Comments on: The Art of Nomography II: Designing with Determinants http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/ Lost Art in the Mathematical Sciences Fri, 10 Sep 2010 06:04:31 +0000 http://wordpress.org/?v=2.2.1 By: John Burroughs http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-1732 John Burroughs Wed, 01 Sep 2010 16:57:33 +0000 http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-1732 <p>Douglas P Adams was my father's cousin so, I guess, mine too. I knew him well. I introduced a fellow engineer to him as he was pursuing mathematical analyses of 4 bar linkages and Doug was interested in nomographic solutions. I felt that if I knew 2 people interested in this esoteric subject it was my obligation to acquaint them. Years later I met my friend and he said that introduction changed his life as Doug inspired him to teach part time. Doug passed away suddenly in the late '70s. Recently the family has been uncovering letters between Doug and my late father which reveal much about their early years growing up poor but undaunted in Charlestown, MA.</p> <em><p>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 <a href="http://www.myreckonings.com/Temp/Developments_in_the_Circular_Nomogram.pdf" rel="nofollow">here</a> and I've extracted my two circular nomograms from the essay in progress so you can see what they look like <a href="http://www.myreckonings.com/Temp/Circular_nomograms_based_on_Adams.pdf" rel="nofollow">here</a>. (Computing mechanisms based on linkages will be the subject of an essay at some point in the next year.) Thanks, John. --- Ron</p></em> Douglas P Adams was my father’s cousin so, I guess, mine too. I knew him well. I introduced a fellow engineer to him as he was pursuing mathematical analyses of 4 bar linkages and Doug was interested in nomographic solutions. I felt that if I knew 2 people interested in this esoteric subject it was my obligation to acquaint them. Years later I met my friend and he said that introduction changed his life as Doug inspired him to teach part time. Doug passed away suddenly in the late ’70s. Recently the family has been uncovering letters between Doug and my late father which reveal much about their early years growing up poor but undaunted in Charlestown, MA.

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

]]> By: Nomograph « Tux World http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-1473 Nomograph « Tux World Thu, 04 Feb 2010 18:25:23 +0000 http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-1473 [...] http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/ [...] […] http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/ […]

]]> By: John http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-1240 John Fri, 16 Oct 2009 21:15:41 +0000 http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-1240 <p>I was introduced to nomograms and determinants by my uncle in about 1950. He was responsible for water purification in the then Gold Coast and developed a set of simple lab routines to calculate the dosages of chemicals for optimum treatment. These involved nomograms, which were drawn to a large scale, printed, waterproofed, and hung on the wall of lab with an attached piece of string. The result was a HMSO monograph describing the whole systems.<br /> 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.</p> <p>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)</p> <em><p>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</p></em> I was introduced to nomograms and determinants by my uncle in about 1950. He was responsible for water purification in the then Gold Coast and developed a set of simple lab routines to calculate the dosages of chemicals for optimum treatment. These involved nomograms, which were drawn to a large scale, printed, waterproofed, and hung on the wall of lab with an attached piece of string. The result was a HMSO monograph describing the whole systems.
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

]]> By: Carnival of Mathematics #56 « Reasonable Deviations http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-1141 Carnival of Mathematics #56 « Reasonable Deviations Fri, 28 Aug 2009 07:32:40 +0000 http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-1141 [...] Doerfler wrote three beautiful posts on the lost art of Nomography. If you like to write code in Python, you can create your own [...] […] Doerfler wrote three beautiful posts on the lost art of Nomography. If you like to write code in Python, you can create your own […]

]]> By: Phil http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-949 Phil Fri, 29 May 2009 18:40:43 +0000 http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-949 <p>Hi Bill, </p> <p>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.</p> <p>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<br /> http://www.dtic.mil/cgi-bin/GetTRDoc?AD=AD605371&Location=U2&doc=GetTRDoc.pdf </p> <p> Best wishes,<br /> --Phil Martel</p> Hi Bill,

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

]]> By: Bill http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-943 Bill Mon, 25 May 2009 17:19:55 +0000 http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-943 <p>I studied under Professor Douglas P. Adams fifty years ago exactly and wrote a paper for him exploring his idea of spinning and summing across a film dotted with coordinate bits and variable bits. Another student as I recall actually built the circuits required. I was intrigued as I had written Univac I programs to test the FOSDIC device designed to translate census form blackened spots onto unitape for census processing ("film operated sensing device for input to computers"). In my subsequent career writing software for computer manufacturers and small and large businesses I never had to address the engineering calculations addressed by this kind of logic. Only in my recent study of robotics do I see how useful this device might have been, in the early days of Moore's law. Now all that's left is the beauty. </p> <p>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.</p> <em><p>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</p></em> I studied under Professor Douglas P. Adams fifty years ago exactly and wrote a paper for him exploring his idea of spinning and summing across a film dotted with coordinate bits and variable bits. Another student as I recall actually built the circuits required. I was intrigued as I had written Univac I programs to test the FOSDIC device designed to translate census form blackened spots onto unitape for census processing (”film operated sensing device for input to computers”). In my subsequent career writing software for computer manufacturers and small and large businesses I never had to address the engineering calculations addressed by this kind of logic. Only in my recent study of robotics do I see how useful this device might have been, in the early days of Moore’s law. Now all that’s left is the beauty.

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

]]> By: Phil http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-790 Phil Sun, 01 Mar 2009 21:25:24 +0000 http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-790 <p>Ron,</p> <p>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. </p> <p> Best wishes,<br /> --Phil</p> <em><p>Thanks, Phil. I am continually amazed at the history that people have with nomography, a subject I've only encountered in the recent past.</p> <p>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.</p> <p>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</p></em> Ron,

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

]]> By: Paul http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-588 Paul Tue, 16 Sep 2008 21:45:00 +0000 http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-588 <p>Very excited seeing this. I took a course in nomography in 1961. It still works!</p> <p>Thanks, Ron - Paul</p> <p><em>You're quite welcome. I'm really gratified by the interest people are showing in this arcane field. --- Ron</em></p> Very excited seeing this. I took a course in nomography in 1961. It still works!

Thanks, Ron - Paul

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

]]> By: John McIntosh http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-165 John McIntosh Sun, 23 Mar 2008 16:22:03 +0000 http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-ii-designing-with-determinants/#comment-165 <p>Here's a possibly-helpful thought about why the determinant works.</p> <p>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 2x2 determinant that detects whether two points are collinear with the origin, but here we have a 3x3 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 3x3 determinant detects.</p> <p><em>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</em></p> Here’s a possibly-helpful thought about why the determinant works.

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

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