Radiolab

Navigate
Return Home

A Very Lucky Wind

Back to Episode

Laura Buxton, an English girl just shy of ten years old, didn't realize the strange course her life would take after her red balloon was swept away into the sky. It drifted south over England, bearing a small label that said, "Please send back to Laura Buxton." What happened next is something you just couldn't make up - well, you could, but you'd be accused of being absolutely, completely, appallingly unrealistic.

On a journey to find out how we should think about Laura's story, and luck and chance more generally, Jad and Robert join Deborah Nolan to perform a simple coin-toss experiment. And Jay Koehler, an expert in the role of probability and statistics in law and business, demystifies some of Jad and Robert's miraculous misconceptions.

Comments [29]

chad from Atlanta

Thanks so much. I haven't read anything so profound since my logic professor's paper exposing Noam Chomsky.

Apr. 14 2014 10:35 PM
Gene Yakub from Italy

For those who believe in coincidences these types of events, and similar ones which can be placed under "coincidence", seem wondrously unrelated and unexpected. But to those, like myself, who know that reincarnation is a reality, everything happens as it is supposed to, as has been chose by us before each reincarnation.
How can it make sense that as we look around us, there is a continuity and a unity even in diversity that has been there since the year dot, all fits together perfectly, everything sustains everything else - or it did before we interfered.
Yet we humans supposedly live a comparatively brief life span and all our experiences and knowledge disappear into thin air with that body? Why would that be true of the most sophisticated component of all creation?
What is human life about then, what is the purpose of being alive? Just to waffle along and accumulate book knowledge so as to earn money? No, life is for learning and growing, to rid ourselves of the negative consequences of the mistaken choices we previously made (the Law of Action and Reaction, Cause and Effect) by having as many other opportunities as necessary to understand where we went wrong and correct ourselves so we can move on.
Destiny v. Freedome of Choice? No versus, they act in tandem when we have to make choices every single moment of our lives because we don't remember what happened in a previous life except during the transition stage between one life another when we make our choices for the next one.

Dec. 04 2013 01:43 PM
Mike Anderson from Australia

Before we can deny meaning and ascribe everything to randomness, we really ought to ask the question: how do we know that "randomness" itself exists?

Apr. 29 2013 01:09 AM
maryam

enjoyed it as usual!

Apr. 28 2013 08:33 PM
Susan from Sea Cliff, NY

27 April 2013
Very much enjoyed this program, as I ALWAYS do! (Superlative=statistical hyperbole?) …So here I am, thought stimulated, free associations flowing…

Would love to hear this conversation broadened to include input from a rich cross section of thinkers and experts! I am neither mathematician, statistician, nor formal student of philosophy, but I believe that there exists a sense of scale, which is a valid participant in the randomness versus pattern theme. I think this sense is most likely species-specific, based on size and reach --physical and technological/cultural-- of each creature (microbes different from ants different from humans, etc. --Ponder the fly flying around inside an airplane flying across a land mass on a planet rotating and revolving…..etc.). Therefore, within the "human scale" of existence --in an atmosphere of cultural exchange, technological reach, our averaged physicality, and certainly our curiosity and intellect-- certain occurrences are legitimately extraordinary or plain, and in that regard, either random or patterned. …Or, as the feature suggests, possessed of some element of magic or manipulation; being on the spectrum of delight, fascination, or fear which makes up the (as yet) unknown; or predictably controlled. If we must always step back and consider scales of the Universe, Eternity, and Infinity, I think we would have no measurements of anything, since by definition, measurements, or numerics, are always relative…to something within our grasp. A disaster for a culture which has come to so worship "measurables." Am I correct that mathematics is a human construct that begins with us? Ten fingers, ten toes; the span of a stride in "feet," a horse is eighteen "hands" in height; time/distance in the pace (and regularity, or not) of the heartbeat; intervals of sunrise/sunset, climate versus weather within our observation.

I would look forward to explorations between a consortium of perhaps existentialists, statisticians, mathematicians, and astrophysicists. But I would take nothing away from your "programmed" attention, to the myopic assumptions to which we too easily fall victim, as we endeavor to stay ahead of bell curves. Patterns are constantly evolving from seeming randomness, particularly in the big data moment currently pressing us. But they are only meaningful to the extent that we can step back far enough in time and space and whatever other dimensions to perceive and apply them to our existence.

Apr. 27 2013 03:30 PM
jen from ayer, ma

@ mills from Virginia, I just saw this after hearing the thing on the radio about the 2 Laura Buxton's 4/25/13 and coincidences... Anyway my father was born on July 4, 1949 and died when I was little in 1977 and my grandfather, his father died on the same day that his son was born years later on, July 4, 2006. We all thought it was weird but We all think it was strange but comforting somehow that they are both together again.

Apr. 25 2013 10:53 PM
dr

awful audio - the effects are not the least bit surreal or provocative... just bloody annoying

Jan. 04 2013 03:42 PM
WatchTheClock from Up

The balloon story was really interesting, but I couldn't help but think of all of the wildlife destruction that is caused by balloons.
PLEASE don't release a balloon. Balloon releases are "celebrating by littering."
Dolphins, whales, turtles, and many other marine species, as well as terrestrial animals such as cows, dogs, sheep, tortoises, birds and other animals have all been hurt or killed by balloons.
More information here: http://balloonsblow.org/impacts-on-wildlife-and-environment

Jul. 14 2012 02:17 PM
shannon from fraser,Colorado

It is so weird and remarkable.well they do say you do have a twin somewhere!

Mar. 25 2012 10:27 AM
BOB

Hi

May. 23 2011 08:01 PM
Jim

I think they were twins, maybe separated, who made up the story to get popularity...

May. 08 2011 09:49 PM
Jay Koehler from Chicago, IL

Sorry to weigh in so late in the game here, but I just saw this site for the first time today (4/27/11). I'm the "statistician" from this particular Radio Lab show that at least one of you asked to hear from.

Yes, some of you math critics are right to say that the chance of the run in question is about twice as large as my estimate. Nice work. But there was some confusion about what was being computed due to edits (confirmed by the producer) and my own on-the-fly estimates. You can see more computational detail than you ever cared to see at this website which was posted by another listener.

http://www.leancrew.com/all-this/2009/06/stochasticity/

For the quick scoop on where my numbers on the show come from, scroll all the way to the end of the posting where it says "Update 6/20/09." Mystery solved.
- JK

Apr. 28 2011 12:14 AM
Joe from England

A similar occurence of mine was when i ended up talking to a young girl at a music festival over here, in England, a couple of years ago. I was 22, she was 16. I was a very withdrawn kind of person who was too anxiety-filled to engage with people i didn't know and so i would just spend the weekend wandering the festival on my own, occasionally being around the folks i went with (they were much older than me and not that interested in the music, being the reason i wasn't with them much), trying to avoid communication with anybody... *sigh*

Anyway, this one night, this young girl who was camping nearby comes over to our tents, the tiniest bit tipsy, and starts talking with us. She was fully lovely & enjoyable company and because i could tell that straight away i felt ok talking. And we talked.

To cut a long story short, it turned out we both had a mother going through cancer - not the most uncommon thing, this one - but also that she had a brother in New Zealand at the time.... as did i. So you start to think "oh, well, this is a bit weird. Of the 30,000 people at the festival, the one person i end up talking to has these such things in common..... (blah blah blah)".

And it got even weirder and more random to me when i mentoned some place we stopped off at on the drive up. I don't travel a lot. My county and London are the only places i've been, really, in England, other than when we lived further north till i was 4. The festival was about 3 hours north from where i lived and 2 hours south from where she lived which, in England, is almost half the country away.

And when i mentioned this one lovely place we stopped off at on the way up to have a drink and some lunch, she just looked in shock and kinda half-screamed, in disbelief, "Oh My God! I know that place!".... It turned out that this one place was the place her and her family go almost every year for a short holiday and it was just pretty mind-blowing, really, to find that out, along with the other connections we had. And by place, i mean the exact same pub/inn, not just a village, or a town or a county.

So the one person i had spoken to, for many years, of whom i previously didn't know, at a festival of nearly 30,000 people turned out to have a mother with cancer, a brother in New Zealand, and knew greatly the one tiny place i had stopped off at on the way and, other than the festival itself, the one place in nearly 20 years i had been to outside of my home county & London.

It's still very weird, to me.

Feb. 07 2011 07:37 PM
Maxwell P. Blakeney

I LOVE radiolab. Every once in a while I re-listen to an old episode. Today was Stochasticity. I'm really hoping you guys can tell me the name of an song in the episode. It start playing It starts playing at about 27 mins into the show right after Jad says something to the effect of "Essentially what you're saying is that basketball players are like coins." It sounds familiar but I can't seem to place it.

-Hoping you can help me out

Dec. 17 2010 01:24 PM
Truman Buffett from Seattle

This link got posted elsewhere, but not here:

http://heymathman.blogspot.com/

(these videos are now >1yr old.....sorry this link didn't get posted here sooner)

Truman

Nov. 25 2010 01:29 AM
James Plaskett from Cartagena, Spain

Right at the end of the Podcast one of the Lauras says she is studying Engliah, History and Classical Civilisation.

I studied those same three subjects when I was that age!

Uncanny?
Er, no...

But some better coincidences visible here -
www.jamesplaskett.com/

Jun. 30 2010 11:04 AM
Victor Salvest from England

I wish that your statistics prof would weigh in with the answer. My assessment is as follows:
A. there are 2^(100-7) ways for the first tosses 1 thru 7 to come up heads; if the first 7 are heads then the next 93 can be anything we like which can be arrived at in 2^93 ways.
B. if the next 2 thru 8 tosses are all heads AND the 7th toss wasn't a head (to avoid a double count of the run we got in A) there are 2^92 ways for this to occur- (run of 7 with 92 tosses which can be anything and 1 which must be a head). In fact ALL runs of 7 after the first can be done in 2^92 ways, we dont care about the 92 other tosses as long as the toss before our 7 isnt a heads.
C. the number of runs of 7 is thus:
(2^93) + (93 x (2^92)) which equals 4.571 x E^29 in scientific notation
D. the total number of possible sequences of throws is 2^100 which equals 1.26765 x E^30
E. the probability of at least one run of 7 heads in 100 throws is C/D or 37% ... I think?!

Apr. 07 2010 02:32 PM
August Mohr from Boulder Creek, California

Dear Mr. Truman Buffett,

I would like to see your video. I think it was Ross Ashby's book, Cybernetics, that presented Markov chains of English words which read like beat poetry that made the concept stick in my mind.

But I got no results for a Facebook search on your name. Would you please try mine? I'm the only "August Mohr".

Ashby's method was brilliantly easy to do in a searchable document like a PDF. Open a book and copy the 1st word. Search for the next instance of that word and copy the word that follows it. (If the 1st word is unique in the book, loop around to the only word that ever follows it, the 2nd word in the book.)

The 2nd word is a statistically like any words that could follow the 1st word, without the extra "meaning" of being the word that follows in the same sentence (unless it's unique).

Search for the next instance of the 2nd word, copy the following word the 3rd word in your Markov Chain. Keep moving through the text and you can make an arbitrarily long sequence in which each pair of words was generated with the probability of those words being found as a pair in the text.

That string of random words will have lots of "interesting" strings of 3 and 4 words, but no meaning. Unless you want to go into Bible Code land, that is.

What is usually omitted from Bible Code "statistics" is that the old Hebrew texts they use have no spaces and no vowels. Strings of only consonants are much shorter strings to match than most modern words and they may be interpreted as a word or words in multiple ways, thus radically increasing the opportunity for the searching mind to find things that correspond with each other. The human mind puts the meaning into the "random" proximities, like seeing Jesus in the spots on a Holstein cow.

What statistical analysis leaves out, is that once a mind has added meaning, there is meaning there. Nothing in the world has any meaning except that which has meaning to someone.

Mar. 09 2010 04:52 AM
Gina Mireault from Vermont

I also teach Research Methods in Psychology as well as Developmental Psychology. In the latter, we explore the "uncanny" similarities between between identical twins who are reared apart. Researchers make the assumption that these similarities (e.g., using the same unusual toothpaste or drinking the same brand of beer) are genetically based, even though they would not apply such explanations to the same similarities found between total strangers (like the Laura's in this edition of RL). I'll use this segment in class to illustrate that coincidence works as a third variable in explaining such similarities, as well as to discuss the human tendency to "see patterns in randomness". Thanks for an outstanding show!

Nov. 22 2009 09:21 PM
Truman Buffett from Seattle, WA

In brief, the probability of such an event occurring is given by the ninth entry in the 1x9 row vector vP^100. Where v = [1, 0, 0, 0, 0, 0, 0, 0, 0] and P is the 9x9 matrix with p_(1,2)=p_(1,3)=.5, and p_(k,2)=p_(k,k+1)=.5 for k=2...8, and p_(9,9)=1 and all other entries zero.

I know this seems dense, but if you send me a message on Facebook (I'm the only "Truman Buffett" with a profile picture) I'll send you a link to a video that will walk you through the problem and the method used above.

Nov. 17 2009 10:00 PM
Yanming from Corvallis

I don't know how to derive that probability easily, but I simulated 100000 sets of 100 coin flips: According to my simulation, the probablity of getting at least 7 tails in a row should be about 0.316. So I will trust Truman above.

Nov. 17 2009 02:49 AM
Truman Buffett from Seattle, WA

Oh No!
It's great to hear MATH on the radio, but how did a calculation that's so far from being correct ever make it through to the final edit? The probability of getting a string of 7 (or more) tails in 100 flips is ~31.752%. The probability of getting a string of 7 (or more) tails OR a string of 7 (or more) heads in 100 flips is ~54.234%.
I used an absorbing Markov chain to find these. Using a TI-83, it took about a minute to solve each. I'll try to come back soon and post a more detailed description of a method to find these numbers. Sullivan and Mizrahi's "Finite Mathematics" is available used for less than a buck at Amazon; they tell you everything you need to know about Markov Chains.

Nov. 14 2009 03:53 AM
Terry Hayes from Lexington, Ky.

I just listended to show on stocasticity recently and thought it was cool enough, until you got to the end and started going all gooey. The part where you spoke about how individual single celled organisms turned on protiens randomely and so forth and started talking about the "mystery" of how that low level randomeness turns into order at higher levels.

I don't really see the mystery here and think that if you had just spoken to that statistician you talked with earlier you might have had a less touchey feely ending about how people are unpredictable blah, blah, blah and just given a randomeness.

If you want to see how a randome item can produce order on higher levels try this.

Roll a single dice one time, a hundred times. Looking at the string of numbers you see randome strings of numbers.

If you roll a simple dice a millions times each single time will be a randome time. If you look at any short sequence of numbers generated so you will see randomeness. But if you AVERAGE those numbers you will get order. With just a few trials you will get a randome number that could be anything between 1 and 6, but will be closer and closer to 3.5 with many trials.

Eventually, with millions of trials you will get 3.5 almost exactly. Thus, millions of cells in a single organisme or a single cell doing something it does millions of time, will produce a rather orderly total.

You really should work harder at being a Radio LAB and not a radio - place that talks about science. There are enough ACTUAL mysteries out there that inventing them to contrive some sort of poetic ending to your show is not science, and thus does not belong in a lab.

Oct. 10 2009 01:37 PM
Irene Cardenas from Minneapolis, MN

How about connections in energy fields, including thought fields, causing coalescing or amplified vibrations that some people think of as co-incidence? Think of what that term, "co-incidence" means in terms of waves in physics. Actually, physical waves of energy co-incide, as many physicists know. Waves of energy fields from all things made of electron fields can go on infinitely, capable of interacting with everything we know on earth.

"Hot hand" can be the momentum of the effective energy flow pattern coursing through neural impulses in muscles and the brain (vision/motor coordination). Neural patterns reinforce and repeat themselves. There's a biological basis. Radiolab did a show about how energy pulses through the neural system before a person is conscious of making his own decision. The holistic perspective (right-brained/feminine) is different than the reductionist perspective (left-brained/masculine), which thinks everything is separate (the belief in ego) and random.

Oct. 05 2009 04:15 PM
EERac from New York, NY

I was just listening to the podcast of this episode and googled this page to see if other folks were bothered by the claim that there was only a 1/6th chance of a run of 7 tails (or heads). The claim is definitely way off, but (1-.5^7)^93 isn't correct either.

Any given run of 7 flips has probability .5^6 of being either all heads or all tails. In the show, they seem to divide the 100 flips into 14 separate chunks of 7 runs, and note that the probability that they all fail is only (1 - .5^6)^14 which is around a 80 percent. The thing is, that's way too pessimistic. Anytime you're flipping the coin, and you switch sides, you have a new shot at a 7 flip run.

On average, runs last for 2 flips, so you'll get about 46 shots at a 7 flips run. As far as I can tell, it's cumbersome to work out the exact probability, but a conservative estimate would to assume you'll have 40 chance to get 7 in a row. This would give a probability of .47 that you'd get a 7 flip run.

Honestly, it's pretty disappointing that an actual statistician got this so wrong. A simple check, if the radiolab folks want to correct themselves, would be to just run a few 1000 computer simulations.

Oct. 05 2009 03:41 PM
Mills from Virginia, USA

These sorts of coincidences are very seductive which is why, I think, they survive in our culture. As an example, this summer my father passed away on July 20 and his funeral arrangements were handled by Murphy Funeral Home here in Virginia. While clearing out his house, I found his mother's death certificate. She died in the 1980s -- on July 20 and her funeral arrangements were handled by Murphy Funeral Home, but in California.

I asked my father-in-law, who is far better at mathematics than I, what the odds were of this sort of coincidence. His response was that the probability was almost certainly between 0 and 1. Okay, I knew that much.

Thanks for the great show.

Sep. 22 2009 09:34 AM
Michael Shulman

@Chris,

I agree with you. The error was distracting me from the rest of the show.

But isn't the probability really (1-0.5^7) * 93 == 73%

(1-0.5^7) ^ 93 == 1.07e-196

-ms

Sep. 12 2009 01:42 AM
Alan

Great show guys. I teach a graduate methods course in psychology and I think I will use of some of these clips to illustrate the tendency for people to see patterns when there is (mostly) just randomness. By the way, if any listeners of your show are interested in learning more about things like the "hot hand illusion" and other errors of perception covered in this segment, Amos Tversky and Tom Gilovich did a lot of great work on these issues, much of which is summarized in very readable form in Tom's book, How We Know What Isn't So. (NB I have no connection whatsoever to that book or its authors or profits; etc.)

Sep. 05 2009 05:29 PM
Chris

Actually, I believe that the likelihood of getting a run of 7 tails in a row, over 100 flips total, is just over 50%. In 100 coinflips, you're looking at 93 (or 94, I'm not sure right now) sequences of 7, any one of which could be a run of 7 (I'm also granting the possibility of a run of 7 being preceded by a tails or followed by one, so technically I quoted the chance of a run of 7 or more), so the chance of NOT finding a run of 7 is (1-.5^7)^93, or approximately 48%.

I realize, statistically speaking, I'm somewhat ignoring icky things like independence, but I'm still fairly certain that I'm in the right ballpark.

Aug. 11 2009 03:14 PM

Leave a Comment

Register for your own account so you can vote on comments, save your favorites, and more. Learn more.
Please stay on topic, be civil, and be brief.
Email addresses are never displayed, but they are required to confirm your comments. Names are displayed with all comments. We reserve the right to edit any comments posted on this site. Please read the Comment Guidelines before posting. By leaving a comment, you agree to New York Public Radio's Privacy Policy and Terms Of Use.