[time-nuts] A philosophy of science view on the tight pll discussion

Ulrich Bangert df6jb at ulrich-bangert.de
Thu Jun 3 08:15:59 EDT 2010


Gentlemen,

the discussion between Bruce and Warren concerning Warren's implementation
of NIST's "Tight PLL Method" has caused quite a stir in our group.

My scientifical knowledge about the discussed topic is so much inferior
compared to Bruce's one that I don't have the heart to enter a contribution
to the discussion itself. It may however be helpful to have a look at the
discussion from a "philosophy of science" point of view.

The most basic form of logic is the propositional logic. A proposition in
the definition of propositional logic is a linguistic entity which can be
assigned a logic value like "true" or "false" or "0" or "1" without any
ambiguity. Whether a proposion is true or false may depend on circumstances.
For example the proposition "Today is tuesday" is true on tuesdays and wrong
on all other days of week. 

Other proposions are true or false due to their logic construction. The
combined proposition "Today is tuesday or today is not tuesday" is always
true from a logic point of view despite the fact that you may consider it as
kind of "useless". 

Propositional logic then deals with the question what happens when two or
more propositions are combined by logic operators as in the second example
with the operator "or". Since a proposition, say "a", and a second
proposition, say "b", can only have the values of "0" or "1" it is easy to
put every possible combination of a and b values into a simple diagram, for
example for the "or" operator:

a  b  a or b
------------
0  0     0
0  1     1
1  0     1
1  1     1

Most if not all of us not only know such diagrams but really make use of
them in digital electronics. The well known operators are the "or", the
"and" and the "negation" and indeed it can be shown that ALL digital
operators can be constructed by a a combination of "negation" and either
"and" or "or". BTW this is the reason why the first logic circuit to appear
as a single chip, the 7400, was a quad NAND gate, a combination of
"negation" and "and". The designers had learned their lesson and made their
very first chip in a way that ALL possible combinations of two input
variables could be realized with one type of chip.

Nevertheless the 3rd column of the above diagram can be considered a
four-digit binay value and so it becomes immediately clear that their must
be a total of 16 different logic operators whith each of them  producing a
number between 0 and 15 (Decimal) or rather 1111 (Binary) in the 3rd column.
Each of these operators has a name of its own. Although widely used in
common speech one of the not so well known operators is the "formal
implication", or "a implies b" as we say or "b follows from a". 

The "formal implication" has the logic diagram (which is identical to "(not
a) or b"):

a  b  a -> b
------------
0  0     1
0  1     1
1  0     0
1  1     1 

What may look unspectular at the first glance in effect holds two of the
most important supports of ALL scientific reasoning:

While the third row of the diagram basically says that it not possible to
achieve wrong results when logic is applied correctly to correct
propositions, rows one and two say that logic may deliver wrong results
(line one) or correct results (line two) if applied correctly to WRONG
(false) propositions. That is why already ancient logicians knew:

Ex falsi omnis

which freely translated from Latin means as much as: "From wrong
propositions everything can be condluded".

One of the consequences of this is the fact that for a true proposition "b"
the inference to the trueness of the proposition "a" from that it has been
concluded is NOT possible.

A second consequence of this is that NO scientifical theory can be verified
by an experiment. A theory may formulate a proposition on the outcome of a
certain experiment. Even if the outcome of the experiment and the
proposition are in good congruence it would be completely wrong to infere
that the theory is correct due to the experiment. 

It is possible to harden the theory by experiments. For this purpose it is
necessary to produce a big number of different and indpendend propositions
based on the theory and test each single proposition with an experiment. The
more propositions and the more experiments the chance that the theory is
correct increases but note that even with an unbound number of propositions
and experiments this is no proof of the theory. Interesting enough that you
need ony a SINGLE experiment to falsify a theory if the outcome of the
experiment is different from the theory's proposition. What can really be
infered from experiments and observations may also be shown by the following
joke:

A physicist, a mathematician and a logician are sitting in a train riding
through Germany. Suddenly they notice a herd of sheep whith all being white
with the exception of one which is black.

The physiscist: "That is a proof that there are black sheeps in Germay" 

The mathematician: "You physicists are using the term 'proof' in a too
relaxed way. If at all this is a proof that there is at least ONE black
sheep in Germany" 

The logician: "Let's get serious: This is a proof that there is at least ONE
sheep in Germany with ONE BLACK SIDE".

So, what the heck has this all to do with the tight pll discussion? One
thing that I had to read in a time nuts mail of the last days was:

>> It doesnt, it only appears to in a very 
>> restricted set of circumstances.

> Bruce, I don't understand you, when presented 
> with visual evidence that this method works 
> you still deny it.
.
.
>> That doesn't work as it has the wrong 
>> transfer function.

> Again, it it does not work, how come the 
> evidence shows that it does, how do you 
> explain that Bruce?

Due to the criteria explained above the term "evidence" is used here in a
too far-ranging way. The experiment performed by John Miles is NOT a
"experimentum diaboli" in the sense that the outcome of the experiment would
enable us to decide whether Bruce's or Warren's theory about his
implementation of the NIST tight pll method is correct. It is not because it
has not falsified anything. 

As far as my limited understanding of the topic allows me to judge: The
outcome of the experiment is not a direct antithesis to anything that Bruce
has remarked and if I see it correct the outcome of the experiment is by no
means contested by Bruce. However, if we want to check who's right and who's
wrong with experiments, we need to know that we need a lot of experiments
with different references and different DUTs. If all combinations of all
DUTs and all references in the hands of time nuts would lead to equally well
results as in John Miles's experiment, that would allow to conclude that the
method works ok for all practical aspects of time nuts life (however without
the guarantee for every future experiment outcome). Having not done these
experiments yet who knows whether there is a falsifying experiment among the
set of combinations?

Best regards

Ulrich Bangert
www.ulrich-bangert.de
Ortholzer Weg 1
27243 Gross Ippener 





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