Did A Few Million Virtual Monkeys Randomly Recreate Shakespeare? Not Really

from the not-yet dept

Slashdot alerts us to a report that a guy who set up a few million virtual monkeys trying to recreate Shakespeare — a la the infinite monkey theorem — has succeeded in recreating its first work of Shakespeare. Specifically, it’s A Lover’s Complaint, which is a narrative poem that was apparently published as an appendix to a book of Shakespeare’s sonnets.

Of course, looking over the details, I’m a lot less impressed than I thought I would be. My understanding of the “infinite monkeys” idea was that you had those million monkeys typing away, and in some potentially near-infinite amount of time, one of them would actually craft the works of Shakespeare. Or, at the very least, that multiple monkeys would individually create the different works of Shakesepeare. But as far as I can tell from the guy’s description, it sounds like he’s taking any 9-character segment that matches any 9-character segment of a Shakespearean work and declaring the segment it “done.” The process continues, filling in other random 9-character segments, until the entire work is done. That’s not nearly as impressive. What would it take to get virtual monkeys to write an entire work of Shakespeare in one go? Or even just one sentence? That seems like a much more challenging problem… so this one is actually a bit disappointing.

In the meantime, as one of the articles about this project notes, when real monkeys were given real typewriters:

“Not only did the monkeys produce nothing but five pages consisting largely of the letter S, they began by attacking the keyboard with a stone, then proceeded to urinate and defecate on it.”

So there’s that. But let’s see the virtual monkeys do something a little more advanced before we cheer them on.

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Comments on “Did A Few Million Virtual Monkeys Randomly Recreate Shakespeare? Not Really”

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120 Comments
Richard (profile) says:

Re: Re: Re:

Although…if some magic computer could do such things quickly…bye bye copyright.

The problem isn’t having it – it’s finding it.

We know (for example) that every work that could be reduced to digital form is encoded (somewhere) in the digits of pi – Finding it is quite another thing however – and you would have exactly the same problem with the monkeys!

Anonymous Coward says:

” My understanding of the “infinite monkeys” idea was that you had those million monkeys typing away, and in some potentially near-infinite amount of time, one of them would actually craft the works of Shakespeare.”

There are moments like this that I am sure that you didn’t get your degree the normal way, because this is one of those basic things that gets talked about somewhere along the line. It’s really surprising to see a line like that coming from the guy who pushed “infinite distribution”, but apparently doesn’t understand the implications.

It’s a question of odds. The chance that a monkey writes the works of Shakespeare is really small, but given an infinite number of monkeys, and an infinite amount of time, even the smallest of chances mathematically becomes close 1:1.

You can read more about it here:

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

Sometimes I just have to shake my head for the things that you apparently just don’t grasp.

freak (profile) says:

Re: Re: Re:2 Re:

I think maybe he’s saying that it’s the odds that matter, not the part where we take the entire works of shakespeare all at once?

See, if you care only that the odds -> 1 over infinite time, then the size of the sample doesn’t matter.

Of course, if I assume he has any intelligence, it would be unfair to think he’s missed the point that much.

Anonymous Coward says:

Re: Re: Re:2 Re:

Please read again. Mike said “My understanding of the “infinite monkeys” idea”. I think it is clear that Mike doesn’t understand it completely, because his understanding just isn’t right.

I understand that he has qualms (or perhaps he is troubled by) the methods used by this guy. My point is only that when Mike says “My understanding of the “infinite monkeys” idea” and then gets it wrong, I have to wonder why he is calling the other guy out, and I also wonder what else he has “understood” so poorly.

Anonymous Coward says:

Re: Re: Re:

It’s because Mike basically stripped away the infinite on both sides (which is the only way this one works out). He limited it to a million monkeys, and then applied a “near infinite” time limit. Given both of those things, the chances that they produce the works of Shakespeare (or even a poem from talentless schmuck marcus carab) are much less than 1:1 – they are almost nil.

The infinite monkey idea is as much to do with the power of infinite squared as anything else, and proof that even a small statistical chance (the chance that a single money in front of a single typewriter would type shakespeare on the first try), and run it to it’s very end. Once you go infinite on it (and in this case infinite squared) the chances mathematically are effectively 1:1.

Mike’s limiting on it in his “understanding” shows a complete lack of understanding of what is and what is not important in the theorem.

freak (profile) says:

Re: Re: Re:4 Re:

*sigh*

I guess I should be fair to you.

Pure Math doesn’t care about the implementation, so you’re still wrong there.

However, when something will have taken ‘near-infinite time’, it means that it is an achievable thing, but that there exists potential to never achieve it, whereas something that takes infinite time never will be achieved, even if the result reaches the desired result at infinity.

In this case, Mike is right for using ‘near-infinite’. It does not take infinity for monkeys to write Shakespeare. To guarantee that every possible group of monkeys write Shakespeare, however, takes infinite time.
We are not looking to guarantee that monkeys can infallibly write Shakespeare in this case; We are looking to get monkeys to write Shakespeare. So ‘near-infinite’ is in fact, correct, since at some finite point in time, the monkeys, no matter which group of monkeys you pick, will have written all of Shakespeare.

For something to which ‘near-infinite’ does not apply, look at the series, Sigma(1/2^i, i=0, i++). (1 + 1/2 + 1/4 + 1/8 . . .).
At no point less than infinity, does that series equal 2.

darryl says:

Re: Re: Re:5 Re:

*SIGH*

However, when something will have taken ‘near-infinite time’, it means that it is an achievable thing, but that there exists potential to never achieve it, whereas something that takes infinite time never will be achieved, even if the result reaches the desired result at infinity.

no, that is ‘very hard to do’ or “almost impossible” or “statictically very small”, NOT, NEVER “near infinite”

Marcus Carab (profile) says:

Re: Re: Re:3 Re:

Dude if you are still trying to googlebomb me with “talentless schmuck” you can’t go accidentally using the word “talent” like that – you are just confusing the algorithms! Get your act together! I’m really eager to hit the top – I’ve got a tweet ready to send out and everything. I think I might even use it as a song title.

Marcus Carab talentless schmuck, Marcus Carab talentless schmuck, Marcus Carab talentless schmuck…

Gabriel Tane (profile) says:

Re: Re: Re:4 Re:

Step 1: Produce some type of talent-based content
Step 2: Piss off some random, anonymous trolls
Step 3: Wait for said trolls to pull a reverse Streisand Effect on your content by trying to insult you with it by repeating it over and over, thus increasing the likelihood that search engines pick up on your name
Step 4: Profit! (Profit= enjoy the fact that your content now has greater notoriety).

Epic, man! I love seeing the manipulation of fools.

Marcus Carab (profile) says:

Re: Re: Re:5 Re:

Heh. You’ve already made it pretty clear that Googlebombing be is what’s on your mind. Now, maybe you should stop hijacking techdirt comment threads for your silly personal vendetta against me. You had brought me up in three comments before I even looked at the site today – what, did you toss and turn all night waiting to get your pathetic little claws into me again? Seriously dude, this is unhealthy.

Richard (profile) says:

Re: Re: Re: Re:

It’s because Mike basically stripped away the infinite on both sides (which is the only way this one works out). He limited it to a million monkeys, and then applied a “near infinite” time limit. Given both of those things, the chances that they produce the works of Shakespeare (or even a poem from talentless schmuck marcus carab) are much less than 1:1 – they are almost nil.

What rubbish you spout. The expectation value of the time taken to generate the works of Shakespeare by a random process is very long – but it is NOT repeat NOT infinite. You can calculate it.

There are 884,429 words in Shakepeare’s works – average (say) 6 characters gives a total of around 6 Million characters given 30 choices per character and 1 second to type a character gives an expeactation value of around 30 to the power 6 million seconds for the time taken to produce Shakespeare’s work. This is a very long time – BUT NOT INFINITE.

The Groove Tiger (profile) says:

Re: Re: Re: Re:

Actually, Mike got it right.

It doesn’t matter if it’s one monkey or a million monkeys (since having a single monkey using “near infinite time” is no different than different monkeys using even less time. It’s called manpower. Or in this case, monkeypower.).

The idea that a million monkeys can write random groups of letters that can then be pasted together to become a work of Shakespeare (or several) is as bad as having a single monkey writing random groups of letters at separate intervals then having a third party pick and choose until he has a complete work (or several).

The theorem actually appears to indicate that an entire work should be typed (and any letter out of place would ruin the work, needing to start over). A single complete play should have been typed continuously.

Otherwise, it would take a TINY amount of time for a computer just generating every keypress of the keyboard (or of the alphabet. If I type the entire sequence from A to Z, numbers and punctuation a thousand times, of course I’ll have At the very least written every possible work that contains a thousand letters or less). How long does it take a computer to press the entire keyboard a billion times? Now all you need is a human picking the relevant letter from each group in the right order and we have every book ever written.

(this sounds suspiciously similar to what Shakespeare would do if given a ton of letters to work and he had to arrange them in the right order).

So yeah, in other words, just more of the same caustic bashing from you.

Mike Masnick (profile) says:

Re: Re: Re: Re:

The infinite monkey idea is as much to do with the power of infinite squared as anything else

I find this statement absolutely hilarious when you realize it’s in the same thread claiming that *I* don’t understand infinity.

Anyone who talks about the power of “infinity squared” needs to start again.

darryl says:

Re: Re: Re:2 Re:

if you use terms like “near infinity” it is a clear indication that you do not understand infinity at all.

What this man was talking about (that went right over your head) is:

INFINITE SQUARES

or INFINTE LATIN SQUARES

or just a Latin Square

Infinite Latin Squares
A Latin square of order n is an n?n array of n symbols in which every symbol occurs exactly once in each row and column of the array

Rudy Rucker poses the following problem:

“I have five fingers on my left hand,” means the same thing as, “When I count up all the fingers on my left hand, the last number I say is five.” What might “I have ∞ fingers on my left hand” mean?

The answer is that it would mean you have infinity-plus-one fingers. A curious thing about infinity is that you never count up to it. You count through every finite stage but never reach the last finger. If there is an “∞ finger”, then it comes after an infinity of fingers and indicates that you have infinity fingers plus one more (which you named ∞).

Do you understand infinity now Mike ????

Richard (profile) says:

Re: Re: Re:3 Re:

Now we know you are mad.

You pick up a few mathematical terms – almost at random since they don’t relate to the problem at hand. Then you assert (with no evidence) that the a/c Mike was replying to (who had probably never heard of that stuff anyway) was talking about them.

btw – when Mike said “near infinite” he was not speaking in precise mathematical terms – but the phrase “near infinite time” can quite properly be taken to mean a finite time that is sufficiently long that for practical purposes it might as well be infinite. This is precisely the case here.

cc (profile) says:

Re: Re:

You are totally clueless.

There are various formulations of this problem, and what Mike says is indeed correct. You could even have a single monkey typing away for infinite time, if you want. You don’t need both infinite time and infinite monkeys.

The moral of the story is that as the number of monkeys tends to infinity, the amount of time needed tends to zero (1 attempt — and vice versa). Infinite monkeys would produce the works of Shakespeare immediately. And of course, given a sufficiently long amount of time it’s almost certain that even a single monkey could do it.

freak (profile) says:

So . . . in 5.4 trillion passes, he’ll be guaranteed to be done? (Actually, substantially less than that, if I think about it)

Wait, why did this take him so long? This is much less computationally expensive then, say, a rainbow table of 9 characters, and that was doable back in the early 80’s.

Ah, right, randomness, he’s repeating a lot of his work. Statistically then, it’s still taking him a lot of time to even get this result. Makes me think his algorithm isn’t very good . . .

Dexter (profile) says:

Nope,

that’s definitely not the way “infinite monkeys” goes.

The complete work has to appear in a single contiguous random stream (i.e., one of the individual monkeys)….which means that eventually (in an infinite time), not only would the fully correct “A Lover’s Complaint” be produced, but also every possible version of the poem with one wrong character (including all the versions with every possible wrong character in each possible position), every possible version with two wrong characters, and so on.

As for this guy’s method: I can get there much faster. Just use single character segments…

darryl says:

Only infinate thing here is stupidity.

I have seen this experiment on a TV doco, and he is exactly right, obviously he cannot have an infinate number of monkeys, even virtual ones.

So this experiment is to determine the concept of the experiment, and to guage how close to ‘infinate’ does it require to create a complete work.

Obviously the number is going to be VERY HIGH, so instead of trying to engage an infinate number of monkeys over an infinate time, he has defined a finate number of monkeys over a finate time.

You can then determine for example that if 1000 virtual monkeys work for 1000 hours to achieve a 9 character section of the bard’s work, then you can extrapolate that to find out how many monkeys and for how long it would take to create a full passage.

It has nothing to do with trying to come up with the complete work, that is not the objective, the objective is to find out HOW MANY and for HOW LONG, would it really need.

Have you totally given up on education in the US ??

What are they teaching you these days ?

also be aware if it was a true ‘infinate’ number you would get an infinate number of exact complete works of shakespere, and a complete SET of every work he has done, as well as a complete set of works that everyone else has done, or will ever do.

Which is totally meaningless, what this guy is setting out to do, is to find the REAL number that is less than infinate that would be required to product a complete work.

It is not going to be infinate, therefore it is going to be finate, large but not infinate.

But judging by the level of education by most of the commenters here I do not expect many to understand this, simple concept…

Thinking and ‘brainwork’ is not something the world see’s America as a leader in.

darryl says:

near infinity is infinite - 1 is 'near infinite'

In this case, Mike is right for using ‘near-infinite’

No he is not,,,,

‘near-infinite’ is infinite

infinite – infinite = infinite
infinite / infinite = infinite

near infinite = infinite

10/3 = infinite

every number is ‘near infinite’ as you can have an infinite number of ‘numbers’ between 1 and 2 for example.

Therefore 1 is ‘near infinite’.

if you have ‘infinite’ time, the monkeys will evolve into an infinite number or shakesperes, after all the original sharkespere is an example of a FINITE number of monkeys working randomly at a keyboard.

freak (profile) says:

Re: near infinity is infinite - 1 is 'near infinite'

I don’t usually even read your posts, but this one was particularly stupid. It nicely demonstrates troll-logic though, in that you reach the opposite conclusion of the original troll.

I’m one course away from graduating with a degree in Pure Math. I am now studying Computer Science.
I understand infinity and related concepts; not as well as most mathematicians, maybe, but I doubt you are anywhere close.

Do you know what aleph null is? What a power series is? Hyperreal numbers? Can you tell me, or prove to me, the difference in density between integers and rational numbers? Can you show the cardinality of two sets are equal?

No? Anyways . . .

No, near-infinite is the right term, although a pure mathematician would never have reason to use it, a computer scientist would.

If you would argue that near-infinite = infinite, you’ve missed the definition.
If you would argue that no number is near-infinite, then you’ve missed the definition as well, since near-infinite does not apply to any number you can name.

My proof that the Monkeys are in fact, a near-infinite time, is this:
Give me a single number of iterations, after which we can guarantee that your group of monkeys have written Shakespeare.

Here, nicely numbered and stuffs:
1) To guarantee that the monkeys type Shakespeare requires infinite time
2) Any group of monkeys will finish in a finite time
3) That finite time is unnameable; no matter what number you name, a group of monkeys can take longer to type Shakespeare. Because the upper limit is infinity, (see point 1), the number can always be larger.
4) So the monkeys represent a number that is finite, but with an upper limit at infinity, thus, near-infinity.

1 has an upper limit at 1, 10^100 has an upper limit at 10^100. An arbitrary number has an upper limit at itself.

TL;DR: Unless you care to name a number that is larger than any arbitrary number, and less than infinity, you’re wrong.

(Also, I might have already had this typed up in the case that the AC replied. :troll:)

darryl says:

Re: Re: near infinity is infinite - 1 is 'near infinite'

I’m one course away from graduating with a degree in Pure Math. I am now studying Computer Science.
I understand infinity and related concepts; not as well as most mathematicians, maybe, but I doubt you are anywhere close.
Do you know what aleph null is? What a power series is? Hyperreal numbers? Can you tell me, or prove to me, the difference in density between integers and rational numbers? Can you show the cardinality of two sets are equal?

Can you ???

I am an electronics engineer, in my line of work, and throught my career I have used quite a bit of math, (a HUGE amount).
Therefore, my skills are in practicle or APPLIED math, so yes I am aware of thigs such as set theory, I understand infinite I think more clearly than you claim you do.

I know all about real and complex and imaginary number, vectors, ‘rate of change’, integration, and differentiation.

Here is a question for you:

How many real numbers exist between the numbers 1 and 2 ??????

Would the set of real numbers that exist between 1 and 2 be greater than or smaller than or the same size as the set of real numbers between 3 and 4 ???

how many sets of real numbers do you think exist ?

would those sets exceed the number of real integers ?

are the integers 1, 2, 3 or 4 ‘near infinite’ OR
do they form a part of an infinite set ? or infinite sets???

is the result of 10 divided 3 and infinite number ?

is ZERO (0) near infinite, or is it infinite, is it even a number ???

can you conceive that anything that is “near infinite” is itself infinite?

is there a special math symbol for ‘near infinite’ ?

Have you heard your professors use that term or seen them derive a ‘near infinite’ proof ?

is it a countable or uncountable infinite set of numbers, either real, integer or imaginary?

Would not a series of sets created by an infinite group (monkeys) over infinite time also be infinite ?

Would an infinite number of combinations of letters created over infinite time result in an infinite number of combinations, therefore all combinations would be created instantly.

do you use ‘estimations’ like “near” and “far” or “big” or “small”, or “close too” when you are working on a pure math problem ?

How often have you had a “near infinite” result ?

My proof that the Monkeys are in fact, a near-infinite time, is this:
Give me a single number of iterations, after which we can guarantee that your group of monkeys have written Shakespeare.

What, that is your proof !!!

Define “a single number of iterations”??

So if I give you a single number, like 10 trillion or 10^trillion gogols, is that number “near infinity”.

I do not think you have grasped the concept of infinity at all !!!.

A VERY big number, no matter how big, is not and will NEVER BE ‘near infinity’.

And you call yourself a ‘would be’ math grad !!!!

Now let me take a wild guess, you are the product of the US education system right ??

1 is as “near infinite” as 100,000,000,000,000, billion, trillion, trillion and 1

no matter what the number is, you have to go an infinite way to be infinite, therefore no finite number is ‘near infinite’ every number (including infinity itself) is an infinite distance away from infinity… (and every other number !!).

Maybe that is the course you have not done yet !

also set theory “infinity” and ‘normal infinity’ are (as you should know two different entities, which is why you are so tied up with ordinal’s and cardinal’s, and “transfinite numbers”.

but when you look into it, as you know (having claims you have studied this) I do not see the term “near infinite” in ANY texts.

My proof that the Monkeys are in fact, a near-infinite time, is this:
Give me a single number of iterations, after which we can guarantee that your group of monkeys have written Shakespeare.

How do you propose to ‘prove’ that ‘single number’ no matter how large is “near infinity” ??

or, DISPROVE, that any single number is not an infinite distance away from infinity.

freak (profile) says:

Re: Re: Re: near infinity is infinite - 1 is 'near infinite'

Allow me to pre-face my reply with this quote, from myself, from the post you replied to:

“If you would argue that near-infinite = infinite, you’ve missed the definition.
If you would argue that no number is near-infinite, then you’ve missed the definition as well, since near-infinite does not apply to any number you can name.”

“Can you ???”

Yes. Would you like some examples?

“I am an electronics engineer, in my line of work, and throught my career I have used quite a bit of math, (a HUGE amount).
Therefore, my skills are in practicle or APPLIED math, so yes I am aware of thigs such as set theory, I understand infinite I think more clearly than you claim you do.”

The more I read of your posts, the more I doubt your qualifications. The proof, they say, is in the pudding, and I’m quite willing to show you my pudding.

“I know all about real and complex and imaginary number, vectors, ‘rate of change’, integration, and differentiation.”

Congratulations, you can pass a 1st year math course.

“Here is a question for you:

How many real numbers exist between the numbers 1 and 2 ??????”

The answer is Aleph 1; otherwise known as “unaccountably many”.

“Would the set of real numbers that exist between 1 and 2 be greater than or smaller than or the same size as the set of real numbers between 3 and 4 ???”

Exactly the same size; Proof: F(x):f->g = x + 2

“how many sets of real numbers do you think exist ?”
I’m not sure what you intend to ask; your question is poorly defined in several ways.
To answer the most useful question, the powerset of the set of real numbers has cardinality aleph 2.

“would those sets exceed the number of real integers ?”
See problem with previous question.
Would the size of the powerset of real numbers exceed the size of the set of real numbers? Yes. Alpeh 2 > Aleph 1

“are the integers 1, 2, 3 or 4 ‘near infinite’ OR
do they form a part of an infinite set ? or infinite sets???”
No nameable number can be near-infinite, since a near-infinite number is one which can only be described as a range, with infinity as the upper bound.
Would you like a strict definition?

“is the result of 10 divided 3 and infinite number ?”
no.

“is ZERO (0) near infinite, or is it infinite, is it even a number ???”
Zero is clearly a number, and is not near-infinite or infinite.

“can you conceive that anything that is “near infinite” is itself infinite?”
Can I imagine something which contradicts it’s own definition?

“is there a special math symbol for ‘near infinite’ ?”
Is there a special symbol for ‘arbitrary’? How about ‘random’? What if I want to differentiate between the different types of random?

“Have you heard your professors use that term or seen them derive a ‘near infinite’ proof ?”
In computer science, we do look at problems which require near-infinite time, how to recognize them, and how create algorithms which minimize the expected time & memory. They also take advantage of this subject to introduce us to how to manage memory & CPU usage properly. IE: to make a maximum that the program will not exceed.

“is it a countable or uncountable infinite set of numbers, either real, integer or imaginary?”
Is what? Near-infinity?
Besides all the other stupidity around the question, this implies that you think that infinity is a set of numbers?
As it is, I cannot discern what this question is intended to mean, or even make a best guess.

“Would not a series of sets created by an infinite group (monkeys) over infinite time also be infinite”
∞ * ∞ = ∞

“Would an infinite number of combinations of letters created over infinite time result in an infinite number of combinations, therefore all combinations would be created instantly.”
Would somethign created over an INFINITE amount of time be created in an INFINITESIMAL amount of time?
errrr . . . no.

But you probably meant to ask, that if we had infinite monkeys creating combinations, would all combinations be created infinitesimally? The answer is still no! All combinations would be created in the time it takes a single monkey to make a single combination.

“do you use ‘estimations’ like “near” and “far” or “big” or “small”, or “close too” when you are working on a pure math problem ?”

Ever hear of ‘neighbourhoods’? Yeah, we do.
And there’s this whole area of pure & applied math, called Statistics, which hinges completely on ‘good enough’.
Estimations, as it happens, has nothing to do with it.

“How often have you had a “near infinite” result ?”

When I’m trying to find out how long a problem will need before it can be solved by an algorithm? Often enough to need to know how to recognize and deal with it.

“My proof that the Monkeys are in fact, a near-infinite time, is this:
Give me a single number of iterations, after which we can guarantee that your group of monkeys have written Shakespeare.

What, that is your proof !!!

Define “a single number of iterations”??”

An iteration = the amount of time it takes a monkey to punch a single key.

The single number then, is the number of keys each monkey will have pressed when they have written shakespeare.
So, give me a number of keys, such that if the monkeys have pressed that number of keys each, then one of them will have written shakespeare.

“So if I give you a single number, like 10 trillion or 10^trillion gogols, is that number “near infinity”.”

No, they would not be. After 100^^^googleplex,(knuth arrow notation), there will still be groups of monkeys who have not finished, so those smaller numbers also do not fulfill the question.

“I do not think you have grasped the concept of infinity at all !!!.”

I can form well-defined questions about it at the very least, which puts me head and shoulders above yourself.

“A VERY big number, no matter how big, is not and will NEVER BE ‘near infinity’.”

I agree, that conflicts with the definition of near-infinity.

“And you call yourself a ‘would be’ math grad !!!!

Now let me take a wild guess, you are the product of the US education system right ??”

I never called myself that; I said I had one course left to graduate. For all you know, I’ve tried that course several times, and failed each time. As it is, I’ve never tried it, since I decided that I wasn’t ready for the masters level, and that I’d rather be studying a field related to complexity theory. Thus computer science.

Also, I’m German-Canadian.

“1 is as “near infinite” as 100,000,000,000,000, billion, trillion, trillion and 1

no matter what the number is, you have to go an infinite way to be infinite, therefore no finite number is ‘near infinite’ every number (including infinity itself) is an infinite distance away from infinity… (and every other number !!).”

See the quote at the top of the reply, would you?

“Maybe that is the course you have not done yet !”

The course I haven’t done yet is General Topology.

“also set theory “infinity” and ‘normal infinity’ are (as you should know two different entities, which is why you are so tied up with ordinal’s and cardinal’s, and “transfinite numbers”.”

Depends on what you mean by ‘normal’ infinity. Definition, please?

“but when you look into it, as you know (having claims you have studied this) I do not see the term “near infinite” in ANY texts.”

*pulls “Data Structures & Algorithms: Edition 5” from the shelf*
Page, 488, on bogosort:
” . . . this algorithm will run for near-infinity, but has an expected value that scales with N!. If the infinite universes theorem of Quantum Physics is true, then the algorithm can take advantage of the infinite universes by running once, and then destroying any universe in which the list is not sorted. This is known as the quantum bogosort, and the result will be a sorting algorithm that scales linearly, even after using infinite computational power, so that is clearly the lower bound for sorting efficiency of an unknown list of known size.”

Bogo-sort:
http://catb.org/jargon/html/B/bogo-sort.html

“My proof that the Monkeys are in fact, a near-infinite time, is this:
Give me a single number of iterations, after which we can guarantee that your group of monkeys have written Shakespeare.

How do you propose to ‘prove’ that ‘single number’ no matter how large is “near infinity” ??

or, DISPROVE, that any single number is not an infinite distance away from infinity.”

The point, which I’ll say again for your benefit, is that no single number will fulfill the conditions set forward in my question.

Now, let’s see if you posted something new while I was typing this up.

freak (profile) says:

Re: Re: Re:2 near infinity is infinite - 1 is 'near infinite'

Long post, so a few errors:

“The answer is Aleph 1; otherwise known as “unaccountably many”.”
Unaccountably should be Uncountably.

And heck, why not give a strict definition?
Near-infinity refers to a number that is:
a) Always larger than an arbitrary number.
b) Finite
c) Has an upper-bound at infinity.

The next question we should have, is, Is this definition useful? Does it describe something that exists?

Compare three cases.
I)Each day, I earn half of what I did before, starting on day 1 with $1. When will I have $2?
II)Each day, I enter a free lottery for a grand total of $2. When will I have at least $2?
III)Each day, an infinite number of people enter a free lottery for $2. When will they all have at least $2?

Now, do you agree that II describes a finite number? Do you agree that after some finite period of time, I will have $2? But, before that day comes, are you able to pin down a day by when I will have $2 with absolute certainty?
A day beyond which, there is exactly 0% chance that I will not have won?

So, we have a finite period of time which cannot be described as a number, is always larger than any arbitrary number, and has no upper limit/has an upper limit at infinity.

Answers:
I) Infinity
II) Near-Infinity
III) Infinity

Since the 2nd problem has meaning in a finite world, and the other two do not, Near-infinity is a useful term.

darryl says:

Re: Re: Re:3 near infinity is infinite - 1 is 'near infinite'

And heck, why not give a strict definition?
Near-infinity refers to a number that is:
a) Always larger than an arbitrary number.
b) Finite
c) Has an upper-bound at infinity.

so an upper bound of a finite number can be infinite !!!! and therefore infinite!!

how can a finite number have an infinite number as it’s upper bound ?

why does an arbitrary number always have to be smaller than a ‘near infinite’ number, can an arbitrary number have an infinite upper bound as well ?

Arbitrary Number
What is it? A number which could be any number it is defined to be but for which no specific value is chosen. It is often used in proofs since it can represent any number but does actually have the value of any number so that the proof applies to more than one situation

The more you say, the less people will think you are such a top math guy, you are clearly showing a clear lack of understanding of even the most basic concepts.

freak (profile) says:

Re: Re: Re:4 near infinity is infinite - 1 is 'near infinite'

Try this; in the monkey problem, the number by which all monkeys will have written Shakespeare is within the range
[1, infinity), correct?

“why does an arbitrary number always have to be smaller than a ‘near infinite’ number”

Because that’s the definition.

“Can an arbitrary number have an infinite upper bound as well”
Yes, but unlike a near-infinite number, an arbitrary number is a specific number, even if which specific number it is is not defined. In contrast, a near-infinite value cannot be defined to be a specific number anymore than infinity can.

freak (profile) says:

Re: Re: Re:5 near infinity is infinite - 1 is 'near infinite'

I feel I was being unclear.

An arbitrary number has a limit of itself on the lower, and itself on the upper.
An arbitrary number is itself.

In picking an arbitrary number, you have no limits on either end.

The result is that you can pick any number upto infinity, and it can be an arbitrary number.
But the arbitrary number, being a specific number with an upper limit of itself, as all specific numbers do, is always lower than infinity, and near-infinity.

If you pick a number of consecutive tries on a lottery, there is always the possibility that you will not win the lottery by that number of consecutive tries.

darryl says:

Re: Re: Re:6 near infinity is infinite - 1 is 'near infinite'

But the arbitrary number, being a specific number

like it both ways ???

BY DEFINITION:

A number which could be any number it is defined to be but for which no specific value is chosen.

you see how ‘arbitrary’ and ‘specific’ are two opposing terms.
At the same time as trying to convince us that you are some kind of math wizz!!.

There is not alot of hope in trying to reason with someone who thinks an arbitrary number is a specific number.

Again, are you an indication of the quality of the US education system ?

freak (profile) says:

Re: Re: Re:7 near infinity is infinite - 1 is 'near infinite'

“A number which could be any number it is defined to be but for which no specific value is chosen.”

From your definition.

Which means an arbitrary number is a number that represents a specific number, but for which no number is chosen.

If you can’t understand subtle english, which you’ve shown you can’t, (actually, can you understand english?), then I’ll have to give a fuller explanation.

An arbitrary number is a number that is fixed before the equation, regardless of the fact that it is not a specific value, it represents a specific value.

We mostly deal with fixed numbers in math. Numbers that aren’t fixed are tricky to deal with, and require a different set of non-trivially resolving rules.

Consider this. I have an infinite amount of objects. 50% of them are round. 50% of them are square. I add a square object. It’s still 50% round objects. I add an infinity of square objects. It’s still 50% round objects. Half of all the round objects are also flat. So 25% of the objects are round and flat. If I randomly pick an object from amoung these infinity objects, it has 1/4 chance of being round and flat. If I take out an infinity amount of round objects, I still have a 1/4 chance of getting a round and flat object. If I take out all round and flat objects, I now have a 33% chance of picking a round object. The amount of objects I took out when I took out all round and flat objects is exactly equal to the the number of objects I took out when I took out an infinity amount of round objects.

These are non-fixed numbers. Arbitrary numbers can never achieve these characteristics, because you have to be able to pick a number that an arbitrary number represents, you just never do pick a number that it does represent.

So, let’s break it down:

A) We know it is a finite value because the monkeys stop after a finite time.
Agree?

B) We know that it is larger than any number you could pick because the monkeys could go on further than that number.
Agree?

C)Any number you could pick = arbitrary number, agree?

darryl says:

Re: Re: Re:5 near infinity is infinite - 1 is 'near infinite'

Try this; in the monkey problem, the number by which all monkeys will have written Shakespeare is within the range
[1, infinity), correct?

NO, not correct it will be a number between 1 and some large but NOT infinite number.

But no matter how big the number is it is an infinite distance away from infinity.

freak (profile) says:

Re: Re: Re:6 near infinity is infinite - 1 is 'near infinite'

Mhm.

And here we see you not knowing basic APPLIED math notation. Which, let me check, YES, is part of standard electrical notation.

[] indicates a limit including the number.
() indicates a limit excluding the number.

So [1,2] indicates a number such that 1 <= x <= 2,
while (1,2) indicates a number such that 1 < x < 2.

And [1, infinity) indicating a number such that 1 <= x < infinity.

So, I’m glad to see you agree with me.

Scott says:

Comparison

Not that this wasn’t a fun thing to do in the cloud, but the way it is being presented is way out of scope. His monkeys aren’t generating the entire Works of William Shakespeare from start to finish, but pulling together character strings 9 chars long, and seeing if they fit into the works of Shakespeare anywhere. The choice of 9 characters is (as far as I can tell) completely abstract: Explanation of the ramifications…
First, he has stated that he has generated 5 trillion strings since August 21, a rate of 135 billion strings per day.
Assuming a total of 62 characters (upper & lower case, 10 punctuation chars) there are 62^9 possible strings = 1.3537e16. The amount of time for him to hit every single string is 100,518 days.
If, on the other hand, he had broken up Shakespeare into 5-char chunks, there would be 62^5 strings = 916 million, which he could generate in about 9.7 minutes.
On the other hand, if left in one piece the Simpsons phrase quoted in the article “it was the best of times, it was the blurst of times” is 52 characters long. In 9-character pieces it will be discovered in 100,518 days. If taken as a whole, it will be discovered in 64^52 attempts, which at a rate of 6.2e82 days. Assuming that the universe is 14 billion years old, this can also be expressed as….4.42 x 10^70 ages of the Universe.
I think Jesse Anderson is going to need a bit bigger cloud.

darryl says:

Infinite ignorance

the only thing I believe is “near infinite” would be what you do not understand or comprehend….

if you use terms like “near infinity” it is a clear indication that you do not understand infinity at all.

What this man was talking about (that went right over your head) is:

INFINITE SQUARES

or INFINTE LATIN SQUARES

or just a Latin Square

Infinite Latin Squares
A Latin square of order n is an n?n array of n symbols in which every symbol occurs exactly once in each row and column of the array

Rudy Rucker poses the following problem:

“I have five fingers on my left hand,” means the same thing as, “When I count up all the fingers on my left hand, the last number I say is five.” What might “I have ∞ fingers on my left hand” mean?

The answer is that it would mean you have infinity-plus-one fingers. A curious thing about infinity is that you never count up to it. You count through every finite stage but never reach the last finger. If there is an “∞ finger”, then it comes after an infinity of fingers and indicates that you have infinity fingers plus one more (which you named ∞).

Do you understand infinity now Mike ????

darryl says:

Learn to count (crawl) before you calculate (run)...


freak (profile), Sep 27th, 2011 @ 6:34am

Actually, “The Map Monkeys create random data in ASCII between a and z.”, from the linked article.

That’s where my 5.4 trillion unique passes comes from, since 26^9 is ~5.4 trillion.

waytogoboygeniuswhatdoyouthinkiswrongwithyourequation?

watch out America, another Math genius on the way.. (WITH SPACES)…

is 27^9 nearer to infinity than 26^9 is ?

Is there any requirement for you to be able to count for a degree in pure math these days ??

if it was ‘random ASCII’ characters it would be

128^9 as there are 128 (0 to 127) characters in the ASCII character set.
For a math genius, dont give up your day job!!!!

darryl says:

still 27 not 26 - Rookie error

If I create random data between a and z, how many characters are I creating?

Dont worry when you enter the ‘big’ world you will soon learn something about reality, until then you might be better off staying quiet.

you create 26 characters, and NOSPACES, does not matter how much random data you create, you do not create any more characters, and text is a combination of characters and spaces. (spaces are also characters in as ASCII, so if you are going to try to copy a passage of text, test that contains spaces and characters you then have to include those spaces into your equation, therefore 27 characters not 26..

Gabriel Tane (profile) says:

@Freak

Wow dude… thanks for the very kickass math lesson. I do love math theory!

But you’re arguing with darryl. My only advice is ‘don’t’… not because he’s ever (EVER) going to be more-right than you (or ‘right’ at all) but because he’s great at not just missing a concept, but actively ignoring a concept so he can be right about what he’s talking on.

To put it another way… darryl walks up to a couple of farmers comparing oranges. darryl overhears the farmers saying something like “hmm… oranges are quite orange this year…” and immediately chimes in with “NO! The apples are RED this year!! You’re wrong! Stupid American Farmer!”. And no matter how much you try to explain that you were comparing oranges, darryl will stand on his soapbox (applebox?) and proclaim how he’s right… the apples ARE red. And, of course, will continue to do so with horrible post-structure and abysmal punctuation.

I’m just as guilty about letting darryl out to run around and tossing the stick for him to chase, so I can’t really judge here πŸ™‚

Again, thanks for the kickass review of near-infinite. Totally going to discuss that with friends this weekend πŸ™‚

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