I periodically collect postings about similar subject matter into one compound posting. This is a new compound posting about measurement. Much of the material is new.
TABLE OF CONTENTS
1) THE UNTOLD STORY OF THE METRIC SYSTEM
2) WHAT THE METRIC SYSTEM MISSED
3) THE REAL STORY OF AMERICA AND THE METRIC SYSTEM
4) MOLES AND COULOMBS
5) THE MOST USEFUL UNIT
6) WHY WE SHOULD COUNT BY TWELVES
7) A VERY USEFUL TOOL
8) THE MEASURABLES
9) THE 720 DEGREE CIRCLE
10) CHART NAMES
11) NEW UNITS OF MEASUREMENT
1) THE UNTOLD STORY OF THE METRIC SYSTEM
Division used to be far more important in society than it's opposite, multiplication.
Time is the most thing that we measure. But time is something that we have in fixed quantities. It can be divided between tasks that have to be done, but cannot be multiplied.
Another thing that comes in fixed quantities is land. Land is divided up into plots for buildings, farms or, homes, but it cannot be multiplied. Being a fixed quantity, it can only be divided.
The meat from animals that had been hunted, the crops that have been grown, pies and bread that had been baked and, eggs that had been collected, are divided up between the people that have to be fed, but are not multiplied.
Clay is divided into bricks. Water is divided between the farms and homes that need it. But neither is multiplied.
Humans can be said to have lived in a division, rather than a multiplication, society. Crops don't multiply, the number of crops is the same as that of the seeds that were planted. The vast majority of investments were governed by addition, rather than by multiplication.
In times past, human population stayed relatively constant, rather than multiplying, the world's population didn't reach a billion until about 1850.
As we might expect the systems of measurement that humans used were intended for division. Time especially was measured in round numbers that were easily divisible. There were 24 hours in a day, averaging 12 hours of daylight and 12 hours of night. There were 60 seconds in a minute and 60 minutes in an hour.
A circle is something that may be divided, but is not multiplied. Should we be surprised that a circle is divided into a nice, round easily divisible 360 degrees?
After addition and subtraction, it was very much a division society.
But the Industrial Revolution, particularly the printing press, changed everything. Even before the perfection of assembly line manufacturing techniques, industry usually involved making multiple copies of some product.
This facilitated the move from a division society to a multiplication society. This was especially true as mechanization increased the efficiency of agriculture, leading more people to work in factories rather than on farms.
The Industrial Revolution also changed our concept of time. In an agricultural society, the calendar is more important than the clock. Planting and harvesting have to be done at a particular time of year, but not at a particular time of day.
Manufacturing, in contrast, requires workers to show up for work at a particular time of day, usually regardless of the time of year. The industrial society thus had it's concept of time based on the clock, rather than on the calendar of the agricultural society.
In 1789 came the French Revolution, which can be said to have opened the modern political era. The revolutionaries were obsessed with the number 10, considering it as a symbol of their implacable hostility to both the monarchy and the Catholic Church.
They wanted to base everything on the number 10. The revolutionaries introduced a year with 10 months, a day with 10 hours, and an hour with 100 minutes. There was also a measurement system, with interconnected units and based on multiples of 10.
The time measurements, based on 10, did not last. The reason being, as we saw above, is that our measurements of time are based on division, blocks of time are something that tend to get divided rather than multiplied. 10 is a poorly-divisible number. Using round, easily-divisible numbers, such as 60-second minutes, 60-minute hours and, 24-hour days is much more practical.
But the system of other measurements, length, mass, volume, electric current, etc., based on multiples of 10 is different. The reason that it is different is that the Industrial Revolution had caused the change from the division society to the multiplication society. In contrast with the earlier division of agriculture, there was now the multiplication of making multiple copies of the same thing by industrial processes.
This is why the measurement system that was introduced during the French Revolution, and based on multiples of 10, is still with us today. It is known as the Metric System.
The reason that a measurement system with the emphasis on multiplication, as opposed to the division of the older system, was not implemented before the French Revolution was simply the entrenched way of doing things. The Industrial Revolution had set the stage but it took the upheaval of a political revolution to get it implemented.
2) WHAT THE METRIC SYSTEM MISSED
Here is something that I have never seen written about the Metric System.
The Metric System is based on the meter as the unit of length. The primary unit of volume, the liter, is defined as a cubic decimeter, which is a tenth of a meter. The primary unit of mass, the kilogram, is defined as the mass of one liter of water.
A gram is defined as the mass of one cubic centimeter, which is a hundredth of a meter, of water. This means that a cubic meter is 10 x 10 x 10, or one thousand, liters. The mass of a cubic meter of water is defined as a metric ton.
There are other Metric units that are unrelated to the meter. The Celsius scale of temperature defines the freezing point of water as zero degrees and the boiling point as one hundred degrees. As with length, Metric units are based on the number ten and it's multiples.
But the meter is an arbitrary unit of length. It could just as easily have been based on some other length. The meter was originally intended to be one ten-millionth of the distance from the north pole to the equator, along the meridian through Paris, but that did not end up being used as the final definition of the meter.
There is one important thing that the Metric System could easily have included, but it missed.
The Metric System was developed by the French Revolutionaries who overthrew and guillotined the king and queen. They considered the number ten as a symbol of their implacable hostility to both the monarchy and the Catholic Church. Aside from the Metric System there was an attempt to implement a year with ten months, a week with ten days, a day with ten hours, and an hour with a hundred minutes.
During the reign of Louis XVI and Marie Antoinette, the Bourbon monarchs that the revolutionaries had overthrown and guillotined, the first human flight had taken place, in a balloon built by the Montgolfier Brothers.
What if the revolutionaries who created the Metric System could have foreseen how important aeronautics would be in the future?
Although the Wright Brothers are generally credited with the first powered flight in a heavier-than-air craft, much of the early development of flight, long after the Montgolfier balloons, took place in France. A legacy of that is the Paris Air Show of today.
When humans were able to fly, the acceleration due to gravity which governs how fast things fall, became more important. This acceleration is defined as 32 feet, or approximately 9.8 meters, per second squared. Although the rate of gravitational acceleration is not perfectly consistent across the earth, the variation is relatively slight.
I have brought up the idea of a "grav", short for "gravity", as a unit of measure. As long as we measure time in seconds a grav would be equal to 16 feet, which is half of the gravitational acceleration per second.
This would be a very useful unit for measure of vertical distances. Doesn't it make sense that the unit used to measure vertical distances should be based on the rate of fall?
If we measured the height or altitude of something in gravs, the square root of that number would be the time that a heavy compact object would take to fall to the surface from that height, neglecting air resistance. If we measured the time the object took to fall from that height, again neglecting any air resistance, squaring the time in seconds would give the height in gravs.
The gravitational acceleration due to gravity is 9.8 meters per second squared, half that would be a grav. That is a rounded figure, a grav would actually be 4.87 meters.
But use of the grav as a unit of measure involves figuring the square root of it, to get the fall time from an altitude in seconds. This is made awkward by the fact that 4.87 meters would be a difficult number to deal with.
What I cannot help wondering is what if the revolutionaries had foreseen flight, and how important vertical distances would become?
The meter is an entirely arbitrary unit, it could have been either longer or shorter. If the meter had been made just a little bit shorter the acceleration due to gravity could have been exactly 10 meters per second squared, instead of the 9.8 that it turned out to be.
This would mean that a grav would be equal to exactly 5 meters, which would have been very easy to work with. The 10 meters per second squared would be ideal for the Metric System, which is supposed to be based on 10.
Clearly it was 1789 and, although people had flown in balloons, the revolutionaries who created the Metric System just didn't foresee how important flight, and thus vertical distances, would become. A slight adjustment in the meter, 10 meters instead of 9.8, would have made it very useful for measuring vertical distances and their associated fall rates.
Ironically the Eiffel Tower would be built in celebration of the centennial of the French Revolution, which brought about the Metric System. It would be the prototype of the modern skyscraper, which would make vertical distances even more important than aircraft would already make them. The Eiffel Tower seems to be a recreation of the balloon flights, taking off for the sky in an elevator instead of a balloon.
3) THE REAL STORY OF AMERICA AND THE METRIC SYSTEM
It has long mystified many people why America, with it's emphasis on technical progress, has lagged behind the rest of the world in adapting the Metric System for measurements. The system has been creeping into the U.S. but the rest of the world has long since been Metric.
There is an answer, but it's complicated.
It goes back to America's beginnings. When America declared independence from Britain, the first country to give America diplomatic recognition was France. It helped America win independence and the appreciation of this help can be seen today in the enduring popularity of the name "Lafayette", for the French general.
France was a monarchy, led by the famous king and queen Louis XVI and Marie Antoinette. They lived in the absolutely fabulous Palace of Versailles.
The original royal palace of Paris was on the island in the Seine River, where Notre Dame Cathedral is also located. They moved from there a short distance away to an even grander palace. The French royals eventually topped that with an even greater palace, and moved there.
There wasn't enough space to build the new palace complex in the city, so the Palace of Versailles was built to the southwest of Paris. The second palace would become what is now the Louvre.
But France's royal glory was not to last. Not too long after it had helped America gain independence, the king and queen were overthrown and guillotined in the French Revolution, which can be said to have begun the modern political era.
Ironically the original royal palace, on the island in the Seine River, would serve as a notorious prison during the French Revolution.
The French Revolution would ultimately result in the rise of Napoleon, as the prototype of the modern dictator. Although he had nothing to do with initiating the revolution. Napoleon collected a lot of art during his conquests, which is what got the Louvre, in the second royal palace, started as a great art museum.
With the French Revolution America lost it's close friends, the king and queen who were the first foreign government to give the U.S. diplomatic recognition and who helped it gain independence.
The French revolutionaries, who had overthrown and guillotined the king and queen, were obsessed with the number ten. They wanted to eradicate anything to do with the monarchy and the Catholic Church.
The revolutionaries introduced a calendar with ten months in a year and ten days in the week. There are still clocks in museums with ten-hour days, with a hundred minutes to the hour.
None of that lasted but there is the system of measurement that the revolutionaries developed, based on the number ten, that is still with us. It has become the global system of measurement and is known as the Metric System.
The Metric System is based on the number ten and it's multiples. Each unit is ten times, or one-tenth of, the previous unit. A meter is the unit of length, a decimeter is one-tenth of a meter and a centimeter is one-tenth of a decimeter, or one-hundredth of a meter.
The different Metric units are related to each other and connected by water. A liter, the unit of volume, is a cubic decimeter. A liter of water has a mass of one kilogram, which is a thousand grams, which is the Metric unit of mass. This means that a cubic centimeter of water weighs one gram.
There is a base unit for each entity that gets measured, length, volume, mass, etc. The Metric System uses the Celsius system of temperature measurement which is, once again, based on water. 0 degrees Celsius is the freezing point of water and 100 degrees is it's boiling point.
The same prefixes are used with each base unit. Kilo, for example, means one thousand so that a kilogram is a thousand grams and a kilometer is a thousand meters. There is a different prefix for every ten, but some of the prefixes are rarely used.
Length is usually always measured in meters, kilometers or a thousand meters, centimeters or a hundredth of a meter, or millimeters or a thousandth of a meter. Units like decameters or ten meters, or decimeters or one-tenth of a meter, are rarely used.
The system that the Metric System replaces is an arbitrary collection of units. 16 ounces is a pound. 12 inches is a foot. 3 feet are a yard. 5,280 feet are a mile. The freezing point of water is 32 degrees and the boiling point is 212 degrees. There is nothing like a common multiple or interconnection of units.
The world has adopted the Metric System, with the curious exception of the United States. Although use of the Metric System has gradually been seeping in.
To see the reason, let's go back in history. America has never forgotten, even if it is not commonly articulated, that the Metric System is a product of the revolution that overthrew and guillotined America's close friends, the ones that were the first to give America diplomatic recognition, and who helped it to gain independence.
That is why America has been so resistant to adopting the Metric System.
This is part of the scenario in the compound posting on this blog, "America And The Modern World Explained By Way Of Paris", December 2015.
4) MOLES AND COULOMBS
This is about something that I mentioned recently that just doesn't make sense. It involves the units of moles and coulombs.
A mole is a quantity such that this number of atoms or molecules of an element or compound would have a mass of the atomic or molecular weight of the element or compound in grams. Mass is the actual amount of matter while weight is the effect of gravity on the mass.
The atomic or molecular weight or mass of an element or compound is simply the number of protons and neutrons in it's nuclei. An atom of oxygen has eight protons and eight neutrons, in it's most common isotope, so it's atomic weight is 16.
A molecule of water consists of one atom of oxygen and two of hydrogen, hence the familiar chemical formula, H2O. Atoms of the most common isotope of hydrogen have only one proton in their nucleus, so their atomic weight is 1. Since there are two atoms of hydrogen in a water molecule, their combined atomic weight is 2. Since an atom of oxygen has an atomic weight of 16, adding this together means that water has a molecular weight of 18.
I should mention that it is a little bit more complicated than this because elements almost always have isotopes. An element is defined by the number of protons in it's nucleus, which is it's atomic number. But the same element may have different numbers of neutrons in it's atoms. Atoms with the same number of protons but a different number of neutrons are known as isotopes.
Isotopes are important in our discussion here because the number of neutrons in the nucleus affects the atomic weight or mass. Remember that the atomic weight or mass is the total number of nucleons, protons and neutrons, in the nucleus.
An example of an isotope is heavy water, which you have probably heard of. Ordinary hydrogen atoms have only a proton in the nucleus, with no neutrons. But an isotope of hydrogen, known as deuterium, also has a neutron in the nucleus. If the hydrogen atoms in a water molecule are deuterium then it will be about 10% heavier than ordinary water because the molecule now has 20 nucleons, instead of 18.
Heavy water is useful in nuclear technology. Ordinary water absorbs neutrons, turning it into heavy water. This makes heavy water, where the hydrogen atoms already have a neutron, useful as a moderator in a nuclear reactor because it slows down, but doesn't absorb, neutrons. When it comes to fusion of atoms deuterium is the easiest atom of all to fuse because it already contains the neutron. That is why a hydrogen bomb consists of an ordinary atomic bomb surrounded by a jacket of heavy water and there are "brown dwarfs", would-be stars that only have enough mass to fuse deuterium atoms but nothing else.
Atoms also contain electrons. But while the electric charge on an electron is equal, but opposite, to the charge on a proton, the electron is so light in mass that it is not even considered in the atomic or molecular weight or mass. A proton has 1,836 times the mass of an electron. A neutron does not have exactly the same mass as a proton, it has the mass of proton and electron combined because neutrons are formed by electrons being crunched into protons by stellar fusion.
A mole is based on Avogadro's number. As long as we measure mass in grams Avogadro's number of atoms or molecules will have a mass of the atomic or molecular weight in grams. Avogadro's number of water molecules will have a mass of 18 grams. If we measured mass in a unit other than grams then Avogadro's number would be different.
Avogadro's number is 6.02 x 10 (23)
Another number that is beyond the scope of human understanding is the coulomb. This is the standard unit of electric charge, defined as the number of electrons. In electricity a current is measured in amperes. An ampere is defined as the flow of one coulomb per second.
Unlike the mole, which is defined by atoms and grams, the coulomb is a somewhat arbitrary unit. It is not really defined by anything. An ampere is the flow of one coulomb per second, but the coulomb isn't defined by seconds.
A coulomb is defined as 6.24 x 10 (18) electrons.
So here is the question. Electrons come from atoms. Electrons are measured in coulombs and atoms are measured in moles. I live in a place where electrochemistry has been very important in industry and just do not understand why these two units were not coordinated.
Moles and coulombs are vast numbers, far beyond human ability to grasp. But yet, relatively speaking, the two numbers are in the same general "neighborhood". A mole is roughly 9,650 times a coulomb.
I am not saying that we should measure electric charge or current in moles, that would be too large of a unit. But if we decreased the size of a coulomb, and thus an ampere, to about .965 of it's present value, so that a coulomb was one-ten thousandth of a mole, that would be very convenient.
It would mean that if a milligram, multiplied by the atomic or molecular weight, of atoms or molecules each gave up one electron, there would be a coulomb of electrons.
The other units of the Metric System, such as length, volume and, mass, are coordinated around water. A cubic meter of water has a mass of one metric tons. A decimeter is 1/10 of a meter, or 10 centimeters. A cubic decimeter defines a volume of one liter. A liter of water has a mass of one kilogram because a gram is defined as the mass of one cubic centimeter of water, which is also a volume of one milliliter.
So why were moles and coulombs never coordinated? This really doesn't make sense, since electrons reside in, and flow from, atoms. If a coulomb were a millimole, or one-ten thousandth of a mole, this would be revolutionary.
If there was a chemical reaction where one mole of atoms each lost an electron to another mole of atoms we would know, without doing any calculations, that the total movement of electrons was ten thousand coulombs.
The most common isotope of copper has an atomic weight or mass of 63. So if we have 63 grams of copper in an electric wire and one ampere of current is flowing through the wire we would know, without any calculation, that each copper atom, on average, is giving out, and taking in, ten thousand electrons every second.
This would be very useful in a myriad of ways.
5) THE MOST VALUABLE UNIT
There is a common measurement that could be extremely useful to us but is rarely used. Whenever we look at an object, it manifests a certain angular diameter in our field of vision. The angular diameter of any object in our vision is proportional to it's actual diameter divided by it's distance from us. Of course, if it is an unevenly sided object, trigonometric functions must come into play.
But measuring and expressing angular diameter is something that we handle very poorly. We usually express angular diameter in imprecise, subjective terms such as "loomed large in the sky".
I believe that getting in the habit of precision measurement of angular diameter would be very useful because it gives us an immediate ratio of the diameter of the subject in relation to it's distance from us. This ratio determines how much of our field of vision, or that of a camera, the object will occupy. Angular diameter could be measured at least as easily as physical diameter using a simple scope or square.
The beginning of the problem is the way that we measure angles. We measure in degrees. 90 degrees is a right angle, 180 is a straight line and 360 is a complete circle.
Measurement in degrees works just fine if we are measuring the outside of a circle, such as latitude and longitude on the earth's surface. But it is my conclusion that we must deal with circles and spheres as two different entities if we are measuring the circle from the inside, instead of the outside.
Whenever we look at an object some distance away, we are forming a circle with us at the center and the object on the edge of the circle. If there is vertical elevation involved, then we form a three-dimensional sphere rather than a two-dimensional circle.
We do sometimes express angular diameter, such as the apparent distance between two stars in the sky. However, the reason that we are not making full use of this measurement is that we try to measure in degrees. While this works fine for the outside of a sphere or circle, it works very poorly for measuring the inside and this is what we are doing when we look at an object some distance away.
My solution is to dig out that old standby of math class known as a radian. This is simply the distance on a circle equal to the radius of the circle, meaning that there are 2 pi radians in a complete circle.
This is a textbook unit that is rarely used in the "real world" and I find that to be a shame because it could easily be extremely useful. Since measurement in radians is a ratio, the actual diameter of the object divided by it's distance from us, we can treat measurement of angular diameter in radians in the same way as trigonometric functions, which are also ratios.
If you look at an object such as a building perpendicular to it's center from a distance equal to the width of the building, it will occupy an angular diameter of one radian. We only have to keep in mind that this angular diameter is the arc of the circle of which the observer is at the center and not the straight line side of the building, which is actually a chord on the circle. This means that if we look at the side of a building along a line perpendicular to the side, we actually have to subtract the sine of the angle which is half the angular diameter of the building.
If the building occupies an angular diameter of 1.57 radians, which is 90 degrees, we would take the sine of half that angle, 45 degrees, which is 0.5. So, if we subtract 0.5 of 1.57 radians, we get 0.785. This means that the side of the rectangular building that we are looking at along a line perpendicular to it's side and which occupies an angular diameter of 1.57 radians, is at a distance from us of 0.785 the length of the side of the building.
Probably the reason that we do not make more use of this versatile unit is that it does not fit with our base ten number system. There is 2 pi, or 6.28 radians in a complete circle. The conversion factor with degrees is 57.3. This means that if you looked at an object from a distance ten times the object's diameter, it would occupy an angular diameter of .1 radian or 5.73 degrees.
The radian would appear to be especially useful in space travel because when a spherical body, such as a planet, occupies an angular diameter of one radian, it means that the observer is at a distance from the planet's surface equal to the radius of the planet, or the distance from it's surface to it's center.
One reason that the radian is such an interesting unit is that it is actually the only completely natural unit that human beings use. The vast majority of units that we use were created arbitrarily. Seconds, meters, feet, miles and, pounds are entirely arbitrary. A degree was chosen to be 1/360 of a complete circle because 360 is a very round and easily divisible number, but even so this is an arbitrary unit that is meaningless in the universe of inanimate matter.
Days and years can be said to be natural units because they are based on the rotation and revolution of the earth. Yet these are natural units only on earth or while measuring it. Further out in space, the day and the year are just as arbitrary as the other units.
Radians, however, are a natural unit anywhere in the universe and as far as I can see, is the only unit of which this claim can be made.
6) WHY WE SHOULD COUNT BY TWELVES
Here is something to really think and talk about. Have you ever stopped to ponder just how inefficient our basic counting system is, the one that we have taken for granted since early childhood? In my book, "The Patterns of New Ideas", I suggested that our present system of counting by tens is woefully inefficient and we began using this system only because we have ten fingers and people in ancient times used their fingers to count. This is surely the supreme example of how we can be technologically forward but system backward.
For ancient people, using their ten fingers to count worked just fine. But the world was to get far more complex. The four basic arithmetical operations are: addition, subtraction, multiplication and, division. Basing our counting system on any number, such as the tens that we use now, will do very well with the first three.
However the last of the four, division, is the tricky one. Division is very important in the flow of daily life, just as are the first three. The difference with division is that not all of the convenient numbers that we could possibly base our counting system on are equally divisible.
I maintain that, for maximum efficiency, the number on which we base our counting system should be as divisible as possible. It does not make sense to base the system on too high of a number because that would mean that more symbols (1,2,3,...) would have to be use and that would hinder communication. However, we have made a really great mistake by counting by tens simply because ten is so poorly divisible.
Consider that by far the most important and most frequent measurement that human beings take is that of time. In fact, we take measurements of time many times more often than all other entities that we measure such as distance, weight, temperature, etc. Now notice when you look at a clock or watch that we base our measurement of time not on the number ten, but on twelve and multiples of twelve. There are twelve hours in a day, sixty seconds in a minute and, sixty minutes in an hour.
You may notice that there was once ten months. The sept- of September means seven in Latin, just as oct- means eight, nov- means nine and, dec- means ten (as in "decimal", for example). But the logic of counting by twelves, rather than by tens, prevailed. Two more months were added to make twelve, July is named for Julius Caesar and August is named for Augustus Caesar.
The truth is that when measuring time, division is very important and people instinctively adapted a system based on twelve, rather than the conventional ten. This is also why eggs are sold by the dozen, rather than by tens, twelve eggs are more likely to be evenly divisible by the members of a family.
Time is not the only measurement in which twelve is very obviously a better base to use than ten because of it's easy divisibility. A complete circle, such as the circumference of the earth, is divided into 360 degrees. This is a nice, round, easily divisibly multiple of twelve.
The Metric System is an absolutely brilliant idea that was conceived at the time of the French Revolution. But yet something is still missing about it. The Metric System is superior to the old English system of feet, yards and, miles.
However, here we are in the Twenty-First Century and that old system still has not gone away and the Metric System usually has to be forced on people by law. The reason is very clear, the Metric System is far better with regard to multiplication and the easy convertibility of units, but the old system still has the advantage of divisibility. Twelve inches are a foot, 36 inches are a yard and 5,280 feet are a mile. Notice that measurement of time was never metricized.
The Metric System is at the mercy of the number base that we use and will never reach it's full potential as long as we count by tens, rather than twelves. Fractions are still as useful as they are because ten is such an awkward number to divide, basing our number system on twelve would change this by incorporating much of the useful divisibility of fractions.
Just think how convenient it would be if we could express time in decimal form based, of course, on twelve, rather than ten. Consider a decimal such as 1.63 hours. It is difficult for us to grasp quickly because it straddles the two number systems.
By using a grid, we can easily express any point on the grid by using cartesian coordinates. What if we could do this with the entire planet? We can, but expression in terms of latitude and longitude are based on twelve but we will have to express the coordinates in base-ten decimal form and it makes for an awkward and inefficient arrangement. Latitude and longitude are getting ever-more important in these days of GPS but we cannot effectively express the coordinates of a point in decimal for and will not be able to most-effectively do so until we count by twelves.
Our number system plainly and simply revolves around twelve but we try to make it revolve around ten because we happen to have ten fingers. This is certainly one of the greatest mistakes ever made. We do not still write in hieroglyphics yet we still count by tens.
THE EXPRESSION OF TIME IN DEGREES
While we are on the subject of counting and measurement systems, let's consider the units of hours and minutes. Hours and minutes are completely arbitrary units and were adapted due to the easy divisibility of the units which we use for time.
We cannot actually measure time but only motion, which is a function of time. Our measurement of time is based on the motions of the earth. The earth rotates 360 degrees in one day. Thus, one degree of the earth's rotation corresponds to 240 seconds or what we would now refer to as four minutes. An hour is fifteen degrees.
Since humans are now spending quite a bit of time in space, in earth orbit, why not express time in degrees? This would base the passage of time on how far the earth has rotated during that interval of time. I am certain that this would be much more convenient and efficient, hours and minutes were merely convenient everyday units in the pre-space age.
7) A VERY USEFUL TOOL
There is a very simple measurement tool that I thought of that can quickly and easily accomplish tasks that are very cumbersome and time-consuming with existing methods. This tool can be very easily homemade and I believe that anyone involved in any kind of building, constructing or, surveying would find it invaluable. I have decided, for various reasons, not to pursue a patent for it any longer. So, I have decided to put it here in the public domain so that anyone can make their own and no one else can get a patent on it.
One day, I drove past some large oil storage tanks in Tonawanda, NY near the South Grand Island Bridges. Just as a mental exercise, I tried to dream up a way to quickly measure the circumference of such tanks or another large, circular object. I started thinking of measuring the curvature over a given linear distance with the idea that the less the curvature per linear distance, the larger the circumference.
But then another idea clicked into my head. What if someone got an ordinary magnetic compass and enlarged either the compass itself or it's mounting so that it was circular and of a known circumference, such as a yard or a meter? Suppose we then placed the edge of the compass against the side of a large oil tank and noted the directional reading given by the compass needle. Then we would note the point on the side of the compass that was in contact with the side of the tank. If we proceeded to rotate the compass over a complete circle and noted the change in the directional reading of the needle, we would have all the information needed to quickly and easily calculate the circumference of the oil tank.
If we placed the compass against the side of the oil tank and noted that the directional reading of the needle was 192 degrees and then rotated the compass a complete circle so that the point on it's edge that had originally contacted the side of the tank was back in the same place, all we would have to do would be to take the fraction of a complete circle that the needle changed during the rotation and multiply it by the circumference of the compass mounting and we would have the answer, the circumference of the tank.
For example, If the compass mounting was one yard in circumference and, upon completion of the rotation the needle had moved from 192 degrees to 196 degrees, the circumference of the tank would be 360/4 times one yard. In other words, 90 yards.
As I stopped to have dinner in a restaurant, my mind really began racing. I realized that I was onto something. I asked the waitress for something I could use for a sheet of paper and by the time I was done, I had filled a side of the paper with all manner of tasks that such a simple device could quickly and easily accomplish. I decided that the device would be called "The Compass Ruler".
I made one of my own by getting a Wal-Mart hiking compass, breaking off the casing and, gluing it onto a piece of plywood I had cut with a jig saw to a circumference of one meter. I knew enough about building and construction to know that such a tool was not in common use. However, I checked extensively to see if such a tool was in use anywhere and found no sign that it was. There was once such a thing as a surveyor's compass, that had fallen into disuse, but it was a compass mounted on a stand and was in no way used like my Compass Ruler would be. On my device, measurements would be taken by actually contacting the side of a structure.
The principle of the operation of the Compass Ruler is simple. Just as a plumb, a weight tied to a string, uses the earth's gravity as a fixed reference point for measurment of vertical angles, the Compass Ruler uses the earth's magnetic field as a fixed reference point for measurement of horizontal angles. The Compass Ruler obviously must be marked around the circumference edge in degrees, just as a protractor would be.
There is an even simpler version of the Compass Ruler. Simply take a square of wood, 1 x 4 for example, and glue a compass in the middle of it. For best results, be sure that it is indeed a square and that each cardinal direction faces toward the middle of one side of the wood. Suppose you have built a corner between two walls or fences and you want to be sure that it does indeed form a right angle. Simply hold one side of your Compass Ruler against one wall and note the directional reading of the needle. Then hold the same side against the other wall. You should get a change in the needle of ninety degrees. Simple.
This method is just as useful if the two walls do not actually contact each other, or for that matter do not even come near each other. This makes the old standby, the builder's square seem awkward and obsolete by comparison. Verifying a right angle by the 3-4-5 Pythagorean Theorem method is also awkward and time-consuming.
Suppose it is necessary to measure the angle beyween any two walls that do not actually intersect. With a builder's square it is impossible. With tape measures it is tedious, time-consuming and, prone to error. With a surveying crew, it is expensive. With my Compass Ruler, it is almost effortless.
What if you have built a long wall or fence and want to verify it's straightness? All you have to do is walk down the wall, taking periodic measurements with the Compass Ruler by placing it's edge against the wall. If the wall is indeed straight, you will get the same directional reading of the needle on every measurement. If it is not straight, by measuring the wall with the Compass Ruler at given intervals, you can tell by how much it curves.
This is also useful for a vast number of other such similar measurements. How would you verify that two parallel walls are truly parallel? Just take a reading on one wall with the Compass Ruler. Then, go to the other wall and put the same edge against that wall. If the walls are parallel, you will get a difference in the directional readings of 180 degrees.
Suppose you wished to set up a series of signs along a road and wished them to all have the same directional orientation. How would you do it? What if you were setting up a sign along the road and wanted it to be set at 45 degrees to the road to give maximum exposure. Or suppose you were building a wall or fence and wished it to run parallel (or perpendicular) to the road.
All of these tasks would be difficult, impossible or expensive with existing methods. With my Compass Ruler, all would be simple and easy. To measure the directional orientation of the road with the Compass Ruler, simply place the device on the road surface alongside a traffic line on the road.
Measurement of curvature is just as easy with the Compass Ruler. Just take readings against the curved structure at regular intervals. Curvature can be expressed as change in the directional orientation of the needle per given linear distance. Another advantage of either version of the Compass Ruler, either the circular or the simpler square version of the device, is that contact measurements, such as those described above, are not hampered if two structures to be measured and compared are not visible from each other or if there is an obstacle, like a row of bushes, between two structures.
Surveying is easy with the Compass Ruler. Suppose you want to get an accurate measurement of the distance to a certain remote point. First, you would either set up or pick out a remote visible reference point to use in the measurements. Then you would mark the local point from which you would take the measurement to the remote point. Then you would establish a measurement point a convenient distance away so that a line from the local point (Point A) to the measurement point (Point B) would form a right angle with a line from point A to the remote point (Point C).
Using a straight-edge, such as a perfectly straight 1 x 4 board, you would sight on the remote point C from the local point A looking straight down the straight-edge. You would use the Compass Ruler to note the directional orientation of the straight-edge as it points from Point A to Point C. You would then go to the measurement Point B that you have selected and take another sighting on the remote Point C from there.
All you would than have to do is take the difference in the angular reading of the two measurements. Using a scientific calculator, you would get the cotangent of the angular difference. You would then multiply the cotangent by the distance from Point A, the local point, to the measurement Point B. That would give you the distance from Point A to the remote Point C.
Obviously, for best results in surveying using the Compass Ruler, measurements must be taken carefully. The distance from Point A to Point B must be accurately measured. And, the same spot on the remote point must be sighted upon. The longer the carefully measured distance from Point A to Point B is in relation to the distance from Point A to the remote Point C is, the better the result will be. It should always be at least 10% of the distance.
It is not necessary to have a right angle between the two lines from points A to C and from A to B, but if not, the simplicity of a cotangent calculation will be lost and a graphical calculation will become necessary. If possible, the baseline for the measurement from Point A to Point B can make use of a pre-existant line, such as a road.
The straight-edge can be built onto the Compass Ruler if it is to be used for surveying. For even better results, the straight-edge can be fitted with a small telescope, a laser pointer, or, both. A vertically diagonal mirror can make it possible to see the compass on the Compass Ruler at the same time that the sighting is being done. For a finishing touch, the entire device can be set on a mounting.
To set up a marker, such as a traffic cone, at a given distance in a given direction from a starting point, use the reverse of this method. Pre-set a sighting from a Point B to that distance and have a rodman walk with the marker until he is in the sight. Then use hand signals or radio/phone communication to have the marker set up at the correct point.
Suppose you are out on the water in a boat and wish to measure how far you are from shore because you notice a shipwreck or some other object of interest under the water and wish to record the position. You would pick out two easily recognizable objects on shore such as trees or large rocks. The two objects should be in a line perpendicular to the line between you and one of the objects. Measure the angle between the two objects from where you are in the boat and record it.
Later, you would carefully measure the distance between the two objects using a tape measure or a map. Then you would take the cotangent of the angle measured from the boat and multiply it by that distance. Alternatively, you could simply take the directional readings of any two (or more) prominently visible, fixed position objects. The position on the water could then be charted using a map or satellite photo of the area.
Astronomers have long used this technique to measure the distance to stars, it is known as parallax. The carefully measured distance from Point A to Point B is referred to as the baseline. The same principle can be used with the Compass Ruler to map an entire area. Simply pick out visible objects such as trees, houses, etc. Measure the distances from a central point to the objects and then measure the angular distances between those objects from the central point. The map then can be easily made using a ruler and protractor. Of course, on complex maps, more than one central point can be used. If the terrain to be mapped is hilly, the logical place for the central points would obviously be on the high ground.
Aside from the contact measurement and surveying versions, there is yet another version of the Compass Ruler, the drawing version. Simply fasten or glue a small compass to a straight-edge such as a ruler and it makes the protractor used in geometric drawings just as obsolete as the builder's square is in construction. To draw two lines at a certain angle to each other, simply draw one, noting the angle indicated on the compass dial. Then move the straight-edge so that the difference showing on the dial is now the desired angle and then draw the second line. To measure the angle between two existing lines, simply reverse this process.
If the drawing paper is securely taped down, aligned either east-west or north-south with the compass for best results, an entire geometric drawing can be made with unprecedented accuracy using the drawing version of the Compass Ruler. Parallel lines will have the same compass dial reading anywhere in the drawing. Perpendicular lines will differ 90 degrees in reading. Existing methods are far inferior to this. Of course, it would be simple to draw a map that was surveyed using the surveying version of the tool, just drawing the measurements on paper.
There are certainly many more everyday applications of this simple but extremely useful device. The device could also bring geometry and trigonometry classes to life. The lessons that now consist of drawing lines and circles on paper could occasionally be done as actual measurements in the gym or schoolyard.
Anyone can make their own of any version of the Compass Ruler, the circular or the simpler square version for contact measurements. Or the surveying or drawing versions with an attached or accompanying straight-edge. It can also be manufactured and sold although it will not be patentable now that I have put it in the public domain.
I will not earn any money on this but I just want to have contributed something to the world. We read of George Washington Carver and how he revealed many things that the humble peanut can be used for. I would like to do the same thing for the simple device known as the compass. Just as GPS systems are becoming ubiquitous and it seems to be of little use any more, we see that there is a whole world of tasks that it can accomplish most effectively. Any simple compass would have it's usefulness multiplied if it were encased with a straight side to perform some of the measurements listed above.
8) THE MEASURABLES
There are 92 elements, or different atoms. But most of these are rare. We have seen how the few common atoms act as points of information that affects how the environment operates. There are two separate "Rules Of Common Atoms", one for the universe of inanimate matter and the other for biology.
You may remember the acronym from biology class, "CHNOPS". This stands for carbon, hydrogen, nitrogen, oxygen, phosphorus and, sulfur. These are by far the most common atoms in biological molecules, and they act as information points. Color does not really exist in the universe of inanimate matter, it is just the way our eyes and brains interpret the different wavelengths of visible light.
But have you ever wondered why there are six basic colors, red, orange, yellow, green, blue and, violet? It is because we are composed of six common atoms, and these act as information points. This applies to all living things, and is the reason that living things are classified into six "kingdoms". This does not mean that the rare "trace" elements are not important but the abundance of these six atoms causes them to act as information points.
Today I would like to add something else to "The Rule Of Common Atoms". There are six basic measurable entities and this is because of the six common atoms, CHNOPS, in the same way as colors and biological kingdoms.
According to the Wikipedia article, SI Base Unit, there are seven basic measurables. These are time, measured in seconds, distance, measured in meters, mass, measured in kilograms, temperature, measured in Celsius or Kelvin, electricity, measured in amperes, amount of substance, measured in moles, and luminous intensity, measured in candelas.
But a mole is simply a number of atoms, actually 6.02 x 10 raised to the 23rd power, of atoms or molecules. This many atoms or molecules of an element or substance will have a mass in grams of it's atomic weight or molecular weight. But that means that the mole is related to the unit of mass, gram or kilogram, and thus is not an entirely separate measurable unit. That leaves us with six basic measurable units, the same number as the common atoms represented by the acronym CHNOPS.
All of the other units that we use to measure, such as meters per second, miles per hour, or newton-meters, are combinations of these fundamental units or their English equivalents.
But what my theory of "The Flow Of Information Through The Universe" points to is that, like the colors, we see these six basic measurables in the universe not really because of what it is but because of what we are. We are more complex than our surrounding universe of inanimate matter and, when we measure anything, we are projecting our complexity onto it and it is reflected back at us, specifically the information brought about by the six common atoms.
The universe is actually only negative and positive electric charges but we have our own scale and perspective when we look at the universe, and this adds information.
My cosmology theory, "The Theory Of Stationary Space", which is separate from this theory about "The Flow Of Information Through The Universe", reveals that time is actually something that is within us and not the inanimate universe around us. Distance is simply the number of electric charges in a straight line in space. Electric charge, in amperage, involves the concentration of like charges in matter. Temperature, the energetic movement of atoms and molecules, is a function of time and distance like any other velocity but we perceive it as heat, rather than the kinetic motion that it is, because of our relative scale perspective.
Luminosity is a function of electric charge since space is, according to my cosmology theory, composed of a multi-dimensional checkerboard of alternating negative and positive electric charges. But, once again, we see it as light, and other electromagnetic radiation, due to our scale perspective. The checkerboard of alternating electric charges ordinarily balances out to zero but we see the waves as electromagnetic because they disturb this underlying balance.
This means that length, electric charge and, mass are all really the same thing. We see it in the different forms that we measure only because we are projecting our complexity on the inanimate universe. The length is the number of charges in a straight line through space. Electric charge is the concentration of like charges, held together by energy, in matter. The mass is actually the energy in matter that holds the like charges together against their mutual repulsion, which we express as the well-known Mass-Energy Equivalence. Weight is simply the effect of gravity on mass.
We can thus see that, once again, we see the universe as we do not only because of what it is but also because of what we are. We see these fundamental six measurable entities because we are projecting our own complexity on the less-complex inanimate universe around us. There are six because of the information of the six common atoms, in the same way as the fundamental colors and the "kingdoms" into which living things are classified.
9) THE 720 DEGREE CIRCLE
This has been added to the compound posting, "Measurement" September 2021.
A circle is divided into 360 degrees. If we had defined an angular degree so that it is half as wide as it is now there would have been 720 degrees in a circle. I am surprised that we didn't do this.
An angular degree is not something that most people would be immediately familiar with. The first example that would occur to many people is that 360 degrees divided by the 12 hours on a clock means that there are 30 degrees between each hour number on the clock.
The sun and the moon are of about the same angular diameter in the sky, about half degree. The diameter of the sun is 400 times that of the moon but it is also 400 times as far away as the moon. The sight of the sun and moon in the sky is something that everyone can immediately relate to.
If we divided a degree in half, so that there would be 720 degrees in a circle, the angular diameter of the sun or moon would be just about exactly one degree. It wouldn't be precise because neither the sun nor moon are at a perfectly consistent distance from earth. But I think the angular diameter of the sun and moon would have been an obvious choice for the unit of measure of angular diameter.
The 360 degree circle is rooted in ancient Babylon, which also paid a lot of attention to astronomy. Maybe if the astronomical community and the mathematical communities had hung out together we might be using a 720 degree circle today.
10) CHART NAMES
For most of human history the vast majority of people have lived in relatively small communities. They knew virtually all of the people that they interacted with. In recent times that has definitely changed. Not only is there more people but the size of cities has grown exponentially. With more moving around knowing the people that we are interacting with is getting to be more the exception than the rule.
First names, such as James, William, Mary, Charles, and so on, are useful only as long as we are dealing with people that we know. A first name doesn't tell you much about a person, other than whether they are male or female and maybe their ethnicity. First names are from the days when people knew most of those that they would interact with.
What if we could make first names more useful? We could do that if names could tell us more about a person, specifically what they looked like.
Suppose that you are working behind a counter and there are thirty people in the room in front of you. You see the person that you are looking for but don't know their name. How would you get their attention? You could shout out "sir" or "ma'am", until they looked your way, but that would disturb everyone in the room.
You see someone fleeing and suspect that they have committed a crime. How would you very quickly describe what they look like?
You send a driver to give someone a ride from an event, but the driver and rider don't know each other. How would you quickly give the driver an idea of who to look for, considering that there might be a hundred people there and a photograph of a person often isn't a good guide to recognition?
You are writing a story and describing what a person looks like. Describing how a person looks is often a laborious process, don't you wish there was an easier way?
So much nowadays has been categorized, to make identification or computer programming easier. The categorization is usually done with numbers, every shade of every color has been assigned a number for example. Why couldn't we categorize what people look like, not by number but by name?
We could make up a chart with drawings or photographs of three hundred different people. Half would be male and half female. They would all look different from one another. One or another of the people on the chart would have every different combination of race, general height, general body structure, general ethnicity, skin tone and, hair color. Everyone in the world would fairly closely resemble one of the people on the chart.
Next we would give everyone on the chart a first name. The name of the person on the chart that you most closely resembled would be your "Chart Name". You wouldn't need to give the name to anyone because it would be obvious by just looking on the chart. But you would look up if anyone called the name. Hard copy charts could be posted on walls in offices and charts could easily be standard features on phones.
The reason this hasn't already been done is that classifying people by their physical features hints at racism. This is not any scientific classification of how people look, it is just for the purpose of recognition. We could also do the classification by numbers but I think it would be better to have a name to call to get someone's attention. The purpose of this is recognition at a distance, and so we probably wouldn't include eye color.
The examples of people on the chart would be in their prime. A general age could also be specified, including if it was a child. Possibly a separate chart of children could be made. It would not include anything uncomplimentary or readily subject to change, or whether the person was disabled in any way.
It would not include any reference to excess weight or baldness or wrinkles. The description would be of the person whole and in their prime. It would have no reference to hairstyle and a person's Chart Name would change if they changed their hair color.
This will not only be helpful in crime fighting, making possible a quick description of a person and bringing up an image resembling the person, but will also cut down on fraud since a person's facial photograph often doesn't look a lot like them, especially if it was taken some time ago.
11) NEW UNITS OF MEASUREMENT
This has been added to the compound posting "Measurement", November 2021.
Units of measure, for length, area, and so on, would be more useful if we could relate to them. This was originally the idea. The yard was based on the length of a king's arm. The mile was when the left foot of a marching soldier had touched the ground a thousand times. The meter was originally supposed to be one ten-millionth of the distance from the equator to the north pole, along the line of longitude that passes through Paris, but has since been redefined by wavelengths of light.
However most of this relatability has since been lost. Acres are widely used as a measure of land area. But how many people seriously know what an acre is? It started as the area that a farmer could usually plow in a day. Below is an acre against a nearby parking lot, where you can see the cars and parking spaces.
Image from Google Earth.
The modern era, particularly cars, has brought the possibility of a new set of units that are easily relatable to everyone. Units of length are the primary unit of measurement, being squared or cubed to form units of area and volume. In the Metric System mass is also based on length, and water, a liter of water weighs a kilogram.
When you turn on the heat or the radio in a car you probably turn a knob. These knobs seem to all be of a standard size and the width of one would make an ideal unit of measurement that everyone could easily relate to.
Then there is the steering wheel, which also come in standard sizes. This would be the most ideal and relatable length unit of all.
The next higher unit of length could be the width of a lane on a highway, again something that is very familiar to everyone.
We could form units of area by simply squaring the units of length. But probably the most familiar unit of area is also automotive in origin. What would be better for a general unit of area than a standard parking space?
Just another thought about measurement, but this is not related to cars. We now know that the universe overall is a very cold place. The average temperature in the universe overall is believed to be 2.726 degrees Kelvin, although that may not be an extremely precise figure.
Kelvin is the temperature scale that begins at Absolute Zero. Heat is the energy of moving atoms and molecules. When something cools down it's atoms and molecules move more slowly. If cooling continued so that all motion stopped it would not be able to get any colder. This point is known as Absolute Zero and is equivalent to -459 degrees Fahrenheit or -273.16 degrees Celsius.
The Celsius scale is defined by the melting and boiling points of water. Water freezes at zero degrees Celsius and boils at 100 degrees Celsius.
This means that the freezing point of water is at 273.16 degrees Kelvin, since a Kelvin degree is the same size as a Celsius degree. Notice that the average temperature of the universe is just about exactly one percent of the freezing point of water, starting at Absolute Zero, and the figure for the average temperature may not be perfectly accurate.
The size of a Celsius degree is one-hundredth of the span between the freezing and boiling points of water. Now that we are in the Space Age, and cosmology is becoming ever more important, why don't we define the average temperature of the universe as one degree? Water will then freeze at 100 degrees and boil at 136.89 degrees.
The freezing and boiling points of water are not as precise as it may seem. The freezing point depends on the purity of the water. The salt water in the sea does not freeze at zero degrees Celsius. The boiling point of water is dependent on the atmospheric pressure.
