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On Beyond Yotta

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By The Metric Maven

Bulldog Edition

When I was a boy, I read a number of books by Dr. Seuss. One that immediately captured my interest was On Beyond Zebra. I don’t recall  much about the book at this point in my life other than the fact that it involved additional letters of the alphabet. Each new letter was introduced and illustrated by the author. The idea there might be unknown letters piqued my youthful interest. Here are the new letters that appeared in that book:

The first book I ever read by Isaac Asimov (1920-1992) was: The Universe, From Flat Earth to Quasar, which I recently re-read. The two books may seem far apart, but I made a connection between them when I came across a section on how the sun generates its energy. The Sun uses nuclear fusion to convert mass to energy. This process is understood using the famous equation E = mc2 developed by Albert Einstein (1879-1955).
The pressures at the center of the sun cause four hydrogen atoms to fuse into a single helium atom. After this process occurs there is a mass imbalance, the four hydrogen atoms have more combined mass than the resulting single helium atom, and the extra mass is converted into energy.

Dr. Asimov states that about 4.2 Tg (Teragrams) of mass is converted to energy every second inside of the sun. He uses pre-metric terms to describe this value as “4 600 000 tons of mass per second.” Unfortunately so does Wikipedia: “the Sun fuses about 620 million metric tons of hydrogen each second.” As I understand it 1 million is  106  and a “metric ton” is a Megagram or 106 grams for 4.2 x 1012 grams per second or 4.2 Tg per second. That’s a lot of grams. Dr. Asimov inquires: “Is it possible  for the Sun to support this steady drain of mass at the rate of millions of tons per second? Yes, it certainly is, for the loss is infinitesimally small compared with the total vast mass of the sun.”  The currently accepted mass of the sun is, approximately 2 x 1030 kg. This means it’s 2 x 1033  grams, and the proper metric prefix would be?—oh, well, there isn’t exactly a metric prefix for this value. The last magnifying metric prefix is Yotta, which allows the mass to be written as 2 000 000 000 Yg (Yottagrams). Which by current convention it appears there are about three extra metric prefixes needed to express the mass of the sun with a 2, and a minimum of two extra prefixes to use 2000 as a magnitude.

So what does “infinitesimally small” mean? Well the mass lost each second, divided by the total mass of the sun, is 4.2 x 1012 grams/2 x 1033  grams. This value is one divided by 476.19 x 1018 or 0.000 000 000 000 000 000 002 which is quite a tiny ratio. I believe this is indeed a small enough ratio to be “infinitesimally small.” Recall we are talking about 4.2 Tg per second of mass loss. Each gram has 90 TJ (Terajoules) of energy contained within it’s mass. If my computation is correct, then 378 x 1024 joules are released each second. This would be 378 YJ (Yottajoules) per second. We are approaching the limits of the metric prefix Yotta, and in only 1000 seconds we would have  378 000 YJ and see that a new prefix might be useful to describe the power released.

What is notable is that the mass of the sun is not readily expressed with a metric prefix, and it’s not all that massive for a star. It appears that the masses of stars are indeed astronomical. The most massive star is suspected to be R136a1 which is approximately 256 solar masses (a solar mass is the mass of the Sun). This means it has a mass of 512 x 1033 grams or 512 000 000 000 Yg. Clearly we are on beyond Yotta at this point. While I’ve made it clear in the past that astronomical distances are readily expressed with metric prefixes, this is not the case for stellar masses. One can see why R136a1 is described in terms of an equivalent number of solar masses and the metric system is not employed.

Asimov also makes this surprising statement:

Release of energy is always at the expense of disappearance of mass, but in ordinary chemical reactions, energy is released in such low quantities that the mass-loss is insignificant. As I have just said, 670,000 gallons of gasoline must be burned to bring about the loss of 1 gram (1/27 of an ounce). Nuclear reactions produce energies of much greater quantities, and here the loss of mass becomes large enough to be significant.

What I’ve been able find in my research on this subject is both minimal and contentious. It is mostly stated that the amount of mass lost in chemical reactions is “unmeasurable.” The few who venture to put numbers to paper (including a textbook example) end up with magnitudes on the order of 10-33 grams. One example computation has 70 x 10-33 grams as the amount of mass lost in the given chemical reaction. This would be 0.000 000 070 yg (yoctograms) and would indicate a possible need for at least two more metric prefixes. It appears that, at least in theoretical discussions, it might be useful to have two more metric prefixes on the dividing side of the prefixes.

Currently there are 20 metric prefixes from yocto to Yotta. Adding two more prefixes on the magnification side would be useful for some of this astronomical work. It would probably make sense to add a pair to the reducing prefixes also. This would increase the total number to 24 metric prefixes. This is a lot of prefixes, but is far less than the number of magnitudes scientific notation would allow, which would be 60. What I would propose is to consider adding the new prefixes, but at the same time remove the prefix cluster around unity: deca, hecto, deci and centi. They could be separated  and relegated into a set of atavistic prefixes which are no longer considered proper modern usage. They would be included as an appendix to the modern prefixes for historical reference, but discouraged for modern use. This simplification would reduce the number of prefixes back to 20 and also provide a larger dynamic range for scientific description.

In early grades it makes sense to me that only the prefixes micro, milli, Kilo and Mega would be taught as the Common Set of Prefixes. These would be the prefixes that students would generally encounter in everyday life (if the US was metric and fully engaged). In Junior High and High School the new set of prefixes I’ve proposed could be taught as the Complete Set of Prefixes. I would argue that all students (and their teachers) should have to memorize and use all these metric prefixes (without the prefix cluster around unity) in their instruction. Textbook authors should not shy away from using Megameters for planetary dimensions, Gigameters for the solar system, and all the other appropriate uses of metric prefixes.

People have objected to my proposal that we teach all students to use all the metric prefixes. They employ the argument that the Common Set of Prefixes is all that is needed for an ordinary person, and the Complete Set of Prefixes is for engineers, scientists and technical people. I reject this view entirely. It produces a scientific apartheid that keeps the public from understanding the important issues of the day, which involve engineering and science more and more everyday. What I have discovered when working with large questions, such as how much the salinity of the ocean would change if we dumped all our fresh water into it, or how much carbon is being belched into our atmosphere over a given period of time, is that these problems are tamed using appropriate metric prefixes. They allow an ordinary citizen to comfortably work with the magnitudes involved. If one talks about hundreds of billions of tons, that is a metaphor, and is not information. If the goal of education in the US is to create the most numerate population on the planet, then a good command of the magnitudes of all the metric prefixes is essential.

I would like to see a song which fixes the order of the metric prefixes in a person’s mind from the smallest to the largest, something similar to Tom Lehrer’s Element Song. Some manner of meaningless acrostic or other method of recalling the order of the 1000 based prefixes should also be developed. With the prefix cluster around unity eliminated, all the magnitudes will be of 1000 and any parsed base unit can be determined.  This would allow anyone to look at 1 000 000 000 000 000 grams and immediately relate it to the acrostic or song and “sound out” the size of the number as 1 Pg (Petagram), or conversely be able to take the 1 Pg and work out how many sets of three zeros one would need to express it. This would also be the case for 0.000 000 000 000 001 grams. It  could be “sounded out” as 1 fg (femtogram).

When all the metric prefixes no longer apply, that’s when a modern student should viscerally realize they are discussing dimensions that are so large or so small they are mind blowing, and on beyond yocto and Yotta. These values truly exist in an amazing far distant realm.

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.

International Dating

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By The Metric Maven

Bulldog Edition

It is a strange aspect of human social interaction that often two people will become embroiled in an argument, part ways, go home, continue to fume, and then be unable to recall what the subject was that  precipitated the argument.

I have had an opposite situation occur when talking with my friend Sven. I find myself involved in a conversation, Sven brings up a point I’m only slightly absorbing. I tend to dismiss the information from my mind as not that important, pay little attention to it, and then go home. When home I suddenly become highly agitated as I recall what he said, think it over, and then violently agree with his point.

This has happened twice that I recall. One instance was my initial half-hearted entertainment of the idea forwarded by Sven that perhaps centimeters might not be a good idea. I only vaguely recall what that conversation was about. In the second instance, my mind cannot recall what initiated Sven’s comments at all. What I do recall, was what he said in response: “You know, you should consider using the International Dating method.” No, this is not a suggestion for a method I might use in order to meet and date attractive women from overseas. What he was suggesting is writing dates as YYYY-MM-DD or year first with a dash hyphen, month next with a dash hyphen and then the day. So the founding of the US would be on 1776-07-04. The Gettysburg Address was given on 1863-11-19. Pearl Harbor was attacked on 1941-12-07. The Day The Music Died was 1959-02-03. Strangely, by coincidence, my father called  for the ambulance that day.

My mind showed about as much interest in the information Sven offered as it might have when shown the losing numbers printed on a year old lottery ticket. I went home, my mind started thinking about what Sven had suggested. It first it struck me that this dating method was a bit odd and perhaps unworkable. The more I thought about it, the more I realized how useful it would be, and then began violently agreeing with him. I realized that International Dating (ID) could solve many problems I had with my business data, engineering data, my outside work—well—it would help with a lot of things.

It is common in the US to write a date like July 4, 1776 as 7/4/76. Of course this leads to a problem that without some prose to provide context, that the date could be interpreted as July 4, 1976, which was the bicentennial of the US. A person in say Britain could look at the 7/4/76 as April 7, 1976. Other countries use day first, month second and year third. These ambiguities are eliminated when International dating is used. It is important to understand that leading zeros must be included when using ID. So 1776-07-04 is the correct way to write July 4, 1776. 1776-7-4 is not a valid representation, there must be leading zeros as shown previously. The date 1976-07-04 is unambiguous as the date of the US Bicentennial.

Our Hindu-Arabic number system always has the largest digit first and the smallest last from left to right. So 1234 has the one-thousand digit first (1), the one-hundred digit second (2), the tens digit next (3) and the final digit is the ones (4). This of course continues if a decimal point is added: 1234.567. It only makes logical sense to have the year first, month second and day third like we do for all other numerical representations.

When dates are written using the international standard (ISO 8601) computers automatically sort files and folders by date. This may seem like a small and inconsequential thing, but it is not. It completely changed how I did my work as an Engineer and non-professionally. The first thing I realized was that I could use it to name engineering drawings and their revisions with greater utility. The file naming form is something like this for most of my files and folders.

Name or Title which is constant YYYY-MM-DD Changeable Title or Description.

Example:

Des Moines Register 1975-08-23 Islands in a Metric World.pdf

This allowed me to have a common method of naming technical papers, newspaper articles and other files so they would automatically sort into the name of the journal, the date and the title of the article. I create folders for my consulting projects with a Project Number-YYYY-MM-DD Client Name and Project Description. Here is a screenshot of my backup folders for this blog:

A UK website has a great explanation of the ways international dating can be implemented. It turns out that one can also uniquely add on the time of day using a 24 hour clock. For instance The Apollo 13 spacecraft was launched on  1970-04-11 13:13 CST. Yes, people forget, Apollo 13 was launched on the thirteenth hour and thirteenth minute that day–well in central standard time anyway. There are a number of useful variants allowed by the ISO 8601 standard.

http://www.flightstats.com

Somewhere during my adventure with International Dating I realized that Pat Naughtin was a promoter of its use. I was sold. When people fly to visit me, I track them on a website that has the departure dates in international format. My father volunteers for a small town historical society. One of their projects was to scan all the old newspapers into electronic format. When I looked at the resulting files, the newspaper files were all named with international dating, and sorted themselves automatically. This provided confidence that the company that scanned them probably knew what they were doing. I don’t recall exactly when I discovered that my computer (PC) could be set for the international date standard—but set it I did. It can also be set for 24 hour time if one wishes. The USMA Website has a nice discussion of how to set your computer to display the international date. I have changed all my computers to display ID. The more I used the ID notation the more I liked it. My computer backup folders are always sorted, and I can erase the oldest with ease.

PC Display when set to International Date Scheme

It is after I used ID for about three to four years that I could really see how nicely it allows one to organize folders and files on a computer. This is yet one more important international standard, which we probably do not teach in our public schools.  Which like the lack of the metric system in our country, hinders our society, and keeps it mired in the past. The time for measurement and standards reform in this country has long passed. We need more than just a new metric board with Congressional authority behind it in this country, we need a US Standards Modernization Board which would implement the latest most efficient international standards into our country, teach them in our schools, use them in our government, and use them in our places of business. We can stand still and refuse to change, but the world will continue to progress forward, and we will suffer for it—even if we are not aware why.

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.