This is the Noperthedron. A portmanteau of “nope” and “Rupert,” it is the only known shape that does not have a trait called Rupert’s property. No matter how you bore a straight tunnel through it, a second Noperthedron cannot fit through. www.quantamagazine.org/first-shape-...

Saturday Morning Breakfast Cereal - A Frankenstein Saturday Morning Breakfast Cereal - A Frankenstein

Relevant SMBC www.smbc-comics.com/comic/a-fran... .

Also, in the current campaign, while the Koavists have some elements from Judaism, they've got a bunch from others. In some sense they are the exact opposite of Judaism since they are pretty close to being literal ovdei kochavim.

Although I've also stolen stuff from other real world cultures and religions, that people haven't noticed. Judaism is easier because I know more about it.

Empirically, it takes very little for a general problem of a puzzle-like form to be NP-hard. I'm not aware of a general theorem that makes this notion precise. Similarly, problems in NP which are not NP-complete are also empirically very hard to come by.

Teaching summer enriched precalculus. Midterm is tomorrow. One thing I did today was to do an "Um, Actually" style game with the students where they had to say what was wrong with each statement. Here's my statement list: drive.google.com/file/d/1-8qk... .

My D&D players were going through a dungeon that had a long corridor with a series of different traps each activated by a pressure plate. They had spotted the pressure plates and were carefully walking by. Then the third plate reached out and attacked them. Turns out it was a pressure plate mimic.

So is the point how shallow markets can go to really weird places? Or that prediction markets can be really distorted by who the user base is?

Or even better "You cannot wish to change the rules of wishing, which includes this rule."

There's a whole bit in "Godel, Escher, Bach"about meta-genies which are used to make wishes about genies, and meta-meta-genies, and so on.

Can you expand on how passing necessarily can prevent a win? I'm not seeing it immediately, especially given that Connect 2 and Connect 3 this is not true for.

Kudos for predicting this!

Cato has published my comprehensive review of the ~240 Venezuelans the US government renditioned 2 months ago to Salvador’s notorious prison. We identified FIFTY who came legally, never violated any immigration law, but are imprisoned at the US government’s request and at US taxpayer expense.

My knowledge base is not great here. Anecdotally though I've generally heard the tot ending in more Conservative and Reform contexts and her the im ending in more Orthodox contexts. I don't know anything anything about the actual history though.

Sure, but this turned out to be correct in the Legends canon and that at the same time Palpatine didn't tell anyone about the threat. Star Wars is fiction, and doesn't really make that coherent consistent political points which shouldn't be surprising given the sheer number of writers involved.

In what is now the "Legends" non-canon, this is surprisingly close to what happened, in that it turns out part of why he was uniting the galaxy is that he knew about an incoming threat from outside the galaxy.

Because Shannon isn't as well known as say Gödel to the general public, and the ability to mark philosophical claims related to his work is hard so they often just don't know about it.

Proofs

I'm really curious what they were saying this about. Also, relevant xkcd xkcd.com/1724/ .

Re: Using Desmos, for the basic Algebra II, I'd say this is fine. For any higher level version of the course, they should be able to do it algebraically to at least show that x=4 is the only solution. But using Desmos to identify a potential solution seems fine at all levels in most contexts.

Both of these seem like reasonable ways of doing this problem. Related: my algebra II students seem to have a lot of trouble deciding when to reject a negative number. e.g. Some will correctly reject -4 in the above, but then will reject log_2 x=-1 in (log_2 x)^2 =1.

New Proof Settles Decades-Old Bet About Connected Networks | Quanta Magazine According to mathematical legend, Peter Sarnak and Noga Alon made a bet about optimal graphs in the late 1980s. They’ve now both been proved wrong.

According to mathematical legend, Peter Sarnak and Noga Alon made a bet about optimal graphs in the late 1980s. They’ve now both been proved wrong. Leila Sloman reports: www.quantamagazine.org/new-proof-se...

Update: Oscar Cunningham has pointed out serious issues with their statistical analysis and has pointed out that using the tests they are using even genuinely random strings of digits don't look "random" so the paper is fatally flawed.

Digits of pi: limits to the seeming randomness II According to a popular belief, the decimal digits of mathematical constants such as π behave like statistically independent random variables, each taking the values 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 wi...

arxiv.org/abs/2504.10394 A neat paper by Paula Roba and Karlis Podnieks just came out showing that the digits of pi (and e and some other constants) don't actually seem to follow a lot of statistical tests we might expect if they were genuinely random.

One thing I find frustrating is that my intuition really strong back up both of these as slamdunk arguments even though I intellectually realize that they are both terrible arguments for exactly the reasons you outline.

My Algebra II students have been making tricky log system problems that have nice answers. drive.google.com/file/d/1Iu6A... has their problems and answers. They had a lot of fun making these, and some of these are just fiendish.

Challenge problem I'm considering giving to my Accelerated Algebra II students:

Can you find all natural numbers a and b such that
log_3 a + log_9 b = log_3 (a+2b) ?

I liked a world where Guards! Guards! wasn't talking as much about the current state of things. (It is however one of my favorite Discworld books.)

We've also learned so much from you. I said to someone a while ago "I'm not a logician, but I read JDH's questions and answers on Mathoverflow regularly."

Huh, really? What's the etymology of how that happened?

There is a bit in the Talmud which asserts that the Tachash was in fact a unicorn. So, I'm wondering why has no one made the obvious suggestion: tachash is a narwhal. 2/2