Mr. Adams is still an influence on me with his excellent book, patents and articles on nomography. In fact, I recently created my first totally circular nomograms (for an essay I’m working on) based on an article he co-wrote in 1948. The article can be found here and I’ve extracted my two circular nomograms from the essay in progress so you can see what they look like here. (Computing mechanisms based on linkages will be the subject of an essay at some point in the next year.) Thanks, John. — Ron

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Unfortunately, I no longer have the monograph he gave me, but it appears that I may need to brush up the subject for a lecture in the maths colloquium of our local U3A (“University of the Third Age”). Your site will be an excellent starting point.

The first and simplest example was deriving the correct jet size for Aluminium sulphate treatment to effectively precipitate suspended colloids without leaving an excess in the output. (shades of Camelford)

Wow, I hadn’t heard of the Camelford incident before and I was shocked when I Googled it and read about the massive water supply contamination with aluminium sulphate! What a disaster. (I also had not heard of U3A until I looked it up—I must really be out of touch.) I hope you are able to reconstruct the basis for the nomograms. If you have questions or need any help, feel free to contact me. — Ron

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As I mentioned to Ron, I did my Master’s Thesis under Professor Adams in 1972. I used TTL logic and (simulated) RAM lookup to replace the counting processes used in earlier versions of Nomographic-electronic computers.

BTW, I Googled “nomographic electronic” and got some interesting hits including a summary of Professor Adam’s report of a study done for the Air Force

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=AD605371&Location=U2&doc=GetTRDoc.pdf

Best wishes,

–Phil Martel

In another class that year I was warmly warned that there are always two ways of calculating – figuring, and asking: data lookup. The mechanics of looking up (by counting) a nomographic calculation beautifully blend the processes without denying their philosophically separate identities.

Thanks, Bill—recollections like yours are very interesting to me. As I’ve poked around the Internet I’ve come across works of Dr. Adams online, including papers and patents. Meanwhile, his book on the used market has gotten quite expensive! — Ron

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I took a course in nomography in 1967. I ended up doing my master’s thesis in the area “A Nomographic-Electronic Computer with a Random Access Memory” (June 1972). Basically, I set up the three curves as six tables in RAM one each for x and y indexed by the scaled parameters. I interpolated the values in two sets of tables to get x1, y1, x2, and y2 then searched along the line formed by (x1,y1)-(x2,y2) for the intersection with the curve specified by the third set of tables, x3 and y3.

Best wishes,

–Phil

Thanks, Phil. I am continually amazed at the history that people have with nomography, a subject I’ve only encountered in the recent past.

The intersection of two technologies seems to bring out the most creative activities. Are you familiar with Chapter 14 (Appendix D) of Adam’s “Nomography: Theory and Application” in which he describes something along the same lines but using an optical reader and counters rather than RAM? He uses the same term, “Nomographic-Electronic Computer” or NOEL, and I gather from the bibliography he provides (which ends in 1963 when he wrote the book) that this was quite an active field of mathematical research. BTW, this book by Adams is my favorite one on nomography, really original and eye-opening.

Thanks again for contributing to the blog. I know from emails I receive that people find the comments at least as interesting as the essays. — Ron

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Thanks, Ron – Paul

*You’re quite welcome. I’m really gratified by the interest people are showing in this arcane field. — Ron*

Normally, determinant = 0 is used as a rule for detecting when a set of vectors based at the origin doesn’t span the whole space. So, for points in a plane, normally you’d have a 2×2 determinant that detects whether two points are collinear with the origin, but here we have a 3×3 determinant that detects whether three points are collinear with each other, not including the origin. So what’s going on? The trick is to take that third column seriously and read it as the z coordinate of the points. Three points in the plane z=1 are collinear with each other if and only if they’re coplanar with the three-dimensional origin … and that’s exactly what a 3×3 determinant detects.

*Very interesting—I haven’t seen this explanation anywhere and it’s a really neat way to conceptualize why the standard nomographic form works. Thanks, John. — Ron*