askthereception

The first question on the first problem sheet reads:

> Describe one aspect of memory that you are absolutely certain is true. Explain how you know– be as specific as possible.

Any thoughts?

For those who are getting confused about the S and K combinators, another definition is implied by the notion of a 'partial combinatory algebra' [1]. It is a set A together with a partial map A x A -> A, viewed as 'application'. You then require the S and K combinators to exist somewhere in A (they are non-unique) and you can prove things like the recursion theorem.

[1] https://ncatlab.org/nlab/show/partial+combinatory+algebra

It's more helpful to view category theory as a language.

Most undergraduates learn mathematics in the language of sets. If they're doing algebra, then the underlying structures of their groups, rings, etc. are always sets. Same for topology and logic (e.g. classical model theory). An extreme example of this set-theoretic thinking is defining the real numbers in terms of Dedekind cuts.

Category theory, very slowly, changes this perspective. If you study this for years, you will come to realise there is more to mathematics than sets. And your way of thinking will shift. You will learn to ask different questions. For example, instead of defining things in terms of their underlying set (often breaking symmetries), you will ask 'does it have a universal property?' and so on. Note, there are still tons of reasons to use sets / ZFC, even when working with categories mostly. But I do not want to get into that and it's irrelevant for the point I'm trying to make.

Final note: the 'language of sets', i.e. the language of undergraduate mathematics, is very different from set theory. 'Set theory' is like the language talking about itself. The same goes for pure category theory.

Perhaps have a look at the paper "Cubical Type Theory: A Constructive Interpretation of the Univalence Axiom" by Cohen et al. [1] which gives the typing rules in the early sections.

[1] http://drops.dagstuhl.de/opus/volltexte/2018/8475/

Your example using the verb "see" is not quite right, but a genuine ACI does exist in English: I want him to swim / I expect him to swim.

For another example, in Dutch it happens to work with "see" (zien): "ik zie hem zwemmen" (I see him [to] swim), it doesn't work with want, and with expect, "verwachten", you would have to add "to": "Ik verwacht hem te zwemmen" (I expect him to swim).

"Unlike the rest of the language, numerals are written left-to-right."

Everyone makes this mistake. It is rather the case that in English (and other languages) numerals are written right-to-left. You can tell since, when reading right-to-left, you will know exactly what each number signifies. If you start from the left, you will not know what the first number signifies until you have reached the end of the whole number.

Interesting to learn though that in Arabic it is still pronounced from left to right, up until the tens.

"There is no team of brilliant and vaguely sinister engineers, cooking up ways to get you binge reading."

There is, and it's called an editor. This is especially why a lot of bestselling non-fiction reads so smoothly. I always have a bunch of these lying around for when I want something easy to get into.

My source is any novel/non-fiction or newspaper article I would be reading when encountering the word. I usually copy the sentence, maybe trim it a bit, and cloze on the word. The hint I give depends on the word, sometimes an English translation, sometimes a definition in the language itself, or sometimes a cognate word in a different language I know.

An additional benefit is that I remember the content of books more easily, since I am passively reminded of passages through Anki. This means I can put aside a book for months and get back into it without problems.

A problem, though, is that because I only use active recall of the word, I sometimes can't remember the meaning of the word when I encounter it, especially when the context is different. This can be quite subtle. E.g. I might put in "aborder" (to approach) in the context of "how would you _approach_ this question", but then when I read somewhere "the man was approaching" I would recognize the word, but be unable to make sense of it.

I have been trying to remedy this by sometimes choosing a more typical example sentence (from a dictionary or something) rather than the encountered one, which could be too poetic. But as I remarked, with all these changes it is hard to measure the effect in the long term.

One issue I have with Anki is that for every new format of cards I try, it takes about a year to know whether it works better or not.

For instance, I have taken a different approach to vocabulary since I found that single words (e.g. in French) were sometimes hard to recall after a very long time. I now almost always use a cloze sentence, and ideally the sentence I encountered the word in, so that I combine active recall with remembering the context, which usually settles the issue of multiple possibilities. However there is no way of knowing how this will work out in the long run. Does anyone have telltale signs that indicate if a card, although you may do well for months, will not do well past the, say, 1yr threshold?

So this is the kind of news that one ought to be careful with now that everyone has had a chance to read the Black Swan.

It has probably more to do with genetic drift. You cannot stumble upon a tribe, take some random property they all share, and then make causal inferences from all the other properties they all share. This holds especially when this property correlates with survival of the tribe; it is actually more informative to investigate a group of people with properties that reduce survival, e.g. bad heart conditions.

What is it with this tendency to speak of a 'Nobel prize' when it concerns a different, lesser known prestigious prize in a field for which there happens to be no Nobel prize (Abel prize, Turing award)? It's a lazy way to try to draw attention to it, and pernicious even because it makes the whole purpose of these named awards questionable.