because the intervals are different. This is an important point because in relativity, the different values of a measurement in different frames of reference are always measurements of different things. Different observers in different frames of reference always measure the same value for the same measurement.

Only 20 components are independent. The Ricci tensor has 10 independent components leaving 10 independent components for the Weyl conformal tensor.

Only a few minutes ago, I came across this YouTube video titled: Are Atheists more Moral than Religious People? Here are the Facts | Phil Zuckerman: https://www.youtube.com/watch?v=RiCqJ_rF384 The conclusion is quite stark: over several issues, secular people are consistently more moral than religious people. An interesting example is animal rights. Because of a belief in evolution, secular people tend to regard humans as connected to other species, whereas religious people tend to regard humans as disconnected from other species and are therefore less likely to support animal rights. The video also said that democracy is a secular concept, and that the notion of democracy does not exist in any religion or religious text.

Yes, we're at a rather special time in history with regards to solar eclipses in that total, annular, and even hybrid eclipses can occur. In the past, the moon was too close for annular or hybrid eclipses to occur; and in the future, the moon will be too far for total eclipses to occur.

I have to say that I do not complain about the crackpots that appear on this or any other science forum. I find that it's the crackpots who drive the discussions, and that banning them too vigorously is a way to kill the forum. If forum regulars want a better range of topics to discuss than crackpot theories and religion, then they should provide it. But bear in mind that there is no guarantee that the other members will engage if the topic is too esoteric or whatever.

I apologise for the thread hijack, but I have a question: If Adam and Eve had not sinned, would they have eventually gone to heaven?

Why are you comparing the intellectuals of ancient times to the average person of today? That's not a reasonable comparison. Today, society as a whole has such a vast body of knowledge that I find it mind boggling that anyone would suggest that ancient knowledge is even remotely comparable.

I also ignore scammers who contact me to say that there is a problem with my internet, computer, bank account, taxation, postal delivery, toll payment, etc, etc, etc. Your scare tactic won't work on me because I have assessed the risk based on what I know and have decided that the risk is worth taking. My philosophy is: why would an ancient book or religious leader have a better insight into the workings of reality than modern science with its impressive technology or the power of mathematical logic? One further point: there are many religions, and their teachings are not necessarily compatible. So how does one decide which religion is the one that should be followed? Your scare tactic might have led me to the wrong religion if it had worked on me.

I have to see for myself: [math]d = \dfrac{c^2}{a} \\ = \dfrac{(299792458 \text{ m s}^{-1})^2}{9.80665 \text{ m s}^{-2}} \\ = 9.16475 \times 10^{15} \text{ m} \\ = \dfrac{9.16475 \times 10^{15} \text{ m}}{9.4607304725808 \times 10^{15} \text{ m ly}^{-1}} \\ = 0.9687 \text{ ly}[/math] That's remarkably close!

I was thinking about making the term "aliquot sum" a link to its Wikipedia article, but because it is a policy of science forums not to do people's homework for them, I decided to leave some room for you to do your own research on the problem.

I have to admit that the idea that the universe is sentient does have some appeal to me. Then our exploration of the universe and its laws becomes a self-awareness of the universe in which the universe is observing itself.