Pinned toot

I'll be cleaning this up over the weeks to come, but in addition to looking for standard funding sources, I'm opening the tip jar.

I'm a math grad student, persistently cashflow-negative, trying to hold up the finances through my masters thesis before I can get into a phd (hence paid) position.

I plan to be more vocal with what I do, and contribute in other ways, but... Patronage of the sciences is a thing, right?

If you really want to know how my day was, I overlooked $$\sqrt{-m}\sqrt{mn}=-m\sqrt{-n}$$ for several hours. And then I made a sign error.

sage: 1/8 * ((z-1/z)+sqrt(-19)*(z+1/z)) * ((z^2-1/z^2)+sqrt(-19)*(z^2+1/z^2)) *
....: ((z^3-1/z^3)+sqrt(-19)*(z^3+1/z^3))
1/8*(sqrt(-19)*(e^(6/7*I*pi) + e^(-6/7*I*pi)) + e^(6/7*I*pi) - e^(-6/7*I*pi))*(sqrt(-19)*(e^(4/7*I*pi) + e^(-4/7*I*pi)) + e^(4/7*I*pi) - e^(-4/7*I*pi))*(sqrt(-19)*(e^(2/7*I*pi) + e^(-2/7*I*pi)) + e^(2/7*I*pi) - e^(-2/7*I*pi))

...useless!

productivity theatre: me adjusting blankets as if propped up with a blanket over my feet is somehow less 'working sick from bed' than propped up with the same blanket up to my waist

My bibliography just spilled over onto the second page...

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hot take:

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@kimreece @hex
Is "kittens always go quantum in the end" the new "cats always land on their feet"?

If I pull a proof out of my hat, at this late stage, ... well I'm not going to claim it's impossible. After all, I haven't proven that it can't be done.

everyone else explaining 1÷1=1: 'so you put one cat in one box,'

me explaining 1÷1=1: 'Viewing division as fractions, and fractions as quotient groups, 1/1 is a representative element of a/a which has the properties of the identity in the quotient group defined by the relation (a/b~c/d iff ad=bc), it must therefore be canonically identifiable with the identity element of the underlying group.'

.. I appear to be contaminated and should probably not be allowed near lower division students? ;)

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this planet isn't going to hack itself

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Anybody know any wiki software that can federate besides FedWiki?
(which is brilliant but bewilders many people. I'm asking about something that offers topic and sub-topic navigation like a typical wiki, but where an instance created by one community can federate with instances created by other communities.

Ok, this one is generic enough to pose...

If $$\pi \in \mathbb{Q}(\sqrt{mn})$$ a totally positive real number, letting $$\jmath : \sqrt{-m}\mapsto -\sqrt{-m}$$ and $$\tau : \sqrt{-n}\mapsto -\sqrt{-n}$$, it is clear that $$\pi^\jmath = \pi^\tau$$. When does $$(\sqrt{-\pi})^\jmath \ne (\sqrt{-\pi})^\tau$$?

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abductive reasoning is when aliens tell you the answer

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@kimreece I'm somehow reminded of the many mathematical uses of the word "regular". Mathematicians are almost as lazy about naming sometimes as colonial road builders: Queen Street, King Street, Regent Street; regular, irregular, quasiregular, pseudoregular...

purely imaginary and totally imaginary do not mean the same thing, and you really want to be careful which one you use.

No good typos yet today. Only, I am getting a lot faster at typing in LaTeX! It can be learned! And I'm so glad that \ key on my keyboard is in a good place so I didn't have to remap it...

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Here is how it came out. Blue in the left is this filament printed with the default pattern. On the right, printed with the hilbert curve pattern. I like it a lot

Very serious math threads we have over there. ;)

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Did you know shaving with heat vision bounced off a mirror is one of the most well-established bits of his canon? Here it is across three different media: live-action, animation, and comics.

I find it hilarious that of all the inconsistent abilities and background elements of Superman's canon, shaving is the one that the authors all agreed upon.

Strangely, no good typos today.