There is that which is, and that which we can know about what is. Both feed the other. Probability belongs to the second subject.
If you want to know what we can know, how certain or uncertain we can be, then you must study probability. A subset of probability is logic, and so if you study probability you study logic, too. Logic is probability when there is certainty. When there is uncertainty, which is in most things, you must understand probability.
To be certain is to know the cause of a thing or proposition. Another word for cause is explanation. You must be able to explain why a thing is so or not so to reach certainty. If you cannot, then you are left with uncertainty, and must have a language to express that uncertainty.
Our goal is always to reach explanations of things. We often cannot reach it. Sometimes causes are hidden. In order to understand cause, we need to understand what is. If what we want to know is the world, then we must have a philosophy of Nature. Nature is a subset of Reality, and so to fully grasp cause we also need a philosophy of Reality itself.
Sometimes we can make all of this quite formal, which in the language of logic and probability is rigor and mathematics. But we cannot always come to formality, and so mathematics is only part of probability. And not the most important part. Though it is still crucial, and so much so that many make the understandable mistake of supposing the mathematics is probability and thus is Nature. When this error occurs we reach the dreaded Deadly Sin of Reification, the Eighth Deadly Sin, and the most common in Science.
Science is, of course, the search for explanation in Nature. But since Nature is not all there is to Reality, Science is not the answer to all things. In both Nature and all Reality, probability is never proscriptive. Probability does not tell you what to do. Therefore Science cannot tell you what to do. It can only tell explanations, and of their uncertainty.
The organized practice of applying probability to Nature is called statistics. The organized practice of forming mathematical descriptions of parts of Nature is called modeling.
In the correct and proper hunger for explanation and certainty, many shortcuts have been developed, especially in Science and statistics. Formulas—rituals, really—have been given which are said to guarantee discovery of cause. They are false. Their use has led to vast and persistent error. Cause is claimed where there is only uncertainty. Because our culture is steeped in scientism, the Fallacy which insists the answers to all questions must be and are scientific, these rituals have had devastating consequence.
The worst thing is that most are unaware of this. Scientists pick off small subsets of Nature and study them. Their interest is in the subsets, and so they devote little time to thinking about the tools they use which promise them causal knowledge. Besides, everybody is using them, and all the best sources swear the tools work.
Over-certainty is more pronounced the more complex cause is, and vice versa. Man being the most complex of all things in Nature (which is not all Reality), those subjects centered around man produce the most numerous mistakes. There are far fewer mistakes and much less over-certainty in systems which are not as complex, say, electronics. The toys we designed for ourselves work well, or well enough, because cause is easier to come by there.
The Class Uncertainty is freely available to all (whatever is needed is provided; there are no texts to buy), and supported by generous patrons and readers for your benefit. The homepage for it is here.
It is designed with as minimal math as we can get away with, and still allow us to grasp the subject. This is partly because math frightens many, and mostly because math is not the essential thing about probability. It is only a tool. And when it is necessary, my hope is that the lessons can still be understood, even when the mechanics (math) of certain things will evade some pupils. Still, math will never not be useful, so it pays to learn what you can of it.
I know of no other Class like this anywhere; assuredly it is at no university. Given our culture, it likely won’t be, either (your host has been deemed “controversial”). But my hope is that in the future others will take it up and make the material broadly available and expanded. For as much information as I can give you, there is still much to do.
The Class list is itself intimidating. There are already over 70 lectures (all are on video too), and many more to come. But not all people will need all of it. So here is the rough breakdown of areas. There is much overlap. You do not necessarily have to begin at the beginning, especially if you are anxious to get to material you need for your own work.
Truth, Induction and Knowledge: Classes 1–5.
Proof Probability Can Be Math & What Kind: Classes 6–9.
Simple & Perplexing Probability Examples: Classes 10–16.
What Random and Chance Are & What Probability Is Not: Classes 17–29
Basic & Common Probability Mistakes: Classes 30–34
Simulations & Information Complexity: Classes 35–39
Cause: Classes 40–46
Models: Classes 47–57
Hypothesis Testing, P-values & Other Enormous Errors: Classes 58–65
Uncertainty & Decision Introduction: Class 66 (much more to come here)
Regression, The Most Ubiquitous Model: Classes 67–72
That brings us up to date. I will add to this list when future Classes are posted. Still to come are treatments of more complex models, especially the many excesses of time series, physics models, coincidence, and a full treatment of decision making. I’m guessing at least 30 more.
Perhaps more if people have more questions about the kinds of models encountered in their own fields.
Video
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Remarkable oeuvre. Tour de force. Congratulations. Thank you.
This is my third time asking, and I’m beginning to think you’re avoiding me.
I have a single die. I want to determine if it is “loaded” to prefer one face. I can roll it as many times as I want.
What mathematical statistic can I use to determine if it is loaded? I say the p-value, but you say that’s useless … so what is useful?
w.
Willis,
I have answered the question each and every time. Go back and look at when you asked, and you’ll find the answers.
The probability of [1,2,3,4,5,6], conditional on whatever evidence you consider. Then some decision rule that says “This much departure from uniformity means loading.” Which rule may be different for you than for me. That is always the answer.
If you open the die and see the load, then what is that probability? If you only take observations, what is that probability?
It’s also interesting that some still use P-values, even after being shown (by at least half a dozen proofs) their uses are fallacious. “Hey, a fallacy is better than nothing.” Which we would never accept as an argument anywhere else. I get this all the time, though.
But you have inspired me. I can see that many have the idea that causes are always occult, and can only be revealed by arcane mathematical formulae. That’s what the P survives.
More on this later.
Or, Willis, you could take the course, study the classes, do the homework. Then, quite possibly, or even probably, you could answer your question yourself. In the end it’s all a question of values, n’est-ce pas?
Thanks, Matt, but you haven’t answered my question, either then or now.
The last time I asked, I got this non-answer:
=======================
Willis Eschenbach
February 27, 2023, 2:25 pm
I’m trying to decide if a certain pair of dice are loaded. I throw them ten thousand times. I test the results, and the high p-value for each possible result, from snake-eyes to double-boxcars, leads me to conclude they are not loaded.
Please explain why my logic is incorrect, and describe what alternative measure you would use to determine if the dice are loaded.
Thanks as always for your most fascinating blog,
w.
Briggs
February 27, 2023, 2:52 pm
Willis,
How does it lead you to conclude that? Specifically, I mean.
And, of course, what flaws do you find in the argument above? Specifically, I mean.
===========
That’s not an answer, that’s a question …
====
This time I asked for a mathematical statistic. If you are not using p-values, WHAT STATISTIC ARE YOU USING? Waffling about “some decision rule” isn’t an answer. What “decision rule” do YOU choose for that question?
Thanks in advance, and thanks for all your fascinating posts.
W.
Assume uniformity, quantify the departure/deviation of observed data from uniformity, and establish a decision rule. Steps for a statistical hypothesis test?! lol, Mr. Briggs.
W: “How do I access the money in the safe?”
B: “The answer is to open the safe.”
Isn’t B smart?
—————————————–
A great way to provide a clear answer is to give a simple example. For example, consider the results of rolling a single die 60 times, as shown below. We wish to determine wether the die is loaded.
{2 2 2 3 1 1 4 6 2 4 6 4 5 3 2 5 3 5 5 2 1 2 1 4 1 4 5 6 2 6 3 1 2 4 2 5 2 5 3 5 2 3 5 2 2 2 2 3 6 4 5 5 3 1 6 1 1 4 1 1}
Or
11 ones, 16 twos, 8 threes, 8 fours, 11 fives, 6 sixes.
Now, follow your responses to Willis E. and explain what your answer entails for this particular example.
How to determine a decision rule? Furthermore, how do you assess the reliability of your decision?
The answer is a question: what did you expect the counts to be? On what premises did you base your expectations? How many hurricanes did you expect this year? Why? What did you expect the low and high temperature to be last Tuesday? Based on what? Some infinite series? Why not roll the dice an infinite number of times? You want an answer based on infinite rolls; better get started.
Try a different Aunt Sally, Eschenbach: an actual physical dice is an object that can be examined and measured to check if it’s loaded or otherwise damaged/imperfect – no statistical measurement is required when actual physical determination can be made, which is unambiguous and can. be replicated by independent parties as necessary. It’s irrelevant to complain you want to use statistics when Briggs has pointed they don’t work and in this example you can do something that does work.
The problem would be with a computer algorithm “dice” or some such virtual thing where mathematical and algorithmic considerations would them come into play. Even in that case statistics isn’t necessary and is certainly not the tool to make a determination – even though you can roll the dice an arbitrarily enormous number of times at will. Modern computer random number generators use thermal noise to seed random numbers and standardized random number algorithms have been examined rigorously using mathematical theory (Information Theory not statistics).
John, you say:
“Try a different Aunt Sally, Eschenbach: an actual physical dice is an object that can be examined and measured to check if it’s loaded or otherwise damaged/imperfect – no statistical measurement is required when actual physical determination can be made, which is unambiguous and can. be replicated by independent parties as necessary. It’s irrelevant to complain you want to use statistics when Briggs has pointed they don’t work and in this example you can do something that does work.”
Dang, miss the point much? Let me clarify. I have no physical tools to measure the physical dice, which I figured would be obvious but I guess to you it wasn’t. So my question remains. How can I determine if it is loaded using statistics?
Remember, statistics was invented by gamblers … the foundations of probability were established in the 16th and 17th centuries by figures such as Gerolamo Cardano, who was an avid gambler and wrote extensively about games of chance, including concepts of probability in his posthumously published work on gaming.
But heck, you could have saved him all that trouble by just telling him to measure the dice …
Me, I’m still waiting for Matt to answer my damn question.
w.
Eschenbach, card counting was arrived at by an empirically derived process. That’s not the same as having bogus statistical theories about imaginary population distributions and sampling. In the real world dice are judged as fair or not by physical measurement, that’s how the casinos do it. You are lining up Aunt Sallies in spite of pretending otherwise.
John, I asked a THEORETICAL question. Pointing out that there are real-world options is MEANINGLESS to my question.
How about you let Dr. Briggs answer the question?
w.
Eschenbach you’re becoming a caricature of modern scientism. I’ve explained to you why your Aunt Sally is bogus and the models people make are as bogus as well because they have no relationship to phenomenal reality. You’re entirely missing the point by insisting on your bogus example. But of course that’s it, you just don’t get it.
Willis,
I have just about finished a brief answer to you (about 3,000 words), which because of the importance and generality of the question will be its own Class. But I already have one for this week, and there is no Class next, so it won’t show until December 4th.
The brief answer is (and must be): Bayes theorem using the hypotheses you think important.
Can’t agree with Briggs on this, I agree with Tesla; “Today’s scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.”
A dice is a real thing. You measure it you don’t use statistics. As I said, Casinos would measure the dice to see if they’re loaded. I’m sure Casinos are happy to use statistics up to a point but what matters to them is the cold, hard cash whatever the statistics say. Although it’s all money laundering anyway in Casinos so I doubt they really have to worry about statistics too much.
Come up with a real world example where you are forced by actual phenomenal reality not a thought experiment to rely on Bayes theorem and can’t do it another way and let’s see if that can be picked apart. Something epidemiological perhaps.
Thanks, Matt, much appreciated.
w.
Thanks, John. Tesla was often right, but there are questions which cannot be solved without statistics. I know a bit about gambling (see below), and I can assure you that the casinos use statistics for something that cannot be done in any other way—detect cheating.
If a dealer comes up with a run where she (most dealers are women) loses money, is she just having a night of bad luck. or is she actually cheating? You can’t measure her like you can measure dice … and despite your claim that “I doubt they really have to worry about statistics too much”, they worry about them a lot because they worry about cheating.
A lot.
Best to you and yours,
w.
http://wattsupwiththat.com/2012/01/26/decimals-of-precision-trenberths-missing-heat/
Willis, I’m trying to get you to think differently, not be antagonistic… although my sister says I’m “on the spectrum” and indeed my social skills are zero. There’s a YouTube Channel called, “Demystifying Science” that’s interesting. Some of their stuff is nonsense but there’s a lot of good stuff there. You should dip into it.
Casinos use accounting to manage to their loses. I doubt they actually care what’s going on as long as they’re winning, and the house always wins.
“Having to use statistics” doesn’t mean statistics is actually a useful tool other than politically.
Let’s take smoking as an example. We’ve now reached the stage where the supposed ill effects of smoking have reached homoeopathy in its powers of massive dilution. Any objective analysis of smoking and health went out the window long ago. For instance, smoking helps with weight control but now we have a slew of new drugs to deal with obesity; nicotine helps with various types of dementia and neurodegenerative diseases but now we have euthenasia; smoking ot relieve stress is replaced by sundry other approved psychoactive drugs… and on and on. You may not live longer if you give up wine, women, and song but it seems like it anyway.
Scientism is the issue: we must use statistics – whether or not it’s really defensible – because governments need a faux moral justification for doing what they want to do anyway. I don’t buy any of it, it’s simply haruspicy dressed up in a white coat and world salad.
John, you seem to be operating under the misunderstanding that I asked you a question or that I care about your answer. I asked Matt a question. But rant on, it’s amusing …
w.
Eschenbach, you’re trolling and Briggs humours you, it is amusing. Somehow Briggs can’t shake off the embrace of scientism in spite of all his rantings.
John, I don’t troll. Never have, never would. Google “projection”, there’s a good fellow.
I asked a question, hoping to get an answer. Matt’s answer above pushed me in the right direction, and further study and research on my own has given me the answer.
You, on the other hand, have contributed nothing to the conversation except complaints, insults, accusations, and bitterness.
Congratulations,
w.
Willis,
Now 4,500 words, but as a compensation it has code, so all can try.
Thanks for pushing me.
Answer’s the same, though.
Thanks, my friend, appreciated.
w.