Re: Digital vs. Binary Computers

From: Bx.C (invalid-email-address_at_invalid.shiragajin)
Date: 04/26/04 

Date: Mon, 26 Apr 2004 00:34:14 -0500

> > In an analogue device, I guess dividing by zero wouldn't be an error
> > unless they could prove it was *exactly* zero...
>
> Aah, in analogue, nothing is _ever_ a "point"...
>
> One of the things we did in those statistics lessons...what's the
> probably of a wave at sea being exactly a metre high? The statistical
> answer is actually _zero_...yeah, not "very small" but actually a
> result of "completely impossible"...so you always have to take
> "ranges" to do any calculations or the answers all come out as "zero"
> / "impossible", which isn't a particularly helpful answer...I remember
> this point because it had to be _stressed_ that you must always take a
> "range" or, yes, it's quite natural to look for "exactly one metre"
> and not realise that your answer of "zero" is a _flawed_ answer...so
> they drum it into you: "Take a range! Take a range! No such thing as a
> 'point' for analogue!"...that the statistician must remember that
> people naturally say "one metre high" but you have to interpret that
> in your calculations as "between just under one metre and just over
> one metre" (by how much? Ah, well, no simple answers to that

ahh.. reminds me of calculus... definite integrals.... if the starting point
of the range and the ending point of the range are the same, then there is
no range at all... thus 0 in length... so the height under the curve,
whatever it may be... times 0... yeilds the area under the curve to be 0....

> question..."statistics" _IS_ an imprecise science...which is, as I've
> said many times before, the really funny thing that people take
> "statistics" so deadly serious as if "the direct word of God" or
> something...but, in fact, statistics is an _imprecise science_...it's
> where mathematics _stops_ being trustworthy...where "interpretation"
> and "opinion" starts entering the picture...proof of the pudding is
> asking two statisticians to come up with conclusions _given the same
> set of figures_...yeah, it's actually _grossly unlikely_ that they'll
> have the exact same results...the "conclusion" might end up being the
> same, like "don't smoke, it's bad for you"...but they'll probably plot
> different graphs, exclude different "outliers" (what's the criteria
> for excluding "outliers"? None whatsoever...it's all done to a
> statistician's "intuition" about these kinds of thing!! ;)...if a
> statistician is biased - their paycheck is coming from the drugs or
> tobacco companies - the, oh boy, totally untrustworthy...even when
> "honest", you can't take the conclusion that seriously...but when
> dishonest...well, ask the tobacco companies' statisticians about
> "passive smoking"...conclusion: "no evidence"...ask every other
> statistician to look at the problem...conclusion: "Terrible! Evil! Ban
> smoking immediately!"...and the big point to realise is that you don't
> actually have to skew your results or "cheat" too much...you just
> choose that your "outliers" will be all the people with lung cancer
> and then, well, just "exclude" them from your figures because they are
> "exceptional" in your "humble opinion"...then what "critical value"
> are you going to use to decide if there is or isn't a "correlation" in
> the figures? Well, most statisticians would use this value...but,
> hmmm, in your "humble opinion" and using your "statistician's
> intuition", you think that this is an "inappropriate" measure so
> you're going to take the value which requires at least 99% of passive
> smokers to be dead as the "level" at which you're going to accept a
> "correlation"...then, your figures - after all this cynical
> manipulation - suggest "there is no correlation but, you know, it's
> pretty damn close to being a correlation, even with all your
> cheating"...but, in their "conclusion", they'll just "conveniently"
> neglect to mention how damn close to getting a correlation you
> actually were...you just report: "no correlation"...the results are
> always a fraction of "probability" between zero and one...so, if it's
> 0.89 and you need 0.9, by your subjective reckoning, to get a
> "correlation" then you "snap" your conclusion _downwards_ to "nope,
> doesn't exceed 0.9 so let's treat that as 0.0 probability"...yes,
> statistics is _that much_ of an imprecise science that does depend far
> too much for a mathematical discipline on "intuition" and
> "interpretation" that when all these statisticians come up with
> completely different conclusions about "passive smoking" then they
> aren't necessarily "lying" in any way...just a case of severely
> "bending" your figures and your "interpretation" of it all...
>
> Yeah, the title of the opening chapter of my statistics textbook, not
> wanting to start by giving any kind of false impression of the
> "trustworthiness" of statistics?
>
> "Lies, damn lies and statistics"
>
> And that's before we even get to the common practice of just inventing
> figures...you know, "90% of time is spent in 10% of code"...yeah, nice
> mathematical figures there...sounds very "technical"...but _exactly_
> 90%? _Exactly_ 10%? Nah, totally made up figures...it's just someone
> trying to say "most time is spent in a small section of code" but just
> trying to make it _sound_ more "technical" and "trustworthy"...you
> know, "hey, look, numbers! Numbers are mathematical! Maths is entirely
> trustworthy! Numbers are always entirely trustworthy! This, therefore,
> must be a 'concrete fact' because there's numbers in it!"...
>
> Nope, sorry, "85.648% of all statistics are made up on the spot and
> are entirely fictious"...

like... umm... "100% of all divorces begin with marriage" (draw your own
obvious conclusions to that one if you wish... hehe)

> The _only_ trustworthy "statistic" is something really simple like
> "raw count of people would answered 'yes'"...that is, basically, when
> all the statistician does is _count_ a bunch of stuff and report
> exactly the number they counted up to...
>
> But, even then, it is "acceptable practice" to "exclude outliers"
> which may be believed to be "skewing the figures"...e.g. ask 100
> people some question and note their ages...most people asked were aged
> 18-25...one person was 83 years old...he answered completely
> differently to everyone else...as including such an age would drag the
> "average" off towards an age that no-one asked actually was (a bit
> like the infamous "2.4" children...how can you have ".4" of a child?
> Well, in statistics you can, because it's just a "mean average" of all
> the results ;)...it _is_ "acceptable practice" in statistics to,
> therefore, "exclude the outlier" and simply _IGNORE_ the 83 year old's
> opinion completely...you can exercise your "intuition" and declare
> this result as "unrepresentative"...also, less common but also
> "acceptable practice" is excluding someone because you simply think
> they were lying...pure and simple, eh? Well, not everyone gives a
> straight and honest answer to someone taking a survey...excluding
> fictious answers like "I've had 7 million girlfriends / boyfriends
> because I'm so damned attractive!!!" does actually make plenty of
> sense (put 7 million into your statistics and the "average" is going
> to be silly...yes, everyone has 6.3 million partners each, don't they?
> That's totally "representative" of the truth...yeah, _one_ person
> lying - if they really exagerrate things to absurd levels - can render
> all your conclusions complete and utter nonsense ;)...BUT, though the
> reasons why such exclusions happen are actually entirely sensible and
> "acceptable practice", there's absolutely NO OTHER WAY to do it beyond
> 100% "judgement call"...well, you could try hooking up all the people
> you're surveying to a "lie detector" but then you might suddenly find
> you're short of "volunteers" (and time in which to go through all that
> complicated procedure ;)...plus, then again, lie detectors aren't
> entirely trustworthy...there's a "probability" involved that it might
> have got it wrong (so much so, some American institutions that once
> totally relied on lie detector technology have now thrown it away
> because further research has shown that they aren't really as good as
> first believed)...a probability of a probability of a lie of a
> judgement call? And most people automatically _trust_ statistics just
> because it's "got numbers in it"? Really, take the reverse "default"
> here, people...don't believe a number of it _unless_ they start
> actually telling you the methods, assumptions, figures and so forth...
>
> Beth ;)
>
>

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