Genady

Here is my intuition. Let's assume that I artificially narrow myself to the range [N, N]. I.e., my range contains only one integer. Does it lower my probability to win? No, it does not. The probability is still 1/N, like that of everyone else.

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Hmmm... My blood is just dark green there. Not fluorescent at all.

This is factually incorrect. Observationally, the cosmic microwave background radiation is redshifted in one direction and blueshifted in the opposite direction. It is attributed to our peculiar motion relative to the cosmological comoving reference frame. Only after this peculiar motion is removed, the universe appears to expand isotropically.

I also am very far from being an expert, rather just a witness. In the case I've witnessed, specific environmental factor has made obvious a very serious form of schizophrenia, but then its signs could be traced back for years of misdiagnosis.

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It depends on the symmetries of a situation. For example, a spherically symmetric case, e.g., Schwarzschild black hole, is usually visualized in 2D, i.e., temporal and radial.

Exactly. In the spacetime, they both have curvature of about 1 lightyear radius:

At the very far distance, the angle between light rays from the star becomes 0, that is the rays are just parallel to each other. Draw the picture and you will see what happens to the shadow when the rays are parallel.

1 metre, 2 metres, 10 metres, assuming the shadow is perpendicular to the light ray.

You are spoiling my question in the post right above yours ... 😉

The main problem with the trampoline analogy is that it has nothing to do with the gravity related spacetime curvature. A curious student should ask after watching it, "How can the tracks of a ball and of a bullet be curved so differently if that curvature arises from the geometry of space?" (MTW, Gravitation (p. 32).)

No, I am not interested in this distinction. Sorry that what I said or how I said it sounded like this distinction is of any importance to me.

One might say whatever one wants.

This analogy doesn't work because a particle does not extend into its field in QFT, but rather it is its field when the latter is not in the ground state.