Isn’t that Wisdom?

And recognizing which fact matters and which one doesn't is the challenge.

Marcelino Deseo that’s Wisdom

@Lo Po yes, but all facts are not relevant in all situations.

Residuals and PCA anyone?

so then why arent you talking about race and IQ?

Yeah. That's why we didn't throw out relativity 6ish years ago when it muons were measured moving faster than light. It turned out that literal bird shit had caused the error, it was on the sensors.

I think it’s a bit loose. Evidence should determine our prior beliefs and new evidence should update them. Thus, evidence should determine belief generally.

Stubborn

​@@criticalcog6363 the calculated posterior can be seen as the updated prior. that's why this sentence is gold.

There's still going to be ones that fail. A subject only makes sense if you're interested in it or have some intuition of what is happening.

As Asanda said, the actual maths teacher has to manage the 50% of the class who don't give a shit about anything, no matter how well it is presented! Then there's the student who will put up their hand and ask "Is this examinable?". Then there's the parent-teacher meeting where you get accused of going "off-track". There are many hurdles to prevent inspired teaching.

@@garethb1961 I think you're missing the point though; all those hurdles will still exist but the maths teacher would not be a hurdle which is definitely not the case for a lot of students unfortunately.

@@stretch8390 I don't think I missed the point at all. That boring maths teacher who can't teach for shit and disincentivizes students may have been good before the system wore him down.

I just want to say that fortunately, any child with youtube and curiousity can have him as a math teacher :D

What does it mean if I still don't understand this theorem intuitively or deep as you?

@@yashaswikulshreshtha1588 doesn't mean anything, everyone learns differently

@@yashaswikulshreshtha1588 update: 6 months after diving deeper into math. I have come to find that applying and understanding the intuition is just the start. I’ve learnt that in fact, I don’t know much 😅

@@justlooking9802 good to know i m not alone

@@justlooking9802 that's the start of wisdom when you realize this

It was bound to happen.

What are the chances, right?

@@DharminShah09 good one

@@DharminShah09 *Shakes Magic 8-ball* ...... "All signs point to you being gay".

Yeah i thought it was probably not gonna happen

Aye that thee will

What about all the professors from the early 2000s who put javascript simulations on their html websites with white background and times new roman as the only font.

he spent so much emphasis of visualization

Couldn't agree more .. his visualisations show such attention to detail , it's awe inspiring

TapOnX they were the primitives

factsssss. i actually understand the math and can visualize while working instead of just using some formula and plugging stuff in

AGI needs this.

SCWAG (Dr. O J Curry ) scientificly computed wild ass guess

What are the others? Can you suggest some names?

@@Naklibatuta Check the Channels column of this channel.

Nominate them for a Webby and vote!

that can be your job. good suggestion.

Agreed. However….. keep in mind that on cable tv, there’s a thing called The Learning Channel. And that channel has now become a relentless purveyor of crappy ‘reality’ shows. Point being that the mass market never will dig this sorta thing.

I would suggest you consider a less scientifically rigid discipline if you expect to be more than a high school teacher with your phd. His hypothesis literally demands you consider datasets that are not presented then guestimate those datasets. Good luck with that gym teacher career

Well I'm an observational astronomer so not really planning on doing anything terribly theoretically rigid! What is your PhD in?

@@andrewjolly319 😂good question....

good reply!

I'm a calisthenics athlete, and this is one of the best BT explanation I've ever seen.

Soo true. When I was attempting a question, the venn diagrams weren't reflecting the actual data given so I ended up with a diagram similar to his. Needless to say I clicked on this thumbnail with the quickness! lol

It's taught in India in 12th grade.

Everyone tries to model the world. Those with the capacity to model with Bayes' theorem but not doing so are inefficient in their modelling, and the resulting errors are horrifying.

It is the most abused bit of math ever. Probability is taught in math and it should be taught as a mathematical concept. Applying math to philosophy and belief is guaranteed to cause misunderstanding between what is true and what is believed.

@@Uhlbelk It would take a very strong argument to convince me you are right about that. You could say that my prior belief is very low. You need a lot of independent evidence to make me update my belief enough to really make a difference ;-)

@@Baekstrom Yes, my belief has been updated by many many independent measurements of Bayes being used correctly and incorrectly and this is my current belief and would require a lot of new data to change.

That begs the question, "What is the probability you'll actually do it?" lol

Well, what were the chances of it being made? I think with this knowledge, we can look in retrospect and update our views on the chances of it occurring.

Thanks for all your hard work and the excellent quality of the content. Look forward to the next release on Bayes.

Dang - but thanks for the heads up! I was about to go searching for it and I'd probably have wasted way too much time looking since I assumed the likelihood the video existed was close to 1.0. Now I need a model for how to update my beliefs given an unknown probability! ;)

You should square off on this one more time..think false binary..inputs

that's almost definitely the case. I wonder if the second version of the question made that fact click for the questioned or if they still thought about it as mutually exclusive options.

Interesting thought! I’d be keen to question these 85% of people that gave an impossible answer and try to understand how they interpreted the question! Because for me I read it as “what’s more likely, A or A&B?”, which is so easy it barely counts as a question!

Yes, I think that is the point though. To show what kind of thinking process people apply depending on the situation and how problems are pressented to them.

I at least misunderstood it as that. Only on second thought did I consider the rigorous interpretation of answer 1 not excluding her being a feminist. And I'm a mathematician & have the context of the video around it being about Bayes theorem. In a different context and without mathematical training, I certainly would have chosen answer 2 because of the misleading language rather than inability of thinking about probabilities.

One assumes the question is not so blindingly easy

Yes, nick. Me too

We need this kind of intuitive thinking. I wanted to study maths in this manner, how he teaches is brilliant.

Drawing out the table truly is a wonder

Not even that: I see "person with property A/property A+B". There is no 'people'. It's only later all these other bank tellers are conjured up to make us who literally are focused on *person* (for that's the scenario) feel stupid. (Am seriously annoyed at 3blue1brown for this.)

Veritasium also did a good video on it, but not as good as this.

@@LeoStaley Yeah! It was good too but this is better.

@@LeoStaley Veritasium's video took me on a ride XD

ah a fellow Indian. You probably know how probability is taught here lmao I have my board exams too XD

@@arhmlmao how did the pre boards go man ;-;

I've always wondered, what jobs to math majors do exactly, other than research?

No it's not

@@mohammadabdulla8601 ok then who has explained better ?

​@@dev0_018 you could make a rough guess what they'd say, based on their username(hate to be racist but ive read too many such yt comments from such usernames. You could say it's my bayesian estimate 💀)

@@friedayy well, hate it to break it to you and face you with facts but your Bayesian estimate is pretty terrible and didn't estimate anything 💀, since i hold similar name and same belief that this name derives from

None of these objections are objections against Bayes Theorem used for updating beliefs however. They only propose that in the specific experiment more steps of updating the belief to get a different prior probability would be needed.

I was taught like that the equation was written on the board and then said "tomorrow we will have an exam on this". Sad.

thank you for your insights. I'm currently in these 5 hours but getting closer. Nothing better than getting an intuitive explanation like here and then testing yourself with real exercises - loads of exercises; goes to show what is wrong with our educational system. Greetings from a Swiss economics graduate

How did the first sentence help me?

Zach Star has something on it if I remember correctly.

Me too ... LoL

Pretty much like battleship, they deduced it (if i remembered correctly) into squares (actually circles but easier to understand in squares as shown in video) and searched a perimeter and ticked off squares as they went, the ship had a given size to which it could be deduced into a probability of multiple squares (they gained evidence of where it was not AND gained evidence as they found wreckage pieces) and in se gave a higher power of finding a higher probability to find the ship in a set square in a set range. Ofcourse they assumed the last position the ship was seen as a baseline. This is what I remembered when I had it lectured to me quite a few years back. Greetz!

They found someone who knew where the ship was. Then they tied him to a chair in a cellar and said "The next person to come into this room will be a shy, meek man named Steve. He will be the one who beats you to death with this hoe if you don't tell us where the gold is. Do you want to have a guess whether he's more likely to be a librarian or a farmer? Or would you prefer to just tell us where the gold is right now?"

@@labibbidabibbadum you forgot the feminist bank teller

Super valid point

Yes, I definitely agree. I think it was always fun to teach the basics of Bayes theorem, and then give students the Monty hall problem the next week (separately without telling them to use Bayes theorem) and then see how different students solve it, considering that even many of those who forgot Bayes theorem have another tool in their skill set that they can use to solve or estimate the answer.

And thank YOU, good sir, for inventing calculus. :-)

Weren't you supposed to be dead?

I for one have always thought you as the chosen one, not that pompous brit.

for a rushed overworked young brain too

The way I think of it is that Bayes Theorem gives you a way to turn some measurements you can make, but which aren't really all that interesting, into something you can't measure, but which you're really interested in knowing. Like in your example, you can turn the probability of getting a positive test result for anyone who actually has a disease (which is measurable and is interesting, I guess, but not of huge importance to most people) into the probability of actually having the disease, given that you got a positive test result, which is not directly measurable but is going to be of extreme interest to anyone who gets a positive test result. The false positive rate doesn't have to be very large for a positive result to be largely meaningless. For anything rare, the odds that a positive result is meaningful is going to be small unless the false positive rate is similar to the rate of the condition in the whole population because there will be far more false positives than real positives.

I agree on your comment about doctors. I am a med student in India and I believe that quite a lot of physicians don't know this well. It's sad.

@@parthashah9257 UK medic here... Check out more docs over the next few years, then update your beliefs :).. in the UK, 40% eligible health staff do not have free flu' jabs, because of false beliefs, mostly "I had the flu' straight after, once..", which appear impervious to the new evidence which in a rational system would update their beliefs :)

@@tim40gabby25 LMAO

Gerd Gigerenzer studied this, and the approach of thinking about absolute numbers instead of probabilities (like in the video) seems to help in practice.

This is an important point. We think that the text is informative, so the added information must provide some additional effect for the consequences we draw from the text, otherwise the speaker probably would not have provided it. Especially in a task like that where the hole point is to draw consequences. The idea that the pieces of information given in a cooperative conversation should be relevant goes back to the philosopher H Paul Grice, his “Maxime of quantity” and of “relevance”. There is lots of articles written about the Linda fallacy but as far as I know nothing makes this point.

That's kinda the point (that humans are predictably irrational).

Even if mathematicians don't know Grice's maxims, you'd think that psychologists would.

Humans like to embellish their answers with fiction as it gives the impression of knowledge even if it is unsupported or fanciful. . The question was which was the more probable. That is why in courts the lawyers often ask the question and insist on a yes or no answer to cut through the irrelevant waffle!

That's the point. Just because we think like that for most questions doesn't mean it's the way to think in this specific context. And such lack of reevaluation of belief can lead to silly situations at best, big mistakes and their consequences at worse.

I think he is doing this right now

Immanuel Kant already figured that one out back in the 1700s so we're a few centuries late with it. He wasn't very good at writing snappy quotes though

Am glad to see someone else picked that up too...😇👍

@@francescocraighero5392 I'm sorry to say that Daniel Kahneman in his book Thinking fast and slow debunks most of the things that says that guy in his blog.

@@Ucedo95 In the last months I encountered that book many times, I think it's definitely time to read it. I don't know where WBW made wrong assumptions, but I think that the contribution that Tim gave by visualizing this topic will still be worth a read

By the way, the current decade will end on 31st December 2020, as there will be 202 decades since Christ was born, allegedly on the 25th December. Considering a decade for 2010-2019 is 10 years ok, but is misleading as one of the previous decades in history must be 9 years only. Because the year 0 does not exist for historians. So the first decade in history was not 0-9 but 1-10.

Exactly. The fact that people don't always interpret questions literally, or the way a logician would, isn't a fault of human reasoning. It reflects our ability to make assumptions about context in which we're being asked things. I wouldn't fault anyone for assuming that option 1 excluded option 2, thinking that this must be the intended meaning since it would be a ridiculous question otherwise. Just another example of psychologists drawing grand conclusions from linguistic ambiguity.

But when they asked about the “100 people”, nobody interpreted this statement with ambiguity, even though many did with “Linda”. Why is that?

@@isabelhuang_1 Because the second way of asking it asks a fundamentally different question; I think any person with a basic grasp of numbers would know that you can't have a subset of a group larger than the group. It further removes some ambiguity by parameterizing the group; we're explicitly told that 100 people fit the description, and to dead-reckon how many are bank tellers and, of those bank tellers, how many are active feminists. BUT - and the video didn't address this, so I wonder if the study did then, too - if we follow up our population estimates by asking the original two questions, we still have the problem where the first question implies "...and is not an active feminist." Based on the answers given in the study, if that ambiguity is in play, you wind up with the same non-Bayesian error: 8 people in the group are tellers and of those 5 are feminists, so it's more likely that Linda is an active feminist bank teller rather than an apathetic one. In the case of the population-estimating version of the question, what we really have to ask to eliminate ambiguity is "Out of 100 people, what are the odds that Linda is a bank teller?" (8%) and "Out of 100 people, what are the odds that Linda is a bank teller AND an active feminist?" (5%). Then when asked which statement is more likely, the ambiguity of which population groups we're discussing is clear ("all bank tellers total vs those tellers who are active feminists", rather than "all bank tellers who are not active feminists vs those tellers who are active feminists").

@@isabelhuang_1 Because of the way most people are conditioned to approach multiple choice questions. On a multiple choice test, generally 1 answer is THE correct answer, and the rest are considered wrong (even if they are factually accurate), if more than one seems applicable we are taught to choose the one that is most accurate. So people are likely to ignore the bank teller portion of both options and focus on the difference between them to decide which is more accurate: is she an active feminist or is she not? The second form of the question doesn't have this ambiguity because there's no multiple choice to trick us into seeking a single best answer, and instead we have 2 separate and open questions. Even if you remove the "out of 100 people" part of this question and ask for percentages or probabilities you're likely to get the same rational results simply because they are now 2 separate questions instead of 2 competing choices to the same question.

Actually there isn't an ambiguity in language, "Linda is a bank teller" includes all bank teller possibilities. People just mentally interpreted that "Linda is a bank teller" means "Linda is a bank teller and is NOT active in the feminist movement," which is a flat out _wrong_ interpretation.

Same thing with the librarian bit. I would be thinking about who wrote the description and would guess that 95% of people would describe a librarian as someone organized and with a farmer they would say something about nature. This perceived probability strongly over rules any % of farmers and librarians in the population. It's not that the farmers don't fit the description, many probably would, but it wouldn't be the first and only thing you say about them.

@@dp2404 Another point with the librarian bit is that it reads like "am I, the writer of this question, thinking of a librarian or a farmer when I made up this character Steve"? If it was phrased like "select a random individual from the actual population of the USA, with these traits" then it would naturally lead to thinking about real-world proportions of farmers and librarians.

@@benjiunofficial exactly! You are more thinking about "why am I being asked this question?"

@@dp2404...but the description includes the fact that "Steve" has "very little interest in the world of reality" -- and that fits precisely 0% of all the farmers in the world. It might fit a non-zero percentage of bankrupt ex-farmers, but working farmers depend on "the world of reality" for everything they do... The video as a whole is excellent, but that one phrase in the description in the beginning really broke my immersion.

I think it's worth to read the book - Thinking fast and slow. It discusses how if fast brain is used we allow our biases to make decisions for us. Which often is useful, but sometimes detrimental.

Yeah. They're basically telling us that she 100% IS a bank teller. So the only question left is whether she's an activist or not. I get what he meant to say but the question doesn't really fit.

No they’re not. They’re saying which is more likely? Not, given that they’re a teller, which is more likely? And these are very different things. Not sure how you’d justify interpreting A or (A and B) as meaning the first A was A and not B either, in response to the initial post

I agree. I had the same interpretation, and I think the problem lies on the difference between verbal language and mathematical language in terms of precision. It requires some "fluency" in math to convert the problem mathematically. (Sorry about my English haha)

@@kellmano1 Well they're asking: 1) A (without B) 2) A with B The way I understand her description she's more likely to be a bank teller activist rather than only a bank teller.

@@ervindark9739 Haha, that's definitely not what they are asking. 1) Is she a bank teller ( including activist /not activist ) 2) Bank teller and an activists, the first actually includes the second options hence the propability is bigger, is it clear now? you added information wrongly to the 1) that "she is not an activist"

The probability is surely 1.

"Bae's" theorem haha

@@shreerangvaidya9264 Yeah, isn’t it 1 in this case ? The angry bae’s cancel out ?

She's hot and crabby.

@@townley1017 (1 * 1) / 1 is still 1 though

Agreed. If you said "What's more likely: Linda is a bank and a feminist, or that Linda is a bank teller and either a feminist or not a feminist" I think a lot more people would get it right.

If the question is asked by a physiologist, it appears that one can assume that the question is _always_ phrased in bad faith, with trick parts of the question that anyone rational will fixate on, but then the physiologist then dismisses as completely irrelevant. The farmer question is relevant here: how many farmers have little interest in the world of reality? Excuse me? What the heck do you think _farmers_ do? They work with real world things like dirt, animals, mortgages, and conniving scientists and anti-farm activists every day of their lives. You are telling me that successful farmers aren't interested in reality? Bullshit. So then as a physiologist you simply skip that most important part of the statement and then say, "no, it says he is meek, and that works for either farmers and librarians, so you are completely wrong."

Thank you for articulating my exact same impression.

@@lwilton the farmer question is a trick because its something we fall for. i asked myself whats the most likely result and caught myself thinking yes or no. when i noticed the sliding %bar in the video and i couldn't give a reason why it might be 55% - 45% over something close like 60% - 40% judging their character i moved on and asked how many libraries compared to farms are there. recognising relevant data was part of the experiment and even though its a trick question it still answers the study. it just implies you work with what you're given i think. but there are much better examples of how to get it wrong using intuitions and show rational thinking is a skill we need to practice

agreed. for the farmer the sample set is implied to be "types of people the question author has thought of" and not "the actual population of the world". An A.I. might have guessed farmer, and been wrong on the majority of texts that would take the time to describe an individual in this way. Steve is almost certainly a fictitious character, so the correct answer is actually "the author is probably thinking of a librarian." I do, however, think it's relevant that arm-chair researchers take into account to what extent real world data might experience this issue. I think the farmer/librarian question could be better phrased as something like "you are a data scientist studying random facebook profiles that have been constructed by an A.I., and see this profile of Steve. If you had to guess that he was either a farmer or a librarian, which would you guess?"

Yeah I'm highly sceptical about the psychological import of these experiments. I feel like it's mostly explained by the vagueness in the word "likely". As soon as you put the problem in context, the incorrect answers disappear. Which totally makes it sound like a communication issue rather than a psychological flaw.

X and not Y is a subset of X. Therefore P(X) = P(X and Y) + P(X and not Y) which implies that P(X and Y) < P(X) which means Lynda is more likely to be bank teller than a bank teller who is part of the feminist movement.

​@@Karthik-lq4gn You've misunderstood. Yes, P(X and Y) < P(X) is always true, but whether P(X and Y) < P(X and not Y) is not known, which is how Alan is saying people are interpreting the question.

@@gorgolyt Yeah, these experiments are no longer considered valid in as far as the original conclusions that were made, but are still important in that they provide good data showing that how a question is phrased can change the way a person interprets a question, and therefore how they will answer it (which is really important in any country where the citizens vote).

but given the prior that the students know it's the first element, the probability for both is equal, so there is no answer more correct than the other. Once you know that Q is hydrogen, which happens before the MCQ, then all you need to do to reach this conclusion is to evaluate the truthfulness probability of the choices by plugging the answer, and this becomes What is the probability for each of the following statements being true? Hydrogen is an element in the periodic table Hydrogen is the first element of the periodic table They are both true, so none of the answer is more correct than the other, since you already knew the answer before the question being asked. The result above can also be determined with the formula explained. Say that we want to test answer 1, which becomes the first tested hypothesis, H1. The formula, as presented in the video is P(H|E) = (P(E|H)*P(H))/(P(E|H)*P(H)+P(E|~H)*P(~H)) To calculate P(H1|E) we need all the above terms, but let's start with the easy ones P(H1) = ? , or in other words, what is the probability that Q is an element? Obviously this depends on how we define our space, but let's use the periodic table as a space, so then P(H1)=1 P(~H1) = ? , or in other words, what is the probability that Q is NOT an element? Obviously, P(~H1)=0 P(E|H1) = ? , or in other words, what is the probability that Q is a gaseous element that reacts with oxygen to create common water given that Q is an element in the periodic table? Well, once again, we know there's exactly only hydrogen out of all the elements, so the answer is P(E|H1) = 1/n , where n is the number of elements in the periodic table. Let's simplify and say that we only discovered the first 100 elements, so n=100 P(E|H1) = 1/100 P(E|~H1) = ? , or in other words, what is the probability that Q is a gaseous element that reacts with oxygen to create a common water given that Q is not an element in the periodic table? Obviously 0, although I suspect the more appropriate answer is undefined. P(E|~H1) = 0 If we plug all these in, we get P(H1|E) = ((1/100)*1)/((1/100)*1+0*0 = 1 P(H1|E) = 1 Same about H2 P(H2) = ? , or in other words, what is the probability that Q is the first element of periodic table? Considering the same space of the periodic table, then P(H2)=1/100 P(~H2) = ? , or in other words, what is the probability that Q is NOT the first element? Obviously P(~H2)=99/100 P(E|H2) = ? , or in other words, what is the probability that Q is a gaseous element that reacts with oxygen to create common water given that Q is the first element of periodic table? Well, we know there's exactly only hydrogen to be first P(E|H2) = 1 P(E|~H2) = ? , or in other words, what is the probability that Q is a gaseous element that reacts with oxygen to create a common water given that Q is not the first element of periodic table? Obviously 0 P(E|~H2) = 0 So, we get P(H2|E) = (1*(1/100))/(1*(1/100)+0*(99/100)) = 1 P(H2|E) = 1 P(H1|E) = P(H2|E) , so both answers should be accepted as being the most correct answers. This problem is different than the Linda problem in the video. To make it equivalent, assume that you personally know that Linda is a bank teller and that she is active in the feminist movement. The 2 problems are also equivalent if you eliminate the priors, and then everyone would give the more inclusive answer. Say that you're only asking your question to people who don't know that Q is hydrogen, or that do not see any correlation between being active in the feminist movement and the evidence presented in the question. Then these people would pick the more likely answer, meaning the first, each time. This means that people are very selective with the priors they use. Moreover, people are often tricked by the fact that hypotheses overlapping, but people guess they are distinct (and sometimes complementary, and sometimes equal). So given H1 and H2, people make the following assumption P(H1|H2)=P(H2|H1)=0 (and sometimes P(H1)+P(H2)=1, and sometimes P(H1)=P(H2)=0.5), which means that the only possible way of testing actual knowledge using MCQ is for choices to hold as manu natural assumptions as possible, but at least the first, P(H1|H2)=P(H2|H1)=0 . So the proper choices for your question should be: 1. Q is an element on an odd position in the periodic table 1. Q is an element on an even position in the periodic table This way, the student will only perform better than chance if they truly know the exact answer.

Yes, and the irony is that he is making us understand by using our intuition. So basically he is using intuition to explain things logically.

that username