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Apollo 11 vs. USB-C Chargers (2020)

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Re: Apollo 11 vs. USB-C Chargers (2020)

#121

Post by kragen »

lisper wrote: post #118
thriftwy wrote: post #114

Earlier quoted context omitted.

Sure, you cannot easily simulate another analog computer, but this is not the requirement. The requirement is turing completeness, which can be done.

It can? How?

as i understand it, with infinite precision; the real numbers within some range, say -15 volts to +15 volts, have a bijection to infinite strings of bits (some infinitesimally small fraction of which are all zeroes after a finite count). with things like the logistic map you can amplify arbitrarily small differences into totally different system trajectories; usually when we plot bifurcation diagrams from the logistic map we do it in discrete time, but that is not necessary if you have enough continuous state variables (three is obviously sufficient but i think you can do it with two)

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

Re: Apollo 11 vs. USB-C Chargers (2020)

#122

Post by thriftwy »

lisper wrote: post #118
thriftwy wrote: post #114

Earlier quoted context omitted.

Sure, you cannot easily simulate another analog computer, but this is not the requirement. The requirement is turing completeness, which can be done.

It can? How?

It would not be very interesting. You will lose all the interesting properties of analog computer and it would be a poorly performing turing machine. Still it would have those loops and branches necessary, since you can always build digital on top of analog with some additional harness.

Re: Apollo 11 vs. USB-C Chargers (2020)

#123

Post by kragen »

eesmith wrote: post #120
kragen wrote: post #92

Earlier quoted context omitted.

i think it's (unintentionally) misleading to describe analog 'computers' as 'computers'. what distinguishes digital computers from other digital hardware is that they're turing-complete (if given access to enough memory), and there isn't any similar notion in the analog domain the only reason they have the same name is that they were both originally built to replace people cranking out calculations on mechanical desk…

What do you regard as the first digital, Turing-complete (if given enough memory) computer? 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…

let me preface this with the disclaimer that i am far from an expert on the topic

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

Re: Apollo 11 vs. USB-C Chargers (2020)

#124

Post by adrian_b »

kragen wrote: post #119
adrian_b wrote: post #109

Earlier quoted context omitted.

The arithmetic circuits alone, like adders, multipliers etc., regardless if they are mechanical or electronic, analog or digital, should not be called computers. 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 th…

as you are of course aware, analog 'computers' do not have the 'central control part' that you are arguing distinguishes 'computers' from 'arithmetic circuits alone'; the choice of which calculation to perform is determined by how the computer is built, or how its plugboard is wired. integrators in particular do have state that changes over time, so the output at a given time is not a function of the input at only th…

Most "analog computers" have been simple, and even if they usually provided the solution of a system of ordinary differential equations, that does not require a control part, making them no more closer to a complete computer than a music box that performs a fixed sequence.

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).

Re: Apollo 11 vs. USB-C Chargers (2020)

#125

Post by kragen »

adrian_b wrote: post #124
kragen wrote: post #119

Earlier quoted context omitted.

as you are of course aware, analog 'computers' do not have the 'central control part' that you are arguing distinguishes 'computers' from 'arithmetic circuits alone'; the choice of which calculation to perform is determined by how the computer is built, or how its plugboard is wired. integrators in particular do have state that changes over time, so the output at a given time is not a function of the input at only th…

Most "analog computers" have been simple, and even if they usually provided the solution of a system of ordinary differential equations, that does not require a control part, making them no more closer to a complete computer than a music box that performs a fixed sequence. I agree that this kind of "analog computers" does not deserve the name of "computer", because they are equivalent only with the "registers + ALU"…

i agree completely; thank you for clarifying despite my perhaps confrontational tone

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

Re: Apollo 11 vs. USB-C Chargers (2020)

#126

Post by gumby »

hinkley wrote: post #38
nothercastle wrote: post #28

Earlier quoted context omitted.

Exactly this. A lot of the systems had built in analog computers. It’s a lot cheaper to build then now with electronics but you need more computing power to do things that were previously done mechanically

Analog computers have to be rebuilt if it turns out the program is wrong though, don’t they?

Typically they were reprogrammed by changing the jumpers. The analogous digital change would be replacing the band of cards in a jaquard loom.

Much less than “rebuilding”.

There have been some hybrids too.

Re: Apollo 11 vs. USB-C Chargers (2020)

#127

Post by gumby »

thebestmoshe wrote: post #19
vlovich123 wrote: post #12

Is the weight/cost calculus sufficiently improved now that it’s cheaper to shield the processor in it’s entirety rather than trying to rad harden the circuitry itself (much more expensive due to inability to use off the shelf parts & limits the ability to use newer tech)? 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…

Isn’t this basically what SpaceX is doing? > 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…

Seems risky. I remember the automated train control system for the Vienna Hauptbahnhof (main train station) had an x86 and a SPARC, one programmed in a procedural language and one in a production language. The idea was to make it hard to have the same bug in both systems (which could lead to a false positive in the voting mechanism).

Re: Apollo 11 vs. USB-C Chargers (2020)

#128

Post by kens »

adrian_b wrote: post #124
kragen wrote: post #119

Earlier quoted context omitted.

as you are of course aware, analog 'computers' do not have the 'central control part' that you are arguing distinguishes 'computers' from 'arithmetic circuits alone'; the choice of which calculation to perform is determined by how the computer is built, or how its plugboard is wired. integrators in particular do have state that changes over time, so the output at a given time is not a function of the input at only th…

Most "analog computers" have been simple, and even if they usually provided the solution of a system of ordinary differential equations, that does not require a control part, making them no more closer to a complete computer than a music box that performs a fixed sequence. I agree that this kind of "analog computers" does not deserve the name of "computer", because they are equivalent only with the "registers + ALU"…

You're describing a "hybrid computer". These were introduced in the late 1950s, combining a digital processor with analog computing units. I don't understand why you and kragen want to redefine standard terms; this seems like a pointless linguistic exercise.

Re: Apollo 11 vs. USB-C Chargers (2020)

#129

Post by kragen »

kens wrote: post #128
adrian_b wrote: post #124

Earlier quoted context omitted.

Most "analog computers" have been simple, and even if they usually provided the solution of a system of ordinary differential equations, that does not require a control part, making them no more closer to a complete computer than a music box that performs a fixed sequence. I agree that this kind of "analog computers" does not deserve the name of "computer", because they are equivalent only with the "registers + ALU"…

You're describing a "hybrid computer". These were introduced in the late 1950s, combining a digital processor with analog computing units. I don't understand why you and kragen want to redefine standard terms; this seems like a pointless linguistic exercise.

because 'computer' has a meaning now that it didn't have 65 years ago, and people are continuously getting confused by thinking that 'analog computers' are computers, as they understand the term 'computers', which they aren't; they're a different thing that happens to have the same name due to a historical accident of how the advent of the algorithm happened

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

Re: Apollo 11 vs. USB-C Chargers (2020)

#130

Post by eesmith »

kragen wrote: post #123
eesmith wrote: post #120

Earlier quoted context omitted.

What do you regard as the first digital, Turing-complete (if given enough memory) computer? 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…

let me preface this with the disclaimer that i am far from an expert on the topic 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 ou…

> is the game?

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.

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