So then you say take someone else's clock and compare it to your own clock, but that is still just a pure number. A speed is not a number, it has units like meters per second. A ratio of two clocks has no units at all, the units cancel. Whatever number you get, 3 or 9, it's just a factor by which two clocks disagree. You can absolutely interpret this ratio as a rate, but that doesn't make it a speed.

And a speed is exactly what the slogan needs, because the diagram/geometry it's using involves a right angled triangle where on one side of the triangle is your speed through space, and on the other side of the triangle is your speed through time, and the hypotenuse of the triangle is fixed at c (since every object travels through spacetime at this fixed speed).

For that to mean anything both sides have to be the same kind of quantity. You can't put meters per second on one side and a bare number on the other and call it a triangle. Nor can you patch it by multiplying the ratio by c to give it units, because the thing you get then grows as you speed up instead of shrinking. Either it has the right units and the wrong behavior, or the right behavior and no units at all. There's no version of this geometry that produces a consistent picture.

Having said that... this is mostly a slogan and makes for good Youtube videos, but it falls apart the moment you subject it to even the most basic scrutiny. For one... it doesn't make sense to talk about a speed through time since speed is literally a measure of change with respect to time, so a change in time with respect to time doesn't make any sense.

But as a slogan, it captures the idea that motion through space and the rate of your own clock are tightly linked together.

For context that means a days worth of image generation emits about the same amount of carbon dioxide as a single transatlantic flight (New York to London). There are approximately 1500 transatlantic flights per day.

You really have to go out of your way to completely misrepresent what's being claimed here in order to make such a wildly off-topic reply.

Autoregressive LLMs generate tokens one at a time, disputing this is just plain wrong. What is true, however, is that in order to generate the next token autoregressive LLMs produce internal/hidden state about future tokens far past the next token so that it's not like the entire machinery of the algorithm deprives itself of representing where the sentence/text is headed.

So "emits the next token" and "has no representation of anything beyond the next token" are two different claims. What autoregressive LLMs cost as a consequence of strictly outputting the next token is commitment. Once a token is output there's no going back. There's no revision or means of correction, and sometimes this can lead an LLM to route around its own earlier mistakes or simply produce false statements/hallucinations instead of going back and fixing them.

[1] https://www.semanticscholar.org/paper/The-PageRank-Citation-...

Really what it means is that past the event horizon you can use the direction in space between you and the singularity as a way to measure time, specifically the amount of time left before you reach the singularity. It's not so mind blowing when you interpret it that way now is it? You can imagine many things in ordinary life that you use to measure time without claiming that time has literally swapped places with it. On a road trip, the number of kilometres to your exit tells you how long you have left, that's using space as a proxy for time... big deal. The notable difference between a road trip and a black hole is that on a road trip you could stop for a break, you could maybe take a detour, you could decide to go back home... and these would all break your use of space as a proxy for measuring time. Well with a blackhole you can't do any of those things, there is no going back, there is no detour, the relationship between the spatial direction towards the singularity and time is fixed and causal and there's nothing you can do about it.

The phrasing used is used almost certainly to evoke some kind of voodoo mind-blowing mystery that completely disappears when you get down to the more strict formalism.

Obviously some of this is for show, but even still it indicates people cared about having a very smooth and snappy user experience back then and that it was absolutely important to showcase performance. Somewhere along the way developers just quietly agreed that latency is the user's problem.

Another common scenario where this comes up and actually results in a great deal of confusion and misconceptions are hash maps, which are said to have a time complexity of O(1), but that does not mean that if you actually benchmark the performance of a hash map with respect to its size, that the graph will be flat or asymptotically approaches a constant value. Larger hash maps are slower to access than smaller hash maps because the O(1) isn't intended to be a claim about the overall performance of the hash map as a whole, but rather a claim about the average number of probe operations needed to lookup a value.

In fact, in the absolute purest form of time complexity analysis, where the operations involved are literally the transitions of a Turing machine, memory access is not assumed to be O(1) but rather O(n).

That's when services start to insert ads into their product.