I thought it was possible to do high-speed digital electronic computation with 19th-century materials and fabrication techniques, using the (ordinary) magnetoresistive effect and differential circuits to obtain nonlinear amplification. This document explains why I thought it was possible.
However, now I think it's not possible, because it involves using iron or otherwise ferromagnetic wires to carry the signals that need to be switched, and those wires, in addition to being magnetoresistive, are extremely self-inductive; the consequence is that they can only practically carry very slowly varying signals (1Hz or worse). You could try to balance the heavy self-inductance with a coaxial sheath to add capacitance, but I'm not convinced that will work adequately.
The rest of this document was written before I knew about this problem.
Electromechanical relays are a relatively simple invention, once the idea is pointed out: an electromagnet pulling a springy bit of metal into or out of electrical contact, opening or closing an electrical circuit. You can make one with a little fuss if you have some wire and ferromagnetic metal, and one version was invented in 1840 by Samuel F.B. Morse for his Telegraph. They are sufficient for building Boolean logic devices to perform arbitrary digital computations, as shown by Claude Shannon in his thesis and extensively exploited for telephone switching in the early 20th century. Indeed, since they're fairly close to ideal switches (very unlike bipolar transistors), logic circuits built using them are quite simple, using only one or two relays per gate or flip-flop, even without any elaborate mechanical tricks.
However, for digital computation, relays have some serious drawbacks. Modern silicon semiconductor devices can operate comfortably in the 4GHz range (i.e. 250ps per cycle) at room temperature; at higher cost, germanium, silicon germanium, gallium arsenide, ECL, and/or further cooling can push speeds higher, past 10GHz (100ps).
By contrast, electromechanical relays typically can't operate faster than about 100kHz (10 μs, 10 000 000 ps). This is a pretty big disadvantage, and it's the reason relays have been out of favor for digital logic since the 1940s. The basic problem is that the metal contacts are macroscopic objects full of baryons, so you have to move an awful lot of electrons through one set of contacts to produce enough energy to move another set of contacts. The vacuum tubes that replaced relays in the 1940s move only electrons, which have three orders of magnitude less mass per unit charge, and semiconductors share this advantage.
(Relay coils also have substantial inductance which limits the speed at which current in them can rise and fall.)
(Semiconductor devices also have the advantage of being very small, speeding up the timescale of anything, but this advantage could in theory be reproduced by other kinds of devices as well.)
A normal single-pole double-throw relay has five terminals:
C1 and C2: two terminals on the coil;A, an armature terminal;NO, a normally open contact which gets connected to A after a
delay when there's current flowing through the coil; andNC, a normally closed contact which is connected to A except
(after a delay) when there's no current flowing through the coil.There are any number of possible ways to do digital logic using relays. This one is among the simplest.
Let's us a kind of "open-collector" convention: we represent logic 0 as a low-resistance path to ground, and logic 1 as the lack of a low-resistance path to ground. In that case, you can construct a basic inverter as follows, with V+ being the power supply rail that doesn't represent logic 0:
X' = Not(X): Relay(C1=V+, C2=X, A=gnd, NC=X')
This inverter is more than it appears: the normally-open contact NO
is actually available as a buffered copy of the input X, and any
number of outputs can be connected to the inverter's input and will be
implicitly ANDed, providing fan-in, the ability to combine different
pieces of information. That is, this isn't just an inverter; it's a
single-relay combination N-ary AND-NAND gate, or a buffer.
(You can safely stick a resistor in series with the coil of each relay operated this way, since the coils are never placed in series with each other.)
You can put together an RS latch in the usual way:
Q, Q' = RS(R', S'): Q' = S' = Not(R'); Q = R' = Not(S')
That is, you hook up the two inverters in a loop, each inverting the other's output — wire-ANDed with an active-low asynchronous reset or set input. This gives you a bistable circuit whose state you can change, which gives you memory, making sequential circuits possible.
The fanout of this kind of relay logic will be limited only by the number of coils whose current can be run through a single set of relay contacts before the resistance of the point of contact creates a substantial voltage drop. Typically the fanout provided in this way is very large. As long as the fanout is greater than 1, you can build circuits that do universal computation.
There are two more features crucial to digital logic: level restoration and inversion.
Level restoration means that, if the input to an inverter only barely qualifies as a logic 1, the output needs to be a logic 0, but not "only barely" — it needs to be a better 0 than the input was a 1, or if the input was barely a 0, the output needs to be more-than-barely a 1. That is, you need a kind of "range compression" between the input and output. Relays make this really easy: when the contacts are open, the resistance across them is some 20 orders of magnitude higher than when they are closed.
Inversion is the ability to get a zero from an all-ones input, or a one from an all-zeroes input. Some kinds of digital logic used in the past were capable of producing various combinations of AND and OR using only diodes and resistors, but not inversion, which requires some kind of amplifying element.
So whatever kind of thing you use for digital logic will need memory, fan-in, fanout, level restoration, and inversion.
Kelvin (alias William Thomson) discovered what is now known as the "magnetoresistive effect" in the 1850s:
W. Thomson, “On the Electro-Dynamic Qualities of Metals: Effects of Magnetization on the Electric Conductivity of Nickel and of Iron”, Proceedings of the Royal Society of London 8, 546-550 (1856-1857). http://archive.org/details/philtrans05965210 http://zapatopi.net/kelvin/papers/on_the_electro-dynamic_qualities_of_metals.html http://archive.org/stream/philtrans09842257/09842257#page/n0/mode/2up
He found about an 0.5% change in the resistivities of ferromagnetic metals when a strong magnetic field was applied, depending on whether the field was parallel to the current or at right angles to it. Importantly (and necessarily for the P-symmetry of the electromagnetic force), the resistivity change doesn't depend on whether the magnetic lines of force run in the same direction as the electrical current or the opposite direction.
0.5% is a pretty small change, and Thomson had difficulty measuring it accurately. (Wikipedia claims he got up to 5%, but I'm not seeing that in the papers he published. Other sources claim you get 5% with a 90% nickel, 10% iron alloy, but I'm not clear on how sensitive that mixture is to impurities.)
But I speculate that you can almost certainly use this "ordinary magnetoresistance" effect to produce a solid-state "relay" that provides amplification, using 1850s technology! Better yet, you can produce a kind of low-quality radio detector, which was the crucial invention that made radio transmission of audio possible, replacing the electromechanical coherer invented in 1890.
This speculation depends on the crucial assumption that the current running through the magnetoresistive element does not produce a magnetic field that tends to diminish the resistance — that is, that the magnetoresistive effect does not diminish at higher current densities. If this assumption is wrong — and I'm still not sure, because I don't understand the physics — then it may not be possible to use a magnetoresistive element to control a larger amount of power using a smaller amount of power.
I argue that this assumption is reasonable for two reasons.
First, consider a long, thin, flat, wide insulated metal tape, folded in half the middle:
-------------------------------+
|
-------------------------------+
An electrical current through this tape will produce magnetic fields that very nearly cancel, but the magnetoresistance (produced by an externally applied magnetic field) of each half of the tape should still be nearly the same as before you folded it in half.
Second, resistivity is typically greatest when the current flows parallel to the magnetic field. But in that case the magnetic field from the current is at right angles to the applied magnetic field, and so will not affect it in any way.
These are not ironclad arguments: the "cyclotron orbits" pursued by the electrons inside the metal might still produce magnetic fields in unexpected orientations.
There's still the issue of the 0.5%, though. If the difference between zero and strongest magnetic field you can provide changes the resistance of your magnetoresistive element by only 0.5%, then your current will vary by only 0.5%, or less still, which means that if you just use that current directly to create another magnetic field, that other magnetic field will vary by only 0.5%. Which is to say, you completely fail at amplification.
But that's not the only thing you can do with a variable resistance. If you balance the resistance of your magnetoresistor with a similar-sized resistor in a Wheatstone bridge configuration, the voltage across the middle of the bridge will be zero when the magnetoresistor is at its reference resistance, but nonzero when its resistance is perturbed by a magnetic field. To be specific, if its resistance varies by 0.5%, the voltage across the middle of the bridge can be around 0.25% of the total voltage applied to the network.
That doesn't sound like much, but that low voltage can be (by my assumption above) providing an arbitrarily large amount of current — current which can be used to energize another coil to an arbitrarily strong field, a field which will be zero when the bridge is balanced.
This means that you can get amplification, which translates into the necessary overunity fanout. Your amplification is limited only by the precision to which you can balance the Wheatstone bridge.
As mentioned earlier, the perturbation in resistance depends on the absolute value and orientation of the magnetic field, not its direction; that means that the perturbation induced by a coil is symmetric around zero in the current applied to the coil. You have some kind of slight resistance bump, up or down, centered on zero.
Typically, this takes the form of "Kohler's rule", which says the extra resistance is proportional to the square of the applied magnetic field.
That's a significant nonlinearity! That means that the average resistance in the magnetoresistor is not the resistance in the magnetoresistor at the average current in the coil. If you have a pure-AC current in the coil, that can still produce a significant magnetoresistive effect, which means you can demodulate AM radio.
How can you do level restoration with magnetoresistive logic? One way is to exploit the symmetry around zero (and indeed the zero derivative at zero implied by Kohler's rule) mentioned in the previous section. You can improve the zero level a bit further by biasing the minimum a bit with a permanent magnet, as described.
You could use a cascade of two inverting magnetoresistive "relays" to restore both the 0 level and the 1 level, but there may be easier approaches; for example, magnetoresistance in many materials saturates at some flux density, and flux density in ferromagnetic materials saturates at some applied magnetomotive force. (Every material tends to relative permeability of unity, in the limit of sufficiently large field strength.)
If the bridge is balanced so as to have zero potential difference and so zero current across the middle at zero applied field, you don't have inversion. But if you balance it a little differently, you can have a potential difference at zero applied field, which shrinks to zero at the applied field corresponding to logic 1, then starts to grow again. Alternatively, you can bias the field using a permanent magnet rather than the resistors, giving you a nice zero derivative in the neighborhood of logic 1. Either way, you get inversion.
How can you connect multiple inputs to a single output? One fairly inconvenient way — analogous to what we do in TTL and the like — is to physically colocate multiple coils, driven by different inputs, to produce magnetoresistance in the same magnetoresistor.
Aside from the usual feedback approach with a couple of inverters eating each other's tails, you might be able to use high-hysteresis, low-coercivity materials for a sort of ferrite core memory, with a nondestructive readout. I'm not entirely sure how you'd erase it, though; perhaps you could saturate your magnetic storage core in either direction, but take the reading at a point where a permanent magnet interferes with the field, either constructively or destructively?