First things first: corrections and clarifications.
It was brought to my attention that some of the language in my recent attempt at being slightly less lazy and cowardly may come across as fatalistic, or over-emphatic of the importance of ‘talent’. That was not the intention, although it is certainly not an unreasonable interpretation of lines such as:
“His brain is so much better suited to the task that the gulf is effectively impassable.”
“…de facto hard ceilings do exist on an individual’s ability to draw ‘well’ in a given context.”
The overall sense that I wanted to convey with that post (and that series) was some combination of the following:
A: It’s fine not to be good at things.
B: Not being good at things doesn’t mean that you can’t have fun with those things.
C: Not being good at things doesn’t mean that you can’t become good at those things.
D: Things at which you are not good are an excellent sort of thing to do if you want to improve in general.
And perhaps I did a bad job at that.
The reason talent, as a concept, came up is really just because I found it interesting and got side-tracked. I do think it’s worth acknowledging, however – not as a counterpoint to the narrative of self-improvability and embracing failure, but as a little bit of extra seasoning. Well, that’s a topic for a different day. I just thought it was important to address any potential miscommunication. Writing is nothing if not an attempt to communicate, after all. Simply being ignored may be a poor way to fulfil that function (although it is kind of an inevitability), but giving the wrong impression is far worse.
That’s part of what’s attractive about fiction, as a medium. Your ideas are couched in a much more overt layer of abstraction, and the reader has an automatic expectation that your ‘intent’ may have a relatively fuzzy correspondence to much of the verbatim content, or may be plural, or only very loosely defined. A more straightforward approach is much more liable to backfire. Today’s ‘idea’, such as it is, is something that I would absolutely have expressed via story in the past – so we’ll try nonfiction and see how it goes.
On another note, this isn’t a report on my tepid adventures in meditation. That is coming (oh, the excitement), but I had a busy weekend, in an intensely slothful sense of the word, and want to try a couple more things first. If I choose something more ‘one and done’ next week then things should end up back on track.
So, today I thought I’d just briefly ramble on a shower thought I had.
It was prompted by the memory of an overheard conversation – I was sitting in a GBK (for some reason), next to a pair of young men who it would be safe to assume were students. Young Man A mentioned something about “Zeno’s paradox”, which isn’t particularly descriptive. Young Man B requested a description, and was supplied with a sort of hybrid of this:
“In the paradox of Achilles and the tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 meters, for example. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 meters, bringing him to the tortoise’s starting point. During this time, the tortoise has run a much shorter distance, say, 10 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles arrives somewhere the tortoise has been, he still has some distance to go before he can even reach the tortoise.”
“Suppose Homer wishes to walk to the end of a path. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on.”
Young Man B expressed his incredulity that somebody so presumably intelligent as Zeno could have said something so obviously stupid, then uttered the words that triggered the shower thought, some weeks later: “Surely that can be solved by…”
I’ll admit that I didn’t hear what followed (probably I was busy eating a burger). It may have been ingenious. It may have been a revelatory new insight into motion, space and/or tortoises. Even if that were the case, however, it wouldn’t matter much to the topic at hand.
What I found striking was the automatic assumption that a paradox is something you’re supposed to solve – a problem for which, given time and thought, a satisfactory answer will emerge. That seems like some combination of optimism, stubbornness, and misinterpretation – but it’s an attitude that we see represented in STEM-ish conversations (and elsewhere) all the time. There’s a sense that if something hasn’t been comprehensively solved, that’s only because we haven’t gotten there yet. There is much less often a sense that ‘getting there’ and ‘solving’ may not be as broadly applicable as we might like.
Now, as ever, this is all overly simplistic. There’s a million different things that somebody might consider to be a paradox, and a million different ways to engage in the practice of ‘solving’ them, and many of the combinations of those two things are going to be totally sensible.
I suppose the gist of what I want to say is this:
A: A paradox is not necessarily a ‘problem’ or ‘statement’, in the sense of being something that should be proved, disproved, or otherwise resolved, and it is not necessarily fruitful to think of one in this way.
B: It may be more fruitful to think of a paradox as being a compact expression of an interesting discontinuity or pitfall in human thought/perception, or as a way of describing a categorically insoluble problem. In other words, they’re thought experiments at heart. Their most consistently valid application is in promoting discussion on a topic that either has not or cannot be solved.
Returning to Zeno, let’s give him more credit than Young Man B did. Zeno is not saying that Achilles cannot overtake a tortoise, nor does he expect for a moment that anybody will ‘agree’ with his account of their race. That doesn’t seem like too big a presumption. What he’s actually saying may be a little fiddlier. Our friend Wikipedia states that it is “usually assumed” that Zeno’s assortment of paradoxes were intended as a defence of Parmenides. That is to say, that he was looking to promote a Parmenidean view of ‘existence-as-one’ by demonstrating the absurdity of the perceived alternative – an infinite descent into discrete fragments. Perhaps that’s the sort of polemic context that leads people into a ‘solving’ mindset rather than an exploratory one. It seems better to look at Zeno’s offerings in the following sense:
A: An obviously true premise. To walk down the entirety of a path you have to walk down half of it.
B: An obviously false conclusion. Therefore, you can’t ever walk down the path.
C: An invitation to have fun in the space generated by those two things.
Now, perhaps Zeno did believe so firmly in the impossibility of motion that he felt like he was presenting statements of pure fact. That’s unlikely, but it still wouldn’t remove the world’s ability to play around with those statements and the disconnect that they express. Likewise, Escher doesn’t expect you to start building impossible structures, “This sentence is false” is not an impossible natural language sentence, and you certainly don’t need to find ways to justify your intuition that one door is just as likely to conceal a goat as the other. Let’s not even touch Schrödinger. All of those things have been excellent at instigating and sustaining discourse in both academic and popular milieux, however. That’s their strength, whether or not there is or ever will be a ‘solution’.
Which is not to say that solutions cannot emerge – especially in fields that are well equipped to develop proprietary solutions to their proprietary paradoxes. If somebody, in paraphrasis via Wikipedia article, were to say this…
“Let us call a set “abnormal” if it is a member of itself, and “normal” otherwise. For example, take the set of all squares in the plane. That set is not itself a square in the plane, and therefore is not a member of the set of all squares in the plane. So it is “normal”. On the other hand, if we take the complementary set that contains all non-(squares in the plane), that set is itself not a square in the plane and so should be one of its own members as it is a non-(square in the plane). It is “abnormal”.
Now we consider the set of all normal sets, R. Determining whether R is normal or abnormal is impossible: if R were a normal set, it would be contained in the set of normal sets (itself), and therefore be abnormal; and if R were abnormal, it would not be contained in the set of all normal sets (itself), and therefore be normal. This leads to the conclusion that R is neither normal nor abnormal: Russell’s paradox.”
(I’ll start using better sources at some undetermined future date. It’s hard. I’m not at university anymore and have become functionally illiterate.)
… then somebody might decide to develop an axiomatic set theory that resolved the issue. Which would be a good thing to do – a lot of people would be happy with that. Of course, it could be argued that the foundations of mathematics form a closed system that generates its own data, and so the role of a paradox therein is quite different to elsewhere. I wouldn’t go so far as to say that myself, though, because I know nothing about mathematics. Regardless, the luxury of defining axioms and then putting them into effect yourself isn’t going to be universally available, and that seems like a game-changing tool to have at your disposal.
The woolly, unsound message here is that, most of the time, a paradox isn’t your enemy. It’s not something that you have to defeat, and it’s not an attack against you or your intuitions, even if it might be being used as one. Your intellect will almost always be better spent treating it as an invitation rather than a challenge. An assumption of solvability might be comforting, but if you cling onto it too tightly then there are waters that you will never really be able to navigate. Without wishing to get too obvious, good luck explaining your existence. To return to Parmenides, ex nihilo nihil fit, and so on. In other words, you’d best start believing in paradoxes… you’re in one. Nobody’s going to solve the universe – not now, not ever, unless something very peculiar happens. That doesn’t mean that there isn’t plenty of universe to discuss and plenty of exceptionally good reasons to do so.
Well, that’s at least as much as one total non-expert should really ever say on the subject. Again, I’m trying to find a discourse method that works. It’s hard to know what to do with these smaller ideas, apart from ‘just don’t express them’, which feels like a totally unsatisfactory solution. It’s possible that their inherent sloppiness is simply better contained by fiction.
In any case, hopefully everything made sense, and feel free to let me know why it didn’t.
That’s all for now.