Tag Archives: mathematics

Population peaks, random walks and Catalan numbers

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Is humanity at peak population? In other words, is the total number of humans in the world currently the highest it’s ever been?

It seems like a simple question. And the answer seems obvious too: yes.

The last significant reduction in the human population occurred during the Black Death in the 1350s. Since then, it has been rising without interruption. It’s risen especially quickly in the last century, from about 2.5 billion in 1950, to 8 billion by 2022. And although the growth rate is now slowing, the population is still rising: it’s estimated at about 8.1-8.2 billion as of February 2025. The UN projects that it will continue to rise until it reaches over 10 billion in the late 21st century, at which point it will start to decline. But clearly, given that we’re still on the upward slope, the population right now is bigger than it’s ever been.

That’s certainly true on a large scale. If we were to take a look at the current population estimate every day this year, the number would always be higher than the previous day. But it’s not so simple on the small scale.

Imagine that we could know, precisely, every time a person was born or died anywhere in the world. In other words, imagine that the Worldometer tally wasn’t an estimate, but a realtime monitor with perfect accuracy. At any given moment, would that tally be at its all-time peak? Well, every time someone dies and the tally decreases by one, the population is not at its peak: it’s one below the previous value. During the brief interval before another birth occurs, the human population is not at its all-time peak. If the next event is another death, it’ll be at least two more events before the population is at peak again. So, considering the population at unit precision, even though births happen more frequently than deaths and the population is rising overall, for a significant proportion of the time it’s not true to say that the population is currently the highest it’s ever been.

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Manufactoria: a brain-expanding puzzle game

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I finally completed Manufactoria.

Manufactoria is an online puzzle game, which is deceptively simple and surprisingly deep. Your task is to build a factory machine from simple components which takes an object, inspects it and moves it around the factory floor accordingly. In later stages, you get to modify the object as well.

At first you think you’re just moving objects around and printing patterns of coloured dots on them, but later, when you’re thinking of blue dots as 1s and red dots as 0s, and the patterns as binary numbers, you realise that the system is Turing complete and the game’s progressively harder puzzles are teaching you how to build a binary adding machine. It’s a beautiful, powerful way to demonstrate the principles behind mechanical/electronic computation.

While some games, like Angry Birds and Candy Crush, are meant to numb your brain with repetitive tasks, the best ones expand your brain with new skills and knowledge: Manufactoria is in the latter class.

Play the game online here: Manufactoria at PleasingFungus Games

How to predict a policy failure

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As soon as the Coalition Government started cutting the flood defence budget in 2010, it was as predictable as the water cycle what would happen next: within no more than a few years and probably within the lifetime of the government which made the cuts, there would be heavy rainfall, resulting in massive floods, and a backtrack on the cuts – emergency spending if not a change to the planned budget – either way, a tacit admission of failure.

This sort of thing seems crashingly inevitable to me. There’s an obvious trajectory, of reduced budgets, reduced regulation or reduced oversight, followed by conspicuous calamity, followed by attempts to mop up the mess which generally involve reimplementing whatever system had originally been in place to prevent the calamity.

I’m not here to congratulate myself on uselessly predicting the flooding crisis (also, because I never went on record predicting it, so there’s no proof I ever did). I want to teach you how to predict similar balls-ups in the future, because the depressing thing is, it’s not that difficult.

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Response to Creationist 16

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16. “What mechanism has science discovered that evidences an increase of genetic information seen in any genetic mutation or evolutionary process?”

Matt Stopera / Buzzfeed

Oh dear. Someone’s been reading technical jargon they don’t understand.

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Response to Creationist 14

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14. “If Evolution is a Theory (like creationism or the Bible) why then is Evolution taught as fact.”

Matt Stopera / Buzzfeed

The theory of evolution is a theory; evolution is a process, a thing which definitely exists and happens. The fact there’s a theory about it is not to say the whole thing is just a wild idea someone pulled out of their arse; it’s scientists’ way of saying “this stuff’s complicated, so we’re going to write it down properly.”

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