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The Magic Cafe Forum Index » » Penny for your thoughts » » Maths for a Billion Monkeys (0 Likes) Printer Friendly Version

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C.J.
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Recently purchased a copy of ParaLies by Joshua Quinn and as a newcomer to mentalism (making a long-overdue move from generic close-up hobbyism) I am finding it astounding. I can see how many "newbies" would find the material intimidating, but I think that Quinn, like Canasta, has found an excellent voice to pitch his routines. He neither speaks over the heads of the inexperienced, nor patronsises the wise. Thanks.

Anyway, for those who know of the Billion Monkeys Book Test, here is some rough maths inspired by the footnote on p130. I intend to offer this as a mini-demonstration to open the book test. Done well it implies to the audience that each step of the test itself is multiplying the odds against the performer.

The keyboard in front of me has many keys. If I were to press them all now one at a time, many would not affect the text displayed on screen (eg Ctrl, Shift, Esc...). I count 50 that would leave mark on my writing - 26 letters, 10 numbers, 11 punctuation marks, space, tab and backspace. To keep things simple for our hypothetical monkeys, I will pretend all of the others do not exist.

The challenge is to see how long it would take a [billion, if you wish] monkeys to randomly type the entire script of Hamlet [or Macbeth in some versions - I'm using Hamlet].

As stated by Quinn in the aforementioned footnote, the full title of the play is "The tragedy of Hamlet, Prince of Denmark" (no comments about Shakespearean "tragedie" please!). Let's make it easier for the monkeys and say that the capital letters are irrelevant - that way they just have to focus on pressing one key at a time. We will also pretend that the backspace key doesn't erase their work. But we can't give them too many free passes - I still expect spaces in the correct spots, as well as that comma in the middle. That means, just to type the title will require a sequence of a mere 39 correct keys. Easy, huh?

The chance of them randomly hitting the 't' required to start the title is 1:50 ("One in fifty"), because they are hitting one key out of the 50 provided.

The chance of them, at any time, hitting a 't' followed by an 'h' is 1:50 for the first key, then 1:50 for the second. In probability these numbers are multiplied together. The total chance of them successfully (randomly) hitting a 't' then an 'h' is a whopping 1:2500 (50x50).

To complete the first word at random, hitting one key at a time, the monkeys only have the odds of 1 in 125,000 (50x50x50). Still, if we have a billion monkeys, we can expect more than one of them to get the word "the" on their page pretty quickly.

Here's the problem: the odds quickly spiral out of control with each new key pressed:

4 correct keys in order is 1:6,250,000 (50^4 or 50x50x50x50)
5 correct keys in order is 1:312,500,000 (50^5)
6 correct keys in order is 1:15,625,000,000 (50^6)

Let's pause there. Given a LIMITED keyboard and allowing them to skip capital letters the monkeys are starting to have trouble because...

If we took every person on the planet and put them in a room, and you selected one person at random in the hope of somehow selecting my cousin's step-dad's sister's best friend from primary school, YOU WOULD BE TWICE AS LIKELY TO SUCCEED than a single monkey attempting to randomly type "The tr"!

[This is a great point to emphasise to the audience that each additional step is increasing the odds against the monkey considerably - those with knowledge of the BM Book Test will see the value in this]

The chance of getting the entire title "the tragedy of hamlet, prince of denmark" with all 39 keystrokes is 50^39 (said "fifty to the power of 39", meaning fifty multiplied by itself 39* times).

I'd like to point out that with an advanced calculator and some tricky shortcuts, I could only get a specific answer as high as 50^21. This answer was:

A chance of one in 476,837,158,203,125,000,000,000,000,000,000,000.

With the assistance of scientific notation, we can *approximate* the total of 50^39 as:
1.8189894 × 10^66
Or in English, about 18,189,894 followed by 66 zeroes. Wanna see it?

18,189,894,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,0000,000,000,000

Erm... and that's just to get the title!

Even with a Billion monkeys working, the odds are still astronomical - cross off 12 zeroes and you're left with the odds that stand against their collective efforts. Phew!

With this buzzing in the spectators minds, it's a good reason to impose the parameters required by the BM Book Test, and I doubt anyone would argue with you asking for a bit of a chance! Oh, and I intend to use a copy of Hamlet as the the foundation for the book test routine, which seems a perfectly valid reason to introduce a book in the context (so "Nyahh" to the booktest naysayers!!)

Personally, I'd end this long intro with a clear reminder that "each step increases the odds more than one would think", and then never speak of it again. It leaves a strong impression, but returning to this after the effect would allow the keener minds in the audience to see the equivoque!

Now I just have to practise! I can't wait to perform this one!




*Footnote for the pedantic: It could be said that really, 50^39 is 50 multiplied by itself 38 times.
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bobser
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If this doesn't capture your audience's attention then nothing will!
But I might take something else with me... just to be sure?
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Jon Hackett
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Elegantly put Bobser.

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C.J.
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Yes, I shudder to think of the danger of trying this without a very tight and fast (and humorous) script. Woe to me if I break an edge-of-your seat mentalism show with a half-hour lecture on theoretical probability mathematics.

Honest question: should I skip the hoo-ha and just present the final number? Or not at all? Many of you have the experience I lack.

*Kicks self for not being smart enough to phrase the entire first post as a question!*


Oh, and for the record, here's what happens when one uses non-theoretical monkeys:
http://news.bbc.co.uk/2/hi/3013959.stm
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Joshua Quinn
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C.J.,

First off, many thanks for the kind words, and I'm glad you enjoyed the book. Second, I'm somewhat embarrassed to admit that it never even occurred to me to incorporate the billion monkeys question into the actual presentation. I had been doing the effect for a long time before I had a name for it; for years I just thought of it as "that book test I do with that thing I came up with." Then when wrote it up for ParaLies and had to find something to call it, I chose the Billion Monkeys name simply because, like the billion monkeys question itself, the modus deals with the random occurrence of a specific series of letters (and also because the phrase "Billion Monkeys Book Test" just made me smile). I then included the explanation of the math behind the billion monkeys question merely as a (hopefully) amusing aside for the reader. But I'm gratified that it inspired you to work it into the presentation, and given the right scripting and the right venue/audience, I think it could play extremely well. Best of luck with it.
Every problem contains the seeds of its own solution. Unfortunately every problem also contains the seeds of an infinite number of non-solutions, so that first part really isn't super helpful.
Brandon Queen
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Hey Quinn! You mentioned in paralies that you were going to be publishing more ideas with BMBT/thought chunnel. Could we possibly get any idea how far along that project is coming?

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Dick Christian
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And by the time C.J. completes his dissertation on the mathematics of the billion monkey challenge half of the audience will have fallen asleep and the other half will have left the theater to watch a soccer game on TV -- and C.J. hasn't even started the test yet.
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Tom Cutts
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CJ,

Because one person can't pull it off doesn't mean you can't.
C.J.
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Quote:
On 2010-04-15 23:55, Tom Cutts wrote:
CJ,

Because one person can't pull it off doesn't mean you can't.

It sure is dangerous to raise your head in these forums if you're not a household name, huh? Smile

The criticisms are appreciated, though. Perhaps I have misunderstood the field of mentalism through my readings so far. Thankfully I can learn from my mistakes before I even make them.
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Pete Legend
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Anything is possible..make a stand up comedy piece based around the idea.The notion could be made into something which could be funny,after all a grown man pondering on that above premise is silly/ridiculous which straight away brings about a smile Smile

I imagine if you pretended to play it straight in a stand up setting it could go well coupled with an impressive piece of mindreading...After all a lot of comedy is based around the most mundane of topics.It's how it would be presented,I'd bring flip charts,graphs,visual aids etc to add to your presentation.Like I said I'd play it straight but make it ridiculous while being deadly serious about it Smile

Good stuff C.J!
Dick Christian
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My comment was not intended to imply that you couldn't make some reference to the probability of a billion monkeys randomly creating a readable text, just that the idea can easily be expressed very briefly in a few well chosen words in lieu of attempting a tedious series of calculations. One of the potential problems with presentations of mentalism -- one that dooms far too many such presentations to failure -- is the tendency of the performer (especially the less experienced ones) to engage in lengthy explanations reminiscent of lectures on psychology or philosophy that most audiences find dry, boring and uninteresting. The experienced performer eliminates all extraneous commentary, feigned struggles to capture the thoughts of spectators, etc. and keeps the focus on the effects and keeps the show moving at a brisk pace, with engaging patter and lots of interaction in order to capture and hold the attention of the audience.
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Tom Cutts
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An experienced performer engages his audience in the manner he feels best gets his message across. Using the generic, trick, trick, trick magic template might not fit everyone. As others have pointed out, it could be a quite entertaining presentation.
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I think that an in depth explanation of the billion monkeys theory has the potential to be very funny. I think it'd be great material for a comic and that there's no reason why it shouldn't be great material for a mentalist. Of course it could be done poorly, but so could anything. To categorically say that it wouldn't work is very short sighted.
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Maybe you could use a puppet...Smile
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Tom Cutts
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Dick,

Part of theater is exploration and discovery. You are dismissive of this, I am accepting of alternate ideas. You seem to know what will work without ever having seen it performed. I'm simply leaving the option open that someone could create very engaging, unique, and sucessful presentations through alternate presentations to the old "trick, trick, trick" magic show template.

See the difference?
Dick Christian
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I'm not quite sure how pointing out the obvious (and generally accepted) fact that audiences seldom find performances of mentalism that involve dry, drawn out explanations and tedious "lecture" style presentation entertaining is somehow inappropriate. I fail to see how my comment that "The experienced performer eliminates all extraneous commentary, feigned struggles to capture the thoughts of spectators, etc. and keeps the focus on the effects and keeps the show moving at a brisk pace, with engaging patter and lots of interaction in order to capture and hold the attention of the audience" (which never mentions, suggests or implies a "trick, trick, trick" presentation) differs significantly from your statement that "someone could create very engaging, unique, and sucessful presentations through alternate presentations to the old "trick, trick, trick" magic show template."

Perhaps you don't understand keeping the focus on the effects, a brisk pace, engaging patter, interaction and capturing and holding the attention of the audience and for some inexplicable reason equate that with "trick, trick, trick."

Unless one assumes that you have a problem with reading comprehension, it would be easy to conclude that you just get some perverse thrill out of finding fault with anything I post. If that's the case it hardly reflects credit on a Café staff member who serves as a forum moderator.
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Tom Cutts
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Dick,

I do find fault when you post that someone whom you have never met and never seen perform is incapable of creating an entertaining presentation in the style he has imagined.

That is what your first post does:

Quote:
"And by the time C.J. completes his dissertation on the mathematics of the billion monkey challenge half of the audience will have fallen asleep and the other half will have left the theater to watch a soccer game on TV -- and C.J. hasn't even started the test yet."


Effectively, you are denying him his vision and denying him his voice as a performer. Especially bad that you have never given him the chance to show his work.

Your follow up post:
Quote:
My comment was not intended to imply that you couldn't make some reference to the probability of a billion monkeys randomly creating a readable text, just that the idea can easily be expressed very briefly in a few well chosen words in lieu of attempting a tedious series of calculations. One of the potential problems with presentations of mentalism -- one that dooms far too many such presentations to failure -- is the tendency of the performer (especially the less experienced ones) to engage in lengthy explanations reminiscent of lectures on psychology or philosophy that most audiences find dry, boring and uninteresting. The experienced performer eliminates all extraneous commentary, feigned struggles to capture the thoughts of spectators, etc. and keeps the focus on the effects and keeps the show moving at a brisk pace, with engaging patter and lots of interaction in order to capture and hold the attention of the audience.


Starts off dismissing the degree to which C.J. is intersted in using his possibly engaging explanation which is a play on the socially known reference to a million monkies ability to create literature. You grant him, sight unseen, "some" use of his presentation idea; characterizing the rest as "lengthy explanations reminiscent of lectures on psychology or philosophy that most audiences find dry, boring and uninteresting." You surely must be psychic to know this without ever having seen it performed.

As to the "trick, trick, trick" line. I have seen it way too often in Mentalism. The "effects" are just tricks, usually visual ones, and the lack of purpose in the performance is made up for with frantic pacing. It is, lets say, the equally destructive polar opposite to the long boring pointless presentation. I'm sure we both agree successful performance lies somewhere in between.
monkeypuzzletree
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Quote:
On 2010-04-16 14:04, Dick Christian wrote:
The experienced performer eliminates all extraneous commentary, feigned struggles to capture the thoughts of spectators, etc. and keeps the focus on the effects and keeps the show moving at a brisk pace, with engaging patter and lots of interaction in order to capture and hold the attention of the audience.


If this works for you, I have no problem with that. But to state it as some kind of 'law' that all performers must adhere to is nonsense.

It is the extraneous thoughts of an engaging and experienced speaker that are frequently the most interesting or funny. 'Feigned' struggles to capture thoughts never appear feigned in the hands of a skilled performer. On the contrary - they are the moment at which the 'real' magic is perceived to happen. Also, a great performer is aware of the importance of light and shade. He knows that if EVERYTHING is kept at a consistently brisk pace, the show will eventually become monotonous.
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Tom Cutts wrote:
Quote:
I was just countering your dismissive attitude toward just about anything posted here which doesn't fit your thoughts.

Doh! Of course someone is dismissive of an idea that contradicts what they believe. Let's not discuss people's attitudes, or the people at all, let's discuss the subject.

Perhaps you missed this Tom:
Quote:
C.J. Posted: Apr 15, 2010 8:14am
Yes, I shudder to think of the danger of trying this without a very tight and fast (and humorous) script. Woe to me if I break an edge-of-your seat mentalism show with a half-hour lecture on theoretical probability mathematics.

Honest question: should I skip the hoo-ha and just present the final number? Or not at all? Many of you have the experience I lack.

*Kicks self for not being smart enough to phrase the entire first post as a question!*

Dick Christian gave his answer. It's fine that you don't agree Tom.

Tom Cutts wrote:
Quote:
Dick,

I do find fault when you post that someone whom you have never met and never seen perform is incapable of creating an entertaining presentation in the style he has imagined.

That is what your first post does:

Quote:
"And by the time C.J. completes his dissertation on the mathematics of the billion monkey challenge half of the audience will have fallen asleep and the other half will have left the theater to watch a soccer game on TV -- and C.J. hasn't even started the test yet."

Effectively, you are denying him his vision and denying him his voice as a performer. Especially bad that you have never given him the chance to show his work.

That's nonsense Tom. Dick Christian is denying him nothing, he's merely giving his opinion, as did you. C.J. explicitly asked for the opinion of performers with more experience than he has when he wrote:
Quote:
Honest question: should I skip the hoo-ha and just present the final number? Or not at all? Many of you have the experience I lack.

As to my own opinion, the implied script C.J. wrote in the first post sounded too long to me for the subject of mathematics. Even C.J. wrote it was a "long intro" in the first post. Could it be made interesting? I don't know, but I do find it difficult to imagine that it would stay interesting to most people as written above if all of it were used as written.

By the way, there is an error of omission; the mathematics is correct only if the probabilities for each of the 50 keys being struck are all equal - not that anyone would care! However, if performing for a groups of scientists, engineers, or mathematicians, some dweeb would come up after the show and point this out. (I wouldn't do that, but I am a dweeb! Smile)

Of course, adding that fact would make it even less succinct and more boring to me.

C.J. wrote"
Quote:
18,189,894,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Erm... and that's just to get the title!

I liked this. It would take a wide banner to show that number!
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Tom Cutts
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Quote:
On 2010-04-18 19:17, Bill Hallahan wrote:
Of course someone is dismissive of an idea that contradicts what they believe.
Well, no. Some people (those who are not dismissive) would take an approach more along the lines of I haven't found it to be so, but hey, try it out. That is how we all grow and learn. Your approach has us simply following the tails of those who went before us. Don't scientists allow for things they don't believe in so they can be sure these things are taken into account and not simply dismissed.

Quote:
let's discuss the subject.
The subject at thand is an idea which got pooped on before it got a chance to show its value. Maybe that the OPer dropped his idea so fast is an indication in his lack of conviction to it, or maybe it is an indication he has been pummeled out of pursuing it. As an example, I could see Barry and Stuart having a field day presenting this ludicrous gymnastic mathmatical undertaking. It would be fun, funny, and engaging.

Opinions read something like this, Bill:

Quote:
As to my own opinion, the implied script C.J. wrote in the first post sounded too long to me for the subject of mathematics. Even C.J. wrote it was a "long intro" in the first post. Could it be made interesting? I don't know, but I do find it difficult to imagine that it would stay interesting to most people as written above if all of it were used as written.


Not like this:
Quote:
And by the time C.J. completes his dissertation on the mathematics of the billion monkey challenge half of the audience will have fallen asleep and the other half will have left the theater to watch a soccer game on TV -- and C.J. hasn't even started the test yet.
which is issued as if it is an edict from The Queen of England. [although I secretly think she has a fancy for chair routines]

ANYhoo, the issue I see with dropping off the meaty bits and just serving up the fat is that people will not get the gravity of the billion monkeys idea. It may well fall by the wasteside and become a "What was that about monkeys typing moment?" rather than, "That guy explaining the preposterous concept of monkeys typing a book was really hillarious!" And now we find ourselves in danger of bewing overshoadowed by our performance and so we take steps to balance that out. Still if you can be known in your own country as the Billion Monkeys Guy you might just have a big enough hook to hang a theater tour, a few TV spots, and a dreadful lot of radio.

Not bad for a little idea presented on an internet forum.

The basics of the idea are engagingly absurd, unique, and easily summed up. The execution is the tough part. Rather than trashing the idea or slashing it to the bone, shouldn't we be giving its theatrical due and see if it sinks or swims on its own merrit.
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