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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The Swedish Chef of Metric

By The Metric Maven

I’ve always had a soft spot for Sweden, even though I have never been there. I spent some of my youth living in the American ersatz version called Minnesota. I liked living there enough that a local grocer in my Iowa hometown would say “we don’t allow Minnesota Swedes in here” to rib me about it.

I try not to read too many of the online comments in reaction to my views on the best usage of the metric system from Europeans. Generally I’m told how they are from long-time metric countries, and I, who live in perhaps the last non-metric country, have no standing to discuss metric. Italians tell me they happily use deciliters, and the French embrace centimeters like freshly baked bread. I don’t get that excited, and tend to yawn at their oral gesticulating. I’m only concerned about the US, and should a miracle occur and it become metric, would push it do so with the best metric implementation possible—by 1000. I also have no emotional connection with Italy or France.

Pierre, the master chef, machinist, woodworker and histrionic anti-metric warrior, loves to go for the emotional jugular when amiably pointing out the “difficulties” in using metric to test my mettle, but he did not have good knowledge of an effective European target. Point to the French all you want Pierre, I have no emotional entanglement. But as a stopped watch is right twice a day, Pierre managed to hit an accidental bullseye when he brought up the Swedes in an email:

Next, bad news for you, I’m afraid. But, maybe I can benefit, so it’s really good news.

As you can see from the book “Scandinavian Quilt Style blah blah blah” Scandinavia doesn’t use the metric system! I’ve deleted the part of the book actually related to the contents, except the important page, which I’ve thoughtfully highlighted for you to make it easier to read. You are welcome.

Money quote:

I work with inches. I have used inches for years, my instructions are in inches and the people I sew with all use inches. All the designs in this book were made with inches and the instructions were written while sewing.

Published by a European publisher. For Europeans.

The good news (for me) is that there may be an opening to be an Imperial measurements consultant in Norway. Somebody’s got to help them transition back into the civilized world. Don’t be afraid of inches tour ’18. Yah!

Well, I did my best to remind myself that the clothing and textile industry from the days of Samuel S. Dale onward have done their best to repel any logical implementation of the metric system. Indeed, for some reason woodworking Swedes also hang onto their non-Anglo-Saxon inches, like crayfish at kräftskiva, but I’m also told that woodworkers often don’t bother to measure anything. I kept averting my eyes from Pierre’s prose, as if I was watching Freddy Kruger chasing down teenagers. Then Pierre continued his schadenfreude laden monologue:

This whole metric system thing is soooooo easy, huh?

Here’s a page from noted Swedish food author Erica Palmcrantz Aziz …. In her brand new book Superfood Boost, she presents a lovely voice trying to convince us to eat raw kale as often as possible. Yum! She also has a page on growing your own sprouts.

Here is that page. I call your attention to that first paragraph. The rest makes more sense, if you don’t mind moving your sprouts around from container to container for no reason.

Now, …. I’m sure that you are just like me and measure out precisely 1.5 fluid ounces of mung bean seeds, each time you sprout. But, how handy to know that in Sweden, she would use, and correct me if I’m wrong, one deciliter of seeds. That sounds like about a pound, which would fill my kitchen sink with product.

I’d use a tablespoon or two per quart jar. Apparently, their metric jars must be much bigger in the festive, kale eating world of Stockholm. (Actual quote from her book, “Kale is not just for Christmas anymore” p.27)

Later she says this: “Massage and toss the cabbage (and by this, she means kale) with some olive oil, salt, and lemon, or

add it to a smoothie or juice, or enjoy it with a creamy dressing. “

So, slather that stuff with a traditional Swedish ranch dressing and it’ll help you get it down. You know, for health.

Another time she says a benefit of kale eating is, “To fill up on chlorophyll, which is said to purify and detoxify the blood”

Now, I have a liver for that function, but your shitty cold-weather desperation tundra food “is said” to detoxify my blood?

We’ll let’s have some of that.

Massage your kale, Maven. Embrace the deciliter. Purify your blood. A wealth of wisdom here. You might want to download it.

So 100 mL and 500 mL was too difficult to use in Sweden?—deciliters are a better idea? Oh…the pain “Børk! Børk! Børk!”

A point I have made over the years is that countries that adopted the metric system in the 19th century are at a disadvantage over those who waited until the late 20th century to convert. Sweden, showing their progressive nature, embraced the metric system in 1876, after ignoring it for 9 years of their 10 year conversion, but like most metric countries, they adopted it, and then never thought about upgrading its use. This lack of introspection really cuts me to the quick. The happy Sven jokes I heard in Minnesota, are not as fun when I think of this fact. The use of deciliters and such by the Swedes indicates they are Mormons Making Coffee when it comes to the metric system. New Zealand (1969), Australia (1970) and South Africa (1971) use millimeters in their housing construction. They fearlessly use milliliters and grams without the prefix cluster around unity to cook.

Please Sweden, don’t leave me bereft, measure your meatballs in grams, measure their diameter in millimeters, and express their volume in milliliters. Until you do, it will perennially feel as uncomfortable as a warm winter for me. Don’t make me wait until Fimbulwinter freezes hell over, although that might still happen before the US becomes metric.

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