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Why Improbable Things Really Aren't

Unknown Lamer posted about 8 months ago | from the learn-to-count dept.

Math 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!"

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Duh (-1)

Anonymous Coward | about 8 months ago | (#46274035)

Feynman discussed this ages ago. And I'm sure he did it better.
-did not rtfa

Re:Duh (5, Funny)

nospam007 (722110) | about 8 months ago | (#46274489)

"Feynman discussed this ages ago. And I'm sure he did it better."

That's highly improbable.

Re:Duh (1)

nine-times (778537) | about 8 months ago | (#46275209)

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.

Re:Duh (2)

flyneye (84093) | about 8 months ago | (#46274523)

BUT, was his research for an IMPROBABILITY DRIVE?
Apparently the only real danger is from falling whales and flower pots.

Re:Duh (1)

gnupun (752725) | about 8 months ago | (#46274707)

Summary of article: Consider improbable event X. Repeat event X numerous times (10s, hundreds, thousands etc). Suddenly, event X is quite probable.

Re:Duh (1)

minstrelmike (1602771) | about 8 months ago | (#46275419)

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.

Re:Duh (1)

gnupun (752725) | about 8 months ago | (#46275573)

Why not? It depends on the probability that one monkey typing for one year can produce Shakespeare.

Re:Duh (0)

Anonymous Coward | about 8 months ago | (#46275653)

No whining yet on the misspelling of "Improbabilty", which should be Improbability?

Re:Duh (0)

Anonymous Coward | about 8 months ago | (#46275761)

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.

Considering that the Earl of Oxford wrote the plays they would have as good a chance.

remember (1)

camg188 (932324) | about 8 months ago | (#46274037)

Mr. Hand

Re:remember (2)

mooterSkooter (1132489) | about 8 months ago | (#46274319)

Mr Hands?

(don't google...your brain will never forgive you)

Sounds unlikely (0)

Anonymous Coward | about 8 months ago | (#46274041)

Greatest improbability?

That there will be any sensible comments here.

Improbability drive (3, Funny)

rossdee (243626) | about 8 months ago | (#46274043)

How improbable is the Heart of Gold?

And Zaphod stealing it...

Re:Improbability drive (2)

Immerman (2627577) | about 8 months ago | (#46274187)

Obviously Zaphod successfully stealing such a thing was phenomenally improbable... and thus became inevitable as soon as they revved up the first drive prototype.

Re:Improbability drive (0)

Dunbal (464142) | about 8 months ago | (#46274299)

Bistromathics > Improbability, but you won't get it if all you did was see the shitty movie.

Re: The day before Fukashima happened (5, Interesting)

Anonymous Coward | about 8 months ago | (#46274055)

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 (5, Insightful)

gnalre (323830) | about 8 months ago | (#46274193)

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 (5, Funny)

Anonymous Coward | about 8 months ago | (#46274265)

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.

Re: The day before Fukashima happened (1)

tomhath (637240) | about 8 months ago | (#46274771)

Any type of working aux generator would have protected it. Although I think a better design would be to have one a few miles inland. That would provide better protection from other natural disasters, accidents, or intentional attacks.

Re: The day before Fukashima happened (0)

Anonymous Coward | about 8 months ago | (#46275023)

While having to waste a ton of money building km long pipes to get water to and from the sea and a ton of money to keep water flowing in these pipes... there's a reason these things are built by the sea/rivers. They need lots of water!

Re: The day before Fukashima happened (0)

Anonymous Coward | about 8 months ago | (#46275649)

yeah -- I think the generator inland would run on diesel or natural gas and have some stored on site. Then the power is sent to the nuclear plant's pumps by power cable. Those would need strength and flexibility in an event like this. But even if the power lines were severed, it would be much easier to repair the power lines than to install plumbing in a flooded aux generator area.

Re: The day before Fukashima happened (0)

Anonymous Coward | about 8 months ago | (#46275139)

How about just letting the generators power their own cooling system directly? Wasn't the Big Problem that the had to go to grid first because >reasons?

Re: The day before Fukashima happened (2)

sixoh1 (996418) | about 8 months ago | (#46275813)

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 radio-nucleotides reach a lower level, something needs to provide the power for the cooling pumps, and to ensure that the trapped hydrogen gas (byproduct of fission) is recycled and contained. There are various schemes to create "fail-proof" nuclear reactors, one of which happened to be the Chernobyl design (and we all know how well that one worked). It was supposedly "impossible!" for Cherynobyl to melt down because of the built-in systems, and the smart, but not smart-enough, engineers wanted to test those "fail-proof" systems...

Re: The day before Fukashima happened (0)

Anonymous Coward | about 8 months ago | (#46275841)

Yes, and they don't work if the event has never happened before due to out-of-sample error, which was the problem with Fukashima.

Re: The day before Fukashima happened (3, Insightful)

Anonymous Coward | about 8 months ago | (#46274429)

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 statistics.

I understand what you're saying but I think much more care and precision is needed when articulating issues of probability. The bar in most discussions is set so hopelessly low that the general population - the people who least understand statistics and are most in need of some help - end up with insane theories as to how and why things occur.

It makes any rational discussion about risk impossible. I'm sure we've all heard some anecdote along the lines of "They say smoking causes cancer, but I've got an Uncle who smoked his whole life and lived to 102! Those stupid scientists don't know anything!"

People who are in a position to help with understanding these concepts do not clearly articulate the correct ideas, whether unintentionally (as in this post) or maliciously (politicians). We as a society need to become better at this.

The probabilities of multiple cot deaths (5, Interesting)

ph1ll (587130) | about 8 months ago | (#46274495)

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.

Re: The day before Fukashima happened (0)

Anonymous Coward | about 8 months ago | (#46274519)

*sheer != shear
Good thing it wasn't English class.

Re: The day before Fukashima happened (-1)

Anonymous Coward | about 8 months ago | (#46275355)

Good thing you are an asshole, you passive-aggressive fuck.

years before Fukashima happened (1)

harvey the nerd (582806) | about 8 months ago | (#46274597)

Fukashima was a multifactorial accident waiting to happen. Never improbable. e.g. Low seawall height, aux power location, tie in location, dense packed stations.

Re: The day before Fukashima happened (1)

minstrelmike (1602771) | about 8 months ago | (#46275485)

One of the issues is the conflation of time with probability. A coin flip is half odds whether you flip it every second or every ten thousand years.
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 one event per millisecond, you get different results for the 'same' amount of risk.

imo, it's why the Drake equations calculating the probability of life in the universe to be almost certain are almost certainly wrong. They calculated star formation PER YEAR for the entire age of the universe. That gives you a lot of events to sift through. A more accurate approach would be to avoid introducing time into the calculations and instead count the number of stars in the universe (10 to the 22nd power) and then realize that translates into life being unique in the entire universe if there are 22 events with a 1 out of ten chance of occurring.

Re: The day before Fukashima happened (0)

Anonymous Coward | about 8 months ago | (#46275675)

A more accurate approach would be to avoid introducing time into the calculations and instead count the number of stars in the universe (10 to the 22nd power) and then realize that translates into life being unique in the entire universe if there are 22 events with a 1 out of ten chance of occurring.

Just to be clear, you are saying it's very unlikely there is other life? That seems reasonable, but how likely are 22 events with 1 in 10 odds? What sort of things have 1 in 10 odds in this way?

It's an interesting way to model the question, I'm just not sure I understand you completely.

Law of large numbers (0, Informative)

Anonymous Coward | about 8 months ago | (#46274063)

http://en.wikipedia.org/wiki/Law_of_large_numbers

This is old news mister Slashdot.

Re:Law of large numbers (0)

Anonymous Coward | about 8 months ago | (#46274305)

This really has nothing to do with the Law of large numbers.

Re:Law of large numbers (3, Informative)

Razalhague (1497249) | about 8 months ago | (#46274323)

Law of truly large numbers [wikipedia.org] is the applicable law here, but the mistake is understandable.

Re:Law of large numbers (3, Funny)

Chrisq (894406) | about 8 months ago | (#46274367)

Law of truly large numbers [wikipedia.org] is the applicable law here, but the mistake is understandable.

In fact fairly probable

42 (5, Insightful)

Dynedain (141758) | about 8 months ago | (#46274079)

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?

Re:42 (0)

Anonymous Coward | about 8 months ago | (#46274155)

And how many pips are on a pair of dice?

40!

Re:42 (1)

Immerman (2627577) | about 8 months ago | (#46274203)

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.

Re:42 (0)

Anonymous Coward | about 8 months ago | (#46275183)

What do you get when you multiple 6(base 13) times 9 (base 13)?

Re:42 (-1)

Anonymous Coward | about 8 months ago | (#46274457)

Mention of dice and no complaint about the beta? How improbable.

Aren't is as bad as ain't (0)

Anonymous Coward | about 8 months ago | (#46274089)

and neither shouldn't never ben't unused, ever.

Seems legit (4, Funny)

smallfries (601545) | about 8 months ago | (#46274107)

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.

intuit (0)

MancunianMaskMan (701642) | about 8 months ago | (#46274127)

Verbing weirds language. Seriously, constructs like this stop my reading flow. Please don't.

Re:intuit (2, Informative)

Anonymous Coward | about 8 months ago | (#46274171)

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.

Re:intuit (1)

tgv (254536) | about 8 months ago | (#46274389)

Neoteric verbiage doth incrassate.

Re:intuit (1)

rossdee (243626) | about 8 months ago | (#46274603)

I still don't know what the relationship is between Quicken (the accounting software) and Quicken Loans

Re:intuit (1)

rjstanford (69735) | about 8 months ago | (#46275427)

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:intuit (0)

Anonymous Coward | about 8 months ago | (#46274261)

Verbing Intuit really Turbotaxes language.

A million to one (1)

bickerdyke (670000) | about 8 months ago | (#46274161)

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?

Re: A million to one (0)

Anonymous Coward | about 8 months ago | (#46274235)

"The chances of anything coming from Mars are a million to one", - he said.

Re: A million to one (1)

rossdee (243626) | about 8 months ago | (#46274609)

But still they come

OOOHHH LAH

Re:A million to one (0)

Anonymous Coward | about 8 months ago | (#46274635)

As in the creation of millionaires at the Wall Street during bull economy? Enough people interacting with an idea of common rules, speaking the same language and behold, the American dream emerges! ;)

Re:A million to one (1)

shadowrat (1069614) | about 8 months ago | (#46275409)

many people in my line of work have decided to use a DateTime value as a primary key in a database. i always see the jr programmers doing this. i'm guilty of it myself. you think, "it's impossible that two users will create records at the exact same nanosecond." You quickly learn how probable improbable things are.

just explaining it to the jr programmers never seems to be enough. they never really appreciate it until they actually screw something up.

Summary. (3, Insightful)

BlackPignouf (1017012) | about 8 months ago | (#46274175)

Why? Because there are 7 billion people on Earth.

Mort (0)

Anonymous Coward | about 8 months ago | (#46274231)

Terry Pratchet blew my mind as a kid when I was reading his book Mort:

“Scientists have calculated that the chances of something so patently absurd actually existing are millions to one.
But magicians have calculated that million-to-one chances crop up nine times out of ten.” - Terry Pratchett, Mort

This simple concept seems to come up again and again in articles and books (e.g. 'The Long Tail'), often heavily dressed up imho.

The concept can be summed up - pun intended - as follows:

The sum of probability of 'unlikely' events is greater than the sum of probabilities of a 'likely' event, therefore making the occurrence of some 'unlikely' event 'likely'.

Further info for pedants: You can choose your arbitrary threshold for likely and unlikely so long as 1 >= likely > unlikely. By 'some', I am not talking about a particular event but rather any 'unlikely' event. Let me know if I forgot something.

Re:Mort (5, Insightful)

martin-boundary (547041) | about 8 months ago | (#46274455)

Being a pedant, I have to disagree.

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.

Wooosh (1)

Anonymous Coward | about 8 months ago | (#46274659)

Pratchett is merely illustrating a narrative trick. If the storyteller really needs them to, all million to one chances will come in, because its a story. One of his characters goes on to say:
"Its a million to one chance - but it might just work"

Re:Wooosh (2)

rjstanford (69735) | about 8 months ago | (#46275447)

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.

Re:Wooosh (1)

Kojiro Ganryu Sasaki (895364) | about 8 months ago | (#46275715)

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.

Re:Mort (1)

minstrelmike (1602771) | about 8 months ago | (#46275557)

I think one of the issues we are missing when teaching stats is that the bell curve (Gaussian distbtn) and the long tail (1/t curve) are both measures of populations.
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 who have one gun. Fewer folks own 2, then 3, then 4. And there are a few folks who own tens or hundreds of guns (and we don't count 101, 102, 103 when performing the measurements).

The bell curve and the long tail curve are just different sides of the same coin (I hope that analogy doesn't confuse anyone ;-)

Ode (0)

Anonymous Coward | about 8 months ago | (#46274239)

Nothing is improbable until WE say it's improbable!! Was it improbable when the Germans bombed Pearl Harbor?

Re:Ode (1)

Anonymous Coward | about 8 months ago | (#46274257)

Nothing is improbable until WE say it's improbable!! Was it improbable when the Germans bombed Pearl Harbor?

Wars are nature's way of teaching people geography. Until a bunch of states in North America federated.

Re: Ode (0)

Anonymous Coward | about 8 months ago | (#46274393)

Whoosh!

Re: Ode (1)

rossdee (243626) | about 8 months ago | (#46275377)

"Whoosh!"

Yep in the parallel universe where the Germans bombed Pearl Harbour, they used jets...

This is why TV news is toxic (2)

LostMonk (1839248) | about 8 months ago | (#46274241)

At any given time there are floods, fires, murders and any possible crime happening somewhere in the world. People, however are designed to react to what's happening in their community -- in their immediate environment.
Having every horror happening, nationwide, shoved down your throat 24X7 is equivalent to poisoning yourself.

Lottery scratch tickets; not so random (4, Interesting)

Trax3001BBS (2368736) | about 8 months ago | (#46274243)

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 (1)

Anonymous Coward | about 8 months ago | (#46274497)

I don't play the lottery, maybe a ticket twice a year

Nice denial going on there.

Re:Lottery scratch tickets; not so random (3, Interesting)

AthanasiusKircher (1333179) | about 8 months ago | (#46274987)

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.

Re:Lottery scratch tickets; not so random (1)

minstrelmike (1602771) | about 8 months ago | (#46275617)

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) This is best done at the sorts of run-down liquor stores where no one takes a lottery ticket anyplace else. .

It wasn't serial numbers. At first glance, it is poor management decision to alter the odds. However, that increases sales which is why slot machines actually pay off something regularly.And if your job is to increase sales of packs of lottery tickets to stores, lots of winners spread thru _every_ store make a lot of sense.

Birthday's not a problem... (0)

Anonymous Coward | about 8 months ago | (#46274249)

...it's a paradox.

Roll a dice... (1)

3247 (161794) | about 8 months ago | (#46274263)

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.

Re:Roll a dice... (2)

oodaloop (1229816) | about 8 months ago | (#46274607)

Roll a dice

Die. Dice is plural. Dice.com sucks. Die, Dice, Die! Wait, what were we talking about?

Re:Roll a dice... (1)

minstrelmike (1602771) | about 8 months ago | (#46275641)

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 (3, Interesting)

Anonymous Coward | about 8 months ago | (#46274279)

Here's a conincidental non-conundrum (0)

moofmonkey (741160) | about 8 months ago | (#46274311)

Here's one improbability that relies on so many coincidences Istill think its barmy anyone thinks this belongs in the realm of credibility:
probability of not getting caught with box-cutters x probability of being able to hijack planes without pilot mayday x likelihood of coincident military exercises reducing intercept aircraft availability x likelihood of coincident simulations to confuse controllers x likelihood of PC simulator and minimum prop training providing the ability to actually fly jet aircraft at speed into targets x airframe remaining controllable and not breaking x steel buildings not being able to sustain collision and fire of little remaining fuel and furniture x probability of a nearby building collapsing symmetrically at near freefall from fires and masonry damage x 19 committed alqaeda terrorists acting alone ..... is so astronomically unlikely and coincidental as to beggar belief.
Of course, certain well-placed insiders could remove a number of those variables, but what would I know, I'm just a lunatic conspiracy theorist.

Re:Here's a conincidental non-conundrum (1)

mooterSkooter (1132489) | about 8 months ago | (#46274347)

>>...but what would I know, I'm just a lunatic conspiracy theorist.

Yes, indeed you are.

re: birthday problem (1)

jinchoung (629691) | about 8 months ago | (#46274341)

one thing to remember about the birthday problem is that in a given classroom or other populated gathering, it's very likely that two people will have the same birthday... BUT... it says nothing about the possibility of any two people having any PARTICULAR birthday. so as long as you don't care what the date is, yes, two people will more than likely have one in common. but the odds that anyone will have a particular one or one that is the same as yours - those are still pretty big odds against.

People round down (3, Insightful)

Alomex (148003) | about 8 months ago | (#46274431)

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).

Re:People round down (2)

Mr Z (6791) | about 8 months ago | (#46274561)

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-intuitive what constitutes a "trial". As the number of people involved grows linearly, the number of potential pairings grows quadradically, and most folks don't really take that into account.

Extending that to the lottery example: It's far, far more likely that two people bought the same numbers than it is that anyone matched the jackpot numbers. (And that's before taking into account the fact that folks that pick their own numbers rarely pick very random numbers.) But nobody's interested in that coincidence until the folks with the same number also match the jackpot number.

Re:People round down (0)

Anonymous Coward | about 8 months ago | (#46275223)

> The odds of any one ticket winning the lottery jackpot are astronomically small
You need to add in: The odds of *someone* winning are fairly high.

Re:People round down (1)

Mr Z (6791) | about 8 months ago | (#46275267)

I usually don't state that explicitly, at least at first. I want to let the idea sink in first. I will state that if someone doesn't get it at first, though.

Re:People round down (1)

minstrelmike (1602771) | about 8 months ago | (#46275751)

Mathematically, the odds of winning are so small they equal zero.
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.

Re:People round down (1)

minstrelmike (1602771) | about 8 months ago | (#46275713)

imo,l the difference between statistics and probability is that every customer in a casino is gambling, but the casino itself is most definitely not gambling. It is the difference between owning one hand of cards and owning ten thousand hands.

I still want to know how to ... (1)

Alain Williams (2972) | about 8 months ago | (#46274453)

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: (1)

gb7djk (857694) | about 8 months ago | (#46274477)

Everybody knows that that vital million to one chance happens nine times out of ten.

Why The Sun Is Not Permitted To Shine (1)

IgnorantMotherFucker (3394481) | about 8 months ago | (#46274499)

We all know that fusion happens in the core of the Sun because it is so hot and has such high pressure. Actually it's not hot enough, and the pressure is not high enough to initiate fusion. We get fusion anyway due to quantum tunneling. That is, particles can escape a potential well if there is a finite distance to another place of low potential. Imagine a marble rolling around in a bowl, but not energetically enough to pop over the rim. Quantum tunnelling provides that from time to time, the marble will spontaneously appear outside the bowl. It is for that reason that I never go near not a gun but a bullet. Quantum tunnelling: Fulminate of Mercury can spontaneously detonate.

Re:Why The Sun Is Not Permitted To Shine (1)

maz2331 (1104901) | about 8 months ago | (#46275261)

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.

Comment on this story. (1)

donnie Freyer (2881319) | about 8 months ago | (#46274539)

Funny how people think that because we have sorted out a few complex puzzles of our reality, this should give us license to the rest. We are surrounded by things we won't ever be able to explain and the funniest part is that we can't even see most of this going on right in front of us. - The worst aspect of intelligence is being trapped by it

Re:Comment on this story. (1)

minstrelmike (1602771) | about 8 months ago | (#46275779)

- The worst aspect of intelligence is being trapped by it

Being trapped by intelligence is the best aspect.
I think ;-)

This article would have been more useful if it (5, Insightful)

oscrivellodds (1124383) | about 8 months ago | (#46274589)

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.

Re:This article would have been more useful if it (2)

jbmartin6 (1232050) | about 8 months ago | (#46274857)

Along the same lines, I remember first encountering this concept of probability during the "Bible Code" craze many years ago. The credulous gushed that the odds of this or that secret message being in the Bible by chance are some billions to one against, and the rebuttal was that there were many billions of places in the Bible to look for it, so the odds were actually pretty good that you would find it somewhere. 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.

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.

Re:This article would have been more useful if it (0)

Anonymous Coward | about 8 months ago | (#46274939)

Then why are there no unicorns?

Re:This article would have been more useful if it (1)

minstrelmike (1602771) | about 8 months ago | (#46275793)

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

Re: This article would have been more useful if it (0)

Anonymous Coward | about 8 months ago | (#46274981)

While I do side with the Darwin theory, I don't get why humans ( from ancient Egyptian times) have not evolved in 6000 years.

Re:This article would have been more useful if it (1)

AthanasiusKircher (1333179) | about 8 months ago | (#46275287)

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 buried in Pre-Cambrian rocks must have been naturally formed by processes in the earth that refined the metals and formed all the gears... all just by the chance forces in the soil. After all, there are HUGE numbers of atoms in the soil, and it would seem "inevitable" that there will be enough pushes and pulls and moving stuff around there to form a pocketwatch.

Of course, most paleontologists who found a pocketwatch buried in Pre-Cambrian rocks would assume that some modern human just happened to be digging there before, and we just hadn't found evidence of the previous excavation -- since that is actually a significantly more likely scenario than a pocketwatch forming from natural processes.

The point to take away from your arguments isn't that design is impossible. It's that we really, really don't have anywhere near enough evidence to even begin to estimate probabilities like how likely life is to evolve in certain ways. The intelligent design people think it's basically impossible; you think it "seems inevitable." In reality, the odds are somewhere in the middle in the vast mathematical gap between these assumptions. And it's hard to draw conclusions about what is "impossible" or "inevitable" from only one example (earth).

Personally, I think the odds of intelligent life evolving are likely much more remote than many people think -- I certainly don't think it's like Star Trek where every other star system has a planet teeming with plant life, if not some bipedal human-like species. I'm joking a bit here, but I think that scientists who are hoping to find evidence of primitive life even in our own solar system may be committing a similar fallacy to the intelligent design folks, in terms of overestimating probability rather than underestimating it.

Of course, I have no real way of knowing, and there's no reason not to look. But until we have some sort of sample of how often life actually evolves in the universe and under what conditions, all this talk of probability estimates is just meaningless speculation -- on both sides of the question.

game (-1)

Anonymous Coward | about 8 months ago | (#46274679)

i like this play game game friv [frivhot.com]

Been trying to make this (1)

TheCarp (96830) | about 8 months ago | (#46274757)

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 set goals like preventing attacks where every single one that happens is a failure, if you are resigned that the next time one happens you will support this or that....then you have already resolved to support it, because it will happen, regardless of what you do.

Every liberty you are willing to curtail in the name of stopping the unstoppable is one you already lost.

inconceivable! (0)

Anonymous Coward | about 8 months ago | (#46274943)

inconceivable!

winning the lottery twice (1)

Danathar (267989) | about 8 months ago | (#46275197)

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.

THAT these things happen isn't the issue (1)

davidwr (791652) | about 8 months ago | (#46275389)

"The simple equations here make it easier to understand that improbable things really are not so improbable," [emphasis added]

Almost everyone who had birthday parties in school growing up knows SOME pair of kids with the same birthday. Anyone in America knows that "big lotteries" usually have at least a few winners a year. Helping people understand that such events happen isn't a big issue.

Helping them understand why they are expected to happen on the other hand....

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