(OT) mathematicians-discover-prime-conspiracy

[Antony Prince]

On March 24, 2016 11:17:58 PM EDT, "Marcio Barbado, Jr." <marcio.barbado at gmail.com> wrote:
>Not sure if it's counterintuitive once tossing can be seen as
>abandoning inertia.
>
>
>Marcio Barbado, Jr.
>
>
>
>On Fri, Mar 18, 2016 at 9:18 AM, Peter Lebbing
><peter at digitalbrains.com> wrote:
>> On 14/03/16 10:37, Fulano Diego Perez wrote:
>>>
>https://www.quantamagazine.org/20160313-mathematicians-discover-prime-conspiracy/
>>
>> So forgive me for the off-topicness, but something in the text caught
>my
>> attention:
>>
>>> Soundararajan was drawn to study consecutive primes after hearing a
>>> lecture at Stanford by the mathematician Tadashi Tokieda, of the
>>> University of Cambridge, in which he mentioned a counterintuitive
>>> property of coin-tossing: If Alice tosses a coin until she sees a
>>> head followed by a tail, and Bob tosses a coin until he sees two
>>> heads in a row, then on average, Alice will require four tosses
>while
>>> Bob will require six tosses (try this at home!), even though
>>> head-tail and head-head have an equal chance of appearing after two
>>> coin tosses.
>>
>> I did try this at home; only I wrote a Python script to do all the
>> tedious tossing and accounting. This is its output:
>>
>>> $ ./cointoss HH HT
>>>
>>> H                   T                   HH                  HT
>>> ----------          ----------          ----------         
>----------
>>> 59821 (49.9%)       60079 (50.1%)       6.044               3.990
>>
>>
>> After over a million coin tosses, it takes 6 tosses on average until
>you
>> see two heads in a row, but only 4 to see head-tail. Obviously, the
>> script is attached. Supply the patterns on invocation, as shown
>above.
>> Any number of patterns of any length are supported (I think). Well,
>> strictly positive numbers and lengths :).
>>
>> Can someone point me in the direction of the solution to this
>> counterintuitive probability theory result? Any of a common name for
>the
>> property, a mathematical explanation or an intuitive explanation are
>> much appreciated!
>>
>> Anyway, to make up for the off-topicness, let's get slightly
>on-topic...
>>
>> To the OP: Please provide at least a short abstract of the text when
>you
>> post a link. That way people can tell from your mail what the text
>will
>> be about.
>>
>> With regards to the article, I'm surprised by the choice of words in
>its
>> title. Other than to draw in more readers, I don't see what place the
>> word "conspiracy" has in it. That's like saying 0 and 1 are
>conspiring
>> to be consecutive on the integral number line. Oh no, pretty much all
>> are computers are based on 0's and 1's and now they are conspiring!
>> Probably against us! Quick, we need neutral numbers without an
>agenda...
>> In my opinion, this title really devalues the article. "Three secret
>> ways to cope with prime conspiracy mathematicians don't want you to
>know
>> about" isn't that much further out. Oh, I hope that phrasing doesn't
>> tickle any spam filters... Ah well.
>>
>> Cheers,
>>
>> Peter.
>>
>> --
>> I use the GNU Privacy Guard (GnuPG) in combination with Enigmail.
>> You can send me encrypted mail if you want some privacy.
>> My key is available at
><http://digitalbrains.com/2012/openpgp-key-peter>
>>
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I've followed the thread for a bit now, but the concept definitely brings some things to light, especially for those less cryptographically or mathematically inclined. By the basics that I know, a 50-50 chance is a 50-50 chance. But as has been pointed out, the chance of getting a specific set of results consecutively is obviously (according to the data), not 50/50 even though the initial probability would imply that. I don't really have much more to add to the discussion other than it made me think a bit more about how probability and the effect that measuring the probability of predetermined sequences within that same set might produce results that are contradictory to the initial expectations. Such is the nature of these things and I merely found it interesting that the results defied the expectation. Which is the essence of discovery and progress.
-- 
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