woopsn

The fundamental driver of the economy will be people, as always, because only people define "value".

Word generating machine will not "figure out how to cure cancer" but it could help, obviously. AI is extremely valuable tool but it does not work on my behalf, except in same sense a coin sorter does. It's a tool. I still see this thing confuse left and right (no exaggeration), which would be fine - tools aren't perfect - except for all bullshit from VCs. That is where the danger lies, not with the tool but idolatry.

I am concerned the system encourages suicide, delusional thinking etc. They need to work that out immediately. Must be held to at least the standard of a lawn mower or couch with regard to safety. Probably should make it safe before hooking it up to 10GW power plant. Does not help perception that author of this blog saying how awesome future will be is also building a hideaway bunker for himself.

This is all on you at OpenAI, Anthropic, Microsoft, Twitter etc. Whatever happens.

You make a lot of good points. Including that the technology to do all that incredibly dangerous to develop - I still can't see a path to terraforming where in the end it's human people left to take pleasure in Mars.

I had thought due to the eons we'd simply have evolved, but even on shorter time frames there is the transhumanist possibility. When we can engineer rabbit that eats chlorine moss, I don't know what we're aiming for at all. "People" by then could have robust gut culture that just digests the regolith.

There's a difference between considering all this vs thinking it's realistic. It's speculation, as any forecast into the centuries ahead must be.

My impression was that pulverized rock/iron is not actually "soil", so after forming the atmosphere you need lengthy biochemical processes playing out on the surface. I admit though, I don't know too much about this.

I didn't think reasonable really has a definition here. The rendezvous with these comets will take centuries or millennia even if we can get out there and kick them the right way (which is much harder than arranging a miss). Only then do we start terraforming, which takes thousands/millions of years in addition. Who/whatever we're preparing the planet for probably wouldn't be "people" anymore. :)

I recommend The Image by Daniel Boorstin. Smart phone is not the dawn at all but I guess more like high noon. The world is replaced by graphics (more generally , images) for a century at least. Books by "digests", heroism by celebrity and so forth. A little bit of media theory goes a long way to making the world "legible" again. Since we are absolutely steeped in media culture.

I would like AI that helps read and understand the text, but don't see real value having textbooks generated by AI.

But working with complex numbers I hardly if ever write (a, b) for a+ib, while I use the "escape hatches" all the time. They solve equations that have no real solution, they give me paths from x=-1 to x=1 that don't cross the origin, etc. There's only so much to learn about C as a vector space, while the theory tying it to R (and even N) is very deep.

I guess this PRNG has recurrence period much less than 52! (or wasn't seeded appropriately), so that only sampled a fraction of the distribution

"... the system ties its number generation to the number of seconds that have passed since midnight, resetting once each day, which further limits the possible random values. Only about 86 million arrangements could be generated this way,"

If you take N samples of a real signal you will get N/2+1 bins of information from the DFT, covering 0Hz out to about half the sampling rate.

The bins do not actually measure a specific frequency, more like an average of the power around that frequency.

As you take more and more samples, the bin spacing gets finer and the range of frequencies going into the average becomes tighter (kind of). By collecting enough samples (at an appropriate rate), you can get as precise a measurement as you need around particular frequencies. And by employing other tricks (signal processing).

If you graph the magnitude of the DFT, signals that are a combination of power at just a few frequencies show just a few peaks, around the related bins. Eg a major chord would show 3 fundamental peaks corresponding to the 3 tones (then a bunch of harmonics)

https://en.wikipedia.org/wiki/Fourier_transform#/media/File:...

So you detect these peaks to find out what frequency components are present. (though peak detection itself is complicated)

It's depressing how common this accusation is become here. Before LLM idiot ruined everything, you know what? People wrote things you wouldn't like, in a way you wouldn't like. Especially on their blogs. HN so smart though they can immediately see, tenured Yale professor has no life and is trying to win the message board game with AI slop!

Convolution with dirac delta will give you an exact sample of f(0), and in principle a whole signal could be constructed as a combination of delayed delta signals - but we can't realize an exact delta signal in most spaces, only approximations.

As a result we get finite resolution and truncation of the spectrum. So "Fourier analysis with pre-applied lowpass filter" would be analysis of sampled signals, the filter determined by the sampling kernel (delta approximator) and properties of the DFT.

But so long as the sampling kernel is good (that is the actual terminology), we can form f exactly as the limit of these fuzzy interpolations.

The term "resolution of the identity" is associated with the fact that delta doesn't exist in most function spaces and instead has to be approximated. A good sampling kernel "resolves" the missing (convolutional) identity. I like thinking of the term also in the sense that these operators behave like the identity if it were only good up to some resolution.

Does the fact that BB(k)=N is provable up to some k < 748 mean that all halting problems for machines with k states are answered by a proof in ZFC?

When was the circle discovered? When it became essential to physics?

You need some additional assumptions. Only near equilibrium / thermodynamic limit is system linear in entropy. What governs physical processes such as you mention is conservation, dynamics pushing equipartition of energy - but outside that regime these are no longer "theorems".

Given that the links work, the quotes were actually said, numbers are correct, cited research actually exists etc we can immediately rule that out.

That alone would be revolutionary - but still aspirational for now. The other day Gemini mixed up left and right on me in response to basic textbook problem.

If the claims about AI were that it is a great or even incredible chat app, there would be no mismatch.

I think normal people understand curing all disease, replacing all value, generating 100x stock market returns, uploading our minds etc to be hype.

I said a few days ago, LLM is amazing product. Sad that these people ruin their credibility immediately upon success.

If I had to write again I might say "same theorems about natural numbers" and capitalize ROUGHLY. It is a conversation, what exactly I am weaseling around (not just nonstandard model theoretic issues), and I take your caveat about consistency strength - with that said would you still call it misleading? Why is it that eg x+y=y+x for x y given takes exponential length proof in Robinson compared to PA? For the reason stated, which is true in a very broad sense.

There is another goal in addition to minimizing the number/complexity of axioms. Some "axioms" like induction actually introduce an infinite family of assumptions, a so-called schema. So in addition to working backwards from our (incomplete) knowledge, we find certain axioms let us make arguments that are obviously valid but would be formally very tedious without them.

Axioms are also introduced in practical terms just to make proofs and results "better". Usually we talk in terms of what propositions are provable, saying that indicates the strength/power of these assumptions, but beyond this there are issues of proof length and complexity.

For example in arithmetic without induction, roughly, theorems remain the same (those which can still be expressed) but may have exponentially longer proofs because of the loss of those `∀n P(n)`-type propositions.

In this sense it does sometimes come back to intuition. If for all n we can prove P(n), then `∀n P(n)` should be an acceptable proposition and doesn't really change "the game" we are trying to play. It just makes it more intuitive and playable.

It's been longer than that, more than 2 years since Time ran EY's moron piece which put the whole field in disrepute and back on its heels basically. That the community spins out literal murder cults and assassins doesn't help.

What is an important question in the objective sense? Is life, or no because that just matter to life? It seems oxymoronic, "objective question", "objectively important".

I don't follow GP's sort of solipsist (?) take, but would say question of whether big bang took place in a black hole is pointless compared to life/experience and how they arise.

Rado has many interesting subgraphs, for example the implication graph of every countable theory. Are arithmetic propositions associated randomly? Not as we see it, but in some sense they could be (even iid). It is not the quite the same but I take the rado construction to be the logical extreme of the position there is no inherent/meaningful truth in such theories. You need to deal with this kind of many-worlds absurdity that falls out.

From your reply though I feel we are not really disagreeing so much. There is a kind of truth which is not propositional or self-evident but teleological. That is a sense in which I think the assigned truth values are meaningful.

The formalist movement was indispensable, I shouldn't have implied it was merely self-defeating. But I believe the philosophy that mathematics is fundamentally arbitrary mechanical symbol manipulation is wrong.

Artificial intelligence is a nourished and well educated population. Plus some Adderall maybe. Those are the key insights which represent the only scientific basis for that term.

The crazy thing is that a well crafted language model is great product. A man should be content to say "my company did something akin to compressing the whole internet behind a single API" and take his just rewards. Why sully that reputation boasting to have invented a singularity that solves every (economically registerable) problem on Earth?

The "fundamental limiter of human progress" is not energy/intelligence lol. No - surprise, it's people. Bear in mind he builds this "gentle singularity" in the great progressive UAE.

When you accept axioms randomly and reject even logical semantics, you wind up working with something like the so-called rado graph of Erdos. Call the first set of assumptions/structure meaningless and choose a new one, also having no grounding in reason - it turns out that would make no difference. "Almost certainly" you wind up with the same structure (the rado graph) in any case.

https://en.wikipedia.org/wiki/Rado_graph

So you can reject meaning (identifying the axioms with simple labels 1, 2, 3, ...) and truth (interpreting logical relations arbitrarily), but in doing so you ironically restrict mathematics to the study of a single highly constrained system.

I only disagree somewhat though - it is all contingent. We do say something like

    IF { group axioms } THEN { group theory }

and introduce even more contingencies in the application of theory. In a real problem domain these assumptions may not hold completely - but to that extent they are false, not having a meaningless truth value. Crucially, we then search for the right set of assumptions, and the conviction of modern science that there is a right set of assumptions is "effective" at least.

In the previous century there was an attempt to identify mathematics with formalism, but it defeated itself. We need to see truth in these systems - not individual axioms per se, but in systems composed from them. This is justified by the body of mathematics itself, to the non-formalist, the richness of which (by and large) comes from discoveries predating that movement.

The generic unit of information is still the "bit", and the word "word" -- which is not a unit of information, depending on entropy of the encoding -- is still standard terminology in communication theory.

Would an alien encountering human language say "whatever it is not fundamentally different from the fact they shed skin cells in each other's space"?

> The research, published in Royal Society Open Science, found that these spikes often clustered into trains of activity, resembling vocabularies of up to 50 words, and that the distribution of these “fungal word lengths” closely matched those of human languages.

I'll be the one to admit I am surprised by this (if true), even with the understanding that any motion or byproduct whatsoever might be communicative.

The thought that an organism is totally isolated from its environment, itself and other organisms is absurd, sure - but no one said that!

To be fair the firm's goal is, explicitly, to "replace most economically valuable labor".

The article would not be so controversial if it weren't outright saying "fake deadline". Of course you need a plan and a push, and stakeholders legitimately need (if only emotionally) some idea of when the builders will deliver. But on a charitable reading there are already terms for what it describes -- expected, target, soft date etc.

In my first engineering job out of college I was manipulated into working (on prem) into the early morning night, after I'd been there a few years. I couldn't help but think of that when I read

> If you think that a prototype might take a month, why not challenge the team to see what they can deliver by the end of the week? You will be surprised, and so will they.

Just being a kid and having my boss, a former professor I looked up to, expect that I could pull it off was enough. You have to be really careful "challenging" engineering reports like this -- need to actually use "see what you can do" language, NOT "deadline" (even if fake) for a 1mo->1wk timeline compression. He certainly acted surprised when I quit sometime thereafter. Hopefully he learned from the experience as well, I still appreciate my time there, just needed more experienced / realistic management.