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02/16/2011 03:12:33 PM · #301 |
Originally posted by eqsite:
The answer is a value that approaches, but never reaches, zero. For expedience sake, we tend to take the value as zero, but this only highlights the limitations of our mathematics when dealing with infinites. I know that you are looking for a static answer, and will say "what do you mean never reaches" - but that is the nature of infinity. |
Exactly, this is the "arbitrarily close" to zero conception. What this type of mathematical navel gazing really highlights is the limits of our tools of mathematical expression. Until Greene can figure out some method for falsifying the hypothesis, it's not science, just speculation.
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02/16/2011 03:21:15 PM · #302 |
| Regarding speculation, Greene says in that first chapter that the ideas in the book aren't scientific, in that there have obviously been no observations or experiments to confirm them. Multiple universes are at the moment the only way to explain the math resulting from current theories. |
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02/16/2011 03:24:50 PM · #303 |
Originally posted by eqsite:
OK, but if you say that you must wait an infinite amount of time for something to happen, then can you actually say that it ever happens? Not with any certainty. |
But you can't actually say that in never happened either. Not with any certainty. That's the compromise.
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02/16/2011 03:26:09 PM · #304 |
Originally posted by Louis:
Regarding speculation, Greene says in that first chapter that the ideas in the book aren't scientific, in that there have obviously been no observations or experiments to confirm them. Multiple universes are at the moment the only way to explain the math resulting from current theories. |
What? We're talking mathematics right now. I hope people understand that when I screamed out "I am right!" up above it was about the monkeys and the Hamlet, not about the multiverse and God as a highly intelligent being. |
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02/16/2011 03:26:16 PM · #305 |
Originally posted by DrAchoo:
Originally posted by eqsite:
OK, but if you say that you must wait an infinite amount of time for something to happen, then can you actually say that it ever happens? Not with any certainty. |
But you can't actually say that in never happened either. Not with any certainty. That's the compromise. |
Oh, I agree with that. You can't say either way. There is no guarantee. Ed's posts above make that clear mathematically. |
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02/16/2011 03:29:01 PM · #306 |
Originally posted by shutterpuppy:
Originally posted by eqsite:
Let's keep it simple and consider a coin toss. Let's say that I'm looking to get a heads - we know that the odds are 50/50. I toss it once and get a tails. Does that guarantee me that my next toss will be a heads? No. I toss it again and still have only a 50/50 chance of heads. I could toss it any number of times and get tails each and every time even though the odds are 50/50. The chances of that are small, but it can happen. I am never guaranteed of getting a heads. |
Not to endorse Greene, but Doc is correct on the pure math (setting aside all the practical problems such as heat death, etc.; and setting aside the pure non-scientific/non-falsifiable nature of such speculative hypotheses).
One can illustrate this by expanding on the coin-flip example:
Every time you flip the coin the odds of it landing on tails is 50/50. This probability does not change for any single flip of the coin. However, the probability that all flips of the coin will land on tails becomes increasingly small the larger the number of flips are made for any single set of flips. When the number of flips for the single set is increased to infinity, the probability that the coin will land on heads, rather than tails, at least one time reaches zero (or "arbitrarily close" to zero, as it is usually expressed). Thus, in any infinite, single set of coin flips there will be at least one flip that results in tails and at least one flip that results in heads.
Now we can move on to where it really gets weird.
Expand the infinite, single set of coin flips to an infinite set of infinite, single sets of coin flips. In the infinite, single set the probability that the set will result in all heads or all tails is zero. But in the infinite set of infinite, single sets the probability that at least one of the infinite, single sets of coin flips will result in all heads or all tails is 1. In fact, mathematically, because the set of coin-flip sets is infinite, it will result in an infinite number of sets of coin flips that are all tails and an infinite number of sets of coin flips that are all heads.
None of which makes Greene's multiverse conception any more practically probable or testable.
However, it does show why mathematics is the preferred scientific discipline for stoners. |
SP, your post makes me cry tears of joy. This is exactly what I am saying, and as of late have not been saying anything more. Thank you!
And I agree. Greene's multiquilted universe makes me shudder...
Message edited by author 2011-02-16 15:30:06. |
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02/16/2011 03:33:43 PM · #307 |
Originally posted by eqsite:
And I will counter my early post about .999... based on this: //en.wikipedia.org/wiki/0.999...
Apparently there are proofs that .999... does equal 1 - but it's a special case as .333... < .4 |
Ahh, I wasn't smart enough to see an actual wiki link for 0.999. Funny. Here we at least have wiki tell us:
In mathematics, the repeating decimal 0.999... which may also be written as 0.9, or 0.(9), denotes a real number that can be shown to be the number one. In other words, the symbols 0.999... and 1 represent the same number.
In the monkey example you can understand that there is an actual real number of tries in which we can say there is a 90% chance that the monkey will type Hamlet (a big number to be sure). But since we have an infinite tries, we can add another number of tries to make it a 99% chance. And then a number of tries to make it 99.9%...and then 99.99%...and then 99.999%. Do you see where I'm getting? If we believe wiki, "In other words, the symbols 0.999... and 1 represent the same number." , we can say the probability, with infinite time, is 1.
LOL. Another nugget of truth from that article. Doesn't this sound like us bickering here about God?
The equality 0.999... = 1 has long been accepted by mathematicians and taught in textbooks. In the last few decades, researchers of mathematics education have studied the reception of this equality among students, many of whom initially question or reject it. Many are persuaded by an appeal to authority from textbooks and teachers, or by arithmetic reasoning as below to accept that the two are equal. However, some are often uneasy enough that they seek further justification. The students' reasoning for denying or affirming the equality is typically based on their intuition that each number has a unique decimal expansion, that nonzero infinitesimal numbers should exist, or that the expansion of 0.999... eventually terminates. These intuitions fail
Message edited by author 2011-02-16 15:37:08. |
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02/16/2011 03:46:10 PM · #308 |
Originally posted by DrAchoo:
Originally posted by Louis:
Regarding speculation, Greene says in that first chapter that the ideas in the book aren't scientific, in that there have obviously been no observations or experiments to confirm them. Multiple universes are at the moment the only way to explain the math resulting from current theories. |
What? |
I was answering shutterpuppy. |
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02/16/2011 03:47:05 PM · #309 |
Originally posted by DrAchoo:
we can say the probability, with infinite time, is 1. |
Originally posted by DrAchoo:
The students' reasoning for denying or affirming the equality is typically based on their intuition that... the expansion of 0.999... eventually terminates. These intuitions fail |
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02/16/2011 03:48:59 PM · #310 |
An engineer and a scientist were placed at one end of a large room with a beautiful woman at the other end.
They were told that for each step they made toward the woman, each subsequent step would cover only half the distance of the previous one. The scientist turned and left the room in acknowledgment that he would never reach the woman. The engineer saw the scientist's action, shrugged and took a very large step toward her. When asked (on his journey), why he took the large step when it was clear he would never reach the woman he replied, "Yes, but I will get close enough to get the job done!". |
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02/16/2011 03:49:15 PM · #311 |
Originally posted by Louis:
Originally posted by DrAchoo:
Originally posted by Louis:
Regarding speculation, Greene says in that first chapter that the ideas in the book aren't scientific, in that there have obviously been no observations or experiments to confirm them. Multiple universes are at the moment the only way to explain the math resulting from current theories. |
What? |
I was answering shutterpuppy. |
Oh, sorry Louis. My apologies. |
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02/16/2011 03:50:21 PM · #312 |
Originally posted by scalvert:
Originally posted by DrAchoo:
we can say the probability, with infinite time, is 1. |
Originally posted by DrAchoo:
The students' reasoning for denying or affirming the equality is typically based on their intuition that... the expansion of 0.999... eventually terminates. These intuitions fail |
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Are you viewing these as contradictory? They, in fact, support each other. Read the 0.999 article on wiki. |
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02/16/2011 03:56:59 PM · #313 |
| As for the monkeys, I will defer to shutterpuppy's post. Given an infinite set of infinite sets of monkeys, there will be an infinite set that do succeed, and an infinite set that don't. The question is, what is the probability that your set of monkeys is in either set. I can't do that math, but I would conjecture that the probably that your set of monkeys is successful is the original probability of any set being successful. Thus the infinities cancel themselves out. That is purely conjecture though. |
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02/16/2011 04:04:01 PM · #314 |
I would just like to take a moment to honestly say I was very offended when Louis declared me to be hubric and Shannon declared I was an "idiot". I entirely understand the limitation of my ability to explain a concept, and to that extent it is my fault. BUT, when arguing about the probabilities of infinity, I was arguing a mathematically sound and truthful concept. Just because you cannot see it at the time does not make me hubric or an idiot.
I'm not posting this to "bitch slap" both of you, but rather just to plead for some respect in these conversations. There are moments, however few they may be, when I do know what I'm talking about, even if I cannot articulate it so you can see.
Carry on...
Message edited by author 2011-02-16 16:04:47. |
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02/16/2011 04:08:01 PM · #315 |
| Please. Maybe if you didn't treat people like children, you wouldn't think they acted like them. |
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02/16/2011 04:14:32 PM · #316 |
Originally posted by DrAchoo:
when arguing about the probabilities of infinity, I was arguing a mathematically sound and truthful concept. Just because you cannot see it at the time does not make me hubric or an idiot. |
The probabilities of infinity do not mean my sparrow example will EVER occur. The odds themselves approach zero (infinity) in any meaningful sense. |
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02/16/2011 04:24:13 PM · #317 |
I was thinking of analogies to the Simian Shakespeare scenario. And here's one; I set up an LCD screen, and feed it random electronic noise, such that each pixel can display any colour at any brightness.
So I sit there, and watch... How long will it be until the pixels arrange themselves into the Mona Lisa? - Or until I get each movie frame of Citizen Kane generated? Probability tells me it's possible. But in reality I could sit there forever and it would never happen (or, like the monkey example I could be on the closing scene of Citizen Kane and one of the pixels is out of place... Fail!) |
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02/16/2011 04:29:36 PM · #318 |
Originally posted by DrAchoo:
I would just like to take a moment to honestly say I was very offended when Louis declared me to be hubric and Shannon declared I was an "idiot". I entirely understand the limitation of my ability to explain a concept, and to that extent it is my fault. BUT, when arguing about the probabilities of infinity, I was arguing a mathematically sound and truthful concept. Just because you cannot see it at the time does not make me hubric or an idiot.
I'm not posting this to "bitch slap" both of you, but rather just to plead for some respect in these conversations. There are moments, however few they may be, when I do know what I'm talking about, even if I cannot articulate it so you can see.
Carry on... |
I'll admit I had a really negative reaction to that post too -- it was quite brusk, Doc, you have to admit. But I can see how it was not intended in the high-handed manner in which it was interpreted.
Such are the perils of online discussion. Same conversation in person, over a beer there likely would have been no offense. (Or, we would have fallen into a brawl long ago. Whichever.) |
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02/16/2011 04:35:38 PM · #319 |
Originally posted by scalvert:
Originally posted by raish:
The chances of any being or thing evolving into something and knocking out the works of shakespeare along with a good few other pearls the bard never quite got round to, in an infinite time span, are 100% |
It's actually zero percent. The model rests on several dubious assumptions that must all be true.
1: Infinite time spans are possible (time apparently began at a finite point)
2. The outcome is possible (a cow will never jump over the moon)
3. Monkeys are random generators. (they're not) |
Sorry my phrasing was imprecise.
The chances of any being or thing evolving into something and knocking out the works of shakespeare along with a good few other pearls the bard never quite got round to, given an infinite time span, are 100%
I can see that the given thing is hardly giveable in any practical sense, but who said anything about practical sense?
The trouble with dismissing infinity on the grounds of its not being an applicable condition, is that mathematical concepts do not essentially require a criterion of tangibility. You can't put two identical things on the table, so let's drop the equals sign and revise all mathematics and all knowledge based on it, in accordance with the new axiom that all equations are false. |
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02/16/2011 04:54:30 PM · #320 |
Originally posted by shutterpuppy:
I'll admit I had a really negative reaction to that post too -- it was quite brusk, Doc, you have to admit. But I can see how it was not intended in the high-handed manner in which it was interpreted.
Such are the perils of online discussion. Same conversation in person, over a beer there likely would have been no offense. (Or, we would have fallen into a brawl long ago. Whichever.) |
Thanks SP. I am human. I get frustrated. Mostly with myself. I can imagine the hell of someone with aphasia who knows what they want to say but just can't get their lips to make the words. I had tried to explain the concept in, what, three or four different ways and it was obvious that it wasn't working. I was probably just crying out in exasperation, "Please trust me! I am correct, but I don't know how to say it!" I agree online conversations rob us of a lot of ability to nuance.
It actually still doesn't look like everybody quite gets it, but I need to learn just to let it go. I can sometimes see true hints of compulsive behaviors in myself and I don't like it (but it doesn't make them easier to ignore).
A virtual beer raised to you sir! Last night, while playing poker I had a Stone Russian Imperial Stout and it was heady stuff! (10.5% alcohol content)
Message edited by author 2011-02-16 17:09:56. |
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02/16/2011 05:04:03 PM · #321 |
Sorry I missed your point too, Doc. It just wasn't coming across to me. I'm glad you're not an arrogant idiot after all :-)
R. |
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02/16/2011 05:08:47 PM · #322 |
Originally posted by Bear_Music:
...I'm glad you're not an arrogant idiot after all :-)
R. |
Well, the probability of that isn't, in fact, zero... :) |
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02/16/2011 05:23:01 PM · #323 |
Originally posted by DrAchoo:
I need to learn just to let it go. I can sometimes see true hints of compulsive behaviors in myself . . . |
Hints? ;)
Originally posted by DrAchoo:
A virtual beer raised to you sir! Last night, while playing poker I had a Stone Russian Imperial Stout and it was heady stuff! (10.5% alcohol content) |
When the temp drops down into the nether regions of the thermostat, a good stout makes waiting for spring a lot more enjoyable. However, the weather here has warmed up a touch here of late - the locals call it the "deep winter thaw" - and in celebration I had a pint of your hated IPA myself from a local brewery, Two Brothers Resistance IPA, to be exact. Lifts my (nonexistent) soul. |
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02/16/2011 05:33:57 PM · #324 |
Originally posted by DrAchoo:
I had tried to explain the concept in, what, three or four different ways and it was obvious that it wasn't working. I was probably just crying out in exasperation, "Please trust me! I am correct, but I don't know how to say it!" |
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02/16/2011 05:54:44 PM · #325 |
| Oh man JH, I need to turn that into a t-shirt... |
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