
Coherent Systems - what are they ?

             by Paul Eric Anderson,    + 3984.0F13 posi-4


This work is about systems of quantification
 - how we measure our universe and how we present that measurement.


We use quantity systems to organize our perception of 
and interaction with our world.

* We measure time using systems of units and timezones which 
   we inherited from various efforts to improve time-keeping throughout history.

* We measure mass using systems derived from 
   linear (spatial) measurements of various materials.

* We derive spatial measurement units from various dimensions of our world.

* We present quantities as a subset of our language system: numerics.

Our systems of depicting numbers and measuring time, mass, distance, and energy
 are all examples of systems that need coherence.

A quantifying system presents the value of a quantity in a numeric format.
This format would, in simple terms, be a string of characters.

=======================================================
= A one-dimensional numeric presentation of quantity
= is the basis for a quantity system.
=======================================================

Coherence - what is it ?

Quoting from Kaye & Laby "Tables of Physical and Chemical Constants":
'A system of units is said to be coherent when derived units are formed from the base units without the insertion of factors of proportionality other than unity.'

I want to surpass this definition.

=================================================
=  Coherence is recursively linear uniformity.
=================================================

Coherence is a property of a quantifying system such that the base scale is recursive in a linear progression.

A quantifying system presents a value in a one-dimensional numeric format.
The format is, in simple terms, a string of characters.

Coherence has the following qualities:
 * the format has a single number base.
 * the format scales linearly in magnitude.


One of the latest attempts at coherence was the development of the 'Metric' system.
This system was developed to provide a common numeric base(10) to units of measurement.
This effort made calculation of physical quantities much more intuitive.


=============   Numerics

The "Decimal" system is a way of presenting quantities.
It has a basic concept of coherency by presenting a quantity 
 as a string of numbers, decreasing in signifigance from left to right.
 example:                       324.17
        most signifigant digit=-^    ^-= least signifigant digit

This makes interpreting the number intuitive, given use.
The "decimal point" marks the boundary between integer and fractional parts
 of the quantity.

The system is coherent:
 there is no difference in scale going from left to right or right to left
   the multiple is always ten.
 the scale always decreases from left to right without exception.

Compare this to, for instance, 
 a numeric quanitity presented in Microsoft's default date/time format.

(This is found in the text that follows: 7/8/1992 1:26:24 a.m. )

Quoting (remember - this is only a single example from a confused planet !)
an MSDN document:
===============================================================================
XL: Using Dates and Times (XE0127) 
Last reviewed: February 2, 1998
Article ID: Q95948 
The information in this article applies to: 
Microsoft Excel 97 for Windows 
Microsoft Excel 98 Macintosh Edition 
Microsoft Excel for Windows 95, version 7.0 
Microsoft Excel for Windows, versions 2.x, 3.0, 4.0, and 5.0 
Microsoft Excel for the Macintosh, versions 1.x, 2.x, 3.0, 4.0, and 5.0 
The following is the complete text of the application note "Using Dates and Times," (XE0127). This Application Note describes how to use new and existing date and time functions in Microsoft Excel 97 and earlier. It also describes how dates and times are stored. 
You can obtain this Application Note from the following sources: 
Microsoft's World Wide Web Site on the Internet 
The Internet (Microsoft anonymous ftp server) 
Microsoft Download Service (MSDL) 
Microsoft FastTips Technical Library 
Microsoft Technical Support 
For complete information, see the "To Obtain This Application Note" section at the end of this article. 
THE TEXT OF XE0127
  Microsoft(R) Product Support Services Application Note (Text File)
                     XE0127: USING DATES AND TIMES
                                                   Revision Date: 4/97
                                                      No Disk Included

 --------------------------------------------------------------------
The information in this Application Note applies to: 
Microsoft Excel for the Macintosh( versions 1.0, 1.03, 1.04, 1.06, 1.5, 2.2, 3.0, 4.0, and 5.0 
Microsoft Excel for Windows versions 2.0, 2.1, 2.1c, 2.1d, 3.0, 4.0, 5.0, and 7.0 
Microsoft Excel 97 for Windows 
General Information
Microsoft Excel stores all dates as integers and all times as decimal fractions. With this system, dates and times can be added, subtracted, or compared like any other numbers. In this date system, the serial number 1 represents 1/2/1904 12:00 a.m. (midnight) in Microsoft Excel for the Macintosh, or 1/1/1900 12:00:00 a.m. in Microsoft Excel for Windows. In Microsoft Excel, all dates are manipulated using this system. Times are stored as decimal numbers between .0 and .99999, where .0 is 00:00:00 and .99999 is 23:59:59. 
The date integers and time decimal fractions can be combined to create numbers that have a decimal and an integer portion. For example, the number 32331.06 represents the date and time 7/8/1992 1:26:24 a.m. if you are using the 1904 (Macintosh) date system, or 7/7/1988 1:26:24 a.m. if you are using the 1900 (Windows) date system. To perform complex date and time calculations, use the built-in DATE and TIME functions in Microsoft Excel. 


==============================================
===============----- end quote------ ===============
====================================================





Month/day/year ?? HOUR:MINUTE:SECOND A.M./P.M. ????
 12 of this, 30 of that(depending on which year, of course) and -
  - which year did you start counting from, anyway ?
Followed by 12 (or maybe 24 ?) units of 60 minutes of 60 seconds ?

We see a scrambled mess, particularly when we get into adding time
 (Is it daylight savings, or A.M./P.M. (why is 12:00 the meridian, anyway ?)

How do you interpret 04/04/49 12:00 A.M. ?  Which time zone ?
You need to know where the date/time applies to... 
... it differs whether the date above is generated from Singapore or Seattle !

The format presents a single point in the time - continuum as being
 a collection of variously different-sized units.


The system is not coherent:

    * Each unit scales differently: 
            Hours have 60 minutes, 
              and there are 24 hours in a day (the scaling is 24 up or 60 down).
            There are 12 months in a year but how many days are in a month ? 

    * Depending on where you ask, 
         the signifigance of each unit from left to right 
         changes in accordance with local custom. 
          In the format shown above, 
             the signifigance ranges from 1 to 6 as follows:
                          04/04/49 12:00 A.M. 
          signifigance:    2  3  1  5  6   4

    * Arbitrary unit demarcation:
           date is presented as:
                   month/day/year     
            or     day-month-year
            or     month day year
            time is normally boundaried by colons(:)

    * Compounding the problem is the matter of the initial reference point
 of the system, as there are different "origins" from which systems count time.

=====================================
Not merely incoherent, it is absurd.
=====================================

How to get a Coherent Numeric System ?

How to describe a quantity ?

Evolving from our present predicament,
 look at what a quantity is, in how we describe it.

We start with a base unit, such as a meter, gram, or second.
We scale the unit to where it is convenient to enumerate,
 such as kilo-grams, centi-meters, or milli-seconds.
The last thing we do is enumerate the scaled quantity.

The result looks like this:

  number scale unit

Metric system example:
   0.454 kilo grams   

(don't laugh - NASA and the next shuttle crew still depend on this one)

---------------------
Scientific Notation
---------------------

The number itself may be so distant that it is awkward to present in this form.
Consider the mass of an electron:  9.10939E-31 kilo-grams

We use "Scientific Notation", because it simplifies the presentation,  which
would otherwise be: 0.000000000000000000000000000000910939 kilograms.

But what is the difference between using "Scientific Notation" and scaling prefixes such as "kilo-", "milli-", or "pico-" ?

Instead of 9.10939E-31 kilo-grams should we say 9.10939E-28 grams ?
Only in the cgs system, but not the mks system.

*******************************************************
************  Coherent Numerics  **********************
*******************************************************

Consider the decimal system.
The problem with using the deci-numeric system is that there are two
 factors (5 and 2) in the base, which leads to incoherent scaling.
Compound this with the greek scaling prefixes used in physics, which are
 mostly (not all of them...) scaling 10^3, we end up with a total of four
 _different_ factors to scale by: 2, 3, 5, and ten.

Using the "hexadecimal system", we can eliminate all factors except 2 and its
 exponentials 4, 8, and sixteen. The system would be coherent around 2.

We can eliminate "greek scalor" confusion by always using the exponent portion
 of a "floating point" format as the unit scalor, eliminating the 10^3 scalor.

9.10939E-31 kilo-grams becomes   + 4.82C0A nega-17  grams


The Coherent Numeric System 


The Coherent Numeric System is proposed to be:

sign mantissa expsign exponent

where:
sign is either "+" or "-"
mantissa is base-sixteen 
expsign is either "posi+" or "nega-"
exponent is base sixteen

any units used are "nude" (no greek prefixes).


This document is still being written...

=========================   the future  ======================

Should mass be defined in terms of the mass of a single proton ?
There are arguments that there is a quantum of distance ...
Is there a basic (quantum) unit of time ?


Always interested to here from you...

Paul Eric Anderson
xplorer@crb.elga.net.id

