Genady

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?

I'd start with simplifying the expression and then finding an extremum using Lagrange multiplier method.

I don't think your answer to a) is correct. On one hand, your formula for the case of 5 random digits doesn't make sense to me because it has k in it. On the other hand, the "general terms" answer, (9/10)k has no justification. If the a) is indeed incorrect, the rest follows.

It gets a min when one xi=1 and all others are 0. It gets a max when all xi are equal.

Isn't it rather d=1/2*a*t^2+v*t ?

It looks like NYTimes missed that as well. Here is their report: Hubble Space Telescope Spots Earliest and Farthest Star Known - The New York Times (nytimes.com) Of course we see it at the earliest time, although it is not the earliest star known.