Computation of Time

We measure time so far in years, months, weeks, days, hours, minutes, and seconds. Seconds can be divided into respectively thousandths, step by step more finely down to the measuring border. But is our computation of time practical?

The following three questions are to clarify the problems:

1. How many days are between 25.01.2004 and 11.11.2004?
2. Which weekday is the 11.11.2004?
3. How many seconds are between 09:12: 06 o’clock and 11.11.11 o’clock?

The answer to question 1 has to consider the different length of the months and leap years.

The answer to question 2 in addition has to include the seven day rhythm of the week and to assume a date with well-known weekday.

The answer to question 3 requires the conversion of hours and minutes in 3600 or rather 60 seconds.

Hence, I suggest the following computation of time:

1. The octal system is used throughout.
2. Time is specified: [[+/-] year,][day].[fraction of the day][additive].
3. An Earthday is inserted between Sunday and Monday within the week.
4. The months have regularly four eight-day weeks.
5. The last twelfth month has deviating 13 days (in the leap year 14).
6. Day 0 is New Year (1.1. so far, Sunday), day 1 is working day (Earthday).
7. The year will be introduced with year 0.
8. Time zones are omitted and Greenwich Mean Time is used world-wide.

Explanations:

To 1. (The octal system is used throughout.):

We mostly use the decimal system (radix 10, figures from 0 to 9). The radix indicates the number of different figures of a number system. Numbers can be equivalently represented in other number systems (only with another “appearance”).

Numbers that are larger than indicated by the highest figure transfer a carry of one to the next left place: After the 9 follows the 10, after the 99 the 100, after the 999 the 1000 etc.

Humans can on the average recognise maximally seven things at one time, without having to count them. The octal system with the radix 8 possesses the figures from 0 to 7 and accommodates here thus the nature of humans.

The octal system can be converted in a simple manner into other number systems that are a power of the radix two. Apart from the binary or dual system (radix 2, figures 0 and 1), there are among these in particular the tetral system (radix 4, figures from 0 to 3) and the hexadecimal system (radix 16, figures from 0 to 9 and from A to F).

Most computers are based on the binary system. The figures 0 and 1 indicate whether current flows or not. Numbers in the decimal system have to be converted for these computers into the binary system so that it can be counted fast.

The longer the numbers are, the more time-consuming the conversion is. For the output in the decimal system, a renewed transformation is necessary. By the conversion between dual and decimal system, frequently transformation-caused truncations arise behind the decimal point.

Here some examples (the subscript number indicates the radix for the distinction of the number systems):

2004₁₀ = 7D4₁₆ = 3724₈ = 133110₄ = 11111010100₂.

If 11111010100₂ starting from right is divided by | into two-blocks in the form 1|11|11|01|01|00₂, then the representation for 133110₄ can be obtained by the following replacement pattern:
00 ≙ 0, 01 ≙ 1, 10 ≙ 2, and 11 ≙ 3. A first block left with a digit remains unchanged.

For the production of 3724₈ from 11111010100₂, three-blocks from right have to be transformed to: 11|111|010|100₂. The replacement pattern reads:
000 ≙ 0, 001 ≙ 1, 010 ≙ 2, 011 ≙ 3, 100 ≙ 4, 101 ≙ 5, 110 ≙ 6, and 111 ≙ 7. A first block with less than three digits has to be completed before by zeros from the left.

For the production of 7D4₁₆ from 11111010100₂, blocks of four from right have to be transformed to: 111|1101|0100₂. The replacement pattern reads:
0000 ≙ 0, 0001 ≙ 1, 0010 ≙ 2, 0011 ≙ 3, 0100 ≙ 4, 0101 ≙ 5, 0110 ≙ 6, 0111 ≙ 7, 1000 ≙ 8, 1001 ≙ 9, 1010 ≙ A, 1011 ≙ B, 1100 ≙ C, 1101 ≙ D, 1110 ≙ E, and 1111 ≙ F. A first block with less than four numbers has to be completed before by zeros from the left.

Generally, if you have a radix of 2ⁿ, there have to be formed blocks of n digits in the representation of the dual system from the right and the first block to the left has to be filled up with zeros up to n digits, beginning from the left. The transformation functions also in reverse from the 2ⁿ-system into the binary system. Furthermore, there are still different algorithms for the transformation.

For the production of 7D4₁₆ from 2004₁₀, 2004₁₀ is continual divided by 16₁₀:
2004₁₀/16₁₀ = 125₁₀ remainder of 4₁₀;
125₁₀/16₁₀ = 7₁₀ remainder of 13₁₀;
13₁₀/16₁₀ = 0₁₀ remainder of 7₁₀.

The two digit remainders are converted into the hexadecimal system and gone through from top to bottom. The desired result 7D4₁₆ is obtained if they are thereby lined up from from left to right: 7₁₀ = 7₁₆, 13₁₀ = D₁₆ and 4₁₀ = 4₁₆.

Generally, the number to be converted has to be continually divided by the radix of the target system, and the multi-digit remainders have to be converted into the notation of the target system. The number searched for results from the lining up of the remainders from left to right if in the division calculation the remainders are gone through from bottom to top.

Naturally, here different transformation algorithms exist – also in the reverse direction. Since the continual division is computationally more expensive than the figure replacement in figure blocks, the mentioned loss of time emerges. Positions behind the floating point are similarly converted.

To 2. (Time is specified: [[+/-] year,][day].[fraction of the day][additive].):

The order results from the sorting capability of the date. + can be omitted; – refers only to the year. If the fraction of the day is omitted, the (normal) date results. The year can be also omitted if the understanding permits that.

The fraction is indicated as sequence of octal figures. For optical reasons, the numbers can be filled up with zeros on the right to an even number (e.g. four or six-digit). Additive may be for example: Christian, Jewish or Islamic or an abbreviation. The standard is without additive.

The seasons spring, summer, autumn and winter and the holidays return regularly. These regularities shall survive with respect to the year, even if there are irregularities in the details.

Hours are not used anymore for reasons of confusion. The day is divided roughly into eight parts (called octs). Furthermore, an oct is divided into eight parts (called lepts). The minute is redefined as the 64th part of a lept. The second is redefined as the 262144th part of a day (64 * 64 * 64 = 262144).

For this reason, time can be indicated approximately three times more exactly with six figures in the octal system as with six figures in the decimal system (262144/[24 * 60 * 60] ~ 3.034). Four lepts, or a half oct, correspond to 1.5 hours and two lepts correspond to a school hour of 45 (old) minutes. The break of five minutes becomes the break of a quarter-lept.

Because 64₁₀ = 100₈, seconds pass naturally into minutes, minutes likewise into lepts and lepts into days. Days cannot pass naturally into years because a normal year has 365₁₀ = 555₈ days. The leap year with 366₁₀ = 556₈ days does not improve anything here.

The new analogue clock dial is much more symmetrically designed than the old one and corresponds better to the compass rose and the sundial. x and + are superposed as principal axes. The 0 is placed at the bottom. The digits follow clockwise from 1 to 7. The division into 64 lines (lepts, new minutes and seconds) optically hardly differs from the conventional one into 60 lines (old minutes and seconds).

To 3. (An Earthday is inserted between Sunday and Monday within the week.):

The weekdays are named after planets in several languages. The Earth was excluded so far. It is appreciated by the Earthday. Finally, it is less crucial, which name a language community uses.

A week with eight days represents at first sight a greater human burden. Wednesday could, however, bring a relief as middle of the week if the afternoon is kept as free as possible, both on the job and at school.

We assume an eight-hour working day and two free weekend days. If we consider 56 days at those 320 hours would have been worked in the seven-day week, 336 hours in the eight-day week, then it results for Wednesday that 16/7 hours per eight-day week would have to be less worked.

If we would begin our work in GMT at 7 o’clock, then we worked on an eight-hour working day till 15:30 o’clock if we assume a half hour of lunch time. On a Wednesday would have to be worked at same beginning time only till approx. 12:43 o’clock.

We are free to work longer at flexible work time the week over in order to be able earlier to terminate our work on Friday for example. Modified solutions are to be used respectively at other work time models and work times.

To 4. (The months have regularly four eight-day weeks.):

Having 32 days, the months can be halved very well by steps of two. The month can be determined in the octal system from the three digits representing the day – where necessary zeros may be completed on the left. 0 – 3 in the second place characterise odd, 4 – 7 even months.

Month is, however, only a transient term and finally derived from the Moon, which has subordinated importance in the new computation of time. Instead the terms half, third, quarter, sixth and twelfth (of the year) are used. The date is to be indicated, if possible, accurately to week or day.

To 5. (The last twelfth month has deviating 13 days (in the leap year 14).):
The position of the leap day in the middle of the year was so far little plausible. At the end of the year, the computation of time can be corrected expediently as missing time units are inserted – in particular in seconds. To New Year, all clocks are then reset to [year],0.000000. Here fields will profit where special accuracy is needed.

The last five (in the leap year six) days can receive own weekday names. The weekday names will become less important, however, in favour of the numbers connected with them.

To 6. (Day 0 is New Year (1.1. so far, Sunday), day 1 is working day (Earthday).):

It has practical reasons that each month begins with Sunday. The beginning of the week with Sunday has historical reasons and is also a concession to the moon calendar. In addition, the 0 resembles the symbol for sun (sun calendar).

Since the Gregorian calendar at present is the most common calendar, New Year is the 1.1. according to it also in the octal calendar. The celebrations around the turn of the year can be committed in well-tried form.

To 7. (The year will be introduced with year 0.):

This happens for practical reasons: The year can be noted briefly (without additive). A clear cut is made concerning the old computation of time. This point is among all of them the least mandatory.

To 8. (Time zones are omitted and world-wide Greenwich Mean Time is used.):

The question, what time in another time zone is valid, is unnecessary. A world-wide communication is facilitated, since all clocks on Earth show the same time if they are synchronised. Greenwich historically has the zero meridian.

Now, instead of the three initial questions, the substantially more difficult one is asked:

How many days are between 25.01.2004 09:12:06 o’clock and 11.11.2004 11:11:11 o’clock?

First, the question is reformulated into the octal system (with truncation at the seconds, chr. stands for Christian):

How many days are between 3724,30.304233 chr. and 3724,473.356511 chr.?

The answer is given by a simple subtraction: 443.052256. The 25.01.2004 would be a Sunday, the 11.11.2004 would be a Tuesday in the new computation of time. There are exactly 443052256 (new) seconds between the two numerical data, rounded 4430523 (new) minutes, 44305 lepts, 4431 octs, 443 days and 44 weeks.

Discussion of important aspects:

The biggest challenge might be – independently from the computation of time – the conversion into the octal system. It is connected with high costs, great need for discussion and preparation for many years. The policy will have to work hard to convince the majority by extensive advertising efforts.

One additional day per week is for all religious communities equal (-ly fair). In relation to other week lengths, the one extended to eight days is certainly most moderate. The representation of the year is not religiously founded. By the additive, every religious community can specify its computation of the year.

I do not doubt that humans can learn. Also handling computers was so far successfully mastered. The gap between humans and computer is strongly reduced by introducing the octal system.

Monthly sums of amount can be easily split to weekly and daily ones. Here, the shortened twelfth month can be better calculated. Equal month lengths, under normal conditions, are fairer regarding the money than the irregular ones.

Everyone not being born at a leap day celebrates the own birthday at the same weekday in a year. This is not a crucial disadvantage. The emotional rhythm of 28 days within the biorhythm is also better mixed.

The SI-unit second would have to be redefined. Here, atomic clocks should have no problem. Introducing the octal system requires to replace terms such as kilo and million respectively to shift the meaning of word beginnings such as mega, micro and nano.

Depending upon the old time zone, the day turns out to be differently related to time. Humans can begin the day, eat, work or learn, meet and sleep as they usually do. Only the time indicated differs.

We need to get used to that including the date line. It remains, however, at its old place. World-wide communication is to be given priority because of its increasing importance. The arising costs are exceeded over years by the saved ones. Calculation and communication become clearly easier.

By introducing the octal system, not everything is done. It should be connected meaningfully with a world-wide source language (as native language), also based on the octal system. Such an efficient planned language is presented below linguistics. Everyone shall be able to talk to everyone on the same level.

Code of computation of time

Further thoughts: Calculating lengths in the octal system

We measure lengths up to now on the basis of the SI-unit metre. In the octal system, there are to form appropriate multiples of 8. What is the practical implementation?

Instead of conventional kilometres of 1000₁₀ m length, octal kilometres of 512₁₀ = 1000₈ m length are used. Since time is measured instead of conventional seconds in octal seconds of day length/1000000₈ ~ 0.33₁₀ s, it follows that almost three octal seconds are counted per conventional second.

On the tachometer, speed is measured in octal kilometre/lept with lepts the 100₈th = 64₁₀th part of the day. 100 kilometres per hour correspond to approximately 73242₁₀ ~ 111.2₈ lepts kilometres (octal). The difference in the numerical value may hardly be noticed and is therefore justified. 100₈ lepts kilometres (octal) correspond vice versa to approximately 87.38₁₀ kilometres per hour.

The speed of light is 299792458₁₀ m/s = 98808549.39₁₀ m/octal second ~ 570731345₈ m/octal second. If the speed of light is specified by about 300000 km/s, we can also specify it by 570000 octal kilometres/octal second.

The 25₁₀-metre lanes are shortened to 24₁₀ = 30₈ m, 50₁₀-metre swimming to 48₁₀ = 60₈ m. Instead of 50₁₀ m, 100₁₀ m, 200₁₀ m, 400₁₀ m, 800₁₀ m and 1500₁₀ m would be to swim: 48₁₀ = 60₈ m, 96₁₀ = 140₈ m, 192₁₀ = 300₈ m, 384₁₀ = 600₈ m, 768₁₀ = 1400₈ m and 1536₁₀ = 3000₈ m. These deviations are justifiable. The long hauls should be multiples of 1000₈.

In athletics, there are also the following distances: 3000₁₀ m, 5000₁₀ m, 10000₁₀ m, 20000₁₀ m and 50000₁₀ m, which could be replaced by the following distances: 3072₁₀ = 6000₈ m, 4096₁₀ = 10000₈ m, 8192₁₀ = 20000₈ m, 20480₁₀ = 50000₈ m and 49152₁₀ = 140000₈ m. The marathon will remain unchanged (42.195 km = 122.323₈ octal kilometres).

In the building industry, measures are valid that are usually exactly determined to the centimetre. Since we can accurately calculate in the octal system to 1/64₁₀ and 1/512₁₀ m, there should be no problems. The same is true for furniture, although it certainly can be accepted to shift measures that are multiples of 0.1 m to those that are multiples of 0.125 m.

© 2001-2008 by Boris Haase

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