mathematic

Article looks like philosophy not physics.

Time travel ahead is possible (use idea of twin paradox), but you can never go back.

I became aware of it a long time ago. I never knew it had a name.

From a math point of view, a scalar is something that is one dimensional, while a vector is something with more than one (usually two or three) dimensions. There are rules for combining them. For example, scalars use ordinary arithmetic. Addition or subtraction of vectors is straightforward but multiplication is more complicated.

log has discontinuity at 0. arc ? - what do you mean?

Graduate school is always a good idea. You need to factor personal needs, such as money, your age.

Without fiction you can ignore the horizontal motion. You need to start with the vertical component of velocity and use the usual formula for gravity acceleration.

Why not? Change a system and it will go to new equilibrium - determined by stat. mech.

Second law is statistical.. It is possible for something weird to happen, but the probability is astronomically small.

Real world complication example: how willing the buyer is willing to pay a given price will strongly correlate how well the care is running.

Another approach cos(x)=sin(90-x), so cos(90)=sin(0). In a right triangle, it is obvious sin(0)=0.

You have assumed the buyer's "satisfactions" are independent, which may not be true.

Question seems premature. Exomoons have yet to be discovered. The description of habitable applies just as well to exoplanets.

Are you asking permission to discuss your idea? If so, you have my blessing.

The statement is a little confusing. I believe its intent was to consider only those values of X which have a probability greater than zero. Simple example: X has 3 values 0,1,-1. f(-1)=1/4, f(0)=1/2, and f(1)= 1/4. g(-1)=0, g(0)=1, g(1)=2. Then E(g(X))=1.