Tuesday, October 23, 2018 Game Recap and Discussion (SPOILERS)

[This Is Kirk!]

I know the Beowulf story pretty well and still put down Beowulf on instinct and didn't think any more about it.

I said Beowulf. I never actually read it in high school; we read Sir Gawain and the Green Knight instead.

Is there a rule that says you're only allowed to read one of those two?

[TenPoundHammer]

I said Beowulf. I never actually read it in high school; we read Sir Gawain and the Green Knight instead.

Is there a rule that says you're only allowed to read one of those two?

At least you read SOMEthing in high school...

[twelvefootboy]

The main thing I objected to about Iain Armitage's clue is that it was incorrect. The number "1" is neither prime or composite.

Pretty straightforward FJ!.

DON'T BUMP THE MATHEMATICIAN!!

I didn't pick up on this because the contestant answered it before the clue showed up on closed caption. TIL that I never listen to the verbal clues, whether by Alex or a guest. My brain prefers not to do the audio compiling when I can sight read the question and mainline to my CPU. At most I'll notice a pronunciation from the audio. Of course, like we all do, I mentally read in Alex's voice (maybe I'll try to use an Elmer Fudd one tonight?).

The commutative property was a funny moment - I am reminded of the cliche that came out about the "New Math"; kids learn that 3+2 equals 2+3 by the commutative law but they don't know the sum.

Off topic, but kind of lottery discussion related, and of interest to the ravenous learners here:
The probability of picking an irrational number at random from the number line is 100%. Not 99.999..., but 100%.

https://www.quantamagazine.org/why-math ... -20180917/

Easy FJ, but only because it has come up before and reminded me of the wasted tuition taking required humanities classes.

[seaborgium]

Not 99.999..., but 100%.

99.999... is 100.

[Wpwells]

Not 99.999..., but 100%.

99.999... is 100.

Beat me to it.

[LucarioSnooperVixey]

52 R (Only missing the bottom three in "Beside Myself")
DD: 3/3
FJ:
LT: (The Lion, the Witch, and the Wardrobe), Genes, Albert Einstein, Commutative, Spain

[twelvefootboy]

Not 99.999..., but 100%.

99.999... is 100.

Beat me to it.

Yeah, familiar with the number theory meme. I think this comes from a different angle - the fact you can pick infinite exceptions but they don't count as contradictions. The parlor tricks that show equality of point-nine repeating to the unit are not mathematical rigor. I expect the "measure theory" alluded to here provides the rigor.

It's still kind of a paradigm shift to think the chance of landing on a natural number at random is zip (technical term is bupkus).

Spoiler

Irrational numbers occupy the vast, vast majority of space on a number line — so vast, in fact, that if you were to pick a number on the number line at random, there is literally a 100 percent chance that it will be irrational.*

* The reason it’s 100 percent and not 99.9999 percent has to do with the strange things that happen once you start thinking about the probabilities when infinity is involved. Around the turn of the 20th century, the mathematician Henri Lebesque helped to develop “measure theory,” which provided a mathematically rigorous way for calculating the probabilities when infinite outcomes are possible.

[seaborgium]

Yeah, familiar with the number theory meme. I think this comes from a different angle - the fact you can pick infinite exceptions but they don't count as contradictions. The parlor tricks that show equality of point-nine repeating to the unit are not mathematical rigor. I expect the "measure theory" alluded to here provides the rigor.

https://en.m.wikipedia.org/wiki/0.999...

There are many ways of showing this equality, from intuitive arguments to mathematically rigorous proofs.

[seaborgium]

I didn't think it was fair for Erik to be negged for "a cheatin'/cheating heart"; the clue asked for a "title thing," not for the title itself, and it's ludicrous to assert that a cheating heart is not the title thing in "Your Cheatin' Heart." It should have been BMSed if not accepted outright.

[Bartleby]

25,400 coryat. Instaget final.

Until Alex said it, it didn't occur to me that "Beowulf" might be the leading wrong answer over "the Lady Warrior/Monster" (Grendel's mother).

[twelvefootboy]

https://en.m.wikipedia.org/wiki/0.999...

There are many ways of showing this equality, from intuitive arguments to mathematically rigorous proofs.

Sigh. How about this:

It's IMPOSSIBLE to choose a random point on the number line that is a rational number. Does that blow your mind? But, but...what about 2?
The magic is embedded in the word "random", which we sophisticates understand is unachievable with our technology, try as we might. (yeah, i'm gonna regret this one )

But seriously, thanks for the pointer to the Wiki. I was wondering if the "parlor tricks" could be defeated in different bases. Nope. The quora story was insightful to me at least. The 100% probability comment doesn't properly explain the awesomeness of this perspective. No wonder Georg Cantor went to the loony bin

[mxc_takeshi]

38 right.

Literary Openings (5), Famous Person High School (2), En Français (4), Stupid Answers (5), Weights & Measures (2), "Heart" of Country (4)
Zebulon PIke's Piques (4), I'm Beside Myself! (2), Prison (3), Math Vocab (0), Contronyms (2), Heart of the Country (5)

Lach Trash: Albert Einstein; Daily Double: The Lion, the Witch and the Wardrobe

I fell into the same trap and said Beowulf at first, but changed it to Grendel just in time.

[seaborgium]

https://en.m.wikipedia.org/wiki/0.999...

There are many ways of showing this equality, from intuitive arguments to mathematically rigorous proofs.

Sigh. How about this:

It's IMPOSSIBLE to choose a random point on the number line that is a rational number. Does that blow your mind? But, but...what about 2?
The magic is embedded in the word "random", which we sophisticates understand is unachievable with our technology, try as we might. (yeah, i'm gonna regret this one )

But seriously, thanks for the pointer to the Wiki. I was wondering if the "parlor tricks" could be defeated in different bases. Nope. The quora story was insightful to me at least. The 100% probability comment doesn't properly explain the awesomeness of this perspective. No wonder Georg Cantor went to the loony bin

As far as different bases go, in any base x, a repeating x-1 after a decimal point represents a series that converges to 1. The decimal form of this represents nine tenths, nine hundredths, nine thousandths, etc. adding together; 10/11 + 10/121 + 10/1331 etc., 6/7 + 6/49 + 6/343 etc., 1/2 + 1/4 + 1/8 etc. are all series that get infinitely close to 1.

[DBear]

Instagot Grendel, looked at the clue for 30 seconds thinking "It can't be that easy, can it?".

[Linear Gnome]

But seriously, thanks for the pointer to the Wiki. I was wondering if the "parlor tricks" could be defeated in different bases. Nope. The quora story was insightful to me at least. The 100% probability comment doesn't properly explain the awesomeness of this perspective. No wonder Georg Cantor went to the loony bin

As far as different bases go, in any base x, a repeating x-1 after a decimal point represents a series that converges to 1. The decimal form of this represents nine tenths, nine hundredths, nine thousandths, etc. adding together; 10/11 + 10/121 + 10/1331 etc., 6/7 + 6/49 + 6/343 etc., 1/2 + 1/4 + 1/8 etc. are all series that get infinitely close to 1.

Looks like I missed an interesting discussion while I was out of town. My go-to argument for why .99999...=1
is the convergent infinite series argument.

I just deleted a digression into measure theory that got a little too long, but I can't let a mention of Cantor go by without mentioning the Cantor set, which has a variety of properties that I found to be mind-blowing when I first learned about it. I'm tempted to say more, but it's easy enough to look it up on Wikipedia if you're interested.

[twelvefootboy]

But seriously, thanks for the pointer to the Wiki. I was wondering if the "parlor tricks" could be defeated in different bases. Nope. The quora story was insightful to me at least. The 100% probability comment doesn't properly explain the awesomeness of this perspective. No wonder Georg Cantor went to the loony bin

As far as different bases go, in any base x, a repeating x-1 after a decimal point represents a series that converges to 1. The decimal form of this represents nine tenths, nine hundredths, nine thousandths, etc. adding together; 10/11 + 10/121 + 10/1331 etc., 6/7 + 6/49 + 6/343 etc., 1/2 + 1/4 + 1/8 etc. are all series that get infinitely close to 1.

Looks like I missed an interesting discussion while I was out of town. My go-to argument for why .99999...=1
is the convergent infinite series argument.

I just deleted a digression into measure theory that got a little too long, but I can't let a mention of Cantor go by without mentioning the Cantor set, which has a variety of properties that I found to be mind-blowing when I first learned about it. I'm tempted to say more, but it's easy enough to look it up on Wikipedia if you're interested.

I am on it, teacher!! I just discovered the Quanta magazine site - I prefer it to watching vids on Numberphile or 3 brown 1 blue. I just do better reading - listening is too slow and too many brain operations per unit input.

I am less mind blown about the zero chance to pick a rational number now that I think about the task as picking a number on the number line (at random) that has a googleplex of digits, and then is required to have an infinite number of exactly zeroes after it. Yeah, that's not gonna happen. Thanks for the prompt - I've got 300+ hits on quanta search for it. BTW, they just did a baby tutorial on the quaternions and octonions :

https://www.quantamagazine.org/the-imag ... -20181025/

I think this is because of the recent quack mathematician/physicist claim to prove the Riemann hypothesis.