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

[Steve Rooke]

Ulrich,

So what's this got to do with black sheep. Was this some form of
Freudian slip by you Ulrich :)

So, lets examine what we are looking at here, this has now been
simplified down to a single true or false value which would be of
value if we were looking at a single single data point. That data
point could be transformed into a value which could produce a correct
answer but, as already pointed out, this is only a single point and
holds no value. To get real here, we have seen the results of hundreds
of collected data points which have been processed mathematically to
give answers for different measurement intervals. If you took John's 2
dimensional graphs and selected a single point along the x-axes you
would make a 1 dimensional graph of a single answer and statistically,
and logically, there would be little trust in it.

We can all see that for different Tau, the data collected and
transformed produces very similar congruence. Now, the graphs we have
seen are not straight lines so this indicates that the data taken by
both measurement systems must have some form of difference when
calculated for each different Tau. To understand what is going on here
it would be extremely coincidental for the full results of the two
methods to show such congruence if one of them was using some
incorrect logic. These graphs are not something that is plotted
linearly with time given the current measurement point. Each point on
the graph is a result of the mathematical transformation of the
collected data before it. It is very unlikely for this to be a
coincidence, you cannot take junk, transform it by junk and expect to
get repeatable congruence between two measurement methods over such a
wide span of Tau values. We have to remember that each data point on
an ADEV graph represents a separate calculation on measurements, not
an individual measurement itself.

I fully agree that this test was only done for one input source and it
should be done for as many different types that can be found before
this method is deemed to be usable but at the same time the initial
results of this test is so very encouraging that it is hard to deny
that something is looking interesting here. Trying to throw the baby
out with the bath water at this stage would be pointless and just
smacks at the initial response to those that said the World is round
and not flat. It is that sort of entrenched belief that we need to
break and get the flat Earth believers to act constructively in this
exploration.

Best regards,
Steve

On 4 June 2010 00:15, Ulrich Bangert <df6jb at ulrich-bangert.de> wrote:
> 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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-- 
Steve Rooke - ZL3TUV & G8KVD
The only reason for time is so that everything doesn't happen at once.
- Einstein