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

Don Latham djl at montana.com
Thu Jun 3 12:40:26 EDT 2010


Does it mean that if you have a can of white spray paint, you can produce
a white crow?
Don

WarrenS
> Ulrich posted a bunch of logic stuff, some of which I did not understand.
>
> but  I do think he missed the main point
>
> This does not need to prove what does and doesn't work with every example,
> only prove that is needed  to answer ALL of Bruce's clams and concerns is
> if
> Oversampling will give good Integration results.
> Bruce has said integration works and non integrating does not work very
> good.
> we both agree on that, No problem
>
> The only problem is that Bruce had got himself in a corner by denying that
> high rates of oversampling will do integration.
> Once he has finally admitted that, now we can move on to the next thing,
> which I guess was why do I like H/W better than S/W.
> Now, I can understand why that would not be logical to many time nuts.
> But to say that oversampling does not provide integration, that is pure BS
> and I could not let it go.
> I don't know how Bruce got into the corner in the first place, I certainly
> give him all the chances to get out before this.
>
> The answer is: that ones needs to integrate the Freq, to get good ADEV and
> there are various ways to do it, each with it's own set of trades.
> The one I choose  is working good enough.
>
> ws
>
> *********************
>
> 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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-- 
"Neither the voice of authority nor the weight of reason and argument are
as significant as experiment, for thence comes quiet to the mind."
R. Bacon


Dr. Don Latham AJ7LL
Six Mile Systems LLP
17850 Six Mile Road
POB 134
Huson, MT, 59846
VOX 406-626-4304
www.lightningforensics.com
www.sixmilesystems.com





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