You actually don't need to do that part in the algorithm. If you don't know the length of the list, you can just choose a threshold that seems reasonable and calculate the margin of error after you're done processing. (or i guess at whatever checkpoints you want if it's continuous)
In this example, they have the length of the list and choose the threshold to give them a desired margin of error.
It makes a lot of sense because obviously having a river there makes the transport of materials a lot easier, but i do wonder how nobody noticed this before.
An n-dimensional space is just a collection of points, each defined uniquely by a set of n-numbers. The semantic meaning of those numbers doesn't really matter. It might be like actual physical space, but it could just as well be something like "time" and "the price of big macs". We have a bunch of mathematical operations that work well on 2 or 3 dimensional space that correlate nicely with our physical intuitions of 'curvature' and 'holes', and that still work perfectly well in more generalized forms in higher dimensions.
I'm not really sure it's that useful to try and visualize what it means on higher dimensions, to be honest.
The letters you're referring to were written in 1753 and 1755, and has he got older, his views on race softened to the point that he was an outright abolitionist by the end of his life. In 1763 he wrote the following in a letter:
This is chiefly to acquaint you, that I have visited the Negro School here in Company with the Revd. Mr. Sturgeon and some others; and had the Children thoroughly examin’d. They appear’d all to have made considerable Progress in Reading for the Time they had respectively been in the School, and most of them answer’d readily and well the Questions of the Catechism; they behav’d very orderly, showd a proper Respect and ready Obedience to the Mistress, and seem’d very attentive to, and a good deal affected by, a serious Exhortation with which Mr. Sturgeon concluded our Visit. I was on the whole much pleas’d, and from what I then saw, have conceiv’d a higher Opinion of the natural Capacities of the black Race, than I had ever before entertained. Their Apprehension seems as quick, their Memory as strong, and their Docility in every Respect equal to that of white Children.1 You will wonder perhaps that I should ever doubt it, and I will not undertake to justify all my Prejudices, nor to account for them.
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I'm not sure that really that excuses being so racist that he thought _Germans_ weren't sufficiently white for america in his 50s, but he did change his views over time.
This is just a consequence of the inflation countermeasures working.
During the inflationary period, people were flush with cash, demand increased, there were shortages, everyone raised prices, profits surged, companies hired workers for higher wages, people got more money, etc.. Everyone was mad because they got big raises, which were obviously the result of all their hard work which corporations suddenly saw and appreciated for a large percentage of people all at once and _also_ "greedy corporations" suddenly en masse decided that they no longer wanted to be charitable enterprises and decided to raise prices to steal money from the pockets of hard working americans.
Or, you know, there was a bunch of inflation and wages and prices went up in parallel.
And now money is no longer flowing into the economy, some companies went too far raising prices anticipating more inflation, and now they're losing sales and that's hurting profits, and they're going to end up cutting prices to increase sales and maximize profits again.
Nature is healing.
I think a lot of people have the impression that inflation reduces how much stuff people can afford and generally it's fairly neutral in that respect. There's a certain amount of production and a certain amount of demand and in general it will balance out and no matter what's' going on with inflation people are gonna be able to afford the same amount of stuff. I think people had this idea that if we got inflation under control that suddenly everyone would be able to afford to buy all the stuff they wanted to buy, and they just can't.
The main reason inflation is bad for most people is instability and you have to keep getting raises to keep up with prices. You get a raise, you can suddenly buy some stuff you couldn't before -- prices go up and now you can't again. Then you get a raise, can afford to buy a bunch of stuff, and prices go up and now you can't again. (not to mention that toll it takes on saving, but even that isn't that bad if you own stock instead of holding cash, because asset prices inflate, also)
I read an article about the "unreasonable effectiveness of mathematics" that it was basically the result of a drunk looking for his keys under a lamp post because that's where the light is. We know how to use math to model parts of the world, and every where we look, there's _something_ we can model with math, but that doesn't mean that there's all there is to the universe. We could be understanding .0000001% of what's out there to understand, and it's the stuff that's amenable to mathematical analysis.
> Yes, absolutely. The US does not trust Tiktok because it is Chinese owned, or is it because of privacy concerns, or is it both?
Does it matter what the reason is? It's a foreign government owned media company operating in the US. The Chinese government doesn't have any rights in america. If the government wants to get rid of it, it can. China has nothing to stand on here. They don't even allow uncensored tik-tok in their own country, let alone facebook, etc.
by the time the rosetta stone was written, the literary language had drifted pretty far from spoken egyptian anyway, which was well on the way to becoming Coptic.
In a practical sense, how you define big O depends on what you consider to be the inputs to the function. If the runtime doesn't change depending on the size of the inputs that you care about, it's O(1).
Like, you might have a function with 2 inputs, N and M, and the run time is like O(m2^n), but n is fixed at a low number every time you'll run it in practice, so it's really just O(m) for your purposes.
The reason it can't do that is that, for example, "twenty" and "20" are nearly identical in the vector embedding space and it can't really distinguish them that well in most contexts. That's true for generally any task that relies on sort of "how the words look" vs "what the words mean". Any kind of meta request is going to be very difficult for an LLM, but a multi-modal GPT model should be able to handle it.
If tens of thousands (or really, even a handful) of people were dying from car crashes caused by, for example, brakes failing, then people would absolutely be attacking the manufacturer of the car. If you sell a feature that _does not work_ and it causes deaths, you should be held liable.
Probably the "it" is whatever one model has that other models don't have. When everyone is using the same architecture, then the data makes the difference. If everyone has the same data, then the architecture makes the difference.
It sounds pretty obvious to say that the difference is whatever is different, but isn't that literally what both sides of this argument are saying?
edit: I do think that what the original linked essay is saying is slightly subtler than that, which is that _given_ that everyone is using the same transformer architecture, the exact hyperparameters and fine tuning that is done matters a lot less than the data set does.