Re: Meaning of Zero and All, Application to archaeology

From: Philip Deitiker (Nopdeitik_at_att.net.Spam)
Date: 01/21/05 

Date: 21 Jan 2005 00:04:19 GMT

In sci.archaeology, Eric Stevens created a message ID
news:4v50v05cu9s9upmirpc1m296iur2f83h27@4ax.com:

> On Thu, 20 Jan 2005 20:14:03 GMT, Philip Deitiker
> <Donevenask@worlnet.att.net> wrote:
>
>>I know that Alan was Joking, apparently Steve didn't catch on.
>>But on a more serious note. This is in response to Doug's
reply
>>
>>"
>>I've never understood that 'old dictum'.
>>Absence of evidence is in fact evidence of absence. Not proof,
but
>>evidence of the probability of absence. And how likely that
is
>>depends upon the context.
>
> The old dictum in fact is "Absence of evidence is NOT evidence
of
> absence" though many would argue that it was.
>>"
>
> --- lengthy exposition snipped ----
>>
>>Thus when a person declares Zero frequency of an event based
on zero
>>events he is also saying that the sampling for (not of) such
events
>>was great, that biasing or sampling errors is not a factor
worthy of
>>affecting the conclusion. And when a person says that a zero
events
>>does not reflect the reality or possibilities he is saying
that
>>sampling is poor, or the sampling was biased or that there
were
>>sampling errors to a degree in which a zero frequency
conclusion
>>should not be drawn. He is also saying, implicitly saying that
>>because he knows that the zero result in terms of binomial
>>probability opens the possibility for an infinite number
events of
>>non-zero frequency, that he has some trend that approaches
with non-
>>zero result the parameter proximal to where the sampling
>>result/parameter crosses the Y=0 axis. If we hold every
argument to
>>this standard of plausibility then many arguments will be
summarily
>>eliminated, sort of a kook filter, right off the bat. Does
this
>>argument mean something to the individual, or is it something
they
>>must ignore because they don't understand it.
>>
>
> It's probably simpler for the ordinary individual to say 'the
reason
> you have no evidence is that you haven't found it yet'.
:-)

Not true, there are many things that have no evidence in which
you while never have evidence because evidence does not exist.

There are 2 essential facts which you can call Jokers. There
will occasionally be found things in which we had no evidence.
Homo floriensis is an example. But on the other hand, I
predicted over 2 years ago that it was likely that some of the
erectines that we lumped into one species was likely multiple
species and that other species might exist. The existence of
such species was implicit in the constriction population sizes
guestimated for humans (mtDNA, X-linked) and Neandertal (mtDNA)
that small populations of hominids in the mid late pliestocene
was not a rare occurance, indicating a pattern of radiation, and
in patterns of radiation the number of clads one has depends
largely on how widely the radiants were distributed before they
radiated. Again this is not a burst, the fissuring process
probably took place over 1 million years. Nor was the small
stature outside the confidence range, already the molecular data
on humans suggested that humans left africa in a diminuitive
stature. What was unexpected based on what we know is a
combination of small stature with a radiant erectoid of somewhat
lower probability. Again since humans were a small stature
erectine and humans speciated and radiated there is a
precedence.

  The other essential fact is that not finding something and
expecting something is occasionally also wrong because the trend
lines are not defined accurately enough by the data.

There are occasion when new finds create shock waves, however
just as in the above, careful examination of old data reveals
that what is 'unexpected' is sometimes expected. The people who
were shocked about floriensis were looking for evidence of
something else, not of radiant hominids. If they had been
looking for radiant hominids based on the
molecular/morphological evidence they would not have been
shocked they would have been varifying and expectation.
 
> Of course this opens up the argument of whether or not there
is any to
> find. You cannot strictly apply your binomial analysis until
you know
> something about the larger distribution. i.e. - does it exist?

Actually that is not true. Statistics is a process based on
assumptions but that assumptions are bounded by data. If the
sample size is 1 then the variation in distribution is not
known, however if the trend in population size to 1 is known,
known well enough to define the smallest range which contains
68.3 % of values per unit time and if that range overlies the
range of 1 then one can do binomial analysis.
 If however the only point one has is a singular point or 2
points then range over 2 dimensional space cannot be defined by
confidence, with 1 pt and no other points range then spreads
over the entire questioned area, and with Zero points range is
spread evenly over the entire query area at a density of zero.
  For this reason as sample size decrease the ability to define
range statistically decreases, and since the ability to
confidence the range decrease the frequency per unit range
decreases for a value of 1, and for a sample value of 0 on then
has the remnant probability on the high end of the CI divided
over the entire sampling area with no occurance, this increases
effectively N and makes the prospect of true Zero greater.
Therefore, example, if one was talking about Anceint Egypt and
contacts with New World, there is no contact area in africa
(points of evidence of contact) nor americas. Therefore there is
no reason to specific that the contact was preferential to one
area or the either, which means that the evidence could be
anywhere in africa or the americas. Since many areas in africa
and americas have been examined, the survey constant is greater
than if we had a single point in either area and were looking
for additional evidence, earlier or later.
  In the case of 'l'meadows' there is a single site and that
site is proximal to those who probably visited that site in
greenland, and there are cultural links. Thus the evidence per
that unit time has linked those sites. At that point on the map
and at the time the frequency of visits is the greatest
probably. As on then extends the argument as evidence for other
regions visited over larger time the frequency drops for those
areas because you are averaging 0 evidence per unit area times 0
evidence per unit time with a known area of contact for a
specific time. As one continues to expand the argument into
times of Zero sample the potential geographic area that contain
all possible variation grows, and the top end frequency drops
and at somepoint any reasonable person would declare that
frequency Zero. Why we can do this is because we know when the
'l'm' site was visited, and so it is possible that vikings
visited other sites, and as time goes on the sites visited are
less bound to this particular site if such visitiation
occurred.Eventually on expansion one reachs a point in averaging
that the net effect of averaging the 1 point is so large of an
area its inclusion is of no benefit relative to assuming zero
value for the time, the trend maxima-CI has crossed as close at
possible to the y = 0 axis. An infinite number of zero measured
events would have the same probability.

  This is the true measure of whether we can yeild zero as
potentially an occurrance waiting for a measured event.

 Our argument changes radically with 3 points of measurement
over a range and 1 point at a different time, because the 3
points can assign a range and the 1 point can hold the range to
a time, this forstalls the dilution effect of geography and time
on that 1 point, particulary geography since it constricts the
original range to a given site, and increases the frequency at
the same time. The 1 point is predictably inside the same
frequency confidence range as the 3 statistically, and so is the
next time measurement of zero, it only during the next time
measurement of zero value that the frequency range for 3 does
not overlap with that of zero since now you can average two time
periods of zero frequency.
   Let us compare this with the arguments of Vikings being
spread from Chesapeake bay to Vancover, based on the 'l'm' as
the single verifyably agreed upon point, once the proponents of
the argument state that this is the range, then their argument
becomes subject to all the sampling over then entire range for
the period in which they claim vikings were present. With no
additional verifyable sites, they have set up an argument for
the acceptance of a zero value as zero. Whereas if the
proponents claim that the vikings were only spread over say a
200 mile region around 'l'meadows' there is considerably less
survey of the time frame of interest, and thus the total N
component is lower and thus Zero can be interpreted as
putatively higher. In addition one could average 1 out claiming
the on site was evidence for longer settlement. The claim of a
wider norse distribution weakens the argument by lowering the
possible starting frequency with the observed event and that the
occurance was at any particular frequency decreased more rapidly
than if the argument is constrained to the region around the
sample site.

  Thus what you should be realizing is that attempts to contain
the bounds of ones hypotheses in these situations improves the
probability of that hypotheses being true if the number of
points in support of the argument are 0 or 1, and thus from a
probability stand point any evidence that can be used to contain
range or time of occupation can aid in creating a maximum
freqeuncy when the measured value is zero. Likewise when range
causes one to average data one has over a large sampling area or
large times such that the confidence frequency range decrease as
a result of a larger survey to the same value one would have if
the entire sample was 0, then one has limited both the time and
range for which that event was possible, to extend the range or
time further places the putative event in the catagory of
infinited number of events that might have happened but for
which there is no evidence.

  From a more common sense perspective, a person making an
argument that Vinland is in St Laurance region, Labrador,
Virginia, Boston, Vancover, St. Louis thinks wrongly that they
have improved the prospects of a correct answer. However what
they have effectively done is increased the number of sites that
are tested with a zero result. Since all of the arguments cannot
be right, in fact only 1 of the choices can be right, by
suggesting all they have shown that there certainty for any site
is 1/all the sites or less.[The basis of the arguement is that
there was a Vinland, and since there are many putative sites but
no single site is definitely the site, each sites probability is
considered separately however if one site is the site then
others are excluded, but if no sites show data as it being the
site, bpd then acts to also suggest none of the sites might be
the spot of Vinland] Binomial probability then weigh in and
says that the actual frequency can be zero at all sites, logic
weighs in and says the number can be zero. Thus the individual
is faced with a prospect that all can be wrong.
  Strenthening the argument the individual could claim that
Vinland was proximal to 'l'm' in which case the number of areas
sampled for the event is markedly reduced and there is a greater
risk that something was missed. Logically increasing putative
areas weakens the argument by created contradictory and
undecisive argument. To strenthen further the argument one could
argue that Vinland exists, but that sample densities per
chronological periods are not uniform and that sample density in
unknown areas are at greater areas than known areas, thus there
is a sample bias in surveying, and this sample bias could
explain why Vinland goes undetected. However the second you
specify the area, and the area is tested, then the argument can
be defeated. Thus wisdom in these arguments suggest not to
create just so arguments, but instead postulate that Vinland
exist, but not where or for how long. The existence of Vinland
then becomes an inverse function of evenness and quantity of the
survey (aspect). The maximum probability that confidence will
allow is then the inverse function of the survey (aspect).
  This improves the argument markedly because if someone says
that they don't believe Vinland is in boston harbor, you can
say, hey, vinland is not likely in boston harbor because this
area has been surveyed by archaeologist and no evidence was
found, but vinland is probably elsewhere if it exists. However
the reverse side of the argument is that Ingerish style
proposals that Norse did X in Vinland Y then become detrimental
to the defense of the argument, so that the fantasy
embellishments of a postulation defeat the postulation.
The improvement of arguement does not make it true either, it
simply increases the likihood one has made the best guess if
evidence does come forth (for example H. floreinsis example).
This is why I say that hyperdiffusionist exhibit concretized
thinking patterns, because they seem dead set on establishing
'atlantis, where, when, how' and less focused on taking more
flexible smaller steps with regard to their hypothesis. 

-- 
Philip
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