Showing posts with label education versus experience. Show all posts
Showing posts with label education versus experience. Show all posts

Thursday, August 23, 2012

Probability And Uncertainty / Chaos And Complexity - Temporal And Perceptual Field Insufficiencies.

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As some of the more advanced members of our growing Braintenance crowd might have guessed based upon enhanced telepathic powers (or by having read the title), this is indeed a post on probability and uncertainty, and on chaos and complexity. All of these are nouns representing ideas or theories based upon observed behaviors, and upon the inherent limitations of observations.

Probability is the likelihood of a given outcome based upon observed experience over an expanse of time. We know that the likelihood or probability of a coin landing with the 'heads' side up is .50 or 50%. And we also know that each toss of a coin is an independent event. Despite this statistical logic, if we toss ten coins and they all turn up 'heads' -- we start to develop an "experiential probability bias," and we start to think (despite ourselves, and despite what we know to be the truth) that the next coin toss is more than 50% likely to result in a 'tails' outcome. We tend to think that way because we forget that probabilities are based upon averages over time, and we start to think that if one result is prevalent for a longer period than expected, there is a "cosmic force" of some sort that must make the ratios fall into line.

But again, probability is based upon observation of a given even over a significant period of time [whatever "significant" means].

Uncertainty is a different situation. Where we haven't observed a certain event enough times to determine a pattern of likelihood, we tend to be uncertain. Some of us will even attribute an arbitrary (but customary) 50/50 probability to an event where we don not have empirical evidence to support a probability pattern.

But what if those patterns are actually there -- but their periodicity is, say, longer than a lifetime. We frequently fail then to observe the probability pattern. If the scope of our observation of an even is limited, we deal in uncertainty and fail at predictability. Geologists and certain other scientist dealing with certain phenomena which take place over great lengths of time are becoming better at seeing patterns and periodicity in certain major events, and are becoming better predictors of the future based upon a greater gathering of experience based upon a longer perspective of history.

My favorite Braintenance analogy is the confusion between chaos and complexity.

Events that we may see or consider as chaotic, or random, may in fact be part of a very grand design which takes place beyond the ordinary scope of our perception (we are limited there), or beyond the period of time required to recognize the occurrence as a pattern. Perhaps we haven't lived long enough to see a recurrence of the seemingly isolated event -- for example, perhaps we have only lived long enough to see the passing through the heavens of Hally's Comet; a change in the Earth's magnetic polarity; a massive climatic change - yet, scientists do not only tell us that these events have occurred more than once before... in some cases they can tell us when they are anticipated to occur next.

In the above case, the relative shortness of our lives does not permit us to see the recurrence of the event and conclude that it is either a pattern or a part of a far greater and more complex series of cause and effect events which contain the pattern. I call our failure to recognize many such patterns as being due to a Human Temporal Insufficiency.

These greater wave-like patterns are either much longer in duration (i.e., they occur over a long period of time and are gradual and continuous enough that we cannot perceive of the change) or they occur at intervals to great for us to readily measure using our senses. Temporal insufficiency can handicap our view of the world, and it usually does. Economic and political cycles are much more recognizable as patterns because their "wavelength" is much shorter than the intervals between, say ice ages.

Other patterns which do not seem like patterns to us from our ordinarily visual perspective, are just too large in size for us to see unless seen from a much higher and greater vantage point. Some examples include many of the greatest wonders of the world (such super-sculptures as the pyramids, long 'runways', and the ever-popular crop circles) as well as astrological patterns and symbols which are not recognizable as such from the hiker's view, but which become very clear when seen from the air.

I refer to our inability to perceive these as non-chaotic and reasonable as Perceptual Field Insufficiency.

Together, our Temporal Insufficiency combined with our Perceptual Field Insufficiency make probabilistically determinable things seem like random events (uncertainty instead of probability), and make very large, potentially meaningful things (as patterns recognizable only from a 30,000 foot view) seem chaotic or discrete, and not a part of something greater.

I would suggest you read this brief article several times over, put your imagination to work [don't confine it to its usual inviolate parameters], and start to enjoy a new view of a far greater, vaster, more meaning-filled universe.

Douglas E. Castle for The Braintenance Blog and for The Daily Burst Of Brilliance Blog




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Tuesday, September 21, 2010

Brain-Twister: Tossing A Coin - Not So Simple...

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Brain-Twister: Tossing A Coin - Not So Simple...

Dear Friends:

Note: This article is secretly a post about Management, and how people think. But I won't tell you that. You see, people take Management very seriously, and they shut down at the mere sight or sound of the term. But if we re-frame the same content as a Brain-Twister, everybody wants to play! Don't speak a word of this to anyone!

When I was a mere tadpole in the New York System (which system has subsequently become a tragic) study in entropy, I was taught about probability. We were all indocrinated about the difference between "independent events" and "dependent events."

Every one of us was absolutely clear that each toss of a "fair coin" (balanced, and not weighted or otherwise structurally altered) was an independent event, with the probability of the coin's landing on Heads being equal to .50 (fifty percent) and the probability of the coin's landing on Tails also being equal to .50 (fifty percent). Each coin toss was independent of any other coin toss, and the probability of a tossed coin landing with the heads side up was exactly the same as was the probability of the same tossed coin landing with the tails side up.

It was an immutable, irrefutable proposition.

What they never told us was that these probabilities were "statistically determined" based upon a "very large" number of tosses. As we all know, occasionally you can toss a coin several times and get just heads, just tails, or some combination that was not quite 50/50. Intuitively, we believed that given enough tosses, the number of times that heads would come up would always be equal to number of times that tails would come up. The notion of an infinite number of tosses tending toward the sacred 50/50 ratio was never questioned -- yet, when tossing a coin just a few times, the outcome was, in fact, very seldom, 50/50.

Here's my question, framed in several different ways:

If you were betting on a coin toss game (which was unfixed, honest and legal), and the first two tosses turned out to be heads, would you bet on heads for the next toss? How about if the first four tosses turned out to be heads? How about if the first seven tosses turned out to be heads (statistically unlikely, but definitely possible)?

Here's my observation:

As the number of heads in a row increased, the odds of your betting on the next toss coming up heads would be reduced. In your mind, you are probably thinking something like this..."Since the statistic is eventually supposed to average out to 50/50 the REAL LIFE odds of the next toss resulting in landing on heads is decreasing with every toss. The next one's JUST GOTTA turn up to be tails."

What is the reason for this type of thinking? It is because we feel that the individual tosses are not truly independent, and that the earlier tosses are "statistically forcing" the outcome of the next toss.

If you had never been taught about this 50/50 statistical tendency (let's say that you were some cave-dwelling type of individual, as were many of my relatives, and that you only knew what you observed) -- you would then behave in just the opposite manner. With each toss resulting in heads, you would become increasingly convinced that the next toss would ALSO be heads. Your reasoning would be based purely upon your observation of a relatively small number of occurences.

Here's My Confession:

After seeing an increasing number of heads coming up in a row, I would become increasingly likely to bet on tails...as if the tosses had to support the statistic based upon the infinite example. I believe that somehow the universe will force the next toss to bring my observations into line with what I'd been taught. This means that I do not fully believe that each toss is truly independent of the next.

Here's Some Food For Thought:

Both the cave-dweller (my great-uncle Farkas) and I would be biased based upon either pre-conceived notions or inadequate testing. We would both be using logic, but we would both be wrong.

Here's a Bit More:

People make decisions either based upon over-education or under-experience.

As always, I welcome your comments.

Faithfully,

Douglas Castle

p.s. Please feel to express your thoughts regarding this post in the Comment Section which follows in the itty-bitty hyperlinks under this article.

Article Appears Courtesy Of http://Braintenance.blogspot.com



Douglas Castle
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