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We know through the works of Babbage, Lovelace, et al. that mechanical computers (computers operating through gears, cogs, etc., and powered by steam or some other arbitrary non-electric power source) are possible.

In our world, it has been observed that electronic computers obey various forms of Moore's laws, with exponential growth.

In a world without electronic computers as we know them, would mechanical computers display a Moore's Law-like exponential curve of improvements? If not, why?

  • Would Moore's Law simply be inapplicable to mechanically engineered non-microscopic components (e.g. gears, cogs, ratchets, etc.)?
  • Would it initially apply, but rapidly hit a "hard" physical barrier/limit?
  • Would it follow some other kind of curve, such as linear growth or polynomial growth?

I would allow limited use of electricity as a power source, but not for driving logical circuits. Cathode-ray tubes, while technically being a form of a vacuum tube, could be allowed for display only, but I'm thinking more the use of mechanical television instead if at all reasonable. Standard electric-dependent computing components such as RAM, ROM, ferrite core memory, and hard disks are definitely out.

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    $\begingroup$ Unlikely! We've had centuries to streamline mechanical efficiency $\endgroup$ – nzaman Jan 20 at 13:10
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    $\begingroup$ @JBH those are not independent questions, but questions to show initial research and indicate the potential structure or nature of an answer. The actual question is the one in the title. The three bullets at the bottom are likewise not additional questions, just possible reasons for a "no" that could be explored. $\endgroup$ – Robert Columbia Jan 20 at 16:50
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    $\begingroup$ Also, please explain if any electricity at all is permitted. Can electric motors drive the mechanical engines? Can cathode-ray tube monitors be used? Or is this 100% mechanical with steam the only mode of turning cam shafts? Displays may be the ultimate limiting factor. $\endgroup$ – JBH Jan 20 at 16:55
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    $\begingroup$ An equivalent "mechanical moore's law" would be easy to create based on history. Start by comparing the number of components per unit volume in say Babbage's computing engines (en.wikipedia.org/wiki/Analytical_Engine#/media/…) with more than 2,800 moving parts inside a 100mm diameter case, in the world's most complex pocket watch (reference57260.vacheron-constantin.com/en/unique-complications) $\endgroup$ – alephzero Jan 21 at 17:38
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    $\begingroup$ You ask: Would it initially apply, but rapidly hit a "hard" physical barrier/limit? The real Moore's Law is rapidly approaching the hard physical barrier. Intel's latest generation has been delayed a year, and it's going to be increasingly hard to make progress in the future. All Moore-type laws, including the actual one, are probably going to behave this way. The big question is: how soon do they hit the limit? $\endgroup$ – Peter Shor Jan 21 at 18:19
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First of all, Moore's law is not a law of physics like Newton's law of gravity. It is just an empirical evidence that has held until now, in a quite surprising way.

While we have been able so far to shrink and shrink the size of electronic components, that is hardly possible with mechanical elements, therefore I highly doubt a mechanical equivalent of Moore's law would hold for more than few generations of calculators.

After that it would just be an horizontal line.

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    $\begingroup$ To be fair, the laws of physics are just empirical evidence that holds up to reality quite well, it’s just that Moore’s Law has a much, much smaller set of experimental evidence and some really dodgy methodology! $\endgroup$ – Joe Bloggs Jan 20 at 13:40
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    $\begingroup$ I would argue we already have shrunk mechanical devices to their maximum potential. Three hundred years ago nobody could imagine carrying a mechanical timepiece in their pockets $\endgroup$ – nzaman Jan 20 at 16:42
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    $\begingroup$ @Mazura I've been hearing people say we'd reach that limit when processors clocked at 1ghz, then 2ghz, then 3 and 4. After that limit didn't come we started going multicore. So if that limit is ever reached, I think it won't be in this or the next decade. $\endgroup$ – Renan Jan 20 at 16:54
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    $\begingroup$ We have absolutely come very close to the limits of Moore's law. Also, due to Amdahl's Law, going multicore can't just keep giving you gains unless the problem inherently has large amounts of parallelism (which many problems simply do not). $\endgroup$ – glaba Jan 20 at 19:54
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    $\begingroup$ Moore's law has held, up till now, as it was used as a target by chip manufacturers $\endgroup$ – Baldrickk Jan 21 at 9:57
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Elmy's answer to a question of mine made me realize what might be the most limiting factor for applying Moore's Law to mechanical computing.

Dirt.

Or, more accurately, your ability to keep dirt out of the works.

The beautiful thing about electronics is, other than heat dissipation, it's irrelevant how dirty it gets. But dirt gets in the way of spinning gears. No matter how well you try to seal it, you'll get dirt (if only in the form of congealed grease, metal shavings, wearing bearings and bushings, etc.).

In other words, you can realistically build a mechanical computer as small as (a) a gear can tolerate a grain of dirt or (b) you can keep the works sealed to prevent dirt from getting in.

Modern mechanical wrist watches demonstrate substantial size reduction in gearing — but they're also so well sealed that you need often need tools just to open the case. They could likely be made smaller, still, but you start getting into the problem of the slightest shaving causing you a problem, and a mechanical computer is much larger than a wrist watch.

So, where Moore's law was originally (and basically) the density of transistors doubles every two years. The mechanical variant of the law would be the size of a gear halves every two years. After 20-30 years, you're down to where the slightest speck of dirt would stop the machine. IMO.

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    $\begingroup$ Mechanical hard drives are incredibly sensitive to dust contamination but millions (billions?) of them are in use every day. We are fairly good at sealing things, and mordern hard drives have gone as far as to fill the enclosure with helium instead of air. I can't see dirt being the limiting factor. $\endgroup$ – Steven Lowes Jan 21 at 9:43
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    $\begingroup$ @StevenLowes True, but keep in mind that the internals of the hard drive don't need any exposure to the outside - only electrical signals. That isn't true for mechanical machines - isolating the outside is much harder if you have to use gears and levers to control the thing. One reason why gears in mechanical computers were much bigger than pocket watches is related to this - you need to interact a lot more with a computer than a pocket watch. "Electric mechanical watches" are extremely reliable compared to wind-up watches for this reason. $\endgroup$ – Luaan Jan 21 at 16:18
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    $\begingroup$ @Mazura, more specifically, it's all over until an amazing technological leap is achieved and the distance between two teeth is much, much smaller than the spec of dirt. I'm have trouble seeing that technological leap without the assistance of intervening steps, which is why I'm suggesting it stops with the grain of dirt. $\endgroup$ – JBH Jan 21 at 18:40
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    $\begingroup$ So small that when random bits of matter coalesce they're already too big to jam the mechanism. That's some food for thought. Apparently you've solved the tin whisker problem... $\endgroup$ – Mazura Jan 21 at 18:42
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    $\begingroup$ @JBH Not in terms of systems. CPU packages are bigger because the northbridge, particularly memory controller and PCI, and graphics have moved in. In any case, the root is anthropomorphic. People are a certain size, so smartphones, laptops, and desktops are bound by that size. Sort of Gustafson's law, the box is set, and the capabilities will expand to fill the box. $\endgroup$ – user71659 Jan 22 at 19:21
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Sorry to be a bit of a spoil-sport, but...

Moore's law doesn't apply.

Moore's law is the recognition that semiconductor complexity (in integrated circuits) increases at a particular rate.

The very Wikipedia article itself you linked to states that

Despite a popular misconception, Moore is adamant that he did not predict a doubling "every 18 months". Rather, David House, an Intel colleague, had factored in the increasing performance of transistors to conclude that integrated circuits would double in performance every 18 months.

The cited source (link, alternative link), in turn, states that

Moore’s law is ba­si­cally about tran­sis­tor den­sity, but there are many ver­sions of the Moore’s law for other ca­pa­bil­i­ties of dig­i­tal elec­tron­ics.

and that

In 1975, Moore re­vised his pre­dic­tion as the num­ber of com­po­nents in the in­te­grated cir­cuits dou­bling every year to dou­bling every two years.

(My boldface all three.)

Since mechanical computers presumably aren't semiconductor-based, nor use transistors or integrated circuits, Moore's law simply doesn't apply to them. If you are referring to some alternative, related observation, then you are referring to something other than Moore's law (but possibly derived from it).

It's likely that miniturization would follow some curve, but I can't imagine you'd get to have cogs in the low nanometer dimensions (the same order of magnitude as features of modern high-density integrated circuits). That's simply because you'd need enough material to hold itself together, while performing some kind of useful work. For example, turning a cog to increase a counter will require some amount of energy, which must be delivered to and ultimately supported by the cog.

To have physical components of those dimensions, you'd likely need some kind of super-material to hold together, and hold its shape, under those stresses. Barring that, it seems to me that you're likely to hit a physical limit at much larger dimensions than those viable for anything resembling a present-day integrated circuit.

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    $\begingroup$ @AleksandrDubinsky, be nice $\endgroup$ – L.Dutch Jan 21 at 14:12
  • $\begingroup$ Small things are tougher than big things, if you just scale them down. The bigger problem is how many gears you can have in a sequence before it all breaks down - and I'd guess that would be the limiting factor of any mechanical computer. Smaller gears help, but not quite as much as smaller transistors. $\endgroup$ – Luaan Jan 21 at 16:20
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Molecular machines

You can in theory make 'mechanical' machines right down to molecular level. They already exist in biology, for example rotary motors:

Three protein motors have been unambiguously identified as rotary engines: the bacterial flagellar motor and the two motors that constitute ATP synthase (F 0F 1 ATPase). Of these, the bacterial flagellar motor and F 0 motors derive their energy from a transmembrane ion-motive force, whereas the F 1 motor is driven by ATP hydrolysis.

And also other machines such as ribosomes and the following:

Cytoskeletal motors

Polymerisation motors

Rotary motors:

Nucleic acid motors

Viral DNA packaging motors

Enzymatic motors:

Synthetic molecular

https://www.cell.com/trends/cell-biology/fulltext/S0962-8924(03)00004-7

Reasearchers are currently working on so-called biological computers that work in a different way from the standard von Neumann machines of today.


EDIT

Mechanical monitors would also have improved at a similar rate, having developed from this mechanical TV: https://www.vox.com/2015/3/25/8285977/mechanical-television

enter image description here

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    $\begingroup$ Are you suggesting that you could have developed the computational capacity to develop the technology necessary to create molecular machines only via mechanical computing? If you'll forgive the hyperbole, 1980s-era computing would have required mechanical computers roughly covering the state of Massachusetts and you have no CRT/monitors in sight. $\endgroup$ – JBH Jan 20 at 16:51
  • $\begingroup$ @JBH - Surely that is where Moore's Law comes in. Maybe the size halves in ten years instead of one. The 1980s would already have been influenced by Moore's Law in mechanical terms so your assumption is faulty. As for monitors, early TVs were tried with spinning disks. I'm sure that could be refined perfectly easily. $\endgroup$ – chasly from UK Jan 20 at 17:00
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    $\begingroup$ I'm familiar with electronic fabrication technology. Based on that experience, you have a chicken-and-the-egg problem. The technology needed to eventually achieve molecular gearing requires more computational power (a lot more) than you can get from non-molecular shrinking. There comes a point before a gear is molecular in size (depending on nuclear forces to keep the gears together) when you can no longer depend on the strength of the metal to keep the teeth on a gear sharp. I can't see a path from A to B that's purely mechanical. Just my opinion, I've not voted either way. $\endgroup$ – JBH Jan 20 at 17:03
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    $\begingroup$ The motor could be a miniature steam one. The illumination could be produced by continuously feeding a strip of sodium into water. The monitor could simply be a reflection of the camera. Btw I was not in any way suggesting you're a creationist. If you manufacture electronics then presumably your experience confirms Moore's Law to some extent. One of the problems is that the OP hasn't specified if we are allowed to use electricity at all. If not then computer input and output will be as it was in the 60s and 70s, i.e. punched cards and tape. Perhaps combined with a steam-cranked typewriter. $\endgroup$ – chasly from UK Jan 20 at 17:34
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    $\begingroup$ @Luaan ATP synthase is mechanical, it is literally a rotary turbine connected to a trip hammer driven by a diffusion gradient. $\endgroup$ – John Jan 21 at 19:58
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The simple answer is: yes, because they did. They didn't follow Moore's Law (which as Moore said was never actually correct, nor did he ever expect the trajectory to continue), but they existed, and the trend to miniaturisation certainly did continue until transistors took over.

People tend to forget that a clock is a mechanical computer. Early clocks were massive mechanical systems. As time went on (pun intended), machining abilities allowed people to shrink the size of clocks until it became possible to build pocket-sized watches. Chronometers followed the same trajectory - Harrison's original chronometer required a large wooden box, but his later chronometers were the size of large watches. Watch movement technology and winding mechanisms evolved over time, and became more miniaturised to the limits possible with machining and materials.

With watchmaking having firmly established how to construct minaturised mechanisms, mechanical computers were extensively developed and used throughout the first half of the 20th century. By WWII, most planes, warships and artillery used mechanical computers called "predictors" to improve accuracy, allowing for windage and (for aircraft and anti-aircraft guns) relative speeds.

These pure mechanical computers were still being surpassed by electro-mechanical computers though, which integrated banks of relays with mechanisms to rotate those banks of relays. Relays are mechanical systems with electrical power. Everything that transistor switches currently do can be done (albeit more slowly) by relays, and in fact early adoption of transistors was simply as drop-in replacements for relays in existing electro-mechanical computers. Had the transistor never been invented, it seems very likely that the direction of travel would have been the development of smaller and more reliable relays. (To digress, Terry Pratchett's novel Strata supposes this as part of the underlying mechanisms in Discworld.)

And then Diskworld. You may say "definitely no hard disks", but that's nonsense. A hard disk is a mechanical system with electrical power. Our current hard disks are a development of drum memory, which is more clearly a classical electro-mechanical system. Hard disks are actually one development which is almost inevitable and independent of electronics. They wouldn't be as good as what we currently have, sure, but they'd be around.

So in your electronics-free world, the end result would be increasing miniaturisation of relays and relay-based computers. Of course this could never approach the size of a transistor, but we might well have pocket calculators, fairly complex landline phone systems, and warehouse-sized computers of the kind that were available back in the 1960s. Moore's Law would probably stall there, in the same way as it has currently stalled for silicon.

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Ugol's Law is a law, in that it attempts to explain nature: ”You're not the only one."

However Moore's Law is not a law at all. It doesn't explain nature, it commands -- well, not nature. It commands research and development.

It is an industry agreement on how to spend profits. Specifically, to give profits over to R&D enough to drive that rate of processor power increase, instead of paying that money to shareholders as dividends.

Or think of it as industry collusion to limit R&D money to a level that doesn't consume all profits and cause companies to bankrupt themselves and each other trying to keep up in an exponential technology race. It allows shareholders to profit-take.

Conversely, it allows management to stand up in shareholder meetings and explain a weak year with heavy R&D investment: "we needed the R&D funding to hit our Moore's Law targets".

So, not a law at all, just a super cool development schedule that allowed shareholders, managers and developers alike to share the dream.

The answer to your question is

Moore's Law bears on mechanical computers exactly as much as that society chooses to make Moore's Law (or some other development target) a part of their national vision/commitment/insanity.

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You get exponential growth if the growth furthers more growth.
For an industry, that means that the products not only sell well, they also help building the next generation of production lines. In the case of integrated circuits, this happened not just with computers helping to the planning for the next generation, there was also the engineering industry that used the research results from generation X's imaging and precision tooling improvements to build the tools for generation X+1.

For mechanical computers, this self-improving cycle never took off. The machines were always too difficult to make, some of them even predated the era of mass production (Leibniz built one), some simply were out of reach for the engineering technology of the time (Babbage, he couldn't find a workshop that would produce the cogwheels at the required precision).

I think we did have exponential growth in mechanical engineering during the Industrial Revolution though, so I believe the answer would be: Yes there was Moore's Law for mechanical stuff, it just didn't happen for computers but for steam engines and related technology.

There was also an explosion of electrical engineering once the basic technologies around alternating current were available.

I.e. my current theory is: technological progress is a series of exponential improvements that run until they hit some barrier (as is typical for exponential growth).

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    $\begingroup$ There's been some sci-fi stories where people forgot how computers originated, and couldn't explain how the first computer was made - that is, they couldn't make a computer without other computers. This is not quite true yet (people still make "extremely simple" computers that don't strictly need computer assisted design), but it's definitely true for commercial computers - a big part of the increase in chip making productivity comes from better design tools and computers that run them, not to mention run the fabs themselves. Some day, it will confuse people as much as evolution :) $\endgroup$ – Luaan Jan 22 at 7:55
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There was exponential growth in electronic computers because the central task in making tiny integrated circuits is, in fact, easy. Lithography is a lot like photography. You're creating machines with billions of components by just taking a picture or making a photocopy. You're both making a billion components, and assembling a billion components! I don't want to understate the many peripheral problems to figure out (eg, how to arrange a billion components) but because those problems weren't intractable and solving each new problem benefited a lot from the previous advances in computation, it led to exponential progress.

Integrated circuits aren't the only example of rapid exponential growth. Nuclear weapons increased in power ~10,000 times in just a couple of decades. Turns out, they were easy too.

Unfortunately, we don't have an easy process for making gears. Manufacturing precise machines remains hard. I think a mechanical computer could be built to be relatively powerful with tiny components sealed from dust and with error correction to work around failures. But building the second would take just as long as the first, and be uneconomical. (Without lithography, we wouldn't have gotten very far with hand-assembled vacuum tubes either.)

If you could imagine a similarly easy way to make mechanical computers, then you could experience some period of rapid exponential progress.

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