Proposals to Redesign Counting, the Metric System, etc.

We don't seem to be getting very far in changing over to the Metric System. While I'll avoid getting into the whole political meaning of this, I think it's a symptom of short-term thinking often practiced in politics as well as throughout society. Instead of trying to make the change and expecting benefits within five to ten years, we must teach Metrics from the lowest grades (It would be learned much quicker than the other "system") and continue to keep it in use through the higher grades. Then maybe in a hundred years... Otherwise, we must restructure our whole economic system, which is the subject of other articles.

We need to go beyond changing to the Metric System. We need to replace the decimal number system and redesign the metric system to match. This is many times more important, but many times less likely to happen. The main reasons for talking about it are that change helps us to evolve; the evolution of our philosophy and ethics is way behind our technology and need a chance to catch up; and it's good mental exercise. If we someday contact a species on another planet, would we want to admit to them that we still use the inefficient base ten counting system because our ancestors counted on their fingers? The most likely way I see to make it happen is through video games which requires learning the new system, and a new language. Kids like to learn languages they think their elders won't understand, such as pig latin and jive. This will be the ultimate in for that.

The New Counting Systems

Hexadecimal, Base 16

(My earlier proposal, much of which still applies)

These systems will seem complicated, but only because we learned the other way first and would have to do a lot of translating until we learn to use "hex" all the time. As computers (and therefore logic) become more a part of our lives, and more available for convenient translating, hex counting may become more popular.

Ten is a poor number to use for a number base. We started it only because we happen to have ten fingers. A number base should be divisible into as many integral factors as possible. This means it should be a power of two. Ten breaks down only into 2 x 5. I used to argue that eight (= 2 x 2 x 2 or 2 x 4) would be the best number base. I've since been convinced that sixteen (= 2 x 2 x 2 x 2 = 2 x 2 x 4 = 2 x 8 = 4 x 4) would be better even though we would need to create more digits. Computer designers and programmers are familiar with the advantages of "power of two" number bases. Microprocessor chips commonly handle eight, sixteen or thirty-two bits of information at a time. Computer memory locations are often talked about as hexadecimal (sixteen-based) numbers, using the letters A, B, C, D, E, F, as the needed additional digits. This means that "hex", 1000 = 1 x (16 digital, 10 hex) cubed + 0 x 10 hex squared + 0 x 10 hex, or digital 4096.

We use powers of two often already, for instance in dividing an inch into 1/2, 1/4, 1/8, 1/16 etc. Once we learn hex, we won't have to be bothered by converting most common fractions to "heximals" as we do at present to decimals. Decimal 1/16, in hex will be written 1/10 or 0.1 and 7/16, will be 7/10 or 0.7. More complex fractions will be relatively just as simple, though more difficult to explain here.

Counting in Binary

(The new proposal, to be further developed) Binary is the most basic of counting systems, very compatible with base 16 or any power-of-two base. But we tend to think that using it day-to-day would be more difficult because of those long strings of ones and zeros. In reality it could be easier because we don't have to deal with multipliers, and we don't need the zeros (except for zero by itself). We only need to specify the powers of two which are occupied by ones. Instead of decimal 512 = 5*(10 to the 2 power) + 1*(10 to the 1 power) + 2*(10 to the 0 power), in my form of binary we would say, 9 = 2 to the 9 power. Of course this is the most binary-positive number. Digital 511 = "binary" 87654321 (or maybe we'd use 9-1 like the roman numeral system). Trying for "random" numbers, I came up with digital 430 = "binary" 875321, 726 = 976421, and 144 = 74. On the average, that's fewer digits than "binits", but, for instance, saying "seven hundred twenty-six" is the same number of syllables as "nine-seven-six-four-two-one". Of course because we'll be counting beyond digital 1023, we need a different system of "binits". A new kind of character (compatible with principles those descibed below) would have one dot (in a 3x4 dot-matrix, with maybe three dots needed to indicate orientation and other information) for each power of two occupied by a one. This means we could write any number up to digital 1023 as one "binary" character, though speaking the number would still be about the same.

The New Metric System

(Based on hexadecimal counting)

This would mean the Metric System would have to be redesigned to match the counting system because for very good reasons, Metric measuring is based on the number base.

Since we're starting from scratch, we should set the basic unit of each kind of measure equal to a power of two of a universal, quantified physical measure such as a wavelength of a certain kind of light or the mass of a proton.

The next improvement would be to get rid of the kind of prefixes presently used in the Metric system. We would use a shorthand version of "scientific notation". Instead of 6.02 x 10 to the 23rd power we would perhaps write 23P6.02 (the most important part of the number first; P is for a plus power, M for a minus power) and find equally compact ways to speak it. (Of course in hex, "Avagadro's Number" would be something altogether different. Would anyone care to figure out what it would be?)

Next we would add time and angles to the Metric System. Time is considered to be included already but doesn't follow metric principles of using powers of 10 (10 defined as the number base, whether decimal or hex). The most common basic unit of time would be the day. Then in hex, 0.8 Days, or 1M8 Days, (half the number base) would be half a day, twelve hours. 0.1 Days = (decimal) 1.5 hours and 0.01 or 2M Days = 337.5 seconds. Since the year isn't equal to a round number of days in hex anymore than in decimal, it would have to remain the base for periods longer than a year. There might also be a universal time scale based on the speed of light, relating distance to time.

The circle would be at least one major basic unit of angle. Then a straight line equals 1M8 Circle; a right angle, 1M4 and 45 degrees, 1M2. The Earth turns one circle in one Day, therefore, in this system, 2M1 circle per 2M1 Day etc. instead of 15 degrees per hour, which leads to the confusion of 15 minutes of arc per minute of time.

The New Language

The next step would be to create a more efficient character set of numbers, and letters. This would be based on a 3x3 dot matrix (expandable to 3x4). More details on this in < href="lang.htm"> Proposed New Language (coming soon). I hope soon to do some simple graphics to show this in more detail.


Send me your thoughts.
Dan Robinson, danrob@efn.org, Eugene, Oregon
My home page: http://www.efn.org/~danrob/