Okay. That's a very convincing analogy. Thanks for the thought out response. Forgive me for being rude.

Uber Black drivers are commercially licensed in addition to satisfying a bunch of other requirements.

Why stop there? They're just as real as any number.

I heard it was supposed to be human body temperature, but they used horse body temperature instead because it was close to human body temperature but more... stable.

You're reducing things to a single issue and have the gall to say my political world is narrow. You're unreal.

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.

That's why my hands are baby soft.

Binary supremacy!!!!!!!

I'll preface this with the fact that I am also not a physicist. I'm also simplifying a few concepts in modern physics, but the general themes should be mostly accurate.

String theory isn't best described as a genre of physics - it really is a standalone concept. Dark matter and black holes are subjects of cosmology, while string theory is an attempt to unify quantum physics with general relativity. Could string theory be used to study black holes and dark matter? Sure, but it isn't like physicists are studying black holes and dark matter using methods completely independent from one another and lumping both practices under the label string theory as a simple matter of categorization.

You are correct to say that string theory is an attempt at a theory of everything, but what is a theory of everything? It's more than a collection of ideas that explain a large swath of physical phenomena wrapped into a single package tied with a nice bow. Indeed, when people propose a theory of everything, they are constructing a single mathematical model for our physical reality. It can be difficult to understand exactly what that means, so allow me to clarify.

Modern theoretical physics is not described in the same manner as classical Newtonian physics. Back then, physical phenomena were essentially described by a collection of distinct models whose effects would be combined to come to a complete prediction. For example, you'd have an equation for gravity, an equation for air resistance, an equation for electrostatic forces, and so on, each of which makes contributions at each point in time to the motion of an object. This is how it still occurs today in applied physics and engineering, but modern theoretical physics - e.g., quantum mechanics, general relativity, and string theory - is handled differently. These theories tend to have a single single equation that is meant to describe the motion of all things, which often gets labeled the principle of stationary action.

The problem that string theory attempts to solve is that the principle of stationary action that arises in the quantum mechanics and the principle of stationary action that arises in general relativity are incompatible. Both theories are meant to describe the motion of everything, but they contradict each other - quantum mechanics works to describe the motion of subatomic particles under the influence of strong, weak, and electromagnetic forces while general relativity works to describe the motion of celestial objects under the influence of gravity. String theory is a way of modeling physics that attempts to do away with this contradiction - that is, string theory is a proposal for a principle of stationary action (which is a single equation) that is meant to unify quantum mechanics and general relativity thus accurately describing the motion of objects of all sizes under the influence of all known forces. It's in this sense that string theory is a standalone concept.

There is one caveat however. There are actually multiple versions of string theory that rely on different numbers of dimensions and slightly different formulations of the physics. You could say that this implies that string theory is a genre of physics after all, but it's a much more narrow genre than you seemed to be suggesting in your comment. In fact, Edward Witten showed that all of these different string theories are actually separate ways of looking at a single underlying theory known as M-theory. It could possibly be said that M-theory unifies all string theories into one thus restoring my claim that string theory really is a standalone concept.

https://twitter.com/latifnasser/status/1750952860131729544

I like this one

This is just a continuous extension of the discrete case, which is usually proven in an advanced calculus course. It says that given any finite sequence of non-negative real numbers x,

lim_n(Sum_i(x_i^n ))^(1/n)=max_i(x_i).

The proof in this case is simple. Indeed, we know that the limit is always greater than or equal to the max since each term in the sequence is greater or equal to the max. Thus, we only need an upper bound for each term in the sequence that converges to the max as well, and the proof will be completed via the squeeze theorem (sandwich theorem).

Set M=max_i(x_i) and k=dim(x). Since we know that each x_i is less than M, we have that the term in the limit is always less than (kM^n )^(1/n). The limit of this upper bound is easy to compute since if it exists (which it does by bounded monotonicity), then the limit must be equal to the limit of k^(1/n)M. This new limit is clearly M, since the limit of k^(1/n) is equal to 1. Since we have found an upper bound that converges to max_i(x_i), we have completed the proof.

Can you extend this proof to the continuous case?

For fun, prove the related theorem:

lim_n(Sum_i(x_i^(-n) ))^(-1/n)=min_i(x_i).