It is probably the best solution if you can't/won't do real MFA.

Changing passwords relies on mail 99% of the time anyway. So if you are using mail+password to authenticate, you are basically doing magic links with extra steps.

Yes. For some people product owners don’t want to hear this. If having access to email means you can access the account then don’t prance around that with complicated recovery steps.

This is not really necessary tho; it only requires that the mathematical model has a certain arithmetic complexity. The usual demo is Robinson Arithmetic, which is addition, multiplication on the natural numbers, and a successor operation.

Godel then latches onto that to create an alphabet of the symbols which then are mapped to numbers; thus formulas are even bigger numbers, and derivations are even bigger bigger numbers. So for any statements there should be a derivation that prove the statement is true or a derivation that proves the statement is false. Of course most statements will be false, but even then there will be a derivation showing so.

Then Godel does some clever manipulation to show that there will be some statements for which there can be no such derivation in either way. But that does not need the physics theory to express things about itself. It only requires to be mathematically complex enough (it'd be weird if a theory of everything was simpler than Robinson Arithmetic) and that it has rules of derivation of its statements (ie, that mechanical math can be applied to deduce the truth of the matter from the first principles of the theory).

Of course, the actual undecidable godel number and the associated physical proposition would be immensely complex. But that is only cause nobody has tried to improve on Godel's methodology of assigning numbers to propositions. He used what was simpler, prime factorization, cause it was easy to reason about, but results in astronomical numbers. But there is no reason a better, less explosive way of encoding propositions could be found that made an undecidible Godel number to be translated into something comprehensible.

But this is largely unnecessary; Godel proof forces the mathematical system to speak about itself and then abuses this reflection to create a contradiction. It means the system is not complete, that there are statements in the system that cannot be proven from its first principles and derivation rules; the fact that the one Godel showed to exist is self referential does not mean all the undecidable propositions _are_ self referential. There well could be other, non self referential undecidable propositions, that could very well have a comprehensible physical interpretation.

And, regardless of the universe being a simulation or not, the physical theory will ultimately need to deal with this incompleteness.

Godel's proof relies on the self-referential nature of the Godel sentence; without that, his theorem does not apply. Generally you need arithmetic, but also (something equivalently expressive to) universal quantification. Physical theories do not need to include that.

Note Godel's proof is mechanically exactly analogous to Turing's proof of the undecidability of the halting problem, because ultimately it's the same thing (Curry-Howard, Prolog, and all that). So you can bypass arithmetic, but you can't really bypass self-reference; just like programming languages need some looping or recursion (or equivalent expressiveness) to be Turing-complete, mathematical theories need universal quantification to be subject to Godel's Incompleteness Theorem.

Of course, you can have a physical theory that _is_ Turing-complete, say the Newtonian billiard ball model (and, y'know, we can build computers); but that doesn't mean the theory will necessarily tell you, as a static, measureable physical fact, whether a particular physical process (say, an n-body system) will ever halt or loop, or go on forever with ever-increasing complexity; so you could (in principle, in Newtonian mechanics) build some (mechanical!) physical system that simulates the Goldbach conjecture, or looks for solutions to an arbitrary Diophantine equation, but if there are no integer solutions you'll never actually be able to show it; the theory is incomplete in the mathematical sense, but just as complete a description of reality's rules.

They have some explicit examples of physics explainable by quantum gravity that resolve but are undecidable, n-body thermalization being one. Of course that’s given a sort of hand wavey understanding of quantum gravity, I guess one that they say should tell us whether a system thermalizes.

EDIT: I should also mention the idea that reality can tell us if a statement about a theory is true, given that the theory is an accurate description of reality. So if there’s an accurate Turing complete theory of reality, and we see some process that’s supposed to encode a decision on an undecidable statement being resolved (I guess in a non-probabilistic way as well), then we can conclude that reality is deciding undecidable statements in some nontrivial way.

Note that in general, a physical instantiation of an undecidable problem must be specified/realized to _infinite_ precision; that is, for any such system S, and for any eps>0, there is a perturbation p with distance d<eps (eg, move a billiard ball an arbitrarily small amount) that is provable; this is analogous to the fact that existence of solutions to Diophantine equations is undecidable, but the theory of real closed fields is decidable, which means that the only undecidable case is when an equation has solutions _arbitrarily close_ to integers, but never quite an integer. I am not a physicist, but I don't believe any physics actually cares about infinitely-precise setups.

Integers exist in quantum physics (e.g. electron charge, spin), which is why I think quantum gravity is important to this argument. Spacetime ends up being discretizable and we can end up having rational valued physical phenomena.

> integers exist

Mostly as an abstraction on top of a continuous wavefunction/quantum field

> Spacetime ends up being discretizable

As far as I know this is speculative and usually assumed by physicists to be false; it's definitely not a required feature of quantum mechanics per se, and as far as I know not of any other well-accepted theory.

> Integers are fundamental in quantum mechanics, particularly as quantum numbers that define the discrete properties of particles, such as energy levels, angular momentum, and spin.

> Quantum mechanics dictates that certain properties, like energy and angular momentum, are quantized, meaning they can only exist in discrete packets or "quanta".

This was from a cursory google search.

yeah, this is the issue. I've used Claude Code to great success to start a project. Once the basic framework is in place, it becomes less and less useful. I think it cannot handle the big context of a full project.

It is something that future versions could fix, if the context a llm can handle grows and also if you could fix it so it could handle debugging itself. Right now it can do it for short burst and it is not bad at it, but it will get distracted quickly and do other things I did not ask for

One of these problems has a technical fix that is only limited by money; the other does not

Synthetic data works as long as it is directed towards a clear objective and curated.

At one point someone generated a Python teaching book from a LLM, took that, trained a second LLM with that, and the new LLM knew Python.

If you are just dragging random content from the web and you don't know what's synthetic and what's human, that data may be contaminated and a lot less useful, but if someone wanted to whitewash their training data by replacing a part of it with synthetic data, it can be done.

If there is an incident where people can see other's people chats there are two possibilities:

-It's a server issue, meaning someone fucked up their javascript and cached a session key or something. It's a minor thing; could get the specific dev fired in the worst case, and it is embarrassing, but it is solvable.

-it's inherent to how the AI works, and thus it is impossible to share a ChatGPT server with someone else without sooner or later leaking knowledge. It would mean the company cannot scale at all cause they'd need to provide each client their own separate server instance.

If this was something Sam knew and kept it from the board, that'd be fireable. And it'd be catastrophic, cause it'd mean no useable product until a solution is found.

I'd somehow doubt it is something like this, but if we see security issues and private chats that keep leaking, it is a possibility.

It's inherent to how it works, it is known and had always been known that nothing you type into these chats is private and there is nothing whatsoever fundamentally to stop the AI from just handing your chats to somebody else or dumping them out to the internet. They aren't even able to theoretically describe a mechanism by which you could provide a kind of memory protection for these models. And of course we have seen real examples of this already. Only a matter of time before the completely and totally insurmountable problems or scaling AI become clear. Sam is and has always been a conman in my view.

It was absolutely, incontrovertibly the former. The go misstates the issue- users saw other people’s chat titles, not chats. It was just a web server thing.