gusl: (Default)
* Bayes Rule: "P(A,B) = P(A|B) P(B)" means "forall a,b . P(A=a, B=b) = P(A=a|B=b) P(B=b)". This is very standard.

* "variance of the estimator" means "variance of the sampling distribution of the estimator". AFAICT, this is unambiguous, and the only reasonable interpretation is for "estimator" to mean the random variable. To make this even more explicit: the estimator(RV) is the result of applying the estimator(function) to the random data.

* "estimate the parameters" means "estimate the values of the parameters"; more confusingly, "choose the parameters" can mean "choose the values of the parameters". This may just be the econometricians I've been reading.

* "distribution" to mean "family of distributions". Very standard. No one blinks an eye at "the Gaussian distribution". I think "family" is typically only used to describe families for which mean and variance are not sufficient statistics.

* "sample" to mean "data point". One should be careful here: in standard usage, a "sample" is a collection of data points. Sometimes, though, one samples just one point, and metonymically calls it "the sample".

* using "correlated" to mean "dependent". This is incorrect, except in special circumstances, such as multivariate Gaussian models.

* using "sufficient statistics" to mean "summary statistics" (e.g. in the context of mean-field approximations). This is incorrect.

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UPDATE: I should write a SigBovik paper titled "Introduction to Statistical Pedantics".
gusl: (Default)
I wonder... if we taught lambda calculus to high schoolers / college freshmen, wouldn't that be an excellent way to give them (1) skills to express themselves precisely, and (2) familiarity with abstract concepts?

As an added benefit, when they become instructors someday, they'll be able to write their textbooks and homeworks in a way that is unambiguous (all mathematical questions can be translated into questions about the output of a single computer program).

I think that most of the confusions experienced by people studying math (regardless of level) are about variable binding, quantifier scope, etc. I have a BS degree in math (and a Master's in logic), and most of my confusions are of this type also, when I'm learning unfamiliar math.

Isn't the meaning of the word "abstraction" fully captured by lambda abstraction?

The idea of first-class functions is all about turning verbs into nouns... Function calls are usually understood as applying a verb to a list of nouns. Dealing with first-class functions involves changing (extending) metaphors: now, functions can be objects too, i.e. verbs can be nouns too. This may be related to the fact that computer scientists like making nouns out of verbs, verbs out of adjectives, etc.

The extended metaphor may be that functions are "machines": they do something but they can also be fed into other machines.

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Tangentially, Kiczales's class has interesting reading: Lucy Suchman - Human Machine Reconfigurations
gusl: (Default)
My compiled rants against physicists. In response to like-minded [livejournal.com profile] quale, I wrote the following:


[livejournal.com profile] quale wrote: I dropped out of being a physics major because everyone was just dogmatically accepting the notion of entropy as the "log of the number of states" and didn't want to question what the hell that really meant.

Me too! Not just they way they gloss over entropy, but also where the Schroedinger equation comes from, etc., and the way they avoid thinking about paradoxes (e.g. Maxwell's demon: is entropy subjective?, this one about classical mechanics). And the fact that nobody bothers to fix the very bad notation traditionally used in some physics is a pretty bad sign too (nobody except for my hero Sussman).

In college physics, I was just told to plug-and-play, which made me very unhappy. I was interested in finding logical relationships between sets physical axioms (e.g. how to prove that energy is proportional to amplitude squared using only the additiveness of amplitude and energy conservation).

Since I like my knowledge network to be dense / tight (i.e. certain), ignoring foundational questions and paradoxes is totally against my cognitive style, but I wonder if being less conservative might sometimes be a good idea, if the goal is to make the science progress: it might sometimes be a good idea to ignore foundational questions.
gusl: (Default)
Tomorrow, after my last session with my math tutee, I will teach him to play around with Lisp. Hopefully, it will replace his calculator.

download (Can anyone suggest a better Lisp environment for Windows?)

Lisp, because of its prefix notation, makes it possible to express empty additions and multiplications. This makes it easier to see why the value of an empty addition is 0, while the value of an empty multiplication is 1.

Other advantages:
* using formal languages prevents notational confusion
* with a formal language, the communication between teacher and student can be completely precise, at least AFA procedures are concerned. For expressing arguments or proofs, something like Coq would be needed. For communicating about intuitions, I have no idea.

Here's some code I'm hoping to go over with him: Read more... )
gusl: (Default)
am I the only person in the world who can't stand math classes because they're not formal enough?

Today I went to a lecture on surreal numbers, saw people struggling with bad notation, and with bringing variables out of quantifiers and then back in (this pisses me off because it's best done by an algorithm, and can be quite taxing for humans)... Some people would argue that if you're searching for a syntactic way of proving something (i.e. without *seeing* the underlying facts), then you're not being a "noble mathematician". I have no such prejudices.
gusl: (Default)
Esperanto may be the most useful language to learn if you want to learn other languages.

http://en.wikipedia.org/wiki/Propedeutic_value_of_Esperanto


I wonder if, analogously, there exists an "easy math". After being comfortable with EasyMath, most kids would have a much easier time learning other math.
Is "logic" an EasyMath? are some video games?

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