Tuesday, March 17, 2015 Game Recap & Discussion [SPOILERS]

[willwoodlen]

High school math teacher here, so this was instaget, of course.

Prime numbers have exactly two factors: 1 and themselves. One is definitely not prime.

Additionally, if 11 had been the answer they would have just said "this is the smallest two digit prime number."

A few theorems wouldn't work if 1 was prime, so we don't call it prime.

The problem is that 1 has sometimes been taught as a prime number; I was taught that it was. An online Q + A forum has the question of whether 1 has ever been considered a prime number. The answer cites several mathematical works that include it among the prime numbers, but characterizes this as a questionable practice that is now completely discredited and abandoned. Still, some of us, perhaps many of us, were taught to include it.

When I saw the FJ question I had doubts, having heard since my school days that 1 is not considered prime, but I decided on 11. I would have smilingly accepted the decision that this was an incorrect answer, but I would have given someone a bit of a talking-to afterward.

A fun and lively game, though, with yet another topnotch player who goes winless, like Erin two weeks ago. Congrats to Kristin.

[seaborgium]

I have NHO "buttonhole" in either of those contexts.

Have you never worn clothes with buttons (or have all your buttons been purely decorative)?

I didn't know it was specifically called a "buttonhole" though. I thought it was just a "hole". (That, and about 90% of the time, I just wear casual t-shirts or, if I need to be formal, a sweater.)

It's a hole for a button. What did you expect? (I assumed that somehow the words "slit" and "garment" threw you off as to the function of buttonholes.)

[TenPoundHammer]

I have NHO "buttonhole" in either of those contexts.

Have you never worn clothes with buttons (or have all your buttons been purely decorative)?

I didn't know it was specifically called a "buttonhole" though. I thought it was just a "hole". (That, and about 90% of the time, I just wear casual t-shirts or, if I need to be formal, a sweater.)

It's a hole for a button. What did you expect? (I assumed that somehow the words "slit" and "garment" threw you off as to the function of buttonholes.)

"Slit" and "Garment" did throw me off considerably, as did not knowing that "buttonhole" can be a verb in that non-shirt-related context.

[OSXpert]

Will you guys quit buttonholing TPH, geez!

[BobF]

And I imagine for the last couple of months Kristin has had a new favorite number, 23. And a new second favorite number of 5800. Couldn't believe that bet on the DD. If he could have buried her, I could see the big wager, but he wasn't even in that position.

However, if he had bet conservatively, Kristin would have had to bet more and have had a larger payday.

ETA: For some reason, the number 37 came into my head first, but of course I thought more about it and realized 23 was the correct answer.

[goforthetie]

The problem is that 1 has sometimes been taught as a prime number; I was taught that it was. An online Q + A forum has the question of whether 1 has ever been considered a prime number. The answer cites several mathematical works that include it among the prime numbers, but characterizes this as a questionable practice that is now completely discredited and abandoned. Still, some of us, perhaps many of us, were taught to include it.

People get taught lots of incorrect and outdated things. Doesn't mean they should be considered correct.

[silverscreentest]

Was "mold" acceptable for the fungus clue?

Possibly. Mold is a fungus and ergot is a fungus but I'm not sure ergot is a mold. My wife and I went to the same huge state university but in different programs so we didn't know each other at the time. The only professor we had in common was a historian who, regardless of the actual content of the course, would get in her theory that the Salem witch trials were caused by ergot. Wet winters caused ergot to form on the rye. Rye was a cheaper grain than wheat and was eaten by the poorer colonists. It caused an effect similar to LSD that made them see visions. That professor wrote a book with "Molds" in the title.

People might know "familiar" from Harry Potter. Those included Harry's owl Hedwig, Hermione's cat Crookshanks, Filch's cat Mrs. Norris and Dumbledore's phoenix Fawkes.

[MitchO]

For the 2nd straight episode, I called my 12 year old into the room for FJ. Prime numbers are his current obsession; he actually said "13! No, 11! No, 23!" all in rapid succession, well within time (I assumed he would have had the same correction time as Kristin). I thought 13 initially as well; like at least one other person on this thread, I was temporarily thrown off by the phrasing of the clue and interpreted it to be two *different* prime numbers.

Add me in on the "Surprised they used a potentially debatable topic for FJ" crowd, and overall I think Colin has a minor beef. I mean, I get the explanations; but it isn't 100% agreed upon IMO and is a relatively (in comparison to a lot of math rules) recent clarification. I was torn; Kristin is clearly going to continue to be an awesome champion, but I liked Colin the minute he made that aggressive 1st DD bet.

[Leander]

The problem is that 1 has sometimes been taught as a prime number; I was taught that it was. An online Q + A forum has the question of whether 1 has ever been considered a prime number. The answer cites several mathematical works that include it among the prime numbers, but characterizes this as a questionable practice that is now completely discredited and abandoned. Still, some of us, perhaps many of us, were taught to include it.

People get taught lots of incorrect and outdated things. Doesn't mean they should be considered correct.

True, but for the average older person who hasn't thought about prime numbers in a long time, the headline "One No Longer A Prime Number" probably got a lot less publicity than, say, Pluto no longer considered a planet

[BobF]

Just found a web page that has references to 1 being considered a prime number by books as recently as 1999, but it's now considered neither composite nor prime.

Which leads to this question. If the clue is the two outermost planets in the solar system, what answer(s) are/is acceptable?

Here is the link: http://mathworld.wolfram.com/PrimeNumber.html

[whoisalexjacob]

This game is a win for the Weak Form of Shore's Conjecture. The second-place player bet "small." --Bob

Kristin played it right. She'd have won with an incorrect response. What two-thirds buys you is that is forces the leader to choose between guaranteeing a win with a correct response (which is what most of them are going to do) or a win on a triple stumper. (Well, a double stumper in this case; poor Irene just didn't have enough scratch to be a factor in this game.)

It's be interesting to see what the percentages of leaders in non-lock games, in order of least to most ridicule :
* Make a lockout bet or an amount functionally equivalent to a lockout bet;
* Bet a low amount designed to give them a win on a triple stumper;
* Overbet and leave themselves unnecessarily exposed to a worse outcome than necessary;
* Bet an amount that guarantees them neither a win with a get nor a win with an opposing miss;

How cute, you're teaching wagering to Bob Shore ... Search for "Shore's Conjecture" if you want to know what he's talking about.

[This Is Kirk!]

It doesn't matter if 1 is a prime number or not; 11 can't be a right answer. The clue specified that "both themselves prime numbers" meaning it couldn't be the same digit.

Not sure about that.... what would you say is the right response to this FJ:

"This 2-digit number is the smallest odd number whose digits are both themselves odd numbers." ?

Perfect example. I don't buy alietr's logic either. It didn't say the numbers had to be different, just that they were both prime.

[lieph82]

It doesn't matter if 1 is a prime number or not; 11 can't be a right answer. The clue specified that "both themselves prime numbers" meaning it couldn't be the same digit.

Not sure about that.... what would you say is the right response to this FJ:

"This 2-digit number is the smallest odd number whose digits are both themselves odd numbers." ?

Perfect example. I don't buy alietr's logic either. It didn't say the numbers had to be different, just that they were both prime.

I think alietr's correct as a grammatical exercise; the problem with OSX's clue is that there's a dissonance between the correct answer if parsed as a grammar snob and the correct answer if parsed normally--the writers would refine the wording to make it unambiguous before using the clue (or they should, anyway). If there were significant evidence that some credible mathematicians still considered 1 a prime number, then a normal reading of the clue would produce 11 as the correct response.

[skullturf]

Just found a web page that has references to 1 being considered a prime number by books as recently as 1999, but it's now considered neither composite nor prime.

Which leads to this question. If the clue is the two outermost planets in the solar system, what answer(s) are/is acceptable?

Here is the link: http://mathworld.wolfram.com/PrimeNumber.html

The work they cite with a 1999 publication date was written by G.H. Hardy, who lived from 1877 to 1947.

I'm a mathematician, and I can state unequivocally that throughout my lifetime and my parents' lifetime, the mathematical community has considered 2 to be the smallest prime, not 1.

However, I still think this wasn't a great FJ (even though it was easy for me), because it is very much vulnerable to the "common misconceptions taught in school" phenomenon. (C.f. taste bud map of the tongue, Great Wall of China only structure visible from space, etc.) Frankly, I don't doubt that some people on this board were told by their teachers that 1 is a prime.

As a specialist, it's sometimes hard for me to objective about these things, but I think it might be reasonable to say that from the general public's point of view, the fact that the primes are considered to start with 2 rather than 1 would maybe count as a slightly obscure technicality.

For anyone interested in more reading:

Spoiler

It appears there has never been a time when most mathematicians considered 1 to be prime, but many prominent mathematicians included the number 1 in lists of primes before the early 20th century. Since the early 20th century, excluding 1 has definitely been the mainstream view (although there might exist some nonzero number of holdouts).

http://arxiv.org/pdf/1209.2007v2.pdf

[This Is Kirk!]

It doesn't matter if 1 is a prime number or not; 11 can't be a right answer. The clue specified that "both themselves prime numbers" meaning it couldn't be the same digit.

Not sure about that.... what would you say is the right response to this FJ:

"This 2-digit number is the smallest odd number whose digits are both themselves odd numbers." ?

Perfect example. I don't buy alietr's logic either. It didn't say the numbers had to be different, just that they were both prime.

I think alietr's correct as a grammatical exercise; the problem with OSX's clue is that there's a dissonance between the correct answer if parsed as a grammar snob and the correct answer if parsed normally

You're going to have to explain this because I don't see what part of it suggests the two numbers need to be different. Are you suggesting "themselves" somehow implies they can't both be the same number? I don't buy it.

[countyguy]

It doesn't matter if 1 is a prime number or not; 11 can't be a right answer. The clue specified that "both themselves prime numbers" meaning it couldn't be the same digit.

Not sure about that.... what would you say is the right response to this FJ:

"This 2-digit number is the smallest odd number whose digits are both themselves odd numbers." ?

Perfect example. I don't buy alietr's logic either. It didn't say the numbers had to be different, just that they were both prime.

I think alietr's correct as a grammatical exercise; the problem with OSX's clue is that there's a dissonance between the correct answer if parsed as a grammar snob and the correct answer if parsed normally

You're going to have to explain this because I don't see what part of it suggests the two numbers need to be different. Are you suggesting "themselves" somehow implies they can't both be the same number? I don't buy it.

Just llike nobody could argue with saying that both of the digits in 11 are 1's, it seems equally outlandish to argue that you can't say both are odd. 1's are a subset of odd digits.

[Kid Charlemagne]

How cute, you're teaching wagering to Bob Shore ... Search for "Shore's Conjecture" if you want to know what he's talking about.

Tee hee...the missing knowledge on my part there is not who Bob Shore is or what Shore's Conjecture is, it's that "Bob" followed by that string of numbers *is* Bob Shore.

[Kid Charlemagne]

As a close relation of Colin's I'd like to thank y'all for commiserating, on account of he won't sign up to do so. Best of luck to Kristin going forward!

Colin did very well for himself. He played the game optimally all the way through and it appears that he had the champ out-knowledged. He sure looked ToC caliber from my couch.

He had the misfortune of running into two critical things (his second DD and FJ) he did not know. Sometimes that is the difference between victory and defeat.

[lieph82]

I thought using "both" instead of "each" and using the plurals "themselves" and "numbers" implied that the numbers would have to be different, but I'm not a grammar expert so I could definitely be (and it looks like the consensus is that I am) wrong.

[This Is Kirk!]

Come to JBoard! The place where we debate the degree of wrongness of wrong Jeopardy! answers (questions?).