Most phenomena lay beyond the existential reasoning of the mind. Those who want to explore this other world must learn the magic of mathematics. Here are a few samples that reveal logical conclusions beyond subconscious reasoning:

1 – Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?

Mathematical probability: Before any doors are opened you have a 1 in 3 chance of winning [ P= 1/3 ]. After the host opens door 3 which has a goat, the chance for winning the car with your current choice still is 1/3 because although the goat is revealed – the number of doors has not changed. The probability that the car is behind the chosen door still is 1/3 but the unopened door now has a 2/3 chance of winning because door three is known. The solution is that switching has a 2/3 chance of winning – so switch.

2 – Albert Einstein is famous for defining the universe as a relationship between mass, time and space. To the human mind, this still seems adequate (frankly it is) but the mathematics of quantum physics say space does not exist, solid subatomic particles do not exist as little billiard balls of energy and more abstractly, all subatomic activity occurs simultaneously regardless of ‘space’ – even 1 billion light-years away.

An experiment was performed a few years ago where the photons from two different stars were aimed at a device which needed two in-place photons to interact simultaneously. Using the star energy, the device acted as expected. This is tantamount to a magician letting you pull a card from his deck and it is matched simultaneously by a deck on the Sun.

The famous layman’s example is Shrodinger’s cat: A closed box is presented to you with a cat inside. Is the cat dead or alive? The answer is yes. This is kept simple by recognizing that whatever led to the state of the cat, time, space or distance, it is irrelevant to your instant experience. A time-distant event will appear instantly when the box is opened. If the cat is dead, did it die recently or a long time ago? Doesn’t matter to you; as far as you’re concerned the fact that it died happened when you opened the box because otherwise it would have been alive.

Don’t ask for the equations. Dozens of books laden with formulas have been written.

3 – This mathematical exercise will provide some relevant information for your real-time brain. Since 2018, 111 children have been murdered in the United States. Population has questionable stability in many nations including the United States. Will killing 111 children affect the future population of the US?

Yes. Using Bayesian probabilities, in 2060, there will be approximately 308 less people in the United States than if no children were murdered. [formulas in ‘the signal and the noise’ by Nate Silver, 2012 Penguin Press] basic formula:

The formulas have several sources on the internet if you want to play with them.

Ancient Mariner