Asimov’s Metric Fossil

The mid-1970s were a period of metric delusion in the US. The entire world was changing over to the metric system, and because of that, people were told we were also doing so. Industry and government had no intention of changing anything, just as they had since the latter part of the 19th century.

It appears that Isaac Asimov was hopeful about metrication in 1975 when he wrote the book The Ends of The Earth about the polar regions of our world. On page 2 he writes:

The Sun, to be sure, is 150,000,000 kilometers* from the Earth …..

The footnote reads:

* Almost the entire world, except for the United States, now uses the “metric system” of measurement. Scientists everywhere, even including American scientists, use it exclusively. To use anything else in dealing with matters involving the whole Earth would be provincial. I will therefore use the metric system and give equivalents in footnotes now and then ….

The metric training wheels come off almost immediately, and the book is essentially all metric after the first dozen pages or so. What struck me was how seamlessly Asimov was able to write with metric. On page 114 he wrote this:

Magellan had no choice but to move farther southward, and on October 21, 1520, he finally came to an inlet that seemed promising. He made his way through it under horribly stormy conditions—550 kilometers of torture—and then came out into the open ocean at last, under conditions of such calm that, with tears running down his cheeks, Magellan called it the “Pacific Ocean” (“peaceful”), the name it bears to this day.

Throughout the book Asimov uses only metric units: grams, meters, Kilograms and so on. It is quite a surprise as contemporary popular science books continue to insist on Ye Olde English units, rationalizing it as Americans don’t use metric.

The book uses cubic centimeters:

Pg 226 Most solid substances that dissolve in water can do so in amounts that vary with the temperature of the water. In almost every case, the warmer the water, the greater the extent to which it can dissolve a particular substance. Consider for instance, a compound known as magnesium chloride. A hundred cubic centimeters of water at a temperature of 20 C. will dissolve 54 grams of magnesium chloride. Bring that same quantity of water to the boiling point, 100 C., and it will dissolve 73 grams.

Which readers know I would eschew, as the medical profession appears to have done in the US. On the next page Asimov shows the redundancy of cubic centimeters:

Pg 227 As it happens, the two gasses that make up the bulk (99 percent) of the dry atmosphere, oxygen and nitrogen, both dissolve only slightly. for instance at 0 C., 100 milliliters of water will dissolve only 0.007 grams of oxygen and only 0.006 grams of nitrogen.

He seamlessly, and it appears unconsciously, substitutes milliliters for cubic centimeters, demonstrating milliliters is fine for volume.

Despite his exceptional effort to use metric only, Isaac succumbs to using Ye Olde English Prefix Modifiers:

Page 275 The Sun is …. surrounded by a “corona,” a very thin atmosphere extending outward from the Sun in all directions in sufficient density to be detectable for millions of kilometers.

Skipping the pigfish prefixing, it could have been: “…. in sufficient density to be detectable for Gigameters.”

The book is a window into what might have been if the US were not so ignorantly sanctimonious about its measures and its inability to reform.

Paul Trusten, Vice President of the US Metric Association contracted COVID-19 in November and passed away on the 5th of December 2020. He often left comments about the essays presented here, and had been active in metric issues since the 1970s. His contribution will be missed.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page.

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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