Incoming links: Personal computer
Consider this is a study in failed computational number theory.
The approximation converges really slowly, and we can't easy go far enough to see that the ration converges to 1 with only awk and primes:Runs in 30 minutes tested on Ubuntu 22.10 and P51, producing:
sudo apt intsall bsdgames
cd prime-number-theorem
./main.py 100000000
Linear vs approximation plot
. and are added to give a better sense of scale. is too close to 0 and not visible, and the approximation almost overlaps entirely with .
. It is clear that the difference diverges, albeit very slowly.
. We just don't have enough points to clearly see that it is converging to 1.0, the convergence truly is very slow. The logarithm integral approximation is much much better, but we can't calculate it in awk, sadface.
But looking at: en.wikipedia.org/wiki/File:Prime_number_theorem_ratio_convergence.svg we see that it takes way longer to get closer to 1, even at it is still not super close. Inspecting the code there we see:so OK, it is not something doable on a personal computer just like that.
(* Supplement with larger known PrimePi values that are too large for \
Mathematica to compute *)
LargePiPrime = {{10^13, 346065536839}, {10^14, 3204941750802}, {10^15,
29844570422669}, {10^16, 279238341033925}, {10^17,
2623557157654233}, {10^18, 24739954287740860}, {10^19,
234057667276344607}, {10^20, 2220819602560918840}, {10^21,
21127269486018731928}, {10^22, 201467286689315906290}, {10^23,
1925320391606803968923}, {10^24, 18435599767349200867866}};As of 2020's and earlier, humans were far far behind. As of 2020s and earlier, even an average personal computers without a GPU, the hallmark of deep learning beats every human.
Chess is just too easy!
As of the 2020's, a slumbering giant.
But the pre-Internet impact of IBM was insane! Including notably:
- some of the most important business computers of the pre-personal computer era
- SQL
- IBM Generalized Markup Language, which is a predecessor to XML and HTML
Open source driver/hardware interface specification??? E.g. on Ubuntu, a large part of the nastiest UI breaking bugs Ciro Santilli encountered over the years have been GPU related. Do you think that is a coincidence??? E.g. ubuntu 21.10 does not wake up from suspend.
Linus Torvalds saying "Nvidia Fuck You" (2012)
Source. How Nvidia Won Graphics Cards by Asianometry (2021)
Source. - Doom was the first killer app of personal computer 3D graphics! As opposed to professional rendering e.g. for CAD as was supported by Silicon Graphics
- youtu.be/TRZqE6H-dww?t=694 they bet on Direct3D
- youtu.be/TRZqE6H-dww?t=749 they wrote their own drivers. At the time, most drivers were written by the computer manufacturers. That's insane!
How Nvidia Won AI by Asianometry (2022)
Source. This company is a bit like Sun Microsystems, you can hear a note of awe in the voice of those who knew it at its peak. This was a bit before Ciro Santilli's awakening.
Both of them and Sun kind of died in the same way, unable to move from the workstation to the personal computer fast enough, and just got killed by the scale of competitors who did, notably Nvidia for graphics cards.
Some/all Nintendo 64 games were developed on it, e.g. it is well known that this was the case for Super Mario 64.
Also they were a big UNIX vendor, which is another kudos to the company.
Silicon Graphics Promo (1987)
Source. Highlights that this was one of the first widely available options for professional engineers/designers to do real-time 3D rendering for their designs. Presumably before it, you had to do use scripting to CPU render and do any changes incrementally by modifying the script.