La biblioteca scomparsa - L. Canfora

There are other books I read in the last months I need to write notes on, but I just finished this one and have something on my mind, so here goes.

I randomly bought this book because I wanted to buy a book and it was about the library of Alexandria, which is a cool topic, so I figured I might as well read it. It turns out that the topic of the book is: Caesar did not actually burn the library of Alexandria, and for the picture we have of it the library of Alexandria is not something that did actually exist.

So first I want to register that I am slightly terrified that you can just figuratively kick a stone and discover that something you were fairly confident about is maybe not necessarily false, but somebody can make at least a fairly good argument for which it is not true. And not like, partially not true, but grundsätzlich false. Like 0/10 true if the argument holds. The terrifying part is that of course you cannot kick all the rocks, but for this kind of things it’s like cockroaches, it’s never just one, and I would also like to say, that like cockroaches they have been selected to not be easy to find. The things which are false and easy to identify as false or dubious you identified. I also want to say that the guy who wrote the book is not some kind of Dan Brown, which at this point would be the easy way out, but this is again not the case. But then again: what if it is the case? That’s another rock to kick.

This is a good point to praise the (purposed) approach to knowledge in mathematical research, which goes like: if you want to use a result, then you have to be able to reproduce the proof yourself. The real life version of this is if that somebody tells you there’s a road up the hill which you can follow and go to the next town, you don’t really believe it unless you go walk it and then reach the next town, if this piece of knowledge is important for you. If it is not important for you then you do not really need to take a stance on believing it or not and you can register it as a claim. The role of transmitted knowledge is this paradigm is not really that it tells you what it’s true, but that it tells you where to look if you want to know something, and hopefully save time. Maybe the road is not there, and Pech gehabt, but if the system works checking existence of roads in this way will be significantly faster than random search. But this also means that the value of transmitted knowledge is just to speed up gain of actual knowledge. So if you can prove a theorem yourself faster than you can look up an article and follow the proof there, then do so. If you see the road from the window go up and check, no need to ask.

The problem is that this approach is in practice not tenable. A principle is somehow bound to be black-or-white, its application will always be some kind of dirty gray. It’s a lot of additional work to determine what is important for you, sometimes it is not even possible to know it in advance, and to first make hypotheses, then determining which statements you would really need to be true to have what you want and then go back and check those is thinkable for pure mathematics, hardly doable in a satisfactory way, and I suspect just not possible in real life. The reason for this is that you are way too slow - one can look at the mathematical physicists. There was a series of lectures in mathematical quantum electrodynamics that arrived in one case up to 4, running four semesters one after the other because the lecturer and students were really motivated. At the end of the fourth class the students could (supposedly) rigorously prove the result of the first class in quantum electrodynamics, without the “mathematical” - they had just scratched the surface. The professor then went to another university and it was not possible to find a lecturer for the same class for the next year, and I have to say that this is not really surprising.

The even more basic problem is that if you are a gamet that looks left and right at every turn you are going to be more successful than the average gamet in terms of getting closer to the egg, because your approach is hopefully better than random, but one of the other gamets is certainly going to have reached the egg before you, or you will have died before getting there. I am aware of this metaphor being wrong on several levels, probably also the logistic does not really have the problem of left and right, but the point holds. The way advancement of knowledge seems to work is not: every individual checks the sources carefully and then we progress, but more: everybody picks something to believe in and the end we’ll see who’s right based on the results. I would say that the group reaches the aim faster, but for the individual it kind of sucks. If you want to maximize your chances of success then you are not going to achieve much, so just have to make an educated guess and live with the fact that you could have done better.

I realize I am framing this in terms of competition, which is not what I wanted but then again. I want to say that we are not throwing the darts, which is a nice image to believe in, we are the darts being thrown and also by somebody who’s not terribly good at it, just happens to have a lot of darts and needing not a lot of centers. This is again a wrong metaphor because it assumes somebody is throwing the darts and that something is needed. Nobody is and nothing is, is what I think.

I lastly want to add how much of this is built in our, or at the very least in my, wiring. The survivor bias or whatever it is called, wanting to buy a ticket of the lottery after having heard that somebody won, makes sense from a group perspective where everybody is a dart. The image of the library burning is something I would call archetypic, hence easily inscribed, or in fact just awoken, in our minds. The big building burning in the middle of the night, everything black except the contour of the flames, the sky in fact in a very dark blue, the stars behind it, this is what an animal sees when the wood is burning and istinctively knows to have fear. Do all animals have this instinctive fear? Another rock to kick. But this image is so easily etched in the brain because it fills a spot which has exactly its shape.

Kick the rock or kick the bucket