# 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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# Realm of Measure

By The Metric Maven

Bulldog Edition

It can be interesting to read books from a bygone era about measurement. The current attometer per Zettasecond pace of metric change in the US requires one to look back historically to notice any change at all. I recently read the 1960 book Realm of Measure by Isaac Asimov. It is an interesting time capsule with which to compare the world of 1960 to current times. Early in the book (pg 4) Asimov asserts:

Even in modern times we are still refining our measurements. And although the world’s nations quarrel so desperately that it would seem they could never agree on anything, all have been honestly co-operating in the establishment of international systems of measurement.

Asimov’s statement indicates that more than one international system of measurement exists in 1960. This makes sense because it was in 1959 when a number of English speaking countries (including the US) finally decided to agree what the length of an inch is—well actually a yard—in terms of the metric system.

After Asimov presents pages of complicated units such as chains and the Russian verst he states (in 1960s vernacular):

Well, surely, you might think, the ingenuity of man can work out a better system. If you think so, you are right. The ingenuity of man has indeed worked out a better system, and this was done a hundred and fifty years ago. Unfortunately, we, in the English-speaking countries, have chosen not to benefit from it.

This better system is of course the Metric System.

Asimov spends time on centimeters and Kilometers in Chapter 3. Twenty-Three years later, when he writes his book The Measure of The Universe, Asimov realizes the non-utility of centimeters, centigrams, centiliters, and so on and makes this clear to his audience. But in 1960 he still introduces a table to convert from hectometers to dekameters, to decimeters, to centimeters. I have argued in the past, that from a twenty first century perspective this usage appears unnecessarily complicated, but when viewed in comparison with the plethora of US Anarchy Units of the era, even this bloated version of the metric system looks like a significant simplification (page 44-47).

The good doctor goes on to introduce the micron (pg 47):

For instance, people who work with cells, bacteria, viruses, and other microscopic objects find it useful to deal with the micrometer, which is one thousandth of a millimeter. (The prefix “micro-” comes from a Greek word meaning “small.”) This unit is very commonly abbreviated to micron, but I think this is sloppy because it hides the relationship to the meter.

Indeed, the micron is still a blemish on the metric system.

The notion of concatenated prefixes is still embraced at this time, which also balloons the metric system with unnecessary complication:

A thousandth of a micrometer is naturally called a millimicrometer, a unit which is invariably abbreviated to millimicron. The millimicrometer is a billionth of a meter and in 1960, the National Bureau of Standards has adopted the prefix “nano-” for a billionth. The millimicrometer may therefore be called the nanometer.

There is also a fatalism and acceptance of eponymous units:

..This unit [nanometer] is small enough to be used conveniently in measuring the lengths of light waves. The Swedish astronomer Anders Jonas Ångstrom suggested, in the 1860s that a tenth of a millimicrometer be used for this purpose. That length could be called a “decimillimicrometer,” I suppose, but no one ever uses that term. It is called simply an Ångstrom unit, in honor of the astronomer. Again, no one can tell from the name what the relationship is to the meter, but the thing is done, and cannot be changed.

The concatenated prefix fun of 1960 does not end there, we can even embrace the bicron if we want (page 48):

The accepted unacceptable ideas of 1960 continue when Asimov explains a contemporary desire to introduce a new unit called the X-unit! A division of this unit would be in honor of Enrico Fermi! Yet another eponymous unit. Here is a table from the text:

Asimov mentions the barleycorn and the mil, which is a feral unit that should have been vanquished from usage decades ago in the US, but is still used ubiquitously in the US Aerospace industry.

The gentle doctor argues for an idea that history and experience will squarely weigh-in against, metric gradualism. If the metric system is slowly introduced in schools he argues, the later adults would not find it so foreign:

Then, little by little, metric measurements should be introduced into common use, without necessarily replacing the common measurements. For instance, distances between cities might be given in both kilometers and miles on road maps. (pg 34)

Dual units only encourage the use of old units. This is clearly the situation in the US. Metric gradualism may eventually work, if one waits 1000 years or so.

The metric system of 1960 often accepts a pre-metric style of usage:

The Megagram is then dissed by Dr Asimov:

Asimov does not indicate that the term Megagram should be commonly used, and just accepts the current farrago of homonyms, where a metric unit is interpreted using a pre-metric Ye Olde English term for context, but I must remember, this is the world of 1960. Unfortunately, it is also the world of 2016. No one seems to notice that metric ton has nine letters and Megagram has eight. So why is the term metric ton so much more acceptable? Too many syllables?

The book lurches back and forth between cgs and mks expression which produces an intellectual vertigo. This dichotomy has always appeared to me as a proxy war between a Ye Olde English usage of the metric system (cgs), with the centimeter as a pseudo-inch, and mks, which would become SI. This struggle continues in the US, but is invisible to its participants. I see cubic centimeters and centipoise used regularly in the US.

One can be thankful that the use of millimicrons, quintals, myriagrams and such have apparently receded into history, even if the micron has not. The idea of X-units, fermis and bicrons have also exited from view. Unfortunately in the US, it is only omission of these bad practices that produce any noticeable change, as metric usage in the the US is of little consequence in the life the average person. It is easy not to use X-units, fermis and myriameters when the entire metric system is invisible in the US, but this omission is not exactly progress.

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The Metric Maven has published a new book titled The Dimensions of The Cosmos. It examines the basic quantities of the world from yocto to Yotta with a mixture of scientific anecdotes and may be purchased here.