Language parsing is a routine process that doesn’t require AI and it’s something we have been doing for decades. That phrase in no way plays into the hype of AI. Also, the weights may be random initially (though not uniformly random), but the way they are connected and relate to each other is not random. And after training, the weights are no longer random at all, so I don’t see the point in bringing that up. Finally, machine learning models are not brute-force calculators. If they were, they would take billions of years to respond to even the simplest prompt because they would have to evaluate every possible response (even the nonsensical ones) before returning the best answer. They’re better described as a greedy algorithm than a brute force algorithm.

I’m not going to get into an argument about whether these AIs understand anything, largely because I don’t have a strong opinion on the matter, but also because that would require a definition of understanding which is an unsolved problem in philosophy. You can wax poetic about how humans are the only ones with true understanding and that LLMs are encoded in binary (which is somehow related to the point you’re making in some unspecified way); however, your comment reveals how little you know about LLMs, machine learning, computer science, and the relevant philosophy in general. Your understanding of these AIs is just as shallow as those who claim that LLMs are intelligent agents of free will complete with conscious experience - you just happen to land closer to the mark.

Imaginary numbers are no more imaginary than real numbers. The name trips a lot of people up. If you want to call imaginary numbers “dark unicorns” then you really should say the same thing of the numbers 1, 2, and all other numbers as well.

You’re thinking of topological closure. We’re talking about algebraic closure; however, complex numbers are often described as the algebraic closure of the reals, not the irrationals. Also, the imaginary numbers (complex numbers with a real part of zero) are in no meaningful way isomorphic to the real numbers. Perhaps you could say their addition groups are isomorphic or that they are isomorphic as topological spaces, but that’s about it. There isn’t an isomorphism that preserves the whole structure of the reals - the imaginary numbers aren’t even closed under multiplication, for example.

You’re mistaken unfortunately. The books don’t start that way. They start by describing Arthur Dent’s house.

Yeah, you’re close. You seem to be suggesting that any measurement causes the interference pattern to disappear implying that we can’t actually observe the interference pattern. I’m not sure if that’s what you truly meant, but that isn’t the case. Disclaimer: I’m not an expert - I could be mistaken.

The particle is actually being measured in both experiments, but it’s measured twice in the second experiment. That’s because both experiments measure the particle’s position at the screen while the second one also measures if the particle passes through one of the slits. It’s the measurement at the slit that disrupts the interference pattern; however, both patterns are physically observable. Placing a detector at the slit destroys the interference pattern, and removing the detector from the slit reintroduces the interference pattern.

Binary supremacy!!!

This problem doesn’t involve cardinal numbers.

In discussions about intelligence we’re always talking about the ability to acquire knowledge, not knowledge itself.

I’m not talking about either of these things. I have already stated that I’m not referring to knowledge. Additionally, I do not agree that intelligence is merely the ability to acquire knowledge. Intelligence is famously difficult to define - but I’m working with a definition akin to a capacity for problem solving and pattern recognition. If we can’t see eye to eye there, then we’re clearly talking past each other.

Thanks for the interesting conversation. I wish you well.

You’re taking my analogy too far. Learning isn’t your ability to exercise intelligence. It’s simply the acquisition of knowledge or skills usually through study or training. You’re going to have to provide an argument or a source to back up the claim that intelligence is innate and that it can’t be changed by adjusting our behavior. You’re going to have to show that intelligence is nearly 100% determined by genetics. Those are the types of claims that eugenicists make regarding intelligence by the way, and I’m pretty sure that would make you uncomfortable given your other comment on IQ tests.

I don’t see how this could be true. It would be analogous to observing a species of bone-thin weaklings that becomes interested in body building over the course of a few hundred years, gaining more muscle mass on average with each passing year, and making the claim that the strength of this species has not changed. Maybe if one of the early weaklings decided to take up their own interest in body building, they may have reached a similar strength to that of their descendants (though even that is debatable since that specific individual wouldn’t have access to all the training techniques and diets developed over the course of its species’ future); however, it seems like an awkward interpretation to say therefore the strength of the species has not changed.

This is similar to the situation we find ourselves regarding intelligence in the human species. Humans gain intelligence by exercising their brains and engaging in mental activity, and humans today are far more occupied by these activities than our ancestors were. This, in my view, makes it accurate to claim that human intelligence has changed significantly since the advent of religion. Individual capacity for intelligence may not have changed much, but the intelligence of humans as a whole has changed.

Note that my argument does not conclude that human knowledge or understanding has changed over time. These attributes certainly have changed - I’m sure not many would doubt that. It also doesn’t conclude that every modern human is more intelligent than every ancient human. Instead, it concludes that human intelligence as a whole has changed as a result of changes in our culture that influence us to spend more time training our intelligence than our ancestors.

You have the spirit of things right, but the details are far more interesting than you might expect.

For example, there are numbers past infinity. The best way (imo) to interpret the symbol ∞ is as the gap in the surreal numbers that separates all infinite surreal numbers from all finite surreal numbers. If we use this definition of ∞, then there are numbers greater than ∞. For example, every infinite surreal number is greater than ∞ by the definition of ∞. Furthermore, ω > ∞, where ω is the first infinite ordinal number. This ordering is derived from the embedding of the ordinal numbers within the surreal numbers.

Additionally, as a classical ordinal number, ω doesn’t behave the way you’d expect it to. For example, we have that 1+ω=ω, but ω+1>ω. This of course implies that 1+ω≠ω+1, which isn’t how finite numbers behave, but it isn’t a contradiction - it’s an observation that addition of classical ordinals isn’t always commutative. It can be made commutative by redefining the sum of two ordinals, a and b, to be the max of a+b and b+a. This definition is required to produce the embedding of the ordinals in the surreal numbers mentioned above (there is a similar adjustment to the definition of ordinal multiplication that is also required).

Note that infinite cardinal numbers do behave the way you expect. The smallest infinite cardinal number, ℵ₀, has the property that ℵ₀+1=ℵ₀=1+ℵ₀. For completeness sake, returning to the realm of surreal numbers, addition behaves differently than both the cardinal numbers and the ordinal numbers. As a surreal number, we have ω+1=1+ω>ω, which is the familiar way that finite numbers behave.

What’s interesting about the convention of using ∞ to represent the gap between finite and infinite surreal numbers is that it renders expressions like ∞+1, 2∞, and ∞² completely meaningless as ∞ isn’t itself a surreal number - it’s a gap. I think this is a good convention since we have seen that the meaning of an addition involving infinite numbers depends on what type of infinity is under consideration. It also lends truth to the statement, “∞ is not a number - it is a concept,” while simultaneously allowing us to make true expressions involving ∞ such as ω>∞. Lastly, it also meshes well with the standard notation of taking limits at infinity.

My superiority complex is stronger than your inferiority complex.

I like this one

I don’t recall any socialized courier or food delivery services.

I see what you’re saying about moving away from smarmy pop culture videos, but the claim that all the “random smart things” ultimately don’t matter is weak when you’re comparing them to topics that literally do not matter at all. I’m not invalidating your example, just pointing something out.

2 may be the only even prime - that is it’s the only prime divisible by 2 - but 3 is the only prime divisible by 3 and 5 is the only prime divisible by 5, so I fail to see how this is unique.