# Nested Units

By The Metric Maven

Bulldog Edition

My friend Kat once told me this joke:

Einstein, Newton and Pascal decided to play hide and seek. Einstein put his head against a nearby tree and began counting. Newton only traverses a couple of paces, then reaches into his coat and produces a piece of chalk. He draws a perfect one meter square on the pavement, and then steps into it.

Einstein finishes counting, looks up, and immediately sees Newton standing near him. Einstein says with surprise, “Newton, you really suck at hide and seek, I immediately found you.”

Newton replies “No, no, no you haven’t, you found one Newton per square meter!—-you found Pascal!”

Longtime readers may recall that I’m very much against the adoption of unit identifiers which are the names of persons. If memory serves, Isaac Asimov argued that the names of units should provide a clue as to what they might be. I’m very much of the same mind. As you might imagine I have a first order aversion to the “nesting” of units named after famous scientific persons. When I was taking some long forgotten class in engineering mechanics, I recall a number of problems which defined pressure in pascals. I didn’t question the pascal, but it always seemed a bit remote as far as gaining an intuitive understanding of the amount of pressure present.

I had not really thought much about those ancient exercises in engineering until recently. I was visiting my father in my small hometown, and he was working with another person installing a new Japanese printing press. A technician was installing air for the pneumatics, but was familiar with using pounds per square inch (PSI). He asked me “what is the conversion between pascals and PSI?” to which I could only reply that I could not recall it off the top of my head. The conversion is 1 PSI = 6894.757 pascal. The PSI is so removed in magnitude from a pascal, that one would need to deal in Kilopascals to obtain 1 PSI = 6.895 Kilopascals. But at that moment I was at a loss and could only blurt out what I thought was a useless statement: “well, a pascal is a newton per square meter.” The countenance of the technician brightened. It was clear that my statement actually helped him to understand that the metric system was not somehow creating a mysterious and esoteric alternative to force over area, but that a pascal could actually be related to a pound per square inch in terms of a newton per square meter.

What struck me was that SI, in its quixotic rush to further fete scientists who will never be forgotten as long as the scientific endeavor and humanity continues, have obscured meaning. When I was a boy and first heard pounds per square inch, I understood the concept immediately. The Ye Olde English unit expressed itself within its name. If I had a small one inch square of wood, and I stood on it and weighted 100 pounds, it would be 100 pounds per square inch. If the cross-section of the wood became smaller and smaller the pressure in pounds per square inch would increase. When the area is reduced to a small point it can puncture objects with little applied force. The spear, and arrow rely on an understanding of this principle, and they are some of the first technological tools used by humans. Understanding force over an area, allows one to comprehend why women in high heels attempt to avoid walking on grass, and when they do, they ramble across it on their toes. The pounds per square inch of their heels will easily puncture the sod and form a vacuum that might capture their shoes in place. When neighborhood boys taught me how to patch the inner tubes of my bicycle tires, there was no confusion when they told me how many pounds per square inch were needed for proper inflation. The concept was very intuitive.

The use of the word newton to describe a kilogram-meter per second squared makes as much sense as the pound, and has a name which cannot claim to be a superior nomenclature. The cgs unit of force, the dyne, at least used a word which was not that of a person, and also attempted to use a word which is similar to dynamic. It attempted to describe in words what the unit describes mathematically. In my view SI then doubles down on anthropomorphism at the expense of explanation by calling a newton per square meter a pascal. If a newton per square meter was abbreviated as NSM for newton per square meter, and dual scale gauges found in the US had PSI and KNSM a person who was transitioning to metric could understand that metric was at least on the same planet as the Ye Olde English units. A pascal is an abstract notion by comparison and only serves to conceal information, and not express it.

When I did EMI testing in a GTEM years ago, the amount of noise generated by electrical equipment (often horrible tones) were measured with a device which required the computation of dBspl (decibels Sound Pressure Level) and I recall immediately converting to newtons per square meter for the math used to process the data. The pascal was never really expressive in a way that attracted its direct use. In my view for SI to become more intuitive and useful, questions like this need to be examined, and possible simplifications should be considered, and if they make sense, instituted. If Einstein could not see an obvious relationship between a Newton per square meter and Pascal—why should we?

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## 10 thoughts on “Nested Units”

1. While proper names for SI units may not be sufficiently illustrative of the unit in question, they may keep at bay those luddites who insist that the SI suffers from terminal complexity. One can find a unit by “finding Pascal,” but kg*m/s^2 might be a harder sell. I suppose it comes down to how American metric education will come down. If the derived unit were always to be stated in terms of the base units instead of being nicknamed, it would be a plus for knowledge, but perhaps a minus for public relations. I do stop to think here that those who guide the BIPM were the ones who opened the gate on proper names, so it may be a question on how much we trust their judgement.

2. Not using Peoples names as unit identifiers is fine with me, but there are times when using compound units can be confusing.

The Reynolds number comes to mind – as well as the messy(or should I say sticky?) units of Viscosity.

https://wiki.xtronics.com/index.php/Viscosity
(Yes, it would be better to get rid of all those cm units from that page.. )

There is a twist here where it has become handy to have a common set of units where 1 = the Viscosity of water that becomes the basis of comparing different substances.

In the end – I suppose the Poise and Stokes should go away – but I’m a little torn as I would not realize at once if I was looking at a stickiness number from Ns/m^2. Perhaps the best way would be to always note it as Ns/m^2(Viscosity).

I think you would have a hard time to talk engineers out of their beloved Reynold’s number. Would m^4gs^2/m^4gs^2 be less confusing?

3. I think I have to disagree. The named units have physical descriptions closely related to the names of men associated with the unit — Newton, laws of motion including relationship of force and acceleration, Pascal, fluids, pressure, hydraulics. Whereas dyne means nothing to me (had classical Latin, not classical Greek).

As the pascal is a relatively recently named unit, the reference pressure for sound pressure level in decibels was 20 µN/m² for a LONG time before it was 20 µPa. You may well have been trained from material older than the pascal; I was. The pascal was approved in 1971. The newton was named in 1948, and was previously (1946) known as the “unit of force,” not a very catchy name.

4. When I think of Pascal, I think of his triangle and the related proto-pachinko machine (he called it a “quincunx”).

• BTW, in pre-tech days (say, before 1980), a modern version of Pascal’s quincunx was used to illustrate the probabilistic connection between a binomial distribution and a normal distribution.

Nowadays, such an illustration is extended to hundreds/thousands of rows of Pascal’s Triangle, with different probabilities, to illustrate a form of the Central Limit Theorem, which is the foundation of many things in science and life, such as the margin of sampling error in a well-designed public-opinion poll.

Now, back to whether or not pascal (Pa) should be the name given to the unit of pressure N/m^2 (and, for me, back to Game 4 of the Rangers-Lightning series…)

5. I think that more complex units like kg m/s² should get names but simple units like N/m² should not. This will keep the metrics system using simple units.

6. In legacy units, a pound is both a force and a mass. That may make PSI slightly more intuitive to an average person because they can relate the force to what they feel when they pick up a 1lb (mass) object. But it makes engineering complicated.

The slug is an obscure unit of mass equal to about 32.2 lbs (mass) designed to make the equation F=ma work to get F in lbs (force).

1 lb(f) = 1 slug * 1 ft/s^2 = 32.2 lb(m) * 1 ft/s^2

But outside of engineering circles, no one knows what a slug is. You can’t go buy a slug of anything anywhere.

The Newton and kilogram correctly separate the concepts of force and mass.

• The slug is obviously an engineering unit. If you place a small saucer of beer in your garden, all the slugs in your garden will be in it getting drunk and drowning.

Numerically, the slug/lbm ratio is standard gravity converted to Imperial. 9.80665/0.3048 or ~32.174 05, actually exact to as many digits as you carry the math, since both factors are exact.

7. I am a first time replyer, longtime listener/reader and I always enjoy the thoughtful comments of your readers. I guess, my thoughts on a lot of this is in the conspersey theories area, the money or both. Keep the money where it is game.

I think a lot of this is a planed dumbing down of the population?
Less competition.

PS, I found a better picture of my Road Runner if you are interested and new reboot of X-Files(6-Hour Movie) is coming back to TV. David Dechovny is also doing a new series on Charlie Manson pre-murder cult years called Aquarius on NBC May 29th.

8. Oh, dear, oh dear. if you carry on like this I change back to the medieval hodge podge :-)))