The memristor skeptics

Illustration of the memristor in electrical network theory. Image from Wikipedia, produced by Parcly Taxel.

Illustration of the memristor in electrical network theory. Image from Wikipedia, produced by Parcly Taxel.

A story of skepticism gone horribly wrong.

In 2008, researchers at HP Labs announced their discovery of the memristor, a type of electrical device that had been predicted by Leon Chua in a 1971 paper titled, “Memristor– the missing circuit element.” Memristors have been in the news again recently due to HP’s announcement of a bold new computing project called The Machine, which reportedly makes heavy use of memristor devices. Thanks to the sudden attention being paid to memristors in the past few years, we now know that they were with us all along, and you can even make one yourself with a few simple hardware items.

Since I teach my department’s introductory course on electronic devices, I’ve been studying memristors to see if it’s time to add them into the basic curriculum. During my reading, I started to notice a small percolation of skeptical voices. They appeared in popular science magazines, blog posts, and comment threads, and said some very unexpected things, like “HP didn’t really invent a memristor” and even “the memristor may be impossible as a really existing device.” I soon noticed that several of the critics were published researchers, and some of them had published their critiques on the arXiv, a preprint site used by credentialed researchers to post draft articles prior to peer review. The skeptics reached their peek in 2012, but fizzled out in 2013. One of those skeptics went out with a bang, crafting a bold conspiracy theory that still echoes in discussion fora and in the comment threads of tech industry articles. This post chronicles the rise and fall of his career as a memristor scholar. I also offer some speculation as to how the debacle could have been avoided.

The beginnings of memristor skepticism

There are a few non-peer reviewed articles in the arXiv that explain the technical details of memristor skepticism. The most commonly cited articles seem to one by Paul Meuffels and Rohit Soni, and another article by Blaise Mouttet. Of the two, Mouttet’s criticisms were the most scandalous: he claimed that the whole theory of memristance is wrong, and over time he developed a sprawling conspiracy theory to maintain this delusion. The real origin of this story happened in 2010, when Mouttet (then a Masters student at George Mason University) spoke at a special session of the International Symposium on Circuits and Systems (ISCAS). Up to that time, Mouttet had made some contributions to memristor research; he published a few articles at conferences, he had a serious article in the arXiv, and he was awarded some patents on memristor applications.

In order to speak at ISCAS, Mouttet would have submitted an article for peer review, and that article was evidently accepted. I’m able to access the article since I own the original proceedings distributed at the conference (Mouttet’s article has since been redacted). The article makes some cautious critical points about memristors, stated in an appropriate academic tone. But when Mouttet gave his presentation, he blew the lid off of those criticisms and upset a lot of people. His presentation was titled “The Mythology of the Memristor,” presented in the same session as some research from the HP team, who were evidently in the audience. Mouttet later posted his presentation online (I won’t link it here), but here are some of the things he said:

  • He described HP’s invention as a “PR stunt that does not withstand scrutiny.”
  • The memristor is not “fundamental,” if it is, then [paraphrasing] you can call anything “fundamental.”
  • HP’s memristor wasn’t the first memristor-like device.
  • HP’s memristor isn’t even a real memristor.

The presentation evidently didn’t go over well; Mouttet’s article was pulled from the conference proceedings, so you won’t find it in any library (that’s actually quite unusual, since articles are usually archived after they pass peer review). Mouttet complained of being blacklisted after the event, and there seems to be some truth to that. But Mouttet thought he was onto something. He thought he’s discovered a miscarriage of science, so he pressed the attack.

In 2012, Mouttet published his most critical article on the arXiv. Mouttet’s attack was answered by a Korean team led by Hyongsuk Kim, but Mouttet continued to press the attack with another article titled “The memristor and the scientific method.” This article was rejected from the ArXiv, and Mouttet was barred from future submissions… so he took his papers over to the viXra (that’s arXiv spelled backwards), a haven for quackery and pseudoscience. I’ve always been curious about the conditions that lead scholars into these dark corners of pseudoscience and conspiracy theory. (In fairness, back in 2010–2012 viXra might not yet have fully cultivated its reputation for pseudoscience.) Here’s what Mouttet said that got him relegated to the fringe:

Advancements in science are not made based on whether large corporations or famous scientists endorse a particular theory or idea. Science progresses solely based upon the formulation, testing, and modification of hypothesis. That is the scientific method.

Corporations have a profit motive and scientists, while typically portrayed as seekers of objective truth, can have their judgments clouded by a desire to enhance their reputations.

The “memristor” was originally proposed in 1971 by Leon Chua as a missing fourth fundamental circuit element linking magnetic flux and electric charge. In 2008 a group of scientists from HP led by Stan Williams claimed to have discovered this missing memristor. It is my position that HP’s “memristor” claim lacks any scientific merit.

If the HP researchers had developed a realistic model for resistive memory (whether it is called “memristor” or by some other name) it could be vetted by other researchers, compared to experimental data, and determined to be true or false. If necessary the model could be modified or corrected and an improved version of the model could be produced.

This is not what has happened.

The article tells a tantalizing story of a small group of researchers who lost sight of the scientific method; Mouttet was merely trying to set us all straight — except that Mouttet was wrong.

The claims of memristor skeptics

I took a close look at the issues raised by Mouttet and others (you can read my detailed thoughts on memristor theory on my Red Matrix channel). The most prominent attacks seem to conflate device physics (DP) with nonlinear electrical network theory (NENT). DP concerns itself with the fine details of particles, materials, junctions, surfaces, fields and their complex interactions. NENT, by contrast, is a more fundamental body of theory that describes conservation laws in electrical systems. Every device model has to obey conservation of mass, energy and charge; any DP model has to conform to the laws of NENT, and memristors belong to NENT. Indeed, Mouttet’s best counterexample — a “square law capacitor” — seems to violate conservation of energy and is therefore non-physical.

One of the particular points made by memristor skeptics is that memristance is based on flux linkage, which is usually understood to arise from magnetic fields. This problem seems to have vexed several serious memristor researchers: where is the magnetic flux in HP’s device? The answer appears to rest on the proper interpretation of flux linkage in NENT. In special cases like a wire loop inductor, flux linkage corresponds physically to magnetic flux. Apart from those special cases, there is not necessarily any connection between the two. This can seem puzzling at first, since many of us are trained to search for “physical interpretations” of abstract theoretical concepts.

So what is the physical interpretation of flux linkage, if it is not equivalent to magnetic flux? I would say that memristance itself provides the physical interpretation, in that it explains the range of behaviors allowed under physical conservation laws. Recent research points to a variety of mechanisms that exhibit memristive behavior; there may not be a simple “cartoon” explanation like we have for, say, capacitors, which are easily visualized as a volume in which electrical charge is stored. Perhaps given more time, we will arrive at more intuitive descriptions of memristive phenomena.

Growth of the conspiracy theory

By the time Mouttet migrated to viXra, he had already begun to nurse a conspiracy theory that mirrors some of the elements of climate change denial or anti-vaccine theory. We have wealthy corporations driven by a desire to protect their patents. We have a community of researchers who are motivated to protect their status. All of them collude together, pumping up the momentum of memristor theory for private unethical motives. In 2012, Mouttet wrote this:

Willliams [from HP] is making false claims about the memristor either out of his own ignorance or deliberate attempt at fraud to advance HP’s business agenda

and then he wrote this:

It seems to me that there is a possibility that those who are invested in HP’s “memristor” may be inappropriately using their influence to suppress opposition to what could very well be the use of fraudulent science to support a corporate agenda.

…and in 2013 he wrote this:

Chua obviously has a self-serving incentive to claim all resistance switching devices are memristors. It seems to me incredible hypocrisy for Chua to claim this since he was arguing for 37 years that the memristor was a missing circuit element. Chua was certainly aware of the research being done in MRAM, ReRAM, and phase change memory but never claimed these memory types to be memristors until after HP’s initial claim.

Perhaps Chua may have more concern for his reputation than accurate science or consistency with his own definition?

The conspiracy theory began to acquire a small following. On the blog “Alpha Meme” at Science 2.0, Sascha Vongehr bought into the conspiracy and wrote this (emphasis added):

This “discovery” is simply a misinterpretation of devices that had been discovered many years before in India. Those original inventors did not misinterpret their work in order to make it into the news. Given the serious doubts that have been presented in many places, one seriously wonders whether the fact that the cheated are ‘just a bunch of Indians in India’ has anything to do with the embarrassing situation of that science media do almost not care. The latter though cannot explain that criticism is effectively censored.

Meanwhile, the popular science media took notice, and articles about the memristor debate appeared in outlets like Wired Magazine, New Scientist and others. This wave of press coverage gave them some attention, and probably explains why some skeptical comments still linger to the present day.

There has been some suggestion that Mouttet pumped up the conspiracy theory because he hired to do so by a competitor of HP. According to the New Scientist article, “Mouttet is hired by firms seeking to invalidate patents they feel are not novel and is writing his rebuttal. He fears that a broader definition could have a chilling effect on firms working on a range of memristor-like devices.” There are nevertheless strong indications that Mouttet was a true believer. In mid-2013, Mouttet took a permanent job outside the electronics industry, and has not had any subsequent involvement in memristor research. But he continued commenting on blogs and articles, advocating his conspiracy theory well after moving into a new line of work. Plus, in 2012 he wrote some things that seem very uncharacteristic of a patent troll or corporate shill (emphasis added):

It is not opinion it is logic. Chua and HP/Williams both have incentive based on financial motivations and reputation to continue this “fourth element” argument but it has no merit when analyzed objectively. I have no incentive to disagee with Chua and HP if they were right. In fact I was an early supporter of the memristor hype and was invited to speak at the first memristor and memristive systems symposium at UC Berkeley alongside Williams and Chua and at 2 IEEE conferences (ISCAS 2010, ICECS 2010). Even strong supporters of the memristor such as Pershin and DiVentra have rejected the “fourth element” interpretation in favor of generalized memristor, memcapacitor and meminductor models. In any case I am several decades younger than Williams and Chua and I can guarantee you I will have a hand in writing the history of the memristor long after Williams and Chua are dead. History will not be kind to them.

He sounds like a true believer to me, and regardless of his motives he has inspired a small cult following of fellow conspiracists.

Reflecting on the controversy

In academic circles, memristor skepticism seems to have fizzled out in 2013. When discussing this debacle with a few fellow researchers, we reflected on some aspects that might help navigate similar situations in the future. First, when young scholars like Mouttet think they may have found a big mistake in accepted science, what’s the appropriate way to address it with the community? Second, how can the academic community best respond to rehabilitate scholars who are headed in the wrong direction?

If nothing else, Mouttet’s early activities demonstrate that the community tolerates criticism in professional venues. His critical article was accepted to ISCAS, and he was allowed to post his thoughts on the ArXiv. He wasn’t censored. So where did he go wrong? Simple: he made direct personal insults and accusations of unethical conduct. Young scholars be warned: if you go around making accusations without solid proof, your career won’t last long. Honestly, a lot of young researchers entertain conspiratorial thoughts; keep those thoughts to yourself.

If you really think you’ve found a problem in the established science, the best thing you can do is frame your criticism as a question. Better yet, offer a positive alternative to the problem theory, so the community has something else to embrace. The memristor skeptics produced one really viable point, in the form of an open question that researchers could ponder: “where is the magnetic flux in the memristor?” This seems to have puzzled researchers enough that they paid attention and figured it out. You can always ask questions, but avoid jumping to premature conclusions (or express those conclusions with a heap of caution). Obviously, all scholars should be conscious of their own capacity for mistakes, so you need to dial back that confidence.

As to the community’s responsibility, it may have been possible to nip this fiasco in the bud through a bit of mentoring. Judging from Mouttet’s blog posts, he seemed completely in the dark as to why he was being blacklisted; as to why he offended the HP researchers at ISCAS. It’s not clear that he understood the expected etiquette, and he began to see himself as a persecuted defender of correct science. When looking over his papers, I noticed that he was the sole author on each of them; usually we would expect to see his academic adviser as a coauthor. I can only speculate as to Mouttet’s situation in the Masters’ program at GMU; it is not uncommon to see self-funded students who direct their own thesis work, and perhaps this describes Mouttet. If that’s the case, then he may have been working and publishing with little or no guidance or review from his faculty mentors. This definitely happens sometimes, and it is a plausible explanation for Mouttet’s lone descent into the fringe. Perhaps his adviser could have kept a closer watch; perhaps it wouldn’t have made any difference. In either case, this story is a reminder that even self-directed students represent their university when they present themselves in academic venues, and it would be wise to keep a close watch on them, lest they wander in unexpected directions.

33 thoughts on “The memristor skeptics

  1. Huh, well that explains why my post attracted the skepticism that it did. I had always wondered if there was a larger story behind the reaction I got as typically I only get comments like that when I’m deliberately trolling or if I post something on the anti-vaxxers.

    Great article by the way Chris, really enjoyed it!

  2. Something has been overlooked. In 2013, the critique by Meuffels and Soni regarding the general memristor concept was endorsed by Di Ventra and Pershin (“On the physical properties of memristive, memcapacitive, and meminductive systems” by M. Di Ventra and Y. V. Pershin ( Non-volatile memristors whose resistance (memory) states depend only on the current (like the HP memristor) or voltage history would be unable to protect their memory states against unavoidable fluctuations and thus permanently suffer information loss, viz., such memristors cannot exist as a solid state devices in physical reality because their proposed behavior – in accordance with the defining state equations – would be inconsistent with fundamental laws of non-equilibrium thermodynamics.

    I don’t think that the memristor skepticism has fizzled out in 2013. There seems to be part of the involved scientific community which is desperately trying to keep the misleading “memristor” concept alive. It can be assumed, however, that many – if not most – of the former “memristor” enthusiasts are now aware that they have been taken in by erroneous publications. Both HP’s famous “memristor” model (“The missing memristor found” (Nature 453, (2008) 80-83)) and Chua’s hypothetical “memristor” concept are based upon severe physical misconceptions. It’s indeed surprising that critical voices are only sparsely heard. Maybe, the majority is merely hoping that the whole “memristor” hype will sink bit by bit into oblivion.

    • mpm5514: Thanks for pointing me to the Di Ventra and Pershin article. I think their analysis of response functions is interesting, but it will take me some time to digest it. In my opinion, their paper suffers from some serious interpretational errors. First, they allude to electrical circuit theory as “mathematical formal analogies,” which is not an accurate characterization. As I noted in this post, nonlinear electrical network theory comprises only the conservation laws of electrical systems. The formulations of NENT are necessary in order to solve and/or simulate the state of a system comprised of interacting electrical elements. This theory has been generalized to allow for joint solution of interacting mechanical, optical and other physical elements subject to similar conservation constraints. Chua observed that memristance is allowed by the conservation constraints that affect charge and flux linkage.

      Di Ventra and Pershin further argue that no “ideal” memristor may be realized. Assuming their argument is correct, I don’t find this result surprising in any way, and it doesn’t appear to contradict the existence of “pinched hysteresis” which is the signature of memristance. There are no ideal resistors, capacitors or inductors either. In practice, every real device must be modeled as a composition of ideal elements; such a composition is necessary in order to simulate the network. Now we know that memristance can be incorporated in those networks for novel purposes, and that memristive devices (non-ideal ones) can be really fabricated for those purposes.

      As to the Landauer argument made by Meuffels and Soni, I’m not convinced that it is correct. It is referenced by di Ventra and Pershin, but that doesn’t certify it. The argument looks quite specious to me. Meuffels and Soni expect the memristor state equations to yield a Landauer limit. But Landauer’s principle rests on an information theoretic aspect: a system must dissipate kTln2 Joules per bit of dissipated information. It doesn’t just fall out of the electrical state equations. For example, the Landauer thermodynamic limit also applies to an ordinary metal wire, modeled as a simple RC network. To demonstrate the limit for the RC network, you have to apply Shannon’s capacity theorem to the system; see the derivation by Mendl, et al, 2000 [link]. In the RC example, it is possible to electrically violate the Landauer limit, with the consequence that you can’t reliably extract the information transmitted on the wire. Hence there’s no physical requirement that the device obey the Landauer limit; there’s just an informational requirement.

      • You need to be very careful about the trap you’re falling into. You are pitting blog comments against hundreds of peer reviewed scientific articles. If you have a genuine criticism of memristors, then you at least need to express it in a different way. It might be the case that memristor applications are affected by the Landauer limit; it is very likely true that memrisors cannot be perfectly non-volatile — neither are capacitors! Are you going to tell me that capacitor theory is fundamentally flawed just because real capacitors leak charge? These criticisms do not affect the science of memristors. For one thing, there are applications of memristance that are unaffected by these problems. For another thing, lots of different physical memristors have been conceived, fabricated, measured and modeled. Plus, the theory of memristance provides a circuit-theory explanation for the behavior of classic devices like the coherer, and for contemporary systems that undergo ionic discharge (see Prodromakis, Toumazou and Chua, “Two centuries of memristors,” Nature Materials, 2012). It looks very much like memristance is as fundamental as resistance, and we now have a body of theory that allows us to systematically model and design systems that exploit the property. You’re staring into an avalanche and saying it isn’t real. You might want to change direction.

  3. The best way to understand the problems with the memristor concept is to perform some simulations: Take an equivalent circuit which is made up of some linear, passive elements and a “memristor” component whose resistance (memory) states depend exclusively on the current (like the HP memristor) or voltage history. Then connect a Gaussian white noise current or voltage source to this equivalent circuit and observe what’s going on in course of time.

    • I would expact the noise source to create a random walk process in the continuous memristor model. For a discrete memristor model (one with quantized resistances) it will induce something like a Markov process. Noise mechanisms are inevitable, and I have no doubt they will affect volatility in applications that require long memory. I don’t see how that’s a problem with the “memristor concept,” since the memristor is defined in terms of its dynamic (i.e. AC) characteristics. Volatility is a separate problem that only affects a subclass of applications.

      • Even if the memristor is defined in terms of its dynamic (i.e. AC) characteristics, it will experience inevitable noise while in operation. So, one can expect some stochastic drifting in course of time. That simply means that the dynamic state equations proposed for memristors describe systems having no stable or metastable equilibrium state. Do you really think that that’s the way nature works?

      • What sort of equilibrium are you expecting? If you mean that the state variables should settle to a constant fixed point, then I wouldn’t expect that. Noise introduces new energy into the system, and systems do not stay constant under energetic perturbation. I’m not seeing what physical laws are violated.

  4. I simply wonder: How does the energy landscape of a memristor system look in thermodynamic state space as a function of the internal state variables?

  5. Oh hell no!

    I’m not going to reiterate my arguments but point you to a recent article from some researchers who are friendly to the memristor hype and nevertheless conclude the following:

    “If the basic equations do not reflect the actual device physics well, as we see for the basic memristor equations, with or without window functions, low predictivity is given..”
    IEEE Transactions on Circuits and Systems – Part I: Regular Papers (TCAS-I), 61, 8, pp. 2402 – 2410, (2014)

    If a model doesn’t match up to experiment it must be modified or abandoned. This is not occurring and people like you are clinging to an incorrect model which is a shame because it diverts attention away from better models that could be useful to ReRAM research. Part of the problem is that the memristor is so over-hyped that people such as yourself don’t even realize there is a difference between ReRAM and the memristor model regardless of the facts. Many just use the “memristor” term even in legitimate ReRAM research papers without an actual attempt to compare with the theory.

    I stand by the conclusions I made during the 2010 ISCAS session and suspect as the years (decades?) pass my positions regarding the memristor will eventually be regarded as correct. I’m glad I was the first to point out some of the defects that others are now echoing. I was very friendly to the memristor concept in the first year or two by the way and did have the opportunity to meet and ask questions to Leon Chua, Stan Williams, Rainer Waser, and other memristor supporters in the first few years. However, I found that they were unwilling to question their own assumptions and have a particular arrogance which did not even want to explore any possible defects (or alternatives to) the memristor framework. Scientific progress does not occur under these conditions.

    By the way I never said anything about a “conspiracy”. Conspiracies are not necessary when so many are willing to ignore reality.

    • You are free to stand by your conclusions, but I would ask you whether, in retrospect, you would want to retract or revise any part of your arguments. Would you add any qualifications, or reduce the scope of your claims?

      I have no skin in this game. I do research in circuit theory, but memristors or resistive-switching devices are not a part of my own research agenda. I am not “clinging” to anything — I am an outside observer who is persuaded by the bulk of mainstream research in memristor theory.

      It is clear from the few “negative” papers that I have seen, such as the one you linked above, that there are many uncertainties and open issues in the modeling of resistance switching devices; I have no doubt that there are problems with all available models, and it is no surprise that older models like Strukov’s have a larger share of problems. But nothing in this paper challenges the fundamental theory introduced by Chua, nor does it challenge the broad interpretation of these devices as memristive systems. The issues raised in this paper are very narrowly directed towards specific models for a specific family of devices. It does not motivate any general conclusions about the larger picture of memristor theory or the science behind it.

      • Yes I stand by my arguments.

        It is hilarious that you refer to the article of Linn et al. as “negative”. Rainer Waser who is a co-author has been a primary supporter of HP’s memristor positions but facts are facts. Do you consider articles “negative” when you don’t like the conclusion? The models discussed in this paper are the major models discussed in the literature for ReRAM (although many papers simply use the term “memristor” or “memristive” without referencing an actual mathematical model fitting Chua’s definitions which is a problem in itself). If you are aware of other more advanced models that fit the definition of either memristor (1971) or memristive systems (1976) and fit experimental data for ReRAM better I would be interested to know about them. As it stands it appears clear that the memristor models proposed by HP do not stand up under scrutiny as applied to ReRAM devices.

        Regarding the broad concept of memristive systems (applied to thermistors, neural synapses, etc) I have less of a problem but it should not be confused with memristors and it is dishonest of Chua and HP to pretend that the terms are interchangeable. Again, I have yet to see a memristive model for ReRAM which can stand up to scrutiny and non-memristive mathematical models can be shown to produce pinched hysteresis so there is no reason to my knowledge to believe a memristive model would be optimal.

        I think falsifiability is a concept which has not been well applied to Chua’s memristor concepts (which is probably a major reason it was mostly ignored by the scientific community before 2008). If memristors are a serious scientific concept then they have to be subject to the same rules as any other scientific hypothesis. In other words the possibility of proving the hypothesis false should exist. It appears to me that you are simply ignoring that possibility and referring to any contrary evidence as “negative”. If you consider the memristor to be too “fundamental” to be falsifiable then you are not advocating science but rather something more akin to a religion.

      • 1. If, upon reflection, you can perceive no weaknesses in your own arguments or claims, then I don’t see how you’re doing any better than the accusations you’ve aimed at Chua and the HP researchers. Anyone should be able to look back at their old work (particularly from student days) and find problems in it.

        2. I describe the article as “negative” only because you cited it to support your general stance against “memristor hype”.

        3. I’m glad to hear you have “less of a problem” with memristive systems. I’m not sure what you mean by them being “confused with memristors”. There are several important distinctions with which you tend to be careless in your own criticisms. One the one hand, there is the theory of memristors and memristive systems. On the other hand there is application of that theory to classify a variety of real devices. On the third hand there is the use of explicit memristive system equations within behavioral models of specific devices.

        4. Falsifiability: this is something that really interests me and that I’ve studied in great detail. It would be very difficult to falsify Chua’s general theory on memristors and memristive systems, because this theory is a collection of mathematical consequences arising from the established theory of nonlinear electrical networks. You can’t just falsify Chua’s work unless you (A) undermine some feature of the general electrical network theory, or (B) demonstrate an uncontrovertible mathematical error in Chua’s analysis. The same is true for memristive classifications: devices which exhibit pinched hysteresis are memristive; to validate this classification it is not necessary to produce an explicit memristive system model for the device being studied. If I understand the theory correctly, pinched hysteresis cannot be produced by passive networks of resistors, capacitors and inductors. Therefore if pinched hysteresis is observed, the device must incorporate memristance or a memristive system. Since this is a mathematical classification, I don’t see where there’s room to falsify. You could perhaps demonstrate that pinched hysteresis is achievable with a passive RLC network, and that would be very interesting, but that results would only extend our understand of memristance, not falsify it.

        Where there is room for falsification is in the construction of specific models for specific devices. If a particular set of equations doesn’t fit the data, then you need better model equations. For example, MOSFETs are not well modeled by switches or linear amplifiers. You need much more complicated equations to describe the functioning of a MOSFET device, and those equations can vary wildly for different manufacturing methods and operating conditions. Nevertheless, we still consider MOSFETs to be switches and amplifiers because they adequately model the qualitative characteristics of those devices.

      • Why should one challenge the fundamental memristor theory introduced by Chua, it is nothing else but a hypothesis; maybe, some like to tinker around with the theoretical concept to make some publications.

        Despite all of the mainstream research in the hypothetical memristor theory, the essential point is: The hypothetical concept cannot be applied to any physically realizable device as it would be inconsistent with fundamentals of thermodynamics, viz., nobody will be able to propose a physical model that satisfies the hypothetical memristor equations (please, don’t point out to HP’s misleading paper “The missing memristor found”).

      • Chua’s theory is only partly a hypothesis. More fundamentally, it is a mathematical deduction from established theory of conservative electrical networks. You can’t discard Chua’s theory and keep the electrical network theory. The “hypothetical” concept of memristance is demonstrated for a variety of physical devices, including biochemical systems, vacuum tubes and the classic coherer device. Hence the hypothesis is confirmed: memristance is not merely a mathematical deduction, it is a physical property of real systems. I am also quite persuaded that the TiOx devices qualify as memristive because they satisfy the mathematical criteria for that classification.

        The papers from HP are only a few drops in a growing torrent of research on this topic. You don’t have the privilege to adopt a simplistic skeptical stance in the face of so much evidence accepted by so many of the smartest people in the field. At this point the burden of proof is turned on you, and you aren’t doing anything but reiterate discredited objections. The problem here isn’t that all these top researchers are bamboozled by false hype; the problem is that you don’t really understand the theory.

  6. 1. You are being silly here. Of course if I look back on my previous writings I’m sure I could find ways to improve my arguments. However, in general they are correct.

    2. Are you even familiar with Rainer Waser and his group? Did you even bother to read the paper? You claim to be an “outside observer” with “no skin in this game” but at the same time do not seem to possess any degree of impartiality or objectivity.

    3. I recognize the distinctions better than most and dealt with them in my 2010 presentation at ISCAS.

    4a. “devices which exhibit pinched hysteresis are memristive” – this is not necessarily true as I demonstrated in a paper I posted on arXiv. Pinched hysteresis is a necessary but not sufficient condition. Of course I expect you to immediately reject any merit of my paper so instead I point you to a paper co-authored by Chua entitled “Three Fingerprints of Memristor” published last year. In addition to the pinched hysteresis there are requirements for frequency response. To my knowledge the frequency response requirements have not been demonstrated in any ReRAM devices.

    4b. “I don’t see where there’s room to falsify” – in my view a non-falsifiable idea is a non-scientific idea and it is somewhat useless to debate it. Pre-2008 the memristor concept was non-scientific and could be ignored by science. The foundation of HP’s claims in 2008 seem to be baseless from the article by Waser’s group (among others). I notice you failed to reply to my inquiry for a paper discussing a better model not covered by the paper of Waser’s group “Applicability of Well-Established Memristive Models for Simulations of Resistive Switching Devices”. This (along with other papers you offhandedly dismiss as “negative”) seem to firmly place existing memristive models into the falsified category.

    Regarding your response to the previous commenter – “You don’t have the privilege to adopt a simplistic skeptical stance in the face of so much evidence accepted by so many of the smartest people in the field.” – This seems to be a somewhat childish statement. Smart people throughout history have turned out to be wrong and scientific truth isn’t measured by consensus. Arguing that other people you consider “smart” believe something to justify your own belief is something a child would do. Frankly you don’t really seem to me to be that aware of the literature and recent publications regarding the memristor or memristive systems to take such a high-handed position.

    • First of all, I want to make it unambiguously clear that I have no problem with the specific findings of the paper you cited or other articles that I refer to as “negative”. As I already stated, I refer to these as “negative” solely because you (or others) cite them as support for your negative position. I don’t actually think they provide that support.

      Second, you may have a valid argument with respect to frequency response conditions, and I will have to take a look at the Chua paper you referenced. Even so, this would be a narrow argument and adds little support to your larger thesis against memristor theory. I’m personally much more interested in neural models, and I can’t see how any of your ReRAM arguments undermine the work being done on memristive neural systems. Yet you seem to think ReRAM is the sole subject matter of memristor theory.

      With regard to falsification, I think you have a trivial understanding of the concept. It is frankly loony to say that Chua’s theory was non-science prior to 2008. It was a sound mathematical deduction from a well validated theory; that’s science. It has furthermore been validated independently of the ReRAM devices that you’re so hung up on. Falsfication of specific ReRAM device models is not in any way a falsification of Chua’s theory.

      Now to your last comments. It is true that smart people are often wrong, but the collective judgement of smart people in their specialized academic professions is our best standard of truth. In order to overturn a prevailing theory, you have to make very careful and rigorous arguments and subject them to peer review. You have to persuade the academic establishment. Instead of doing that, you have chosen to make superficial arguments, and when those arguments fell flat you opted to criticize the motives of major players in this area. You insulted them repeatedly in a variety of ways. You declared yourself a lone outsider champion of science, in opposition to the corrupt mainstream. In short, you adopted the very common tropes of crackpots and science deniers who troll the pages of sites like Vixra. From my vantage point, your grand thesis against memristor theory looks indistinguishable from the role played by climate change deniers: claiming to have overturned a large body of established science by nit-picking at peripheral issues.

      • Firstly, you still have not provided a reply to my inquiry for a paper discussing a better model not covered by the paper of Waser’s group “Applicability of Well-Established Memristive Models for Simulations of Resistive Switching Devices”. The paper clearly indicates the existing memristive models do not work for non-volatile memory models.

        Secondly, the frequency response requirement is also clear from the original 1976 paper by Leon Chua and Steve Kang introducing memristive systems.

        Thirdly, where do you think the memristor has been claimed to be physically validated separately from ReRAM? Please cite a reference if you know one. Note I’m not talking about memristive systems but actual memristors (i.e. a device described by a non-linear function relating charge and a time integral of voltage).

        Fourthly, my arguments didn’t fall flat. Why do you think Chua had to publish the “Three Fingerprints of a Memristor” paper? He earlier tried to argue pinched hysteresis as a defining characteristic of memristors in a paper entitled “Resistance Switching Memory are Memristors” but had to modify that which was very likely a consequence of my pointing out the ridiculousness of that claim.

        Fifthly, if I think someone’s motives should be criticized then I’ll criticize them. I never declared myself a “lone outsider” or “champion of science”. If my behavior seems unusual to you perhaps it is because I am not in academia as a career (never have been). I am not looking to protect any academic reputation and I don’t really care about publishing papers. My current job is related to patent analysis the same as it was before HP’s 2008 paper.

      • After reviewing Chua’s “three fingerprints” paper (which appears to be the maturation of Kim’s rebuttal paper, cited in my post), I can only conclude that you’re being totally dishonest or you really don’t understand what you’re talking about. The paper gives several examples of physically demonstrated memristors or memristive systems that have nothing to do with ReRAM. The “frequency response requirement” is a very basic requirement for physicality, and it demonstrates that your arbitrary counter-examples are nothing more than aphyisical gibberish. The “frequency effect” is acknowledged by experimentalists and I have observed it in my own memristive experiments; in fact, the greater surprise would be to discover a device that violates the frequency effect. Since the frequency effect is predicted by a thoroughly verified physical theory, the burden of proof lies on critics to find counterexamples. If you find a device that exhibits pinched hysteresis at arbitrarily high frequencies, then it could have very interesting ramifications for electrical network theory. But instead you have your science inside-out.

        The fingerprints paper is a great example of science working the way it should: they have taken the time to provide a detailed and rigorous response to your half-baked counter-examples. Instead you keep reiterating yourself, claiming to find counter-evidence where none exists. The Waser paper presents no challenge to the theory of memristance. By your reasoning, we could just as well make arguments like these: “Switch models are poor predictors for MOSFET behavior, therefore they are not switches and switching theory is discredited.” Or this one, “Since CMOS amplifiers are not really linear or time-invariant, the theory of LTI systems is discredited.”

        As for your behavior, it has nothing to do with being outside academia. There are many respected non-academic researchers and engineers who don’t behave the way you do. Just last week I served on a panel with a patent analyst who is also a respected scholar. Your behavior does not arise from your job or your non-academic vantage point. It arises from the fact that you are an unrepentant crank.

        I think I’ve given you a fair shot at responding to my post. Unless you have something especially brilliant to add, this conversation is closed.

  7. Yes, I agree there are memristive models for non-ReRAM devices but I asked for a true memristor (i.e. a device described by a non-linear mapping of charge vs. time integral of voltage or magnetic flux) besides HP’s model for ReRAM. Chua’s fingerprints really only cover memristive systems although he tends to use the terms “memristor” and “memristive systems” interchangeably which is one reason I consider him intellectually dishonest.

    Approximate models are fine but a line has to be drawn between a bad approximation and a false model. Otherwise no model, no matter how ridiculous, could ever be falsified. The line should be determined based on how closely the model matches experiment and it seems the memristor model for ReRAM, as proposed in 2008 by HP, is well into the falsified category at this point.

    In any case it is still early in the game. It has only been 6 years since HP’s paper. I’ll be interested to watch how things turn out.

  8. cjwinstead writes: “I am also quite persuaded that the TiOx devices qualify as memristive because they satisfy the mathematical criteria for that classification.”

    What is termed “memristor” by HP are TiOx based memory devices utilizing nothing else but “resistance switching” effects. “Resistance switching” behavior is often observed on metal/insulator/metal structures after a soft-breakdown of the insulating material has occurred. These phenomena are well known since decades and are in no way related to the theoretical concept of “memristor/memristive” systems. Probably, most resistance switching effects result from localized, partly reversible chemical/physical changes (phase transformations) in or along defective regions of the insulating layer. Such changes can be induced, for example, by local Joule heating effects and/or solid state electrolytic decomposition processes under electrical stressing.

    Owing to the stochastic nature of the various physical process underlying such complex “resistance switching” behavior one occasionally observes some current-voltage (I-V) characteristics which might remind of those hysteresis loops that are thought to be the fingerprints of genuine “memristors”, viz., such characteristics will be found from time to time when examining a huge ensemble of “resistance switching” devices. That is, however, a simple matter of statistics in case probabilistic processes rule the overall behavior. One generally finds significant spreads in switching parameters and shapes of the I-V switching curves when measuring on a set of similar devices. Thus, individual observations are not sufficient to claim that a “memristor” has been found, i.e., curve fitting of a selectively chosen I-V-characteristics is no substitute for a thorough physical understanding. Nevertheless, there are still some groups tinkering around with sophisticated models to “fit” individual memristive or “resistance switching” current-voltage characteristics, having no inkling of probabilistic processes and the appropriate statistical methods.

    • You have said exactly one thing that potentially matters: if resistive switching devices do not generally exhibit pinched hysteresis, then they do not generally fit the criteria for memristors or memristive systems. I’m not much convinced by your claim, however, since most papers on these devices show Lissajous curves with the characteristics pinched hysteresis. Take a look, for example, at the recent paper by Vavlov et al. (Waser’s group), “Nanobatteries in redox-based resistive switches require extension of memristor theory,” Nature, 2013. The article shows very explicit pinched hysteresis over many repeated traces, and also demonstrates an extended model that accounts for the non zero crossing behavior in these devices. Obviously there is no “ideal” memristor, but as I said before there is no “ideal” device of any kind. Every real device is a mixture of ideal elements.

      Let’s look at a related example: diodes. In nonlinear electrical network theory (NENT), diodes are classified as nonlinear resistors. This classification is not based on their nano-scale physical properties; it is based on their “black-box” terminal characteristics when embedded in a conservative electrical network. This classification models the behavioral attributes of diverse devices with very different physical mechanisms. There are vacuum diodes, PN junction diodes, tunnel diodes, silicon liquid diodes, and more. From a circuit standpoint, their terminal behavior matters much more than their underlying physical mechanisms. Each of these “resistor” models has to be extended under different circumstances: at high frequencies we need to add depletion and diffusion capacitances; if optical interactions are involved then we have to add active components representing those effects; in some devices it may be necessary to model “tail currents” that persist due to incomplete carrier recombination when the device is abruptly switched “off”. In spite of these details, we still say all these devices are diodes and classify them as nonlinear resistors when referring to their near-DC behavior in closed conservative networks.

      From the standpoint of NENT, you have to look at memristors the same way. If pinched hysteresis is observed in a passive two-terminal device, then you have terminal behaviors that are not obtainable from RLC networks. Therefore a memristive classification is appropriate and you can say the device is “memristive” or that its model “exhibits memristance” or “contains a memristive system” or, for short, you could just call the damn thing a memristor.

    • I’ve read the paper, it makes a weird philosophical argument that, in my opinion, is deeply mistaken about the nature and course of scientific discovery, and is not a proper way to undermine a scientific theory which has both a sound mathematical formulation and an abundance of physical evidence. The paper’s argument is reductionist, and fails to grasp that memristance is a byproduct of nonlinear dynamics. The theory exists at a higher level of abstraction from raw physical forces; it belongs to the domain of nonlinear conservative networks. You wouldn’t attack a theorem of Boolean algebra based on electric field interpretations. Similar one shouldn’t attack memristance simply because we lack a simplistic visualization of physical forces associated with it. Memristance falls out of the math, and when that happens we need to either build new visualizations to aid our understanding, or we need to abandon that simplistic activity if it isn’t helping. People are making a lot of excuses for why the memristor should considered an inauthentic discovery. Some claim Chua didn’t originate the concept. Some claim HP didn’t invent their thin-film structure. Some complain that they don’t see how the theory is useful for their purposes, or that accurate behavioral models of specific devices are more complex than the memristive idealizations. All of these complaints miss the point: memristance is a behavioral theory, novel to the domain of circuit design and analysis, which is now synthesized with a variety of real devices that exhibit memristive behaviors and can be used to understand and realize novel circuits.

      There are reasonable criticisms of memristor theory that attack it on the basis of how we should interpret “ideality”, which is a good question for refining the theory but does not undermine the value or utility of the theory itself.

      • Who the hell is still believing that the “memristor” – the so-called fourth basic component of electronic circuits – exists in physical reality? Meuffels and Soni (“Fundamental Issues and Problems in the Realization of Memristors”, arxiv:1207.7319 (2012)) have pointed out that one will be confronted with severe physical inconsistencies when imagining that “memristors” – as originally hypothesized – would exist as two-terminal solid state devices in physical reality – a critique which was finally adopted by the former “memristor” adherents Di Ventra and Pershin (“On the physical properties of memristive, memcapacitive, and meminductive systems”, Nanotechnology 24 255201 (2013)). Please, ask yourself: Why is up to now nobody of the current “memristor” enthusiasts able to refute these critical arguments?

        It should thus be clear that the “memristor” is nothing else but a mathematical curiosity. When analyzing the “memristor’s” operating principle under physical aspects, it will immediately become clear that no implementable two-terminal solid state memory device will ever function in the proposed way. Therefore, don’t mix up resistance switching effects (which are based upon localized, partially reversible phase transisiton) with the misleading “memristor” concept.

        This raises now the question: What are the claimed experimental “memristor” implementations all about? That’s very simple: The catchy label “memristor” has been and is merely used in a lot of publications to sell old wine (resistance switching effects) in new bottles. Don’t trust the hype!

      • In the IEEE Xplore database there are 433 peer-reviewed articles related to memristors in the past eighteen months. A search in Google Scholar returns 1730 matches for 2015 alone. It looks like quite a lot of people are on this bandwagon. Have you considered that you have followed a small band of denialists down a rabbit hole of meaningless and pseudoscientific semantic disputes?

  9. Hi– as a young researcher in the electrical engineering/ nanosciece field studying neuromorphic computing with memristive system dynamics, wanted to offer my thanks for such a clear articulation of some of the underlying fallacies- scientific as well as cognitive- behind some the thinking that continues to drive ‘memristor denialism’. Although skepticism is healthy, petulant skepticism that files in the face of experimental realities can actually impede the progess of the scientific community. I too found ‘The Missing Memristor Has Not Been Found”, to be spectacularly reductionist. In truth, couldn’t believe it had been accepted in Scientific Reports. In contrast, the papers by Linn and Waser , (especially ‘Nanobatteries in redox-based resistive switches require extension of memristor theory’) present valid nudges towards a more complete realization of a theory for physical memristive systems. Thanks again for your clear exposition, cheers.

  10. Thank you for clarifying a lot in this article. Especially your responses to responses were very insightful.

    The problem with theories that do not yet have a device showing off the theory’s implications always reminds me of Einstein’s rings. They were predicted but could not be proven (seen.) Einstein himself feared that – and was proven wrong not earlier than half a century later. Until we have a device that’s 90% an ideal memristor, there will be sceptics. Which is, of course, healthy for science, as long as those sceptics express their critique as you have suggested: professionally.

    • Part of the problem is that people get too hung up on what “ideal” means. Ideality is defined based on utility or convenience, and that definition can shift based on context. Pinched hysteresis is sufficient to identify memristance, and we see that in lots of places. The concept of “ideal” doesn’t need to be pinned down at this stage.

  11. The unit of passive elements
    Inductance L : [H]
    Resistance R : [Ω]
    Capacitance C : [F]
    What is the unit of memristance?
    The unit of memristance is ohm [Ω].
    (Similarly, the unit of impedence is ohm[Ω].)
    In addition, all passive elements are constant.
    Memristance is not fourth passive element regardless of charge-magnetic flux relationship

    • Junk argument. Units are [i]attributes[/i] of objects. Cones and cylinders both have the attribute of volume, but you wouldn’t say they are the same shape.

  12. I’m inclined to say based on a reading of and and et al, that HP’s device does not really fit the one suggested in 1971, because the original device implies and requires the existence of magnetic monopoles. Since none have been found in nature, it is not surprising that such a device does not exist physically.

    While the post author and some commentators seem to be of the opinion that the only relevant issue is whether the physical behavior of the device approximately matches the mathematical black box description, including not consuming external energy as active circuits do. But Chua’s original paper suggests a deeper ontological relationship between his proposed typology and the terms of series expansions of solutions to Maxwell’s equations. While physical realizations of these equations may not behave identically to them, in principle one can get arbitrarily close to them up to quantum limits by careful manufacturing control.

    I mean, there are other physically realizable energetically passive two-port devices, such as diodes and spark gaps. However, their behavior relies on bringing in other physical laws outside of classical electromagnetism. The HP implementation is fundamentally electrochemical and quantum, similar to other semiconductor devices with memory effects, like antifuses. It cannot just “fall out” of Maxwell’s equations the way the other passive devices do.

    Ultimately though, this debate is mostly academic. Science is developed largely for practical ends, and insofar as the HP device can perform useful functions, and Chua’s original paper offers an understanding of the I-V-t characteristics of this and other devices and systems, they are useful tools, regardless of whether they fit neatly into the same metaphorical box. I’m honestly shocked, no pun intended, and a little disturbed by the amount of vitriol that has been slung around over this matter. If HP wants to market its device as a memristor, that’s between it, its consumers, and its investors. No one owns the meaning of words except the people who use them. Hardly seems like the kind of thing to ruin one’s academic career and get kicked off of ArXiv over.

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