
Friday, 13th January, 2012, 02:01 AM #11
ah, now we enter the subject of math, or that which I am not an expert.
If you were going to pay me $20 if a six showed up on any of the dice that I might roll, and then allowed me to roll 1 or more dice at the same time, I would of course choose to roll more dice, so as to improve my chances.
Thus thinking that, somebody once pointed out that I was wrong, and that regardless of how many dice I rolled, the actual chance of a 6 showing up on any of them remained 1 in 6. I thought that was ridiculous, until I ran all the iterations and confirmed it (remember, not a math guy).
I would certainly accept that my primitive experiment was flawed (I wrote a bit of code to loop and count the occurances). But it seemed to confirm what the somebody said and demonstrated through a bit of math.
so here is your chance to mathematically resolve the matter. I'm interested in seeing it done correctly.
(and yes, the thread has forked, but I think the mystery of the dice does relate to life on other planets as a matter of analogous statistics)

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Orcus on an OffDay (Lvl 22)
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ø Ignore Morrus
You don't need to calculate it. Just think through the logic. I'm curious as to what your friend thinks all those one million d6s are showing.
If, as he claims, you will get the same number of 6s, there will be one 6, a 5, a 4, a 3, a 2, and a 1.
What's on the other 9999993 dice if not a 1,2,3,4,5, or 6?
What he probably meant was that the chance of any specific dice being a 6 will still be the same. The chance of you getting a 6 on any dice, though, is extremely close to certainty.
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ø Ignore Kaodi
I was at a nice talk once given (three years ago or so) by Seth Shostak, a SETI scientist, who predicted that we would locate other intelligent life in the galaxy within ten to twenty years depending on whether there were tens of thousands of other civlizations out there or just thousands.
Kaodi
Good name in man and woman, dear my lord,
Is the immediate jewel of their souls.
Who steals my purse steals trash; 'tis something, nothing;
'Twas mine, 'tis his, and has been slave to thousands;
But he that filches from me my good name
Robs me of that which not enriches him
And makes me poor indeed.
Iago, Shakespeare's Othello, Act III. Scene III. Lines 180186.
bear in mind, this was some years ago. the original premise was that regardless of the number of dice, the odds of a 6 showing up on a Nd6 remained one in six. In redoing the experiment with d2's (in excel), I think I see the mistake:
Assuming 1 is our winning number (easier to pick out)
All the permutations (or combinations one of those words means something similar but different and I can't remember which).Code:0 1 1d2 = 1 in 2 chance of a win 0 0 1 0 0 1 1 1 2d2 = 3 in 4 chance of a win 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 1 1 3d2 = 7 in 8 chance of a win
In any event, I think from the original conversation, the math got done and I lost my point because we looked at the occurances of the winning number, which did indeed remain consistent. But since the payout is about ANY of the dice having the winning number, that's not the answer.
So, thanks to Morrus, I can now see I was originally right (now quite some time ago) and can now be right again.
I'm not sure how that figures. If other planets got started about the same time as ours, life would probably progress about the same rate. Thus only in the last hundred years or so have we even begun to generate radio signals.
Thus our radio waves would at best reach a hundred light years. To be picked up by an equally advanced civilization.
Of course, not all planets got started at the same time, and mayhap our dinosaur overlords would be more advanced had the iceage not killed them.
But it seems pretty hopeful to assume 2 people, standing really far apart and operating on completely different time tables could hope to be looking at the right time the other is broadcasting.
not that I'm down on alien life. Just that I suspect it is a shot in the dark that we would have our ears open to listen for coyotes just when the coyote howls from another star happen to be reaching us.
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ø Ignore Umbran
Okay, when talking about probability, *exact* wording is important.
If you have one d6, there are 6 ways the die can come up, and one of them is a 6. So, chance of rolling a 6 is one in six.
If you have 2d6, there are 36 possible combinations. That's a small enough number that we can easily list them:
1,1 1,2 1,3 1,4 1,5 1,6
2,1 2,2 2,3 2,4 2,5 2,6
3,1 3,2 3,3 3,4 3,5 3,6
4,1 4,2 4,3 4,4 4,5 4,6
5,1 5,2 5,3 5,4 5,5 5,6
6,1 6,2 6,3 6,4 6,5 6,6
Of those 36 pairs of numbers, how many include at least one 6? The answer is 11.
So, the chance of getting at least one 6 on a pair of dice is 11 in 36. Just shy of one in three.
(The naive would say it is "A six on the first die or a six on the second die  an "or" means add probabilities, so it is 1/6 + 1/6 = 1/3. But that actually doublecounts the boxcars.)
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ø Ignore Kaodi
I suspect that is partially where the " thousands or tens of thousands " comes in.
But also remember, detecting other intelligent life may not be limited to detecting radio signals. Perhaps the thought is that if you know what you are looking for, there may be other ways to figure out if a planet and its neighbourhood have been doing something unnatural...
Kaodi
Good name in man and woman, dear my lord,
Is the immediate jewel of their souls.
Who steals my purse steals trash; 'tis something, nothing;
'Twas mine, 'tis his, and has been slave to thousands;
But he that filches from me my good name
Robs me of that which not enriches him
And makes me poor indeed.
Iago, Shakespeare's Othello, Act III. Scene III. Lines 180186.
Once it enters the realm of detecting by means of something clever, i reckon all bets are off.
The problem I note, simply by way of magic super telescope with perfect vision, is that what we're looking at now is a picture of a given star as it WAS, not it's present.
In the case of alpha centauri, if they just started watching us with a nice new scope, they may have noticed the ISS, the biggest piece of manmade space thing around.
If they had a "watch Sol" project running for the last 10 years, they had a pretty good chance of noticing it. But the farther away they are, and technologically in sync with us, by the time they CAN watch our planet, we may have died out, or are simply looking at the dinosaur age.
Both parties have to be aligned at the right staggered amount of time to be doing detectable things AND watching for detectable things.
It's kind of like you deciding to watch for model rockets being shot off in your neighborhood sometime this year and me deciding to shoot off a model rocket in your neighborhood this year.
if I launch in January, and you get the idea to start looking in June, you will never see it.
If you start looking in February and get bored by August (species die off) and I finally finish building my kit and launch in September, you will never see it.
Your only hope is that you start, before I launch (acounting for time elapse of signal to recieve) and are able to continue watching daily until I actually launch.
replace launching rockets with "detectable thing". Then consider the travel time for signal which means what you see is VERY old information that may predate the actual civilization on the planet. Plus the fact that each planet's life may start and develop at slower or faster paces such that they may have missed the window to be watching or watchable.
The star trek method of actually visiting planets and dropping off monitoring systems is probably more practical to detect life than watching/listening at stars.
I think the concept that every star likely has planets is very cool, but there are still too many variables for determining the likelihood or numbers of other possible intelligent life.
Of those 10 billion Earth sized planets, how many are in the "habitable" zone of their star...?
And for that matter, how accurate is our assumption of what the "habitable" zone of a star is...? So far, that assumption is based on a sample of 1...
And even if life is common, intelligent life (at least as we know it) may be extremely rare.
Some use the fact (at least fact to them) that we haven't already been contacted by an intelligent spacefaring species, variably as evidence for a lack of intelliegent life in the Galaxy, or proof of the impossibility of FTL, or that inteligent aliens all develop some sort of "Prime Directive".
There's just too many variables, which leaves most all ideas concerning this as mere assumptions...at least until we can get out their ourselves.
No, it doesn't.
The formula would look more like this:let's assume that if alien life exists, it probably starts on a planet.
Previously, it was asssumed most stars did not have planets.
Now that that's reversed, a galaxy with billions of stars equals nearly billions of chances for life.
There will still be plenty of stars that don't have the right planets. the % chance for a given star to have the right planet is probably the same.
But now the number of stars that get that chance went up.
though statistically, this may be one of those math fallacy things (the odds of a 6 showing up on a 1d6 is the same as using 2d6). More chances opportunities doesn't actually improve the overall odds.
X*Y=Z
Where X=the ratio of planets that do support life to those that don't (say, 1/6),
Y =the total number of planets,
and Z=number of planets sustaining life.
This would mean that the quantity of inhabited planets rises as the total number of planets do, but the ratio remains static.
YET, the actual probability is independent of our perspective; there is either a 0% chance that life exists on other planets, or 100%.
Last edited by Rune; Friday, 13th January, 2012 at 10:12 PM.
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