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

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. Follow me for more AI

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

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.

Got me thinking already

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

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.

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.

If you are not a gritty person, it's OK, there's lots of ways your life can succeed. YES THANK YOU!!!

Great lecture! Thanks

Thanks for the talk! I enjoyed watching it with my kid!

Needs an Oxford comma in the title, of course.

Great lecture, thank you for posting it!

Very interesting, highly recommended

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!

Wonderful lecture!

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.

thank you so much

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).

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

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.

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

That was a well-coordinated crowd at the end.

great! all these ways of thinking are from macro perspective to see the world. so that we can see the pattern, trending, development of organic system.

I like Ronald Fischer, from being a Eug@nics advocate to going 80 years ageless teaching at Oxford about Himself in "Four Ways of Thinking: Statistical, Interactive, Chaotic and Complex"

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

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

Why not change the title to “three ways of thinking” ? One can hardly not feel abused (time wise) when told “go buy the book” for the fourth-complex!

Interesting, but I prefer the six thinking hats, simpler and yet more complex!

A bit more intuition on the "Complex" segment would have made it a lot more worthwhile, it while being a brilliant talk without a doubt. The two examples were good, but I guess it needed a few more words from him. I suppose the time limitation at hand...

My way of thinking about medical science, engineering or mathematics in general =simple. Believe me I have spent a lifetime trying the most simple things that Nikola Tesla or Albert Einstein would have never thought would be so complex.

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.

Descriptions meaning and information content depend on the formula or algorithm evaluation it. It is always a sort of function giving the se of possible source data meaning in the result space.

Mr. Kolmogorov is the favourite one

23:28 where did this come from? i'd rather learn more about this way of thinking

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.

i'm exited about this presentation

🎯 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.* Made with HARPA AI

Yes, Dr. Muriel Bristol, the subject of Ronald Fisher's famous tea-tasting experiment, was indeed able to tell whether the milk was poured into the tea or the tea was poured into the milk, according to the results of the experiment!!! Please don't leave us hanging.

Great talk. As regards the slight relationship between grit and success the terms 'statistically significant' vs 'practically significant' come to mind. The problem then is practically significant for who? As we move through life we meet individuals and it is a foolish person who makes any assumptions about an individual based on secondary characteristics. But what about those who are making evaluations in bulk? Suppose someone has found a similar slight relationship between 'grit' and programming skills and is charged with hiring 100 programmers for a project. The temptation might be to use 'grit' as an evaluative proxy when hiring. But what if 'grit' has some cultural factors that influence it? Then the hiring process might be biased against some groups and this bias might be incorrect. Bean counting micro-optimisation is (unfortunately) a common feature in business, moreover increasing use of 'AI' is likely to hide such biases behind a wall of pseudo-objectivity. Bringing us back to the Fisher problem.

Milk at 4 C is significantly more viscous than water at 60 C (let alone 100 C) and is thus less likely to aerosolize when poured onto a hard porcelain surface. When you pour tea into milk it cushions the tea with its own viscosity to prevent aerosolization. Tea stains are more difficult than milk stains because of the presence of tannins. Tannin stains are a pain, both in clothes and wood.

I've only seen thru 32 min of this video, am enjoying it, have skills and education in math, and suggest that there is a stronger correlation between the LOUDNESS of applause (coupled with the peak loudness correlation) and enjoyment of the "event" rather than the length of time of the applause. Just a spontaneous theory here. Could be wrong...

That was very good. Thank you.

Thx

He is very smart spoken.

The chaos example with yin and yang hit home so hard i might be able to sleep tonight 😂

This is one of those videos where you can't decide whether you feel smarter or dumber after watching.

I write this comment around 9.00 minutes. The second method, "B" , isn't "fair". One has to keep in mind that humans use their MEMORY. The second test assumes that a human can instantly reset their pallette after a short taste-test, this is simply NOT the case. When the difference in taste is subtle, then all the interpretations become one big jumble for a human's brain if the taste tests are set too close after each other. Also , the first thing that sprung into my mind was, "Maybe it's due to a difference in TEMPERATURE, that the lady can tell the two variants apart with a significant amount of certainty." So, is there a difference between T(t) and T*(t)? T(t) is the temperature curve when milk is poured first, and T*(t) is the temperature curve when tea is poured first.

This professor just destroyed the foundation of racism and stereotyping people.

i'm a "sugar before coffee" man myself. There is definitely a difference in milk before tea: the complex colloid solution of proteins and solutes in milk will react differently based on the relative concentration of milk and tea -- especially with regard to the relative concentration of heat in the tea. I always put two cubes of ice in my coffee after brewing to cool the solution so that the cream doesn't gunk up. The undesirable byproducts of heat on milk are less if there is more milk which allows it to heat more slowly.

I don't like football, but I admit my interest was at least disturbed when I found out that statistics is a BIG thing in football nowadays. Data Scientists and -Analysts must be pretty ecstatic working in that field.

I wish he could have elaborated on why complexity is distinct from chaos, but he cut it short. Seems he was only describing the same thing - chaos is macro-behaviour that emerges from the complex interaction of micro-motives. So not sure why they merit a separate category.

How many maths were you good at?

15:30 - right right i remember her Ted talk about "Grit"....what a god awful way to do analysis. the gist, as you can plainly guess, was "well, those that succeeded had....grit...because they were the ones that...succeeded in the end" talk about water is wet. kind of like the survivor bias, amirite? show a bunch of people pictures of where bombers, who returned to base, were shot full of holes and you'd rightly assumed it would be "hey, let's strengthen those bits that are more likely to be shot up"...except they forgot that this ignored the ones that were shot up in the places not full of holes in the survivors...and didn't make it back to base.

I shouldn't have to ask this because credit should have been given in the slide deck, but can anyone identify the artists behind the Twitter art @54:19 ? Note: In 2024, the X, formerly known as Twitter, character limit is 280 not 240 as suggested in this video.

Well, to understand the world around you you'd better start watching it. As a physicist I do respect many mathematicians (most of them did some nice works last years), but they are not as lunatic as this speak.

These are great stories. But what about the tea: which was better? And what did explain success better than grit & IQ at 4A% each?

Always pour the added liquid down close to the inner edge of the cup, like a good Chemist, and then it doesn't matter much which went first.

Great talk. There seems to be some confusion between mathematics and psychology though. Some mathematical principles are wrongly generalized to the human behavior and sometimes he just puts out unsolicited claims about psychology. It is interesting to have both of these fields meet but this is obviously not what the talk is about nor what the professor is fluent in. So yeah, it might be another instance of what was pointed out in the talk; mathematicians getting caried away and trying to explain everything

17:21 Bird shot variance.

Concerning the tea cups, it probably also depends on the length of time the milk and tea had to mix, their different densities, temperatures of each liquid and cup etc.

@48:18: But there was room for errors at NASA. During the first successful moon landing, Apollo 11, they encountered programming alarms 1201 and 1202. There was a question on whether to abort the landing mission or not, and they went ahead.

He didn't give the fourth option: "I don't know which one is better", for what the effect is of the way you present the experiment.

Not a stats expert, nor a futbol expert, but as a scientist I strongly suspect the explanation for these strikers' performances has a lot more to do with how the other players on the field react to a goal being scored. You can't separate a player from his team, at least not with such crude data

In the real world, perhaps it is true to say there is no such thing as chaos? Orders born of differing magnitudes all relate back to the smallest factors, whether or not we perceive them. Inverting the Margaret Hamilton example imagine however, a system capable of infinite complexity designed to apply order from a macro perspective, but without the capability for seeing below a certain quantity... lets say in practical terms its design allows for '0' after other numbers, but not before them, and somehow requires the storing of a data in a minimum number of functional memory 'locations' to give a value in calculating. Suppose it's a system with a functionally infinite number of decimal places, that can't however 'hold' numbers starting under a value of 2 separate integers - in effect saying it can make 'two' by 1+1, but cannot make 'one' by 0+1. Designed to bring 'Order' and in abstract terms capable of perceiving division and multiplicity, it's attempting a 'real world' unity based on 'perfect' conception, but lacking the capability for a small yet important part of 'Loving' - the forgetting of self.

On Tea and Cookies: I think there is a big difference between the two methods and she is right. Tea is acidic and milk is a base. As the milk is added to the tea, it heats up quickly and is overwhelmed by the acid and curdles. Adding tea to the milk slowly warms the milk and the acid is quickly neutralized by the milk which doesn't curdle (form a colloid) and that's better.

OK I agree option B is the better way to design the trial but what about the answer? Could she tell if the milk was put in first or added after the tea?

Cowboy hat being labeled "chaotic" caught me off guard not gonna lie

on 🔛 to be Thninker in life amazing gift !

It's pretty amazing how a whole field of mathematical inquiry began because a guy just couldn't believe that a woman knew how she liked her tea and had to - HAD TO - prove her wrong.

Maths is magic and magic is maths

Rubics cube, paths to solution, I had to watch 55min 31s to ... we all want the power of action at a distance.

7:21 oh, good methodology 21:42 clever isn't the same as smart. 33:56 where does the thinking come in?

Incorrect @10:08 - No matter how many ways there are to present four cups of tea, there are always 2 cups 'milk first' and 2 cups 'tea first' on the table. So, the chance of getting the first cup right is 50% (there are 2 cups of each). If the first guess was right, there are 3 cups left on the table: 1 'milk first' and 2 'tea first'. Now, the chance of getting the second cup right is 33%. And, if the second guess was right, both other guesses are per definition also correct. (The only cups left are the 'tea first' ones.) So, the chance of getting your guesses right in the second set-up are 50% x 33% = 16,6% or 1 in 6.

Confusing lecture, but interesting. I hope his books are more clear on demonstrations

Fisher is one of the encyclopedia examples of “that guy.”

The first example with the tea doesn’t seem like either of the experiments are measuring what the milk first is really conveying: whether the milk first gives a sense of ritual and a small pleasure of identity, or if the milk first created a different temperature variance for immediate consumption. ?

I plead guilty ... Once my then wife complained when I put the milk in her cup and then added the coffee. The next time I prepared her coffee out of sight and asked her which method I had been using. Actually when I suspect that the milk might be close to "expiry" I always put the milk first and test with a minimal amount of coffee. "Shaken, not stirred" ... some scientist did the test.

How about just getting to the point?

I wonder what kind of thinking was at play to come up with an idea to persistently decrease the video's effective surface area by 20% in favour of displaying three distracting logos.

I guarantee that the book is quite more interesting than this lecture. The lecture is alright, but because of its format he wasn’t able to give more illustrative examples of the four ways. Though the book is also short, it is way more fun to read. One of my favourite books of the last couple of years

Here, I am maths teacher.

He forgot a fifth option: use all seventy combinations but present Pair-wise. I.e. present some "no win" options, and some "no loose" options. If you don't gaslight your rat then are you really a scientist?

Combine all and you have a human

Is language a medium of chaos?

i hope a generous person give timestamp to this great video

Maybe I just gotta go back and re-watch, but I missed how the interactive method of thinking was able to to predict things that statistical thinking could not.

19:20

🌹👍🌹👌🌹🙏🌹

The real probability of getting a lady to identify 4 cups out of 8 given two possibilities correctly is 1/256. The lady must evaluate each cup, and given only two outcomes, she would have to correctly label all 8, if she was guessing, no matter the orientation of the cups she would have only a (1/2)^8 or 1/256 chance of correctly identifying all 8 of the teacups. As the test is practically described, this is what happened. A complicating factor is if you decide that she can use process of elimination or observes the cups not all at the same time she could avoid observing all 8 cups and avoid categorizing all 8 cups. But the ladies inability or ability to taste 8 cups of tea at the same time is not part of how this experiment is described. What Fisher describes, when he says "1/70" maybe because he gets a kick out of making people repeat falsehoods, is really the probability of what would happen if she picked out the correct order without observing the cups individually.

Tea experiment presumes the variable is the taste, rather than care for the bone china cups where very hot tea can cause it to crack/ cause an existing crack to open up. First check your basic assumptions don't include bias.

0:08 the most funniest part is how they didn’t use the Oxford comma here despite this video literally being published by Oxford Mathematics 😂

Fisher designed the tea tasting experiment. But did Dr Bristol actually do the experiment with him???

I'm here SOLELY to settle the tea vs milk first debate - WHAT HAPPENED IN THE EXPERIMENT!? Aren't we going to get the result after all?!?!?! 0_o

mathematics can t be taught it is only learned through sheer practice its a sheer thought process for the human brain and can be used to derive the real life management applications

Muriel Bristol was able to identify the cups into which tea had been poured first, if anyone else was wondering...

Didn't some bloke called de Bono come up with Six Thinking Hats already? Which hat is the one for ripping off ideas?

Cool, but what about the most intriguing unanswered question- Could Dr. Bristol tell the difference between whether milk or tea was poured into the cup first?

5:00

I used some amazing mathematics to predict over 70/1s in football 😊 can't believe that England won 7-0 1314 days after they last won 7-0 on king Charles bday in 2019 it was mathematically amazing 👏 I measured before the game and won 3/5 bets 65/1 70/1 and 45/1 the hatrick kane let me down and my cover bet 8-0 haha

By abandoning the fixed numbers of 4 tea-first and 4 milk-first and having each cup one or the other at random you have 2^8 = 256 possibilities