How can maths help us make better predictions? – with Kit Yates

Find out how non-linearity and randomness can cause problems for our decision-making - and how can maths help.

00:00 Intro and famously bad predictions from school reports
05:42 What is linearity?
10:42 How can linear thinking trip us up?
14:20 What is non-linearity?
16:54 How do positive feedback loops work?
24:57 What is exponential growth?
29:34 What does true randomness look like?
36:10 Why do humans look for patterns?
38:43 Why the iPod Shuffle algorithm wasn’t actually random
40:42 Why are humans bad at being truly random?
46:41 How to use randomness to choose lottery numbers
52:17 How to change your mind
55:26 Using maths to reason better in life

Ever since the dawn of human civilisation, we have been trying to make predictions about what's in store for us. We do this on a personal level, so that we can get on with our lives efficiently (should I hang my laundry out to dry, or will it rain?). But we also have to predict on a much larger scale, often for the good of our broader society (how can we spot economic downturns or prevent terrorist attacks?).

For just as long, we have been getting it wrong. From religious oracles to weather forecasters, and from politicians to economists, we are subjected to poor predictions all the time. Our job is to separate the good from the bad. Unfortunately, the foibles of our own biology - the biases that ultimately make us human - can let us down when it comes to making rational inferences about the world around us. And that can have disastrous consequences.

This lecture was recorded at the Ri on 6 July 2023.

Kit Yates is a Senior Lecturer in the Department of Mathematical Sciences and co-director of the Centre for Mathematical Biology at the University of Bath. He completed his PhD in Mathematics at the University of Oxford in 2011.

His research demonstrates that mathematics can be used to describe all sorts of real-world phenomena: from embryo formation to locust swarming and from sleeping sickness to egg-shell patterning. He is particularly interested in the role that randomness plays in Biology. His research into Mathematical Biology has been covered by the BBC, the Guardian, the Telegraph, the Daily Mail, RTE, Scientific American and Reuters amongst others.

Along side his academic position, Kit is also an author and science communicator. His first book, 'The Maths of Life and Death', was published in 2019 and has since been translated into 25 languages.

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[thewiseturtle]

Note that in actuality, each of the three potentially random patterns he showed us are equally random because randomness is about all patterns being equally likely. I think what he, and others, are often imagining is that randomness means the bell curve middle patterns. Or, in his case, patterns generated by certain processes (like coin flipping). But real randomness means that 10101, 00111, 10011, 10000, 11011, and every other possible combination of 5 binary digits, are equally likely, and are equally random.

What does actually happen more often, though, is a fairly even balance of each of the binary digits, so outcomes with 2 ones and 3 zeros, or 3 ones and 2 zeros are more likely to happen than outcomes with 5 ones or 5 zeros, because there's only one way to get 5 of the same thing, while there are a number of different ways to get to 2 of one and 3 of the other. That's the bell curve peak of similarity that often gets thought of as "feeling random", or as Kit mentioned the feeling of (fairly) equal spacing in a pattern.

So, really, the problem is that we're not teaching folks what mathematical randomness is, and instead let the mainstream pop culture concept of randomness as "not having an obvious or appealing pattern" be the definition. Mathematical randomness, instead, is where all possible specifically-ordered patterns are equally likely to happen. So pleasing, notable, and obvious patterns can be totally random, as long as the outcome had no bias, where the outcome of each element is disconnected from the other elements in the set, e.g. the first roll of a die has no affect on the fifth roll of that die. If there is a relationship, or effect, then it's not random, but follows some sort of causal (linear or non-linear) influence.

[stevelandsaw]

I asked the exact question to ChatGPT and this was the answer it gave me:

If 3 towels take 3 hours to dry on a line, assuming that the drying rate is linear and that there's enough space on the line for all towels to hang freely and receive equal air and sunlight, 9 towels would also take 3 hours to dry under the same conditions. This is because the drying time is not dependent on the number of towels if they all receive the same environmental conditions (wind, sunlight, etc.).

[craiginboro]

How come my conscious mind finds maths difficult yet I'm capable of catching or throwing a ball and estimating it's speed, weight and momentum. Can this purely be experiencial estimation?
How do my eyes know how far apart they are so I can instantaneous calculate size and distance?
It feels like when I was born I only got the licence to "Home edition" rather than the "Professional" edition and therefore I was denied access to the full powers of the operating system.

Surely it takes more arithmetic and cumputations to guesstimate some than to have the formulae (the cheat sheet, the enigma codes?)

[CarolynFahm]

Brilliant lecture from a superb lecturer.

[CharlesProoth]

Fantastic presentation! I loved every second. Thank you Kit Yates!

[exoyt]

Excellent speaker! Very interesting talk!

[Crunch]

Small nit pick, If you are going to use Hendrix's music as an example of feedback, you then need to describe a guitar's feedback and not a microphone's feedback. A microphone's feedback is due to the audio waves being looped back into a microphone which works by audio waves physically moving a mic's diaphragm. An electric guitar's feedback is due to the audio waves adding additional vibration to the guitar's steel strings, which then causes additional disturbance to the magnetic field of the guitar's pickup, thereby causing a louder pickup output. A guitar's pickup is not a microphone.

All this is pedantic though on my part, and does not affect your description of a feedback loop . Thank you for the great presentation and lesson!

[Slarti]

32:06 - I generated some random positioning of CO2 particles inside a 3D cube and saw a similar pattern to A.
It's strange how the randomness appears to almost cluster in circular half-moon shapes.

[roguelegend]

look how the students are sitting randomly on the seats, true most choose to sit in the middle, and others not too close at the ends, they are not afraid of sitting apart from the clusters of students...

[Uradumbxss]

He was my lecturer at uni of bath, one of the best

[maskddingo]

Interesting. The reason I chose "A" for the random distribution is because it showed NO patterns. The other 2 were way too ordered. To elaborate... both B and C were highly favoring certain x or y coordinates. A seemed to be the only one that was considering all coordinates along each axis.

[maxheadrom]

How about the cost to make a pizza? Is it closer to a linear relationship with respect to the diameter or closer to a non linear relationship? (it's probably non-linear but the question is "closer to" one of the other). I'm asking the question because I have a feeling it's closer to linear and, therefore, pizza places aren't necessarily tricking consumers.

Now I'm hungry for pizza ... I can order from two places - one costs 20 dollars and the other 10. The cheaper one has more stuff and a thicker pie but the 20 dollar one tastes much better because the dough and ingredients are of a better quality. This is an awesome talk because decisions about the future are hard to take because reality is non-linear and "tastes better" is hard to put a price on.

[savagebolt]

I always order the largest pizza. Whatever doesn't get eaten makes a great breakfast, and lasts a few days in the fridge.

[tenzinrose]

You’re using 3.5 (the green icon gives it away). I tried with the 4 and it got it right

[mawkernewek]

36:50 could also be Karl Marx in that tortilla

[Kelticfury]

Is anything in the universe actually random or do we just not grasp all the interactions that led to that "random" happening?

[AbAb-thqe]

This is more like a pop psychology lecture than a maths one

[jonbaker]

The instructions on my dishwasher say for best cleaning place items randomly. So one day all the silverware ended up in one compartment - it didn't wash well at all. I guess they didn't really mean randomly.

[foobar]

The distribution of played rows played in European Eurojackpot lottery are not published, but amounts of winnings in different winning classes are published for every draw. For over seven years they used to have two "Euro numbers" in the range from 1 to 10. Although probably a large portion of actual played lines are generated by merchant machines and are thus random, this along with the winning numbers of each draw allowed to indirectly estimate the popularity of "random" low-digit numbers. I did this, and unsurprisingly seven was the most popular, followed by three; ten was least popular, followed by one. Combination of three and seven as the Euro numbers was dramatically more likely than any other combination, and this was quite observable on at least one of the draws. So, if there's something to learn from this, don't play those specific numbers if you don't want to share your winnings with a larger crowd!

[TioneJoseph]

a program @ LANL on a new computer wasnt right. we plotted the x, y output of the compuer, and got diagonal lines. NOT random. be safe. and don't trust compuers. "to err is human, but to really screw things up takes a computer"