Core Knowledge Collection

How these were chosen

There is no end to things worth knowing, but the set that actually gets used repeatedly is smaller than expected. Collected here are ideas that recur across every field once understood: how to read numbers, how not to misread probability, how to judge whether information is trustworthy. The selection criterion is that these are tools for thinking rather than isolated facts.

A sense for numbers

Most numbers encountered day to day mislead if taken at face value. A percentage is meaningless without knowing what it is a percentage of; an average hides its distribution; a growth rate feels entirely different depending on where it started. Whether a 50% rise means two became three or two hundred million became three hundred million is a completely different story — and headlines routinely omit the base.

• Always ask what a percentage is a percentage of
• Averages are pulled by extremes — read the median too
• Growth rates look large when the starting point is small
• Be wary when only the more flattering of absolute or relative is shown

Where probability trips people

Probability is where intuition fails most often. The classic error concerns independent events: after five heads in a row, the sixth flip is still an even chance, because the coin does not remember. The other is conditional probability — a positive test result does not establish the chance you have a condition from test accuracy alone, since the underlying prevalence dominates the answer.

Correlation and causation

Two things moving together does not make one the cause of the other. A third factor may drive both, it may be coincidence, or the causal direction may be reversed. Ice cream sales and drowning incidents rise together because both follow summer. When a claim says doing X produces Y, consider these three possibilities first.

• Is there a third factor driving both?
• Could the causal direction be reversed?
• Is the sample large enough and unbiased?
• Is the effect within what chance would produce?

Judging whether to trust something

A few practical tests decide most cases: can you trace it to an original source, does it engage with contrary evidence, does the party making the claim benefit from it, and does the claim hold up over time. Tracing the source is especially powerful — follow many online claims back and the original is either far more cautious, or does not exist.

Write it down rather than remember it

One final practical piece of knowledge: human memory is far less accurate than it feels. Memory is reconstructed on each recall rather than retrieved intact, so it shifts a little every time. Commitments, the reasons behind decisions and numbers are better written down than remembered — which is the real reason productivity tools exist.