In response to my posting about memristors the other day, Forrest Bennett made intriguing comments which I followed up with some questions that he has kindly taken the time to answer. I usually split the interviews over a few days but this time I think it’s best that the interview remain in one piece. First a few biographical details, then the Q & A. [Square brackets indicate a detail that I've added for clarification.]
Forrest H Bennett III is a senior research scientist at Genetic Programming, Inc. He has published 55 papers and a book, “Genetic Programming III: Darwinian Invention and Problem Solving”. He holds 7 patents in machine learning, automatic programming, analog circuit design, molecular mechanics, modular robotics, programmable smart membranes, reconfigurable hardware, and control systems.
Q & A
> 1.. Could you expand your comment [in response to my blog posting of April 5, 2010] that memristors have potential by indicating what those are?
The main potential of memristors is to replace current flash memory devices. Flash memory is used in almost all digital products: cell phones, cameras, camcorders, USB memory sticks, music players, ebooks, PDAs, and increasingly netbooks, notebooks, tablets, and servers. Flash memory is currently a $20 billion market and growing. Flash memory storage is preferred over hard disks because it is smaller, faster, lower powered, and inherently more reliable because it has no moving parts.
So there is a large and growing demand for inexpensive higher capacity flash memory. This requires chip makers to shrink these flash memory chips ever smaller and smaller. The problem is that this is getting quite challenging, and will become more so in the next few years.
Memristors could meet this demand for low-cost high-density memory. Memristors are inherently simple, small, fast, and low powered. Moreover, engineers at HP claim that they can construct memristor memories in 3D instead of just the 2D of current flash technology. Memristors are not exotic to manufacture, and hence could be quite inexpensive. In fact, current memristors are produced using standard chip production facilities, but not yet in sufficient quantities for productization.
There is also a lot of discussion recently about using memristors to build “neuromorphic” systems. Neuromorphic systems are supposed to work analogously to the way brains work. Memristors could be used to build neuromorphic systems that are smaller, faster, and cheaper than could be built using conventional digital technology. The reason that memristors are considered for this task is that mathematically they behave similarly to the synapses in neurons.
> 2.. Is the criterion (or one of them) for defining a new fourth element circuit that someone assigns a unique measurement for the element?
There isn’t really a rigorous way to define what a new circuit element would have to look like. But there are three arguments against the idea that a memristor is a 4th circuit element:
First, the weakest argument is that memristance is measured in the same units (ohms) as resistors, whereas the standard 3 circuit elements each have their own units of measure. This is a very simple and intuitive way to think about it, but it’s not a rigorous argument.
Second, a stronger argument is based on what we now know about memcapacitors and meminductors. Now you might be temped to regard memcapacitors and meminductors as the 5th and 6th new fundamental circuit elements, but nobody does. Why?
If you stand back and look at the actual behavior of these 6 circuit elements, it is very clear that they naturally fall into two groups. One group is the normal resistor, capacitor, and inductor. The other group contains the new memresistor, memcapacitor, and meminductor. There is no way to consider the memristor to be the 4th element of the first group. The unmistakable distinction between these two groups is that the first group are “linear” elements, and the second group are “nonlinear” elements. What does that mean?
In a linear element there is a very simple relationship between the inputs and the outputs. So if you double the input, it doubles the output. If you cut the input in half, it cuts the output in half.
But in a nonlinear element the relationship between the input and the output can be much more complex. In fact, nonlinear elements can have arbitrarily complex relationships between inputs and outputs.
The third and strongest argument against the 4th element idea actually comes from Chua’s own 2003 paper, “Nonlinear Circuit Foundations for Nanodevices”, which is a wonderful paper. It actually contains an idea even more exciting than the idea of a “4th element”. He shows an entire periodic table of circuit elements! Not only that, it’s an infinite periodic table of circuit elements! If you think he might just be pulling elements out of a hat, I must point out that he proves in this paper that all of these circuit elements are *required* if you want to be able to build all possible circuits.
Now if you look at this periodic table of circuit elements, you will see that they fall naturally into 4 classes. There is one class that contains both capacitors and memcapacitors, another class that contains inductors and meminductors, and another class that contains *both* resistors and memristors. That is the strongest argument against the “4th element” idea: Chua’s own paper puts resistors and memristors into the *same* class of elements.
You may have noticed that I mentioned only 3 of the 4 classes in the periodic table. That’s right, there *is* a 4th class of devices that you’ve never heard discussed, but it’s not memristors!
> Does Chua still theorize that the memristor is a fourth circuit element?
Yes, he is still sticking by that as of 2003 at least. If you want to call memristors the 4th, memcapacitors the 5th, meminductors the 6th, then you are forced keep going through the entire periodic table and talk about the 7th, 8th, and so on up to infinity. That’s fine. However, you can not say that a memristor is as different from a resistor as a capacitor is from an inductor – that’s not true. And you can see that it’s not true by looking at Chua’s own periodic table.
> 3.. In mentioning the memcapacitors and meminductors along with memristors, you suggest that all of them are non-linear “generalizations” and more accurately viewed as subsets rather than new categories. Could you explain the concept of a non-linear generalization in language that could be understood by a non-technical audience?
(See above explanation of linear vs nonlinear.)
Since a linear element is a very restricted special case, and a nonlinear element can be arbitrarily complex, that means that linear elements are subsets of nonlinear elements. Which means that nonlinear elements are generalizations of linear elements. (I think you said it backwards.) [Yes, I did.]
> 4.. Are there any analogies or metaphors that you could suggest that a writer (such as myself) could use when trying to explain memristors and such to a non-technical audience?
Electrical current is analogous to water flowing in a pipe. The diameter of the pipe acts like a resistor. If you make the pipe smaller, there is more resistance to the water flow. Similarly, if you make the electrical resistance larger, there is more resistance to electric current flow.
In our water example, the memristor is much like a pipe in that its size controls the resistance to the water flow. And both resistance and memristance are measured in ohms.
The difference with a memristor is that the more water that flows through the pipe, the bigger the pipe gets – so the resistance goes down. Then if you run the water through the memristor in the opposite direction, the pipe gets smaller and smaller, and the resistance goes up. So with a memristor, you can control how big the pipe is by which way you run the water through it, and by how long you run the water through it.
> 5. Is there anything you’d like to add?
So why are memristors useful? Sticking with our water analogy, I can make the pipe bigger or small depending on which way I run the water through it. And, when I turn off the water, the pipe stays at whatever size it’s at. So the pipe has a memory. This means that I can use it to store data. I can run water through it in one direction to make the pipe big, and treat the big pipe like a stored digital ONE. Or can run water through it in the other direction to make the pipe small, and treat the small pipe like stored digital ZERO. Presto! We have a digital storage device. It may not sound very exciting when described like this, but the excitement is about just how small, low powered, simple, and 3D these devices can be.
But memristors can store more than just ONEs and ZEROs. They can also store intermediate values between ONE and ZERO depending on how long and hard I push the water through the memristor. This is what makes a memristor useful in simulating a neural synapse.
Thank you Forrest for your memristor insights.