# Dear Dirichlet, Issue 12

Books, business and barns are the topics readers have sent in to the professor’s postbox this issue

Peter Dirichlet thinking about love.

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

### Dear Dirichlet,

I have recently entered retirement, having handed over my day job—writing bafflingly popular hyper-violent thrillers which end with the villain getting crushed by an oak bookcase—to my younger brother. But I now find myself with time (as well as coffee and cigarette stains) on my hands. I’m thinking of dipping into movie making. Any good plot ideas?

— Leigh Children, now Wyoming apparently?!

Dirichlet says:

I had a dream last night about a sixth Terminator sequel, but this time with replicating Terminators. Like babushka dolls, each Terminator spawns l, 2, or 3 new Terminators, causing red-eyed havoc. Linda Hamilton returns to find a way to halt the exponential clone takeover… I call it ‘$R_0$ Schwarzenegger Is Greater Than One’.

It’s a winner, Leigh. That’s for damn sure.

### Dear Dirichlet,

I have recently taken over the family business, writing bewilderingly successful super-brutal novels which culminate with the bad guy getting squashed by a large piece of hardwood furniture. Despite the fact that my brother never seemed to bother planning his stories before starting, without any new ideas I’m really struggling. I don’t want to let the family down—any outlines?

— Andrugh C., Wyoming

Dirichlet says:

A chemical substance is let out onto the streets of small-town America, but this stuff is dangerous. Formed of two elements, it replicates itself! Left alone, it grows in size. The only law it obeys is the iron law of geometric progression. It attracts a lot of attention… I call it ‘Compound Interest’.

You can’t lose, Andrugh.

### Dear Dirichlet,

Last week, a farmer friend invited me round to her barn to catch up: a few drinks, mostly outside, meet her horses etc. After I arrived, I realised she had invited loads of other people. All in the barn, nowhere near enough social distancing, rule of six evaporated. I’m feeling fine but I’m worried I might have been exposed—any advice to help me calm down?

— Neigh-sayer, Hartlepool

Dirichlet says:

I’m afraid it all depends on the eigenvalues of the barn. Positive eigenvalues lead to exponential growth. If you’re not sure, were there any computers or security cameras installed, maybe to watch over the horses? That’s a classic sign of `in-stable-IT’. If not, you might be OK: negative eigenvalues tell you that the barn was asympto(ma)tically stable.

### Dear Dirichlet,

As the nights draw in, I thought I might use the time in the evenings to learn some new piano music. I fancy singing along to some of Tom Lehrer’s newly public domain party pieces, but they’re all a little high for my singing register. I could do with bringing them all down a few notes, but that’s going to take forever to rewrite. Any tips to speed it up?

— Agnes, The Pub/Club/Loo

Dirichlet says:
Here, I’ve transposed it for you.

### Dear Dirichlet,

We’re sneaking a few weeks’ holiday next month, and we reckon we’ll be driving past your cottage in Belgium. If you see us, give us a wave!

— Prue & Paul, Essex

Dirichlet says:

I’ll give you one in both directions:
$u(x,t)=F(x-ct)+G(x+ct).$

## Heed Professor Dirichlet’s previous advice:

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• ### 2020 Book of the Year vote

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• ### The Wonder Book of Geometry

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• ### Hello Numbers! What Can You Do?

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• ### Why Study Mathematics?

We review the fifth of this year's nominees for the Book of the Year
• ### Molly and the Mathematical Mystery

We review the fourth of this year's nominees for the Book of the Year