SoylentNews is people
SoylentNews
Arthur T Knackerbracket has found the following story:
One of the most striking features of quantum theory is that its predictions are, under virtually all circumstances, probabilistic. If you set up an experiment in a laboratory, and then you use quantum theory to predict the outcomes of various measurements you might perform, the best the theory can offer is probabilities—say, a 50 percent chance that you'll get one outcome, and a 50 percent chance that you'll get a different one. The role the quantum state plays in the theory is to determine, or at least encode, these probabilities. If you know the quantum state, then you can compute the probability of getting any possible outcome to any possible experiment.
But does the quantum state ultimately represent some objective aspect of reality, or is it a way of characterizing something about us, namely, something about what some person knows about reality? This question stretches back to the earliest history of quantum theory, but has recently become an active topic again, inspiring a slew of new theoretical results and even some experimental tests.
If it is just your knowledge that changes, things don't seem so strange.
To see why the quantum state might represent what someone knows, consider another case where we use probabilities. Before your friend rolls a die, you guess what side will face up. If your friend rolls a standard six-sided die, you'd usually say there is about a 17 percent (or one in six) chance that you'll be right, whatever you guess. Here the probability represents something about you: your state of knowledge about the die. Let's say your back is turned while she rolls it, so that she sees the result—a six, say—but not you. As far as you are concerned, the outcome remains uncertain, even though she knows it. Probabilities that represent a person's uncertainty, even though there is some fact of the matter, are called epistemic, from one of the Greek words for knowledge.
This means that you and your friend could assign very different probabilities, without either of you being wrong. You say the probability of the die showing a six is 17 percent, whereas your friend, who has seen the outcome already, says that it is 100 percent. That is because each of you knows different things, and the probabilities are representations of your respective states of knowledge. The only incorrect assignments, in fact, would be ones that said there was no chance at all that the die showed a six.
-- submitted from IRC
(Score: 2) by VLM on Wednesday May 03 2017, @01:56PM (10 children)
OPs coming from a philosophy of classical mechanics where randomness seems very inappropriate or strange because in classical mechanics it would in fact be pretty strange strategy to stick a rnd() function in there.
"We'll talk about quantum stuff but I don't agree with it, so I'll call it 'strange' or whatever"
Like when you talk to kids about how zero point nine repeating equals one, some with strange flexibility problems won't wrap their minds around that but will come up with some fairly creative narratives to avoid them.
Its actually like mentioning hate-facts to lefties, you tell them the sky is blue and you'll get the craziest narrative to avoid double plus ungood badthink.
(Score: 2, Disagree) by Gaaark on Wednesday May 03 2017, @04:21PM (9 children)
but zero point nine repeating ISN'T one, it is only rounded to one.
If you take a piece of string and keep cutting it in half, it will never be eliminated as there will always be more to cut in half.
Errm, at least until you get beyond the quantum level.... errrrr.....
MAN, IT'S POINT NINES ALLLLLLL THE WAY DOWN!!!!
--- Please remind me if I haven't been civil to you: I'm channeling MDC. ---Gaaark 2.0 ---
(Score: 1) by khallow on Wednesday May 03 2017, @05:38PM (1 child)
If you take a piece of string and keep cutting it in half, it will never be eliminated as there will always be more to cut in half.
The obvious rebuttal is that you have to consider the final stopping point, not the intermediate points. The remaining string bit keeps getting shorter and shorter without bound as you keep cutting it in half. There is no shortest string of positive length because you can keep cutting it in half to get shorter strings. Similarly, no matter how long your starting string, you can keep halving its length until it's shorter than any string of a fixed positive length with further halving leaving the string below that length. It is only when you get to zero length that the process stops.
We're not speaking of finite processes, but infinite ones. If you can show that your sequence of numbers gets and permanently stays arbitrarily close to a particular number, then the limit of that sequence, which is the value of an infinite decimal number, is the particular number. That is how you get zero point nine repeating exactly equal to one.
(Score: 2) by Azuma Hazuki on Thursday May 04 2017, @03:56AM
Since space, time, and energy are quantized, you'll eventually hit the Planck limits. In the case of the piece of string, once you get down to a single molecule of cellulose or lignin or whatever, you can't cut it any further because it would then not be made-of-the-stuff-of-which-a-string-is-made...
I am "that girl" your mother warned you about...
(Score: 0) by Anonymous Coward on Wednesday May 03 2017, @06:06PM (3 children)
I know at least four ways to show that 0.999 repeating is equal to 1.
One is the limit method mentioned already.
Another is to show that 0.999... is equal to 9/9 which is equal to one.
Another is to show that for any two real numbers, there are an infinite number of numbers between them, and there is no room between 0.999... and 1.
Another is to subtract 0.999... from 1 and show that it is 0.
There are probably others.
(Score: 2) by Gaaark on Thursday May 04 2017, @12:45AM
And yet it is not one, quite.
Example: to run your computer, you need EXACTLY 1 unit of power. Giving it .99999999 repeating will not power it. What use is your computer.
But my computer goes to 11, so I don't care. ;)
--- Please remind me if I haven't been civil to you: I'm channeling MDC. ---Gaaark 2.0 ---
(Score: 1) by toddestan on Thursday May 04 2017, @12:52AM (1 child)
The easiest I found to understand is that 1/3 = 0.333.....
And strictly speaking, 0.333.... * 3 = 0.999....
But we also know that 1/3 * 3 = 1
Therefore, it also follows that 0.999... = 1.
(Score: 2) by Azuma Hazuki on Thursday May 04 2017, @04:00AM
This is an argument over bases rather than quantities from the looks of it. When I was studying computers and figuring out binary, it was a shock and a revelation to figure out that some decimal numbers straight up cannot be represented in any reasonable number of bits in a floating-point type. Immediately it hit me that the decimal system was *not* immune to this simply because it's familiar to us.
All this comes back to epistemology eventually, it seems...
I am "that girl" your mother warned you about...
(Score: 2) by VLM on Wednesday May 03 2017, @06:35PM
If you take a piece of string and keep cutting it in half, it will never be eliminated as there will always be more to cut in half.
A better analogy is you take point three repeating and divide it by point nine repeating of string, you divide them and the repeating cancels out and you get 3/9 or 1/3, right? Well, point three repeating is supposed to be 1/3 so thats chill, right? I mean you've done a couple decimal places of the long division, right? I mean just humor me for a minute that dividing my point nine repeating is OK..
So you try again add a third with point six repeating and divide it by point nine repeating, you divide them and the repeating cancels out and you get 6/9 or 2/3, right? Well, one third plus one third usually comes up as two thirds, so no surprise.
So you try one last time add one more third resulting in point nine repeating (where have I seen that before?) divided by point nine repeating and the repeating cancels out and you get 9/9 or oh snap...
There's a certain implication above that you can't divide by anything but 1 and get the original result back, so doesn't that imply that dividing by point nine repeating always gets the original result back? But the only number that works for is dividing by one, anything smaller gives a bigger result and anything larger gives a smaller result, so the separation between one and point nine repeating is infinitely small, lets say... zero? Implying they're the same thing.
I'm too tired to play the analogy game where you chop a length point nine repeating length of string out of a length 1 piece of string and that itty bitty remainder of string, whatever you claim it is, has properties indistinguishable from zero, so apparently point nine repeating equals one because the gap between is a zero. The hard part of this analogy is convincing someone you're constructing the point nine repeating segment of the string correctly.
(Score: 0) by Anonymous Coward on Wednesday May 03 2017, @08:54PM
Zero point nine repeating can be one [youtube.com], or maybe not. In the immortal words of Bill Clinton, it depends upon what "is" means.
By the way, an infinite number of mathematicians walk into a bar. The barkeep asks them what they want. The first one orders a pint. The second one orders a half a pint. The third one orders an eighth of a pint. The fourth opened his mouth to give his order, but the barkeep says, "Nevermind" and he puts two pints on the bar and walks away.
(Score: 3, Informative) by HiThere on Wednesday May 03 2017, @11:34PM
You are assuming that space-time is continuous, and this not only hasn't been proven, I find it a dubious assumption.
OTOH, when the pieces get small enough you won't be able to tell the pieces of string from the virtual particles.
Javascript is what you use to allow unknown third parties to run software you have no idea about on your computer.