He tried not to make too much noise as he made his way to his seat.

Meanwhile, the professor was already writing on the second blackboard.

He looked the title of the lecture:
"Everything you wanted to know about nothing much in particular".

The professor's voice droned on....

"The main thing that you need to remember about the
Humdinger Ambiguity Principle (H.A.P.) is that 
everything at a fundamental level is ambiguous.

Fortunately, there are different measures of ambiguity.
The most important consequence of the H.A.P. is that it
allows you to determine the limits of ambiguity.
(The Ambiguity Calculus will be explained later in this lecture).

Of course, the limits of ambiguity are themselves ambiguous and so, 
one can apply the H.A.P. to these limits, 
continuing in this fashion, ad infinitum,
one would finally arrive at a meaningless result.

So what is the point if all you get is meaningless result?
Well, the H.A.P. would always, predict
that one could attain this meaningless result with
a high degree of unambiguity! 

In fact, this preceding discussion is an outline 
of the proof of the existence of the H.A.P.
(I leave the details as an easy homework exercise.)

Now, let me proceed with the formal statement of the H.A.P.:

[1.0]  'Let P be a  set of statements.
        Let M be an unmeasurable space.
        Then, there exists an ambiguous function A,
        such that A maps P to M, where A(p) = p*H for all p in P.
        where H is the Humdinger Constant.'

Physicists are currently trying to measure the value of H.
Experiments have shown that 

exp(-12341235878025981273051.28375) < H < exp(98723459237049871235127511820512.35079)

Various experimental teams using more advanced techniques
are trying to extend this result to several more significant figures.
However, they have not been able to get a uniformly unambiguous answer...

Having made this formal definition, we can make
the following corollary:

[2.1]  'Every ambiguous statement is the result of an earlier ambiguous statement.'

It is now an easy exercise to apply this result, 
using "reverse induction" (or is it "inverse reduction"...) 
in order to prove that

[2.2]  'Every ambiguous statement will result in a further ambiguous statement.'

In fact, what we have proven is the 
[2.3]  First Fundamental Theorem of Ambiguity (F.F.T.A.),
       which states that "The universe is ambiguous".

So what are the practical applications of this theory?

This theory is so general that it has no particular applications.

                *       *        *

As a historical side-note, you might be interested in knowing that this theorem 
was proven by Dr Ernest Humdinger in his PhD dissertation
and has caused shockwaves in the academic community.

As you may know, physicists have been searching for the
Grand Unified Theory (also known as Theory of Everything) for decades.
In a remarkable stroke of genius, twelve-year-old Ernest Humdinger 
has beaten all of them to it.

The ultimate conclusion is

[3.0]   "The universe, everything that we know is ambiguous!"

Every theory is just a special case of this result.

Of course, many physicists are skeptical
and seek to disprove his results on experimental ground.

What is at stake are millions of research dollars
that have funded the annual research trips to Hawaii 
during the december months to do fundamental research in wave mechanics.
(Apparently, only Hawaii has the necessary conditions to generate
the types of waves that are of interest. 
However, funding was cut before this theory could be validated.)

Other research teams are horrified that they are no longer able
to travel to the Soren-Kierkegaard-Institute (S.K.I.) at the Swiss Alps.  
(The S.K.I. teams possess the best equipment on this planet to detect S.N.O. particles.
"S.N.O." stands for "Still Not Observed")

But it is not merely the research dollars.
There are also the reputations of thousands of scientists
who have been embarassed that a twelve-year-old working on 
a limited budget of $1.61 (with which he bought a notepad a pencil and a jelly donut.)
while working during recess, was able to do what these eminent scientists
were unable to do, despite the fact they had laboured for decades 
using powerful supercomputers.

The technology edge that the scientists thought they possessed,
ultimately proved to be their undoing -
You see, the H.A.P. was at work in the physics of their supercomputers!
Thus, any model that these supercomputers sought to evaluate
was in and of itself affected by the H.A.P. principle.
The result was naturally highly ambiguous.
However, because the scientists were searching for UN-ambigous results,
they were not able to see the Ambiguity that was right in front of them!

                *       *        *

Humdinger has developed the Ambiguity Calculus in order 
describe the degrees of Ambiguity of any physical system.

According to the Ambiguity Calculus, 

[4.1]  The First Ambiguous Number is "0".

It represents the number of people who will agree on the results
of any experiment to determine ambiguity.
(Early on, it was observed that "0" was greater than "2",
but later it turned out to be experimental error.)

[4.2]  The Second Ambiguous Number is "infinity".

It represents the size of the result set that any experiment on ambiguity
will produce.

We will now define the operator "+" in the Ambiguity Calculus:
[5.1]         0 + 0        = 0           
[5.2]  infinity + infinity = infinity.

In order to demonstrate the power of the Ambiguity Caluculus
we will use it to prove the Trinity.

[Theorem 6.1]  

Note that both
    0    +     0    +     0    = 0             ("economic Trinity")
infinity + infinity + infinity = infinity.     ("immanent Trinity")

Therefore God is three-in-one.   QED.

We can define an operator "<" and ">" where
[7.1]         0 < infinity  and 
[7.2]  infinity > 0.

[8.1]  Note that "0" is called the "Least Ambiguous Number" and
[8.2]  "infinity" is called the "Most Ambiguous Number".

[9.0]  Observe that 0 < H < infinity where H is the Humdinger Constant.

(So far, this is in line with experimental data.)

Now researchers in Advanced Ambiguity Calculus are
divided as to what the result of what "0 + infinity" should be.
However, this is completely predicted by H.A.P.!
(What a powerful theory indeed!)

This is the motivation for the "or" operator in Ambiguity Calculus
which we will define as follows:
[10.1]     0 + infinity = 0         or 
[10.2]     0 + infinity = infinity

After a short break, we will use this result to prove
a corollary, also known as Rahner's conjecture:

[11.1]    "economic Trinity = immanent Trinity"

           *           *            *

It is now time for a break.
Please excuse me while I get a jelly donut...


J.K.
November 2001