Any given computation either halts or it doesn't. You can encode that information in a single bit, as a specific number. Since there is a countably infinite number of possible computations, you'd need a countably infinite number of bits.
So you can never find enough storage to hold the full solution of the halting problem in the real world. But you can find enough storage in a real number. Because real numbers can have a countably infinite number of digits after the decimal point. So you can stuff your countably infinite number of bits representing the solution of the halting problem in there.
Which specific real number you get depends on the details of the encoding, but it's definitely some real number. And it cannot be computed, because if it could, you could read the solution to the halting problem off its digits, but the halting problem is known to be uncomputable.
Scaling laws mean that there's not much need to actually scale things to the skies. Instead, you can run a bunch of experiments at small scale, fit the scaling law parameters, then extrapolate. If the predicted outcome is disappointing (e.g. it's unlikely to beat the previous scaled-to-the-sky model), you can save the really expensive experiment for a more promising approach.
It would certainly be nice though if this kind of negative result was published more often instead of leaving people to guess why a seemingly useful innovation wasn't adopted in the end.
It's more likely that he gets pardoned after a few years. President Park Geun-Hye only served less than 4 years of her combined 32-year prison sentence.
The reality is that presidents (in almost every system), like MPs, are representatives of some faction of entrenched interests somewhere or another, or they wouldn’t get to be president.
It’s the same for dictators, and well pretty much any singular leader.
The factions may fight back and forth, and counting coup by imprisoning the figurehead for one of them certainly has some attraction - but the pendulum swings, and nobody wants to end up really getting punished at the end of the day when it swings away from them.
That’s how you get murderous resistance instead of (relatively) sane transfers of power.
Use of AI is based on self-reported data. From the paper:
> The respondents to the interviews are senior managers or financial directors with responsibility for investment decisions and how investments are financed – for example, the owner, chief financial officer or chief executive officer
> Firms are asked the following question: “To what extent, if at all, are big data analytics and artificial intelligence used within your business? A. Not used in the business. B. Used in parts of the business. C. Entire business
is organized around this technology.”
AI adoption is defined as the manager answering B or C.
I'm doubtful that this data is going to be very robust. Some senior tech managers are very keen to talk about AI, while at the same time knowing little about how much AI is actually being used by workers. At other companies you'll have people using free or personal ChatGPT accounts without the knowledge of management.
Also "big data" is not exactly AI.
The productivity information is robust as it's based on company accounts, albeit from 2024 so a couple of years out of date now.
Of note, "AI adoption" here means using "technologies that intelligently automate tasks and provide insights that augment human decision making, like machine learning, robotic process automation, natural language processing (NLP), algorithms, neural networks" and not just LLMs.
As far as I can tell "robotic process automation" mostly seems to be the deeply unglamorous process of building stuff to drive old applications that can't be given API access?
"A project to digitize Cistercian manuscripts at Western Michigan University is not requesting
the characters be in Unicode, so this is just an informational document. [...] We recommend the UTC make the following disposition: Notes this document (L2/20-290) but takes no further action."
For something to be added to Unicode, someone actually has to request it and shepherd it through the process.
So you can never find enough storage to hold the full solution of the halting problem in the real world. But you can find enough storage in a real number. Because real numbers can have a countably infinite number of digits after the decimal point. So you can stuff your countably infinite number of bits representing the solution of the halting problem in there.
Which specific real number you get depends on the details of the encoding, but it's definitely some real number. And it cannot be computed, because if it could, you could read the solution to the halting problem off its digits, but the halting problem is known to be uncomputable.
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