Moonlighting agony uncle Professor Dirichlet answers your personal problems. Want the Prof’s help? Send your problems to email@example.com.
My wife and I are having difficulty with her shift times as a Northern line tube driver. We’re always tired when we see each other and I just feel that every point in our relationship ends up leading to an argument. Can you help?
— Complexified, High Barnet
According to the theory of Monsieur Argand, a quick look at the complex plane will tell you that every point has an argument. The good news is that it will also have a finite length. You may wish to coincide your disagreements with engineering work on the tube: any branch cuts will let you arrive at the same point by different arguments.
My parents were away for the weekend and so I invited a handful of my best friends over for a secret party. Horrifically, hundreds of randomers from Facebook turned up and made it a complete disaster. Now my parents are furious and I’m terrified.
What should I do?
— Irrational, Reading
It sounds like you hosted a non-discrete function. This is not surprising because all the functions you see in school tend to be continuous (I’m looking at you, sin(x)). The easiest way to make your functions discrete in the future is just to limit the domain. Maybe only the integers next time?
I’m taking Spanish classes to be able to speak to my boyfriend in his native language.
But when I try to speak to him at home with my new skills, he doesn’t seem to appreciate it.
Help me Dirichlet!
— Infinitely Differentiable Operator, Anglesey
You appear to be experiencing translation invariance. That is to say, $\forall x, f(a+x)=f(a)$. Don’t worry though, because there are a few things with this property that you can use even with this handicap. The less-than property is translation invariant, as is the Fourier transform. Let me know how you get on.
PS. Are you sure your boyfriend is Spanish?
My supervisor gave me a right rollocking recently for citing his full name in a paper I submitted.
Apparently he feels it is essential to not only abbreviate his first names by single letters, but also to dot and space them in a certain way, and is quite touchy about it.
Is this normal?
— S.H. Moschen, Liverpool
This sounds like a classic case of sensitive dependence on initial conditions. It is quite common in professors looking to evoke the grand age of academia, when there were few enough people in a field that everyone knew each other. It is also sometimes found in PhD students thinking they are important enough to get away with it. The style guide of the paper will ultimately dictate which convention to use, so don’t worry!
You might also like…
- Think outside outside the box in our latest issue. No more tennis puns, primes mod 4, plus all your favourite regulars.
- Pigs, popes and produce are among the topics of discussion in this issue's Dear Dirichlet advice column
- Win £100 of Maths Gear goodies by solving our famously fiendish crossnumber
- The definitive chart of the best dates
- Race to be the first to get five-in-a-row
- Vote for your favourite unit