When we think about computers and computing today, almost invariably we think about digital computers, the ever-present objects today. But reading this question in the Chemistry stackexchange, How are the atomic orbitals for multi electron atoms obtained?, there's a great answer that delves a bit into the history of quantum theory and matter modeling, with this interesting picture, reminding us that it wasn't always like that:

Douglas Hartree (left) and Arthur Porter (right) with the meccano differential analyzer.

That photo shows matter modeling pioneers, Douglas Hartree and Arthur Porter, together with a computer they built themselves to solve differential equations and study quantum-mechanical systems, in the 1930s, generating tables like these:

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That was no ordinary computer, at least not in the sense we use the word today, because it predates digital machines like ENIAC and Colossus by several years. It was an analog computer, a differential analyser built from parts of a children toy invented in 1898, called Meccano, kind of a 19th century Lego. So Hartree and Porter pulled the equivalent to someone today building a working supercomputer from scratch, out of lego blocks, and using it successfully to do groundbreaking research. It was surely an impressive feat at the time. They were real-life McGyvers.

Before the digital revolution, analog computers like the one used by Hartree were used to tackle all sorts of hard problems you couldn't calculate by hand, like ammunition trajectories and even to put men in the moon and bring them back safely. But as time passed and digital programmable devices were developed, and then became small and cheaper, analog computers became a road not taken in science, mostly forgotten, a footnote in history.

Yet, I could find a paper (1) from the 70s showing how to solve the particle in a finite potential well with them. Also, once I watched a talk by late physicist Freeman Dyson where he says it was proven (2, 3) in 1981 that some numbers are analog-computable but not Turing-computable, and thus analog computers are more powerful than digital computers, at least in principle.

That makes me wonder, the use of Analog Computers really died out in Matter Modelling, or there's still people researching their use today, to tackle problems in the field?

  1. Marron, Michael T. “Analog Computer Solution of a Particle in a Finite Well. A Physical Chemistry Experiment”. Journal of Chemical Education, vol. 50, no 4, abril de 1973, p. 289. DOI.org (Crossref), doi:10.1021/ed050p289.

  2. Richards, Ian. The wave equation with computable initial data such that its unique solution is not computable. core.ac.uk, https://core.ac.uk/reader/81930022. Acessed jul 17, 2020.

  3. Dyson, Freeman J. Birds and Frogs: Selected Papers of Freeman Dyson, 1990–2014. WORLD SCIENTIFIC, 2015. DOI.org (Crossref), doi:10.1142/9158.

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    $\begingroup$ +1. Interesting. Of course there's quantum annealers (a type of analog quantum computer) being used in materials modeling. But better answers are encouraged. $\endgroup$ Jul 17, 2020 at 21:59
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    $\begingroup$ I might try to put a answer together, but these articles might form the basis of two different answers if someone wants to beat me to the punch: news.mit.edu/2016/analog-computing-organs-organisms-0620 (analog simulations in biological modeling), spectrum.ieee.org/computing/hardware/… (analog chips for approximate differential equation solutions), link.springer.com/chapter/10.1007/978-3-030-26807-7_3 (using chemical reactions as a form of analog computer) $\endgroup$
    – Tyberius
    Jul 19, 2020 at 19:10
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    $\begingroup$ I gave my +1 here a long time back, but a user has strongly criticized questions like yours here: mattermodeling.meta.stackexchange.com/q/312/5 You may want to take a look, especially since they selected this exact question as an example, and several other of your questions. For the record, I upvoted the answer by Camps and do not approve of most of the others, so I am not saying that this question is off-topic. $\endgroup$ Jan 6, 2022 at 2:54
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    $\begingroup$ Hi ksousa! I'm just curious if my last comment might have discouraged you in any way from asking more questions here? I see that you asked 1 question since that comment. I'd like you to know that I like your questions and appreciate your overall contributions to the site, and that comment was just to let you know that you had been mentioned several times in a Meta post from who user (and that I disagreed with that user). $\endgroup$ Nov 5, 2023 at 14:51
  • $\begingroup$ No worry, @NikeDattani , it didn't discourage me. It's just, as the site became more established, I'm trying to lean more towards answering than asking. But as my answers tend to be long form, those don't come as often. $\endgroup$
    – ksousa
    Nov 5, 2023 at 22:08

1 Answer 1


I don't think analog computers are quite at the level they need to be yet, but there are people working to make them applicable to matter modeling applications.

Dr. Rahul Sarpeshkar at MIT developed simple circuits to model a particular pair of cellular protein production processes and mimic the differing pathways to the same result. They cite the continuous encoding/representation as being crucial for the simplicity of the implementation. They have also worked to address one of the biggest challenges of analog computing (the difficulty of hand crafting new circuits for each new type of problem) by developing an analog compiler to simplify going from an algorithm to a finished circuit.

Dr. Yannis Tsividis at Columbia University has worked on making analog chips that can aid digital computers in solving a problem. They found that they could obtain fast, reasonably accurate solutions to systems of differential equations. They mention the goal of passing these fast analog solutions as guesses to the digital computer, greatly decreasing the time and energy consumption needed to solve a problem. This is still a few steps away from actual matter modeling, but its easy to see how this could applied to, for example, find guesses for various electronic structure methods.

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    $\begingroup$ +1. Wow, did you just happen to know these? Or they came up while doing some research on the topic? $\endgroup$ Jul 29, 2020 at 3:18

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