It seems like they've been assuming Twitter is the way it is because it was staffed by technically incompetent leftists, and if only they could apply their own get-things-done attitude and "neutral" politics, then the problem would be trivially fixable.
Where does this fallacy come from? Is it because of the illusory simplicity of the tweet format? Something like: "We just need to come up with the right algorithm and do an embarrassingly parallel run over these tiny 280-character chunks of text. How hard can that be. In my own Very Serious Day Job, I deal with oompabytes of very complex data. This tweet processing stuff should be child's play in comparison."
I've seen enough engineers presume they can easily become experts in law; I haven't seen many lawyers presume they can easily become experts in engineering.
Why?
But it definitely does seem to be especially pronounced with engineers.
(NB. I am a software engineer, and not a sociologist, so, argh, this is potentially getting a bit meta.)
Dunning-Kruger is, approximately "I'm good at the thing I do" (by someone who is actually incompetent).
What I'm talking about is "That thing that other people are doing is really easy; I'd be good at it" (the thing is not easy, and they would not be good at it).
If the person in the latter case actually ends up doing the allegedly easy thing, they may realise that actually they are not good at it, in which case it's not Dunning-Kruger. This is pretty common, I think; person barges in, saying "this will be easy, because I've decided the thing I'm good at is more difficult than it", admits it's not easy, and either leaves or learns. Alternatively of course they may retreat into full Dunning-Kruger; see the Musk Twitter debacle, which is _both_, say.
Nope, but I can overlook because DK is misunderstood this way by almost everyone, and the authors have caused & encouraged the misunderstanding.
Dunning and Kruger didn’t test anyone who’s actually incompetent at all! The use of that word in the paper is so hyperbolic and misleading it should have been rejected on those grounds alone. They tested only Cornell undergrads. They didn’t check whether people were good at what they do, they only checked how well people could estimate the skill of others around them. The participants had to rank themselves, and the whole mysterious question in the paper is why the ranking wasn’t perfect. (And is that a mystery, really?) It is hypothesized that DK measured nothing more than a statistical case of regression to the mean, which is well explained by having to guess how good others are: https://www.talyarkoni.org/blog/2010/07/07/what-the-dunning-...
Contrary to popular belief, DK did not demonstrate that people wildly overestimate their abilities. The primary data in the paper shows a positive correllation between self-rank and skill. There’s no reversal like most people seem to think. Furthermore, they only tested very simple skills at and least one of them was completely subjective (ability to get a joke.) Other papers have shown that no such effect occurs when it comes to complex subjects like engineering and law; people are generally quite good at knowing they didn’t major in a subject.
Very complicated algorithms and mathematical proofs can still be understood by a single person, and be explored by a small number of people who all know each other. Brain surgery is done by a small team of people. These are typical "smart people" occupations.
Something as simple as Twitter still needs machinery that spans across technical skills, needs 24 hour monitoring, and needs lawyer and accountant support, so nobody can actually to it.
People think they can do it, because it's easy to spin up a demo that sends messages to a few thousand people and then shut it down again. They don't think about how to scan for CSAM, or how to respond to foreign government censorship requests.
WhatsApp was 55 people big when they got acquired, and to me that sounds about right.
Twitter employed 7,500 people. 7,500!!!! So please tell me where the complexity lies? Surely not in the front-end code I can tell you that.
Let's compare it to something WAY-WAY-WAY more complex, like a game with multiplayer, awesome mod tools, etc.: ROBLOX: 2,200 employees. Do I need to mention they wrote their own physics simulation engine and keeping realtime multiplayer going?
So please, explain this to me: how is Twitter more than 3 times more complex than Roblox???
Maybe I'm wrong, that's very possible, I've been wrong in the past. But just explain this 1 thing then: Twitter needs more than 3 times the manpower than Roblox?
Then nothing happened. At least, nothing that I personally observed as a casual Twitter reader. The goalposts were moved to "it will go down with the New Year's Eve spike", and once again nothing happened. Then the narrative became "the cracks will only be noticeable in a few months", and here we are and yet again, nothing.
So Musk and Geohot came out as the saner voices of that whole debacle. Of course Geohot said exaggerated things like "you only need 40 engineers to run Twitter", but if it turns out it takes 300 engineers, then I would consider this as Geohot being proven mostly right.
I don’t think that qualifies as “nothing happened” when features used in high-profile events fail, with the CEO and a potential future president left on the line. Any other platform wouldn’t have struggled with a stream of this size.
I guess you might say that’s just one thing, and other than the CEO’s live streams not working, everything is fine. But there are numerous other examples of accumulating paper cuts and failures at Twitter. I think this is close to what most of those doomsayers expected would happen.
https://mashable.com/article/google-ai-maps-search-event-bin...
> the AI falsely said the James Webb Space Telescope took the first ever picture of an exoplanet
> During the announcement about a new Lens feature, the demo phone was misplaced and the presenter wasn't able to show the demo
> Google seemed to say, "let's pretend this never happened," and immediately made the livestream recording private after the event
Are you sure ? Others say 6.5 M listened to the livestream that was delayed 20 mins
But yeah, it could have gone better for various reasons.
There was a lot of "ooh, it will catastrophically fail within weeks", which was fundamentally an assumption that the previous team was entirely incompetent. (Any halfway decent team tries their hardest to build resilient systems, not things that need hand-holding all the time.)
The current trajectory is exactly on the expected failure path predicted by anybody who does actually work on large systems - a steady increase of smaller failures, punctuated by the occasional large failure. (Cf. DeSantis announcement)
In essence, a reduction in staff will result in worse SLO results. It will result in less coverage of edge cases (technical and UX). Smaller teams are more constrained to travel on "the happy path". And the fact that marginal utility of additional engineers decreases means you can usually reduce teams a lot before impacting that path.
In complex systems, reductions also mean you're more vulnerable to a black swan event being irrecoverable, but that still requires a black swan first.
I don't think anyone argued Twitter was run by technically incompetent people. Where was this, if so? By leftists, yes, and by far too many people, yes. Both were argued repeatedly. But those things are now proven objectively true. The Twitter files showed just how systematic their enforcement of left wing orthodoxy was, and Musk fired most of the staff yet the site kept trucking and even launching new changes which is more or less the definition of having been over-staffed.
That's definitely more outrageous than saying that frontend is trivial. Whatever, I never took him seriously anyway.
https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Gra...
Maybe something that pretends to be the real numbers, like a matrioshka doll of infinite containers inside containers.
I think we could only do this with an even more absurd scenario like if each room was filled with pregnant women who are giving birth, and the children rapidly age, and also give birth at an infinite rate? That would create an infinite nesting doll like situation for each guest
Related: the Schröder–Bernstein theorem [4], "if there exist injective functions f : A → B and g : B → A between the sets A and B, then there exists a bijective function h : A → B.".
Not related, but great: Max Cooper (sound) and Martin Krzywinski (visuals) did a splendid job visualising "ℵ_2" [5].
[1] https://en.wikipedia.org/wiki/Cardinality_of_the_continuum
[2] https://en.wiktionary.org/wiki/%E2%84%B6
[3] "Cardinalities and Bijections - Showing the Natural Numbers and the Integers are the same size", https://www.youtube.com/watch?v=kuJwmvW96Zs
[4] https://en.wikipedia.org/wiki/Schr%C3%B6der%E2%80%93Bernstei...
[5] "Max Cooper - Aleph 2 (Official Video by Martin Krzywinski)", https://www.youtube.com/watch?v=tNYfqklRehM
As for the set of real numbers, we have the subset of irrational numbers which are uncountably infinite (see cantors diagonalization argument) thus making the whole set of real numbers, a set whose cardinality is ℵ_1.
The annotated turing book goes into this pretty well in the first couple pages.
It turns out the 'continuum hypothesis' can be true or it can be false. Neither contradicts standard ZFC set theory: the hypothesis is 'independent'.
[1] Using the concept of polycomputing from There’s Plenty of Room Right Here: Biological Systems as Evolved, Overloaded, Multi-Scale Machines: "Form and function are tightly entwined in nature, and in some cases, in robotics as well. Thus, efforts to re-shape living systems for biomedical or bioengineering purposes require prediction and control of their function at multiple scales. This is challenging for many reasons, one of which is that living systems perform multiple functions in the same place at the same time. We refer to this as 'polycomputing'—the ability of the same substrate to simultaneously compute different things, and make those computational results available to different observers.", https://www.mdpi.com/2313-7673/8/1/110
On the relative fringes, there are serious studies on alternative interpretations. See for example
https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_...
(You can skip to the part that discusses Cantor's arguments, but I suspect that if you haven't heard about related concepts you probably want to understand what it is first.)
The "cardinality" section of that Wikipedia page describes my objection well. I don't doubt the real numbers are not recursively enumerable, but that doesn't mean they have a larger cardinality than the integers.
If you're trolling to troll, then expect the hate because you're being annoying.
If you think you're right and all the mathematicians are wrong, pony up. Hell, you'll have a lot more lulz when you win a fields metal.
If you don't pony up I don't know why you would be surprised people assume you're arrogant. You can doubt the status quo without being arrogant. We both know that you're not going to take someone's word just because they said so, so why expect others?
Math is all about definitions and what follows from these definitions. So, you can define "integer", "real number", "cardinality", "equals" and so on however you like, and make all sorts of correct statements — as everyone will see by following your arguments all way from the definition/axiom and until the very end of your proof. But if you don't provide any definitions of your own, then you rely on some other definitions, and everyone has no other choice than assume that these are the very much "mainstream" ones, as you are referring to them as if they are well-known.
Now, it is unquestionably true (and easily provable) that the set of all computable numbers is countable, and anyone who says otherwise is wrong. But unless you specifically define real numbers as a subset of computable numbers, as constructivists are inclined to do, your listeners won't assume that, since this is not how real numbers are generally defined, and by virtue of not providing your own definition you are implicitly referring to a "general definition". (And, honestly, you shouldn't even call any subset of computable numbers "a set of Real numbers": this name is already taken.)
These general definitions and assumptions lead to all sorts of complications, and I personally have my doubts that real numbers exist in any meaningful sense (although I'm not committed to that statement, since there are several mathematical constructs that I would like to dismiss as "clearly nonsense", except they allow us to prove some very "no-nonsense" stuff — I don't know how to deal with that, and I never heard that anybody does). But I definitely cannot say that cardinality of integers is the same as the cardinality of reals, because this is simply not true under the common definitions (which is easily provable). (And less importantly, but worth saying that the contrary is not proven by constructivist methods — as half of the actually useful math in general ends up being, unfortunately).
So, as a somebody, who doesn't quite believe in non-computable numbers, I am very sympathetic to anybody who says that Real numbers do not exist. I don't understand how could they, what does it mean for an object that we cannot define to exist. Yet, I can accept (as a game) some well-known theory which talks about these non-quite-existant "Real numbers", and prove some statements about them, and one of these easily provable statements is that cardinality of continuum does not equal the cardinality of Natural numbers.
I think we're in agreement here in principle. (Since we're on the topic, I'd like to add that naming this suspicious set "real" numbers is a tad bit ironic)
That said, I don't like the idea of having a group of people "owning" words as if they had a monopoly over them. The statement "the cardinality of integers is the same as real numbers" can be understood to mean "real numbers should actually be computable numbers".
I didn't bother to look up what Hotz wrote on twitter that triggered this discussion, I was just providing context that the issue of cardinality isn't as settled as some might think. It's probably not fruitful to argue whether a statement from hearsay uses words accurately or not though.
That's not a sum in the traditional sense so don't think about it this way.
Infinities are used quite often in mathematics for rather mundane things. Calculus doesn't work without it. It is also quite important to the foundation of many other areas but this is often hidden unless you get into advanced works (in this sentence we're not considering a typical undergraduate Multivariate Calculus, PDEs, or Linear Algebra as "advanced")
If I had a dollar for every job that I didnt get where I estimated the correct degree of difficulty, and they laughed, went with the person who said it would be easy and they could bang it out in a day of sleeping - I would be rich.
The loud optimist wins the 5.1 mil every time.
As soon as there is a dead serious one, I've noticed everyone get serious and starts ignoring the rainbows and unicorns people. If it's a slap on the write the rainbows still win.
It's likely there was some humor and bravado, as is the culture of his east coast origins.
The truth of his engagement with Twitter was, Just based on my watching him and his live streams during that time, that he was looking for a thing to do while he ceded control over comma AI, to a new executive leadership group.
Of course, he should know better than to throw claims like that.