Why Improbable Things Really Aren't 166
First time accepted submitter sixoh1 writes "Scientific American has an excellent summary of a new book 'The Improbabilty Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day' by David J. Hand. The summary offers a quick way to relate statistical math (something that's really hard to intuit) to our daily experiences with unlikely events. The simple equations here make it easier to understand that improbable things really are not so improbable, which Hand call the 'Improbability Principle:' 'How can a huge number of opportunities occur without people realizing they are there? The law of combinations, a related strand of the Improbability Principle, points the way. It says: the number of combinations of interacting elements increases exponentially with the number of elements. The 'birthday problem' is a well-known example. Now if only we could harness this to make an infinite improbability drive!"
remember (Score:2)
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Mr Hands?
(don't google...your brain will never forgive you)
Improbability drive (Score:4, Funny)
How improbable is the Heart of Gold?
And Zaphod stealing it...
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Obviously Zaphod successfully stealing such a thing was phenomenally improbable... and thus became inevitable as soon as they revved up the first drive prototype.
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Re: The day before Fukashima happened (Score:5, Interesting)
The day before Fukashima happened I was writing a paper for an Industrial Safety class on the subject of Nuclear safety. My conclusion essentially made the argument that "Although individual improbable events are unlikely, the shear number of opportunities to experience an improbable event on a day to day basis are staggering." Any specific improbable event is highly unlikely to occur, but the occurrence of improbable events in general is a practical certainty.
The next day I saw on the news that mother nature had done her best to prove my point. The timing worked out to be an incredibly unlikely coincidence, but on a daily basis I rarely notice when unlikely coincidences fail to occur. :)
Re: The day before Fukashima happened (Score:5, Insightful)
There are well defined techniques for measuring the probability of events happening in industrial safety. Safety Integrity Levels or SIL are used to categorize the possibility of a life threatening event occurring.
The problem is how low a risk do you need and how much will it cost you to get there. Fukashima would probably not have happened if the sea wall had been higher, but the designers had to make the judgement that it was not worth the millions of cost required to build a bigger wall compared to risk of it being breached. Unfortunately decisions like that in hindsight always look flawed.,
Re: The day before Fukashima happened (Score:5, Funny)
They didn't need higher sea wall. A wall can permanently hold water away and that is overdoing. What they needed to do was to make a watertight, anchored to the ground building for auxiliary generators and connect them to main building by undersea power cables. Basically, build a submarine on land, complete with snorkel. When there is a water surge, it holds generators safe and dry so that they function after the water recedes.
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If they had put the generators behind (uphill) the main building AND put the generators in a water RESISTANT building, all would have been fine. If they had installed the hydrogen traps most of the problems (the earth shattering kaboom) would have been avoided. If they had followed their engineers advice and dumped sea water on the core, most of the bad problems would have been avoided.
All of those improbable problems would probably have been mitigated if TEPCO had competent upper management. Now, how li
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When the core is "shut-down" to prevent accidental thermal runaway (aka meltdown, or "china-syndrome") the system still contains a rather significant amount of heat for quite a while due to the secondary radioactive products, but this heat is not nearly enough to drive the normal steam turbine dynamos which generate the utility load - it takes a rather large amount of torque to generate megawatts of electric current. Until the heat is removed and the reactor core, fuel rods, and associated secondary decay r
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"Not quite true."
Neither of those is quite true.
The test involved intentionally shutting down some of the safety systems. But when another power plant shut down, calling for more electricity from Chernobyl, the planned shutdown was postponed.
When the test was postponed, the Emergency Core Cooling System remained turned off (though that did not turn out to be a major factor in the eventual accident).
The whole thing is a long story, but in brief, it was a long chain of accumulated human error that caused the accident
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Really, Chernobyl all boiled down to human error. Not just one or two errors, but a whole string of errors, while simultaneously some of the automatic safety systems were turned off.
While I'm here, though, I want to mention that OP got it very wrong. The book isn't about why improbable things aren't really improbable. It's about why they ARE improbable, but happen anyway. Not the same thing.
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From human perception, there is no difference between these statements, and that's the problem addressed. The fact that something is statistically likely to "someone" (i.e.: not you) does not make something "probable" for you, which is included in the SA summary of the book.
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"From human perception, there is no difference between these statements, and that's the problem addressed."
From a mathematics perspective, there is a world of difference. One is correct; the other is not.
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When I first got into safety engineering I always imagined myself explaining the concept of a SIL level or the ALARP principle to a grieving widow. On an academic level I know exactly why it makes sense and that it's the best thing overall but it took a while to get rid of that feeling in my gut that it wasn't right.
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Are there any well defined techniques for determining how may possibly fatal low probability events are extant? I doubt it. You may be able to say "Of the things we've considered, there are these things which each have this probability", but you can't calculate the things you haven't considered...which is most of the universe. Granted the liklihood of being stomped on by Godzilla is too low to consider, there are lots of things "metaphorically similar to Godzilla" that are more probable.
(I'm saying Godzi
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Just a bit of a nitpick. Mother nature did not "prove your point". Statistics infer data for a population from a sample. A single event from that sample does not prove or disprove anything about the population, nor the sample. Had there not been an event at Fukushima that day, your statement would not have been any more true or false, or any less proven. Your point is proven with statistical significance tests on the sample, not by taking one event and saying "here's proof". That's the opposite of statistic
The probabilities of multiple cot deaths (Score:5, Interesting)
Another example is in the curious case of Professor Meadows [wikipedia.org] - a great paediatrician but a shite mathematician.
He endorsed the dictum that “one sudden infant death is a tragedy, two is suspicious and three is murder, until proved otherwise“. The trouble is, given enough numbers, multiple cot deaths are an inevitability.
Unfortunately, his expert testimony convicted an innocent woman. Fortunately, she was released on appeal when the math was reviewed.
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However, when you flip a coin every second for ten thousand years,you get different results. The million monkeys typing a million years to produce Shakespeare is a perfect example of how multiplying probability by time is like dividing integers by zero. Things get funky.
If the Fukushima risk analysis looks at one event per day versus one event per hour or on
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42 (Score:5, Insightful)
My theory of the question for life, the universe, and everything.
The books rely heavily on probability (even as far as powering the faster than light engine as alluded in the summary).
A pair of dice is one of, of not the most common symbol for probability, chance, and luck (at least in Anglo-American culture). And how many pips are on a pair of dice?
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Nice catch! That's *got* to have been intentional. It's way too improbable... to be... coincidence...
Damn. I think there's a flaw in my illogic somewhere.
Seems legit (Score:5, Funny)
I found it highly improbable that an article on that topic could be boring. It explained to me in laborious detail why I was wrong.
A million to one (Score:2)
Did someone else notice that if the chances for something to happen are exactly a million to one, there is a 1 to ten chance that it actually happens?
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just explaining it to the jr programmers never seems to be enough. they never really appreciate it until they actually screw something up.
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Did someone else notice that if the chances for something to happen are exactly a million to one, there is a 1 to ten chance that it actually happens?
Million-to-one chances work nine times out of ten.
Re: A million to one (Score:2)
I stand corrected.
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But still they come
OOOHHH LAH
Summary. (Score:4, Insightful)
Why? Because there are 7 billion people on Earth.
This is why TV news is toxic (Score:2)
Having every horror happening, nationwide, shoved down your throat 24X7 is equivalent to poisoning yourself.
Lottery scratch tickets; not so random (Score:5, Interesting)
Very interesting article on it http://www.lotterypost.com/new... [lotterypost.com] been a long time since I've read it (bookmark), but this guy can tell which scratch tickets will pay off by by reading their serial numbers, winning wasn't as improbable as one is led to believe - and yes, of course he's a statistician.
I don't play the lottery, maybe a ticket twice a year, but my son likes the scratch tickets, I told him that they were predictable, he refused to listen; he wouldn't even pick up the link I printed out. He refused to imagine that it wasn't anything but random. It was just an odd reaction, I can't begin to explain the reasoning behind it.
The link is old so I imagine the serial number gig has been fixed (yet I have no clue one way or the other), but supports the improbability disclaimer.
Re:Lottery scratch tickets; not so random (Score:4, Interesting)
The link is old so I imagine the serial number gig has been fixed (yet I have no clue one way or the other), but supports the improbability disclaimer.
While this may be interesting to some, it has very little to do with TFA.
TFA is arguing that random events are often more probable than we might think, because we often fail to take the context of an event into account.
Most of the scenarios in TFA are variations on the "birthday paradox," which basically amounts to people looking at an event X with a very tiny probability P in a specific case, and assuming that P is the probability it would happen. But we often forget that there are Q number of combinations or situations that would all result in X being true... so P is a gross underesimate of the probability of X.
Your link deals with a poorly designed computer algorithm that actually isn't random which is spitting out lottery tickets. The scratch-ticket system has to make money, so the numbers can't be entirely random -- they must only payout so many tickets within a given batch. The guys who designed the computer system that chooses the numbers didn't take into account that there were statistical clues that could allow someone to "crack the code" to the fake randomness.
There are two completely different phenomena. Finding a flaw in pseudo-randomness is completely different from miscalculating odds of genuinely random events.
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The link is old so I imagine the serial number gig has been fixed (yet I have no clue one way or the other), but supports the improbability disclaimer.
While this may be interesting to some, it has very little to do with TFA.
TFA is arguing that random events are often more probable than we might think, because we often fail to take the context of an event into account.
Most of the scenarios in TFA are variations on the "birthday paradox," which basically amounts to people looking at an event X with a very tiny probability P in a specific case, and assuming that P is the probability it would happen. But we often forget that there are Q number of combinations or situations that would all result in X being true... so P is a gross underesimate of the probability of X.
Your link deals with a poorly designed computer algorithm that actually isn't random which is spitting out lottery tickets. The scratch-ticket system has to make money, so the numbers can't be entirely random -- they must only payout so many tickets within a given batch. The guys who designed the computer system that chooses the numbers didn't take into account that there were statistical clues that could allow someone to "crack the code" to the fake randomness.
There are two completely different phenomena. Finding a flaw in pseudo-randomness is completely different from miscalculating odds of genuinely random events.
Accepted.
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As far as the old article is concerned, the problem was that the Lottery commission, in order to maintain sales, interfered with the actual randomization. Every pack of 1,000 tickets sent to a store has so many $2, $5, and $20 winners. A clerk at the store paying attention would open a new pack of a thousand tickets and keep track of the winners. If there were fewer than expected, then it actually made sense to buy the last 150 tickets of the pack (using friends and accomplices)
Nope. While this may be another way to hack some lottery tickets, this is not what happened in the GP's link scenario. You can read more of the details about the statistician who publicized the problem here [wired.com].
Basically, on the tickets in question, there were a lot of exposed numbers on the tickets that were visible before you bought the ticket. There were a few hidden numbers that you scratched off after you bought the ticket and tried to match to the ones that were already visible.
The problem was that
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but this guy can tell which scratch tickets will pay off by by reading their serial numbers, winning wasn't as improbable as one is led to believe
CSB:
My elementary school set up a sort of lottery during a yearly festival.
So two classes were tasked with preparing the winning and losing lots for the lottery by writing the kind of price or something like "no win" on little paper squares.
They then folded the paper squares and stapled them shut so you couldn't tell what was written inside.
During the festivities the kids ran a stand were you could buy and draw the lots from a couple of big, open bowls.
Almost all of the prices went to a handful o
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but this guy can tell which scratch tickets will pay off by by reading their serial numbers, winning wasn't as improbable as one is led to believe
CSB:
Well, the winning and losing lots had been prepared separately and, not thinking about it and lacking the direct comparison, the teachers in charge of the two groups had been unaware that their staplers were loaded with silver- and copper-colored staples respectively.
So by looking at the color of the staples, you were able to pick only winners out of the open bowls.
That required one to look at the paper squares, I can go one better.
A new computer store had a drawing for an Osborn, I put in a slip in hopes of a win (duh).
I had high hopes so showed up for the drawing. A family was there just looking; they asked the teen daughter if she would pick out a slip. Surprised and fairly embarrassed she reached in and pulled out a wad of paper and the winner.
Since that day I've crumple up any drawing entry to make it larger and more accessible.
At a elementary school event they h
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Yeah, well, we run raffle/lotteries several times a month. The wadded-up mumbles of paper are *not* the ones that get pulled out when we're fishing for winners. Just sayin'.
Nor are the illegible scribbles even considered as possible winners. "Penmanship, people! PENMANSHIP!" If I can't read your winning name, then you ARE NOT the winner.
This is especially funny because our market is elementary school teachers. Yes: the ones who should be teaching children how to write legibly.
Yeah, right...
Roll a dice... (Score:2)
Roll a dice. Each of the outcomes only has a probability of 16.p6 % (assuming a fair d6), which is fairly unlikely. Yet, there's a 100 % probability that you will obtain one of these unlikely results.
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Roll a dice
Die. Dice is plural. Dice.com sucks. Die, Dice, Die! Wait, what were we talking about?
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As far as I can remember: the 'correct' singular of 'dice' is 'dix'!
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Roll a dice. Each of the outcomes only has a probability of 16.p6 % (assuming a fair d6), which is fairly unlikely. Yet, there's a 100 % probability that you will obtain one of these unlikely results.
unless one die rolls into a crack or becomes a leaner against the table or rolls under the refrigerator in which case there is a result but it's more along the lines of Schrodinger's cat or Christ could come back to earth and take up your friends in rapture along with the dice and leave you hanging or the universe could explode. I'd give it five 9s instead. 99.999%
Oblig XKCD (Score:3, Interesting)
http://xkcd.com/1331/ [xkcd.com]
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Same information, but the visual aspect of the animated GIF is somehow much more accessible. One more data point on how the human brain is so poorly adapted to statistical inference as compared to our natural abilities with visual information like "is that tiger going to eat me", or "can I make it across the gap between this tree and that tree when I jump".
People round down (Score:4, Insightful)
Often when the probability of an event gets close to 1-in-100 people just say "impossible", i.e. they round down to zero.
They also forget that one can increase the chances of the event happening by repeating the trial. E.g. funding a 1-in-100 chances of blow-out-success company sounds like a risky bet, but if you fund 100 such companies, it is a rather safe bet. Hence VCs.
This is a counter-intuitive situation in which increasing the occurrences of the risky behaviour makes the whole situation safer. (Contrast this with Russian roulette in which increased trials is definitely a bad thing).
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The way I like to summarize it when talking to non-technical types is this: The odds of any one ticket winning the lottery jackpot are astronomically small. Regardless, people win the jackpot quite regularly.
Low probability per trial × many trials = reasonable probability of occurrence overall.
Rounding small probabilities down doesn't fully explain all the ways folks get tripped up thinking about probabilities. For example, the Birthday Paradox doesn't fit that model directly, because it's counter-
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I explain this by saying I've won $20 twice in the lottery without ever entering.
Once I received a lottery ticket from a Realtor (a somewhat standard marketing technique) and I've gotten them as prizes at work contests. I've never bought a lottery ticket because my chances of winning don't actually change.
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I still want to know how to ... (Score:2)
generate a small amounts of finite improbability .... to break the ice at parties by making all the molecules in the hostess's undergarments leap simultaneously one foot to the left, in accordance with the Theory of Indeterminacy.
As the Venerable Terry Pratchett says: (Score:2)
This article would have been more useful if it (Score:5, Insightful)
applied to debunking so-called "Intelligent Design". There are a few high profile proponents who claim that the probability of an organism as complex as humans evolving from single celled ancestors is so small as to be impossible, therefore we must have been "designed" by "someone" (a variation on the God of the gaps principle used by others for the same purpose). They like to point out eyes as organs that are so complex they could not have evolved, even though we have numerous living organisms that have organisms with photosensitive sensitive organs that aren't quite eyes, perhaps on their way to becoming eyes, many generations/mutations down the road.
In a single field of view under a microscope I can see tens of thousands of bacteria swimming around in a drop of water. Multiple that by all the drops of water in the world and you quickly realize that the number of living organisms is a HUGE number. With all that genetic replication (with errors that sometimes result) and gene swapping going on, and all the DNA floating around freely in the waters of the world, it seems inevitable that there will be enough mutations taking place to produce the variety of life we see on earth.
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I think ultimately someone made a page demonstrating how to find Shakespeare using the same technique. Or maybe finding the same messages in the works of Shakespeare.
Well, the classic debunking occurred by finding similar patterns in Moby Dick, but there were also things found in War and Peace (particularly the Hebrew translation!), as you can read about here [anu.edu.au].
This has always been my answer to the "Strong Anthropic Principle" which claims that some agency must have tuned the universe to be able to support conscious life. Since no one knows how many repetitions exist, the SAP has no legs to stand on.
While I think SAP is a bogus argument, your rebuttal also makes little sense.
(1) It doesn't matter "how many repetitions exist" -- it only matters what the odds are, and whether that seems a reasonable way to evaluate the nature of the universe. I can draw a 1 in 1,000,000 poker hand the first time I ever play c
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It doesn't matter "how many repetitions exist" -- it only matters what the odds are
Incorrect, this was the point of the article. If the odds are one in a billion, but you have a billion repetitions of the event, the odds of a hit are much higher than one in a billion. I agree there is little reason to lend credence to any given estimate of how likely or unlikely a human-friendly universe is. My point was that, even if you had a good measure of the odds, saying "the odds of a human friendly universe are a trillion to one against" is not illuminating since you do not know how many universes
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Incorrect, this was the point of the article. If the odds are one in a billion, but you have a billion repetitions of the event, the odds of a hit are much higher than one in a billion.
Actually, no -- that was NOT the point of the article. The article mentions the law of large numbers at the beginning, but the rest of the article is not simply about many chances at an event = higher probability.
Instead, the article is about variations on birthday paradox, that is, if I attend a small party and find that someone has the same birthday as I do, everyone at the party is often surprised. Your response is that if I attend hundreds of parties or if there are hundreds of guests at the party,
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One last thing: I know that speculative physics (particularly string theory) is actively involved in trying to imagine stuff outside of our universe -- other dimensions, brane theory, etc. Some of these models have been created to try to explain problems in the way physics seems to work in our universe.
Once we have some actual emprical evidence of some sort of interaction from outside the universe that actually gives some merit to these speculative mathematical theories, I'll be the first one to step up
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Which makes me think of Stairway to Heaven; I checked, the Jesus freaks were right. But there's no way possible that anyone could have done that on purpose. It's clearly just a wild coincidence.
I remind the Jesus freaks that a prayer said backwards is a prayer to Satan, so that song is in fact a Christian song.
Ever hear Helter Skelter backwards? It changes to "I like smack" (and, well, that one may have been deliberate).
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it seems inevitable that there will be enough mutations taking place to produce the variety of life we see on earth.
Hold on a sec. Just because we might significantly underestimate the probability of something is NOT evidence that it is "inevitable" (or even highly likely).
Note that I'm on the side of evolution here. And I think the "intelligent design" movement is largely a smokescreen to get religious teachings back into schools.
But we still have to be careful about skewing our perceptions of odds the opposite way. If we don't EVER accept the possibility of design, then we must assume that a pocketwatch found bu
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http://www.youtube.com/watch?v... [youtube.com]
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The arguments that the proponents of 'Intelligent Design' use to attempt to discredit Evolution, are far more effective at showing the absurdity of a 'Creator'!
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Then why are there no unicorns?
Because Noah couldn't get them on board. They were out in the rain playing silly games.
The Unicorn by Tom Lehrer
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What do you mean by evolve?
Been trying to make this (Score:2)
This is a point I bring up occasionally in regards to the so called "war on terror". The thing is these highly rare events, on average, don't happen. Your chances of ever encountering an attack is nearly nil. However, given long enough time spans, and large enough areas, they do happen with occasional frequency.
That is the thing, you can expect anything that could happen is going to happen occasionally given a large enough population that it could happen in and a long enough time for it to happen.
So if you
winning the lottery twice (Score:2)
The fact that people win big lotteries twice in a lifetime (sans any fraud) still blows my mind. If that can happen, just about anything can.
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Imagine how the experience of winning the lottery messes with your sense of how likely it is that you'll win the lottery. Especially given that you probably had a bad sense of that in first place, since you were a person who played the lottery.
There already is a word for this.... (Score:2)
It's called 'probability'. Yes people don't understand it well, but inventing new terminology isn't the answer.
It was a million-to-one shot (Score:2)
But everyone knows that million-to-one shots occur nine times out of ten.
You didn't need to go throught all this trouble . (Score:2)
Simple. I'll make some Tea. (Score:2)
Now if only we could harness this to make an infinite improbability drive!
From HHGTTG, quoting from here: Infinite Improbability Drive [wikia.com]:
The principle of generating small amounts of finite improbability by simply hooking the logic circuits of a Bambleweeny 57 Sub-Meson Brain to an atomic vector plotter suspended in a strong Brownian Motion producer (say a nice hot cup of tea) were of course well understood
If ... such a [infinite improbability] machine is a virtual impossibility, it must have finite improbability. So all [one has] to do in order to make one is to work out how exactly improbable it is, feed that figure into the finite improbability generator, give it a fresh cup of really hot tea... and turn it on!
Remember (Score:2)
" magicians have calculated that million-to-one chances crop up nine times out of ten."
Terry Pratchett
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Intuit has been in use as a verb for more than two hundred years. Your personal shortcomings do not and should not dictate what is acceptable in a Slashdot summary unless you happen to be the one writing said summary.
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Neoteric verbiage doth incrassate.
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I still don't know what the relationship is between Quicken (the accounting software) and Quicken Loans
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Simple: the former will tell you how much money in interest you've given to the latter. It'll even put it into a nice pretty graph for you.
Oh, a business relationship? Yeah, I'm not seeing that either.
Re:Law of large numbers (Score:4, Informative)
Re:Law of large numbers (Score:4, Funny)
Law of truly large numbers [wikipedia.org] is the applicable law here, but the mistake is understandable.
In fact fairly probable
Re:Mort (Score:5, Insightful)
Firstly, Pratchett's comment has nothing to do with a paradox something of the sort. It's a simple claim that scientists are bad at estimating very small probabilities, and typically get them wrong by a factor of hundreds of thousands. This is actually true and rather insightful in a the-emperor-has-no-clothes kind of way, and also not very deep at all.
The concept of the long tail is somewhat more interesting, but not that deep either. It's merely about realizing that many processes aren't Gaussian, unlike what students are lead to believe in highschool and various introductory courses which are not primarily about statistics.
However, your distinction between likely and unlikely events is confused. If you are going to label two events as likely and unlikely, then you are asserting that the likely event is to be observed with higher probability than the unlikely event. This is always true by definition.
What you are trying to say is that, if you restrict yourself to a particular family of events and you compare the probability of occurrence of an unspecified member of the family with the probability of occurrence of a single specified member, then the former can be larger.
As an example, consider the family of events {the hour of your death is N}. It is fairly unlikely that I can predict the hour of your death (not being a serial killer myself), so if I specify the event {the hour of your death is 12am} then the probability of occurrence is small. But if I do not specify the event, by saying {the hour of your death is N, where N is some hour in the day}, then that event is certain. Of course I haven't said anything interesting *with certainty*, whereas in the case of 12am I have said something interesting *with low probability*.
The tragedy of statistics is that the great majority of things we know with high probability aren't interesting, and the majority of things that are interesting have low probabilities or cannot be estimated accurately.
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Consider gun ownership in the US
There is approximately one gun per person in the nation; however _most_ people, more than half, do not own a gun. This situation is modeled like most any other unequal one (but it also matches the atomic configuration of atoms during a phase change). Most folks don't own a gun. The next largest group is those
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Actually, many of his characters go on to say that in many of his books. It was a minor plot-point in Guards, Guards! for example, with the main characters concerned that nobody ever said, "Its practically a certainty, but it just might work," (or similar) and going to great lengths to get the odds just right.
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It's also the solution to a puzze at the end of the first Disworld adventure game.
You will have to gather a set of items (eye patch, tattoo (i think) and some other stuff) to make sure that your chances of winning a fight against a dragon is EXACTLY a million to one.
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Furthermore, in some books the million-to-one-chance even has an embodiment of sorts as "The Lady", one of the Discworld Gods http://en.wikipedia.org/wiki/D... [wikipedia.org]
But yeah, Pratchett was mostly poking fun at the heroes in stories alway succeeding against all odds.
Another Discworld example would be a group of people being hesitant to attack a single guy if the guy looks harmless and smiles or if he shows characteristics in line with being a story's hero - because everybody just knows ta a vastly outnumbered
Re:Duh (Score:5, Funny)
"Feynman discussed this ages ago. And I'm sure he did it better."
That's highly improbable.
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And yet it happened!
Honestly, I don't know, but this certainly isn't a new idea. I actually had arguments about this idea back in 2004, though I don't know how to look that far back in my post history. The reason I know it was in 2004, though, is because I have a couple of blog posts about it that are still live. It wasn't a new idea back then, either.
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Oh, well if you read about it then no one should never write about it again because clearly everyone know it.
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BUT, was his research for an IMPROBABILITY DRIVE?
Apparently the only real danger is from falling whales and flower pots.
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BUT, was his research for an IMPROBABILITY DRIVE? Apparently the only real danger is from falling whales and flower pots.
I find the idea of an infinite improbability drive to be very unlikely...
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I find the idea of an infinite improbability drive to be very unlikely...
But it's finitely unlikely. Perhaps there's a solution in there somewhere. Somebody get me a hot cup of tea.
Tea (Score:2)
I find the idea of an infinite improbability drive to be very unlikely...
But it's finitely unlikely. Perhaps there's a solution in there somewhere. Somebody get me a hot cup of tea.
IIRC, there was some cake in there too. Don't forget that.
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Summary of article: Consider improbable event X. Repeat event X numerous times (10s, hundreds, thousands etc). Suddenly, event X is quite probable.
You mean like a million monkeys typing for a million years will produce Shakespeare?
I just made that example up.
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No whining yet on the misspelling of "Improbabilty", which should be Improbability?
We're talking about improbable things. Not inevitable things. Remember, this IS Slashdot.
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Fulminate of Mercury hasn't been used as a priming compound in ages. Modern primers use lead styphnate, which is stable unless heated above 330 C, or hit with a sharp impact.
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"Whoosh!"
Yep in the parallel universe where the Germans bombed Pearl Harbour, they used jets...
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- The worst aspect of intelligence is being trapped by it
Being trapped by intelligence is the best aspect. ;-)
I think