Apollo 11 vs. USB-C Chargers (2020)(forrestheller.com) |
Apollo 11 vs. USB-C Chargers (2020)(forrestheller.com) |
Analog computers don't get the respect they deserve. There's one more computer, the FCC. The Flight Control Computer is an analog computer in the Saturn V that controlled the rocket gimbals. It's a two-foot cylinder weighing almost 100 pounds.
the only reason they have the same name is that they were both originally built to replace people cranking out calculations on mechanical desk calculators, who were also called 'computers'
the flight control 'computer' has more in common with an analog synthesizer module than it does with a cray-1, the agc, an arduino, this laptop, or these chargers, which are by comparison almost indistinguishable
ENIAC, for example, was not a stored-program computer. Reprogramming required rewiring the machine.
On the other hand, by clever use of arithmetic calculations, https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.37.... says the Z3 could perform as a Universal Computer, even though, quoting its Wikipedia page, "because it lacked conditional branching, the Z3 only meets this definition by speculatively computing all possible outcomes of a calculation."
Which makes me think the old punched card mechanical tabulators could also be rigged up as a universal machine, were someone clever enough.
"Surprisingly Turing-Complete" or "Accidentally Turing Complete" is a thing, after all, and https://gwern.net/turing-complete includes a bunch of them.
If we could optimize a set of programs down to the FPGA bitstream or even Verilog level, that would approach the kind of programs analog computers run.
I can't tell anything about Turing completeness though. It's a fully discrete concept, and analog computers operate in the continuous signal domain.
Turing completeness is a tar pit that makes your code hard to analyse and optimise. It's an interesting challenge to find languages that allow meaningful and useful computation that are not Turing complete. Regular expressions and SQL-style relational algebra (but not Perl-style regular expressions nor most real-world SQL dialects) are examples familiar to many programmers.
Programming languages like Agda and Idris that require that you prove that your programs terminate [0] are another interesting example, less familiar to people.
[0] It's slightly more sophisticated than this: you can also write event-loops that go on forever, but you have to prove that your program does some new IO after a finite amount of time. (Everything oversimplified here.)
> The Flight Control Computer (FCC) was an entirely analog signal processing device, using relays controlled by the Saturn V Switch Selector Unit to manage internal redundancy and filter bank selection. The FCC contained multiple redundant signal processing paths in a triplex configuration that could switch to a standby channel in the event of a primary channel comparison failure. The flight control computer implemented basic proportional-derivative feedback for thrust vector control during powered flight, and also contained phase plane logic for control of the S-IVB auxiliary propulsion system (APS).
> For powered flight, the FCC implemented the control law $ \beta_c = a_0 H_0(s) \theta_e + a_1 H_1(s) \dot{\theta} $ where $ a_0 $ and $ a_1 $ are the proportional and derivative gains, and $ H_0(s) $ are the continuous-time transfer functions of the attitude and attitude rate channel structural bending filters, respectively. In the Saturn V configuration, the gains $ a_0 $ and $ a_1 $ were not scheduled; a discrete gain switch occurred. The Saturn V FCC also implemented an electronic thrust vector cant functionality using a ramp generator that vectored the S-IC engines outboard approximately 2 degrees beginning at 20 seconds following liftoff, in order to mitigate thrust vector misalignment sensitivity.
https://ntrs.nasa.gov/api/citations/20200002830/downloads/20...
Who said women can't do math?
https://www.smithsonianmag.com/science-nature/history-human-...
Asimov.
https://literature.stackexchange.com/questions/25852/where-d...
The straw man?
Nobody
The software (and hardware) of the Apollo missions was very well-engineered. We all know computation became ridiculously more powerful in the meantime, but that wouldn't make it easy to do the same nowadays. More performance doesn't render the need for good engineering obsolete (even though some seem to heavily lean on that premise).
If I recall correctly this was one of the areas being explored by the mars drone although not sure if Mars surface radiation concerns are different than what you would use in space.
> The flight software is written in C/C++ and runs in the x86 environment. For each calculation/decision, the "flight string" compares the results from both cores. If there is a inconsistency, the string is bad and doesn't send any commands. If both cores return the same response, the string sends the command to the various microcontrollers on the rocket that control things like the engines and grid fins.
This is a very minor point... but three of something isn't triple redundancy: it's double redundancy. Two is single redundancy, one is no redundancy.
Unless the voting mechanism can somehow produce a correct answer from differing answers from all three implementations of the logic, I don't understand how it could be considered triply redundant. Is the voting mechanism itself functionally a fourth implementation?
The LVDC was a highly redundant can not fail design. the AGC had no redundancy and was designed to recover quickly if failure occurred.
Today it's even more the case. You have fully programmable CPUs in your keyboard, trackpad, mouse, all usb devices, etc.
Wild to think the thing that charges my devices could be programmed to put a human on the moon
I didn't know that was just for the LVDC.
> emulate this voting scheme with 3x microcontrollers with a 4th to tally votes will not make the system any more reliable
I think that's clear enough; the vote-tallier becomes a SPOF. I'm not sure how Tandem and Stratus handled discrepancies between their (twin) processors. Stratus used a pair of OTC 68K processors, which doesn't seem to mean voting; I can't see how you'd resolve a disagreement between just two voters.
I can't see how you make a voting-based "reliable" processor from OTC CPU chips; I imagine it would require each CPU to observe the outputs of the other two, and tell itself to stop voting if it loses a ballot. Which sounds to me like custom CPU hardware.
Any external hardware for comparing votes, telling a CPU to stop voting, and routing the vote-winning output, amounts to a vote-tallier, which is a SPOF. You could have three vote-talliers, checking up on one-another; but then you'd need a vote-tallier-tallier. It's turtles from then on down.
In general, having multiple CPUs voting as a way of improving reliability seems fraught, because it increases complexity, which reduces reliability.
Maybe making reliable processors amounts to just making processors that you can rely on.
Tell them both to run the calculation again, perhaps?
Apollo 11 Guidance Computer vs. USB-C Chargers - https://news.ycombinator.com/item?id=22254719 - Feb 2020 (205 comments)
> IBM estimated in 1996 that one error per month per 256 MiB of RAM was expected for a desktop computer.
https://web.archive.org/web/20111202020146/https://www.newsc...
It will. Not too long and not very reliable, but will.
From history of space rockets, they was definitely first created as "two purpose" (except, may Vanguard, which was totally civilian program), so their electronics considered possible radiation from nuclear war, but fortunately, in space found natural radiation, but slightly other type (spectrum). Currently, SpaceX just use industrial grade computers on rockets (not RAD hardened).
Well, look at tech details: for RAD digital electronics exists two types of problems.
1. Random spikes (switches) from high energy charged particles. Unfortunately, only Military RAD grade parts have integrated safety mechanisms, for Civ/Industry grades, could make shield with EM field and thick layer of protecting material, like Lead or even Uranium. When thyristor effect happen, need to power circle (turn off/on and boot), and this is risks source for mission, but most probably, it will withstand flight to Moon.
2. Aging of semiconductor structure from constant flow of particles with high penetration - basically it is just high speed diffusion, which destroy semiconductor structures. But for Earth-Moon environment, this is issue for long term operations (months or even years).
So, will work.
Previously calculators were a room full of people, all of which required food, shelter, clothing and ... oxygen.
The Apollo program consumed something like half of the United States’ entire IC fabrication capacity for a few years.
https://www.bbc.com/future/article/20230516-apollo-how-moon-...
The amazing thing is that they did manage to make it fit into 2 ft³, even though the integrated circuits it used had not yet been invented when the contract was written.
8KB of RAM! But hundreds of pounds vs 70lb for the AGC with fairly comparable capability (richer instructions/registers, lower initial clock rate).
The AGC was quite impressive in terms of perf/weight
TBH, it's kind of amazing that a custom computer from 50 years ago has the specs of a common IC/SoC today, but those specs scale with time.
Back then, consumers got nothing, governments got largge computers (room sized+), then consumers got microcomputers (desktop sized), governments got larger mainframes, consumers got PCs, government got big-box supercomputers,...
And now? Consumers get x86_64 servers, governments get x86_64 servers, and the only difference is how much money you have, how many servers can you buy and how much space, energy and cooling you need to run them.
well, "normal users" get laptops and smartphones, but geek-consumers buy servers... and yeah, I know arm is an alternative.
I wish more people understood this, and could better see the coming crisis.
AFAIK, this is typical of USB controller chips, which generally have about 20-30 I/O pins, but I’m sure there are outliers.
The AGC seems to have four 16-bit input registers, and five 16-bit output registers[2], for a total of 144 I/O pins total.
[1] https://ta.infinity-component.com/datasheet/9c-CYPD4126-40LQ...
[2] https://en.wikipedia.org/wiki/Apollo_Guidance_Computer#Other...
What I find more interesting is to compare how complicated the tech we don’t think about has become. It’s amazing that a cable, not a smart device or even 80s digital watch, but a literal cable, has as much technology packed into it as Apollo 11 and we don’t even notice.
Playing devils advocate for your comment, one of the (admittedly many) reasons going to the moon is harder than charging a USB device is because there are not off-the-shelf parts for space travel. If you had to build your USB charger from scratch (including defining the USB specification for the first time) each time you needed to charge your phone, I bet people would quickly talk about USB cables as a “hard problem” too.
That is the biggest takeaway we should get from articles like this. Not that Apollo 11 wasn’t a hugely impressive feat of engineering. But that there is an enormous amount of engineering in our every day lives that is mass produced and we don’t even notice.
A simple looking object, but in reality it had a lot o tought put in to get to this form.
It also goes along the lines of "Simplicity is complicated"[1].
[0] - https://www.youtube.com/watch?v=XwUkbGHFAhs
[1] - https://go.dev/talks/2015/simplicity-is-complicated.slide#1
Otherwise, I completely agree.
I think this is the whole point of articles like this. I don’t think it’s sensationalist at all to compare older tech with newer and discuss how engineers did more with less.
Sure they had and often still have, it's called wetware.
>so computation power is not the single deciding factor on the performance and success of such an endeavor
The endeavor to charge a phone?
Water less so.
Plenty of engineers on the ground had no computers, and the privileged ones who did had mainframes, not personal at all.
A computer was too valuable to be employed doing anything that didn't absolutely need a computer, most useful for precision or speed of calculation.
But look what happens when you give something like a mainframe to somebody who is naturally good at aerospace when using a slide rule to begin with.
With a large enough lithium battery, a charger can easily take you part of the way there.
https://www.quora.com/Could-the-Apollo-Guidance-Computer-hav...:
“P64. At about 7,000 feet altitude (a point known as “high gate”), the computer switched automatically to P64. The computer was still doing all the flying, and steered the LM toward its landing target. However, the Commander could look at the landing site, and if he didn’t like it, could pick a different target and the computer would alter its course and steer toward that target.
At this point, they were to use one of three programs to complete the landing:
P66. This was the program that was actually used for all six lunar landings. A few hundred feet above the surface the Commander told the computer to switch to P66. This is what was commonly known as “manual mode”, although it wasn’t really. In this mode, the Commander steered the LM by telling the computer what he wanted to do, and the computer made it happen. This continued through landing.
P65. Here’s the automatic mode you asked about. If the computer remained in P64 until it was about 150 feet above the surface, then the computer automatically switched to P65, which took the LM all the way to the surface under computer control. The problem is that the computer had no way to look for obstacles or tell how level its target landing site was. On every flight, the Commander wanted to choose a different spot than where the computer was taking the LM, and so the Commander switched to P66 before the computer automatically switched to P65. [Update: The code for P65 was removed from the AGC on later flights. The programmers needed memory for additional code elsewhere, and the AGC was so memory-constrained that adding code one place meant removing something else. By that point it was obvious that none of the crews was ever going to use the automatic landing mode, so P65 was removed.]
P67. This is full-on honest-to-goodness manual mode. In P66, even though the pilot is steering, the computer is still in the loop. In P67, the computer is totally disengaged. It is still providing data, such as altitude and descent rate, but has no control over the vehicle.”
https://www.petervis.com/Vintage%20Chips/PowerPC%20750/RAD75...
The next generation (at least according to NASA) will be RISC-V variants:
https://www.zdnet.com/article/nasa-has-chosen-these-cpus-to-...
[1] Example: https://www.militaryaerospace.com/computers/article/16726923...
[2] Example: https://xiphos.com/product-details/q8
The reason why the controls of Dragon and Orion look the way they do is that they are no far off from modern digital cockpits of jets like the F-22 and F-35 and everyone is used to graphical interfaces and touch controls.
Having non intuitive interfaces that go against the bias astronauts and later on civilian contractors already have by using such interfaces over the past 2 decades will be detrimental to overall mission success.
The other reason for why they’ll opt to use commodity hardware is that if we are going back to space for real now you need to be able to build and deploy systems at an ever increasing pace.
We have enough powerful human safety rated hardware from aerospace and automotive there is no need to dig up relics.
And lastly you’ll be hard pressed to find people who still know how to work with such legacy hardware at scale and unless we will drastically change the curriculum of computer science degrees around the US and the world that list would only get smaller each year. We’re far more likely to see ARM and RISC-V in space than z80’s.
Kermit and xmodem probably aren't what you want to use, they are actually a higher level than what is normally used and would require a big overhead, if they even worked at all with latencies that can reach 5-10s. Search for the keyword "CCSDS" to get hints about data protocols used in space.
Here's kermit in space ... coincidentally in a 20 year old article. Software I wrote supported diagnosing kermit errors.
https://www.spacedaily.com/news/iss-03zq.html
I guess now I'm old.
[1] https://www.zdnet.com/article/nasa-has-chosen-these-cpus-to-... [2] https://www.nasa.gov/news-release/nasa-awards-next-generatio...
They've got their own chips and protocols going back just as far, like https://en.wikipedia.org/wiki/MIL-STD-1553
If course, from a certain point of view, they're many of the same people and money.
But the juiciest engineering challenges involve figuring out business logic / mission decisions. This is done increasingly in software while the other disciplines increasingly make only the interfaces.
https://www.dailymail.co.uk/news/article-524390/The-women-ad...
Granted, that same search will show you many examples of content accusing unnamed other people of having this attitude.
https://www.science.org/content/article/both-genders-think-w...
It’s an antiquated notion in my mind, but I don’t think it is a thing of the past.
Women being bad at advanced math would make sense as an antiquated notion, but those in charge of hiring decisions until about 50 years ago evidently thought women were great at basic math.
The study you linked showing that women lag behind men in math to a degree proportional to some gender disparity metric is also interesting, but doesn't really tell us how we got here.
The Space Shuttle Avionics System top level documentation specifically calls out having "no Z80's, 8086s, 68000's, etc."
https://ntrs.nasa.gov/api/citations/19900015844/downloads/19...
And also, sigh, to demonstrate once again that when I worked in space it was 20 years ago, https://www.nytimes.com/2002/05/12/us/for-parts-nasa-boldly-... (https://web.archive.org/web/20230607141742/https://www.nytim...)
Knowing how 8086 timing and interrupts worked was still important for what I was doing in the early 2000s. I don't pretend to remember any of it these days.
There is still active research in the area, eg. https://www.lix.polytechnique.fr/~bournez/i.php?n=Main.Publi...
you can't simulate an 11-integrator general-purpose analog computer or other differential analyzer with a 10-integrator differential analyzer, and you can't simulate a differential analyzer with 0.1% error on a (more typical) differential analyzer with 1% error, unless it's 100× as large (assuming the error is gaussian)
the ongoing research in the area is of course very interesting but a lot of it relies on an abstraction of the actual differential-analyzer problem in which precision is infinite and error is zero
probably numerous eddies in natural turbulent fluid flows have been digital turing-complete computers, given what we know now about the complexity of turbulence and the potential simplicity of turing-complete behavior. but is there an objective, rather than subjective, way to define this? how complicated are our input-preparation and output-interpretation procedures allowed to be? if there is no limit, then any stone or grain of sand will appear to be turing-complete
a quibble: the eniac was eventually augmented to support stored-program operation but not, as i understand it, until after the ias machine (the johnniac) was already operational
another interesting question there is how much human intervention we permit; the ias machine and the eniac were constantly breaking down and requiring repairs, after all, and wouldn't have been capable of much computation without constant human attention. suppose we find that there is a particular traditional card game in which players can use arbitrarily large numbers. if the players decide to simulate minsky's two-counter machine, surely the players are turing-complete; is the game? are the previous games also turing-complete, the ones where they did not make that decision? does it matter if there happens to be a particular state of the cards which obligates them to simulate a two-counter machine?
if instead of attempting to measure the historical internal computational capability of systems that the humans could not perceive at the time, such as thunderstorms and the z3, we use the subjective standard of what people actually programmed to perform universal computation, then the ias machine or one of its contemporaries was the first turing-complete computer (if given enough memory); that's when universal computation first made its effects on human society felt
Sure. One of the "Surprisingly Turing-Complete" examples is that "Magic: the Gathering: not just TC, but above arithmetic in the hierarchy ".
See https://arxiv.org/abs/1904.09828 for the preprint "Magic: The Gathering is Turing Complete", https://arstechnica.com/science/2019/06/its-possible-to-buil... for an Ars Technica article, and https://hn.algolia.com/?q=magic+turing for the many HN submissions on that result.
but then we have to ask thorny ontological questions: does a card game count if it requires a particular configuration to be turing-complete, but nobody ever played it in that configuration? what if nobody ever played the game at all? what if nobody even knew the rules?
I have no idea if people still use ARINC-429 or IRIG-B. Embedded RTOS was all proprietary back then for instance, like with VXWORKS. I'm sure it's not any more. I hated vxworks.
But at least for the components we're developing, we have basically standardized on ARM, the TMS570 specifically since it offers a number of features for safety critical systems, and simplifies our tooling and safety analysis to use the same processor everywhere.
Z80 is pretty retro, and while I'm sure there may be some vendors who still use it, it's got to be getting pretty rare for new designs, between all the PowerPC, Arm, and now RISC-V processors available that allow you to use modern toolchains and so on, I'd be surprised if many people were doing new designs with the Z80
The conclusion of that study was that parallel development mainly accomplishes a false sense of security, and most of the additional reliability in those projects came from other sound engineering techniques. But I have lost the reference, so I don't know how much credibility to lend my memory.
Leveson also wrote the report on Therac 25.
Searched "run linux on hard drive without cpu or ram" on Google - third result.
What do you expect US government to do with lots of computing power? I wouldn’t expect military to need supercomputers. Maybe the NSA would have a lot for cracking something or surveillance. But the big tech companies have more.
Because the government isn't building them. They are Cray supercomputers, supplied by HPE. Not entirely built with standard parts. Proprietary interconnect and cooling system.
High scale is about using commodity components (hundreds of) thousands of times.
Unless you typically salvage digital computers from the wreckage of a failed rocket test and stick it in the next prototype. If the FCC is wrong, kaboom.
Much less than “rebuilding”.
There have been some hybrids too.
do you want to call them all 'computers' now?
When the arithmetic circuits, i.e. the "central arithmetical part", as called by von Neumann, are coupled with a "central control part", as called by von Neumann, i.e. with a sequencer that is connected in a feedback loop with the arithmetic part, so that the computation results can modify the sequence of computations, then this device must be named as a "computer", regardless whether the computations are done with analog circuits or with digital circuits.
What defines a computer (according to the definition already given by von Neumann, which is the right definition in my opinion) is closing the feedback loop between the arithmetic part and the control part, which raises the order of the system in comparison with a simple finite state automaton, not how those parts are implemented.
The control part must be discrete, i.e. digital, but the arithmetic part can be completely analog. Closing the feedback loop, i.e. the conditional jumps executed by the control part, can be done with analog comparators that provide the predicates tested by the conditional jumps. The state of an analog arithmetic part uses capacitors, inductors or analog integrators, instead of digital registers.
Several decades ago, I had to debug an analog computer during its installation process, before functioning for the first time. That was in a metallurgic plant, and the analog computer provided outputs that controlled the torques of a group of multi-megawatt DC electric motors. The formulae used in the analog computations were very complex, with a large number of adders, multipliers, integrators, square root circuits and so on, which combined inputs from many sensors.
That analog computer (made with op amps) performed a sequence of computations much more complex than the algorithms that were executed on an Intel 8080, which controlled various on-off execution elements of the system, like relays and hydraulic valves and the induction motors that powered some pumps.
The main reason why such analog computers have become obsolete is the difficulty of ensuring that the accuracy of their computations will not change due to aging and due to temperature variations. Making analog computers that are insensitive to aging and temperature raises their cost much above modern digital microcontrollers.
you can even include multiplexors in your analog 'computer', even with only adders and multipliers and constants; x · (1 + -1 · y) + z · y interpolates between x and z under the control of y, so that its output is conditionally either x or z (or some intermediate state). but once you start including feedback to push y out of that intermediate zone, you've built a flip-flop, and you're well on your way to building a digital control unit (one you could probably build more easily out of transistors rather than op-amps). and surely before long you can call it a digital computer, though one that is controlling precision linear analog circuitry
it is very commonly the case that analog computation is much, much faster than digital computation; even today, with microprocessors a hundred thousand times faster than an 8080 and fpgas that are faster still, if you're doing submillimeter computation you're going to have to do your front-end filtering, upconversion or downconversion, and probably even detection in the analog domain
By doing so, you get to make a point—perhaps via analogy, perhaps via precision, perhaps via pedantry—which is illuminating for you but now confusing for your reader. And to explain yourself, you must swim upstream and redefine a term while simultaneously making a different point altogether.
Much has been written about jargon, but a primary benefit of jargon is the chance to create a domain-specific meaning without the baggage of dictionary-correct associations. It’s also why geeks can be bores at dinner parties.
By analogy to HCI: words are affordances. Affordances exist because of familiarity. Don’t make a doorknob that you push on, and expect people not to write in telling you to use a door-bar on that door instead.
Unilaterally changing language is not forbidden, but if The Culture Wars™ has thought us anything, it is that people are allergic to talking about what they see as mandated changes to their language, even if it is reasonable and you can explain it.
Colour me stoked, but you could still just do it unilaterally and wait till somebody notices.
However my caveat with viewing everything as computation is that you fall into the same trap as people in the ~1850s did when they wanted to describe everything in the world using complex mechanical devices, because that was the bleeding edge back then. Not everything is an intricate system of pulleys and levers it turned out, even if theoretically you could mimic everything if that system was just complex enough.
(Also to protect against physical failures it works, because physical failures are more independent than software ones, as far as I understand.)
https://arxiv.org/pdf/2008.08886.pdf
The cooling system is also proprietary to HPE. Not saying that other vendors don't offer their own liquid cooling systems.
An HN comment search, https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu... , finds a few more lay examples, with https://news.ycombinator.com/item?id=21210043 by dwohnitmok being the easiest for me to somewhat make sense of.
I think the idea is, suppose you have an oracle which tells you if a Turning machine will halt, in finite time. There will still halting problems for that oracle system, which requires an oracle from a higher level system. (That is how I interpret "an oracle that magically gives you the answer to the halting problem for a lower number of interleavings will have its own halting problem it cannot decide in higher numbers of interleavings").
https://risingentropy.com/the-arithmetic-hierarchy-and-compu...
The closest I could find - with your search query - was #6, and it’s a Reddit conversation that contains this link. I don’t usually click on Reddit links.
If you use DDG it’s nowhere to be found.
given these hypothetical abilities, you can of course simulate a two-counter machine, but a bigger question is whether you can compute anything a turing machine cannot; after all, in a sense you are doing an infinite amount of computation in every finite interval of time, so maybe you could do things like compute whether a turing machine will halt in finite time. so far the results seem to support the contrary hypothesis, that extending computation into continuous time and continuously variable quantities in this way does not actually grant you any additional computational power!
this is all very interesting but obviously not a useful description of analog computation devices that are actually physically realizable by any technology we can now imagine
> Prior to this work, no undecidable real games were known to exist. Demaine and Hearn (2009) [10] note that almost every real-world game is trivially decidable, as they produce game trees with only computable paths. They further note that Rengo Kriegspiel {Rengo Kriegspiel is a combination of two variations on Go: Rengo, in which two players play on a team alternating turns, and Shadow Go, in which players are only able to see their own moves.} is “a game humans play that is not obviously decidable; we are not aware of any other such game.” It is conjectured by Auger and Teytaud (2012) [1] that Rengo Kriegspiel is in fact undecidable, and it is posed as an open problem to demonstrate any real game that is undecidable.
> The approach of embedding a Turing machine inside a game directly is generally not considered to be feasible for real-world games [10].
Regarding your ontological question, that we don't know if something is Turning complete doesn't mean it isn't.
People explored the Game of Life before it was proven to be Turing complete. The 1970 SciAm article says "Conway conjectures that no pattern can grow without limit." so Martin and Gardner didn't even know about gliders then. People don't say GoL wasn't Turning complete in 1970.
I pointed to a 1998 paper claiming the Z3 machine from the 1940s was Turing complete, that author clearly believes that a particular physical configuration is not required.
Nor did Turing construct a physical representation for his paper.
FWIW, the MtG preprint gives a concrete example of a 60-card initial deck. I would be surprised if neither the authors nor anyone else has ever tried it.
The ontological question is even more fully resolved because no one has ever created a real Turing machine. We always have the proviso "if given enough memory".
Similarly, the video game "Minesweeper" is NP-complete as the size increases, and with an infinite board - clearly not physically realizable - is Turing complete. https://en.wikipedia.org/wiki/Minesweeper_(video_game)#Compu...
well, maybe one thing: if it doesn't matter whether anyone played the game or knew the rules, then magic: the gathering was turing-complete before the first magic deck was printed, before the first human was born, before the first star was formed, perhaps before the big bang
If you go down that route you'll realize there are an uncountable number of games that have never been created, and will never be created, which are Turing-complete.
And start wondering if mathematics is created or discovered.
https://en.wikipedia.org/wiki/Core_rope_memory input wires were energized, and they were coupled (or not) to the output wires depending on if they shared a magnetic ring (or not).
Do you have a source for that? Everything I've ever read about Airbus says the various flight control systems are doubly redundant (three units). Twelve sounds like it would be far beyond diminishing returns...
https://www.rightattitudes.com/2020/04/06/airbus-flight-cont...
I'd imagine every computer relies on redundant stick/pedal encoders, which is how a 12-way notion appeared.
> I'd imagine every computer relies on redundant stick/pedal encoders, which is how a 12-way notion appeared.
That's disingenuous at best. The lug nuts on my car aren't 20x redundant... if you randomly loosen four, catastrophic failure is possible.
It’s a more solid 3x or 3x+3y, which… if you had a power failure at a chip doesn’t take a 6x to make it 5x. It makes it 4x with the two remaining PHY units because two logical cores went down with one error.
The x being physical units, and the y being CPUs in lockstep so that the software is confirmed to not bug out somewhere.
It’s 6x for the calculated code portion only, but 3x for CPU and 1-3x for power or solder or circuit board.
I know it’s pretty pedantic, but I would call it the lowest form for any quality, which is likely 2-3x.
That's the reason I sometime see that for RAID systems, it is recommended to avoid buying all same disks at the same time, because since they will be used in the same way in the same environment, there is a good chance for them to fail at the same time, defeating the point of a redundant system.
Also, to guard against bugs and design problems, critical software is sometimes developed twice or maybe more by separate teams using different methods. So you may have several combinations of software and hardware. You may also have redundant boards in the same box, and also redundant boxes
>> The microcontrollers, running on PowerPC processors, received three commands from the three flight strings. They act as a judge to choose the correct course of actions. If all three strings are in agreement the microcontroller executes the command, but if 1 of the 3 is bad, it will go with the strings that have previously been correct.
This is a variation of Byzantine Tolerant Concensus, with a tie-braker to guarantee progress in case of absent voter.
I was taken to task for mis-spelling "consensus"; I used to spell it with two 'c's and two 's's, like you. It was explained to me that it's from the same root as "consent", and that's how I remember the right spelling now.
I agree that this kind of "analog computers" does not deserve the name of "computer", because they are equivalent only with the "registers + ALU" (RALU) simple automaton that is a component of a CPU.
Nevertheless, there is no reason why a digital control part cannot be coupled with an analog arithmetic part and there have existed such "analog computers", even if they have been rarely used, due to high cost and complexity.
It is not completely unlikely that such "analog computers", consisting of a digital control part and an analog arithmetic part, could be revived with the purpose of implementing low-resolution high-speed machine learning inference.
Even now, in circuits like analog-digital converters, there may be analog computing circuits, like switched-capacitor filters, which are reconfigurable by the digital controller of the ADC, based on various criteria, which may depend on the digital output of the converter or on the outputs of some analog comparators (which may detect e.g. the range of the input).
this is sort of like how biologists try to convince people to stop calling jellyfish 'jellyfish' and starfish 'starfish' because they aren't fish. the difference is that it's unlikely that someone will get confused about what a jellyfish is because they have so much information about jellyfish already
my quest to get people to call cellphones 'hand computers' is motivated by the same values but is probably much more doomed
Sometimes it has been applied to the kind of computers mentioned by me, with a digital control part and a completely analog arithmetic part.
However it has also been frequently used to describe what were hybrid arithmetic parts, e.g. which included both digital registers and digital adders and an analog section, for instance with analog integrators, which was used to implement signal processing filters or solving differential equations.
IMO, "hybrid computer" is appropriate only in the second sense, for hybrid arithmetic parts.
The control part of a CPU can be based only on a finite state automaton, so there is no need for any term to communicate this.
On the other hand, the arithmetic part can be digital, analog or hybrid, so it is useful to speak about digital computers, analog computers and hybrid computers, based on that.
in some sense almost any circuit in which a digital computer controls an analog multiplexer chip or a so-called digital potentiometer could qualify. and cypress's psoc line has a bit of analog circuitry that can be thus digitally reconfigured