Jach's personal blog

(Largely containing a mind-dump to myselves: past, present, and future)
Current favorite quote: "Supposedly smart people are weirdly ignorant of Bayes' Rule." William B Vogt, 2010

Proofs for and against God

I think I need a simple precursor to my post about proof. This post is meant to destroy the notion that there is anything we cannot prove. I have two preliminary subpoints.

There is no difference between a positive and a negative claim because one can be expressed as the other. I claim "God exists". That is a positive claim. I also claim "God is not nonexistent." This is a negative claim but says exactly the same thing as the first claim.

"Burden of proof" is an expression that signals you are suffering from diseased thinking. There is no such thing as "burden of proof" except in a legal context, where legal proof is the same thing as legal evidence. Proof in general, however, is not the same thing as evidence in general. Much confusion arises from conflating the two. In matters of Truth, there is only "burden of evidence."

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For Else in Python

I have the unfortunate brain wiring where once I understand something complete, or do some task such that it works, that thing suddenly seems trivial to me. I think this is generally true for most individuals who have spent even as little as a year in a narrow field of study, like programmers with a particular programming language. If you're a half-decent programmer, did you know you could make some money by writing a beginner's book? All that stuff that seems trivial to you now, you could monetize! Or be like me and point to other references that are free...

Anyway, the subject of this post. Python has a construct where the for loop or the while loop have an optional else block you can attach to them. The rule that determines whether the block gets executed or not is at first unintuitive, but it becomes immediately clear with an example.

You probably think the else block should execute only if the loop never ran once? If you think that, you are wrong. The rule is: execute the else block if the loop completed normally; that is, without a break statement. (Or raised exception.)

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Conditional probability is the only probability and stay out of the rain

If you have had "normal" math classes, you'll probably be used to seeing entities like "the probability of being struck by lightning." You have probably been misled. For background reference, the number of people who are struck by lightning in the US is about one per million. (They don't necessarily die.)

That's a number. A ratio. A frequency. It is not a probability. Not yet. If you had a normal math education, you should want to argue with me on this point. You were taught that probabilities are just frequencies, which are just facts about the world like the lightning fact. Another number might be two in four balloons are red, in a bag containing two red and two blue balloons.

The lightning number can be turned into a probability, though, provided we provide some conditions. I say all probabilities are conditional probabilities, but you should ask: "Conditional on what?" This depends on the relevant information we have. The only information we have about the one in a million number is that it's for people who live in the US. Thus we might express the above lightning number as $$Prob(being\ hit\ by\ lightning | live\ in\ US) = 1/1,000,000$$. The $$|$$ is read as "given" or "supposing" or "on the condition that the following is true", so you would read that mathematical equation as "The probability of a person being hit by lightning given that person lives in the US is one in a million." But this fact shouldn't make you feel safe if you find yourself in the middle of a nasty thunder storm without shelter.

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Circus Math Considered Harmful

(I always wanted to use that phrase in a title.)

There's a problem with math education. I don't mean a specific field of math, but math in general. At every level of schooling, the problem rears its head. The problem even extends into other disciplines where the math is meant to be a tool rather than the subject.

This isn't a new observation. The problem is recognized by a lot of people, who attack it from different directions. Students claim they don't like "math". How can we get more students to like math? Is it really math they dislike? Or is it just "math"? Teachers claim students are doing worse on tests, so while they're making the tests easier in order to keep their jobs and funding, they ask how can we get students to master more complicated material? Is it really that the material is so hard, or are unrealistic expectations being made, or are artificial barriers being created to buff up the apparent difficulty?

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Are you a rationeliezer?

That's all. Apparently I'm the first one to come up with this, so I'm being the early bird that catches the Google Crawler by making a post with it as the title.

What's a rationeliezer? It's not quite a "rationalist" in the traditional sense of the word, though many of us go by that label anyway. We seem to have won, go google "Rationality". We're definitely not "rationalizers", aka people who rationalize everything. That's such a horrible word! It's like calling lying "truthalizing". (That example is known to rationeliezers.)

No, rationeliezers are people who are interested in correct human rationality as written in great lengths by Eliezer Yudkowsky. There's cultish counter-cultishness around him, because god damn it you shouldn't be accused of being a cultist when one) you don't do any behaviors normally associated with cults (like reading exclusively from a selection of the Great Leader's library, or frequenting forums filled with only other like-minded cultists, or believing you know the One True Way, or poisoning yourself, or...) and two) when you're right, so I'm bringing back some old contrarian counter-cultish-counter-cultishness with this term and this image:
Not that it all originates with EY, he just helpfully synthesized it for the rest of us. I'm sure there are genuine original gems in there too. If you agree with over 75% of this grand synthesis spread out over the Sequences, you just might be a rationeliezer too.

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What does it mean to prove something?

Update: Please read this post after... Or maybe before? People shy away from having an opinion about a proposition because "it isn't proven one way or another". They either haven't seen any proof/disproof or they have a disconnected view of what "proof" means. Sometimes they'll even say things like "You can't prove a negative."

What is proof, though, and what does it mean to prove something? The easiest way to demonstrate is with a syllogism that even an Ancient Greek could grasp let alone a modern toddler. We are going to prove that this object in my hand is green.

Premise: All books are green.
Observation or Given: This rectangular object I have in my hand is a book.
Logical step: modus ponens.
Conclusion: This object is green. (I don't have to look, I just proved it.)

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Religious Thinking: The Cults of Moral Grey and Moral Black and White

The cult of moral grey says: everything is uncertain to the same degree, therefore you can't prove I won't win the lottery or that there is no god or that hunting down and slaughtering a slave trying to escape is evil.

The cult of moral black and white says: silly grey people. Hunting and slaughtering a slave trying to escape is evil. We are absolutely certain of it because it's self-evidently true. Because some minority of religious people believe God is capable of violating logic, I can disprove all possible conceptions of God because it's self-evidently impossible to violate logic. If there is any privatization in the economy, the whole system is evil and must be scrapped. Or if there are any public government entities in the economy, they are wholesomely evil and must be eliminated.

The rest of us sane people say: silly grey people and black and white people, silly zero-bit and one-bit people. "Certain" and "uncertain" are subjective categorizations that create artificial boundaries on the math. One may be satisfied with the weatherman's prediction of 70% chance of rain tomorrow, and say "Rain is certain." Another might say "Rain is uncertain." A grey person will say "Rain is uncertain and it could just as well snow or be 100 degrees, because nothing is certain." A black and white person will say "Rain is certain because it's been raining all week." A sane person says "There is a 70% chance of rain. If the weatherman is accurate, I expect to go back in his history and find that for every 10 predictions he's made of 70% chance of rain, then there should have actually been rain 7 times." We say that hunting down and slaughtering a slave trying to escape is evil, we are certain in this judgement with a number that's very close to 100% but not quite, and we can imagine that there may be some convoluted context where the evil action actually isn't so evil but such a chance of that happening is minuscule and doesn't obliterate our confidence in the judgement of evil.

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