What is probability?

I think the world is deterministic and that chance is a measure of degree of missing information. Thus entropy (which quantifies missing information) is more fundamental than chance.

Effect of antidepressants on REM sleep

Nearly all antidepressants cause increased REM latency and reduce total REM sleep time.

If you prevent REM sleep in a patient with depression the mood becomes better. Interesting maybe it is one of the ways antidepressants work.

R value of ideas

Infectious disease have R values. I wonder what the R values of memes or ideas are.

Fundamental uncertainty principle.

If you have a R space and somewhere in this space is a particle. It has position x.

Then the only way to know the position of this particle is to do measurements.

And a measurement consists of a hypothesis you can falsify. A binary hypothesis.

In this way your uncertainty about the particle will shrink as:

$$ \Delta x = c\cdot \frac{1}{n} $$

Here n is the amount of measurements you do and c is the area you examine to exclude/include particle.

This is related to the fact that the uncountable infinity is bigger than countable infinity.

This is also related to why entropy is defined as a log.

How to do CPR in the 50’s

Solution of bertrands problem

Imagine you have a factory that produces square plates with sides between 1 and 3 meters. The question is, what is the probability that if you randomly select a plate, its side is between 1 and 2? That is 50%.

Next: what is the probability that a randomly selected plate has an area between 1 and 4? That is 37.5%.

These results do not match! How come? This is because the sample space is initially between 1 and 3, but when considering the area, the sample space is between 1 and 9! The larger values are squared, making them larger than the smaller values.

Now you have two different answers for the same question.

The paradox arises from the ‘principle of indifference.’ Here, all ‘states’ are counted, and the probability of a specific group of ‘states’ is the ratio to all states.

Perhaps the problem arises from the continuum. It doesn’t occur with discrete states.

The solution is: you cannot have infinite measurements. There is no way to measure a plate to indefinite numbers behind a comma, i.e. 1.23123129879……; So, you have to divide this ‘continuous’ space into discrete space because you can only measure rational numbers. Then the problem disappears and the probabilities become equal.

We must all suffer from one of two pains:

“We must all suffer from one of two pains: the pain of discipline or the pain of regret. The difference is discipline weighs ounces while regret weighs tons.”