Stream of Metric Consciousness

By The Metric Maven

A coffee klatch denizen, NY Joe, kindly brought me a book titled The Macmillan Dictionary of Measurement. It has over 4250 entries and Joe was sure I’d find it interesting reading. He was right, there are many interesting aspects of the book that caught my attention, and some not in a good way. One entry took me by surprise and would have been a nice addition to my DBTC chapter Multiple Metric Systems and Metrology. There I point out the existence of the MKS (meter-kilogram-second), CGS (centimeter-gram-second) and MTS (meter-tonne-second) systems. I encountered an entry about the crinal in this dictionary, which I reproduce below:

Yes, the DKS decimeter-kilogram-second system!? I’ve encountered this system no where else in my research over the years. One might almost think it a joke, but then I’ve seen the seemingly unending historical pre-metric units, and many of them also appear to be jokes. My favorite reference has a crinal in it, and the first definition is 1 decinewton. Indeed, let’s just rid ourselves of the prefix cluster around unity. This is unit proliferation, pure and simple.

I also learned that base ten logarithms, like that used to define the decibel, are called Briggs logarithms after the early British mathematician Henry Briggs (1561-1631). In 1616 he drew up the first base ten logarithm tables. Who knew? For those who find British Thermal Units too straightforward, there is also the CHU or centigrade heat unit, equal to the quantity of heat required to raise the temperature of 1 pound of water by 1 degree celsius. That is a serious pigfish definition. It is also known as the pound-calorie. The international angstrom is a unit of length, but it is defined with a red line in the cadmium spectrum, at a temperature of 15 C and a pressure of 760 mm of mercury which is 6438.4696 international angstroms. “It is very nearly the same as an ANGSTROM UNIT (10-10 m).” What? very nearly the same? Why not call it “the horseshoe?” We also encounter a prefixed angstrom called a milliangstrom. We need a unit that is 10-13 m in length? There is also the kip, which is a: “Little-used unit of mass for measuring the load on a structure equal to 1,000 pounds avdp. (half a short ton). It was named after the first letters of kilo imperial pound.” This is serious pigfish on parade. Shoe sizes are defined, but mondopoint does not have an entry, or a single mention in the dictionary. I have written about mondopoint here and here.

The dictionary even relates a unit called the eric:

Eric [comparative values] In medieval Ireland, the blood money paid by a murderer or accidental killer (to his family) to the victim’s family in full and complete satisfaction for the death, so that no further punishment or obligation would be imposed or sought.

There is also “the finger.” As we know a hand is about 100 mm in width. Four fingers of width implies a finger would be about 20 mm (25 if the world made sense). Of course in old timey movies we see western characters order two or three fingers of alcohol, which is not exactly independent of the size of the glass.

This dictionary has very little use for milli. Millimeters and milliliters appear depreciated for centimeters and centiliters. When millimeters do appear it is often with mixed fractions.

The dictionary has the Kilotonne, which is a metric prefix applied to a Megagram which is actually a Gigagram as I point out in my essay A Kilotonne is how much in metric? The dictionary lists (with lower case of course) a megabar, megabit, megacurie, megadyne, megahertz, megajoule, megaparsec, megarad, megaton, megavar, megavolt, megawatt, and megaohm, but no Megagram! Clearly the authors of this reference, need to become a bit more acquainted with the metric system in my view. They proudly have listed tonne and kilotonne, but no megatonne, or gigatonne. Both of these nested concatenated prefix “units,” which are megamegagrams or gigamegagrams are seen constantly in reporting about global warming and elsewhere, rather than using Teragrams or Petagrams, which are properly expressed, and devoid of the archaic pre-metric “ton”, which only serves as a thumb to suck, or a skirt to hold are absent. Of course the dictionary also has metric ton and tonne

One day while using public transit to meet with me over brunch, Sven noted a fellow wearing a tee shirt like the one below:

Over the years, there has been a meme of sorts that indicates that spelling is somehow a measure of something that is intellectually indicative about a person. As I’ve pointed out, we have a number of Shakespeare’s signatures, and no two are spelled the same. The two people who wrote this book identify themselves on the dust jacket: “[one]….is a packager who produces popular dictionary and reference books in the fields of science, semantics and medicine” and “[the other]…is an editorial consultant who specializes in religion, foreign languages, place-names, and music.” They both spend an inordinate amount of time defining collective nouns, such as a murder of crows, murmuration of starlings, or a muster of peafowl. These are not exactly precisely defined units or values. The reference is indeed written like what one would expect from specialists in language, who I’m sure can spell, but have no metrology background.

Often people ask me to talk about old archaic pre-metric units, but I have no interest in doing so. There are so many “metric” and “pigfish” sub-optimal units to discuss, and then plead for people stop using; I want to concentrate on them. I encourage people to switch-over to pure efficient metric, without the tonne, micron, angstrom, or other “exceptions.” If you want to know about archaic or obsolete units that no one has ever heard of, consult John Quincy Adams. Relating numbers in the most meaningful manner possible begins with good streamlined metric usage.

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Gravitas of Prefixes

By The Metric Maven

Recently I read the book Gravitational Waves by Brian Clegg in conjunction with attending a talk on the subject. Both were quite interesting and had their method of numerical presentation in common. During the presentation it was revealed that the distance of the source of the first gravitational wave detected was 1.8 Billion light years. “Is this a lot?”—as my friend Dr. Sunshine likes to ask when putting numbers in context. I immediately wanted to know the distance with a metric prefix. If it is in Exameters, then it would be inside of our galaxy. Our galaxy is about 1000 Exameters or a Zettameter. I did not stop to estimate the values as I wanted to listen to the presentation.

First we have an Olde English prefix with a ersatz “unit” called the light year. 1.8 billion of them is 1.8 Giga units, and the light year unit is 9.4607 Petameters. We end up with  1.8 * 9.4 x 109 * 1015 = 16.92 x 1024  or about 17 Yottameters. Wow! the observable universe is about 880 Yottameters, can this possibly be right? It seems very large, just based on the metric prefix. I go to Wikipedia to see if I can verify this number. They currently quote it as 1.4 +/- 0.6 billion light years. It’s a bit less, but same magnitude. They also state it is 440 Megaparsecs. A parsec is about 31 Petameters, so we have 440*31 x 106 * 1015  or 13.64 Yottameters! I’m immediately able to  grasp the size of this number in metric, and it seems astonishing.

Assuming I haven’t made a mistake, what are the detection distances in ascending order of the gravitational wave observations to date?

GW170817 2017-08-17         1.24 Ym

GW170608 2017-06-08       10.54 Ym

GW150914 2015-09-14       13.64 Ym

GW151226 2015-12-26       13.64 Ym

GW170814 2017-08-14       16.74 Ym

GW170104 2017-01-04        27.28 Ym

This is a rather amazing list to me. They are all further out than I would have expected gravitational waves to be detected. There is an unconfirmed observation that occurred at 31 Ym. This gives me some idea of the approximate detection limit for the current version of LIGO. This list gives you metric units that allow you to compare the distances to the size of the observable universe. As our Milky Way Galaxy is about 1 Zettameter across, we could write the list in a way that allows us to use our galaxy as a measurement touchstone:

GW170817 2017-08-17        1 240 Zm

GW170608 2017-06-08       10 540 Zm

GW150914 2015-09-14       13 640 Zm

GW151226 2015-12-26       13 640 Zm

GW170814 2017-08-14       16 740 Zm

GW170104 2017-01-04       27 280 Zm

That is a lot of galactic lengths from us. According to Brian Clegg, it is expected that around 2020 a LIGO upgrade has the potential to increase the detection distance by about a factor of three. If my estimate is right, this will be about 75 Yottameters. The detection volume will increase by 30 %. A set of enhancements scheduled for implementation from now to 2026 (LIGO A+) are expected to double the sensitivity distance again. So if my estimate is good, it would be out to 150 Yottameters! With this sensitivity, several black hole mergers per hour are expected to be detected.

There are discussions of a 40 Kilometer long LIGO receiver in space called the Cosmic Explorer. This is expected to increase the volume of sensitivity to black hole merger detection to cover the entire 880 Yottameter extent of the visible Universe. That would be amazing.

Why stop there? Brian Clegg discusses a concept known as LISA (Laser Interferometer Space Antenna). The arms of the interferometer would be formed between three satellites in a triangular configuration with 2.5 Gigameter sides!  LISA would orbit the Sun following along Earth’s orbit at a distance of about 50 to 65 Gigameters! Wow that seems just really big. Below is an animated GIF of the LISA satellite array orbit.

LISA Motion — Wikimedia Commons

In Brian Clegg’s words:

Unlike a ground-based observatory such as LIGO, LISA would have the chance to take in the whole of the sky. Rather than orbit the Earth as most satellites do, LISA is planned to be  in an orbit around the Sun, following the Earth’s path at a distance of between 50 and 65 million kilometres, about a quarter again the distance at which the Moon orbits. (pg 142)

Did I compute this distance wrong? 65 * 106 * 103 meters = 65 Gigameters. The distance from the Earth to Venus is about 42 Gm unless I’m mistaken. The length of the arc the Earth travels around the Sun is about 940 Gm. This is about one-fifteenth the distance arc length of the orbit. The animated gif above seems consistent with this value.

The distance from the Earth to the Moon is 384 402 Km or 384 Megameters. 1.25 multiplied by this number is 480 Megameters. The number is not even in the right metric prefix “area code.” The Olde English prefixes when used with metric are a pigfish disaster. They provide no real magnitude distinction when concatenated with metric prefixes. I’m still concerned I’ve made a conversion error or misinterpreted Glegg’s prose.  He seems to be conflating a distance in Gigameters with one in Megameters. Perhaps the Megameter distance is the closest approach of each satellite.

Clegg discusses the history of LISA on Page 142-143:

LISA was originally a joint venture between the European Space Agency (ESA) and NASA, but in 2011, suffering severe funding restrictions, NASA pulled out. Initially, ESA looked likely to go for a scaled-down version, known as the New Gravitational Wave Observatory, but with a renewed interest in gravitational waves after the LIGO discoveries, in early 2017 a revamped version of LISA, now featuring 2.5-million-kilometre beams, was proposed at the time, was proposed and at the time of writing has just been accepted for funding. This followed the test launch in 2015 of the LISA Pathfinder, as single satellite with tiny 38-centimetre (15 inch) interferometer arms……

He uses the pseudo-inch known as the centimeter with conversion to barleycorn inches next to it to express the tiny arm length. Would writing 380 mm arms killed him?

I don’t want my readers to get the wrong impression. I like Brian Clegg’s book. It is well worth reading if you are interested in gravitational waves. (I recommended it to the audience at the talk I attended) Its pigfish metric usage is common in science writing. He is doing what essentially all other contemporary science writers do. Astronomers only offer the same manner of visceral push-back at using metric units that citizens of the US exhibit. For those of you who might be interested in metric astronomy, I recommend my essay Long Distance Voyager.

On page 58-59 Clegg explains the density of a neutron star thus:

But a neutron star consists only of neutrons. With no electrical charge to repel each other, these particles can be pulled closer and closer by gravity until the exclusion principle kicks in when they’re practically on top of one another, enabling that great mass to be squeezed into a ridiculously small space. The result is that a teaspoonful of neutron star material would weigh about 100 million tonnes.

Once again an Olde English prefix (million) and a retro Olde English “metric” value tonne serve to obscure as much as impress. When the Olde English prefix is converted to metric and the tonne converted to metric we have a MegaMegagram or Teragram! Wow 100 Teragrams! The total mass of humanity is about 423 Teragrams, so about 65 mL of neutron star would contain the mass of all the humans on Earth. If you cup both of your hands together side-by-side, they would easily contain all of humanity at this density.

The future of gravitational wave astronomy is bright, it would be brighter if it was expressed exclusively with the metric system.

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