This is an attempt to explain what the recent memristor research is all about, and a harsh criticism of what was broadcast around regarding the subject.

The news I wanted to read:

Researchers at HP labs announced last 2005-08-30 that a certain new nano scale device they have been working with happens to be very well modelled by a kind of passive non-linear electronic component that was only theoretically predicted 30 years ago, but never seen in practice in such an explicit way.

The element is the memristor, which was named by its discoverer Leon Chua, inventor of the well-known chaotic Chua circuit. Chua idealised memristors when studying the generalisations of passive electronic components (resistors, capacitors and inductors) to non-linear versions. The models of these devices are:

R: v = R(i)
C: v = C(integral i dt) = v = C(q)
L: L(i) = integral v dt = L(i) = phi

Chua idealised a fourth element he named memristor, where we have the time integral of voltage (magnetic flux, phi) related by a non-linear function to the time integral of current (charge, q), yielding a fourth “missing” equation, with integrals on both sides:

M: integral v dt = f(integral i dt)

This equation can be differentiated to yield a more natural-looking one:

v = M(q)i

where dq/dt=i. This is just one class of memristors, the thing can be more complicated than that, but this gives a taste. (Of course, it can get even much much more complicated, yielding every possible non-linear equation.)

So, by “completing” the first equations, memristors complements the holy trinity of linear time-invariant electronics — R, L and C — when they are generalised to non-linear components. There are even some memristive circuits that cannot be replaced by a passive non-linear RLC circuit.

A linear memristor, with a constant M function, is simply a resistor. This is also how this specific model presented behaves for small-signal currents (possibly with a zero DC level!).

In his 1971 article, Chua infers the memristor from basic restrictions to the Maxwell’s equations, similarly to what is done to the other components. He shows the possibility of the existence of such a passive component, and also a way to build an active circuit that simulates a memristor, with the q-phi curve given by a non-linear resistor.

Memristor-like differential equations have already been used to model a number of phenomena, such as the amorphous “ovonic” threshold switch, E-cells, and even the Hodgkin-Huxley neuron model. That doesn’t mean that these devices cannot be modelled with other non-linear passive RLC circuits… Theory does say that some memristor circuits cannot be modelled only with passive RLCs, but of course “pure” memristance is not necessary to justify its use in an analysis. If the memristor model of a system looks nice, even if not unique, than it is fair enough!…

What HP researchers found was exactly that, a nano-metric device that is very simple in form, but with a very complex behaviour, and that happens to be very well described by the memristor model (regardless of being a case that can be also model by passive RLCs or not).

Non-linear dynamics is a no-man’s land, and to work with a system that can be described by a model from a family that already has a name is always very pleasant!… It is also very pleasant to find a system that can be model by a theoretical electronic element that in the past was only used as a component in more complex models with competing alternatives.

The technology HP is researching, if the researchers manage to tame the beast, will be used in nano-metric electronics. The first applications in mind are semi-non-volatile memory, and (kind of obviously) a kind of artificial neural network circuit.

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The news I was forced to read:

The stories presented by the press regarding this research were very badly written. They were really over the top, and demonstrated very bad understanding of electronics and electromagnetism. There was no scientific scrutiny at all, unlike other stories where other experts in the field are called to give their impressions, and “calm things down” when necessary. This was specially needed at this story, since the finding came from a company. We can even rise suspicions of a swindle to boost up shares value, not that I really think that is what happened…

I was specially disappointed at Nature magazine for presenting this as a kind of “novelty” story, just like it could be presented in any other newspaper, an infotainment story, different from what I expected from a scientific magazine, or better, from a “journal of science”. The actual article is alright, I have a few critics, but anything like my critics to the media coverage.

Let me make a list of the small things that pissed me off. Just like there are many ways to define a non-linear function, there are many ways to make a wrong article, so criticisms are always numerous when things go wrong…

1_ First, I would like to question Chua’s comparison of his work to that of Mendeleev. Mendeleev predicted characteristics of unknown elements, and predicted a way to classify and order them. The way turned out to be the atomic number. Chua started from Maxwell’s equations, imposed some restrictions, and derived equations for the problem in question, as it is always done with Maxwell’s equations. How could this be compared? If he had inferred the equations form the elements in first place, then OK.

I want to predict an electronics circuit element too. It has the equation:

v = N(i’) i

The voltage is the current multiplied by a nonlinear function of the DERIVATIVE of the current, instead of the integral… It is called the Nicstor. It presents the electronic characteristic of Nicstance, and I have a neuron model based on it. I wish someday someone stumbles upon a natural occurrence of this element… Would that make me Mendeleev? What if I tell you that I thought of this equation in a dream??

(I don’t know if it can even be passive, I hope it does.)

His comparison with Aristotle is also very unfair. First of all, it is unfair to say that Aritotle’s “force” is precisely the Newtonian “force”. The word can be used without a rigorous mathematical theory underneath. More then that: velocity IS proportional to the force applied when there is drag over the body.

Anyway, all electric scientists today always look at a curve and think of its many order integrals and derivatives. They don’t lose their time looking at the integral of the signal they should be looking, they look all possibilities… Perhaps even because of the work of great electrical engineers of the past, such as Chua himself. There is no “natural” variable to look at, charge is not “more ontological” then current. The distinction is specially meaningless when all it takes is a linear transformation between the functions… The “natural” variable to look at will be the one that helps.

The actual natural variable is neither. This idea of a certain mathematical model being inherently more right than others, like the idea that the heliocentric model is better than the geocentric, and that inertial references would be inherently more auspicious is a kind of anthropocentrism.

2_ All headlines said that the memristor would complement the resistor, inductor and capacitor as the fundamental elements of electronics. Said like this, the reader immediately imagines we are talking about linear, time-invariant (LTI) electronics. The good old electronics taught at high-school, and about which there are numerous books out there. Let me quote the nature article that implicitly talked about books needing to be changed:

High-school physics students grappling with the delights of capacitors, inductors and resistors will be groaning into their exercise books. Electronics experts in California have finally succeeded in proving the existence of a fourth fundamental unit of electronic circuits: the ‘memristor’.

Any reader minimally knowledgeable of the subject of electronics, and able to use his reason the way Socrates used to compel us to do, would immediately question the veracity of the claim.

In linear electronics, R L and C are pretty much complete. It’s either a proportional i-v relationship, or one a derivative of the other. An element where the derivative is proportional to the derivative in the other side turns immediately into a resistor, because in a linear system the derivatives “cancel out”.

It is very easy to see that R L and C, the holy trinity of electronics, are complete by using the concept of impedance. L anc C are merely the positive and negative purely imaginary impedances. A resistor is a real impedance. A negative purely real impedance is not passive. There is simply no way to complement that, LTI electronics is complete in that sense.

That is the a kind of thing I like very much to study… It is not for no reason that my blog is named “necessary and sufficient conditions”. So I was very much interested at first when I heard about a “missing element”, and then puzzled when I started to see that this could not be true… And then disappointed when I realized people were explaining things badly to make the story greater then it really is.

The worst thing is that there was no necessity to do that. Chua’s work is very interesting. HP’s research is very interesting. But someone along the way thought they needed to make things seem more important then they actually are (even though they were big already), and mixed the story with claims that made it sound like something so big as a “missing link” in electronics could exist. They inflated the importance of this research to the point of plain absurd.

Summarising: the stories did not said with the necessary intensity that this research concerns non-linear electronic phenomena, and that the memristor is an inherently non-linear device. High-school electronics, and all the books that would have to be rewritten concern linear electronics, so all claims or needing to change our notion of the fundamental components of (linear) electric circuits were pretty much lies.

The other day I heard in Nature about a discovery regarding a certain cell of the immune system, that it seems people thought were generated some other way… Now that is “needing to rewrite books”… Electronics are different, folks, sorry. It is built from the ground up!… It is not like biology, you can’t discover something like that!…

I might dare to say that linear electronics is pretty much like Euclidean geometry. I imagine that gives a nice picture of things. Would nature ever publish a story of someone claiming to have fond a missing element in Euclidean geometry, just like the point, circle and the straight line?

That’s all regarding the revolution that this research would have caused to electronics… Now let’s move to what it does, and the non-linearity.

3_ If there is something I learned in my still short life and superficial professional experience is that: when things get non-linear, my friend, be humble. Check everything twice, think of alternatives, avoid bold claims.

With non-linear dynamics, things that you say can go flying, turn into a snake in mid-air, come back like a boomerang and bite your ankles.

First I would like to mention a couple of things someone said that actually regards linear electronics yet. This came from an IEEE Spectrum blog article

The reason that the memristor is radically different from the other fundamental circuit elements is that, unlike them, it carries a memory of its past.

When you turn off the voltage to the circuit, the memristor still remembers how much was applied before and for how long.

Now, that is a great description of a capacitor, except for the “how long” part, that I doubt is the case with memristors. You might be able to calculate the “how long” knowing a few more other things.

Chua himself also talked about memristors not “going dead” when you “unplug” it. I really hope he wasn’t talking of anything as basic as storing charge.

I also read in other places about the memristor being very peculiar because, unlike the other “reactionary” components, it would have a sort of a memory… Well, only a person who doesn’t know absolutely nothing about electronics would dare saying something like that. If there is one thing said one time too many about capacitors and inductors is how they have “memory”!!…

If there is one thing people should know about capacitors, is how you can store voltage in it, remove from the source, and take it somewhere else. For example, you can hide a capacitor in your hand, and surreptitiously give an electric shock to a friend of yours, who might stop being your friend afterwards. Electric engineers do that every day at electronics labs… Sometimes it’s even a nuisance, you must discharge capacitors in your prototype with a metallic object for things to work properly. There is absolutely nothing fantastic about an element that you can remove from a circuit, and it still “remembers” how much you charged it with. Certainly not a breakthrough.

3_ People also talked about we the memristor being useful to build computer memories that don’t go away when the computer “turns off”. For example, from the BBC article

Today, most PCs use dynamic random access memory (DRAM) which loses data when the power is turned off.

I saw in many places this being mentioned as a great breakthrough, a revolutionary concept. That is ludicrous.

First of all, this is called “non-volatile memory”. It has a name, it is not something you explain like it is unheard of. And haven’t this people heard of the non-volatile memory device of the century? The flash memory? These morons carry flash-memory based pen-drives, cameras and cell phones everywhere they go, believing that we are still to manufacture a “computer memory that doesn’t go away when the computer turns off”? Give me a break.

By the way, non-volatile RAM existed in the past as in ferrite-core memories. An HD can be used as a non-volatile memory. Today there is another candidate as a good non-volatile memory, by the way: MRAM. I even suspect I read about it at Nature itself the other day…

Plus, computers will always have volatile SRAM cache memories right over the processor. Non-volatile memory is not something that will suddenly appear and change everything, it exists already, in memories that are relatively slower, which are more distant from the working memory of the processors, like HDs… Everything depends on the requirements of the application…

When it is communicated that this device will “make this possible”, this whole debate and previous knowledge and attention to subtleties are lost. It seems like the reporters “flashed” their memories, or that the capacitors in people’s minds today have very strong leakage currents, that no refresh can overcome, and they forget everything when see an opportunity to publish a sensationalist story.

4_ By the way, I doubt it that these devices do not have imperfections, such as a leakage current. MOSFETs have very low conductance, may take years to discharge significantly… What is the value of the parallel conductance of this thing? It MUST exist, show me the figures!… I believe the fact that a reviewer wanted to know this is the reason the actual scientific article brings the word “semi-non-volatile memories” instead of just non-volatile…

5_ Regarding the application to build neural networks. Who cares? Anyone can pick up any non-linear thing and say “look, we can perhaps build an artificial neural network with this thing here!” And then speculate that it might be able to do things that the computer can’t, because the computer would have some kind of inherent limitation making it impossible to do the same things the brain does…

That is such a complicated subject!!… People should not talk about this that way. Myself, I doubt it very much that artificial neural nets can do anything a computer simply “can’t”, meaning, compute something a computer can’t. It might compute some things faster, and faster in terms of time, not computational complexity…

6_ Conclusion: all news regarding this device lacked scientific scrutiny. They should at least have invited another scientist to comment on it, as it is done with the other articles. Why didn’t this article have an external commentator??…

7_ I could talk more, but I am really tired, and I already spent too much time with this. I am now not only disappointed, but angry at everybody, because I had to spend my time trying to right the wrongs left by all articles regarding this research… I won’t receive any money for that, but HP sure will.