Dear Dirichlet, Issue 19

20 May 2024

Moonlighting agony uncle Professor Dirichlet answers your personal problems. Want the prof’s help? Send your problems to deardirichlet@chalkdustmagazine.com.

Dear Dirichlet,

I’ve decided to set myself a physical challenge. I’m going to train up and apply for BBC One’s primetime show of contenders versus professional athletes. Any top tips for how to best prepare myself?

— Where’s Wolf, Derby

Dirichlet says:
Personally I’m a big fan of Dual. But I reckon I’ve cracked the Eliminator. Just run as straight as you can. If you curl at any point, you will never be able to diverge from your opponent, since

$\cdot$ $($

$\times\boldsymbol{F}) = \mathbf{0}.$

Sorry, this is about Gradiators, right?

Dear Dirichlet,

I’ve been working on a remarkable form of green transport where I take aircraft and make them fly using merely a clever arrangement of springs. The tension in the springs requires a bit of tuning, but once it’s done, the planes just bounce off the ground. I took a prototype from my workshop in Newcastle down to a field in Folkestone for an across-the-channel demo, but it was an embarrassing failure: the plane wouldn’t leave the tarmac. Was it the climate? The accent? Can you offer any technical tips?

— Roger Whittaker, Durham

Dirichlet says:
I’m sorry to hear your venture hasn’t taken off. I recommend building an associated passenger lounge, but building it on wheels. If you fix it to the ground, the plane can never take off because its terminal velocity will always be zero. As for moving the spring-based flight system to Kent, this was always a fool’s errand. As my mother used to say… “never Hooke a lift force in the south”.

Dear Dirichlet,

I got a bit excited watching Only Connect on Monday and spilled coffee over my settee. My other half is unimpressed and half a can of Vanish hasn’t fixed it. Help!

— Cif-ted flax, Chester

Dirichlet says:
For your furniture, you don’t want Vanish — you want Mr Sheen! Spray a few spots of pole-ish, imagine a circle around them, and bang! The dirt is gone! An immediate consequence of the Couch-y residue theorem.

Dear Dirichlet,

I’ve written a little Python script that runs a Twitter account. If you tweet it a mathematical expression made of brackets, it expands it out for you! How useful! But users are complaining that it’s too slow. And indeed, every time I test it, it doesn’t do anything until I look away. Is it just my lousy coding?

Attached: LOVE-LETTER-FOR-YOU.TXT.vbs

— Anna, via email

Dirichlet says:
Glad to see you are fighting in vain to make Twitter fun again. I’ve recently decided to sell half my shares in Mathstodon, AKA ‘Proof Social’, and make billions. Anyway, I’ve got bad news regarding your little project: no optimisation can improve its response time. After all, a watched bot never FOILs!

Dear Dirichlet,

After a nasty battle with some people I’m writing a paper with over whose name goes first, I received a wax-sealed letter under my door last night:

‘By order of the collaborators, you have been murdered! Signed, Anonymous.’

Who could it be from? The ghost of Erdős?

— Pichael Perry, Trieste

Dirichlet says:

Paul just couldn’t be Anon … but Gauss is.

Heed Professor Dirichlet’s previous advice:

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