deeThrow94

Also, it doesn't make sense to price homes in absolute terms. Surely relative to wage would be a better indication of the health of the market. Unless we can bring the wealthy to heel of course.

If you can't learn from a shallow dismissal, that's your problem.

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Can you come up with some conception of recursion that doesn't involve symbols referring to themselves, directly or indirectly? Ie what is left of recursion when you remove the linguistic component?

I agree that there's enormous value in carving out mathematics from other linguistic reasoning, but I don't see defining as something as mathematic rather than linguistic is generally useful. You use the same skills to look for incoherency in both situations, but human language is generally expected to be incoherent on some level.

Besides, a lot of what people mean when they say they're bad at math is that they're bad at arithmetic, which is honestly understandable.

We don't call this recursive... it's just incrementing x

That's not a recursive function as it's written, but you could certainly consider it a form of symbolic recursion. This just isn't a very useful characterization in an iterative/imperative context. You could frame incrementing as recursive, though—this is just peano axioms/church encoding.

That's fair. I agree that there's more to problem solving than just linguistic ability, so I rescind my claim that they're indistinguishable, but I still think there's a deep relationship between the two.

I have a very difficult time trying to extract the difference between "linguistic ability" and "critical thinking", though:

1. The core difference between "critical thinking" and "uncritical thinking" is the ability to discern incoherency from coherency.

2. Coherency is evaluated at the linguistic level: do the terms bind in meaningful ways to the problem? Do any statements contradict each other?

3. The remaining aspect is "creativity": can you come up with novel ways of approaching the problem? This is the hardest to tie to linguistic ability because it sort of exists outside our ability to operate within an agreed context.

So while I agree these are distinct skills, I still have difficulty identifying what remains in "critical thinking" after linguistic ability is addressed.

There are two ways that recursion intersects with language that are relevant here:

1. Our spoken and especially written grammar is recursive. We do handle this unconsciously. This is not related to our ability to reason about recursion at a high level, and recursive grammars are not necessary to do so. This is not a skill in the normal sense and we have only (very) limited ability to improve our capacity to interpret deeply nested grammars. However, this is still a useful illustration of what recursion IS, which is why I brought it up.

2. Language also introduces the ability to semantically reason about recursiveness. This is still a linguistic thing—you need a symbol and relations among symbols in order for recursion to be meaningful—but this is a skill and is likely very related to linguistic skill. This is the part that really helps you to program: ultimately, you're just reasoning about symbols and looking for incoherency.

Recursive functions are just a subset of all possibly recursive concepts. In the case of human spoken language, the recursion exists in our characterization of the grammar. You could just as easily frame this in "iterative" terms just like you can make any recursive function iterative, but that's less convenient for analysis.

So in this case, "recursive function" would be "clause" or something like that; I'm no linguist. But clauses can embed clauses which can embed further clauses, etc.

I think your usage of recursive functions is just high-level logic—you're describing an inductive proof. We also frame a lot of our social games as recursive processes. But these are conscious processes that we can evaluate consciously; the recursion in spoken language is largely unconscious and very shallow.

If you define recursion as a symbol referencing itself, either directly or indirectly, and if you define language as a system of relating symbols to each other, recursion is a linguistic concept, it is a concept that describes a relationship between symbols. There are good reasons to define each concept differently, but if you identify recursion empirically, recursion won't "actually" exist outside of the description of the process. It's our characterization of the process that reveals the recursive structure, even if that characterization doesn't actually exist outside of language.

To be clear, the symbols themselves don't bother me so much as trying to refer to them in spoken english. I have no particular beef with the use of symbols in code, which can be quite readable.

That problem solving skills are relevant is pretty obvious, but language less so.

To me, problem solving ability is precisely the same as the ability to articulate the problem and a solution. I don't see a major difference.

If you can solve a problem but you can't articulate what the problem is or why the solution will address it, I wouldn't call you a good problem solver. If you can articulate the problem well but not come up with a solution, you're already doing better than a lot of programmers in the world, and I'd probably prefer working with you over someone who presents the solution without "showing their work".

In fact, what is problem solving without such articulation? It's hard to even grasp what the skill means in a raw sense. Arguably creativity in this context is just the ability to reframe a problem in a more approachable manner. Many times, if not most times, such framing implies some obvious solution or sets of solutions with clear tradeoffs.

I don't really know what you mean by "conjecture", but I thought apriori was implied by positing it as a linguistic construct. "Fundamental" doesn't imply empiricism at all. All of apriori knowledge for a language is a set of all sets of coherent statements: the outer set represents a set of implied axioms required to make the statements cohere. Recursion just broadens the complexity of the statements you can express, but it's fundamentally a concept that arises from language and can be evaluated for coherency (like all other apriori concepts).

Edit: added a definition of apriori knowledge.

Edit2: to put this another way, nobody is arguing that recursion doesn't exist. Or that it is empirically-derived. No, it's a useful construct to show certain relations.

Edit3: added a sentence

Edit4: The extent to which our own grammars are inherently recursive vs this being culture or technology is irrelevant to identifying the concept of recursion as an apriori, linguistic concept.

Edit5: i suppose you might also be referring to the idea that we naturally process recursion. I mean, we clearly, evidently do; whether or not that's inherent to being human is a separate question entirely. Hell in the free software world there's a whole recursive acronym meme that taps into some part of our brain and tickles it.

I'd argue none of that math is really necessary. While I have used most of my classes at least once, it was never a barrier to advancement in my career. Hell you could say the same thing about any of the theory. Like yea it's cool I know what a "merkle tree" is but it ultimately is a distraction from most of the skills you need to work with git.

Anyway, both computation and math are grouped under "apriori" knowledge. Any semantic distinction is ultimately silly. But we could just as easily be teaching programming as a craft in the context of the real world—I think this is closer to how it's done outside the US. I am not at all convinced the American style is what people ought to be paying for.

I can't speak for other forms of FP, but symbol operators make communicating about haskell very annoying. Outside of that FP seems to be doing fine, IMO.

How do you communicate an inductive proof without language? Even formal symbolic logic is fundamentally linguistic.

I'm a terrible speller; it's taken me ten years of typing "ammend" to learn its proper spelling. It also sort of goes against the "programmers are lazy" meme: why memorize what a computer can detect and correct?

100% agree, I've been saying this for years. I'm terrible with arithmetic but great with symbols and relations. Recursion is also fundamentally linguistic, and although our internal "stacks" for processing it naturally are quite small, language remains the easiest demonstration of recursion in our daily lives.

Oddly, I also use spatial intuition when thinking about stuff like stacks and the shape of data structures.

I highly recommend reading Schumpeter, both "Business Cycles" and "Capitalism, Socialism and Democracy".

He discusses how motivations fundamentally change after profit margins peak and argues that profit after this point necessarily produces less economically efficient processes (in terms of the flow of demanded goods and services, not the shareholder, who does receive further productivity gains). In this context, undesired market advantage (legal or illegal) is just a symptom of profit, but it can be analyzed like any other sort of inefficiency. The core prescription is to nationalize the process or otherwise remove the profit motive around peak profit (which is, to be clear, not always easy or possible to identify... but in the worst case, this would open further opportunity for private capital to invest in the next generation of improvements).

He also discusses how failed investment cycles can resonate into market crashes faster than capital can rationally reallocate. Both of these above observations seem very very relevant to our current situation in the US today, and should cause everyone to look askance at people who aren't concerned about how healthy our political economy actually is.

fundamentally undermined by science and technology creating a new market that upends the old one.

The kicker here is that there's no reason to expect either to continue yielding the same rewards. Some industries have projectable, plannable, investable growth patterns; others do not. Almost all the industries with predictable growth rely on consumption driven by yields from the lucrative exploitation of frontiers, mostly technological recently as you point out. I suspect that the market is going to get incredibly volatile as capital sees this frontiers dry up and adjusts expectations. ideally by cannibalizing itself and not eating us, but it might need a little help in that regard....

This is true, and it is disgusting.

then it wouldnt be long before it was invaded by Russia or China

I would be lying if I claimed I hadn't dreamed of being liberated by a foreign power with more cultural competence at governance (which excludes Russia, obviously, but they probably at least aren't worse), but realistically anything but a slow scale-down in military power would probably entail the bloodiest world (and civil) war in history. Maybe nukes, too.

But, there's a fork in the road. We can choose to scale down our military presence (and control of trade) today, and figure out how we actually want to exist in a global community outside of letting our corporations swing their dicks freely... Or we can blow trillions of dollars continuing to make fools of ourselves rampaging through other countries rather than building high speed rail before we lose our grip on hegemony anyway as a matter of pure economics.

Or, I suppose, we can just murder anyone who disagrees with us until we're just miserably exploiting each other inside of high walls armed with automated guns. Something tells me that's the option we're going to pick.

Philosophy as a concept isn't an issue; but we tend to romanticize the tendency to neurotically examine even when we know finding "truth" isn't possible, and I've noted a tendency in people so devoted to unconsciously emotionally attach to what are ultimately word games. This concerns me. Perhaps we should instead romanticize living a contented existence, some of which will surely still involve reading and discussing philosophy (in moderation, of course).

I had thought the clear need for anti-trust had tickled down to the plebs on here. Unfortunate to see that people still casually refer to free markets as if it's a meaningful concept.

If you really truly think that regulation is dragging down some market, it's easy to talk about in specific terms. It is only possible to employ "free markets" in bad faith.

Very good points. I've been trying to figure out whose interest is in our "national interests" my entire life. It sure ain't protecting my interests or those of anyone I love that justifies a trillion dollar a year military.

Ah it's just romantic; let's not be so harsh. LinkedIn would be so lucky to get a post like this.

I enjoyed this article.

I am confused though how this was a difficult problem to begin with, particularly with the internet. It is not exactly hard to find intellectually stimulating concepts if that's what gets you off.

I also find "philosophy" to be a pretty miserable and unrewarding topic to think about, and I tend to run quickly away from those who want to talk about it. I find it very curious that the author finds it to be a natural place for your focus to land. I think this is a red herring: the secret to long-term contentment is not thinking at all if it's not strictly necessary. Aristotle got "contemplation is the greatest good" dead wrong.

A win is a win

So it adds legitimacy to the free market spirit seen in markets like EU, which has been criticized for making up arbitrary rules for self-interest.

I'm confused a) who is taking the concept of free markets seriously, especially in this context where markets (and competition) are arbitrarily defined and owned by corporations and and b) who would view self-interested laws as either surprising or bad? Of course laws are in self interest. Why on else else would you pass a law?

This isn't a problem with the technology; it's easy to observe that it doesn't happen with better-known languages. Your problem is that you don't have a model for your target language.

technically, you're correct. But I don't expect to see much given how resources for ai licenses are calculated.

I know any of us can demo a feature, but how specifically is an LLM gonna correct your tone when it can't understand tone itself?