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# Dear Dirichlet, Issue 05

Prof. Dirichlet tackles political arguments and werewolves in answering your personal problems

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 personally have a very deep, long-held belief in free-market capitalism and the value of hard work, but I was recently shocked to discover when I switched subjects that most people in my new research area are staunch followers of Karl Marx! I’ve had many arguments with my new colleagues on this. I can feel my energy slowly draining with every passing debate. How do I resolve this?

— Feeling blue, Surreyv

Dirichlet says:

Your problem is simply connected to the fact that you now work in a non-conservative field. It is quite typical in these fields for your energy to slowly decay away over time. Since you come from a conservative field, you understand that the value of work is absolute, but that’s just not the case in non-conservative fields: the value of your work can be different depending on the path you take through life! If you ever want to escape an argument, though, try curling up into a ball. Since you come from a conservative field, your curl will vanish.

### Dear Dirichlet,

I am extremely proud that my husband is a decorated major in the Army—when we met he was just a private! Now the kids have all grown up and moved out, we’re contemplating an early retirement to somewhere in the sun. But my husband heard rumours that a couple more pips on his shoulders might be coming his way soon. Without being awkward, how can we find out if he’s likely to be promoted this year, or whether the whispers are just nothing?

— Fingers crossed, Redditch

Dirichlet says:

As a keen amateur military strategist myself, I see the problem here: will your husband get rank… or nullity? For any linear map $T:V\to W$ on vector spaces $V$ and $W$,
$$\dim(\operatorname{Im} T) + \dim(\operatorname{Ker} T) = \dim V.$$
By conservation, therefore, I advise the major to look as shabby as possible and to destroy his image. Only this will increase his chances of making… colonel.

### Dear Dirichlet,

Once a month, beneath the light of the full moon, I feel inhuman strength, an animal instinct, and an overpowering bloodlust consume me, before blacking out and waking up in strange places. But there’s more: I also feel an overwhelming urge to solve exact integrals, generate pictures of pop culture characters using graphs, and perform useless calculations with obscure trivia. At first I thought I was just becoming a werewolf, but now I’m not so sure. Can you help me?

— A husky fellow, Hounslow

Dirichlet says:

Your symptoms have only one explanation: you are not a werewolf, you are a wereWolfram. It’s a known side effect of using Wolfram Alpha too much. But worry not, the solution is trivial: simply perform an inverse Furrier transform on yourself and you’ll be back in normal space in no time.

### Dear Dirichlet,

I work mornings as a cleaner in the local primary school, and whenever there’s an election on, the people who come into the school to cast their votes always leave so much litter! It can often take a lot of effort to go through and find everything they’ve left behind. Any advice on how to make the process easier?

— Swing seat sweeper, Bedford

Dirichlet says:

Tell me about it! The public really are the worst. That’s why I now live exclusively with badgers. Anyway, a contour integration should easily pick up any residue left at the polls. It’s then up to you to find the right path around them all, but it’s really not that complex.

### Dear Dirichlet,

I’m working on your divisor problem but have a few questions. Have you received my previous letters asking for help?

— M N Huxley, Cardiffc

Dirichlet says:

• ### Summer puzzles

Have a go at these puzzles, adequate for your holidays!
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New issue out now! Graphical linear algebra, slide rules and game theory in nature. Plus all your favourite fun pages.
• ### Prize crossnumber, Issue 05

Win £100 of Maths Gear goodies by solving our famously fiendish crossnumber
• ### What’s hot and what’s not, Issue 05

Mathematical fashion advice for an ever-changing world
• ### Comic: The Inverse Homotopy, part 4

Part 4 of our mathematical comic's adventure