soist

The computer can't do anything other than arithmetic

TypeScript has a Turing complete type system so it's as powerful as it gets in terms of what can be expressed in the type system. As for learning and understanding what is going on with type systems in general you'll have to go through a textbook if you really want to develop an understanding. Type systems (not Turing complete ones) are fundamentally logical systems and I don't know how you can understand type systems without actually going through the trouble of understanding the underlying logical fundamentals.

No one at the commercial AI research labs knows what they're doing. As far as they are concerned there is nothing beyond gradient descent but it's accepted among academic researchers that gradient descent is insufficient for creating anything truly intelligent.

Perfect demonstration of the psychopathic technocratic delusion. You really need to think through what you're actually suggesting.

Eventually people will realize any underdetermined system of equations has infinitely many solutions. Give me any open source AI model and I will beat any SOTA benchmark. Why am I so confident? Because curve fitting can be applied to any data set to get as good of a result as needed. Combine this approach with mixtures of "experts" and any predetermined set of benchmarks will fall to a curve fit to the benchmark.

The hype is really getting tiresome. There is no way to get from here to any intelligent system with the current techniques. New breakthroughs will require insights into discrete spaces which are not amenable to curve fitting with gradient descent.

How do you define an imbalance and an intervention to "fix" them? It's important to use the correct terms to avoid biased frames and conclusions. In this case they're defining certain measurable features as anomalous among a population of people. An anomaly does not mean it is a deficiency that needs to be fixed with medical intervention.

There used to be a company that tried to do this to directly generate electricity: eSolar (https://www.cbsnews.com/news/an-interview-with-esolars-bill-...)

How do they verify the output preserves semantics of the input?

Intentions are not reducible to computational implementation because intentions are not algorithms that can be implemented with digital circuits. What can be implemented with computers and digital circuits are deterministic signal processors which always produce consistent outputs for indistinguishable inputs.

You seem to be saying that because we have no clear cut way of determining whether people have intentions then that means, by physical reductionism, algorithms could also have intentions. The limiting case of this kind of semantic hair splitting is that I can say this about anything. There is no way to determine if something is dead or alive, there is no definition that works in all cases and no test to determine whether something is truly dead or alive so it must be the case that algorithms might or might not be alive but because we can't tell then me might as well assume there will be a way to make algorithms that are alive.

It's possible to reach any nonsensical conclusion using your logic because I can always ask for a more stringent definition and a way to test whether some object or attribute satisfies all the requirements.

I don't know anything about theories of consciousness but that's another example of something which does not have an algorithmic implementation unless one uses circular logic and assumes that the brain is a computer and consciousness is just software.

You're using circular logic. You are assuming all physical processes are computational and then concluding that the brain is a computer even though that's exactly what you assumed to begin with. I don't find this argument convincing because I don't think that everything in the universe is a computer or a computation. The computational assumption is a totalizing ontology and metaphysics which leaves no room for further progress other than the construction of larger data centers and faster computers.

It's like asking if a probability distribution is truthful or a liar. It's a category error to speak about algorithms as if they had personal characteristics.

If OpenAI had an embedded python interpreter or for that matter an interpreter for lambda calculus or some other equally universal Turing machine then this approach would work but there are no LLMs with embedded symbolic interpreters. LLMs currently are essentially probability distributions based on a training corpus and do not have any symbolic reasoning capabilities. There is no backtracking, for example, like in Prolog.

Good luck on your journey

No problem.

So what is your question? The standard definition of a topos spells out the structural constraints for subobject classifier, finite limits, and Cartesian closure. You can write out these definitions for the topos of sets and any "small" structures in your topos which are points of the specified logical/structural variety will be small toposes internal to the topos of sets.

None of your examples are expressible in first order logic either. Those are all instances of mathematical structures which can be formalized in different toposes with different logics.

Groups in the topos of sets are different from groups in the topos of smooth sets. The structure of a group can be expressed as a diagram which can then be interpreted in any topos with the prerequisite mathematical structures. Toposes have products (finite limits) so every topos can potentially have group objects just like every topos can have a natural number object which is an initial algebra (colimit) for a certain diagram.

In any case, there is no royal road and if you're not willing to spend the time and effort to learn what others have written about toposes then there isn't much I can help you with here. There are no royal roads in mathematics.

The category of sets is a topos and can be expressed/presented with first order classical logic but the general logic of toposes is intuitionistic and non-classical. There is no single topos with a single logic, each topos has its own logic and the common thread is that they're non-classical and higher order.

The logic of toposes is higher order intuitionistic logic. The logic of higher toposes is presumed to be intensional dependent type theory. The best introduction to these logics is probably the homotopy type theory book.

Still doesn't make sense. So it's 100% after 20 years or does that mean if it doesn't happen in 20 years then it's never going to happen?

In any case, these predictions have been happening for 50 years and it's always 20 years away.

Why isn't it 100%?

I know that feel bro.

That's how the free market works. AI CEOs that deliver value to their shareholders will thrive while those that don't won't. Trust in the wisdom of the market and everything will be fine.

Rarely will you be in compliance after they flag your account. There are various agencies that oversee them so they'd rather get rid of any kind of liability like your business before the auditing agencies catch on and fine them.

Every other payment processor will do the same thing. If some kind of internal audit catches your business then they will proactively get rid of you to reduce their liability with external auditors.

The brain is not a computer. Computation is an abstraction of thinking but it does not coincide with it.

Do you know about the manifold hypothesis and why that's the inductive bias in current neural networks?

There was one such group but they determined it was impossible because of Rice's theorem and other limitations of formal systems for computation. Logical incompleteness, Tarski's theorem, and Rice's theorem are the main meta-theoretical results that make alignment fundamentally unsolvable. If you're really concerned about robots taking over the world then understanding basic computational theory should be a prerequisite but most people are not willing to spend the time to learn the theory and instead focus on vague and ill-defined science fiction concepts which are very unlikely to be actually physically possible/implementable because of various physical and formal limitations of computers.

I've decided anyone concerned about these issues knows almost nothing about computability theory so their theories are either nonsensical or just outright crazy. Very few understand the required formal concepts to have any useful ideas about how computers should be programmed to prevent "unsafe" results (which is often left just as ill-defined as most everything on AI safety and alignment research).