Everyone has good days. You’re focused and creative and the work you produce is great. That’s the work that best reflects you; it’s the way you want to be known and remembered.

Except, this is an illusion. It has gradually dawned on me that I can’t wait until I feel perfect before I start work on a particularly beloved or difficult project. The opportunity cost is too great. I must accept that I’m not as good as my best; I’m only as good as my average.

This is not to say that I don’t pay any attention to the way I’m feeling. I still chew gum and drink coffee to improve focus. I still look for easy tasks like filing, shredding and organising when I’m feeling particularly wretched. I still call it a day when struggling with a problem that only a good night’s sleep can solve. But I’ve stopped waiting for that perfect feeling and learned to just enjoy it when it happens. The key to...

Optimal foraging theory has always fascinated me. It is an attempt to formalise and explain how animals allocate time and energy to best exploit the resources within their environment. Thus an animal judges how to offset the energy it loses whilst searching for and handling food against the energy it gains from consuming food. The basic assumption, as with all optimality models, is that the animal makes perfect decisions based on the information available. This assumption, along with the extreme simplicity of many attempts to model foraging behaviour, has led some to dismiss the theory as irrelevant. In terms of predictive power, it’s difficult to argue with this position: foraging is hard to quantify in anything other than the most simplistic and contrived of scenarios. For me, however, the beauty of the theory is not in its predictive power, but in the rich vocabulary it offers for...

It is sometimes said that children are the effortless, unencumbered philosophers that we wish we could be, delivering queries on free will, consciousness and the nature of time. But I have discovered their secret. For every intellectual jewel there’s a tonne of rubble to sift through: “Why do I have to wear trousers?”, “Are we there yet?”, “Would you like to eat my smelly socks?”. If children produce nuggets of wisdom, it is because parents are panning for gold.

What John Conway’s ‘life’ teaches us about data compression, gene expression and the description of organisms

The mathematician John Conway is responsible for a simple but thought-provoking game called ‘life’ that has become a popular tool for demonstrating how complexity can emerge from the simplest of rules. Life is not, strictly speaking, a game, rather it is a type of model – a cellular automaton – that comprises a two-dimensional grid and a set of rules which determine the status (‘alive’ or 'dead’) of each cell across successive generations. The rules are as follows:

• Isolation: less than 2 live neighbours kills a cell
• Overcrowding: more than 3 live neighbours kills a cell
• Goldilocks: 2 or 3 live neighbours allows a cell to stay alive
• Birth: dead cells with precisely 3 live neighbours come to life

Whilst most starting configurations result in patterns of activity that quickly...

During the period from 2008 to 2014, I spent a great deal of time commuting into Sheffield on the Supertram. It was a reasonably long journey – around 40 minutes each way – which afforded plenty of time to think and observe, and after a while I got into the habit of writing tweets to pass the time. It was a bit like a game or a puzzle: I’d spot something interesting and attempt to distil what I saw into 140 characters. Tram travel is a fairly mundane affair, but I found that it holds its own unique and understated interest and I attempted to convey some of that in my tweets. At the time, people were kind enough to say that they enjoyed reading them and some people suggested that I compile them. For me they hold a certain sentimental value being as they are a record of my often dreary commutes through Sheffield: a city that for all its architectural mishaps has a special charm that is...

In his 1999 book, the geneticist Steve Jones describes a problem with industrial soap production that he encountered as a young man. The process involved blowing liquid through a nozzle at high pressure in order to produce soap powder. Due to nozzle’s imperfect shape, it was prone to clogging and a better design was sought; however, designing a three dimensional shape that would work more efficiently and consistently than the original was beyond the skills of the engineers, such are the challenges of fluid dynamics. Despite this, a better nozzle was eventually created and the method employed in finding its shape neatly encapsulates the process of evolutionary problem solving:

Take a nozzle that works quite well and make copies, each changed at random. Test them for how well they make powder. Then, impose a struggle for existence by insisting that not all can survive. Many of the altered...

Shopping on a Saturday night is a quiet affair; most people have better things to do. I don’t. I choose to take advantage of the calm conditions. On my way, I listen to loud dance music in the car. An old couple in the car park give me a wary glance and I realise that the bassy music is intimidating. As I emerge from the car, their anxiety melts away at the sight of my scarf and driving glasses. No danger here, just a head buzzing with reverse cymbal, a sound that is surprisingly hard to get out of one’s mind: reverse cymbal as I inspect the cauliflowers; reverse cymbal as I browse the tinned fish. Nobody notices the incongruity of my internal soundtrack in the sedate, brightly lit aisles, but I do. There’s no one to get in my way so I take my time and do a careful shop, and I start to grow attached to the contents of the trolley. What if someone made off with the trolley? I’d lose all...

Inception and The Matrix are films that tell compelling stories about people living within simulated worlds. In the case of Inception, the simulations are created in the dreams of corporate spies known as ‘Extractors’; in The Matrix, the simulated world is an illusion created by machines as a means of enslaving humanity. Both films explore the issue of how someone could possibly know if they were in a simulation, and the feeling we get is that perhaps we wouldn’t.

Whilst people might be prepared to acknowledge the power of such an illusion for the characters in a film, presumably rather fewer would accept that there is a genuine chance they are in a simulation right now. One barrier to taking this notion seriously is the fact that there is currently no technology capable of performing such simulations. But that is not to say this technology will always be beyond us. It is reasonable to...

Children are fascinating for all sorts of reasons, from their mind-boggling learning abilities to their unshakable cheeriness and desire to have fun (apparently frontal lobes turn you into an arsehole), but lately the thing that particularly interests me is their uniqueness.

This individuality owes much to the genetic relationship between parent and offspring. Children contain half of each parent’s genome, but in a form that is truly unique, the chromosomes having been created from a process of random selection and recombination as part of the magic of meiosis. The result, as we all know, is that children look and behave differently to both parents but simultaneously exhibit that peculiar trait known as family resemblance: the similarity that occurs when unrelated adults are linked in our minds by the phenotypic bridge provided by their children. Furthermore, owing to a giant mismatch...