Thoughout the history of mathematics, physics and engineering
there has been a widely employed technique that has never been
officially recognised.

Refered to commonly by names like "fudge factor", it has never
recieved mathematical status to justify it's usage.

I propose that this area should now be formalised.

Firstly, a more dignified name is required:
  
   "FUDGE OPERATOR" or "FUDGE TRANSFORMATION"

Then an impressive mathematical symbol:

         _
          )
         /
        /
        (_
         .

 (i.e like a cross between a reversed Integral and a question mark)
         
Unfortunately this beautiful symbol will need to be simplified to 
something like "?" for brevity on ASCII keyboards.


We are all familiar with situations where after carrying out a
stream of calculations (algebraic or numeric), one arrives at an
answer that is ALMOST but not quite what one is looking for.

Now, one is well aware of the type of answer one is expecting
and thus knows that there is just some simple slip-up somewhere
in the calculations.

One can then go through the lengthy process of re-checking the
calculations to find the simple mistake, which is very inefficient 
in todays' high pace world - or more practically one can simply 
perform an obvious transformation on the result in order to
make it conform with the expected answer.

Thus one very efficiently compensates for trivial mistakes
made in the calculations.

Of course this sort of thing happens everyday but the procedure
is not formalised, so it is not shown explicitly in calculations
and therefore is open to abuse.

My proposal is to introduce the FUDGE OPERATOR (or F.O) formally into
WRITTEN calculations.

IMPORTANT: Now you can't simply create ANY answer you want using the F.O.
That would be anarchy.

The VALIDITY of the F.O lies in it's ability to efficiently compensate for
PARTICULAR CLASSES OF COMMON ERRORS expected in the types of calculation 
being performed.

For example

- Order of magnitude errors
  e.g  One obtains the answer 1.23 but expected 12.3
       Obviously a decimal point shift has inadvertantly crept
       into the calculations.

       One would use the F.O thus:
       ? (1.23) = 12.3
	
- Sign errors
        ? (-X) = X

- Number base errors (common in computer applications)
        ? (64) = 100  (i.e 64 hex => 100 decimal)

- Numberator/denominator inversion
        ? (X/Y) = (Y/X)

- Trigonometric confusion
	? (sin X) = cos X
	? (sin X) = arcsin X

- Logarithmic confusion
		       X
	? (log X) =  10  

- Imaginary/real reflection 
	? (i*X) = X

- Inequality inversion
	? (X > Y) = (X < Y)

And so on..... I'm sure these are familiar to you.
One cannot deny the mathematical beauty of these transformations.

Now of course in most cases the answer obtained from the F.O will
then be checked against another source such as experimental results.

But the point is that if the F.O produces a correct result:
THERE IS NO NEED TO WASTE TIME RE-CHECKING THE CALCULATIONS.

Another person can glance at your calculations to understand
the general intention of the solution - and upon seeing the
usage of the F.O in the last step can recognise that the solution
is largely sound but it just contains some trivial error that
distorted the initial answer.

So much for the initial proposal:
What is needed is a comprehensive list of valid FUDGE OPERATIONs
and the classes of calculations to which they may be applied.