The Genie Bade Me Think About Language

I've sometimes read other people's blogs and found websites where they talk about themselves in a relatively informal fashion. So, I thought, why not me too? Why not indulge. If I'm to have a website, it should have some personality. Meanwhile, I can practice my English as well.

So I was playing Baldur's Gate II the other day. I don't know if you know it, it's a relatively old game from the early 2000s, back from the good old days when things still made sense. A fine game for the PC, if anyone's interested. I personally love the change in perspective some old games give me, because they're seemingly unencumbered with the last decades of video game history. It sort of feels like the influences are more pure, if that makes any sense. Probably because of the web and how it's affected things over the years. Or maybe it's just me, to use a trite turn of a phrase.

Anyway, in the game, there's this genie fellow who asks the player a question. The question goes like this:

"A princess is as old as the prince will be when the princess is twice as old as the prince was when the princess's age was half the sum of their present age. Which of the following, then, could be true?"

The options are:

a) the prince is 20 and the princess 30

b) The prince is 40 and the princess 30

c) The prince is 30 and the princess 40

d) The prince is 30 and the princess 20

e) Both are the same age

f) Don't know

I'll show my own solution later on, in case the reader is interested.

Anyhoo, it's such an interesting question because the first gut reflex you get is this horror mixed with confusion and desperation. "Do I really need to use math?!!!" It's vomit-inducing. But then, once you start rolling out the algebra, it turns out to be an easy problem to solve, especially because of the options given. There's at least two ways to do the math, maybe more (in fact, the genie gives you more information than you strictly need).

But this is exactly what made me think about things. Why is it that using natural language to solve problems causes head trauma, but writing some equations with variables makes things easy?

Moreover, as I was playing, I remembered this age-old question I've pondered every now and then about whether mathematics actually is natural language instead of "its own thing" – that is, whether mathematics "arises" out of language use, possibly due to severe repetition (training), or whether one should think mathematics somehow more fundamental a building material that gives rise to basic grammar and therefore all the languages.

Personally, I haven't decided what to believe. If you held a gun to my head and forced an answer out (because apparently everyone's carrying one these days), maybe I'd be most inclined to answer that mathematics and natural language are one and the same thing, but that there's some relatively mysterious reason as to why they look different (probably related to hormones or something). Certainly mathematics is more terse. But what makes this somewhat titillating a question, perhaps, is that people seem to consistently confuse language use with having some sort of a revelation or discovery. So there is an underlying belief there about some sort of primacy of the tool, as though the tool existed separately to the person wielding it. However, if I remember my high school philosophy class correctly, one cannot so easily discern where the ship of Theseus begins and ends, about what exactly gives it its identity as its bounds shift arbitrarily across time.

No, perhaps there is actually nothing there, and we humans are simply using language arbitrarily, whatever that means. For me, it means "getting what I want", which conveniently also often ends the discussion.

But then, it shouldn't come as a surprise after all that large language models (LLMs) have the capacity to learn how to do math, especially if you feed them questions like the one I mentioned, the genie one. So is the same thing true for humans? Personally, I'm undecided yet again: some people learn things seemingly quickly and without any help, while some people never learn a thing no matter how much you give them. And then you have everything in between, of course, regarding mathematics as well. So why do you suppose that is?

Maybe everyone should just read a ton of books, see if that helps anything.

But I digress. The reason the genie made me think about language, I suppose, is that I wonder if abstraction simply isn't a rudimentary kind of compression. Because, obviously, instead of having a separate "representation" for each case you have a single "abstraction" that may or may not fit very well everywhere. You may interpret representation and even abstraction loosely. The abstract in all its glory being just a template, a lossy switcheroo that you pull.

But if that's the case, then humans apparently have this strange compulsive behavior of compressing things down with varying success. Abstracting away or – dare I say it – explaining away, as though the "space" inside the mind was indeed limited, that you have to do that. Possibly to speed things up or God knows why.

In my mind, this is how intelligence could be general, as in, say, AGI or human. But the thing I don't yet know is whether this kind of generality is truly about space savings or rather about recognition – about recognizing what to compress. Because if there is no recognition about that, then what you get is random behavior. And if that's what's happening, then I'd be shocked to see a Gaussian bell curve in there somewhere.

I've heard it said someplace that the abstract is more ever-present and in that sense more real than the immediate experience. I can't remember who it was who said something like that. I myself wonder if the continuous process of abstraction is exactly what robs life of its meaning, quite literally, because there's less meaningful things after you abstract them away, one after the other, you see.

Of course, one thing I've realized is that pictures (as in visual sensations) are language too. A much more redundant language than what vectors of characters or sounds could compose, perhaps, and rather closer to what it means to be a human being. But if pictures are language, then I don't see why there should exist an external physical world. Sound weird? If you know "the brain in a jar", then it shouldn't be so strange at all. But you don't need to think there's a brain, and you don't need to think there's a jar either. The point is that, as humans, it's impossible to discern whether there really is a star in the night sky or whether someone or, rather, something is telling us that there is. You see what I mean?

Of course, the physical world is there, because I remember it's there, and that mysterious something keeps telling me it is. But it's just not there by virtue of "the atoms" or something like that. Rather, it's there because I was told it's there in a special language that my mind found convincing, because my mind couldn't help it even if it wanted to – regardless of what exactly the mind is supposed to be.

This is not to say that physics is wrong or whatever drivel like that. This is to say that nature, insofar as it is understandable for a human, is a part of the message, and therefore must make sense assuming the message is acceptable. In other words, if you don't understand physics, then either you're not a human or you don't belong to the target audience (yet).

And the very interesting conjecture that more or less follows is that, because the message "makes sense", no matter what you observe always makes sense. Now, it sounds like I'm merely repeating myself, doesn't it?

So what would be the difference between "the atoms" and "the language", really? Well, I suppose the difference is that, instead of what's there, it's all about what it's trying to tell you, and how everything seems to organize towards that end, on the surface. Here's hoping that *that* makes sense – and perhaps it will, further on.

Anyway, I believe many people have had these language-kind of ideas in the past as well. Not that I recall any of them, but I find it nonetheless interesting how this kind of thinking opens the door to not only a possibility of belief in greater powers and seemingly mysterious phenomena but to a kind of categorical thinking about the nature of the world.

You see, one thing I've been contemplating is whether everything is indeed relative in a sort of infinite manner, or whether everything is rather absolute and categorical, in that only the order (time) and the magnitude (space) count regarding the perception of reality – it's my one-eyed computer science background talking. But the idea being that, for a language to be concretely demonstrable, it need only to occupy a certain position in time and a size small enough to allow a sense organ to accept it. You see what I mean? Again, feel free to interpret "sense organ" loosely. And feel free to forget about the idea of "location" as well, as all of that is only conveyed by language anyway.

You see, you have to ask yourself: what is synesthesia? Why does a taste sound like something and why do letters appear a certain color even when they are not? This has boggled my mind for a long time.

But the answer seems to lie in the observation that even insanity must be recognizable. So, one is advised not to get carried away with how the same rules don't apply to everyone, but rather to observe that everyone follows some rules, after all. That's a strange discovery in and of itself, and explains – to me, anyway – why "mathematics describes nature surprisingly well", as they say. Because there'd be nothing to explain, if it didn't. Can you see what I mean? By this, I mean several things and not just the claim.

Indeed, I was once asked, a few years ago, something about what is important or relevant in digital video that's subject to compression. I've already forgotten the exact question, but I still remember that I found the particular phrasing of it rather tricky, because I didn't know how humans come to know about what is relevant in a general sense. But I do know that there are things that are required for perception to occur in a digital image, and we can identify some of the things that most people don't need in order to perceive what we want them to perceive. It's sort of beside the point whether some people would enjoy it more if there was more data involved, because the properties of the viewing device you're using also presumably play a role in regard to your viewing pleasure, not to mention any psychological phenomena that could be tacked on there. So how *do* you know what is relevant?

But to come back to the core of the matter, the thing is, I don't know which one, language or mathematics, is the more fundamental one. Actually, it could be that there is no such thing as something "fundamental" at all. Notice how, if you entertain the "language-kind" of ideas I expressed earlier in a more general fashion, beyond natural language or mathematics, it doesn't matter at all whether you are a dualist or a monist or whatever, because then there is no substance to language whatever. There is nothing to occupy space and there is no constitution to begin with, because language is what makes those things, or doesn't, in which case they're not there. Instead, there is merely a particular sense in which talking about substances is reasonable.

Indeed, I have the sneaking suspicion that the belief in something fundamental existing is generally mistaken, because every science, it could be argued, is fundamental. You simply lay the foundation wherever you please. No wonder humanity seems to be progressing and everything seems to speed up according to some, because the origin point is being continuously shifted, just like taking harder and faster shortcuts. Personally though, I find it makes far more sense to think that one should argue for "true" things rather than "fundamentally true" things, although that may in turn steer one towards a strange definition of truth – but it may be that I'm simply tripping myself up with semantics here as well. And besides, I'm not about to start arguing for truth in general either. You *can* verify things by looking, can't you? And if you have a sound recorder, you can play those sweet sounds you've heard back a thousand times. And it isn't as if I too hadn't abused the word, "fundamentally", all the time. Still, I can't help but think that letting this entire line of thought be false simply because of faulty semantic overture is precisely the kind of reasoning you'd use to show that language use doesn't generally provide any new information whatever, hinting at the possibility of a subtle contradiction – the contradiction being that you'd have to show that you are continuously committing the exact same mistake in order to show that a particular mistake was made.

Nonetheless, I suppose what I'm saying is that in this way of thinking the words "language" and "pattern" are synonyms. There's no difference. And so, I feel compelled to ask: do you think there can exist a pattern that is not "perceptible" by anything at all? Perceptible being interpreted loosely, as is our custom.

We could look at evolution, for example, and notice that any message that has no receiver is completely useless, and therefore only hinders propagation by wasting resources – which is to say nothing about messages that are useless while still being received. The same could be said for receivers that never receive any messages, as well. And yet, there always exists "stuff out there", just beyond the outlines of anything perceptible that does not fall under any category, or, any "abstraction". And so, there you have a natural "explanation", if you will, for what happens to those messages that are not being received. One thing is for sure, though, and it's that they are not being recognized as receivers either.

A receiver that is not recognized as such never receives a message intended for it. Such receivers would then be subject to random messages or nothing at all – entropy. So, obviously, you then ask: "why does redundancy exist in the world at all?" Well why do you think? It's there to form patterns. In other words, maybe chaos is a language in and of itself, but it sure doesn't mean anything, because it can't, you see. And so you have to go in the other direction – and we're all just simply repeating ourselves all the time (to a degree).

So, to come back to my earlier question about whether the "meaning of life" is lessened through abstraction, yes. Yes it is. Because ultimately there's only one meaning to be observed.

I suppose there's just one more thing I should briefly discuss so as to make my earlier lunacy slightly more sensible. After that, I'll finally cease this incessant blabbering.

So, earlier on I had this naïve-sounding intuition about time and space, vis-à-vis the international computer science curriculum. About what makes language "concretely demonstrable", as I put it. Nearing the end of my blog post, I suddenly realize that saying it like that raises some questions about time, as well. I suppose that, in this line of thinking that I'm entertaining and playing around with here, the point is to realize that time isn't really time at all.

That is, time, as people seem to talk about it usually in my observations, is really just space. Instead, in my thinking, "human" is a synonym for time, rather like "language" is one for pattern. Notice how there really is only *now*. The past only ever exists right now in your memories, which could be false, and the future only ever exists right now in your expectations about what's going to happen next, or insofar as you can see (your "ken" as I suppose you could say). And once you pay attention to what's happening next, it is here in the now. Of course, it is a different thing to *imagine* what might happen next, compared to truly expecting it to happen "right now" as it should. If you truly expected something to happen, and it didn't, you'd be surprised and you'd think that you've made a mistake – perhaps because you're tired or you have a brain malfunction or something. And so, how do you suppose it could be even in principle possible to discern whether that future time that "moved" from future to now already in some sense existed, before this transition came to pass? This is where philosophers seem to pull out the "determinism" card, or some flavor of it. But look: the future could still be anything at all from the seemingly infinite possibilities, it just cannot be anything that does not "make sense". And tracing a path through space and connecting the dots is by definition what makes sense. That is what intelligence is generally supposed to solve, so to speak. And so, if you're using your intelligence, which you should, then you might accidentally trip over your own feet, is what I'm suggesting – by believing that your maximum likelihood estimate was the only possibility to begin with, even though you of course had to consider all the others before arriving at the conclusion in question. In other words, what I'm saying is that it is almost beside the point whether the future is predetermined, in any sense of the word, because once you have the final effective mapping from here to there you might as well be there now. Or, yet in somewhat different words, once your mind has worked out what's going on, then it has worked it out and you're there. The only variables are "that it's you" and "what you can contain in the now". Continuing our tradition, even that is to be interpreted loosely, because of the problematic word "you" (remember Theseus's paradox). Indeed, there's certainly more I could say about this, but I'd rather not quite yet.

Anyway, I think that's enough about me in regard to my strange thoughts and musings. Perhaps in the future my thoughts develop some more, or I might blabber on even if they didn't. Or maybe I'll find myself to be mistaken later on. Could be an opportunity to learn something. Here's my solution to the genie's problem:

princess | prince |

--------------------------

x | y | now

x1 | y1 | future

x2 | y2 | past

Here's what we know (in algebraic form):

x = y1

x1 = 2(y2)

x2 = (x+y)/2

x2 - y2 = x - y = x1 - y1

The last equation:

-y2 = x - y - x2

y2 = y + x2 - x

Also we know that time passes:

x2 < x < x1

y2 < y < y1

From this we directly see that:

y < y1

y < x

Also:

x < x1

x < 2(y2)

x < 2(y + x2 - x)

x < 2(y + (x+y)/2 - x)

x < 2y + x + y - 2x

x < 3y - x

2x < 3y

x < (3/2)y

So end up with:

y < x < (3/2)y

We can test the options:

a) 20 < 30 < (3/2)*20 = 60/2 = 30 => false

b) 40 < 30 => false

c) 30 < 40 < (3/2)*30 = 90/2 = 45 => true

d) 30 < 20 => false

e) x < x for some x => false

f) don't know => false

Turns out, only option c) works.