On this page you can find various tweet-size (or so) pieces of thought that I felt worth sharing. Since I don’t have a Twitter account (and I don’t intend to have a Twitter account any time soon either), I figured it must be a good enough place to post them.

**(24)**Can we make a point of teaching the technique of symmetric extensions as part of the basic forcing course,

*always*? I’m sick of writing exposition to symmetric extensions in every single paper just so people will feel it’s self-contained enough to read. Now I know how the authors of the first papers about forcing must have felt. (Link here)

**(23)**Random logician thought of the day: how do constructivists feel about the phrase “

*not unlike*“? I know I dislike it (I mean, is it so hard to eliminate the double negation?). (Link here)

**(22)**Scientific research (mathematical or otherwise) is very much atomic, and the researcher is very much “electronic”. You start at a ground state, and the more effort you put into it, the more excited you become and the further you get from the nucleus of previous knowledge. And of course, there is a huge vacuum of which we know very little in between. (Link here)

**(21)**Taking a symmetric extension is like having buyer’s remorse with respect to your generic filter (in most cases, anyway). You buy a generic filter, and you think it’s nice. You add it to your model, you use it for a little bit, then you immediate regret it and return it to the store. And you generally argue that you may have wanted a similar but slightly different generic filter instead. So you try a similar-but-slightly-different filter, but you decide it’s not a good fit either. You end up using a bunch of these filters and then you give up and don’t add a generic filter at all to your model… But you still have all those new sets that were left from using all those filters. And that ends up being a model of ZF. Okay, I went too far with this analogy. (Link here)

**(20)**Philosophical quadruple whammy: We are brains in a vat, and the entire reality fed to us is being manipulated by Descartes’ demon, and that demon and the whole reality in which he exists (with our brains and the vats) is a computer simulation ran by Laplace’s demon in another reality, which in itself is a thought experiment in my own personal brain. (Link here)

**(19)**Greenspun’s Tenth Rule of programming states that

*“Any sufficiently complicated C or Fortran program contains an ad-hoc, informally-specified bug-ridden slow implementation of half of Common Lisp.”*This extends to mathematics. Every elementary proof that avoids some abstract technical construction will contain an ad-hoc, informally-specified and slow implementation of half the technical concept it tried to avoid. For specifics see any proof about cardinal arithmetic that avoids ordinals in favor of Zorn’s lemma. (Link here)

**(18)**New Year’s resolution for 2016: To fulfill exactly those resolutions which I end up not fulfilling. Hey, wait a minute… (Link here)

**(17)**My phone is non-constructive. Whenever I plug it to the wall it tells me “Charging (AC)”. Apparently the axiom of choice

*does*have physical applications! (Link here)

**(16)**Irony is when someone who essentially tries to disprove the existence of infinite sets says that the way his ideas are being rejected is similar to how Cantor’s ideas were rejected back at the day. (Link here)

**(15)**When your proof or theorem go down in flames, do not despair. From their ashes, like a phoenix, are born new theorems, new proofs and new methods. You only need the will and tenacity to dig through the cinders and find the unhatched eggs. (Link here)

**(14)**The motto for choiceless mathematics

*“If you can’t decide which finger to choose, take the entire hand.”*By this I mean, of course, if you can’t choose one – take everything! (Link here)

**(13)**Good indexing the the key for any sequential construction, and the bad indexing is the bane of every sequential construction. Did I mention how much I despite the process through which you get to the right indexing sometimes? I don’t think I’ve complained about that enough by now. Indexing sucks. (Link here)

**(12)**

*Corollary from a conversation with Yair Hayut:*Every theorem you prove is actually a theorem of Tarski, since it is equivalent to a theorem of Tarski. If you prove that something is in fact independent then it is not a theorem of Tarski, but the proof of its independence is in fact a theorem of Tarski… (Link here)

**(11)**I love “No Country For Old Men” by the Coen Brothers. It’s a lovely movie, full of rich and wonderful characters. But as much as I admire the unstoppable angel of death which is Anton Chigurh, or the wonderful sheriff Ed Tom Bell, the best character in that movie is Ellis, without a doubt. And I dare anyone to dispute that without being wrong. (Link here)

**(10)**Being a mathematician means being wrong 99% of the time, and hopefully being only remembered for that other 1%. (Link here)

**(9)**The axioms of set theory only tells us what sort of basic properties sets should have. Much like some basic rules about what counts as a place fit for human living should be (running water, bed, kitchen, etc.). But then you can look at different structures and see different things. Some of them will look completely different than others; and some despite looking almost the same will be different from one another when you look at their content. Similarly models of set theory can be very similar, but still different, or entirely different in more way than one. (Link here)

**(8)**They tell me that every hydrogen atom in the universe is the same. Wouldn’t it be great if we eventually learn to read the quantum field in which electrons live, and start to discern between different atoms of hydrogen? Wouldn’t it be magnificent if each atom is unique, and everything has a unique footprint in the physical cosmos? I think it would be spectacular. But I don’t know if any of us will live to see such wonder. (Link here)

**(7)**In a totally disconnected space no one can hear you scream. (Link here)

**(6)**I have grown to appreciate Ben Affleck, both as an actor and a director. But am I the only one afraid that Zack Snyder’s direction of Batman in the upcoming “B versus S: DotJL” movie is going to be a blend of Rorschach, The Comedian, and Leonidas “The Scot”? I sure hope that I’m wrong, and there’s nothing more that I’d love than that. Well, except maybe a lot of other things. In any case, I’m confident that Affleck will pull off his own Batman movie. And there’s nothing more that I’d hate than to eat that last sentence (except maybe a lot of other other things). (Link here)

**(5)**Someone needs to convince Calvin Klein to name their next perfume “omega one”, then the media will be full of $\omega_1^{CK}$ ads and banners. Wouldn’t that be great? (Link here)

**(4)**Clarke’s third law of set theory: Any sufficiently advanced argument with forcing, large cardinals and combinatorics is indistinguishable from black magic. (Link here)

**(3)**I never understood why people have such a hard time conceiving that real numbers and other mathematical objects can be represented as sets. Do they know that a computer converts their pdf files, the code of the reader used to open them, and the compiler used to write that reader into electric signals? Do they not have a problem with that? (Link here)

**(2)**People who say that “you don’t really understand something until you can explain it your grandmother” have at least one living grandmother, or they didn’t understand the proverb. (Link here)

**(1)**Sets are more fundamental than integers. We like to think that mathematics evolved from arithmetics and the need to count how many animals are in a group, or something. But first you need to identify a collection, and know that you want

*that*specific collection to be counted. If anything, numbers evolved from the need to assign cardinality to sets. (Link here)