expressivity

hmm... proof theory... (imagine a lip-licking emoticon, or a Homer Simpson voice)

from Around Gödel's Theorem - Ch 6.4: On the size of proofs

...
Theorem on the Size of Proofs.If T is a fundamental formal theory, and a closed formula H is not provable in T, then for each computable function f(x), which grows to infinity, there is a theorem K of T such that

|K|_T+H < f(|K|_T). [ |K|_T+H means "the size of the proof of K in theory T+H" ]

For example, let use take f(x) = x/100. There is a theorem K1 of the theory T such that its proof in the extended theory T+H is at least 100 times shorter than its shortest proof in T. You can take also f(x) = x/1000, or sqrt(x), or log10(x) etc.
...

I wonder if this is relevant to the broader concept of expressibility.

Obviously there can't be a (shortest proof <~> shortest program)-analogous result: since all good languages are Turing-equivalent, then for all problems, its Kolmogorov Complexities are bounded by a constant of each other (the size of the interpreter for the language into a standard computing machine).

When thinking of Logic and Computation side by side, I always think of this difference: logics have limited expressivity, whereas computational systems always have maximum expressivity.

So when we talk about "expressivity" in the context of programming languages, we mean something else entirely: how easy and natural is it to express what we want? Maybe we should use a new word, like "expressibility".

The literature on this subject seems to be very poor: Felleisen being the only reference I could find, besides fare of course. I think this warrants a philosophical essay at the very least, in order to properly define "expressivity/expressibility" and discuss possible measures.

can liberating medicine increase the price? Claritin.

This reminds me of the "identify the fallacies" part of the GRE Writing section

from here

When Claritin recently became available without a prescription, the health insurance industry and the companies they cover were licking their chops over the nearly $1 billion in prescription cost savings they'll enjoy each year. As for allergy sufferers, instead of a $15 to $20 co-payment to be diagnosed and prescribed the medication, they now have to pay around $1 per pill for over-the-counter Claritin, which adds up to hundreds of dollars per allergy season. While this plan is one heck of a deal for the HMOs, it perhaps can best be described as a whopping tax increase on average Americans with allergies.

The question, of course, is why over-the-counter Claritin would be more expensive. Perhaps this is a good case for archeological economists.

For one thing, they sell more, so they become cheaper to mass-produce... OTOH, being the only over-the-counter drug of its kind, it enjoys a sort of monopoly.

How well can you read emotions by the eyes?

Reading the mind from the eyes">How well can you read emotions by the eyes? via cbird

My score: 23 / 35

I thought quite hard about them... I'm not very surprised with my score.

Spoiler: don't read before you've taken the test yourself
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