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From The Desk of...The Chief Scientist

"EmDrive"

Written by Paul Sutter on Monday, 02 January 2017. Posted in From The Desk of...The Chief Scientist

Hanna Twining, one of our excellent educators in the Center for School & Community Partnerships, fired off a question to me about the so-called "EmDrive". You may (or may not) have heard about it in the news recently, and she wanted to be ready in case any students asked about it.

Well hold on to your hats, 'cause this one's a doozy.

First, the claims: some folks are building devices ("EmDrives") that bounce microwaves inside of a fancy cavity and say that it produces thrust. Difficulty: there are no holes in the cavity, so how can the rocket...you know, rocket? A couple month ago some engineers at NASA built their own and published a paper measuring a detectable thrust. Interesting.

What's the Big Deal? The Big Deal is that if these claims are true, then momentum is not conserved - after all, how else could a chamber full of radiation start moving around if it's not pushing on anything?

But conservation of momentum is on a pretty solid foundation: everything from General Relativity to Quantum Field Theory *rests* on conservation of momentum. The principle has been tested literally millions of times over hundreds of years.

Yes, of course we could be wrong about momentum. That's life. But given the paucity of evidence, here are the most likely explanations for the EmDrive, in order:

1) They're not measuring anything at all and just fooling themselves.
2) They're measuring thrust, but it's from something mundane like a leak in the cavity or an interaction with Earth's magnetic field. ...
3) Momentum is not conserved in our universe.

I talked about this at length on the November 25th episode of the Weekly Space Hangout (look for it on youtube), and I argue that the big NASA paper is riddled with errors: their estimates of uncertainty are way off and they're not really measuring anything. So I'm still waiting for someone to clear hurdle #1.

In a way, the EmDrive is a boon. If a student asks about it, this presents a great opportunity to talk about momentum, experimentation, and the process of science. Which are great things to talk about!

"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.

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