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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Counting Your Metric Good Fortune

By The Metric Maven

James Panero, a person who likes to think of himself as the “preeminent voice of American cultural conservatism” demonstrated his reactionary bone fides (that’s Latin you know) by attacking the metric system on world metrology day in the Wall Street Journal. The essay is thankfully paywalled. The value should be meted in a negative denomination, like -$1.00, as you will want your money back after you’ve read the essay. Apparently, realizing that some of his readers, might not have the patience to read, he explained his views to Tucker Carlson on Fox News in a video. Panero is, of course, horrified that the metric system came out of the French Revolution (despite the fact Englishman John Wilkins originated the metric system in 1668) , which sanctimonious “science communicators” also need to actually research. In Panero’s view even:

Worse than the abandonment of human measure is the imposition of decimal division. From calendars to clocks, French radicals went all in for 10. That works well for abstract calculations, as with dollars and cents, but not when measuring things in the real world. The Romans counted in 12s, as in the hours on a clock and the inches in a foot. The Babylonians used 60, from which we get minutes, seconds and degrees. A simple system of 8 still exists in our ounces—and in computer bytes. Eight, 12 and 60 divide easily into halves and quarters, even thirds, while a decimal system does not. A third of a meter is roughly 33.33 centimeters, a third of a foot exactly 4 inches.

James Panero, an ersatz version of the ersatz writer John Bemelmans Marciano, demonstrates the rational superiority of pre-metric measures by expounding on their divine complexity. The Romans, of course, did not “count in 12’s,” yes they did have 12’s on the clocks they inherited from earlier civilizations, but they counted in tens. I will refer to Wikipedia, which states:

Roman numerals are essentially a decimal or “base 10” number system. Powers of ten – thousands, hundreds, tens and units – are written separately, from left to right, in that order. Different symbols are used for each power of ten, but a common pattern is used for each of them.

So, no they didn’t use 12 for counting. But he is right, they did have 12 inches in a Roman foot. Which is a point I will get back to, after not ending this sentence in a preposition. So he argues the merits of 60, 12, and 8, and in the only irrelevant cliche metric antagonists can ever seem to offer, he reacts with horror that 1/3 of a meter is 33.33 centimeters. I react with horror that he did not use 333 millimeters, but that is a tell of ignorance so bad he would be quickly vanquished from any poker game.

So he is impressed that 12 and 60 both can be divided by half and thirds? Well they also can be divided by 2, 3, 4, and 6 (not counting 1 and the number itself). That’s just four factors for 12! Why 60 can be divided by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30! Wow that’s ten factors. With just the right amount of ignorance about a subject, in this case the metric system, I’m sure our heroic cultural critic thinks I’m making his point for him. He does not realize that when using metric to build a dwelling, the basic module is 400 mm, which can be divided by 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100 and 200. That is 13 factors not counting 1 and 400. In other words, by actually planning and evaluating the arithmetic chosen, metric has easier usage than units that have been selected by the magical method of technical or market Darwinism. Panero’s preference is clear:

Nearly all customary units derive in some way from use. The acre was the amount of land a yoke of oxen could till in a day. The fathom is 6 feet, the span of the arms, useful when pulling up the sounding line of a depth measure. The meter is unfathomable, ……..

As Penero is so conservative that he certainly must use oxen on his farm, perhaps an acre makes sense. I might point out that a fathom is also about 2 meters. People can generally count by groups of 2s. You know, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 meters ……. which is close enough metrology for a “cultural critic” who uses oxen. But the “meter is unfathomable”?—I think I just pointed out it completely is fathomable in 2 meter increments.

The topic of this essay is counting. Put simply, it is the advantage that is obtained when a counting system has the same base as a measuring system. Take the Romans and their 12 inches in a Roman foot, yet, they used a counting system based on ten, and used feet with 12 inches. We currently use a base 10 system which uses 0-9 to represent numbers. If we want to use 12 as a base, we need to add symbols, perhaps a and b, like hexadecimal does. So it would be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a and b. So we would have a = 10 and b = 11 and 10 as 12. I’m sure it will be perfectly logical to understand that page a is old page 10, in all the newly numbered books in our duodecimal utopia, and page b is now old page 11. The next page is of course 10, which is old twelve. It all makes sense now!—the simplicity is obvious!

People say they want base 12 counting, but don’t really understand what that means. What they actually mean is the use of a grouping of base 10 integer numbers by 12. In other words they want integer groupings that are easy to divide with decimal numerical representation! When discussing small numbers of items we often just use direct base 10 values. For instance, we purchase a six-pack, or eight-pack, or 12-pack or 24-pack. Those are a mouth full, but we live with the long designations.

We also have collective pet names for useful integer groupings. For instance we purchase a dozen eggs, but not 0.99 dozen eggs. We would reject the non-integer number of eggs as one is clearly broken. What happens at a grocery store when you select a dozen eggs, you, or often the cashier, checks to make sure one of them is not broken. A dozen is 12 integer items, period. We have created more pet names using this pet name. For instance a square dozen is a gross or 144 items. A great gross is a cubic dozen or 1728 items. A small gross? That is ten dozen!—or 120 items. This is not a measurement system, as it only contains groupings of integer values. A googol is a pet name for 10100. These are useful values for dividing up integer objects. In the case of metric construction, the millimeter is the integer value, and a grouping of 400 millimeters is a module–with 13 factors.

We have collective nouns for animals without a clear numerical designation, such as a murder of crows, which I guess means more than 1, as a group is two or more according to dictionary definitions.

There is a clear advantage to using base ten for counting, and also for a measurement system, as there is no numerical “pet name” conversion. The grouping is the same for the integer part of a measurement value, and for the decimal part of the measurement value. 123.465 meters has a grouping of 100, with a grouping of 10, and then one for the integer part. The decimal part has groupings of 1/10, 1/100, 1/1000. They are all multiples of base 10. Now if we use a length of 123 yards, 2 feet, 7 inches and 2 barleycorns, we have reverted to other groups or pet names. We have three feet in a yard, and 12 inches in a foot and 3 barleycorns to an inch, the cognitive confusion is almost optimum, and the usefulness minimum when compared to a consistent grouping. I would think this would be obvious to a grade school student, but not perhaps to a Wall Street Journal cultural critic.

He chortles with a furtive shot at the redefinition of the Kilogram, but also uses a very, very high pitched dog whistle:

With the European Union being cut down to size, can we hope for a return to British imperial units, which the U.K. was forced to abandon after it joined? A pint’s a pound, the world around, and it beats walking the Planck.

As I point out in my essay How Did We Get Here?, the origin of A Pint’s a Pound the World Around comes from the lines of a 19th century song with these lyrics:

For the Anglo-Saxon race shall rule
The earth from shore to shore
Then down with every “metric” scheme
Taught by the foreign school

A perfect inch, a perfect pint.
The Anglo’s honest pound
Shall hold their place upon the earth
Till Time’s last trump shall sound!

It’s quite a celebration of colonialism and racism Mr Penero. As a cultural critic, you should be aware of from whence this has come. And by the way, the pint is not a pound the world around.

Pet names for units can be fun though. For instance a mouth is about 3 inches, and a foot is 12 inches, so a foot in the mouth would be 15 inches, or one Penero.