Just a Theory

Remainders are just wrong.

By which I mean both mathematically and morally.  Division is such a natural idea that I can no longer accept that it might not "come out evenly".  It is still acceptable to have division result in a decimal, but not in a remainder.  Here is my logic:

I call it my theory of Intelligent Division.  A search of the text of the bible reveals that the word "remainder" is only used to describe the outcome of subtraction, never division.  This is a clear indication that a "remainder" upon division is not an acceptable result.  Rather, we must postulate that in all instances of division, an intelligence greater than ourselves is guiding the outcome, and such an intelligence would never allow something as sloppy as a "remainder".  Look, for instance, at the decimal result of any division.  There is a clear sign of an intelligence at work, because the numbers after the decimal point show non-randomness to a high degree.  To ignore that pattern (in favor of "remainders") would be to ignore the obvious intelligent hand guiding the process of division.

Our culture has clearly lost its way when so-called "number theorists" discuss the notion of ugly "remainders".  Such immorality has spawned completely unnatural processes such as "modular arithmetic" in which 350 times 2 equals 34 ("modulo 666", a clear sign of unscrupulousness) when we all know it must equal 700.  These "mathematicians" tell everyone that "remainders" are an established fact in number theory, and that they explain all sorts of facts about numbers.  But they never explain to you that number theory is only that:  just a theory!

And this theory has huge flaws.  The most glaring of these is the remainderist idea that "you can't divide by 0".  Any theory with such huge gaps in the evidence cannot possibly stand up to intense scrutiny.  The bible contains the word "divide" 129 times (the word "add" only 53 times, "subtract" not at all, and "multiply" only 48 times), and surely it is impossible that such a holy operation would be so fatally flawed.  The time is clearly ripe to overthrow the intellectual hold that remainderists have had on our education system for years.

America's children are being taught about these "remainders" from as early as 8 or 9 years old, and it is time for change!  I demand that Intelligent Division be taught along side "remainder" division so that the 8- and 9-year-olds can make an informed decision about what is mathematically correct.  We cannot let the remainderists set the curriculum for our youth.  If you live in a family-oriented school district (especially in Kansas), please let the school board know that there is an alternative.  They can demand that students be exposed to all ways of looking at division, not just the ways the remainderists insist upon.  The future of country is at stake here.

Comments

[Polymath]

The question has been raised (in Pharyngula's comment section) about whether Intelligent Divsion has anything to do with the Pythagorean school of thought.

The answer is an emphatic no. As I understand it, the Pythagoreans believed (at least until they secretly proved otherwise) that all numbers had to be rational. But if you take a remainder and express it as a fraction (another division), and take that remainder and make it a fraction, and so on...you get a continued fraction, which can be an irrational number.

This fact provides more support for Intelligent Division: when you deny the possibility of remainders, you can generate all sorts of numbers. Remainderists have to stop calculating once there is a remainder, and then create whole new sets of numbers from scratch. Surely Occam's razor favors the guiding of some supernatural intelligence in the process of division.

[Moebius Stripper]

I just realized that I had some Intelligent Division proponents in my precalculus class last year. One student emphatically declared that the boat in a question couldn't be rowing at a speed of ten and a half kilometers per hour, because "the speed can't be a fraction."

[Alon Levy]

Besides, remainderism stops working when you include evidence from more general number fields - just try to divide with remainder in Q[SQRT(-19)].

[Xerxes1729]

As if you need any further evidence for your argument against Remainderism and Number Theoryism, just think about this:

number theory -> numerology -> witchcraft -> satan

Alternatively,

number theory -> cryptography -> secret messages -> child porn and terrorism

The logic is irrefutable. Number Theorismists have been undone!

[vlorbik]

all i know is i graded
an algebra paper yesterday where
the solution to 7x = 60
was given as "8 R 4"
(no mention of "x", natch).

and *now* i know why i didn't like it!
remainderism must be eliminated!

[Robert Marks]

The value of Pi given in 1 Kings 7:23 is a whole number (integer), viz., 3, which is consistent with Intelligent Division. At least no-one can accuse God of being inconsistent.

[steve]

This looks to be almost as powerful as the recently announced Intelligent Falling theory (http://www.theonion.com/content/node/39512 ).

[brian]

666=500+100+50+10+5+1
666=600+60+6
666=the sum of 6(10^(n)) from one to three

[milo gardner]

Remainders were used by 2,000 BCE Egyptians for
subtraction:

2/p - 1/A = (2A -p)/AP

the so called Hultsch-Bruin
method, rediscovered in 1895, used for remainder arithmetic subtraction, or

2/p = Q + R

with R being stated
as a multiple of p,
as (2A -p)/Ap surely
is for scribal division.

Scribal division can be generally shown as inverse
statement of unit fraction series, or one (1) divided by 2 2/3, a quotient and remainder, becomes

1/(8/3) = 3/8 = 1/4 1/8,

as written in the AWT,
RMP, Reisner and every
other ancient hieratic
text.

In addition, in general
Egyptian scribes wrote
out remaindes as unit
fraction series, their
ancient form of numeration
a notation that scholars
have oddly confused, since
most or Classical scholars
accepting odd views of Euclid, that used the same form of unit fraction arithmetic!

That is, rewriting the
history of fractions and
ways of base 10 division,
as you have begun, seems like an odd and misdirected task, and therefore one that hopefully will be abandoned for the traditional 4,000 year old view, ASAP.

Best Regards,

Milo Gardner

[D B]

Did you forget that division IS only glorified subtraction - just as multiplication IS only glorified addition?

[Clinton]

Remainder suck therefore they should be eliminated from the surface of the planet. Remainders are crappy baby math (no offense to babies). 16/2 = 4R4 NO. 8 you people. 5/2 2R1 NO 2.5 :( Remainders are for squares. Point Proven.

[Clinton]

Sorry 'bout that last comment a little crude ;(