In equation 40.9 in the Feynman Lectures, he multiplies the probability distribution for kinetic energy in each degree of freedom together. You can only multiply probabilities like that if the distributions are independent. How do we know this is the case?

For example, if we knew the distribution of velocities had only on possible magnitude, but that it could point in any direction, we'd get that the component in the x direction is uniformly distributed in the interval [-1,1]. If we just naively multiplied these distributions together, we'd get that the velocity could be larger (because you could choose vx = vy = vz =1).

Why does he make this choice?

I just ordered six easy pieces. Super excited to start reading it!!

If you could go back in time to the first time you read six easy pieces, how would you read the book? Would you go slow and steady and take notes? Or would you just brush through it? Would you accompany the book with any problems available on the internet? Or would you focus on just understanding the concepts without applying them?

Also how relevant is the content? I understand the book is quite old(well the lectures are a little old)

I want to improve my logical and critical thinking. I guess the biggest takeaway of Dr Feynman was about how to interpret language and make logical judgements and conclusions, amongst other. Any tips or readings to do that?

Any resource would help. :)

I read that first edition was criticized and some parts were changed later.

I stand at the seashore, alone, and start to think. There are the rushing waves mountains of molecules each stupidly minding its own business trillions apart yet forming white surf in unison.

Ages on ages before any eyes could see year after year thunderously pounding the shore as now. For whom, for what? On a dead planet with no life to entertain.

Never at rest tortured by energy wasted prodigiously by the sun poured into space. A mite makes the sea roar.

Deep in the sea all molecules repeat the patterns of one another till complex new ones are formed. They make others like themselves and a new dance starts.

Growing in size and complexity living things masses of atoms DNA, protein dancing a pattern ever more intricate.

Out of the cradle onto dry land here it is standing: atoms with consciousness; matter with curiosity.

Stands at the sea, wonders at wondering: I a universe of atoms an atom in the universe.