Recently there was a brouhaha on the Twitters about 2+2=5 that went viral and, unfortunately, political. The argument is that post-modernists are trying to tear down mathematics as a "white supremacist social construct" and trying to say that "2+2=5" is as valid an answer as "2+2=4". Which sounds pretty bad, so I looked into it.
The original Tweet thread was a math nerd who jokingly, and not incorrectly, illustrated how it was mathematically possible for 2+2 to sometimes be 5. The argument may have been weak, and some people may not have found it convincing, but it was a mathematical argument, meant as a joke for a small Twitter audience.
Through the Twitter telephone, many retweets and steps later, the original argument - considered, funny, valid, perhaps weak - somehow transformed into "2+2=4 is a mere social construct, and 5 is a valid answer" - which, yes, would be a disturbing trend if that were actually the argument. Thus the unduly passionate took up "2+2 is 4 not 5" as a political rallying cry. People I otherwise respect as rational began tweeting this.
It became complicated because there are always people who believe dumb things, like "mathematics is merely a white supremacist social construct", and as always with the unduly passionate, extreme opinions are held up as examples of dangerously typical. The author of the original thread was bullied by a mob.
It's complicated even further by the existence of an actual replication crisis in academe, in part driven by post-modern ideological pressures; there is actual loss of academic freedom even for the tenured.
But the lesson at the end of the day, to my mind, is that articles about whatever goes on over at Twitter, such as this one, such as this my post here, are always going to involve mobs of people being shitty, because the nature of the medium. Maybe they are as inevitable as "mobs of people are gambling in Las Vegas"
It amplifies meaningless shit into the stratosphere with its trending algorithms, aided by the fact that the largest userbase on twitter seems to be political extremists of both left & right. It's created an environment where making a comment like "mathematics is merely a white supremacist social construct" is now somehow acceptable to the left.
The platform literally exists to make things look like they're a bigger deal worldwide than they really are. It's dangerous.
I quit twitter a while back - when I was on the platform, all my news consumption revolved around it. I was deeply concerned about the state of the UK and the US because of the constant stream of political propaganda from both sides.
Since I quit my brain feels like it's been completely freed of political dogma and I'm in a significantly better mood generally. I've not missed the trending page, that's for certain.
The biggest issue is the loss of academic freedom you alluded too, mainly & ironically being pushed heavily by the 'Twitter Left'. Twitter is like a heavily left leaning version of /pol/ these days.
I'd like to be clear that I would consider myself on 'the left', to be a progressive person & I am absolutely aware that the extremist cesspit that is twitter does not represent the genuine left, much as it doesn't represent genuine moderates or genuine conservatives.
It's the most extreme weaponized propaganda & rent-a-mob tool thats ever existed in human history.
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It amplifies meaningless shit into the stratosphere with its trending algorithms, aided by the fact that the largest userbase on twitter seems to be political extremists of both left & right. It's created an environment where making a comment like "mathematics is merely a white supremacist social construct" is now somehow acceptable to the left.
It is like unleashing a neural net that amplifies whatever it sees in a image but fed with white noise IMO. And then it just keeps on spiraling in on itself.
It scares me how much people on twitter believe that what they see trending on there from the news and other sources is being seen and blown up worldwide when it's not. It's being blown up worldwide ON TWITTER.
The vast majority of the world never sees or hears any of it.
It causes delusions of grandeur across the userbase.
> It scares me how much people on twitter believe that what they see trending on there from the news and other sources is being seen and blown up worldwide when it's not. It's being blown up worldwide ON TWITTER.
Unfortunately, "Twitter users react to..." is an entire genre of news article these days, even on otherwise-reasonable sources like the BBC.
I've seen commenters here claim that the majority of all human communication and interaction takes place on and is controlled by a few social media silos.
The fact twitter has so much political sway in the real world is appalling considering how small the user-bases are relative to populations.
We find ourselves in a position where the media can use twitter to amplify opinion and provide a false sense of majority to implement political pressure.(See cancel culture)
Along with that, the beltway bubble, where "reporters" mostly follow each other leads to, quite frankly, bizarre stories along with a unhealthy dose of outright wrong reporting.
>[Twitter] amplifies meaningless shit into the stratosphere with its trending algorithms
Doubtful, given how popular it is among people and ogranisations that carefully measure the RoI of their marketing & outreach operations, and constantly adjust balance of their efforts among 2, 3, 4 different communication channels (YT, Insta, mail, in-person events, topical forums, old style media, etc.).
A more fitting hypothesis would be, "Twitter opened up a couple new paradigms of influencing people". The paradigms are complex, opaque, and subtly inter-related; quite hard to grasp for people that aren't fully "in the loop". That's why there appearance of chaos and, at the same time, we see highly organized action emerges from this chaos.
> >[Twitter] amplifies meaningless shit into the stratosphere with its trending algorithms
> Doubtful, given how popular it is among people and ogranisations that carefully measure the RoI of their marketing & outreach operations, and constantly adjust balance of their efforts among 2, 3, 4 different communication channels (YT, Insta, mail, in-person events, topical forums, old style media, etc.).
I'm not sure why you think that the two are incompatible, or opposed.
I don't mean to suggest that marketing is entirely meaningless, but surely the ROI of any particular marketing effort is largely independent of its meaningfulness?
That's fair - I wasn't trying to make the point that it can't be weaponized. In fact it's quite the opposite.
I guess my main point with that quote is that it amplifies things (sometimes organically viral, sometimes engineered) and then places them all on the same level. So the userbase starts to believe that something that trended on twitter is just as globally important/well known as the genuine world news story that trended beside it, because it's all in one pot.
There's a bit more to it than that - once reactionaries started saying that 2 + 2 could only be 4, anyone who was woke and knew a bit of maths started brainposting about how actually 2 + 2 could be defined to mean 5 in various ways, and that was perfectly valid mathematics, and the reactionaries were showing their mathematical ignorance - all as a dunk on the reactionaries, not a defence or explanation of the original joke.
I'm not sure how widespread this was. I may be friends with an abnormally high number of radical leftists who like abstract algebra.
This was all mildly irritating, but the worst thing was when some of them said 2 + 2 could be 5 in modular arithmetic.
The whole thing was pointless and stupid. It was perfect Twitter.
So, 2+2=5 is true in the ring Z/Z (arithmetic modulo 1) which is just the trivial ring consisting of a single element. It's not true in any of the other modular arithmetic rings. So, it's not particularly interesting.
If you move away from modular arithmetic and the numbers 2 and 5 being in any way related to their standard meanings, you can of course redefine them to mean whatever you want (e.g. rotations of a cube or whatever) and then you can make 2+2=5 work. But I suspect no sane mathematician would do that, it would just be totally confusing.
It's possible there is some deeper structure out there in which you can reinterpret something like 2+2=5 to be actually useful, though But I doubt it.
So in a sense, it's true: You can construe a mathematical world where 2+2=5, but doing so reduces either the whole affair to a triviality (everything is equal to itself), or is just deliberately using confusing notation.
I think there's probably an interesting argument in here about how on the one hand languages and structures are man-made and arbitrary (nobody decreed that 2 should be the symbol denoting the concept of two-ness), and yet on the other hand, how once you fix meanings and rules, the mathematics is fixed and not up for debate, and also how just changing standard meanings without good reason would annoy even mathematicians.
IIRC the moral of the original 2+2=5 guy's comment was "if someone reaches a different conclusion than you, ask them under which axioms they reached that conclusion." I think that's valuable advice. Note that he didn't say you have to accept their axioms. Clearly working in arithmetic modulo 1 is meaningless in most circumstances, and you can criticize that. But if you're not reasoning under the same axioms, you cannot have a productive discussion.
If so, then the argument he makes is totally braindead. He doesn't even consider special algebraic structures or anything. He's just coming up with the most obvious observation ever: if your mathematical model doesn't match the reality or asks the wrong questions, then the results are worthless.
This is probably obvious to any high school student but that's certainly no reason to run around and say that 2+2=5. In any case, there is zero mathematical insight there, he doesn't even make a mathematical argument for it, and the "I am a former mathematician" part only serves to distract from that fact.
I could go onto an entire different rant about his infinity argument and how mathematics seemingly haven't figured out how to work with infinity "naturally" (I don't know what he means by naturally, but they certainly have figured out how to work with it precisely), but let's leave it at that.
Sure, this is true. But it's also true that some people just like shifting the goal posts or redefining terms whenever it suits them (not in mathematics, outside of it, that is).
So in terms of a productive discussion, saying 2+2=5 without context and then backtracking and saying "well but I'm talking about Z/Z (or R/Z, see uncle comment)" would be kind of annoying and it's not generally what mathematicians do.
I think this is one of the fascinating and difficult aspects of maths:
On the one hand, once you fix your axioms, there is no way in hell you can avoid the conclusions - they might be hard to find (sometimes even impossible to find), but if you find and verify them, they are unmistakably true. This can turn off some people that are more used to thinking about everything being just shades of gray and there always being multiple valid opinions. Maths is the subject where you can't just make up your mind, the evidence when you're wrong is deafening.
On the other hand, real maths can also turn off some of the more OCD-ish kind of people that think maths is all about the one single truth and everyone agreeing about everything, whereas maths is infinitely malleable and you can say things like "what if the parallel axiom is wrong" or "what if negative numbers have square roots" and even if it sounds silly, you can create proper maths out of it. If you've ever seen people with only high school maths knowledge arguing passionately online about the correct order of operations or whether the square root of -1 is i or -i (or, in another context, Grammar nazis), you know the kind of people I mean.
I think mismatched-axioms misunderstandings happen all the time and it really is a useful mental model to ask people about their axioms. In fact, I think it's even helpful when people are arguing in bad faith. If they have to state their axioms you pin them down and there are then at least some things they can't redefine on the fly.
I think even really high profile debates suffer from mismatched-axioms misunderstandings, such as the abortion debate. For instance, I think a lot of people have very different definitions of what constitutes a person. You're probably not going to have a meaningful discussion about abortion if you disagree about that, you probably have to argue about the definition of personhood first.
I think your characterization of maths is spot-on and most people don't understand what "mathematical truth" means. But my impression is that the 2+2=5 guy understands all of this (I think he was a maths PhD student too) and his point was completely valid, including its application outside of mathematics. The reactionaries who caricaturized his argument, however, don't understand any of this and believe he was making a different point entirely, namely that all truth is relative and that every person's point of view is valid. Of course, this misunderstanding is on them.
I don't doubt that the guy with a maths PhD understood the mathematical content. And I would even go farther than to say that many disagreements are based on different axioms. Many disagreements are even due to different definitions (such as "free will"). I think that was one of the key points of late Wittgenstein.
So yes, in many cases, laying out the assumptions carefully is a good idea, I agree. I just didn't think 2+2=5 was the best example.
Yes, and perhaps more importantly, Twitter seems like the wrong forum to bring up such a subtle point. Especially in a political debate where you have hordes of people who will simultaneously not understand what you're saying and be very eager to turn your argument into a viral caricature.
R/Z is also a group where 2+2=5 is technically correct, and this abelian group is actually useful. For example, if you consider the quotient topology on R/Z, you find that it is homeomorphic to a circle.
While that is also true, in this group all integers are equal to each other. The point is that there is nothing particularly interesting about the specific 2+2=5 example, not that groups in which this is true can't be interesting.
Comedians have a tough enough time doing jokes with face-to-face communication and body language as it's been done for thousands of years.
So most of the people on Twitter are already behind them, but then they want to try and do jokes on a brand new human medium that lacks a lot of information from face-to-face communication.
And then they get upset that someone didn't get their joke.
I learned a while back that twitter is a sludge fest in the abscess of the internet. Any meaningful commentary is drowned out by a deluge of downright bafoonery and willingful ignorance.
Twitter, social media, and now even regular media stories are a game of telephone, with slight misinterpretations snowballing as the minutes and hours go by. People lining up to fight on both sides of accidental straw man theses is a weekly occurrence.
I'd say that part of the reason for such a reaction is that stuff like "mathematx" actually exists - so people don't bother checking when a claim sounds like it's related.
The original Tweet thread was a math nerd who jokingly, and not incorrectly, illustrated how it was mathematically possible for 2+2 to sometimes be 5. The argument may have been weak, and some people may not have found it convincing, but it was a mathematical argument, meant as a joke for a small Twitter audience.
Through the Twitter telephone, many retweets and steps later, the original argument - considered, funny, valid, perhaps weak - somehow transformed into "2+2=4 is a mere social construct, and 5 is a valid answer" - which, yes, would be a disturbing trend if that were actually the argument. Thus the unduly passionate took up "2+2 is 4 not 5" as a political rallying cry. People I otherwise respect as rational began tweeting this.
It became complicated because there are always people who believe dumb things, like "mathematics is merely a white supremacist social construct", and as always with the unduly passionate, extreme opinions are held up as examples of dangerously typical. The author of the original thread was bullied by a mob.
It's complicated even further by the existence of an actual replication crisis in academe, in part driven by post-modern ideological pressures; there is actual loss of academic freedom even for the tenured.
But the lesson at the end of the day, to my mind, is that articles about whatever goes on over at Twitter, such as this one, such as this my post here, are always going to involve mobs of people being shitty, because the nature of the medium. Maybe they are as inevitable as "mobs of people are gambling in Las Vegas"