Re: Meaning of Zero and All, Application to archaeology

From: Eric Stevens (eric.stevens_at_sum.co.nz)
Date: 01/21/05 

Date: Fri, 21 Jan 2005 17:42:30 +1300

On 21 Jan 2005 00:04:19 GMT, Philip Deitiker <Nopdeitik@att.net.Spam>
wrote:

>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.

You can only say the evidence does not exist when you have evidence
that it does not exist. Consider the Higgs boson. They have been
searching for it for more than 30 years and so far, nothing. Yet they
still keep looking. It's like a treasure hunt. You have to have faith
that the treasure exists somewhere. That you eventually loose faith
and give up does not mean that the treasure is not out there somewhere
in the garden.
>
>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.

Yet, although the eventual find proved you correct, had you gone
hunting for an example on a random basis you almost certainly would
never have found it. Yet quite clearly the continuing absence of
evidence (for your prediction) would not mean there was no evidence.
All it would have meant was that you had not yet found it.
>
> 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.

But now you are hypothesising that the data set is 1. In the real
world you cannot know that.

> 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.

No, I'm not going to folow you there. I'm getting a headache. :-)
>
> 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.

At least that's your hypothesis. :-)

Eric Stevens

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