Maths

[Blumf]

Crucially, that problem only makes sense if the host knows what's behind the doors and isn't obliged to tell you you've picked the car if you do so first time. The behaviour of the host completely affects the probabilities, leading to all manner of confusion and mathematicians losing their shit because they understand the maths but not what the question is actually asking. Failure to state the problem correctly leads to chaos.

Nah, that's the whole point of the puzzle. The host actually provides you with useful information, despite seemingly not doing so.

It's somewhat analogous to those puzzles where people wear hats or something and can't see their own.

[Twit 2]

Nah

I'm not sure what you're disagreeing with. Of course the information you're given helps. Hence the behaviour of the host affects the probabilities.

[Blumf]

I'm not sure what you're disagreeing with.

leading to all manner of confusion and mathematicians losing their shit because they understand the maths but not what the question is actually asking

No mathematician is losing their shit or misunderstanding the question.

[pancreas]

No mathematician is losing their shit or misunderstanding the question.

I confirm this to be the truth. I think you may have misunderstood what is going on, Twitters.

[Twit 2]

No mathematician is losing their shit or misunderstanding the question.

It's famous for exactly that. Read the wiki. Lots of esteemed mathematicians embarrassed themselves:

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

[jamiefairlie]

It's famous for exactly that. Read the wiki. Lots of esteemed mathematicians embarrassed themselves:

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

They did but because they were wrong. I made the same mistake and had to brute force the solution (map out all the possible outcomes in a matrix) to satisfy myself that it was indeed correct.

[kalowski]

Just remember that your first choice is more likely to have been the goat, therefore a switch is the sensible move.

[Johnny Yesno]

Crucially, that problem only makes sense if the host knows what's behind the doors and isn't obliged to tell you you've picked the car if you do so first time. The behaviour of the host completely affects the probabilities, leading to all manner of confusion and mathematicians losing their shit because they understand the maths but not what the question is actually asking. Failure to state the problem correctly leads to chaos.

I think that's actually the most interesting take away from the problem. It's made me much more cautious around probabilities and that has to be a good thing. The 'imagine if it was a million doors' scenario is also very illuminating.

[Johnny Yesno]

Yep. Little colour to help highlight:


⬤⬤⬤⬤⬤⬤⬤⬤⬤⬤⬤
⬤⬤⬤⬤⬤⬤⬤⬤⬤⬤⬤
⬤⬤⬤⬤⬤⬤⬤⬤⬤⬤⬤
⬤⬤⬤⬤
⬤⬤⬤⬤⬤⬤
⬤⬤⬤⬤⬤⬤⬤⬤⬤⬤
⬤⬤⬤⬤⬤⬤⬤⬤⬤⬤⬤
⬤⬤⬤⬤⬤⬤⬤⬤⬤⬤⬤
⬤⬤⬤⬤⬤⬤⬤⬤⬤⬤⬤⬤

⬤⬤⬤⬤⬤⬤⬤
⬤⬤⬤⬤⬤⬤⬤
⬤⬤⬤⬤⬤⬤⬤
⬤⬤⬤⬤⬤⬤⬤
⬤⬤⬤⬤⬤⬤⬤
⬤⬤⬤⬤⬤⬤⬤
⬤⬤⬤⬤⬤⬤⬤⬤

I kind of get this now I've seen the solution but I feel your instructions are confusing here:

Now, the puzzle:

Figure out how 8 equal triangle numbers plus 1 will always form a square.

For example, 1 triangled is a single dot *, 8 of them, plus 1 dot *:

*********

Which is 9 dots in total, which as we saw above can be arranged as 3 squared:

***
***
***

8 isn't a triangle number, is it? But 9 is a square. Surely if we're going to go from a triangle to the square number 9 by altering one *, then that triangle needs to be 10 and we need to remove a * not add one.

As I say, I get it now but that's why I was at a loss as to what this puzzle was about.

[Blumf]

I kind of get this now I've seen the solution but I feel your instructions are confusing here:

Figure out how 8 equal triangle numbers plus 1 will always form a square.

For example, 1 triangled is a single dot *, 8 of them, plus 1 dot *:

8 isn't a triangle number, is it? But 9 is a square. Surely if we're going to go from a triangle to the square number 9 by altering one *, then that triangle needs to be 10 and we need to remove a * not add one.

8 isn't a triangle number, but 1 is, 8 of those ("8 equal triangle numbers") makes 8, i.e. 1 (the first triangle number) times 8 (plus 1 = 9 = 3²)

For comparison, the sample visual solution uses the third triangle number which is 6, and 8 of them makes 48 (plus 1 = 49 = 7²)

I used the first triangle number as it's easy to layout the square without hinting at the solution.

I don't know, maybe "take 8 copies of the same triangle number" would have been a better phrasing.

[pancreas]

It's famous for exactly that. Read the wiki. Lots of esteemed mathematicians embarrassed themselves:

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

This page is a fucking sewer.

Erdos is indeed a top notch gold plate mathematician. Like beyond parallel. Like I am not bad, in the grand scheme of things, but I would be less than the shit on his shoe. So I simply do not believe that he didn't understand the point that was being made, unless it was explained so poorly it was not possible to understand. The citation here:

https://web.archive.org/web/20140413131827/http://www.decisionsciences.org/DecisionLine/Vol30/30_1/vazs30_1.pdf

Is barely literate. I don't trust it.

[Zetetic]

Erdos is indeed a top notch gold plate mathematician.

For context, Erdős has been dead for 25 years.

[pancreas]

OH IS HE

[Johnny Yesno]

8 isn't a triangle number, is it? But 9 is a square. Surely if we're going to go from a triangle to the square number 9 by altering one *, then that triangle needs to be 10 and we need to remove a * not add one.


8 isn't a triangle number, but 1 is, 8 of those ("8 equal triangle numbers") makes 8, i.e. 1 (the first triangle number) times 8 (plus 1 = 9 = 3²)

For comparison, the sample visual solution uses the third triangle number which is 6, and 8 of them makes 48 (plus 1 = 49 = 7²)

I used the first triangle number as it's easy to layout the square without hinting at the solution.

I don't know, maybe "take 8 copies of the same triangle number" would have been a better phrasing.

Yes, I think it was using the first triangle number that was confusing, though I do see why you chose it. Also, I mistakenly thought what you meant by 'equal triangle number' was one where all the sides were equal (again, in retrospect, this is obviously not the case). Your suggestion of 'the same triangle number' is definitely more clear, though.

[Johnny Yesno]

For context, Erdős has been dead for 25 years.

No wonder he's rubbish at maths.

[pancreas]

I doubt anyone who reads the article cited in wikipedia would need convincing, but just in case:

Its 'internationally recognized author, researcher and educator', who claims to be a mathematician:



and

[kalowski]

Maybe Vazsonyi has an Erdös number?

[pancreas]

MR Erdos Number = 3
Andrew Vazsonyi    coauthored with    William Karush    MR0086718
William Karush    coauthored with    Richard Ernest Bellman    MR0152371
Richard Ernest Bellman    coauthored with    Paul Erdős1    MR1543984

Same as mine, fwiw.

[Chedney Honks]

Maths = peado

[kalowski]

MR Erdos Number = 3
Andrew Vazsonyi    coauthored with    William Karush    MR0086718
William Karush    coauthored with    Richard Ernest Bellman    MR0152371
Richard Ernest Bellman    coauthored with    Paul Erdős1    MR1543984

Same as mine, fwiw.

That's cool. Your Erdös number, not Vazsonyi's.

[Ferris]

I would be less than the shit on his shoe.

Never heard of this Erdös berk but I've been making this point re: pancreas for years.

[Twit 2]

Failure to state the problem correctly leads to chaos.

So I simply do not believe that he didn't understand the point that was being made, unless it was explained so poorly it was not possible to understand.

This is what I said to begin with. Do keep up.

[kalowski]

I'm still amazed (even though I've seen a proof) that the sum of the reciprocals if the squares is π²/6.
That is
1/1² + 1/2² + 1/3² + 1/4² + ... = π²/6

[Johnny Yesno]

This is what I said to begin with. Do keep up.

To my mind, it's as much a language puzzle as it is a maths one. Little details like 'the host, who knows what's behind the doors' critically influence the outcome.

[Bigfella]

MR Erdos Number = 3
Andrew Vazsonyi    coauthored with    William Karush    MR0086718
William Karush    coauthored with    Richard Ernest Bellman    MR0152371
Richard Ernest Bellman    coauthored with    Paul Erdős1    MR1543984

Same as mine, fwiw.

Any chance of a 'layman's terms' here?  Does everyone have an Erdos number?

[kalowski]

Not if you've never authored a mathematical paper.
If you wrote a paper with Erdös your Erdös number is 1.
It you wrote a paper with some who has authored a paper with Erdös your number is 2, and so on.

[Ferris]

I'm still amazed (even though I've seen a proof) that the sum of the reciprocals if the squares is π²/6.
That is
1/1² + 1/2² + 1/3² + 1/4² + ... = π²/6

I mentioned it on the first page but can anyone explain how the sum of all integers =-1/12 in a way that won't make me say "err bullshit that mate".

I made a maths lecturer quite cross by saying "err don't think so mate, sums to infinity mate, not a convergent series is it mate?" and he said it wasn't relevant and asked me to send him an email separately (no thanks pal you are crackers).

[pancreas]

This is what I said to begin with. Do keep up.

Yeah but the Monty Hall problem is not contentious whatsoever in the mathematical community, which is what you seemed to be implying.

It entirely possible that this Vazsonyi guy had Erdős[nb]It seems the Hungarian 'ő' is ASCII 0337, Unicode HEX: U+0151: Latin small letter o with double acute[/nb] staying with him, because apparently Erdős never rented anywhere himself and spent his time flitting from one person's couch to another and remunerating them with joint papers. Obviously Vazsonyi was not much cop as a mathematician, so it is unsurprising that he didn't write such a joint paper.

It is therefore possible that Vazsonyi had occasion to tell Erdős about the Monty Hall problem.

It is just possible—though unlikely—that Vazsonyi is telling the truth that Erdős's immediate reaction was to say the sight of a goat shouldn't make any difference; this assumes he was distracted and uninterested in what Vazsonyi was saying, which is possible since he was on amphetamines 24/7. But if it did happen then probably having Vazsonyi telling him he was wrong and bleating at him about 'decision trees' (which structures I would guess have zero mathematical value) generated a short conversation in which Vazsonyi decided to believe that Erdős could not be convinced that it is better to change the door.

It is certainly not the case that Erdős went to his grave believing p(door chosen is correct | sight of goat) = 1/2 if he gave the problem any further thought whatsoever.

[kalowski]

I mentioned it on the first page but can anyone explain how the sum of all integers =-1/12 in a way that won't make me say "err bullshit that mate".

I made a maths lecturer quite cross by saying "err don't think so mate, sums to infinity mate, not a convergent series is it mate?" and he said it wasn't relevant and asked me to send him an email separately (no thanks pal you are crackers).

I can't remember the "proof" but your lecturer friend is right. It's a non convergent series so does not have a sum to infinity.

[kalowski]

I suppose it is a bit like.1-1+1-1+1-1+1-1+1-1... = A
Obviously A = 0:
(1-1)+(1-1)+(1-1)+(1-1)+... =0
Or A = 1
1 +(-1 +1) +(-1 +1) +(-1 +1) +(-1 +1) +... =1