Mathos

Carl Sagan when asked, "Are you a Socialist?"

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This thread shows a neat way of answering a question which comes up in university entrance interviews.

(Apologies for the lack of alt text -- I can't do symbols)

And one which the computer says can only be solved by brute force. I disagree.

sudokupad.app/bgwryrf3cb

And one with non standard regions

sudokupad.app/l58oja5ymx

And another

sudokupad.app/cosbmua5uy

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A few variant sudokus just for fun on Friday!

sudokupad.app/qo60vvqcj7

"The Creation of Adam"
#mathart #chaos

Old friend just laid off by USDA, 1 mos short of his probationary period as senior researcher. Brilliant person who left a tenured faculty position several yrs ago to join USDA. Bright early-career researchers also being laid off. USDA is terminating a generation of highly-qualified scientists.

Yesterday, I said "tomorrow" ... and the answer is a/b/c = 10/2/2025.

YouTube video by ProPublica “We Want the Bureaucrats to Be Traumatically Affected”

Scientists, as well as bureaucrats.

This is the head of OMB, folks. He coauthored Project 2025. This is the playbook we are seeing with the attacks on DEI efforts, on healthcare, on NSF and NIH funding.

They want us out of the way so they can destroy many institutions and resegregate the rest.

Given that a,b,c are natural numbers and a^(b+1)+b^a+1=c=∑_1^(a-1)▒i Find the smallest possible values of a/b/c. Answer tomorrow.

1. From morning EST to evening PST, I receive an email roughly once every three minutes. Overnight the pace slows, but not all that much. If I did nothing but read email and reply 12 hours a day I could probably keep up.

A once-wonderful productivity technology is killing any hope of productivity.

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If I were being interviewed, I would feel much safer using the direct approach than the assume and solve approach.

And the equation whose roots are a,b is x^2-√24 x+1 So x=(√24±√(24-4))/2=√6+√5

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If we set a=√(11+√120) ,b=√(11-√120) then ab=√(11^2-120)=1 So 〖(a+b)〗^2=a^2+b^2+2ab=11+√120+11-√120+2=24 a+b=√24

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Here is another example where the direct approach seems far safer…

Simplify

√(11+√120)

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YouTube video by blackpenredpen I got this asked as a Cambridge interview question and I didn't have a f**** clue

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Mostly, in the videos I have seen, they do the simplification by assuming the form of the likely answer – eg that it will be r+s√n for some integers r,s and then solving for these integers.
www.youtube.com/watch?v=naGk...
There is a direct way, which seems neater to me…

A text including mathematical expressions

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This thread shows a neat way of answering a question which comes up in university entrance interviews.

(Apologies for the lack of alt text -- I can't do symbols)

That may be ok for a conversational partner, but it's a really bad thing for search and retrieval, let alone for conducting scientific analysis.

So yeah, you typed the same query I did and got a different result. That hardly a rousing endorsement of an information system.

Yet more from the @quantamagazine.bsky.social archives: always useful in #cryptography to know more about primes! www.quantamagazine.org/a-numerical-...

I’ve been thinking about this guy’s post a lot and I think it encapsulates a lot of what disturbs me about GenAI - people keep trying to use it to automate things that are actually important to us as humans (creative thought processes, social interaction) AND

those things also coincidentally tend to be things our society devalues.

Like playing with a 6yo. Listen, that shit is fucking exhausting. This age is peak Needs A Ton Of Stimulation. They want to riff and improv on imaginary narratives. It’s developmentally normal af. But they need a human.

So it struck me that she enjoyed the “top hat and shoes” she made WITH HER DAD. It wasn’t about an interest in fashion, it was about her finding a way to play with the toy with her dad. Another human. The social interactions involved in that form of play.

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And it is surprising that a logical step by step solution can be found (by a human, not by the computer) for this one.

Can you find it?

sudokupad.app/s2rj8n1va1

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Short thread on Anti-chess sudoku.

In anti-chess sudoku, as well as the normal rules of sudoku, the following constraints must be met:
• no digit can be a king's move or a knight's move away from another instance of that same digit;
• consecutive digits must not be orthogonally adjacent.

What Is Entropy? A Measure of Just How Little We Really Know. | Quanta Magazine Exactly 200 years ago, a French engineer introduced an idea that would quantify the universe’s inexorable slide into decay. But entropy, as it’s currently understood, is less a fact about the world th...

The information version of entropy is very important in cryptography! And the quantum version is becoming steadily more important too.... from @quantamagazine.bsky.social www.quantamagazine.org/what-is-entr...