Early-Years science: Intro 5 May 2021 Whilst I was on paternity leave, I made up simple science experiments and activities to do at home with K     and E     . I still do now.

What I do is very simple. I usually make up science activities on the spur of the moment, using whatever materials we have around the house. Often ideas for experiments come from questions K     or E     ask me, or things we notice whilst out and about. Very often the experiments don't work first time. Then K     , E     and I discuss together why it didn't work, think about ways to adapt it, and try again.

My intention isn't to "teach them science". Knowing by age 4 that plants needs water and light to grow, or that electricity only flows in circuits, is irrelevant. What I want to introduce them to early is how to look at the world scientifically and how to think like a scientist.

Early-Years Science: Buoyancy and Displacement 1 May 2021

Early-Years Science: Floating and Sinking 17 May 2020

Early-Years Science: Cress-Growing 29 April 2020

Toby's ten commandments of being scooped 25 July 2018

[To be read in alongside Luc's ten commandments of authorship.]

Rule 1

Never consult a list of rules regarding being scooped.

Rule 2

Be happy: it implies \(\geq 1\) other person is interested in the problem you solved.

Rule 3

You hear about the other author's paper before it's posted on the arXiv, and are on friendly terms with them. Politely ask if they'd be willing to post to the arXiv simultaneously. This is a win-win: both papers will look more important and get more attention. If they don't agree, go to Rule 6. In either case, cite the other paper and be generous in crediting them.

Rule 4

You agree to post simultaneously, but then they ask for more time. Be generous and give them plenty of extra time. You will feel good. When you post yours, cite the other paper and be generous in crediting them.

Rule 5

You agree to post simultaneously, but then you need more time. Go home, have a beer, tell them you're not going to make the agreed date and let them post first. When you post yours, cite the other paper and be generous in crediting them.

Rule 6

The other results appear on the arXiv before yours, but you can post your results soon enough that it's clearly independent work. Go ahead and post them. You'll still get credit for the work. Cite the other paper and be generous in crediting them.

Rule 7

You're not ready to post soon without stressing about it, but the differences in your results are interesting and you're motivated to work on them. Work on those, post your paper when you have interesting new results. Be happy, smile. You've advanced science a few more steps. Cite the other paper and be generous in crediting them.

Rule 8

Your results are very similar, and the differences aren't interesting enough to you. Get your mind off it—crying, sex, indulging, smoking, hallucinating, and swimming in the North Sea may help. After doing \(\geq 1\) of those activities, look at the differences with fresh eyes. If they look interesting now, go back to Rule 7. If not, let this one go. There are infinitely many new and interesting problems to work on: go and work on one of those.

Rule 9

It happens - do not get stressed about it.

Truths about proofs and groups 9 February 2018

A while back, a PhD student in our group asked me whether the sum over all elements of a stabilizer is a projector. If you know what this means, you're probably (a) a quantum information theorist (in which case, stop reading here) and (b) already know the answer and how to prove it (unlike me, who'd forgotten both).

The answer is no doubt well-known to anyone who works on quantum stabilizer codes, and we could have just googled for the result. It seemed like a nice, self-contained mathematical question, though. So rather than googling, we tried to figure it out for ourselves at the blackboard.

If you just want to see the simple final answer, skip to the end. But then you'll miss all the fun and the main point of this post. The way we came up with the solution makes for a nice toy example of the convoluted, messy and inelegant process by which mathematical results are really proven. Before they get polished up into the simple, elegant, pristine proofs "from The Book" that are all you ever get to see in textbooks and research papers. The unspoken (or at least unpublished) reality is that elegant proofs invariably emerge after following numerous blind alleys, unjustified intuitive leaps, and inelegant, round-the-houses arguments. All of which get simplified away in time for publication. (Or maybe that's just my proofs!)

Instead of just explaining the elegant final answer, I'm going to explain the inelegant process we went through to reach it.

Research interests

Publications You can also find most of my papers on the arXiv (which is sometimes more up-to-date than this list).