chongli

That's false. Z[n] in rings does not mean "an array of integers of length n", it means the subring generated by Z union with {n}, where n is an element of some other set. For example:

Z[i], the Gaussian integers, is the subring (of C) generated by Z union {i} where i is the imaginary unit in C, the complex numbers. The Gaussian integers correspond to the integer grid-points of the complex plane, if you want to visualize them.

No, math is difficult to approach because it's genuinely deep. Trying to verbalize what is going on is extremely difficult, because you end up saying stuff like "and then do that to all of these things, and then do it again to all of the results, and so on ad infinitum, and then take the collection of all of that, and join it with the collection of doing the same procedure as before starting with a different set of objects, and then join those to yet another set of objects and the results of their operations, ad infinitum, ad infinitum..."

People genuinely struggle to think verbally or visually once we extend beyond 3 dimensions and start talking about infinite-dimensional constructs, uncountable sets, and so on...

Mathematics would be much more approachable if it just used plain English like `sum(0, Infinity, my_func)` instead of a big Greek sigma with nested function nomenclature

First of all, no, mathematics would be far less approachable if it did that. Most of the Greek letters used in mathematics don't have a universal meaning, they're context-specific and defined by convention or just prior to use.

Second of all, mathematics is optimized for hand calculation on paper, not long-term programming and code maintenance. Writing out long names over and over on a whiteboard gets tiring extremely quickly, so mathematicians prefer to stick to single-letter symbols.

I remember reading some of his columns growing up and I used to intensely dislike him for his dismissive takes on a lot of products and technologies I thought were important (most infamously, he dismissed the mouse)! Later on, I saw him as one of the regular guests on Leo Laporte's TWIT podcasts, and it totally changed my perception of him. The guy was genuinely hilarious and a real lovable curmudgeon, not a true naysayer.

I hadn't read or heard anything from him in recent years, though I had heard he had a falling out with Leo Laporte. He might have reconciled more recently but I am not sure. I know Leo will genuinely mourn him, as they were friends and colleagues for many years. I really miss him now too!

And that intervention was just an accidental discovery. Someone thousands of years ago stumbled onto a freak plant with no seeds and had the foresight to take a cutting of it.

I don't think so. There are a ton of varieties of banana that are grown from seed. Humans have cultivated them and selectively bred them from seed for thousands of years, just like every other plant. The seedless bananas that dominate western grocery stores are 1 variety, Cavendish, that have been endlessly cloned from cuttings. They weren't the first seedless variety commercially available, they were preceded by Gros Michel. But either way, travel to southeast Asia and you'll find a lot more varieties on sale.

A hundred million is table stakes. They get better results by stoking the fires (bluffing) and keeping their opponents locked in a war of raising and re-raising the stakes. By amping up the pressure, they drive more and more investment into the bubble.

China also benefits massively through all of the commodity hardware they make. Sure, they aren't competitive in the chip arms race, but they dominate all the component and power electronics markets. Think about all the power supplies and other commodity components needed to build a gigawatt-scale data centre.

You don't have to believe it. It's a bet. If you're wrong, everybody loses their money. If you're right, you want to be the biggest winner.

The premise I was responding to was that the energy infrastructure would be built during the rise of the AI "bubble" and subsequently be repurposed after the collapse. If we're just connecting data centres to the grid then I don't see how that is providing any new infrastructure whatsoever. On the other hand, if we're building lots of new power plants to power the data centres (and connecting them to the grid) but then at some point the data centres are shut down, we end up with a huge glut of unneeded power.

Furthermore, to elaborate on my point above: building new power plants in tandem with data centres that demand GWs of additional power does nothing to address the needs of the grid itself. The grid is not built to handle all that new power, and the consumer electricity demand is not there anyway.

Energy infrastructure for powering a data centre isn't the same as energy infrastructure for powering a city. One is a simple point-to-point link (power plant to data centre), the other is a grid.

It's like comparing a railway line from a mine to a smelter with a city's road network.

Doesn't that only apply if the capital is reusable? If we end up with a bunch of data centre GPUs after an AI bubble collapse, there's no guarantee those GPUs will find productive use for other things.

It's like the tulip bubble of the 17th century [1]. Having a bunch of money tied up in useless tulip bulbs didn't do anything productive after the collapse.

[1] https://en.wikipedia.org/wiki/Tulip_mania

That definition of wealth is all well and good for books about how markets are magical fix-everything pixie dust

No, it actually means something. We have access to refrigeration, climate control, near-limitless computation, entertainment, transportation, knowledge, communication, and medicine. All of this stuff would BLOW THE MINDS of medieval kings. Even if you're living in a 1BR apartment, working at Walmart and struggling to pay rent, you enjoy many luxuries Charlemagne could scarcely dream of.

Go to the store, grab a pineapple off the shelf, take it home, and eat it. Then read about the great lengths [1] the wealthy people of the past went to in order to try to grow pineapples in Europe, and how obsessed the culture became with this fruit.

[1] https://en.wikipedia.org/wiki/Pineapple_mania

Stockfish already does that. You run it as long as you want. When it's calculating evaluations for move k+1, it already knows what move k was, because it has that evaluation. It can explore that tree first, before exploring other trees to try to improve on move k.

Stockfish never settles down to an exact move, unless it sees a forced mate sequence. You could leave it running indefinitely, but the exponential blowup will soon grind you to a halt.

What new versions of Stockfish buy you are optimizations and better heuristics. An older version of Stockfish can still beat a new one, if given enough of a compute advantage.

Note this is different than knowing how to orient yourself in a million line codebase quickly.

Hence my library mention. Humans have been doing this for millennia: orienting ourselves within a library (the physical kind, full of books) and calling upon its information resources as needed to accomplish tasks (research). Ultimately, it's all just one big cache hierarchy. Your short term memory, your long term memory, the book in your hands, the desk at the library, the nearby shelves, the card catalogue, the stacks, the inter-library loan system.

To manage it all, we humans have developed our abilities for abstraction. When we build clean, tight abstractions we reduce our cognitive load. Perhaps the best abstraction we've built so far is the TCP/IP and web stack. We don't need to care at all about the hardware details of a server in order to talk to it. It's such a powerful and airtight abstraction that we take it for granted.

I'd like to hear from more people who have spent a lot of time building with LLMs, because so far what people are saying is that these models do not have the ability to reason about and build the kind of marvellous abstractions us humans have built.

Humans built codebases many millions of lines long, well before LLMs existed. Human memory has not been a restriction on us in a long time.

Look at all the libraries full of books we've built. It's useful for more than mere training sets.

Why are people upvoting this? I thought I was missing something.

The person had a 6 figure job. They’d end up having their salary garnished to pay the debt. It would be far worse than just giving the money back.

By that point I've lost interest in the project. Not a very good elevator pitch if you're losing people before they even see what it looks like.

But in a world where AI is able to both produce math theorems, and figure out practical applications for them, human understanding has minimal practical value to society.

We have examples of AI producing theorems but there is no evidence that AI will be able to find all of the practical applications of mathematics, at least not any time soon.

As I understand it, most of the theorem proving work done by AI today consists entirely of “glue code” style work: combining a bunch of different known results to prove a new result. This is great for those who desire completeness in the mathematical project but it’s often outside the areas of interest for mathematicians who are pursuing “big idea” problems whose solutions likely require development of entire new branches of mathematics. One famous example of such was Fermat’s Last Theorem.

They got into their field because they love the beauty of mathematics… As someone who isn't a mathematician, the main value I get out of math is its practical applications in science and technology

I have some sad news for you. 99% of the work mathematicians do has no immediate application, nor even an obvious path toward application in the near future. You mentioned cryptography, so for an example consider number theory: no apparent practical applications, going back thousands of years to the time of Euclid and earlier.

It’s been religion, philosophy, and recreation that have provided the motivations to study mathematics all these years, not applications. Applications have almost always followed long after the development of the pure mathematical theory. For number theory, that was the development of cryptography during WW2, millennia after the ancients laid those foundations.

Most unfortunately, it’s the truth value and the understanding which drive applications of mathematics, not the proof work itself. If the AI revolution decapitates the institution of mathematics which produces the understanding, and is unable to replace it, then the applications will cease as well.

Carbon dioxide is produced as a metabolic waste product from exercise. Any sort of fat-burning you want to do is limited by the rate at which you can exhale CO2. This is why vigorous exercise is accompanied by heavy breathing. This includes not only cardiovascular training but also weight training. Lifting heavy weights will have you breathing very hard!

Unfortunately, if you don’t lift heavy (or if you use electrical stimulation that’s mild enough to sleep) then you’re not going to put your muscles into hypertrophy, so you won’t gain muscle mass either.

And what happens if your zig app happens to be a network driver running on a microcontroller?

Adding pumps isn’t the same as adding battery storage. More batteries means more peak power. Peak power for hydro is limited by the peak power output of the turbines, not the dam capacity.

Overcast winter days tend to be very calm as well. These are periods of minimal solar+wind generation and maximal heating demand.

Having a grid with no baseload generation and only storage is going to spell disaster during extended cold+calm periods. Rolling blackouts when it’s -30C outside…

I don't know of they fail to see this because they are blinded by their hope or there is a more complex viewpoint I'm missing.

There is. "We want to escape" is a very different viewpoint from "we want to liberate the masses."

Freeing yourself from the social media is definitely doable. Depending on how firmly engaged you are at the moment, it can vary in difficulty between fait accompli and moderately challenging. It's obviously possible for anyone to do themselves.

Liberating the masses? Morpheus said it best:

"The Matrix is a system, Neo. That system is our enemy. But when you're inside, you look around, what do you see? Businessmen, teachers, lawyers, carpenters. The very minds of the people we are trying to save. But until we do, these people are still a part of that system and that makes them our enemy. You have to understand, most of these people are not ready to be unplugged. And many of them are so inured, so hopelessly dependent on the system, that they will fight to protect it."

We're talking about Ontario. I live in Ontario. The sky is overcast 8 months of the year. We're not building enough storage to charge for 4 months and drain for 8.

Doesn’t have to be a naked scam though. Dario could be caught in the dictator’s dilemma: he was a believer at first but now he’s on the tiger’s back so he dare not get off.

The positives aren’t there though, beyond what people are already using it for (pair programming aid, fancy auto complete, refactoring tool). Hence the article’s thesis: the doom justifies the valuation.

What else is there? The product as delivered today doesn't come anywhere near a justification for these valuations. All of it is built on an expectation of future capabilities, and that's where the Dario-penned doom papers come in.

Technically, it's the time discounted rate of future profits that determine valuations

Close, it's the time-discounted expectation of future returns. This seems related to future profits but it need not be. Historically, stocks tend to perform poorly after IPOs. There's no guarantee that (say) Anthropic's stock price would ever recover after a post-IPO drop.

The recent attempts by Anthropic et al. to circumvent the usual rules for inclusion in indices have raised red flags all over the place, with many calling it a naked attempt to raid everyone's pension funds for hundreds of billions in ill-gotten capital.

people at Anthropic (and OpenAI, for that matter!) really, genuinely do believe

The same could have been said (and has been said) about other tech company employees for all sorts of other reasons in alignment with those companies' goals. Don't you remember how much people used to laugh at Tesla employees for worshipping Elon Musk as some kind of god of engineering and entrepreneurial genius? Or Apple employees in the Steve Jobs reality distortion field?

I would have thought at this point that it'd be well known that the employees of all cult-like tech companies can't be trusted to make a sober evaluation of their companies' justified valuation. We can talk about conflicts of interest and we'd barely be getting started! How about biased selection by hiring managers for the most fervent believers in the company's mission from the get-go?