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We've all heard about the 1822 Babbage Difference Engine and other mechanical computer ideas of the 19th century. Sadly, Babbage's computer and printer ideas were never implemented in our world, and computers did not exist until the 1940s.

Now imagine a world where this was accomplished, as was in short order his more elaborate Analytical Engine, and the industrial and mechano-computing revolutions went hand in hand. According to the Lovelace law of computation (1843), the amount of computation columns per troy pound of steel machinery doubles every 5 years.

Now it is important to note that the Analytical Engine (in Babbage's theoretical machine design as well as in our alternate world's everyday practice) was what we in our world have come to call Turing complete, i.e. is a universal computer. Digital, fully programmable.

Leaving aside the world-changing implications of such an advent, I'm curious to think about the limits of the 'Lovelace Law' -- just how miniaturized and just how powerful could a mechanical computer conceivably be, before some Kuhnian revolution would be required, such as moving to electromechanical devices?

We're not starting from a high bar. For a starting reference, the initial Analytical Engine design had the equivalent of a 16.7 kB memory, and the central processing mill could handle a multiplication of two 20-digit numbers in about 3 minutes. Thomas de Colmar's first arithmometer was not a general purpose computer, but could multiply two eight-digit numbers in 18 seconds.

Would we be able to reach, say, 1950 era computer levels?

† Outside a partial reconstruction in a museum, 170 years later

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    $\begingroup$ Babbage is attributed with one of my favorite quotes (that very frequently applies on this site): I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question. $\endgroup$ – Samuel Aug 6 '15 at 23:31
  • $\begingroup$ Fervently do I hope, earnestly do I pray that the quote does not apply to my question. $\endgroup$ – Serban Tanasa Aug 6 '15 at 23:32
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    $\begingroup$ Oh, and Gibson and Sterling's 'The Difference Engine' steampunk novel is almost a required reading here. $\endgroup$ – Serban Tanasa Aug 6 '15 at 23:38
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    $\begingroup$ Not a full programmable computer, but an extremely advanced mechanical astronomical calculator: Antikythera mechanism, dated from about 150BC. The design was centuries ahead of the manufacturing precision of the time. $\endgroup$ – Hoki Aug 7 '15 at 13:29
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    $\begingroup$ I believe the main issue is not the power of a big mechanical computer, but its reliability. A computer made of millions of mechanical pieces like those in the mechanical watches of the 1950s would be unreliable and would have something broken after the first hours of operations $\endgroup$ – Basile Starynkevitch Feb 14 '16 at 12:21
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Have a look at Rod Logic. This is a technology that uses moving molecular rods in a solid matrix to perform logical operations by the expedient of the rods having side groups opening or closing channels. It can be implemented from the macroscopic scale (with Lego as one example) to the atomic scale.

Such a nanoscale computer with a power equivalent to our silicon-based electronics would be positively tiny, on the order of cubic nanometres, and memory densities extremely high, say 10^20 bits (86.74 exbibytes or 100 exabytes) per cubic centimetre. Power requirements would be extremely low too.

This would allow the construction of personal computers of a power almost incomprehensible to us now, or manufacturing nanoscale robots that could be injected into the body to perform medical tasks.

So, yes, you'd be able to reach 1950's electronic computing power - and much, much more.

EDIT

nano-scale Rod Logic is currently theoretical, but has been implemented in macro-scale using tools such as Lego. I won't go into how you'd build it, since - as with our own computers - you use the computers you have to help build the next generation in an iterative process. The logical endpoint of the development of mechanical computing is likely some variant on rod logic. There would be a lot of intermediate-capability designs between early Babbage engines and a nano-scale rod logic machine.

I dare say that there are very few people who really understand how a modern CPU does what it does.

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    $\begingroup$ Rod logic certainly looks promising, +1. However, I don't see where you're getting the memory density value or how you're relating that to computing power. An SD card has very high memory density, but no computing power. How do you construct nanoscale devices without computer aided design, CNC, or lasers? $\endgroup$ – Samuel Aug 7 '15 at 0:38
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    $\begingroup$ @Samuel You construct them by bootstrapping. If you developed the crude macroscopic scale computers, you would have computer aided design, and CNC because you would have computers. Lasers may be more trouble, but its possible. $\endgroup$ – Cort Ammon Aug 7 '15 at 1:19
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    $\begingroup$ As someone who has worked on the development of MEMs devices (oscillators specifically, with a nanometer process) I think a (conference!) paper from 1989 (the 800 nm process was brand new back then) discussing the feasibility of nanorods is now more hypothetical than theoretical. Not because they were wrong at the time, but because we know so much more now about how difficult these micromechanical systems are. I mean, you have to worry about covalent bonds mucking up an AND gate. $\endgroup$ – Samuel Aug 7 '15 at 15:58
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    $\begingroup$ Why would rod logic be more dense or powerful? A semiconductor gate is 30 NM log or 300 atoms(angstroms) how could you build mechanical rods and channels and motors that are less then 300 atoms in size? Also it would be much slower because you have to accelerate a physical rod with friction and electrostatic forces, where electrons move at the speed of light. Just as a point of reference a current chip the size of you finger tips is over a billions transistors each doing a billion operations per-second. Rod logic is cool but has to many limitations to catch up. $\endgroup$ – sdrawkcabdear Apr 1 '16 at 18:15
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    $\begingroup$ Good question @sdrawkcabdear. I do notice the meaurements stated are 3 dimensional. What is the volume of modern cmos gates, which are fabricated as only one layer on a 2D surface? 30nM^3 is 3.7e16 gates per cubic cm, if they were layered in 3D. If it takes 1 order of magnitude worth of gates to make a bit of storage, that's about 2000 times less dense than the number quoted above for rods. $\endgroup$ – JDługosz Apr 3 '16 at 22:21
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It's the other way around,

If you start building mechanical computers you will stop using them to build more powerful devices as soon as electromechanical devices are invented.

In other words, instead of reaching a plateau in the development of mechanical devices, you will stop using purely mechanical principles simply because YOU CAN use electromechanical ones... It's like vacuum tubes, as soon as transistors became more reliable. We stopped using vacuum tubes without testing how far we could have reached with them.

At the same time, the development of mechanical computers will create a will to find more effective devices, so you might have someone inventing relays way before in our current line of time.

Its too hard to calculate how powerful mechanical computers could become. To talk about this we must find what is the major factor that would limit their construction. The limiting factor for vacuum tubes was heat and reliability. They work hot, and a lot of vacuum tubes side by side will cause a lot of heat. The speed on vacuum tubes is limited because they are harder to integrate, so you have long wires running all the way around. On mechanical computers the limit is inertia, friction losses, etc. Those elements are overcome by using stronger sources of mechanical power. Mechanical power is the result (in a rotating mechanism) of torque multiplied by rpm multiplied by some constant. So more power means more torque. More torque means the materials that the computer is made out of needs to be stronger. So, the fundamental limit on computer power for mechanical computers is at the material engineering level, if we don't know yet all about materials how could we tell?

TL;DR

You stop using older technology not because you can't use it any more, you do so because you CAN use something better.

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    $\begingroup$ One way to limit this would be a religious aspect: electricity is the work of the devil, etc. Obviously, less religious groups without those restrictions would advance much faster then. $\endgroup$ – Katai Aug 7 '15 at 11:34
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    $\begingroup$ The fact that this answer is even here, seems to be telling me that there are two questions being asked here: "What is the most powerful mechanical computer that can be built without electric technology?" And "How far could/would mechanical computers advance before a switch to electrical computers?" Or something like that... ... Am I wrong? $\endgroup$ – Malady Aug 7 '15 at 12:01
  • $\begingroup$ In some cases, "old" technology is discovered to be a useful solution. I have heard of tiny vacuum tubes in Soviet planes, because they were less harmed by EMP. $\endgroup$ – Christopher Hostage Aug 27 at 18:02
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Lets assume that nano technology had advanced and the Mechanical logic gates can be constructed at a molecular level. I feel that a mechanical logic gate could be as small as one of today's transistors.

There would be lots of problems like the resistance to mechanical force jamming the machine, or the force imputed being increase to deal with the depth of gates that it needs to travel, until it breaks the fragile components. But I think that these could be nutted out if it were the only viable means of computing.

I think that computers 'could' be as powerful as today's computers if they were mechanical, but they would develop at a much, much slower rate. I mean, consider that we are only able to conceive the idea of nano-technology, due in part, to the convenience that electronic computing contributes to science. Without electronic computers, scientific research itself would be stunted. So how could we develop such an unviable form of computing? It's a bit of a catch-22.

The technology would take a LOOOONG time to progress.

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Well, William McLellan made a working electric motor that would fit inside a cube 1/64 inches on each side. McLellan, at that time living nearby, achieved this feat by November 1960; his 250-microgram 2000-rpm motor consisted of 13 separate parts.

That was a result of a challenge made at Richard Feynman's [There's Plenty of Room at the Bottom] Lecture.

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  • $\begingroup$ Why do I feel like I've seen/done/dreamed this before? Is it the whiteness reminding me of Wikipedia?! $\endgroup$ – Malady Aug 7 '15 at 1:20
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I assume that you are assuming that electricity, electronics and products produced thanks to electronics (such as nanotechnology) are unavailable, i.e. the machine needs to be powered by water or steam or something. If you can create a mechanical, clocked flip-flop then you can imagine that a mechanical computer could conceivably perform the same functions as a 1950's valve-based machine, but it would be gigantic and very slow. At a minimum, it would at least be as many times larger than the computer it duplicates, as its basic mechanical switching component is than the electronic equivalent. It would need even more space for reticulation and probably cooling.

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It would be possible construct macroscopic mechanical computers which could manipulate substantial amounts of information, but they would have to do it very slowly by modern standards. If speed were not an issue, it would not be overly difficult to design a grid of rods, each of which could be pushed in or out, along with a device which had a group of push rods used as address wires, another group used as data wires, and a "read/write indicator" push rod, and which would visit the rods indicated by the address and either move the memory rods to reflect the state of the data-bus rods, or move the data-bus rods to reflect the state of the memory rods.

Given that, it would not be overly difficult to design a mechanical equivalent for something like a 6502 processor. A skillful person might even be able to hand-build such a thing at a scale that could fit on a typical table top.

Using modern "macroscopic" fabrication techniques--nothing exotic beyond the ability to produce lots and lots of intricate parts--it would be feasible for someone with the time, money, and inclination to build a device which would emulate a 1980s computer, but do so very slowly. Fast memory would be expensive, but slow memory might well be about the same cost per bit as the magnetic core memory which was widely used in electronic computers until integrated-circuit memories became practical. Write-once tapes would probably have a relatively low per-bit cost, and a reel the size of a cinematic movie film reel could probably hold a few megabytes.

I don't know that speeds could reach those of even 1960s computers, but storage capacities and computing power (aside from speed) could probably go well beyond what would be achievable in 1960. I'm not sure to what extent mechanical computers could play a role in mechanical manufacturing, but it would certainly seem plausible that they could do so.

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  • $\begingroup$ Considering that computers in the 1960s were typically what we today refer to as "Turing complete" (I don't know if the term was in common use back then, or had even been coined), in what way would you quantify "computing power" that does not include "storage capacities" and "speed"? $\endgroup$ – a CVn Feb 16 '16 at 9:58
  • $\begingroup$ I am very sceptical about the hand building part, consider that a limiting factor for the difference engine where manufacturing precission. $\endgroup$ – lijat Aug 28 at 17:03
  • $\begingroup$ @lijat: In the 1700s, John Harrison hand-built a clock out of wood that can (still does!) measure time accurate to six significant figures. The iterative process of carving parts to be slightly oversized, measuring them, carving them a little more, measuring, etc, is much slower than reproducing parts with a jig, but it can yield incredible levels of precision if one is willing to put forth the effort. $\endgroup$ – supercat Aug 29 at 14:58
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Mechanical computers do a much better job in analog form. The mechanical digital computer was never given time to develop. They were simply obsolete by the time technology was sufficiently advanced to require them. Relay and tube computers didn't last long either. There was already a transistorized computer in 1953 - just fifteen years after the Z1, and the ENIAC was still running.

Without electronics there wouldn't be much of a world to require digital computers, but in a purely mechanical world there probably would have been some clever engineering techniques to speed up mechanical calculator and do so reliably. Turbines can rotate at hundreds of thousands of rpm, so a few kFLOPS might have been eventually possible.

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