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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Sunday, August 12, 2012

Most Commonly Misspelled Words [English]

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There are many words which we tend to misspell in our writing. Some are so common that our eyes barely notice them. These are not grammatical or usage mistakes (for example, "Notary Republic," or Mondegreens) -- these just result as a function of how we tend to use the QWERTY-formatted keyboard, how infrequently we read things which have been properly spelled, and our spellcheck-type autocorrect functions:

Here's a watchlist of  the top 100 misspelled (or mistyped) words, courtesy of [Warning: This is a LONG post. Please put your scrolling gloves on, Braintenancers - you might even want to pack a lunch] --


  • acceptable - Several words made the list because of the suffix pronounced -êbl but sometimes spelled -ible, sometimes -able. Just remember to accept any table offered to you and you will spell this word OK.
  • accidentally - It is no accident that the test for adverbs on -ly is whether they come from an adjective on -al ("accidental" in this case). If so, the -al has to be in the spelling. No publical, then publicly.
  • accommodate - Remember, this word is large enough to accommodate both a double "c" AND a double "m."
  • acquire - Try to acquire the knowledge that this word and the next began with the prefix ad- but the [d] converts to [c] before [q].
  • acquit - See the previous discussion.
  • a lot - Two words! Hopefully, you won't have to allot a lot of time to this problem.
  • amateur - Amateurs need not be mature: this word ends on the French suffix -eur (the equivalent of English -er).
  • apparent - A parent need not be apparent but "apparent" must pay the rent, so remember this word always has the rent.
  • argument - Let's not argue about the loss of this verb's silent [e] before the suffix -ment.
  • atheist - Lord help you remember that this word comprises the prefix a- "not" + the "god" (also in the-ology) + -ist "one who believes."


  • believe - You must believe that [i] usually comes before [e] except after [c] or when it is pronounced like "a" as "neighbor" and "weigh" or "e" as in "their" and "heir." Also take a look at "foreign" below. (The "i-before-e" rule has more exceptions than words it applies to.)
  • bellwether - Often misspelled "bellweather." A wether is a gelded ram, chosen to lead the herd (thus his bell) due to the greater likelihood that he will remain at all times ahead of the ewes.


  • calendar - This word has an [e] between two [a]s. The last vowel is [a].
  • category - This word is not in a category with "catastrophe" even if it sounds like it: the middle letter is [e].
  • cemetery - Don't let this one bury you: it ends on -ery nary an -ary in it. You already know it starts on [c], of course.
  • changeable - The verb "change" keeps its [e] here to indicate that the [g] is soft, not hard. (That is also why "judgement" is the correct spelling of this word, no matter what anyone says.)
  • collectible - Another -ible word. You just have to remember.
  • column - Silent final [e] is commonplace in English but a silent final [n] is not uncommon, especially after [m].
  • committed - If you are committed to correct spelling, you will remember that this word doubles its final [t] from "commit" to "committed."
  • conscience - Don't let misspelling this word weigh on your conscience: [ch] spelled "sc" is unusual but legitimate.
  • conscientious - Work on your spelling conscientiously and remember this word with [ch] spelled two different ways: "sc" and "ti." English spelling!
  • conscious - Try to be conscious of the "sc" [ch] sound and all the vowels in this word's ending and i-o-u a note of congratulations.
  • consensus - The census does not require a consensus, since they are not related.


  • daiquiri - Don't make yourself another daiquiri until you learn how to spell this funny word-the name of a Cuban village.
  • definite (ly) - This word definitely sounds as though it ends only on -it, but it carries a silent "e" everywhere it goes.
  • discipline - A little discipline, spelled with the [s] and the [c] will get you to the correct spelling of this one.
  • drunkenness - You would be surprised how many sober people omit one of the [n]s in this one.
  • dumbbell - Even smart people forget one of the [b]s in this one. (So be careful who you call one when you write.)


  • embarrass (ment) - This one won't embarrass you if you remember it is large enough for a double [r] AND a double [s].
  • equipment - This word is misspelled "equiptment" 22,932 times on the web right now.
  • exhilarate - Remembering that [h] when you spell this word will lift your spirits and if you remember both [a]s, it will be exhilarating!
  • exceed - Remember that this one is -ceed, not -cede. (To exceed all expectations, master the spellings of this word, "precede" and "supersede" below.)
  • existence - No word like this one spelled with an [a] is in existence. This word is a menage a quatre of one [i] with three [e]s.
  • experience - Don't experience the same problem many have with "existence" above in this word: -ence!


  • fiery - The silent "e" on "fire" is also cowardly: it retreats inside the word rather than face the suffix -y.
  • foreign - Here is one of several words that violate the i-before-e rule. (See "believe" above.)


  • gauge - You must learn to gauge the positioning of the [a] and [u] in this word. Remember, they are in alphabetical order (though not the [e]).
  • grateful - You should be grateful to know that keeping "great" out of "grateful" is great.
  • guarantee - I guarantee you that this word is not spelled like "warranty" even though they are synonyms.


  • harass - This word is too small for two double letters but don't let it harass you, just keep the [r]s down to one.
  • height - English reaches the height (not heighth!) of absurdity when it spells "height" and "width" so differently.
  • hierarchy - The i-before-e rule works here, so what is the problem?
  • humorous - Humor us and spell this word "humorous": the [r] is so weak, it needs an [o] on both sides to hold it up.


  • ignorance - Don't show your ignorance by spelling this word -ence!
  • immediate - The immediate thing to remember is that this word has a prefix, in- "not" which becomes [m] before [m] (or [b] or [p]). "Not mediate" means direct which is why "immediately" means "directly."
  • independent - Please be independent but not in your spelling of this word. It ends on -ent.
  • indispensable - Knowing that this word ends on -able is indispensable to good writing.
  • inoculate - This one sounds like a shot in the eye. One [n] the eye is enough.
  • intelligence - Using two [l]s in this word and ending it on -ence rather than -ance are marks of . . . you guessed it.
  • its/it's - The apostrophe marks a contraction of "it is." Something that belongs to it is "its."


  • jewelry - Sure, sure, it is made by a jeweler but the last [e] in this case flees the scene like a jewel thief. However, if you prefer British spelling, remember to double the [l]: "jeweller," "jewellery." (See also pronunciation.)
  • judgment - Traditionally, the word has been spelled judgment in all forms of the English language. However, the spelling judgement (with e added) largely replaced judgment in the United Kingdom in a non-legal context. In the context of the law, however, judgment is preferred. This spelling change contrasts with other similar spelling changes made in American English, which were rejected in the UK. In the US at least, judgment is still preferred and judgement is considered incorrect by many American style guides.


  • kernel (colonel) - There is more than a kernel of truth in the claim that all the vowels in this word are [e]s. So why is the military rank (colonel) pronounced identically? English spelling can be chaotic.


  • leisure - Yet another violator of the i-before-e rule. You can be sure of the spelling of the last syllable but not of the pronunciation.
  • liaison - Another French word throwing us an orthographical curve: a spare [i], just in case. That's an [s], too, that sounds like a [z].
  • library - It may be as enjoyable as a berry patch but that isn't the way it is spelled. That first [r] should be pronounced, too.
  • license - Where does English get the license to use both its letters for the sound [s] in one word?
  • lightning - Learning how to omit the [e] in this word should lighten the load of English orthography a little bit.


  • maintenance - The main tenants of this word are "main" and "tenance" even though it comes from the verb "maintain." English orthography at its most spiteful.
  • maneuver - Man, the price you pay for borrowing from French is high. This one goes back to French main + oeuvre "hand-work," a spelling better retained in the British spelling, "manoeuvre."
  • medieval - The medieval orthography of English even lays traps for you: everything about the MIDdle Ages is MEDieval or, as the British would write, mediaeval.
  • memento - Why would something to remind of you of a moment be spelled "memento?" Well, it is.
  • millennium - Here is another big word, large enough to hold two double consonants, double [l] and double [n].
  • miniature - Since that [a] is seldom pronounced, it is seldom included in the spelling. This one is a "mini ature;" remember that.
  • minuscule - Since something minuscule is smaller than a miniature, shouldn't they be spelled similarly? Less than cool, or "minus cule."
  • mischievous - This mischievous word holds two traps: [i] before [e] and [o] before [u]. Four of the five vowels in English reside here.
  • misspell - What is more embarrassing than to misspell the name of the problem? Just remember that it is mis + spell and that will spell you the worry about spelling "misspell."


  • neighbor - The word "neighbor" invokes the silent "gh" as well as "ei" sounded as "a" rule. This is fraught with error potential. If you use British spelling, it will cost you another [u]: "neighbour."
  • noticeable - The [e] is noticeably retained in this word to indicate the [c] is "soft," pronounced like [s]. Without the [e], it would be pronounced "hard," like [k], as in "applicable."


  • occasionally - Writers occasionally tire of doubling so many consonants and omit one, usually one of the [l]s. Don't you ever do it.
  • occurrence - Remember not only the occurrence of double double consonants in this word, but that the suffix is -ence, not -ance. No reason, just the English language keeping us on our toes.


  • pastime - Since a pastime is something you do to pass the time, you would expect a double [s] here. Well, there is only one. The second [s] was slipped through the cracks in English orthography long ago.
  • perseverance - All it takes is perseverance and you, too, can be a near-perfect speller. The suffix is -ance for no reason at all.
  • personnel - Funny Story: The assistant Vice-President of Personnel notices that his superior, the VP himself, upon arriving at his desk in the morning opens a small, locked box, smiles, and locks it back again. Some years later when he advanced to that position (inheriting the key), he came to work early one morning to be assured of privacy. Expectantly, he opened the box. In it was a single piece of paper which said: "Two Ns, one L."
  • playwright - Those who play right are right-players, not playwrights. Well, since they write plays, they should be "play-writes," wright right? Rong Wrong. Remember that a play writer in Old English was called a "play worker" and "wright" is from an old form of "work" (wrought iron, etc.)
  • possession - Possession possesses more [s]s than a snake.
  • precede - What follows, succeeds, so what goes before should, what? No, no, no, you are using logic. Nothing confuses English spelling more than common sense. "Succeed" but "precede." Precede combines the Latin words "pre" and "cedere" which means to go before.
  • principal/principle - The spelling principle to remember here is that the school principal is a prince and a pal (despite appearances)--and the same applies to anything of foremost importance, such as a principal principle. A "principle" is a rule. (Thank you, Meghan Cope, for help on this one.)
  • privilege - According to the pronunciation (not "pronounciation"!) of this word, that middle vowel could be anything. Remember: two [i]s + two [e]s in that order.
  • pronunciation - Nouns often differ from the verbs they are derived from. This is one of those. In this case, the pronunciation is different, too, an important clue.
  • publicly - Let me publicly declare the rule (again): if the adverb comes from an adjective ending on -al, you include that ending in the adverb; if not, as here, you don't.


  • questionnaire - The French doing it to us again. Double up on the [n]s in this word and don't forget the silent [e]. Maybe someday we will spell it the English way.


  • receive/receipt - I hope you have received the message by now: [i] before [e] except after . . . .
  • recommend - I would recommend you think of this word as the equivalent of commending all over again: re+commend. That would be recommendable.
  • referred - Final consonants are often doubled before suffixes (remit: remitted, remitting). However, this rule applies only to accented syllables ending on [l] and [r], e.g. "rebelled," "referred" but "traveled," "buffered" and not containing a diphthong, e.g. "prevailed," "coiled."
  • reference - Refer to the last mentioned word and also remember to add -ence to the end for the noun.
  • relevant - The relevant factor here is that the word is not "revelant," "revelent," or even "relevent." [l] before [v] and the suffix -ant.
  • restaurant - 'Ey, you! Remember, these two words when you spell "restaurant." They are in the middle of it.
  • rhyme - Actually, "rime" was the correct spelling until 1650. After that, egg-heads began spelling it like "rhythm." Why? No rhyme nor reason other than to make it look like "rhythm."
  • rhythm - This one was borrowed from Greek (and conveniently never returned) so it is spelled the way we spell words borrowed from Greek and conveniently never returned.


  • schedule - If perfecting your spelling is on your schedule, remember the [sk] is spelled as in "school." (If you use British or Canadian pronunciation, why do you pronounce this word [shedyul] but "school," [skul]? That has always puzzled me.)
  • separate - How do you separate the [e]s from the [a]s in this word? Simple: the [e]s surround the [a]s.
  • sergeant - The [a] needed in both syllables of this word has been pushed to the back of the line. Remember that, and the fact that [e] is used in both syllables, and you can write your sergeant without fear of misspelling his rank.
  • supersede - This word supersedes all others in perversity. This is the only English word based on this stem spelled -sede. Supersede combines the Latin words "super" and "sedere" which means to sit above.


  • their/they're/there - They're all pronounced the same but spelled differently. Possessive is "their" and the contraction of "they are" is "they're." Everywhere else, it is "there."
  • threshold - This one can push you over the threshold. It looks like a compound "thresh + hold" but it isn't. Two [h]s are enough.
  • twelfth - Even if you omit the [f] in your pronunciation of this word (which you shouldn't do), it is retained in the spelling.
  • tyranny - If you are still resisting the tyranny of English orthography at this point, you must face the problem of [y] inside this word, where it shouldn't be. The guy is a "tyrant" and his problem is "tyranny." (Don't forget to double up on the [n]s, too.)


  • until - I will never stop harping on this until this word is spelled with an extra [l] for the last time!


  • vacuum - If your head is not a vacuum, remember that the silent [e] on this one married the [u] and joined him inside the word where they are living happily ever since. Well, the evidence is suggestive but not conclusive. Anyway, spell this word with two [u]s and not like "volume."


  • weather - Whether you like the weather or not, you have to write the [a] after the [e] when you spell it.
  • weird - It is weird having to repeat this rule so many times: [i] before [e] except after...? (It isn't [w]!)
Answers to last post:

By the way, if you need an automatic full factorial calculator just click *HERE*. I never leave the house without mine. It beats trying to figure out 123! either in my head (which is rather full) or on the back of all of my wife's best linen table napkins with my Bic.

Here's one for You:

If I own fourteen suits, and I wear two different suits during any given week, how many different combinations of suits will I be able to wear?  

182 possible combinations of suits weekly times 52 weeks in the year (based upon our shortcut formula) = 9,464 total combinations!

Here's another for You, with a slight twist:

If I publish 50 different blogs, and I reference all of the other blogs on each one of the blogs, how many total links will I have to any one given blog on each of the others, (inclusive of that blog itself)? Hmmm? And how many links will I have which link one blog to another?  

This one's a bit tricky... since you must eliminate any instance where a blog has a link to itself. Each of the 50 blogs will have links to the other 49, so the answer would be 50 multiplied by 49, or 2,450 total links.

Those are the answers.

Douglas E. Castle for The Braintenance Blog

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Saturday, August 4, 2012

Exploring Exponential Expansion: Combinations!

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I am fascinated, as are most people, at rates of expansion, growth and change. Albert Einstein once said (in a Swiss accent whilst tripping over an untied shoelace) that "the most powerful force in the universe is the compounding of interest."

The idea of arithmetic, geometric, exponential and logarithmic expansion, looked at singly or comparatively, give us accessible, understandable metrics about how much things change as a result of the rate or power of growth. Everyone has an interest in these things...from the little tike saving up his meager allowance for his first WonkaBar lottery ticket purchase, to the epidemiologists (mostly the ones in the shows on late night television anyway) who must estimate the potential for a virus or other threatening bio hazard to spread, the the idiot from some fourth-world nation who sends out a chain letter to a whole group of people saying to each of them that if he or she sends the letter to an additional seven people enclosing one [insert any imaginary unit of currency], he or she will become a billionaire [i.e., that he or she will receive one billion units of the imaginary units of currency] within seven weeks - or, alternatively, that if he or she (poor recipient) fails to  do as instructed (gasp!!!), that he or she will be visited by the angel of halitosis and be breathed upon until his or her skin is covered with festering boils...or worse.

One area worth exploring for all those of you involved in business and networking, or search engine optimization and link-building, is that of combinatorial analysis. This is the process through which we answer the question "How many combinations of r objects each are possible out of a total group of n objects.

The formula used to solve this type of problem is:

where n is the number of things to choose from, and you choose r of them
(No repetition, order matters)

As a practical, yet tepid and unimaginative example, let us assume that We are invited to a business power breakfast at the local Olympia Diner. If there are ten invitees in total, and each person shakes hands once with every other person at the end of the meeting (without anyone  leaving a tip for Rayette, the waitress with a prominent mole who calls everybody "hon' "), how many handshakes will there be in all?

This question, restated without the cynical editorial commentary, is simply, "How many combinations of 2 are possible out of a group of 10, in total?"

Using the above formula, we take 10!, and divide it by (10! - 2!), simplify it to 10! divided by 8!, further simplify to 10 x 9, and we obtain an answer of 90 possible handshakes.

By the way, if you need an automatic full factorial calculator just click *HERE*. I never leave the house without mine. It beats trying to figure out 123! either in my head (which is rather full) or on the back of all of my wife's best linen table napkins with my Bic.

Here's one for You:

If I own fourteen suits, and I wear two different suits during any given week, how many different combinations of suits will I be able to wear?

Here's another for You, with a slight twist:

If I publish 50 different blogs, and I reference all of the other blogs on each one of the blogs, how many total links will I have to any one given blog on each of the others, (inclusive of that blog itself)? Hmmm? And how many links will I have which link one blog to another?

Stay tuned for the answers.

Douglas E. Castle for The Braintenance Blog

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Douglas E Castle
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