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.

See Full Post and Comments

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?

See Full Post and Comments

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.

See Full Post and Comments

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.)

See Full Post and Comments

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.

See Full Post and Comments

We should probably be burning the Qur'an

By "we" I mean the US government, officially. We should also spam this image around; print out millions of copies and attach one to each of the US-funded air-dropped care packages to Muslim groups.

What's the goal? The goal is either how can we get more Muslims to be atheists, or how can we get the proportion of the minority of violent Muslims to regular Muslims to be about the same as the minority of violent Christians to regular Christians. The intent is to piss people off.

Will this anger people? Yup! I don't think it will actually cause violence, though. My reasoning is that for a person so far gone that they're willing to commit violent acts like suicide bombing, burning or not burning a book isn't going to change that. But if those extremists want to infantize their movement and make it about something as silly as burning a book, let them be silly, it will hurt their movement as saner Muslims realize it's just a book and there are millions more as well as infinite digital copies.

See Full Post and Comments

Intellectual Gratification

Where do you get your intellectual gratification from? Do you read science books? (Not pop-sci, but real science books.) Do you read math books? Do you read philosophy? Do you study history? Do you build things? Do you have a smart friend you like to chat with for hours at a time? Or maybe you graduated school and don't think you have any need to gratify your intellect, you have a job to do and a family to feed, oh where oh where will you find the time?

Does the majority of your intellectual gratification come from a school environment? Or if you finished, was that the primary source?

For the purposes of this post, there are generally four types of students. There's the average student who goes through the system and emerges with a Bachelor's Degree (it doesn't matter what in) and goes on to work for 40 years, then retires. These are the most common but are losing ground to the second group. The second group is made of students with little ability. They don't understand the meaning of intellectual gratification, anything intellectual seems pointless or a chore and they would rather cycle through their short list of websites/games/t.v. shows all day. Thanks to modern mediocrity and races to the bottom, every education system graduates more of these people every year because hey, they have to live to support their mindless consumerism and too many jobs above minimum wage require a degree. The third group is the opposite of the second group, it is made of people with very high ability. They get high grades, they major in the harder Sciences, they get their work done. They have some ratio between consuming for intellectual pleasure and for other pleasure, as well as a ratio between consuming in general and producing. The fourth group is an almost bipolar mix of the second and third groups. They generally have the ability, and they'll have their successes, but they also have their spectacular failures too.

See Full Post and Comments

Older Posts Newer Posts