A simplified and less confusing notation for numbers – Part 2 (further explanations, extensions and examples)

Under construction

Link to Part 1 (introduction and summary)

Extensions for logarithmic notations

Defense in a forum discussion

I have been dealing with the problem of more efficient numbers over decades (see). Only after having given up the attempt to use new words for the digits from 0 to 9 I could start to really profit from the new notation.

The best way to prevent an idea from getting realized is to promote similar ideas, so that those who in principle would be in favor of the original idea get divided and fight each over more or less irrelevant details instead fighting together for their goal.

In any case, all those profiting from confusion concerning probabilities of concrete threats such as getting a victim of e.g. the latest killer-virus or of (often staged) terrorist attacks, have to try to prevent such a simplified number system from becoming generally accepted.

It would be great if readers could create versions in their own languages. If you have suggestions, criticism or relevant links, please let me know: info@pandualism.com

#212  –  2016-10-05

Dave Rogers in #209:

What he's actually doing is starting from a number say, 333 – then converting it to scientific notation – 3.33 x 102. He's then replacing the 102 part with a number-letter combination, where the number is the modulus of the power of ten and the letter p or n to represent its sign, placing this before the 3.33, and dropping the decimal point by assuming that the first digit precedes it. Thus 333 becomes 2p333, 200 becomes 2p2, and 170 g becomes 0.17 kg becomes 1n17. The ease of use of the system can best be assessed by the fact that he himself screwed it up and rendered that last one as 9n17.

Why not invest a few minutes: A simplified and less confusing notation for numbers

The purpose of this number notation:

·         transparency of order of magnitude in calculations

·         ease of writing

Fundamental principle of notation:

0p = 00p = 000p = 0000p = … = 100 = 1
0n = 90n = 990n = 9990n = … = 10-10 = 100 pico
00n = 900n = 9900n = 99900n = … = 10-100

The sequence from kilo to milli (always division by 10): three.po, two.po, one.po, zero.po, nine.ne, eight.ne, seven.ne

A few examples:

00p375 ∙ 00p2 = 00p75
03p375 ∙ 06p2 = 09p75
23p375 ∙ 16p2 = 39p75
99n375 ∙ 06p2 = 05p75
99n375 ∙ 00p2 = 99n75
99n375 ∙ 99n2 = 98n75
83n375 ∙ 17p2 = 00p75
83n375 ∙ 16p2 = 99n75
83n375 ∙ 90n2 = 73n75

Dave Rogers in #213:

My apologies, I appear to have got it wrong. Your system is less simple and more confusing than I thought, and is clearly a lot harder to master than scientific notation despite giving no advantages over it.

The Hindu-Arabic numeral system is apriori simpler and more effective than the Roman numerals. Nevertheless, to the persons having grown up with Roman numerals, the new decimal system seemed more confusing than the accustomed one.

Thus, as long as you have to translate e.g. 8p2998 m/s into 299,800 km/s, or 0n25 meter into 2.5 Angstrom = 2.5 x 10^-10 meter, the new systems only represents an additional complication. Yet if you have assimilated the concept eight.po as "hundred mega" (2p1 ∙ 6p1), or as "zero point one billion" (…999n1 ∙ …009p1), or as "ten raised to the power of eight", then 8p2998 is easily recognizable as around "eight.po three = 8p3". And in a mental calculation it is easier to use the concept "eight.po two nine nine eight meter" than "two hundred ninety nine thousand eight hundred kilo-meter".

jaydeehess in #229:

Moving the order of magnitude in front of the significant digits is odd and counter intuitive.

From a logical point of view, it seems more reasonable to move from the general to the specific, e.g. starting with country, continuing with town, street, apartment, and ending with name of addressee. (It is true that postal address is written the other way round, but it is normally read from bottom to top by the postal service.) Thus in principle, we should even start with the unit. Order of magnitude is meaningless without unit. And significant digits are meaningless without order of magnitude and unit. (One must not confuse the absence of a unit with the default unit piece.)

From the psychological point of view, it is less demanding to understand "meter eight.po three eight four" than "three-point-eight-four times ten-raised-to-the-power-of-eight meter". After "meter" we know that we deal with distance in space, after "meter eight.po three" we may recognize a distance close to a light-second. The rest simply adds less and less important accuracy.

Dave Rogers in #240:

No, I think I see how it works, and why it doesn't. He notates negative exponents from 1 to 9 by subtracting the exponent from 10, from 10 to 99 by subtracting it from 100, from 100 to 990 by subtracting it from 1000, ...

The principle is more straightforward: In order to get a negative exponent, we simply apply the standard subtraction rule, i.e. we regularly subtract from zero:

…01000 minus …00001 equals …00999
…00100 minus …00001 equals …00099
…00010 minus …00001 equals …00009
…00001 minus …00001 equals …00000
…00000 minus …00001 equals …99999

pi  = …000p314159… ≈ 0p31416 = p31416 ≈ p314
1/pi = …999n318309… ≈ 9n31831 = n31831 ≈ n318

Let us also reexamine "83n375 ∙ 90n2 = 73n75" (3.75 x 10^-17 ∙ 2 x 10^-10 = 7.5 x 10^-27) of my previous post. 83n means an exponent of …99983 (i.e. 17 below zero). 90n means an exponent of …99990 (i.e. 10 below …00000). In this system multiplication of numbers always results in direct addition of exponents. So we get "…99983 + …99990 = …99973" resp. "83n ∙ 90n = 73n".

I always get confused when I have to multiply or divide numbers in scientific notation with negative exponents. In the system proposed here, multiplication always results in addition, and division in subtraction of an exponent. And computer science demonstrates every day that implementing negative numbers by regular subtraction from zero works fine.

If you have learned the elementary charge as 1.602 x 10^-19 Coulomb, then creating the exponent by regular subtraction from zero as in 81n1602 Coulomb obviously seems more complicated. Yet after having grasped the principle of regular subtraction from zero, you can logically derive the meaning of 81n16 C. In case of 160 Zepto-Coulomb or 0.16 Atto-Coulomb however, the meaning is much less straightforward.

What is the electric charge of the electrons of one mole of hydrogen (with total weight of 1 gram = 7n1 kg). One mole of hydrogen contains 23p6022 ≈ twenty.three.po six electrons with each an elementary charge of 81n1602 C ≈ eighty.one.ne one six Coulomb. As 23p6 = 23p1 ∙ 0p6 and 81n16 = 81n1 ∙ 0p16 we get 23p1 ∙ 81n1 ∙ 0p6 ∙ 0p16 = 4p1 ∙ 0p96 = 4p96 ≈ 5p1 Coulomb = 100 kiloC.

How much energy corresponds to 1 kg according to E = mc2E ≈ 1 kg ∙ 8p3 m/s ∙ 8p3 m/s = 16p9 kg m2/s2 = sixteen.po nine Joule.

When you do similar calculations with Apollo units such as slugs for mass (see #196) and miles for distance, then such simple mathematical relations become quite opaque.

jaydeehess in #242:

3p126 I read as 126 x 103 = 126000

Such reading would destroy the main advantage of the number system, which is easy recognizability of orders of magnitude. The most important information is next to the po-ne-indicator: 3p126. In case of 23p6022.1408, the last digit "8" is the least important part. For comparison: 6.022,140,8 x 10^23.

Dave Rogers in #245:

So, for example, 6.626e-34 is not significantly harder to type than 66n6626 - two extra characters not requiring shift or control keys - and its actual magnitude is much clearer.

The decisive point: 66n = six.six.ne or sixty.six.ne is a schematically created concept in the same way as 'ten' = one.po, 'hundred' = two.po, and 'nano' = one.ne. And "six.six.ne six six two six" is also shorter and simpler than "six point six two six exponent minus thirty four".

© – No rights reserved – Wolfgang G. Gasser – 2016-10-24