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Subject: Question about randomness.... rss

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sunday silence
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May sound like a silly question but here goes:

I often think about whether there really is such a thing as randomness or whether it is some construct that simply exists in our mind as we have no other way to explain/deal with this issue.. But whether it is real or not remains open, at least to me.

To expand on this concept; what if I ask you:

What is the smallest sequence out of a list of numbers in serial order that you can shuffle and still maintain that it is a "random" order?

I mean here are two numbers 1, 2. No matter what you do 1-2 or 2-1 they still seem like an ordered set to me.

What about 1-2-3? Can we make that random sequence; 2-3-1? hmm I dunnot it's hardly convincing.

So what do you think what is the smallest sequence of numbers that would appear to be in random order?
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2

Coin flip is a good example. Random result.

The fact that you know it *could* be heads or tails is irrelevent. You don't *know* it will be heads or tails. Therefore, 1-2 or 2-1.

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Markus Hagenauer jr.
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I agree: 2
As soon as ther can be more than 2 result, you have randomness
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Matt Davis
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What we perceive as random and what is actually random are often two entirely different things. I played Metropolys once. At the start of the game, you distribute some tokens around the board at random - I think every space gets one. So we put them out, and someone started objecting to the way they were put out since there were a couple of places where two tokens of the same type were adjacent. It didn't seem "random" to him. But in fact, a configuration where no two like tokens are touching is very difficult to achieve. It's rare and therefore unlikely to happen randomly.

From a mathematician's perspective, there is a certain order in randomness. If you ask a class to go home and flip a coin a hundred times in a row and write down the results, you can tell who actually did it, and who just wrote down a string of T's and H's that they thought looked good. The "cheaters" will do a whole lot of alternating back and forth:

THTHTTHTTHHTTHTHHTH

They will avoid long strings of the same result, as a rule. But if you flip a coin a hundred times in a row, you will almost certainly get 6 heads or 6 tails in a row at some point. And the chances of hitting a 7 in a row are not shabby. Does that look random? Not to us, but if you flip a coin enough times, it will happen.
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Ben Stanley
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Excellent reply by coolpapa. A single result can be random. Randomness is not subjective. It doesn't matter if it "seems" random or ordered, the question is how the result was obtained, whether through a random process or not.
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sunday silence
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but I was talking about a series of numbers. If I write down a series 1-2-3 that is considered random, then?
 
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*How* did you come up with 1-2-3? Randomly? If so, then 1-2 would be a smaller set and just as random.

Therefore, the answer is 2. Because a single itemed 'set' cannot be random, and 3 is more than 2.
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Matt Davis
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Think about it this way. There are 6 ways to write down sequences of three numbers.

1. 1-2-3
2. 1-3-2
3. 2-1-3
4. 2-3-1
5. 3-1-2
6. 3-2-1

If I roll a die to randomly select one of these and I roll a 1, then I have randomly selected the sequence 1-2-3. Assuming a fair die, it was just as likely as any of the others, and it was a random result.

Or maybe this way. We're about to play a game (Brass, say) and we need to randomize turn order for 3 people. So I grab the scoring markers, shake them up in my hands and throw them down the table - the person whose marker is farthest goes first, next farthest is second, and closest is third. Now, it just so happens that I end up going first, and the person to my left is second. This is saying that my entirely random scoring marker-throwing process chose the permutation 1-2-3. With true randomness, sometimes you do get things that don't appear random.

Now, I know your question is also about that perception, and I think the answer is never. I'm not sure we ever intuitively understand randomness - no matter how big the set is, we're just bad at it.
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Seth Owen
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coolpapa wrote:


Now, I know your question is also about that perception, and I think the answer is never. I'm not sure we ever intuitively understand randomness - no matter how big the set is, we're just bad at it.


It's not my field (but I read a lot ) and I believe that researchers who look into that sort of thing have demonstrated that people are hardwired to seek order and see patterns even when none exist. An obvious and ancient example are constellations. The visible stars are distrubuted more or less randomly acrss the sky and yet people saw patterns in them that allowed them to form constellations.

Because of this pattern bias people are poor judges of randomness (something casinos and card sharks exploit) and you can really only trust mathematically vetted randomness for practical use.

There are, of course, deeper philosophical debates over whether anything is truly random, but I think we can safely ignore those as far as their practical impact on gaming goes. If you're correctly rolling a fair die, the results are close enough to random for our purposes as gamers.
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Daniel Shultz
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Speaking about randomness I was recently at a Claude Shannon exhibit here in Berlin. He didn't think that people were a good source of exhibiting random behavior even when they tried so he built some 'mind reading' machines. I found a funny applet that you can try which displays this. Check it out:

http://www.cs.williams.edu/~bailey/applets/MindReader/

try clicking on the left or right side of the applet randomly and if the computer predicts which side you click on it will raise a little black bar. It's not so easy to keep it below 50%

(Claude Shannon was an amazing person btw. If you don't know anything about him you won't be sorry for looking into his life and works)
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Matt Davis
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guitarsolointhewind wrote:
Speaking about randomness I was recently at a Claude Shannon exhibit here in Berlin. He didn't think that people were a good source of exhibiting random behavior even when they tried so he built some 'mind reading' machines. I found a funny applet that you can try which displays this. Check it out:

http://www.cs.williams.edu/~bailey/applets/MindReader/

try clicking on the left or right side of the applet randomly and if the computer predicts which side you click on it will raise a little black bar. It's not so easy to keep it below 50%

(Claude Shannon was an amazing person btw. If you don't know anything about him you won't be sorry for looking into his life and works)


That's a fantastic link. Thanks.
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sunday silence
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well then can you explain to me why John Von Neumann and others spent so much time and energy trying to generate random numbers? I mean they seem to go to great lengths to create these and I type 1-2-3 and you say it's random.

So why didnt they just type 1,2 3, 4, .....10,0000 and be done with it??

Curiouser and curiouser.
 
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Matt Davis
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I think you're misunderstanding. Randomness is about the process, not the result. Here's an example. Let us assume for the moment that a random number generator is possible, and you ask it to choose a whole number between 1 and 6. (A d6 would be a very close approximation of such an experiment.) Do you agree that "4" is a very plausible outcome from this random number generator?

Now, consider asking this program to do the same thing for you:



Same result, but very non-random.

How about poker? A royal flush doesn't look random. There's a lot of order and structure in that set of 5 cards. But once in a (very great) while someone gets dealt a royal flush honestly and randomly. No one stacked the deck, it's just that sometimes you get dealt a good hand.

I perhaps was unclear with my discussion of students legitimately flipping coins or pretending to. It's not that one will never see HTHTHTHTHTHT... in a sequence of 100 coin flips, just that it's very very unlikely. When we're talking randomness, etc., it's all probability. Something that doesn't look random does cast doubt on the process involved, and make you wonder about it, but it's the process that matters.

1-2-3 is one possible outcome from a truly random process that puts the numbers 1,2,3 in a random order, just like 2-3-1 and 3-1-2 and the others. I think (though my understanding of the actual math involved is sketchy) that what von Neumann and the other inventors of Monte Carlo methods wanted was not one random outcome, but a bunch of them. It's like sampling methods for polling - ask 500 random people what they think about stuff and extrapolate. You want an actual accurate picture of what, on average, people think. Same with Monte Carlo stuff - you want an actual idea of what 100000 random inputs into such and such a function give you back.
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Matt Davis
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wargamer55 wrote:


It's not my field (but I read a lot ) and I believe that researchers who look into that sort of thing have demonstrated that people are hardwired to seek order and see patterns even when none exist.


What's even more exciting is that sometimes even in randomness, order and patterns have to exist. It's highly OT, but:

http://en.wikipedia.org/wiki/Ramsey_Theory
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Ryan Gatti
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sundaysilence wrote:
So what do you think what is the smallest sequence of numbers that would appear to be in random order?

While others have correctly pointed out that a sequence is random if the method to generate it is properly random (even though the resulting sequence may not appear random, and in fact, many sequences that appear random are less random than sequences that do not appear random, especially when values are allowed to repeat.), I think you're question is an interesting one.

You're not asking "what IS random," but "what APPEARS TO BE random?" (and more precisely, given a sequence of non-repeating elements, what is the smallest number of elements that can produce a series that doesn't appear to be formulaic?) Which are entirely different things.

I'd say you'd likely need at least 5 elements. You might be able to get away with 4, but there are few enough elements that one could likely come up with a formula to describe any of the 24 possible arrangements.

Do the following appear to be random?
25314
52413
14253
35241

None of them are, but I'd guess they appear to be random (especially if seen just by themselves).
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Clay
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wargamer55 wrote:


There are, of course, deeper philosophical debates over whether anything is truly random, but I think we can safely ignore those as far as their practical impact on gaming goes. If you're correctly rolling a fair die, the results are close enough to random for our purposes as gamers.


As a determinist, this was precisely the angle my post was going to take (That there does not appear to be any truly "random" events as we normally use the term), but I will concede that it has no practical impact on gaming.

So, to the OP, no, I don't think there is any randomness but there is definitely the perception of randomness. Being a perception, however, the tipping point at which something appears to be either random or not random probably varies slightly between individuals.

This may or may not help you.
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Russell Martin
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In principle, if I know the speed of rotation, angle of release, height of a die upon release, coefficient of friction of the surface I'm rolling it on, etc, etc, I could calculate to determine the number that would appear on a die. (I think the difficulty lies in being able to determine all of those things. ) Similarly, if I know the rotational velocity, initial speed of ascent, blah, blah, I should be able to calculate which side of a coin will appear after I toss it.

I recall going to a talk by Persi Diaconis (another interesting person to read more about the work he's done) wherein he described how, with the help of the physics department in his university, he built a coin flipping "machine" that would always (ok, well maybe 99.9% of the time) flip a coin and come up heads. (Or, I suppose, tails if you reverse the coin from the original loading position.) I think I also recall Diaconis claiming that he was able to flip a coin and get it to come up heads at least 75% of the time (or some sufficiently large percentage, I forget what exactly).

I'm sure with sufficient patience and practice, anyone could do the same thing if he/she wanted. It's a matter of physics.

Some things that I think demonstrate some randomness (at least to our untrained eyes)... the motions of a lava lamp and the least significant digit (after the decimal place, that is) of the Dow Jones industrial average (at least since they started using decimal numbers rather than multiples of 1/8).
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Ben Horner
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I think the definition of randomness is something like an event that can only be predicted probabilistically.

If you already have a sequence of numbers, you can't have randomness, just some measure (possibly subjective) of how well-mixed they are. You can only have randomness if you don't have a sequence yet, and then construct one in such a way that the end result can only be predicted probabilistically. The probabilities only exist before hand, once you've constructed the sequence, it's not random anymore, it's a 100% fact.

You could say that a sequence was randomly generated, but you couldn't say that it was "more random" than any other sequence.

From the examples given, I think the question may be more about a list being well-mixed or shuffled. Can you really mix a list of 3 numbers well? You will always have two numbers next to each other that are only one apart numerically, like the "1-2" in 3-1-2. If we jump up to 4, perhaps 2-4-1-3 is the most mixed? But there are obvious patterns there as well.

-Ben
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Ryan Gatti
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bhorner wrote:
From the examples given, I think the question may be more about a list being well-mixed or shuffled. Can you really mix a list of 3 numbers well? You will always have two numbers next to each other that are only one apart numerically, like the "1-2" in 3-1-2. If we jump up to 4, perhaps 2-4-1-3 is the most mixed? But there are obvious patterns there as well.

This is a good example of the natural bias and perception of randomness versus actually being random.

For example, if you asked 12 million people to arrange the numbers 1, 2, and 3 "randomly," the normal uniform probability distribution would predict that you'd get back approximately 2 million sets of each combination. (I'm using a very large sample set so that the averages should trend toward predicted probabilities. This is the Law of Large Numbers that large samples trend toward the expected values.)

However, human bias is likely to give you back something different. I would guess you'd get back very few 123 sequences, and probably fewer 132 and 321 sequences than you'd expect. The bulk of the results would likely be 213, 231, and 312. Obviously the sequential nature of 123 and 321 would make people less likely to consider these "random," even though these results should be equally likely to all others, if the results were truly random. You might also get a lot of 132 results, but I suspect people are hesitant to place the first item of a sequence in the first position when trying to be random.
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craw-daddy wrote:
In principle, if I know the speed of rotation, angle of release, height of a die upon release, coefficient of friction of the surface I'm rolling it on, etc, etc, I could calculate to determine the number that would appear on a die. (I think the difficulty lies in being able to determine all of those things. ) Similarly, if I know the rotational velocity, initial speed of ascent, blah, blah, I should be able to calculate which side of a coin will appear after I toss it.

I recall going to a talk by Persi Diaconis (another interesting person to read more about the work he's done) wherein he described how, with the help of the physics department in his university, he built a coin flipping "machine" that would always (ok, well maybe 99.9% of the time) flip a coin and come up heads. (Or, I suppose, tails if you reverse the coin from the original loading position.) I think I also recall Diaconis claiming that he was able to flip a coin and get it to come up heads at least 75% of the time (or some sufficiently large percentage, I forget what exactly).

I'm sure with sufficient patience and practice, anyone could do the same thing if he/she wanted. It's a matter of physics.

Some things that I think demonstrate some randomness (at least to our untrained eyes)... the motions of a lava lamp and the least significant digit (after the decimal place, that is) of the Dow Jones industrial average (at least since they started using decimal numbers rather than multiples of 1/8).


I'm not sure that fellow proved anything other than the well-known fact that if you cheat then you don't have randomness. Learning how to flip a coin so that it's 75% likely to give you a particular result is no different than a loaded die, putting your finger on the roulette wheel, stacking a deck of cards or other techniques that upset the random element.

As for the determinists out there, there's really no way to argue with you because your arguments are premised on a belief that's basically held on faith. As there is no way to actually know all the things that could theoretically affect the toss of a fair die there is no way to test your theory. You can't have a discussion about randomness or its cousin luck without a determinist chiming in within minutes. It's like flies and honey. Hence my attempt to preempt that line of discussion by noting that the POV exists. I don't think it has much constructive to add to the discussion, but there it is.

In some Army wargames I'm familiar with they used a pre-generated random number table so the players wouldn't have to roll dice (maybe to make it see less game-like. I don't know).

This sort of thing creates its own questions. In one sense, of course, its not random at all any more once it's been generated. All the numbers in the sequence are fixed. But from a player's point of view, they're the same as rolling dice. The player making the decision that's about to be resolved equally doesn't know whether the next result is a 10 or a 1 -- regardless of whether the result comes from rolling a die or looking at a tabular form that has series of 1s through 10s. It's effectively random either way.
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wargamer55 wrote:
As there is no way to actually know all the things that could theoretically affect the toss of a fair die there is no way to test your theory.


Perhaps I should have added another emoticon to my words. That was part of the point of my first emoticon and the reasons for the words "in principle", i.e. the point being how are you going to measure all those things accurately enough? People who try to cheat on roulette wheels using fancy computers can only really improve their odds of guessing about the quarter (or so) of the wheel where the ball will land as it's so difficult to accurately determine all of the rotational velocity, blah, blah, blah to do these sorts of calculations.


Perhaps I should also point to this page.

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

"[Diaconis] is particularly known for tackling mathematical problems involving randomness and randomization, such as coin flipping and shuffling playing cards."

"Professor Diaconis achieved brief national fame ... in 1992 after the publication (with Dave Bayer) of a paper entitled "Trailing the Dovetail Shuffle to Its Lair" (a term coined by magician Charles Jordan in the early 1900s) which established rigorous results on how many times a deck of playing cards must be riffle shuffled before it can be considered random according to the mathematical measure total variation distance."

"Does Anything Happen at Random?"
Speakers: Persi Diaconis and Daniel Fisher



Would it also help if I said that part of my research is on randomized algorithms? So I'm interested in how one could find good random numbers. (At least in theory, some of my work would rely on the ability to generate "good" random numbers.)

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

(P.S. I'm not a determinist, 'cause I believe in quantum mechanics, not that I understand the principles other than on a layman's point of view. ninja )
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rgatti wrote:

Do the following appear to be random?
25314
52413
14253
35241

None of them are, but I'd guess they appear to be random (especially if seen just by themselves).


They do not appear random to me. they appear contrived. Taking the first number and the difference between it and the next, you get:

25314 - No; +3/-2/-2/+3 See the pattern?
52413 - No; -3/+2/-3/+2 See the pattern?
14253 - No; +3/-2/+3/-2 See the pattern?
35241 - No; +2/-3/+2/-3 See the pattern?

ninja
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markgravitygood wrote:
rgatti wrote:

Do the following appear to be random?
25314
52413
14253
35241

None of them are, but I'd guess they appear to be random (especially if seen just by themselves).


They do not appear random to me. they appear contrived. Taking the first number and the difference between it and the next, you get:

25314 - No; +3/-2/-2/+3 See the pattern?
52413 - No; -3/+2/-3/+2 See the pattern?
14253 - No; +3/-2/+3/-2 See the pattern?
35241 - No; +2/-3/+2/-3 See the pattern?

ninja


Actually... Ryan are you a juggler? Because they're all valid 3 objects siteswaps.

25314 and 14253 are both the same pattern only started in different places. And the same goes for 52413 and 35241.

(btw Claude Shannon was also a juggler!)
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coolpapa wrote:
What we perceive as random and what is actually random are often two entirely different things. I played Metropolys once. At the start of the game, you distribute some tokens around the board at random - I think every space gets one. So we put them out, and someone started objecting to the way they were put out since there were a couple of places where two tokens of the same type were adjacent. It didn't seem "random" to him. But in fact, a configuration where no two like tokens are touching is very difficult to achieve. It's rare and therefore unlikely to happen randomly.

From a mathematician's perspective, there is a certain order in randomness. If you ask a class to go home and flip a coin a hundred times in a row and write down the results, you can tell who actually did it, and who just wrote down a string of T's and H's that they thought looked good. The "cheaters" will do a whole lot of alternating back and forth:

THTHTTHTTHHTTHTHHTH

They will avoid long strings of the same result, as a rule. But if you flip a coin a hundred times in a row, you will almost certainly get 6 heads or 6 tails in a row at some point. And the chances of hitting a 7 in a row are not shabby. Does that look random? Not to us, but if you flip a coin enough times, it will happen.
I agree, but I would put it this way: there is an order to non-randomness. The order in randomness is non-order.
 
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Ben Horner
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rgatti wrote:
bhorner wrote:
From the examples given, I think the question may be more about a list being well-mixed or shuffled. Can you really mix a list of 3 numbers well? You will always have two numbers next to each other that are only one apart numerically, like the "1-2" in 3-1-2. If we jump up to 4, perhaps 2-4-1-3 is the most mixed? But there are obvious patterns there as well.

This is a good example of the natural bias and perception of randomness versus actually being random.

For example, if you asked 12 million people to arrange the numbers 1, 2, and 3 "randomly," the normal uniform probability distribution would predict that you'd get back approximately 2 million sets of each combination. (I'm using a very large sample set so that the averages should trend toward predicted probabilities. This is the Law of Large Numbers that large samples trend toward the expected values.)

However, human bias is likely to give you back something different. I would guess you'd get back very few 123 sequences, and probably fewer 132 and 321 sequences than you'd expect. The bulk of the results would likely be 213, 231, and 312. Obviously the sequential nature of 123 and 321 would make people less likely to consider these "random," even though these results should be equally likely to all others, if the results were truly random. You might also get a lot of 132 results, but I suspect people are hesitant to place the first item of a sequence in the first position when trying to be random.


I think your example doesn't necessarily imply social bias, but rather a broad lack of knowledge of the definition of randomness... Unless you're saying that the actual definitions of words are those that are most commonly understood, but then the argument comes full circle, and there is no bias after all. :) (Since the result of the survey would give you the true answer to the question you asked.)

I think it's unlikely that a person could produce randomness, even if they fully understood what it meant, without introducing some external element that is actually random (such as a die). I think the human brain is geared much more toward learning, which is essentially in conflict with producing randomness. Even if you put two people together to play paper rock scissors, and based your "50/50" event off of which person won, I'm betting that the probabilities would shift, rather than remaining constant as each player tried to guess what the other player would choose. They would learn subtle tells ("the smirk that means rock"), and then realize their own tells, and use them to their advantage, or try to eliminate them etc...

I'm, of course, coming from the perspective that the mathematical definition of randomness is the one true definition, which is probably not fair. Perhaps this discussion is simply a matter of alternate definitions? Some (even most?) use the definition "lacking order", or something like that? I probably tend toward the mathematical definition since it makes the word objective and not subjective. I prefer questions that can be answered correctly, the same answer for everyone.

-Ben
 
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