8 ms·

The lost art of Nomography

61 points by xtacy 15y ago

jfoutz 15y ago
This is fascinating. I'm a programmer, and somewhat familiar with digital circuits. I'd never really understood how someone would go about constructing an analog computer. This is it, bang on. Resistors for linear changes, capacitors for exponential curves. Pretty neat, an array of meters coupled with a bunch of analog components would solve (approximately) really complicated stuff. It's also pretty neat you can get an approximate solution in a single step, rather than cranking through a bunch of operations. It seems like a compression problem in information theory, especially when you consider the two step or multi step graphs.
- kragen 15y ago
  Capacitors (well, RC systems) are exponential in time, but their relationship between voltage and current is purely linear. So if you want to use capacitors to do exponentials, and your machine inputs are in voltage or current, you need a way to convert a voltage or current to a time delay. More typically, I think electronic analog computers used the exponential region of a semiconductor diode to do logarithms and exponents, and thus multiplication and division, in nanoseconds, using 1950s technology. You can use capacitors and inductors to integrate and differentiate time-varying functions.
dimitar 15y ago
I upvoted this article because it is really interesting, but unfortunately I disagree that nomography can be relevant today. It is forgotten so easily because its not worth the effort with the availability of computers. Computers aren't hard to use and to learn how to use. Try doing through the exhaustion of doing numerical calculations for a day with a slide rule and nomograms to see why.
- dmlorenzetti 15y ago
  Have a look at the nomograph in this paper: http://eetd.lbl.gov/ie/pdf/LBNL-1519E.pdf http://eetd.lbl.gov/ie/pdf/LBNL-1519E.pdf The anthrax attacks in the fall of 2001 brought to light a number of uncertainties about how to tell whether a building is clean enough to re-occupy (How effective is sampling? What's the anthrax dose-response curve look like? What's the distribution of spores in a building?, etc.). As part of his investigation, a colleague of mine constructed the nomograph in this paper, to illustrate the tradeoffs involved. By presenting the uncertainties graphically, the nomograph helps visualize the tradespace, in a way that simply running multiple numerical calculations won't necessarily do. By the way, this also shows that these are not an entirely lost art.
- sophacles 15y ago
  These could be really useful to include in spec sheets for various solid state electronics components. They always include graphs of current and voltage characteristics, but perhaps including a nomogram instead (or as well) could help people understand the properties of the component. They also could be really helpful to teach graphic learners about how certain relationships work -- I am certain I would have understood many concepts much faster with one of these -- particularly in physics.
- hadronzoo 15y ago
  I think nomagraphs could be very useful in realtime dashboards, where one needs to convey several interrelated values and their relationships simultaneously. Moreover, many engineers prefer nomographs because they're actually faster and more intuitive than trying to solve a problem with a computer. That's why they teach you how to use psychrometric charts in thermodynamics and Smith charts in antenna design (or at least I was taught both ~8 years ago).
  - netrus 15y ago
    Psychrometric charts where an important part of my thermodynamic lectures last semester. In engineering they are pretty useful, both because their accuracy is sufficient in many real-life situations and they give you a very good understanding and guessability for the complex formulas you are using.
- neonkiwi 15y ago
  I disagree with the sentiment that nomography has lost relevance. Anybody worth their salt doing interface design for complex systems is exploiting these principles and combining nomography and computing. For example, a power plant is littered with sensors, reading various pressures, temperatures, valve settings, etc. The traditional interfaces—a dial for every value, as per Three Mile Island—does not help a human operator in understanding the relationships in the data. Today, interfaces are designed to better explain how different parts of a system interact, and a nomograph can help an operator build a better mental model of how a change in a series of inputs affects an output. A simple calculation on a computer can produce all of the numbers defining the operating point of a turbine, but a good nomograph will convey the physical relationships of the system. I realize these types of displays aren't seen by most people on a regular basis, but they're far from irrelevant.
  - dimitar 15y ago
    I imagine something like a dynamic bode plot, from which you can judge the stability of a system. But that is a plot of data, not an analog computing method on paper. You can simply improve the presentation or organization on data. I suppose operators have computers nowadays :-).
- jacobolus 15y ago
  What I’ve always liked about nomograms, even more than their (1) usefulness for directly calculating as a practical tool is that they (2) make numerical relationships explicit/concrete, and (3) show an entire multivariate possibility space at once. This has advantages for someone trying to understand a system over both symbolic equation representations, which are very abstract, and cartesian type graphs, which often are not good at plotting more than one or two variables at once. I agree with you that with fast interactive computers it's possible to come up with other possibly better kinds of graphical representations, but the creators of those can still learn a lot from the design of nomograms.
hadronzoo 15y ago
I'm surprised the author didn't mention the Smith chart: http://en.wikipedia.org/wiki/Smith_chart http://en.wikipedia.org/wiki/Smith_chart
- shithead 15y ago
  First thing in the series of blog articles: http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-i-geometric-design/ http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomo...
jotango 15y ago
Nomographs are often used in airplane manuals. When your power plant dies, you still want to be able to calculate your range based on speed, altitude etc.
smoyer 15y ago
I'm probably older than most of the people here, but the slide-rules that I used for 10th grade chemistry were essentially nomographs (fortunately I had a calculator by the time I took physics in 12th grade). I have a couple that I keep around for sentimental reasons but haven't used them in years.
phren0logy 15y ago
Meta-comment: I know I saw something about this before, but why is it that any PDF gets a [scribd] tag, even when it has nothing to do with scribd.com? It doesn't make any sense.
- 0x12 15y ago
  Because HN promotes scribd (A YC company).
  - marchdown 15y ago
    I don't get scribd. It's annoying to get a link to their site with various limitations and cludges screwed on top of otherwise perfectly readable document. Since this is YC company, don't you happen to now if there is some not-trivially-googleable place where I can read about their agenda or fundraising pitch?
    - rgovostes 15y ago
      Scribd is awful and it's an embarrassment to this site and to Y Combinator. There have been countless posts here decrying paywalls set up by academic journals, yet while Scribd is hardly any better, they're accepted and even promoted within this community. On the surface, the ability to convert a PDF to an almost-lossless HTML document is great technology for those who use archaic browsers that balk at PDF files. For this, I give them a pass for inserting obnoxious dynamic advertisements in between pages of the document and in the sidebar. The actual service, however, is misleading and downright hostile towards users. Let me try to download the linked PDF from Scribd, using the attractive green "Download" button. Oh, I need an account. Let me log in with Facebook. This is what it requests from me: * My name, profile picture, gender, networks, list of friends, and other shared profile information. * My e-mail address, so it can send me e-mail. * The ability to post to my Wall. * The ability to access all posts in my News feed, including friends' posts. * Access to my data even when I'm not using Scribd. Mind you, this is just to download a PDF, which Scribd did not author! What's worse, after some amount of time, the linked PDF will be moved into the Scribd Archive, from which it can only be downloaded after you upload something new, or agree to pay at least $5. After opening up your private life to Scribd, you can open up your wallet too.
gking86 15y ago
I'm a CBRNE specialist, and we use these for estimating yield of nuclear detonations based on various paramaters (flash-to-bang time, angular width of cloud top, etc.)

61 points by xtacy 15y ago

This is fascinating. I'm a programmer, and somewhat familiar with digital circuits. I'd never really understood how someone would go about constructing an analog computer. This is it, bang on. Resistors for linear changes, capacitors for exponential curves. Pretty neat, an array of meters coupled with a bunch of analog components would solve (approximately) really complicated stuff. It's also pretty neat you can get an approximate solution in a single step, rather than cranking through a bunch of operations. It seems like a compression problem in information theory, especially when you consider the two step or multi step graphs.

kragen 15y ago
Capacitors (well, RC systems) are exponential in time, but their relationship between voltage and current is purely linear. So if you want to use capacitors to do exponentials, and your machine inputs are in voltage or current, you need a way to convert a voltage or current to a time delay. More typically, I think electronic analog computers used the exponential region of a semiconductor diode to do logarithms and exponents, and thus multiplication and division, in nanoseconds, using 1950s technology. You can use capacitors and inductors to integrate and differentiate time-varying functions.

dimitar 15y ago

I upvoted this article because it is really interesting, but unfortunately I disagree that nomography can be relevant today. It is forgotten so easily because its not worth the effort with the availability of computers. Computers aren't hard to use and to learn how to use. Try doing through the exhaustion of doing numerical calculations for a day with a slide rule and nomograms to see why.

dmlorenzetti 15y ago
Have a look at the nomograph in this paper: http://eetd.lbl.gov/ie/pdf/LBNL-1519E.pdf http://eetd.lbl.gov/ie/pdf/LBNL-1519E.pdf The anthrax attacks in the fall of 2001 brought to light a number of uncertainties about how to tell whether a building is clean enough to re-occupy (How effective is sampling? What's the anthrax dose-response curve look like? What's the distribution of spores in a building?, etc.). As part of his investigation, a colleague of mine constructed the nomograph in this paper, to illustrate the tradeoffs involved. By presenting the uncertainties graphically, the nomograph helps visualize the tradespace, in a way that simply running multiple numerical calculations won't necessarily do. By the way, this also shows that these are not an entirely lost art.
sophacles 15y ago
These could be really useful to include in spec sheets for various solid state electronics components. They always include graphs of current and voltage characteristics, but perhaps including a nomogram instead (or as well) could help people understand the properties of the component. They also could be really helpful to teach graphic learners about how certain relationships work -- I am certain I would have understood many concepts much faster with one of these -- particularly in physics.
hadronzoo 15y ago
I think nomagraphs could be very useful in realtime dashboards, where one needs to convey several interrelated values and their relationships simultaneously. Moreover, many engineers prefer nomographs because they're actually faster and more intuitive than trying to solve a problem with a computer. That's why they teach you how to use psychrometric charts in thermodynamics and Smith charts in antenna design (or at least I was taught both ~8 years ago).
- netrus 15y ago
  Psychrometric charts where an important part of my thermodynamic lectures last semester. In engineering they are pretty useful, both because their accuracy is sufficient in many real-life situations and they give you a very good understanding and guessability for the complex formulas you are using.
neonkiwi 15y ago
I disagree with the sentiment that nomography has lost relevance. Anybody worth their salt doing interface design for complex systems is exploiting these principles and combining nomography and computing. For example, a power plant is littered with sensors, reading various pressures, temperatures, valve settings, etc. The traditional interfaces—a dial for every value, as per Three Mile Island—does not help a human operator in understanding the relationships in the data. Today, interfaces are designed to better explain how different parts of a system interact, and a nomograph can help an operator build a better mental model of how a change in a series of inputs affects an output. A simple calculation on a computer can produce all of the numbers defining the operating point of a turbine, but a good nomograph will convey the physical relationships of the system. I realize these types of displays aren't seen by most people on a regular basis, but they're far from irrelevant.
- dimitar 15y ago
  I imagine something like a dynamic bode plot, from which you can judge the stability of a system. But that is a plot of data, not an analog computing method on paper. You can simply improve the presentation or organization on data. I suppose operators have computers nowadays :-).
jacobolus 15y ago
What I’ve always liked about nomograms, even more than their (1) usefulness for directly calculating as a practical tool is that they (2) make numerical relationships explicit/concrete, and (3) show an entire multivariate possibility space at once. This has advantages for someone trying to understand a system over both symbolic equation representations, which are very abstract, and cartesian type graphs, which often are not good at plotting more than one or two variables at once. I agree with you that with fast interactive computers it's possible to come up with other possibly better kinds of graphical representations, but the creators of those can still learn a lot from the design of nomograms.

hadronzoo 15y ago

I'm surprised the author didn't mention the Smith chart: http://en.wikipedia.org/wiki/Smith_chart http://en.wikipedia.org/wiki/Smith_chart

shithead 15y ago
First thing in the series of blog articles: http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomography-i-geometric-design/ http://myreckonings.com/wordpress/2008/01/09/the-art-of-nomo...

jotango 15y ago

Nomographs are often used in airplane manuals. When your power plant dies, you still want to be able to calculate your range based on speed, altitude etc.

smoyer 15y ago

I'm probably older than most of the people here, but the slide-rules that I used for 10th grade chemistry were essentially nomographs (fortunately I had a calculator by the time I took physics in 12th grade). I have a couple that I keep around for sentimental reasons but haven't used them in years.

phren0logy 15y ago

Meta-comment: I know I saw something about this before, but why is it that any PDF gets a [scribd] tag, even when it has nothing to do with scribd.com? It doesn't make any sense.

0x12 15y ago
Because HN promotes scribd (A YC company).
- marchdown 15y ago
  I don't get scribd. It's annoying to get a link to their site with various limitations and cludges screwed on top of otherwise perfectly readable document. Since this is YC company, don't you happen to now if there is some not-trivially-googleable place where I can read about their agenda or fundraising pitch?
  - rgovostes 15y ago
    Scribd is awful and it's an embarrassment to this site and to Y Combinator. There have been countless posts here decrying paywalls set up by academic journals, yet while Scribd is hardly any better, they're accepted and even promoted within this community. On the surface, the ability to convert a PDF to an almost-lossless HTML document is great technology for those who use archaic browsers that balk at PDF files. For this, I give them a pass for inserting obnoxious dynamic advertisements in between pages of the document and in the sidebar. The actual service, however, is misleading and downright hostile towards users. Let me try to download the linked PDF from Scribd, using the attractive green "Download" button. Oh, I need an account. Let me log in with Facebook. This is what it requests from me: * My name, profile picture, gender, networks, list of friends, and other shared profile information. * My e-mail address, so it can send me e-mail. * The ability to post to my Wall. * The ability to access all posts in my News feed, including friends' posts. * Access to my data even when I'm not using Scribd. Mind you, this is just to download a PDF, which Scribd did not author! What's worse, after some amount of time, the linked PDF will be moved into the Scribd Archive, from which it can only be downloaded after you upload something new, or agree to pay at least $5. After opening up your private life to Scribd, you can open up your wallet too.

gking86 15y ago

I'm a CBRNE specialist, and we use these for estimating yield of nuclear detonations based on various paramaters (flash-to-bang time, angular width of cloud top, etc.)