Four Ways of Thinking: Statistical, Interactive, Chaotic and Complex - David Sumpter

Mathematics is about finding better ways of reasoning. But for many applied mathematicians, the primary mission is to shape their minds in a way that gets them closer to the truth. The calculations are secondary, the real question is: how we can better understand the world around us?

In this Oxford Mathematics Public Lecture, David takes us on a journey through applied mathematics from statistics all the way to complexity theory, lifting examples from his work with football clubs - signing the best players (statistical thinking) or organising an attack (complex thinking) - and from every day life - bickering less with our partners (interactive thinking) and learning to let go (chaotic thinking). David reimagines applied mathematics as a set of tools for life, from big work decisions to how we treat our friends, family and work colleagues. No problem is too big or too small for a mathematical solution.

Professor David Sumpter is author of five books including Soccermatics (2016), Outnumbered (2018) and Four Ways of Thinking (2023). His research covers everything from the inner workings of fish schools and ant colonies, through social psychology and segregation in society, to machine learning and artificial intelligence.

[jamil.]

Exactly the reason why i chosed to study mathematics and physics that is to understand the world around me.And i love studying these two subjects.When i study these two subjects properly i get totally involved, you can say i live in those moments fully.

[ChronicleContent]

Timestamps:
0:00:02 - Introduction to talk on applied mathematics and thinking styles.
0:03:03 - Ronald Fisher's life and work at Cambridge University.
0:05:57 - Testing if milk affects tea taste with experiments.
0:08:42 - Designing experiments using combinatorics.
0:11:31 - Gary Neville statistic measures player performance after conceding a goal.
0:14:17 - Statistics used to rank top players, limitations of measurement.
0:17:00 - Explaining the limitations of statistics in 10 words.
0:19:46 - Eugenics, smoking, and misuse of statistics.
0:22:25 - Context matters in statistical significance and causation.
0:25:13 - Balanced chemical reactions and ecological models explained with math.
0:27:46 - Mathematical modeling of foxes and rabbits.
0:30:32 - Analysis of applause and social recovery in groups.
0:33:12 - Human behavior equation: non-smiling person + 2 smiley people = 3 smiley people.
0:35:55 - Using physics-based models to scout football players.
0:38:51 - Introduction to chaos theory and Margaret Hamilton.
0:41:29 - Weather simulation error due to decimal input mistake.
0:44:05 - Generating divergent numbers through a simple process.
0:47:06 - Chaos, Margaret Hamilton, and the importance of control.
0:49:55 - Finding balance between order and chaos in life.
0:52:33 - Simple rules create complex patterns in simulations.
0:55:21 - Capturing complexity in science through detailed descriptions.

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[alexandrosmusica]

02:50 Statistical 
23:20 Interactive
39:15 Chaotic 
52:10 Complex

[mightytitan]

i love this youtube algorithm which recommends random great video just like a random variable

[PeterStinklage]

The smoking bit reminds me of a silly anecdote when Bertrand Russell was asked if he was concerned about smoking impacting his health. He said that one time he was going on a flight, and they told him he couldn't smoke on the airplane, so he decided to delay his trip rather than go without smoking for a few hours, and the plane ended up crashing.

[xlerb]

A relatively minor point in the talk as a whole but the bit about grit being a good indicator of success is spot on in my experience. I've worked in a technical field for ~30 years so I've observed plenty of folk through those years. Grit is a much better measure of how good an engineer a person will make than GPA or similar.

[CuriouslyBored]

My statistical way of thinking: of a mindset care for probabilities, historical data, an assessment of assets and liabilities before pursuits of actualization occurs.
My interactive way of thinking: of a mindset care that awaits or hunts for societal circumstances that appears to 'door' or facilitate pursuits of actualization.
My chaotic way of thinking: of a mindset care for rolling the dice-- a 'just do it' actualization pursuit that minds no statistical odds or favorable circumstances and may even lack certainty of what actualization looks like. It is a pleasant surprise when no sense of chaos follows an unstudied action.
My complex way of thinking: of a mindset that utilizes statistical and interactive cognitive intelligence to facilitate pursuits of actualization.

I do believe success is most likely when complex thinking is applied. Additionally, the way of thinking determines what the mind is inclined to focus upon; what we focus upon occurs within mindsets. If I am of a Will to think in a manner that invites the possibility of chaos, there would be no consideration of mindsets associated with statistical or interactive thinking. Often, it is the actualization objective and not the Will that dictates the mind's cognitive cascade options-- care of success demands management of one's Will, usually.

There is a control 'care' in mathematical logic; through an understanding or a care of the answer, one controls the problem.

The lecture's turn towards discerned marital controls that are implemented and sustained, if "care" exists, is of complex thinking that minds objective (statistical) and subjective (interactive) truths. The identified existential marital problem has a determined answer that is not natural within our lecturer-- conscious, willful "control" of his natural inclinations is the answer that he believes "care" will sustain. If a strong "care" becomes weakly felt, the answer and the "manipulations required" will feel a key to a prison versus a key to greater marital happiness; sustaining a marital reality that survives upon an unnatural answer, of little care, is difficult-- even grit requires passion to exist in its application.

Addendum: What is in grit? A Will to persevere, despite any headwinds of statistical and/or interactive inform. What does perseverance require? A deeply held belief that a pursuit will see actualized success. What is in belief? A measured patience that is governed by an adjustable long view.

When the long view dies, all that underpins grit dies; grit may require an ability to visualize and intensely feel an anticipated actualization of victory. What a grit-gifted victorious actualization satisfies is dependent upon the state of one's ego and other psychological influences; a satisfied ego (no circumspect psychological insecurities or of a felt need to proof/validate identity associations of gender, abilities, intelligence, etc.), scar-free interactive psychological truth (never felt derisively underestimated or had declared goals disparaged and/or discouraged) and/or of no passion to defy odds-- less likely to endure pursuits of actualization that requires grit.

Some form of anticipated internal resolution, validation or balm-- beyond the externalized actualization pursuit-- exists in the long view of a grit-driven pursuit, I believe.

[grantbeerling]

John Maynard Keynes 'principle of uncertainty' in economics states that we can predict the very near future with some degree of success, but the more distant, the more uncertain we become; thus, mathematical modelling in economics is not a science of absolutes; rather, it's a social science of human infinite variability—a perfect example of chaos theory. Daniel Kahneman later backed this up in behavioural economic theory.
Also Adam Smith wrote, that the market in the long run will return to an equilibrium, to which Keyens replied, in the long run we're all dead! (ie the disaster that was 1930s and the 2010s, both unnecessary suffering, we can always afford a war, so let's win the peace).

[Boxedpapi]

This was one of the best lectures ive ever watched in my life. Loved it

[mariazamora]

The more ways of thinking a person have, the more complete a person is going to be.
In my perspective creativity plays a huge role when we apply different ways of thinking, as well as how we organize the language( numbers, symbols, information, knowledge, etc), how we understand the language, the information and how we apply.

[edwinmizrahi]

🎯 Key Takeaways for quick navigation:

00:02 *🎓 Sumpter uses applied math to understand the world through stories from football, science, and life.*
02:48 *📊 Fisher pioneered powerful statistical methods but had problematic views on eugenics and smoking.*
11:28 *⚽ Statistics can measure player attitude and performance in football, with limitations.*
23:25 *🧪 Lotka used "unbalanced" equations to model exciting biological and social patterns.*
37:31 *🧩 But Lotka never found a grand theory. A key limitation was not knowing chaos theory.*
39:18 *🦋 Hamilton and Lorenz discovered chaos - small errors cause drastically different outcomes.*
47:54 *🚀 Hamilton left chaos for Apollo software, showing the need to eliminate errors in critical systems.*
50:00 *☯️ The yin-yang of randomness: control what matters, let go of the rest.*
52:03 *🧩 Complex patterns emerge from simple rules in cellular automata and tiny code tweeted graphics.*

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[ThomasToPC]

Yin-yang is chaotic manifestations; taiji is the orderly existence of the whole... if I was to apply this side of classical Chinese philosophy. This of course in no way detracts from what a great talk this is. Thank you!

[jarkkoaitti]

at 6:15, there is this milk-tea problem. i've done a highly scientific research of drinking coffee with vegetarian based (oat and soymilk) milk and because these conditions are a lot more extreme, it enabled me to do some practical tests with clear results. many of those vegetarian "milk" products curdle or accumulate to nasty bit and pieces easily in coffee. to prevent that, pour milk first so it is the strong coffee introduced to a lot of milk first vs. a wiff of milk in a strong coffee. in both cases, a vigorous mixing will help alot. also there has to be enough of milk to make the mix mild enough. yes, i know i missed the point :) so she was right, milk first! also the toilet paper should come out from top side.

[JeremyHelm]

55:11 A pattern is as complex as the length of the shortest description that can be used to produce it.

Andrei Nikolaevich Kolmogorov

[varunsingh]

earphones on and my volume was up, the sound in the beginning almost made me deaf. great content btw.

[KarlLew]

For the curious, Dr. Muriel aced the tea test and thereby hoisted Fisher on his own petard.

[AAkCN]

brilliant and easy to understand. Thanks for publishing

[georgechristou]

For the milk tea test. The difference with the pairwise option, is that there is extra information that 1 of those 2 cups is milk first and the other is tea first, that's why its more probability for her to get it right. For the 3rd option: 8 choose 4 = 70, as from 8 positions choose 4 for the milk first option.

[archimedesCNC]

the art of the measurement becomes the reality to the measured ambitions of the narrowness of arrogance. i found David Sumpter's beauty in these 4 measures the protagonist toward the Long Term Capital Management story. really appreciate this opportunity of sublime serendipitous interaction the youtube algo sought out my desire for such. thank you.

[SSNewberry]

Needs an Oxford comma in the title, of course.