# Stuperior Units

Those of you who have read this blog from the beginning know that I’m not a big fan of light-years. They are a “unit” so small, it takes 4.25 of them to describe the distance to our nearest star. As Douglas Adams said:

Space is big. You just won’t believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to space.

Light years don’t cut it. Light years want to be both a dessert topping, and a floor wax. One could make the argument that light years are useful because we can get an idea how long ago we are looking at the light of given galaxy, or star is. From every star we see light from a different time period. Well, why not just put the time in seconds? The time delay unit could be seconds. Why not designate a star with a distance in the metric system, and a time delay
in seconds with a metric prefix? I’ve used prefixes in the past to define the distance boundaries to celestial objects:

The farthest back in time we can see when we look at stars within our galaxy are 3333 Petaseconds or 105 626 960 years. Using a Ye Olde English non-prefix we have about 106 million years as the limit of time delay. Let’s take a couple of examples:

I used this as an example, but it’s not a great use of Naughtin’s Laws. We might want to construct the table this way:

It seems we can use all Petameters and Megaseconds for stars inside of our galaxy without much heartburn. There is the distance and amount of time delay in Petameters and Megaseconds.

I was recently reading the book A Brief History of Time Keeping by Chad Orzel. The book has some interesting information, but clearly he had thought about time more than distance. It looks like he has some affinity for using metric when he states on Page 208:

Of course the speed of light is enormous—186,000 miles per second in American units, 300,000 km/s in the rest of the world.

All through the book he could not help but almost exclusively and constantly use English “metric inches” (aka centimeters). Then he offers this observation:

Given the high speed of light (very nearly one American foot per nanosecond, about the only place that measurement system is superior),…..

So the author is celebrating a pigfish description?—Feet per nanosecond, as superior? Apparently the author finds this superiority so obvious, he does not have to clarify what he means. The simple argument seems to be that a foot is a better unit than 300 mm. Is he arguing that he has a better “feeling” for the distance of a foot than for 300 mm? This “feeling” he experiences makes it superior? If the author had only learned the metric system, would a foot be anything other than meaningless? I can’t see a technical reason for the fact that light travels in a nanosecond about a foot is of any advantage in any computation. This is also about three hand widths for an adult male human. A US foot is 304.8 mm, and is only 4.8 mm from the magical length that light travels in a nanosecond. Of course the US unit is superior as it is very close to this arbitrary value of a light-nanosecond. Look how close it is to an abstract value of a male human adult foot—amazing!

Let’s suppose for a moment that one wanted to measure the distance over a long interval using one’s body. Well, putting one foot in front the other would be tedious. Apparently the US Military realized this, and does not address using feet. Instead, they use pace count. It is stated online that “A pace is equal to one natural step, about 30 inches long.” Why not 36 inches? I guess feet and yards are not as perfectly attuned to the body that one might expect this “natural system.” I expect an Asian pace might on average be shorter than those of the Nordic countries. I can tell you Sven’s is much longer than mine. What to do?

Well here is the suggestion—calibration:

One way to measure ground distance is the pace count. A pace is equal to one natural step, about 30 inches long. To accurately use the pace count method, you must know how many paces it takes you to walk 100 meters. To determine this, you must walk an accurately measured course and count the number of paces you take. A pace course can be as short as 100 meters or as long as 600 meters. The pace course, regardless of length, must be on similar terrain to that you will be walking over. It does no good to walk a course on flat terrain and then try to use that pace count on hilly terrain. To determine your pace count on a 600-meter course, count the paces it takes you to walk the 600 meters, then divide the total paces by 6. The answer will give you the average paces it takes you to walk 100 meters. It is important that each person who navigates while dismounted knows his pace count.

Every person is metrologically different? Say it’s not so John Quincy Adams! There are further complications:

(1) There are many methods to keep track of the distance traveled when using the pace count. Some of these methods are: put a pebble in your pocket every time you have walked 100 meters according to your pace count; tie knots in a string; or put marks in a notebook. Do not try to remember the count; always use one of these methods or design your own method.

(2) Certain conditions affect your pace count in the field, and you must allow for them by making adjustments.

Under (2):

``````(a) Slopes. Your pace lengthens on a downslope and shortens on an upgrade. Keeping this in mind, if it normally takes you 120 paces to walk 100 meters, your pace count may increase to 130 or more when walking up a slope.

(b) Winds. A head wind shortens the pace and a tail wind increases it.

(c) Surfaces. Sand, gravel, mud, snow, and similar surface materials tend to shorten the pace.

(d) Elements. Falling snow, rain, or ice cause the pace to be reduced in length.

(e) Clothing. Excess clothing and boots with poor traction affect the pace length.

(f) Visibility. Poor visibility, such as in fog, rain, or darkness, will shorten your pace. ``````

Perhaps some clever person could realize that perhaps this might better be done in pace-seconds?—-please tell me you realize I’m joking. This exercise points out how poor and variable a measure the human body is for accurately determining distance, and also how easily distracted humans are. Everyone who uses a ruler, Asian, Nordic, girl, boy, woman, or man have access to the same length measure using metric. Don’t add time to your rulers. Despite what you hear, their is no “length of time.”

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: Our Crumbling Invisible Infrastructure. It is a succinct set of essays  that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website,  but the book has them all in one place in print. The book may be purchased from Amazon here.

The second book is titled The Dimensions of the Cosmos. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.

The third book is called Death By A Thousand Cuts, A Secret History of the Metric System in The United States. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.

# 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.

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.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: Our Crumbling Invisible Infrastructure. It is a succinct set of essays  that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website,  but the book has them all in one place in print. The book may be purchased from Amazon here.

The second book is titled The Dimensions of the Cosmos. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.

The third book is called Death By A Thousand Cuts, A Secret History of the Metric System in The United States. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.

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