mechanical computation: with Merkle gates, height fields, and thread

[Kragen Javier Sitaker]

On Fri, Jul 02, 2010 at 03:49:55PM +0200, Dave Long wrote:
> Le 28 juin 10 à 09:37, Kragen Javier Sitaker a écrit :
> 
> >But braking can provide amplification. Imagine that you have a thread
> >running along the surface of a cylinder; it can slide freely, as far
> >as it as long as no force presses it against the cylinder. If another
> >thread is wrapped loosely several times around the cylinder and the
> >sliding thread, the sliding thread can still slide; but if the wrapped
> >thread is then pulled taut, it presses the sliding thread against the
> >cylinder, preventing it from sliding.
> 
> if the cylinder is externally powered, a single thread suffices; when  
> it is wrapped loosely no power is coupled, but a little tension on  
> the input side produces a lot on the output side.

Aha! I had forgotten about that! 

Considered as a part of the computation itself, it has some advantages
and some disadvantages. The rotating cylinder won't exert much
back-force on its drive if the thread doesn't catch, which is an
advantage. On the other hand, it weighs thousands of times as much as a
thread, which increases the force needed to move it at a given speed by
thousands of times, and thus the energy at risk of dissipation.

On the other hand, it may be highly practical for coupling the outputs
from such a machine to things larger and heavier than threads. I think
the gain of such an amplifier can be arbitrarily high, so you're limited
only by noise.

> cf differential analyzers (previous century) and capstans (previous  
> millennium) Friction-effect transhawsers?

I had forgotten about C.W. Nieman's torque amplifiers used in the MIT
differential analyzer. I never understood how they worked. Now I see, in
the diagram here:
<http://web.archive.org/web/20080302043939/http://www.dalefield.com/nzfmm/magazine/Differential_Analyser.html>
Thanks for drawing the connection!

> (early automated feedback applications were for windmills; I wouldn't  
> be surprised if the separation of power and control had also been  
> useful relatively early for animal-driven milling...)

A friend of a friend constructed an analog automated feedback system out
of rope and sails to keep their small sailboat on course while they were
slept as they crossed the Caribbean. 

But what applications would justify a universal computing machine with
hundreds of somewhat finicky parts before the 20th century, other than
embedded control, even assuming you knew it could be built? Perhaps
astrological ephemerides, cryptology, accounting, gambling, the
computation of navigational tables, certain kinds of mathematical
investigation such as tabulating prime numbers, perhaps long-distance
communication.

With some degree of embedded control, though, in addition to milling
grain, you could imagine applications to the copying of books, the
weaving of tapestries, process control in breweries and bakeries (not to
mention other fermented foods like natto and yogurt), the irrigation of
fields, the unattended recording of measurements, and the locking of
doors — as well as some crude form of CNC manufacturing. 

How early could CNC manufacturing have been developed?
<http://open3dp.me.washington.edu/2009/09/xtra-white-ceramic/> describes
a recipe for 3-D printable clay: 1000 units of a white slip clay, 250
units powdered sugar, 250 units maltodextrin.  Onto this powder you
spray, or, presumably, drip water, to harden parts of it.  Apparently
maltodextrin can be produced from starch by roasting with acid, by
applying saliva, or, I think, by malting. You wouldn't need a great deal
of dimensional accuracy or power to make useful articles out of ceramic
in this way.