At the end of May I was at a conference in Munich on the philosophy of computing in natural science. I presented a paper "Wallace J. Eckert on Scientific Machine Computation and the Machinery of Science" on some of the attitudes of Wallace Eckert to computing. At the conference one issue that came up was how to properly understand the distinction between digital and analog computation. In particular Corey Maley gave a talk, entitled Analog Computation and Representation, about how the usual distinction made defining digital as discreet and analog as continuous is inadequate. Pointing out examples of clearly analog machines whose basic operation is discrete, as with a mechanical clock with a discrete set of gear positions. Maley suggests instead we understand analog representations as ones where what is doing the representing covaries monotonically with what it represents. For example the angle of the second hand of a mechanical clock increases proportionate with the time.
At the time I was reminded of the way that some people I had read distinguish between analog and digital machines by defining analog machines as ones based on measurement. For example:
It is not surprising that IBM development has been primarily along digital lines rather than on the non-digital or continuous methods. You are of course, familiar with these terms: by "digital" we mean a machine which essentially counts; by "non-digital" we mean a machine that measures something.
Wallace Eckert 1947, Proceedings of the Research Forum, Endicott, New York, August 26-30th, 1946, p. 76.
Note the distinction is still essentially along the lines of digital as discrete and analog as continuous but the concept of measurement is perhaps suggestive of a more nuanced distinction. I had a few other thoughts on his talk which I sent him at the time. These issues continued in the back of my mind as I went on to do other things.
Late in June I went to South Bend, Indiana, for the Notre Dame history of astronomy workshop where I gave a talk on the automatic Star Measuring and Recording engine, a device that starting from an approximate position of a star on, a photographic image, found a more precise position and punched that position onto a punched card The machine illustrates some of the trends in the work of astronomer Wallace J. Eckert and also some trends in the role of women in astronomy and computing at the time. In preparation for this talk I read the patent for the device, which I had not done previously relying instead on shorter written accounts when I had talked about it in my Phd dissertation. The device both uses and creates digital records, but measures the position of a star in an analog format, and so is a digital to analog and analog to digital converter. The patent itself discussed how the machine bridges the analog and digital:
Another object of the invention is the provision of digital to analog converting devices wherein the conversion is reversible within the same device; i.e., a digital to analog value is immediately changed back from an analog to a digital value again. The input is a comparatively coarse digital value in tenths of millimeters and the output digital value is finely divided and expressed in tenths of microns.
Column 3, lines 61-68 of Lentz, J. J., R. L. Bennett and W. J. Eckert (1960). United States Patent Office 2,922,332, "Electronic Devices for Locating and Measuring Indicia", patented January 26, 1960.
However it was when reading the following bit, a claim for the device made at the end that caught my fancy and got me thinking about the ideas Maley had discussed.
36. In a device for changing the reading of a counter under control of a value representing means, a counter containing a number, an electronic balancing device for comparing a digit of said number with a digit of said value, increase and decrease control devices operated under control of said balancing device and means under control of a selected control device for operating said counter to make it conform with said value representing means.
Column 58 lines 29-37 of patent 2,922,332
I should say "a value representing means" is patent-ese for "a means [mechanism] for representing a value" as the word "means" confused me for some time. The thing I noted is that the quantity measured is a value, while the thing the counter accumulates is a number (although both have digits?). This led me to devise the quip "A digital computer knows the number of everything but the value of nothing and an analog computer knows the value of everything but the number of nothing." I wrote Corey Maley with my bon mot and he appreciated it. I thought I should record it somewhere public for posterity since I am not sure if I will ever elaborate it.
A related incident also worth recording, on Twitter philosopher Stathis Psillos was in Switzerland and asked what the difference between a plaque and statue of Swiss philosopher Jean-Jacques Rousseau as representations. I commented that a key difference is that while a plaque relies on abstract literal encoding the statue relies on physical resemblance (shape and so on) between the statue and the person.
I added that one could confuse the plaque with a representation of fellow IHPST Toronto alumnus Jean-Jacques Rosseau (if only the name were encoded), but not a statue of one for the other. I then had a thought that not all statues represent on the basis of physical resemblance, I recalled that in the British Museum I had run across busts of various famous Ancient Greek philosophers, it seems as though they were often created long after the life of the philosopher and so the bust of Socrates I saw probably did not resemble the historical Socrates.
A few weeks later, I was in choir rehearsal at an Anglican church and I realized that crucifixes provide a stark illustration of this sort of representation, since different crucifixes portray Jesus with widely different physical attributes, however each crucifix clearly represents Jesus. Even for example this well muscled Jesus who has been making the rounds. This sort of symbolic or iconic representation is perhaps more like written representation, where an abstract type stands for a particular individual without having any clear resemblance.
Anyway the abstract symbolic literal resemblance of a plaque strikes me as largely analogous if not the same as the digital mode, whereas the physical resemblance of a from life statue strikes me as in an analog sort of mode.
So those are some of my thoughts on the distinction between analog and digital representation and machines.
Edit December 28th, 2020: Just an addendum on an issue I mentioned here I quoted Wallace Eckert defining what we would now call analog machines as involving measurement. Today I had occassion to look at the entry on "Calculating Machines" from the 1949 edition of the Encyclopedia Britannica, which Eckert added to. One section he added was a discussion of non-digital (analog) calculating methods he begins by noting:
In all the machines described so far the basic operation is that of counting discreet units; these machines are called digital machines. There is also a large class of calculators which involve measurements rather than counting; in these devices physical quantities such as length, angle, electric current, hydrostatic pressure, etc., are combined and measured. In the non-digital machines the accuracy is limited to the precision with which the quantities involved can be measured whereas in the digital machines the accuracy may be increased to any desired limit by increasing the number of counter units.
"Calculating Machines" Wallace J. Eckert and D Baxandall, Encyclopaedia Britannica: A New Survey of Universal Knowledge. Volume 4 Brain to Casting. The University of Chicago, London, 1949, page 553.
This quote reiterates Eckert's definition of analog machines as measurement machines and suggests something of the salience of the definition.
As noted one of the deficiencies of analog machines compared to digital is the difficulty in increasing the precision of accurate calculation, whereas in digital machines adding accuracy is simply a matter of adding another digit to the counting mechanism. This limitation is seen in say the older description of slide rules in the same article that notes that "To secure an additional significant figure, the length of the logarithmic scale has to be increased ten times." Whereas a digital calculator just has to add a fixed amount of machinery to add another digit, thus to make a 3 digit adder four digits requires only a 1/3rd increase in complexity, difficulty and size, to make a 3 digit slide rule good to four digits of calculation would require either increasing its length 10 fold or equivalently (and of similar difficulty) making each of its divisions 10 times more fine. In a digital machine the relative difficulty of adding another digit goes down (the absolute difficulty of each change remains the same) whereas in the analog machine the relative difficulty required for each new digit remains the same (or the absolute difficulty of adding each digit goes up). This limitation is arguably the singular reason for the fading from use and prominence of analog machines as a means of performing calculations. In Eckert's case where he worked in astronomy where precision is often at a minimum of 5 or 6 digits devices like slide rules are to crude to even consider for calculations, unlike in many branches of science in the first half of the 20th century.
Eckert's definition of these sorts of machines as measurement machines suggests immediately a plausible argument for why they are limited in their ability to add accuracy and precision to their calculations. Such increases in accuracy and precision of calculation would require an equal increase in accuracy and precision of measurements of the fundamental quantities manipulated. I am not sure if the implicit argument here does fully generalize to all the machines that are or can be called analog but it is suggestive none the less, so I note it here.
