what are the chances that two of them will have the same birthday?

The answer is, better than even.

If the party had 60 guests,

then chances would be greater than 99%.

It's an example of how we often are too impressed by coincidences,

because we forget about how many ways there are

for coincidences to occur.

The tendency to see meaningful connections

between completely unrelated things

is what psychologists call apophenia.

It means we often see patterns in random information,

and this can be deeply problematic.

When we hallucinate things that aren't there,

we can make foolish decisions.

We can imagine that there are conspiracies

because several bad things happen in a row.

We can believe in malevolent deities

because we underestimate how easy it is for misfortunes to cluster.

We can be victims of the 'gambler's fallacy',

and think, for example, that if the roulette wheel has landed on red

six times in a row, it's due for a black,

even though, of course, the roulette wheel doesn't have a memory

and a desire to play fair.

The 'gambler's fallacy', also known as the 'Monte Carlo fallacy',

is the incorrect belief that a past event will influence

the outcome of a future event.

So why do so many of us fall for it?

The whole point of having a brain

is to figure out what's going on in the world.

That's a useful thing in a natural environment,

because we don't have a direct wire from our brain to reality,

we're always interpreting patterns.

We see shapes hidden, partly obscured by leaves,

we see fish under the surface of the water,

we always go beyond the information given.

But it does mean that we can overshoot

and interpret things that aren't actually there.

Not just in the realm of visual shapes,

but in the realm of events.

This failure to appreciate randomness can lead to all sorts of problems.

It can lead some people to dismiss climate change

after a record cold day,

when in fact, if they were able to step back

and look at the overall trend,

it would be clear that it was a completely normal,

if random, fluctuation.

And that can lead us to attribute meaning

to totally unrelated life events.

When events happen randomly in time,

they often fall into clusters,

because there is no process that's trying to space them apart.

That's something that is very hard for us to appreciate.

Now when it comes to events in our lives

that might be distributed randomly in time,

from the perspective of our minds seeking patterns,

they seem to come into clusters, and so we may believe

that bad things happen in threes, that God is testing our faith,

that we're born under a bad sign.

Another common illusion is prior probability,

sometimes called the 'Texas sharpshooter fallacy',

after the marksman who fires a bullet into the side of a barn

and then draws a bullseye around the hole afterwards.

There's the story about the stock market adviser

who sends out several thousand newsletters,

half of which predicted that the market will go up,

and half that predicted it would go down,

he then discards the names on the mailing list

who happen to get the incorrect prediction.

Well, you can see where this is going.

After a year, there'll be a certain remainder who will think this guy

is a genius.

It's a fallacy that we are all prone to,

it's why we are often impressed by psychics and soothsayers

whose predictions are amazingly accurate,

after they've occurred, we tend to forget all the false predictions.

So if we know that we are prone to falling for these delusions,

to seeing patterns that aren't there,

what can we do about it?

An awareness that we are all vulnerable to fallacies

and illusions, biases, doesn't mean we should just fatalistically

throw up our hands and say humans are irrational

and therefore we need some kind of benevolent despots

to make decisions for us,

that democracy was a big mistake.

Probably none of us is that wise

that we can notice our own fallacious thinking,

we're often very better at noticing the other guy's fallacious thinking.

And we can harness that ability

in communities that have free speech, open debate, an adversarial process,

checks and balances, editing, fact checking,

so that one person's mistaken first impression,

their illusory snap judgement,

can be spotted by someone else, and the community as a whole

implements the most reasoned decision.