davidgalbraith

Simple Explanations for Things

Below are some notes of the best ways of explaining certain concepts, to help teach my son when he grows up.

Based on the assumption that given enough time, any idea can be broken into sufficiently small concepts and explained so that anyone can understand.

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Logarithms

The log of a number is the number of digits it has:
log 100 = 3

Where:

(a) The number of digits doesn’t need to be a whole number.
log 150 ~= 1.1761

(b) The subscript of the log refers to the base. Since the number of digits depends on the base it is written in.
128 base ten = 1000000 base 2
log2 1000000 (binary) = 7

(c) The base doesn’t need to be a whole number, but should be positive.
base e ~= 2.718, log base e is written as ln, natural log.
In base e, the number of digits a number has is the same as the power.
100 (base e) = e^3
ln e^3 = 3

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Special Relativity

If the measure of something’s speed (light) is always the same in any direction even if you are moving and you accept that its speed really is the same then either speed of the hands on the speed dial change (time) or the distance measured (space) stretches or contracts, or both, depending on your own movement relative to the light source.

With stretchy space and time, there is no fixed background or preferred static point in space, you can take any point for a relative frame of reference.

Here is a nice simple description of this.

In fact space and time are the same type of thing, but because we can’t see more than one bit of time at once (unlike space where we can view a landscape) we must be looking at the 4th dimension edge on.

NB the energy mass equivalence that is a result of the special theory is often described wrongly as if mass can be converted into energy - NO, mass IS energy, they are equivalent. When a nuclear explosion happens mass energy is converted into heat energy.

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