The Metric System is an old system of measurement, originating during the French Revolution. The basic unit of length, the meter, is an arbitrary unit. That doesn't mean we can't use it but a natural unit, meaning based on some important natural phenomenon, would be more useful.
The Metric System is from the days before aviation and tall buildings so it does not take gravity into account as far as providing a natural unit. It was also not designed with navigation in mind, where the circumference of the earth might have been the basis for a natural unit. It was developed long before space travel. Finally, the Metric System is based on the number ten which, while our number base because we have ten fingers, is a poorly divisible number.
Our measurement of time and circumference is based on the number twelve and it's multiples, which are much more divisible, and the measurement of time was never successfully incorporated into the Metric System.
Here are some thoughts about moving beyond the Metric System. It includes last week's posting, "The Grav And The Grav Mile".
TABLE OF CONTENTS
1) THE UTILITY ALPHABET
2) THE SPACE AGE CALENDAR
3) COUNTING BY TWELVES
4) THE GRAV AND THE GRAV MILE
5) THE KEYPAD SYSTEM OF NAVIGATION
6) CARDINAL DIRECTIONS BEYOND EARTH
7) THE DAYS OF THE WEEK
8) MISNOMERS
9) NATIONAL SYMBOLS
10) OTHER THINGS TO BE CHANGED
1) THE UTILITY ALPHABET
Some letters of the alphabet form useful descriptive shapes. A structure may be described as an A-frame. Some things are C-shaped or D-shaped. A structure may be arranged like an H, or may be constructed of I-beams. A curve may be described as resembling a J. An obvious way to describe a circle is like an O. There is an S-curve, a T-junction and a Y-junction. Things may be described as V-shaped or Z-shaped.
But the rest of the alphabet is of little use as descriptive shapes. With modern technology, we should be making maximum use of the alphabet for descriptive shapes. This is the alphabet that I came up with. Eleven of the letters have been replaced.
The letter M has been replaced by a similar form that will be more useful. The one replacing Q is a right triangle, but four sided because the hypotenuse is broken into an angle. The letter replacing G is two semi-circles that don't touch. The one replacing R is two semi-circles that do touch.
With the technical descriptions that are widely used today, this will be a much more useful alphabet.
2) THE SPACE AGE CALENDAR
Have you ever thought that we could use a new calendar? The Gregorian Calendar, named for Pope Gregory, that we now use is from a medieval time when most people worked in agriculture. The idea of calendar reform is not new. The days do not fit evenly into a year and there has been the idea of "leap weeks" instead of an extra day in a "leap year", every four years.
I have a calendar too. My calendar is called the "Space Age Calendar". As the name implies it is intended to help with space exploration. The calendar is based on the earth's distance from the sun.
The earth's orbit around the sun is elliptical, rather than circular. The point at which the earth is closest to the sun is known as perihelion, and the furthest point from the sun is aphelion.
Why do we need months? Months were based on the orbit of the moon around the earth, which is 29 days and does not fit evenly into the year. This might have been useful in agriculture, to keep track of the best time to plant, but months are completely irrelevant today except as a convenient billing cycle.
I have long thought that we should name the weeks, rather than the months. Our expression of weeks, which are far more important than months, is very inefficient. We describe weeks as "the week of June 24", expressing them in terms of months. The weeks should definitely have their own names.
In my calendar the days are simply numbered, from 1 to 365, with day 366 added every fourth year. We will still keep the weekdays. Today we live much more by the clock than by the calendar, and much more by the week than the month. Months have been mostly irrelevant since the Industrial Revolution, except for setting holidays and religious observances by the lunar cycle.
The convenient monthly billing cycle can continue on multiples of 30. Day 30, Day 60, Day 90, etc. The date will be expressed with three digits following the year. Today will be 2024298
The solstices and equinoxes, when the day or night is longest and the other shortest and when the two are equal, will still be there. But today it really matters to very few people exactly when the seasons begin. It is only temperate latitudes that really have four seasons anyway.
If the year were to begin with either perihelion or aphelion the date, the number of the day, would tell us how far the earth was from the sun. There is a difference of about 3 million miles, or 5 million kilometers, between perihelion and aphelion. This distance makes a difference. For an example spring tides, where the gravitational pull of the sun and moon is coordinated, will be stronger at perihelion but weaker at aphelion. But neap tides, when the sun and moon are at right angles to each other, will be the opposite.
One issue with space travel is that there is no ready way to tell directions in space. There is no north, south, east or, west. We might refer to the northern or southern hemisphere of the moon or sun or one of the planets. But we are only going by earth's northern or southern hemisphere. This is less-than accurate because each planet has a different axis of rotation that is not parallel to earth's.
The earth rotates eastward. The moon revolves around the earth in the same direction, as does the earth around the sun. So we might say that the earth revolves eastward around the sun. But it is only eastward relative to the earth, there is no real "eastward" in space.
But using a line between the points of aphelion and perihelion, which remain fixed, gives us a meridian or baseline from which we can establish directions in space. Two lines perpendicular to it, both intersecting the original meridian at the center of the sun, would be all that we need to establish directions in space, just like on earth. We would easily find exactly where in space we were because the date would give us both the position and the distance from the sun. We just have to factor in that the earth does not move at a constant pace in it's orbit around the sun, it moves faster when it is closer to the sun.
I was thinking of beginning the year on January 4, because that would be closer to the present New Year. But aphelion occurs, just by chance, on America's Independence Day. What would Americans think of the year beginning on what is now the Fourth of July?
3) COUNTING BY TWELVES
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? 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.
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 divisible 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 supposedly 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 successfully metricized, although the French revolutionaries tried.
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.
I have never been entirely pleased with the Metric System. The meter is the basic unit of length and provides the units of area and volume. Combined with water the liter, as the unit of volume, provides the unit of mass. A liter of water has a mass of one kilogram. The units operate as multiples of ten so that a kilogram, for example, is a thousand grams and a kilometer is a thousand meters.
But the meter is an arbitrary unit. That doesn't mean we can't use it but it would be more useful to have a natural unit that accomplished something. Examples of natural units are days, because that is how long it takes for the earth to rotate, and years, because that is how long it takes the earth to revolve around the sun. Divisions of time, such as hours, minutes and, seconds, are partially arbitrary but they are divisions of a natural unit.
Water does add a natural element to the Metric units of mass but the meter itself remains an arbitrary unit. A 360 degree circle is somewhat arbitrary but an angular degree is a convenient unit of angular distance and 360 is a round, easily divisible number. The Fahrenheit scale of temperature is entirely arbitrary. The Celsius and Kelvin scales have some naturalness as they are based on the freezing point of water and absolute zero. Latitude, based on the Equator and the poles, is natural but longitude, based on the Prime Meridian, is arbitrary.
There actually could be a natural unit of angular distance. Both the sun and moon have an angular diameter of about half a degree. The sun has an actual diameter about 400 times that of the moon but it is about 400 times as far away as the moon, so that the two appear as about the same size in the sky. We cannot be too precise about the angular diameters of the sun and moon, since the distances to both vary, but the two are very close to the same size in the sky at about half an angular degree.
What if we divided an angular degree in half? Then there would be 720 degrees in a circle, instead of 360. But this would be a very natural unit of measurement since both the sun and moon would then have an angular diameter of one degree.
We could make the measurement of time into more of a natural unit by measuring it in degrees of the earth's rotation. With a 360 degree circle, the earth rotates one degree every four minutes. If there was a 720 degree circle, it would be a degree every two minutes. This would make it more useful in dealing with space and such things as satellites and launches.
Coming up with a natural unit of linear measure is not as readily obvious. A meter was originally intended to be one-ten millionth of the distance from the north pole to the equator, although it has since been redefined in terms of wavelengths of light and this multiple of ten still wouldn't fit well with the 360 degree circle used with latitude and longitude. A mile was originally a natural unit based on a thousand paces, the left foot touching the ground a thousand times, of marching soldiers. The prefix "mil" means one-thousandth.
The Metric System was introduced during the French Revolution and Napoleon's enthusiasm for it is the reason we are using it. I have wondered what would have resulted if sailors had developed the Metric System.
There actually are two natural units of linear distance, both based on the earth. The circumference of the earth has long been important to navigation and now to satellites and radio communication. If we consider a circle as 360 degrees then this brings the possibility of a unit of length based on the earth's circumference. A degree is divided into 60 minutes. These are minutes of arc and are not the same thing as minutes of time, which are based on the rotation of the earth.
One minute of arc, on the circumference of the earth, is defined as a nautical mile and has long been used by sailors because it is a natural unit and is useful for determining position, based on latitude and longitude. A nautical mile is about 1.16 statue miles, which were commonly used on land before the Metric System became widespread. The U.S. still prefers miles.
A natural nautical mile cannot be too precisely defined simply because the earth is not a perfect sphere.
The other natural unit of linear distance involves the acceleration, due to gravity, of a falling object. The acceleration, due to gravity, of a weighty compact object, so that it has minimal air resistance, is 32 feet, or 4.75 meters, per second squared.
This means that the velocity of the falling object is 32 feet per second at the end of the first second and 64 feet per second at the end of the second second, and so on. Since the object starts with a velocity of zero and steadily increases to the 32 feet per second during the first second of fall, that means that the average velocity during the first second is 16 feet per second so that the object falls 16 feet during the first second.
The falling object starts the second second at 32 feet per second and finishes the second at 64 feet per second. That means it's average velocity during the second second is 48 feet per second so that it falls 48 feet during the second second.
Notice that 48 is 3 x 16. This reveals the pattern that the object, neglecting air resistance, falls 1 x 16 feet during the first second and 3 x 16 feet during the second second. Continuing with the math, it would fall 5 x 16 feet during the third second and 7 x 16 feet during the fourth second.
Thus we see that, if we are going to measure time in seconds which are a division of the rotation of the earth, 16 feet is an important distance with regard to gravity and this makes it a natural unit of linear measurement. The Metric System was developed during the French Revolution, before tall buildings and aircraft so that this was less of a factor. I have written about this before and refer to 16 feet as a grav, for gravity.
Now let's go back to the other natural unit of linear measurement, the nautical mile. Remember that there is no precise definition of a nautical mile, which is 1/60 of a degree of the earth's circumference, simply because the earth is not quite a perfect sphere. The British version of a nautical mile was called the Admiralty Mile, and was defined as 6,080 feet. This was very useful when used with the system of latitude and longitude.
Notice that 6,080 feet is evenly divisible by 16 feet. 380 x 16= 6,080. So why don't we make the 16 foot grav into our basic linear measurement and define 380 gravs as a grav mile?
Unlike the arbitrary units of the Metric System or the obsolete definition of the statue mile, these are two natural units that accomplish something that is important to us. This is gravity and the circumference of the earth, which we use with our system of latitude and longitude. I think that this is as close as we are going to get to making the most out of natural units.
Has anyone wondered when it will be time to move beyond our current system of navigation, using GPS coordinates? Might there be a better system out there?
So much of the way we convey information involves the use of keypads. I think that keypads actually represent an ideal system that we could use for navigation.
Consider a rectangle that is subdivided into nine smaller rectangles, like a phone keypad but without the zero. Now suppose that we number the smaller rectangles from 1-9, just like on a phone.
Next, we superimpose a map of the world on the rectangle so that the map of the world is subdivided into nine sectors by the smaller rectangles. So each sector of the world map would have a number from 1-9.
One issue that we soon run into, of course, is that of projection. The earth is a sphere and it is impossible to render the surface of a sphere onto a flat map without any distortion. Many projections have been developed for mapping, the best-known is the Mercator Projection, but none can ever render a sphere on a flat map without any distortion.
Most wall maps of the world use the simple Cylindrical Projection. This is the one without any "gaps" in the map. The distortion of Cylindrical Projection is that east-west distances near the equator will appear shorter than they really are, and east-west distances at higher latitudes will appear longer than they really are.
The following image is from the Wikipedia article "Mercator Projection". The red circles show the proportional distortion of the map. Areas closer to the equator appear as smaller than they actually are and areas closer to the poles appear larger. Africa is about fourteen times as large as Greenland but the two appear as about the same size.
One advantage of Cylindrical Projection, other than it's simplicity, is that a straight-line route on the earth will also show as a straight line on the map.
Now suppose we get our Cylindrical Projection map of the world and superimpose our nine-section keyboard on it. What we could do to compensate for the inevitable distortion in east-west distances is to have the equatorial regions of the world consisting of three narrower sections while the higher latitudes, both north and south of the equator, consist of three wider sections.
What this could accomplish is to make it so that each of the nine sectors represents an equal area of the earth's surface.
We see that each of the nine sectors represents an area of the earth's surface. What we can do next is to subdivide the indicated section into a further nine sections. And then those into a further nine.
Suppose that we indicated an area of the earth's by the numbers 379. The first number indicates section 3, out of 9. Then section 3 is itself divided into into nine and section 7 is chosen. Then section 7 is divided into nine and section 9 is chosen.
By using this method we can pinpoint any place on the earth's surface with as much accuracy as we wish. More numbers mean greater accuracy. 379 would give less accuracy than 37941264. This gives it an advantage over GPS because sometimes we want to specify a wide area.
The zero is not used in the keyboard of nine. This means that we can use zeros to join two points together. 3790412 would mean points 379 and 412. This would mean a route or line between those points. More points could be added to indicate an area or the corners of a map.
The nine sectors of the earth's surface would be predefined. But that doesn't mean that maps of limited areas could not be adapted from this system. All that would be necessary is to define the four corners of the map, and then it could be subdivided into the nine sectors in the same way as the whole world map.
GPS could be "running in the background" of a map that used this keypad method. Any keypad map could be initiated at anytime, all that would be necessary is to define the corners of the map. The keypad method is not actually a new way of determining locations and distances, just a much easier way of expressing it.
This is something that is simple yet revolutionary. I have never seen it pointed out and it is about time that it was. It involves expressing direction while traveling in space.
How do we express directions in space? On earth we express direction with the cardinal directions of north, south, east and, west. To some extent we can extend this system into space. Since the moon is tidally locked to earth, meaning that the same side of the moon always faces earth and the moon doesn't rotate other than it's revolution around the earth, the moon's poles match those of earth and so it is clear which is the north, and which is the south, lunar pole.
Since all of the planets in our Solar System orbit the sun in roughly the same plane we can also apply this to most of the other planets. The north pole of the planet is the one closest to earth's north pole.
The magnetic poles of planets tend to be fairly close to the geographic poles, because the magnetism results from the spin of the planet. So we can also define the north and south poles of the planet by magnetism. But this is complicated in the case of Uranus because the planet has apparently been knocked on it's side by an impact and it's south magnetic pole is actually closer in geographic direction to earth's north pole.
But what about outside the Solar System? Many "exoplanets" have been discovered in orbit around other stars although, at this point, we cannot tell much about them. How can we express directions on those planets, since their orbital planes may be nowhere near the same as in our Solar System?
I have a simple solution that would enable us to express directions on any planet or star in the universe. Virtually everything in the universe rotates, planets, moons, asteroids, stars and, galaxies. The earth rotates eastward. Why don't we just define east as the direction of rotation? Then, when we are facing east, west is behind us, north is to our left and south is to our right.
This means, of course, that the cardinal directions of north, south, east and, west will be relative. Since the rotation of Venus is opposite to that of the earth it's north and south poles must be the reverse of earth's. But this would be a simple yet revolutionary way to be able to express what we could call "local direction" on any astronomical body.
When dealing with planets or stars we only have to deal with directions in two dimensions, since direction on the surface of a sphere can be expressed in two dimensions. That is why the cardinal directions of north, south, east and, west are sufficient, two opposite directions for each of the two dimensions.
But what about directions within our galaxy? We live in a barred spiral galaxy that is rotating. But we have no real easy way to express directions in the galaxy. How would you describe which direction one star is from another in our galaxy? There is no easy way to do it. We cannot use the orbital plane of our Solar System as an effective reference point because it is not the same as the rotational plane of our galaxy, there is a difference of about 60 degrees.
But if we use this principle of definition of direction by rotation it becomes simple, except that we need two additional directions because we are now dealing with three dimensions, rather than two. Let's call the two additional directions "top" and "bottom".
Our barred spiral galaxy is rotating, that gives us a starting point. Suppose we are looking at our galaxy from outside, from the same plane in space as the galaxy is aligned, as if we were looking down at earth's equator. Consider the galaxy as rotating "eastward" but instead of calling what would be north on earth, let's call it the "top" of the galaxy with the "bottom" being in the opposite direction.
So if we were looking at our galaxy from outside, along the rotational plane of the galaxy which is congruent to looking down at earth from above the equator, and the galaxy was rotating from our left to our right, what would be north on earth will be defined as the "top" of the galaxy and what would be south on earth will be defined as the "bottom" of the galaxy.
But to define direction within the galaxy we still need another reference point. We could just define east within the galaxy as the galaxy's direction of rotation, as we would on planets and stars. The trouble with that within the galaxy is that, if we are near the center of the galaxy, east will be one direction on one side of the center and the opposite direction on the other side of the center. So doing it that way probably wouldn't work very well.
So to express directions within the galaxy we need some kind of reference point outside it.
It seems that every galaxy is part of some larger galactic group. The group that our galaxy is in is known as the Local Group. Our galaxy is not the largest galaxy in the Local Group. The Andromeda Galaxy has a double nucleus, making it seem as if it is actually two galaxies that merged together.
Every galactic group has a common gravitational center. Within the galaxy why don't we define "north" as the closest line to the line between the center of the galaxy and the common gravitational center of the galactic group? North may not be the same line because remember that we defined east as the direction of the galaxy's rotation and the line between the center of the galaxy and the gravitational center of the galactic group may not be in the same geometric plane.
Remember that, within a galaxy, "north" is not the same as "top" and "south" is not the same as "bottom". We are dealing with a three-dimensional space, unlike the two-dimensional surface of the earth, so we need six cardinal directions, rather than four.
So when we have "north" within the galaxy defined as the direction along the axis of rotation that is closest to the line between the center of the galaxy and the gravitational center of the local galactic group. Again the reason the two lines may not be the same is that the line between the center of the galaxy and the gravitational center of the local galactic group may not coincide with the rotational plane of the galaxy.
Once we have "north" defined within the galaxy, "south" is naturally in the opposite direction. When we are facing directly "north" "east" is to our right and "west" is to our left. Remember that "east" within the galaxy is not the same thing as the direction of rotation of the galaxy, as it is with the earth and planets and stars. The direction of rotation of the galaxy defines it's top and bottom but not the remaining four directions of "north", "south", "east" and, "west".
With modern astronomy and space exploration we definitely need an effective way to express directions in space. At present we usually try to impose the cardinal directions of our earth on other planets and it is not very efficient.
Here is something for Christians, Moslems and, Jews to unite on. Have you ever thought about where the names of the days of the week come from? Four of the days are named after Viking gods, and three are named for astrology.
Saturday is named for Saturn
Sunday is named for the sun
Monday is named for the moon
Tuesday is named for the God of War
Wednesday is named for the God named Woden, or spelled Odin.
Thursday is named for Thor, the God of Thunder, who is sometimes considered as the Viking equivalent of Jupiter.
Friday is named for Frigg, the goddess wife of Woden (Odin).
Isn't it something that, not only are we destroying the earth that we live on by global warming and pollution, but it doesn't even get a day named for it, although the moon and Saturn do?
How is it that the Book of Genesis describes the seven day week being inaugurated by the one Holy God himself, but then the days end up being named for these pagan gods? This is unreal.
How about some more appropriate names for the days of the week?
Monday becomes Righteousday
Tuesday becomes Earthday
Wednesday becomes Peaceday
Thursday becomes Almsday
Friday becomes Lifeday
Saturday becomes Goodnessday
Sunday becomes Holyday
Wouldn't this be better than the present paganism?
8) MISNOMERS
There are still misnomers around, which are gradually being corrected. There used to be "tidal waves", except that they are caused by undersea earthquakes and have nothing to do with tides. A better term is the Japanese word for it, "tsunami".
We are in the Space Age but there are still references to "the dark side of the moon". The same side of the moon always faces earth and this refers to the side that faces away from earth.
But not only is it not "the dark side of the moon", it actually gets more sunlight than the side that faces earth. I say that the far side gets more sunlight because it is totally facing the sun (new moon) when it is between the earth and the sun, meaning closer to the sun, while the side that faces the earth is totally facing the sun (full moon) when the moon is on the opposite side of earth from the sun, meaning further from the sun.
9) NATIONAL SYMBOLS
So many nations have vicious wild predators, such as lions and eagles, as their national symbols. How much sense does it make to have a predator as the national symbol, and then lock people in prison for conducting themselves like the national symbol?
Why don't we have plants as our national symbols? Canada has the maple leaf. But this does not mean marijuana.
This is being written near the city of Buffalo and I have always thought that the buffalo would make a better symbol for America than the eagle. There are eagles in much of the world but the buffalo is more uniquely American. There are statues of Buffalo all around the city. Image from Google Street View.
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