Ah, but John. 1 in 27^16 is a big number, but infinity is more than 10^100^100 times bigger 
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it is indeedAh, but John. 1 in 27^16 is a big number, but infinity is more than 10^100^100 times bigger
However, having just asked Mr Google, I've just found (be it true or not!)I imagine that we cam probably agree that, although uyndeniably 'less than' infinity', 27^3,695,990 IS "an exceedingly large number"
In fact, no computing resource to which I have access can even scratch the surface of such a number - the highest I can get is 27^215, which my machine evaluates as about 5.54 x 10^307However, coming very slightly (not much!) more down to earth, consider that 1 in 27^16 change of getting just the first 4 words of Mr S's works. Imagine that (fast) monkeys take about 5 seconds for each of their attempts to type those 16 characters. 'On average' (i.e. the average of many attempts at the experiment, what is technically known as the "Expected") answer, it would take (27^16) / 2 runs of the experiment (attempts at typing 16 characters) before one got a 'success' . By my (quick!) reckoning, at 5 seconds a go, that 'average' would amount to some 6.3 x 10^15 years, which I think (maybe wrong!) is over 600,000 times the expected remaining life expectancy of the Solar System
Kind Regards, John
Yes but if you had a near infinite number of monkeys to attend to it then it might make the problem very slightly easier IMHO
You would (of course) need TTUP grounding in the live circuit, with a triple-pole extractive cutout switch, in case the monkeys suddenly stopped holding hands through the letterbox..
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Dare I ask what the monkeys are doing holding hands through a letterbox?
Passing electrons from one to t`other maybe!
Well, yes, if there were lots of monkeys doing it simultaneously, that would markedly reduce the 'expected' time to achieve a 'success'. However, even 'markedly reducing' a number which is 'close to infinity' still produces an answer which is still 'close to infinity' (albeit slightly less closeYes but if you had a near infinite number of monkeys to attend to it then it might make the problem very slightly easier IMHO
).As you will realise, I was talking about the number of attempts, regardless of how many monkeys were making those attempts. Hence, it could be (as my words were assuming) one monkey for 6.3 x 10^15 years, but it could equally be a million monkeys for working simultaneously for 6.3 x 10^9 years or whatever! I
Kind Regards, John
I didn't think electrons usually moved far enough to get from one monkey to another ?
Well OK then I suppose it might vary with the type of Monkey (Rhesus example) or Chimpanzees or things further up/down the evolution scale such as the age old chicken/egg problem (easy answer really as it was the egg! but hey ho!))
Uhmmmm - with billions or more quinetic monkeys, there could be some ';interference' issues with the wireless communication
In case there are some sceptics out there, to illustrate that the real world does reflect theoretical maths, I've just undertaken a simulation of attempts to get the word "even" (plus a space) by random typing on that 27-key typewriter.
I simulated 1 billion attempts at doing that, which took about 24 minutes on my laptop ....
.... and this was the result ....
69 out of 1 billion is about "1 in 14,492,753" which is pretty close to the theoretical figure of 27^5 (which is "1 in 14,348,907") . If I had been patient enough to simulate even more than 1 billion attempts, the answer would undoubtedly have been even closer to that theoretical figure.
Kind Regards, John
Was it "Random" or "Pseudo Random" John - not that I would nit-pick about it though.
I reckon I mentioned in the past my two goes with random on computer . one i developed for a school fete horse race game and the other to see if my theory played out on the age old how many people in a room to have a reasonable expectation that at least two sharing the same birthday.
Oh it was fun all those years ago on a ZX Spectrum in Spectrum Basic.
I never became a computer programmer (feigned surprise!!!) but still I reckon I had a better idea in some little bits about things than some so called computer programmers often do - nonsense input trapping subroutines) .
Anyway, it was great fun. But I kept mee day job though.
Sorry, I side tracked meeself - I reckoned 28 people in a room to have that expectation of at least two sharing birthdays , compared to 366 to be absolutely sure (excluding leap years etc so basing it upon 365 days in a year).
So, comparing 365 to 28, I wonder if we could apply something not unsimilar here?
I reckon I mentioned in the past my two goes with random on computer . one i developed for a school fete horse race game and the other to see if my theory played out on the age old how many people in a room to have a reasonable expectation that at least two sharing the same birthday.
Oh it was fun all those years ago on a ZX Spectrum in Spectrum Basic.
I never became a computer programmer (feigned surprise!!!) but still I reckon I had a better idea in some little bits about things than some so called computer programmers often do - nonsense input trapping subroutines) .
Anyway, it was great fun. But I kept mee day job though.
Sorry, I side tracked meeself - I reckoned 28 people in a room to have that expectation of at least two sharing birthdays , compared to 366 to be absolutely sure (excluding leap years etc so basing it upon 365 days in a year).
So, comparing 365 to 28, I wonder if we could apply something not unsimilar here?
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Essentially 'by definition', no algorithm can create truly random numbers, so in software they are all "pseudo-random number generators" (PRNGs). If you want to get what we believe to be truly random numbers, you have to look to physical processes, like radioactive decay. However, modern PSNGs are very close to truly random - certainly close enough for virtually all likely practical applications.
I'm not a professional programmer, either, but I've had to do a fair bit of programming in the course of my work. In case you (or anyone else) is interested, the code I wrote to do that simulation was very simple. Those reading this will probably not be familiar with the programming language I used (SAS), because it was 'near to hand', but anyone who is familiar with programming in any language should be able to understand what is going on here. In fact, the simulation itself is all within the two nested DO...END loops - just 8 lines of code. "ranuni(seed)" returns a random number between 0 and 1 from a uniform distribution and "byte(x)"returns the character corresponding the the (decimal) ASCII value specified as x. The symbol "||" concatenates two string variables ....
data monkeys (drop = x i seed char tim ) ;
length word $5 tim $20 ;
seed = 12345678 ;
Failures=0 ; Successes = 0 ;
tim = put (time(), time.) ; put "start: " tim ; *** write start time to log ;
do i = 1 to 1e9 ; *** 1 billion iterations ;
. .. word="" ;
... do char = 1 to 5 ;
...... x = ceil(ranuni(seed) * 27) + 64 ; *** note: ASCII 91 (dec) ( a [ ) used to simulate space ;
. ..... word = trim(left(word)) || byte(x) ;
... end ;
. .. if word = "EVEN[" then Successes = Successes + 1 ; else Failures = Failures + 1 ;
end ;
output ;
tim = put (time(), time.) ; put "end : " tim ; *** write end time to log ;
run ;
proc print noobs data=monkeys ; run ;
[ Edit; I've had to put some 'leading dots' in to create some degree of indenting - using the BB code 'code' does not seem to work]
Yes, that one is very non-intuitive, even for statisticians - but nowhere near as non-intuitive as the "Monty Hall problem" - which has had eminent academic statisticians almost "coming to blows"
In both those cases, and many others like them, the way of convincing oneself (or others) that the non-intuitive answer is correct is by undertaking a simulation, like I did above.
Kind Regards, John
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Yep the Monty Hall one got me, I could not get to sleep properly for three nights cos I hadn`t solved it.
So I gave up.
A couple of weeks later, shaving with mirror I looked at myself and solved it whilst not thinking about it. Simples. Blooming heck!
So I gave up.
A couple of weeks later, shaving with mirror I looked at myself and solved it whilst not thinking about it. Simples. Blooming heck!
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