[Python-ideas] real numbers with SI scale factors

[Ken Kundert]

Wow, things have suddenly turned very negative. I understand that this is very 
normal for these types of forums where it is easy to lose sight of the big 
picture. So let me try to refocus this discussion again.


MOTIVATION

The way the scientific and engineering communities predominately write real 
numbers is by using SI scale factors.  These numbers almost always represent 
physical quantities, so it is common to write the number with scale factor and 
units.  So for example, the distance to Andromeda is 780kpc, the pressure at the 
bottom of the Mariana Trench is 108MPa, the total power produced by a typical 
hurricane is 600TW, the number of base pairs in human DNA is 3.2Gb, and the Bohr 
radius is 53pm.  These numbers are the language of science and engineering, but 
in recent years they have also entered the realm of popular culture. For 
example, an article by Ars Technica that calculates that the value of the music 
that can fit on a classic iPod as over $8G (that is the total penalty that can 
be accessed if they were all stolen copyright works).

http://arstechnica.com/tech-policy/2012/06/from-gigabytes-to-petadollars-copyright-math-begets-copyright-currency/

In all of these examples the numbers are either very large or very small, and 
they employ the use of SI scale factors to make them easy to write and 
communicate.  This way of writing numbers is so well established that it was
formally standardized as part of the International System of Units (the Système 
international d'unités) in 1960.

The problem is that most general purpose programming languages do not support 
this way of writing numbers. Instead they force people to convert the numbers to 
and from exponential notation, which is rather inconvenient and hard to read, 
write, say, or hear (it is much easier to say or hear 53 picometers than 5.3e-11 
meters).

When working with a general purpose programming language, the above numbers 
become:

    780kpc -> 7.8e+05
    108MPa -> 1.08e+08
    600TW  -> 6e+14
    3.2Gb  -> 3.2e+09
    53pm   -> 5.3e-11
    $8G    -> 8e+09

Notice that the numbers become longer, harder to read, harder to type, harder to 
say, and harder to hear.


NEXT STEP

So the question is, should Python accommodate this widely used method of writing 
real numbers? Python already has many ways of writing numbers. For example, 
Python allows integers to be written in binary, octal, decimal and hex. Any 
number you can write in one form you can write in another, so the only real 
reason for providing all these ways is the convenience of the users. Don't 
Python's users in the scientific and engineering communities deserve the same 
treatment?  These are, after all, core communities for Python.

Now, Python is a very flexible language, and it is certainly possible to add 
simple libraries to make it easy to read and write numbers with SI scale 
factors. I have written such a library (engfmt). But with such libraries this 
common form of writing numbers remains a second class citizen. The language 
itself does not understand SI scale factors, instead any time you want to input 
or output numbers in their natural form you must manually convert them yourself.

Changing Python so that it understands SI scale factors on real numbers as first 
class citizens innately requires a change to the base language; it cannot be 
done solely through libraries.  The question before you is, should we do it?

The same question confronted the developers of Python when it was decided to add 
binary, octal and hexadecimal number support to Python. You could have done it 
with libraries, but you didn't because binary, octal and hexadecimal numbers 
were too common and important to be left as second class citizens. Well, use of 
binary, octal and hexadecimal numbers is tiny compared to the use of real 
numbers with SI scale factors.

Before we expend any more effort on this topic, let's put aside the question of 
how it should be done, or how it will be used after its done, and just focus on 
whether we do it at all. Should Python support real numbers specified with SI 
scale factors as first class citizens?

What do you think?

-Ken