Genady

No, it is not.

If we look deep inside, we get to interactions between particles, which are described by QFT. Momentum is always conserved in QFT. On the other hand, all interaction in QFT are "direct collisions", i.e. happen at a point. And then this momentum is carried by a particle to any distance. So, the momentum of the massive bodies, mv, is not necessarily conserved. But that momentum plus the momentum carried by the massless EM field is conserved.

Yes, mass of the rope is one question. The other question is, how the rope can move when Bob starts pulling if it is stretched and Alice holds the other end? Here is a related quote from The Feynman Lectures on Physics Vol. I Ch. 10: Conservation of Momentum (caltech.edu):

And what about Bob and Alice holding two ends of a stretched rope? The momentum of the system is 0. As soon as Bob pulls himself along the rope, he starts moving toward Alice. Nothing else moves until the other end of the rope pulls Alice. The system has a non-zero momentum all this time. Thus, the total momentum is not conserved. What is wrong here? You are correct. The relativistic effect here is not related (at least, not directly) to the relativity of simultaneity, but rather to speed limit of a signal. You are also correct that the electromagnet will not "wait" an indefinite time until the field reaches the permanent magnet. It will rather start moving quite soon, before the permanent magnet will. That's why I think it is simpler to analyze the conservation of momentum question in a system without EM involvement, e.g. Bob and Alice above. Certainly EM fields within the rope are involved in the "signal" transmission from Bob to Alice, but they have no connection to Bob's mass and velocity and thus to the total momentum of the system. --- On the second thought, the EM fields in the rope "know" about Bob's momentum because they transfer this momentum to Alice. So, perhaps this is where the answer is...

Moreover, rituals predate humans. Other mammals, birds have rituals. My dogs love rituals and don't like when a ritual goes "wrong". Maybe religions predate humans as well?

Since the post is in the Anatomy, Physiology and Neuroscience forum, I guess the question is about an existence of the mind's eye as an identifiable anatomical, physiological or neural entity. In that sense, I think it doesn't exist. On one hand, the signals coming from eyes spread to different parts of brain very fast. On the other hand, different parts of brain are activated when we visualize and this set depends on the visualization content.

Yes, however since not all people can control these forces, to me (as an example) they are just an external destructive force that I need to deal with. A tsunami in slow motion.

The discovery of the microbiology itself, by Leeuwenhoek was serendipitous and puzzling.

Yes (/ yes )

- No need to control geology and cosmology to control forces. - The evolution is not about hope but rather about some evidence becoming irrelevant. P.S. I am a human and I can control my greed, short-sightedness and power-lust.

The first P2 is wrong. Specifically the phrase, "forces beyond human control." There are various degrees of human control of various forces and they (the degrees) are evolving. The evidence has been cherry-picked and doesn't represent the whole picture. Plus, the whole picture is evolving.

Just a mistake.

What makes you think so?

Why "inevitable" and "uncontrollable"? We can take measures to protect against or prevent / minimize effects of natural disasters.

It is back to the same what I've left 43 years ago.

Isn't a social disaster just another natural disaster akin earthquake, flood, meteor strike, etc.? Why would it require a different response?

Here is a friendly reminder of the origin of that thread and that phrase:

Yes, I think it is correct. A direct collision, or a system is small enough / our time scale is long enough that we can ignore time delays due to relativity.

I've suggested a purely mechanical system for this question, above. Yes, but the rope doesn't move, so it doesn't change a momentum. The question of the momentum conservation is the same.

I don't think it is possible to assume it a close system when taking relativistic effects in consideration. Because to assume the system to be closed we need to consider it all at once, but there is no simultaneity for the spatially separated bodies. To analyze this condition, we don't need EM. We can consider a simple, purely mechanical system. Let's assume Alice and Bob are holding the ends of a stretched rope 1 light-hour long. Bob starts pulling himself along the rope, moving toward Alice. It will take an hour until Alice starts being pulled toward Bob. I don't think we can assume it to be a closed system.

Momentum is conserved when there are no external forces, which is not the case here.

I think, after a delay of (distance between them) / (speed of light).

The approach above should give you the max(f())=ln(n) quite fast. To get min(f), assume that ln(xj) is the smallest of all ln(xi), take the condition x1+x2+... xn = 1, multiply it by -ln(xj): -(x1+x2+... xn)*ln(xj)=-ln(xj). Because all ln(xi)>=ln(xj), -(x1*ln(x1)+...+xn*ln(xn))>=-ln(xj). The left side is -ln(x1^x1*x2^x2*... xn^xn), the right side -ln(xj)>=0. Thus -ln(x1^x1*x2^x2*... xn^xn)>=0. And we know how to get it =0. Thus 0 is the minimum.

Thermodynamic equilibrium is a probabilistic phenomenon. There is a VERY small probability of a VERY RARE arrangement of constituents particles. This probability is not 0 though, so if we wait THAT long, it will perhaps happen.

I guess I'm missing something. Are we talking about strings of random digits or sets of random digits?