[SEQ RERUN] How to Convince Me That 2 + 2 = 3
Today’s post, How to Convince Me That 2 + 2 = 3 was originally published on 27 September 2007. A summary (taken from the LW wiki):
The way to convince Eliezer that 2+2=3 is the same way to convince him of any proposition, give him enough evidence. If all available evidence, social, mental and physical, starts indicating that 2+2=3 then you will shortly convince Eliezer that 2+2=3 and that something is wrong with his past or recollection of the past.
Discuss the post here (rather than in the comments to the original post).
This post is part of the Rerunning the Sequences series, where we’ll be going through Eliezer Yudkowsky’s old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Occam’s Razor, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day’s sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.
I think this is a subject where contemporary analytic philosophy is considerably ahead of Less Wrong.
How would you convince a contemporary analytic philosopher that 2 + 2 = 3?
I mean the more general subjects of philosophy of mathematics and the concept of analyticity. This post doesn’t really address any of the important questions. Which is fine, its just that little else has been said on Less Wrong on the subject. The discussion in the comments section of this post is just dismal, though, and could be improved vastly by people just reading a few relevant SEP articles, first.
If it’s something that less wrong should get better at, post a couple of links in the discussion section.
The discussion in the comments section of most of the old OB posts is well below the standards of LessWrong today. I’m not sure if that’s because LessWrong attracts higher-quality commenters than the old OB did, or because reading the sequences dramatically improved the quality of discussion, or both.
But don’t judge understanding of a 2007 post by the quality of the comments.
Sorry, maybe you could provide some specific links or suggestions, or even outline the relevant concepts briefly?
With a very special sort of lesion.
Mathematics is a representation of reality. A representation of the workings of our universe.
What would be necessary to convince me, that 2+2=3? (It’s easier to grasp if you imagine the numbers as “dots”) The only way I would be convinced, is if constantly one quarter of matter and energy around me would simply cease to exist...
If you have 2 atoms and another 2 atoms and suddenly there are only 3 left, with one having completely disappeared (not transformed into energy or changed location → it has to literally disappear!) then I may be persuaded. But a universe where one quarter or stuff just disappears seems rather unstable and unsuitable for life. Then there would also be the question, how often or how fast “one quarter of everything is disappearing”. If it happens more than just once, the universe will keep getting smaller (or emptier) at a faster and faster rate. A universe where 2+2=3 would simply eat itself up.
2+2=4 because that’s the only stable universe we could hope to find ourselves in. Mathematics is really an expression of fundamentally real facts about our universe, like the fact that energy cannot be created or destroyed.
This isn’t a statement about the stability of the universe. For example, a few days ago I mis-added 12 and 19 and got 41. This doesn’t impact the stability of the universe. It is possible a priori that all humans for the last million years have just been misadding this one equation. It is also possible that you have just had a stroke that had wrecked your mathematical intuition so that while you think the alternative to 2+2=3 is 2+2=4, the actual correct equation is 2+2=5.
But if 2+2=3 is correct and 2+2=4 is the arithmetic error then a universe that artificially made 2+2=4 would by your logic have all sorts of extra atoms appearing.
I’m not disagreeing about anything you said. But you’re right, I probably misinterpreted the quote from Eliezer...
I interpreted this statement as “what would it take for Eliezer to believe that •• + •• = ••• ” Consequently I found it weird that he seemed to choose social indicators to justify this belief, when in actuality it should be rather immediately physically visible, if you live in a universe where ” •• + •• = ••• ”
But yes, you’re right that probably wasn’t what was meant by the quote. The quote seems to be about a scenario where you get whacked hard on the head and forget, whether the shape “3” means ••• or •••• and look for social cues to update your belief. I didn’t even consider, that that’s what was meant because… well duh, how is this even worthy of discussion? How could anyone possibly disagree with that?
But it isn’t just social cues. It could turn out that we’ve all been misadding for a million years, including you. It might very well turn out that •• + •• = ••• . What? It looks wrong to you? Well you’ve just miscounted again.
The point is that even a statement as intuitively obvious as 2+2=4 should still be allowed to be overthrown.
I think including the idea of changing beliefs in this post was a mistake, for it’s not the point, but most of the discussion is spent on it. A belief as obvious as “2+2=4” should still have a reason behind it, the way you come to believe even the simplest things should be set up so that you’d believe them correctly, whatever they turn out to be, instead of having them fixed by the magical “a priori”.
We’re talking about completely different things here!
I was talking about “what if reality was actually like •• + •• = ••• and how would we know”. I wasn’t talking maps.
You wouldn’t believe how much brain hemorrhage this last statement is giving me right now. My map of the world says “If I lived in a universe where the territory is like •• + •• = ••• my brain and my map itself would start to disappear—they don’t, so my map can’t possibly be wrong about this”. It truly seems impossible to me that we could be wrong about the territory in such a fundamental way… I can think the words “oh sure I would update if I came across evidence to the contrary”, but every fiber in my brain screams “this is retarded, I exist and that’s why in our universe •• + •• must be •••• and nothing else, end of story”.
Cogito ergo sum, ergo •• + •• = ••••
On the other hand it seems easy to say that my map could be mistaken about the physical implications of the hypothetical •• + •• = ••• scenario but it’s just so… argh.