kens

It would be nice if someone used AI and/or Lean to sort out the abc conjecture, an important unsolved problem in Diophantine analysis. A mathematician (Mochizuki) claimed to have proven it in 2012 using a new theory called "Inter-universal Teichmüller theory" that almost nobody understands. Some mathematicians think the proof is correct while the majority don't. So the conjecture is in this annoying limbo where its status is a social construct rather than a decided fact.

https://en.wikipedia.org/wiki/Abc_conjecture

Curiously, Eswatini (formerly Swaziland) is capitalized eSwatini, as if it is an e-commerce site.

Curious fact: France's longest border is with Brazil.

Most horrifying is a 2014 Science paper on Ebola with 58 authors, 5 of whom died of Ebola before publication. https://www.science.org/content/article/ebolas-heavy-toll-st...

Yes, even Rojas says, "From a practical perspective, and in the way the Z3 was really programmed, it was not equivalent to modern computers." https://www.researchgate.net/publication/3330654_How_to_make...

The argument that the Z3 is universal "was an impressive party trick, but diverged entirely from the way the machine was designed, how it was actually used, or indeed from anything that would have made sense in the 1940s."

Source: ENIAC in Action p255.

There are different ways of implementing core memory. The "traditional" way uses the inhibit line. The module I examined uses a "2½D" approach, which is what you originally pictured: separate current drivers for each bit and no inhibit line.

The Polaris ballistic missile computer, developed at the MIT Instrumentation Laboratory, was the predecessor to the Apollo Guidance Computer. It used germanium transistors along with magnetic core shift registers for memory. The Polaris computer used discrete three-input NOR gates, while the AGC used three-input NOR gates on integrated circuits. The book "Journey to the Moon" by Eldon Hall, creator of the AGC, has lots of details.

I assume you're interested in magnetic core logic computers in general, not specifically Parametrons. In the late 1950s, NASA considered core-transistor logic for a spacecraft navigation computer due to its lower power consumption. The prototype version of the Apollo Guidance Computer (1962) used core-transistor logic. But improvements in transistors made core-transistor logic less appealing, not to mention the arrival of ICs. At the end of 1962, NASA decided to use ICs for the Apollo Guidance Computer and abandoned core-transistor logic. The updated AGC kept the core memory and core rope ROM of the earlier AGC, though.

The main reason was the "inhibit recovery problem". The inhibit line required a large current that went through all the cores. This caused electrical noise, requiring a delay while the noise settled down. Doing away with the inhibit line thus helped performance. The drive lines are also shorter, which also helps performance.

The paper "2 1/2 D High Speed Memory Systems: Past, Present, and Future" explains this, but not entirely clearly: https://ieeexplore.ieee.org/document/4038821

Core memory is very resistant to radiation. When the Shuttle computers were upgraded to semiconductor memory, radiation became an issue. The solution was to add six extra bits of storage to each word and use ECC. A background process scanned for errors and corrected them. The computer could encounter 100 bit flips per flight, so radiation was significant. (There was even an incident where a single cosmic ray flipped 14 bits.) The other problem with semiconductor memory was its volatility, so the computer had NiCd batteries for backup power to the RAM.

For details on how radiation affected the Space Shuttle's computers, see this paper: https://klabs.org/DEI/Processor/shuttle/oneill_94.pdf

I've already written articles about the French computer and FRAM; enjoy :-) https://www.righto.com/2026/05/reverse-engineering-spacelab-... https://www.righto.com/2024/09/ramtron-ferroelectric-fram-di...

Author here for all your core memory questions...

One weird unit for angles is the mil, defined as 6400 mils in a circle. This unit is very useful for artillery, since 1 meter displacement at a distance of 1 km is 1 mil [†]. Thus, you can see how much you missed by, divide by the distance, and easily determine how much you need to adjust your aim in mils. Another interesting thing about artillery is they traditionally do a binary search to get the distance correct, which they call "bracketing". Link: https://unitedtaskforce.net/training/sop/communication/artil...

[†] Note that this isn't exactly correct since it corresponds to pi = 3.2. A mil is almost the same as a milliradian, but 6400 mils in a circle is much more convenient than 6283.18... milliradians in a circle.

The history of computing is usually described as a nice progression from vacuum tubes to transistors and then ICs. But parametrons are only one of the many forgotten technologies that popped up along the way. Magnetic core logic such as transfluxors was used in several computers. Superconducting cryotrons were going to revolutionize computers. Tunnel-diode logic was also briefly the wave of the future. Other significant technologies were microwave logic circuits and electroluminescent logic circuits. I have to say that the 1950s came up with the best names; modern technologies just don't measure up to transfluxors, parametrons, and cryotrons.

See Digital Computer Design Fundamentals, 1962, chapter 6.

I wrote an article on the history of magnetic amplifiers: https://spectrum.ieee.org/the-vacuum-tubes-forgotten-rival

The quick summary is that magnetic amplifiers started in the US in 1901, but Germany came up with much better magnetic alloys during World War II. This led to a post-war boom in mag amps, which were used in industrial control, aerospace, and computers such as the Univac Solid State. These magnetic materials also led to core memory. Transistors mostly killed off mag amps, although PC power supplies used them into the 1990s.

I'm too busy trying to reverse-engineer the Intel 8087 floating-point chip, although it would be interesting to look at this puzzle chip.

Thanks for filling in the details! I figured that I was already going into too much history in my article :-)

Cute, but the steps don't make sense. E.g. each cycle shows both an ion gun and wire deposition. But only the first layer would use the ion gun, and only the following layers would have metal deposited. (Front End of Line vs Back End of Line). Not to mention the lack of diffusion and oxidation. The whole "loop" metaphor gives the wrong idea of what's happening.

Author here. I've powered up another tube module from the IBM 604, so let me know if you have questions...

It's kind of hopeless to try to prove that a microprocessor works according to spec, since you're dealing with physical objects in the real world. For instance, early versions of Intel's 386 processor had a 32-bit multiply problem that only showed up in some chips under particular combinations of temperature, voltage, and frequency, probably due to a transistor that wasn't large enough to provide an electrical margin under worst-case conditions.

Serious question: does Figure 1 in the article make sense to anyone? If you understand the symbols, do you look at the diagram and it's clear how logistics works?

The short answer is the "14-day" rule, which doesn't allow development of the embryo beyond 14 days. The article gives specifics under the heading "Ethical and legal compliance"

Oops, I've fixed that now.

It's unlikely that you'd get a simultaneous tie; you'd expect one computer to go bad before the other. But I think in that case, the astronauts switch to the Backup Flight System, the fifth computer.

Mission STS-9 had two computer failures, causing landing to be delayed by 7 3/4 hours. They carried a sixth computer as a backup for following missions.

As far as how the voting works, each computer has a signal indicating what it thinks the status is of each computer, including itself. (Computers can detect many failures from self-checking, such as parity errors.) Each IOP uses these votes to determine the "redundant set", calculating the votes in hardware. The status is also displayed to the astronauts in a 5×5 grid. Astronauts can power down a computer or reboot it.

There have been a fair number of GPC failures [1], and computers have been voted out. I haven't looked closely enough to see how many were "disagreements" versus hard failures or self-check failures.

[1] Search for "GPC" in the Mission Summary report: https://newspaceeconomy.ca/wp-content/uploads/2023/05/space-...

Sorry, I don't know anything secret :-)

I don't know if these boards were flown. They were coated with conformal coating (which I hate for reverse-engineering), which is usually omitted from prototypes. I believe that bodge wires are okay for flight if they are done properly.

Yes, the low density and TTL chips (instead of MOS) helped against radiation. When the Shuttle computers moved to semiconductor RAM, they needed extensive error correction, as well as a process that constantly fixed bit errors, as the memory would get multiple errors per flight due to cosmic rays.

As far as redundancy, it's complicated. During critical flight phases, four computers would run the main software (PASS, Primary Avionics Software System), while the fifth computer was ready with the Backup Flight Software (BFS). The backup software was written by a completely different team to ensure that a software bug couldn't crash all the computers at once. In orbit, they used fewer redundant computers to free up computers for payload operations and stuff.

The four computers constantly checked the results from each other and would vote out a faulty system. Voting ensured that a bad computer couldn't vote out the good ones (Byzantine failure). Moreover, the actuators hydraulically voted on the results from the computers: if one computer tried to push a valve in a different direction, the three good computers would physically overpower the bad computer's action at the level of the hydraulic pistons.

Author here if you have questions...