# "More fun with numbers"

on Monday, 02 January 2017. Posted in From The Desk of...The Chief Scientist

Last week I talked about John "lucky steaks" Reemtsen and his one-in-three-million chances of winning the big prize three times in just five spins of the wheel. One of my favorite parts about mathematics is that you can prove some pretty outrageous things. And I mean "prove" in a really serious sense: you can get counterintuitive results that fly in the face of common sense but simply cannot be argued against. Go ahead, try. You won't get anywhere.

Take, for example, odds. Every time John spun the wheel he had a 1/32 (or 3.125%) of winning steaks for a year. His chances of winning three times in five attempts were incredibly small. Let's say he had another crack at the wheel - what are his chances of winning free steaks yet again?

One might be tempted to think that there's no way his lucky steak streak would continue. His chances of winning again must be absurdly, pathetically low. One might think that, but one would be wrong. John's chances of winning steaks again are exactly, precisely, provably 3.125% - the same as his first pass.

Flip a coin and get heads 99 times in a row. What are the chances of getting heads on the next flip? 50:50. No better or worse than the last 99 flips, or the thousands of flips that came before you got your hands on the coin.

To think that your chances of winning or losing are based on your past successes or failures is known as the "gambler's fallacy", and it trips up a lot of people, especially when it comes to, well, gambling. But thankfully math is here to set us straight.

# "Fun with numbers...and free steak"

Written by Paul Sutter on Monday, 19 December 2016. Posted in From The Desk of...The Chief Scientist

So there's a certain Texas-themed steakhouse chain that's in the habit of giving away prizes during the holidays. They let you spin a big wheel with 32 spots on it, and if you're lucky you win free steaks for a year and they make a big hurrah. Last year John Reemtsen (COSI's Web Manager) won the year-long steaks not once, but twice in two attempts. He got another three chances this year and, lo and behold, he will not be wanting for steaks in 2017.

John knew he got very lucky, but he asked me just how lucky he was to get three meaty wins out of five chances, when there was only a 1/32 (3.125%) chance to win at every spin.

Well then, game on.

To work out probabilities you count up all the ways that you get what you want and divide that by all the ways of getting any possible result. Assuming the wheely-spinny thing is fair and each spin is independent, we start by counting up the ways to get 3 wins in 5 attempts.

For example, John could win on his 1st, 2nd, and 3rd attempt. Or he could win on his 2nd, 4th, and 5th attempt. And so on. The situation is small enough that we can just type out all the possible combinations of getting three wins:

W-W-W-L-L
W-W-L-W-L
W-W-L-L-W
W-L-W-W-L
W-L-W-L-W
W-L-L-W-W
L-W-W-W-L
L-W-W-L-W
L-W-L-W-W
L-L-W-W-W
There are 10 different ways to win three times with five chances. Of course there are handy mathematical formulae for easily calculating larger problems, and for the curious I recommend looking up "combinatorics".

Now we need all combinations for all results. There are 32 spots on the wheel and 5 different spins, giving 32*32*32*32*32 possible outcomes in total.

So John's final probability of winning 3 times out of 5 is 10/(32*32*32*32*32), or .0000298923%, or about one in three million.

We can all agree that John was a lucky dude. And that he owes me a steak.

# "The Christmas Star"

Written by Paul Sutter on Monday, 12 December 2016. Posted in From The Desk of...The Chief Scientist

Every year I get a fresh round of questions about the Star of Bethlehem, the fabled celestial sign that led three wise men (read: astrologers) from Persia to a backwater town in Judea to hang out with the baby Jesus, his family, and - if manger scenes are meant to be taken literally - an assortment of farm animals.

Now I'm usually reluctant to answer this sort of question; any response I give that sits on the intersection of science and religious is often used as ammo to further one agenda or another. But in this case the answer is so deliciously unsatisfactory to all parties involved that I don't mind answering at all.

So let's get to it: looking at this story from the perspective of an objective astronomer, was there anything funky happening in the skies above the Middle East around two thousand years ago? Whatever happened had to be visible in the eastern skies from Mesopotamia and last a couple months, in order to support the wise dudes' trek.

A supernova would be a great candidate; they're sufficiently noteworthy and last several weeks. Unfortunately we don't have any records of ones appearing around that time. That doesn't rule them out, but the Chinese were fabulous notetakers of the night sky and we're pretty sure they would've caught it.

Halley's comet visited in 11 BCE, which is a tad early. Also, comets at the time were seen as Very Bad Omens - something to be avoided rather than chased. There are no convenient eclipses, either. But that's fine, since they don't last long enough anyway.

That leaves conjunctions, when planets happen to be close to each other on the sky. Those are pretty cool, and Jupiter and Venus were in conjunction in the eastern dawn sky in 3 BCE. The trouble with that is that King Herod - who the wise men visited - died in 4 BCE, so the timing is a bit off.

So there you go: something interesting did happen in the sky back then, but not quite at the right time. And that's all I can say.