### Class 16: Binomial Sins!

Lesson 16: Binomial Sins!
We deduced probability can be math; we deduced its functional form. We deduced it can be represented by numbers, and we discovered, via more deduction, what these numbers can be. With that, we deduced our first formal model, the hypergeometric model.
Today we deduce an APPROXIMATION to that model. And we warn, as vigorously as we can, against treating that APPROXIMATION as anything other than that. If we do not, we risk the Deadly Sin of Reification - a sin rife in science. It's so common we can call it the plague of science.
HOMEWORK: With B = M red balls, N total balls, and so N - M white balls, and with R_i = red drawn on i-th draw, and L = "At least one red in k previous draws", what is Pr(R_k+1|BL)?
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/52506/
https://wmbriggs.substack.com/
Permanent class page: https://www.wmbriggs.com/class/
Uncertainty & Probability Theory: The Logic of Science

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### Class 15: Acausal Effects & Probability's Directionless

Lesson 15: Acausal Effects & Probability's Directionless
Uncertainty & Probability Theory: The Logic of Science
I renamed the video, coming up with a better title only after I had finished recording. I want to emphasize that future knowledge can influence past events! Not the events themselves, but our knowledge of the events. Past events are not caused to change. The change is acausal and with respect to our uncertainty.
This has profound consequences. It means that we can't get cause from probability models. We bring cause TO models. This means the enormous number of causal claims we see based on probability models are not justified. Not to say they are wrong, because modelers may have guessed right. But they can't know it.
https://www.wmbriggs.com/public/briggs_breaking_law_averages.pdf
HOMEWORK: With B = M red balls, N total balls, and so N - M white balls, and with R_i = red drawn on i-th draw, what is Pr(R_3|B)?
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/52506/
https://wmbriggs.substack.com/
Permanent class page: https://www.wmbriggs.com/class/

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### Class 14: No "UNfair" Dice & 1, 2, 3, Many!

Lesson 14: No "UNfair" Dice & 1, 2, 3, Many!
Uncertainty & Probability Theory: The Logic of Science
Last week's homework was recalling Pr(M_6|E) = 1/6, and we did Pr(M_6|E + "fair") = 1/6 (a circular argument!). Now give us Pr(M_6|E + "unfair") = ? We learn that there is no answer! It depends on what you bring to the word UNFAIR. There is no definite meaning.
Which brings up our TWO MOST IMPORTANT PROBABILITY LESSONS. (1) CHANGE THE EVIDENCE, CHANGE THE PROBABILITY. (2) PROBABILITY IS NOT REALITY: OUR UNCERTAINTY OF THINGS ARE NOT THE THINGS THEMSELVES.
See also the main site for a link to my other (free!) book so you can learn counting. Or download here:
https://www.wmbriggs.com/public/briggs_breaking_law_averages.pdf
HOMEWORK: (A) How many TOTAL groups can you get from groups of 5 from the numbers 1 through 70 AND one group of 1 from the numbers 1 through 25? (B) Which gives a higher TOTAL number of groups? Adding 19 numbers to the first batch (so we have 1 through 99), or we keep the 70 but choose groups of 6 instead of 5?
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/52506/
https://wmbriggs.substack.com/
Permanent class page: https://www.wmbriggs.com/class/

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### Class 13: No "Fair" Dice & Jaynes Symmetry

Lesson 13: No "Fair" Dice & Jaynes Symmetry
Uncertainty & Probability Theory: The Logic of Science
We learn that adding "fair" to the evidence of a die toss gives a circular argument: it assumes what it sets out to prove, that the probability is symmetric. We examine Jaynes's attempt to provide a proof of equi-probability, but we see that fails because of the same circularity. So does a proof by Diaconis, which you can read on the blog. Next time we do Stove's proof - which works!
Homework: We did Pr(M_6|E) = 1/6, and we did Pr(M_6|E + "fair") = 1/6 (a circular argument!). Now give us Pr(M_6|E + "unfair") = ?
The Infamous Coin Flipping Machine!
https://youtu.be/8XX0iRAN--8
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/51979/
https://wmbriggs.substack.com/
Permanent class page: https://www.wmbriggs.com/class/

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### Class 12: Psychic Card Guessing & The Proportional Syllogism

Lesson 11: Psychic Card Guessing & The Proportional Syllogism
Uncertainty & Probability Theory: The Logic of Science
We solve the psychic guessing cards problem, and then, at long last, return to assigning numbers of probability. We do this using the proportional syllogism. We learn that adding necessary truths to Qs (or any logical argument) does not change their conclusions or probabilities.
Homework: Q = "The Metalunan interoctor (a die) must take one of 6 states when tossed: s1 = 1, s2 = 2, and so on." P = "It takes state s6 = 6". What is Pr(P | Q & "fair die")? (We add "fair die" to the Q.)
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/51979/
https://wmbriggs.substack.com/
Permanent class page: https://www.wmbriggs.com/class/

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### Class 11: One Son Born Tuesday & Relevance

Lesson 11: One Son Born Tuesday & Relevance
Uncertainty & Probability Theory: The Logic of Science
Homework: RELEVANCE. A psychic is guessing cards from a standard poker deck of 52 cards. She must guess the exact card, suit & value. When she guesses right, she receives a chocolate. When she is wrong, she gets nothing. In the first 10 cards, she got 4 right and 6 wrong. What is the probability P = "She gets the 11th correct"? The exact number is good if you can get it, but it's much, much more important to explain your reasoning. I mean, what is your Q?
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/51979/
https://wmbriggs.substack.com/
Permanent class page: https://www.wmbriggs.com/class/
Uncertainty & Probability Theory: The Logic of Science

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### Class 10: Minding Your Ps & Qs & Monty Hall

Lesson 10: Every time, without fail, when you hear somebody say "The probability of P is x", ASK FOR THEIR Q. Reminder: all probability fits the schema Pr(P|Q). Therefore we must always know what the Q is. And we must know before P has been revealed to us. Anybody can come up with a post hoc Q that gives a high value for P. Anybody. Indeed, all mainstream statistics relies on this trick. Never fall for it. Insist on demonstrating real predictive accuracy. Get their Q before P is revealed. We also do the infamous Monty Hall Problem, which shows how difficult finding Q is.
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/51979/
https://wmbriggs.substack.com/
Permanent class page: https://www.wmbriggs.com/class/

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### Class 9: Nothing Has A Probability

NOTE: The correct formula at the end of the video/homework is : Pr(PQ|E) = Pr(P|QE)Pr(Q|E)
Lesson 9: There is no probability life on other planets exists. There is no probability life on earth exists. There is no probability you are alive. There is no probability you will die by cancer. Because NOTHING has a probability. De Finetti shouted, and we agree, PROBABILITY DOES NOT EXIST. We go through the true meaning of probability today.
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/51979/
https://wmbriggs.substack.com/

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### Class 8: Uncertainty & Probability Theory: The Logic of Science: What Probability Is 1

Lesson 8: What Probability Is 1.
We start by answering an excellent question.
Anon asks:
"I have a question about Bayes' Theorem and philosophical arguments. I ask because I have a broad scholastic approach to philosophy that relies metaphysical demonstrations.
"Is the contrast between probabilistic vs deductive arguments unhelpful? It seems like deductive arguments mask the uncertainty of probable premises. If each premise of an eight-step argument is 95%, the lower bound would be 66% (given independence).
"For some reason, this doesn't sit right with me. Bayes' Theorem seems useful for when deciding theories within the world, but not applicable to first principles (like the reality of change). But I don't have much of a mathematical background. Any assistance you can provide would be extremely welcome."
This leads us to show probability, being logic, doesn't care about the premises. Just about the CONNECTIONS between premises and the proposition of interest.
HOMEWORK: THERE IS NO SUCH THING AS UNCONDITIONAL PROBABILITY, I.E. THERE IS NO Pr(A), only Pr(A|B). If you think not, find a Pr(A)!
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/51635/
https://wmbriggs.substack.com/
Permanent class page: https://www.wmbriggs.com/class/

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### Class 7 Part 2: Uncertainty & Probability Theory: The Logic of Science: Logic Intuition Check

Class 7: Uncertainty & Probability Theory: The Logic of Science: Logic Intuition Check
This is ONLY Part 2. Rumble only allows 2 GB files, so I had to break this into two.
Lesson 7: Logic Intuition Check.
I'm starting to get some good questions. Some of them by folks who have clearly had training in probability and physics before.
These people will have the most difficult time following this Class.
For the very excellent reason that we, all of us, when confronted with new information seek to put it into buckets in our mind, if you will, buckets which we have formed over many years. This is entirely natural, and even helpful.
Unless those buckets are the wrong shape. Which if you have had training about "random variables", "p-values", and the like, are, I insist, wrongly shaped. Not always, and not always badly, but to some extent.
Review!
We have done so far, and ONLY what we have done, is this:
1. Posed some logical questions: could logic handle uncertainty?
2. Demonstrated the crucial differences between local and necessary truths;
3. That having a philosophy is inescapable, and that belief was an act, a choice;
4. That logic was a mix of subjectivity---picking premises and proposition of interest---and objectivity---rigorously showing the connection between the premises and POIs. That logic was only about those connections; that logic was therefore a matter of the mind and not things;
5.That induction and intuition were of at least five different kinds, and that induction provides our most certain knowledge (induction provides us with the rules of logic, for instance, as do axioms, for which there is no and can be no empirical proof); and that there was no escaping faith (at least that your senses were working properly at times);
6. That probability could be represented as a mathematical function, and we discovered the form of that function (Bayes's Theorem); that certainty was given by the number 1, and falsity by the number 0.
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/51635/
https://wmbriggs.substack.com/
Permanent class page: https://www.wmbriggs.com/class/

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### Class 7 Part 1: Uncertainty & Probability Theory: The Logic of Science: Logic Intuition Check

This is ONLY Part 1 of 2. Rumble only allows 2 GB files, so I had to break this into two.
Lesson 7: Logic Intuition Check.
I'm starting to get some good questions. Some of them by folks who have clearly had training in probability and physics before.
These people will have the most difficult time following this Class.
For the very excellent reason that we, all of us, when confronted with new information seek to put it into buckets in our mind, if you will, buckets which we have formed over many years. This is entirely natural, and even helpful.
Unless those buckets are the wrong shape. Which if you have had training about "random variables", "p-values", and the like, are, I insist, wrongly shaped. Not always, and not always badly, but to some extent.
Review!
We have done so far, and ONLY what we have done, is this:
1. Posed some logical questions: could logic handle uncertainty?
2. Demonstrated the crucial differences between local and necessary truths;
3. That having a philosophy is inescapable, and that belief was an act, a choice;
4. That logic was a mix of subjectivity---picking premises and proposition of interest---and objectivity---rigorously showing the connection between the premises and POIs. That logic was only about those connections; that logic was therefore a matter of the mind and not things;
5.That induction and intuition were of at least five different kinds, and that induction provides our most certain knowledge (induction provides us with the rules of logic, for instance, as do axioms, for which there is no and can be no empirical proof); and that there was no escaping faith (at least that your senses were working properly at times);
6. That probability could be represented as a mathematical function, and we discovered the form of that function (Bayes's Theorem); that certainty was given by the number 1, and falsity by the number 0.
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/51635/
https://wmbriggs.substack.com/
Permanent class page: https://www.wmbriggs.com/class/

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### Class 6 PART 2: Uncertainty & Probability Theory: The Logic of Science: Probability's Entrance!

This is ONLY Part 2. Rumble only allows 2 GB files, so I had to break this into two.
Lesson 6: Probability's Entrance! We PROVE, and do not assume, probability can be a number. We PROVE probability is an objective matter of logic. We PROVE all probability is conditional. We PROVE the interpretation of probability is the certainty in a proposition given assumed evidence.
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/51635/
https://wmbriggs.substack.com/
Permanent class page: https://www.wmbriggs.com/class/
Class 6: Uncertainty & Probability Theory: The Logic of Science: Probability's Entrance!
<a href="https://www.wmbriggs.com/class/"><em>Link to all Classes.</em></a>

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### Class 6 PART 1: Uncertainty & Probability Theory: The Logic of Science: Probability's Entrance!

This is ONLY Part 1. Rumble only allows 2 GB files, so I had to break this into two.
Lesson 6: Probability's Entrance! We PROVE, and do not assume, probability can be a number. We PROVE probability is an objective matter of logic. We PROVE all probability is conditional. We PROVE the interpretation of probability is the certainty in a proposition given assumed evidence.
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/51635/
https://wmbriggs.substack.com/
Permanent class page: https://www.wmbriggs.com/class/

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### Do Our Rulers Really Believe What They Say They Believe & What To Do About It

Do our rulers, Experts, elites and celebrities really believe what they say they believe about "gender", "climate change", "racism" and so forth? For instance, when these people say that that man over there in a dress is "really" a woman, do they truly mean it?
Some do, some don't, some will, some won't.
More at https://www.wmbriggs.com/post/51580/
More at https://open.substack.com/pub/wmbriggs/p/do-our-rulers-really-believe-what?r=b9swm&utm_campaign=post&utm_medium=web&showWelcomeOnShare=true

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### Class 5: Uncertainty & Probability Theory: The Logic of Science: Induction & Intellection

Lesson 5: Induction & Intellection. Logic needs induction, which provides our most certain kind of knowledge. There are at least 5 different kinds of induction. From most to least certainty: intellection, intuition, argument, analogy, and finally probability.
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/51436/
https://wmbriggs.substack.com/
Permanent class page: https://www.wmbriggs.com/class/

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### Class 4: Uncertainty & Probability Theory: The Logic of Science: The Return of Logic

Lesson 4: The Return of Logic. We discover that we cannot learn logic emprically, that something more is needed (induction!). And that logic, like math, is not purely formal and that equations cannot be used unconditionally on Reality
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/51436/
https://wmbriggs.substack.com/
Permanent class page: https://www.wmbriggs.com/class/

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### Class 3: Uncertainty & Probability Theory: The Logic of Science: Belief & Logic

Class 3: Uncertainty & Probability Theory: The Logic of Science: Belief & Logic
Lesson 3: Belief & Faith. We finish Chapter 1 of "Uncertainty". I give a plea why philosophy is necessary. The blog/Substack have an excerpt from this chapter again.
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/51347/
https://wmbriggs.substack.com/
Permanent class page: https://www.wmbriggs.com/class/

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### Class 2: Uncertainty & Probability Theory: The Logic of Science

Lesson 1: Uncertainty. We start with Chapter 1 my Uncertainty. An except is provided at the blog and Substack.
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/51265/
https://wmbriggs.substack.com/
Permanent class page: https://www.wmbriggs.com/class/

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### Class 1: Uncertainty & Probability Theory: The Logic of Science

Lesson 1: Logic. We start with Chapter 1 of ET Jaynes's "Probability Theory: The Logic of Science", and discover logic is both easier and harder than we thought.
All questions will be answered in the following Monday's lecture.
Written lecture: https://www.wmbriggs.com/post/51104/
Permanent class page: https://www.wmbriggs.com/class/

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### Voting In Democracies Causes Discord, Increases Strife & Causes Divisions

More at https://www.wmbriggs.com/post/43330/
Including links to the previous articles on shared and unshared goals, and their effects on voting.

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