A Brief History Of The Birthday Effect With Stephen Hawking

Two days ago Professor Stephen Hawking died at the age of 76; quite coincidentally he died on the same day Einstein was born, which I found to be random but pleasing.

I posted this trivial fact onto my Facebook page, and somebody replied that there was a 50/50 that 2 people within any randomly chosen set of 23 people, will share a birthday.

To which I replied; true, and that if you go out onto the street and ask about 30 people you will find one who shares your birthday.

I got a few answers to that, some saying that the figure was actually 180 overs saying that it would be a few hundred; and that's the point, probabilities are counter-intuitive, so they always sound wrong to us.

A Lottery Of Choices

The reason why we find probability so difficult to grasp, is because it is either using obscure mathematics that we are not familiar with, or the numbers involved are so large that we find it difficult to hold a picture in my mind.

For instance, if I tell you to think of five apples, a picture of 5 apples pops up in your head. Maybe you have even put them in a scenario like a shop or your hands, the main thing is that you can visualise 5 apples.

Now what about 20 cars? You can still do that can't you? However it took a little longer than instantly calling up in your mind what 5 looks like.

In fact when I said 5 apples before, you may have even arranged them in that classic dice-dot shape. Maybe you can even go as far to say that 5 has an immediate abstract visual representation, however the same cannot be said for 20.

Now think of a hundred cars, or one million coins, or 14 billion grains of sand. Yeah, exactly, you just think of a bunch of stuff having no idea if you are being accurate in your mental representation.

This is why people play the lottery, and it is definitely why people buy more than one ticket.

Counter Intuition Is Probability's Greatest Weapon!

I once saw a man spend around £50 ($75) on lottery tickets. I watched the man's face as he bought them, there was genuine hope in his eyes, and I could tell that he felt that he was significantly increasing his chances of winning by buying so many tickets.

I repeated this story to a friend a few days later, and told him how sad I was for the man, he was wasting his money because buying 100 lottery tickets was practically the same as buying one.

My friend immediately called me up on this and said that the man was increasing his chances by 100 times.

Yes I said, however the difference between 1 and 100 within the statistical reference frame of a lottery, was completely negligible.

For instance I said; most people think that they are doubling their chances of winning by buying 2 tickets, when they are in fact increasing their odds by an almost imperceptible degree.

But they are doubling their odds!

Oh dear . . .

The UK lottery gives you a chance of 1 in 14,000,000 chance of winning. If you buy two tickets most people will represent that by saying, I now have a 2 in fourteen million chance of winning, ergo I have doubled my odds.

When in fact the truth is you have reduced your odds by around a 14 millionth of a percentage point.

Instead of 1 chance in 14,000,000 - you now have 1 chance in 13,999,998. This is because the second number represents all the chances you have to not win the lottery.

To truly double your chance of winning (in the way that most people understand the term of doubling), you would need to halve the odds to one chance in seven million, the only way of doing that is to buy 7,000,000 tickets.

Bamboozling With Numbers

So our minds can only hold small amounts of whole numbers, or simple fractions like halves and quarters (it is easy to think of an apple cut into 4 quarters, not so easy to imagine eight twenty sevenths).

This is why it is hard for people to grasp concepts like evolution as it happens over such vast time scales, they become meaningless to us, so in order to understand the big numbers, we boil them down to what we're used to.

So 1,000,000 years we think of as 100, because even though you may not have lived that long, a century is a manageable concept.

It is also why we will continue to gamble on stupid things like the lottery.

Sure, someone's got to win it (not true by the way), but I can bet you right now, that it won't be you.

Further reading:

The Birthday Problem: Wiki

Why Our Brains Do Not Intuitively Grasp Probability

Letters From Darwin - Understanding Probability With A Universe In A Box

Letters From Darwin - An Evolutionary Coin Flip

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WHAT IS YOUR RELATIONSHIP WITH NUMBERS AND STATISTICS; CAN YOU WRAP YOUR HEAD AROUND THEM OR DO YOU BREAKOUT INTO A COLD SWEAT IN THE PRESENCE OF NUMBERS? AS EVER, LET ME KNOW BELOW!

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