This one.
Wait that can't be right. I guess it doesn't have an answer. Wait, that means...
Thursday, July 29, 2010
Laci's Riddle
I checked the site:
http://lacigreen.blogspot.com/2010/07/anon.html
For the riddle.
"The answer is not simple, and the question has already been asked."
I think I solved it after a few seconds.
Highlight here for the answer: The riddle itself is the answer..
Alternatively: What's the answer? has a lot to recommend it.
St. Thomas Aquinus
I use to live near a school called that. I'm saddened I didn't know what his miracle was. It reminds me a bit of the woman who a Mother Teresa idol cured who was really cured by doctors.
Monday, July 26, 2010
Kepler is producing results...
Here's to one of the coolest stories of our lifetimes...
http://www.torontosun.com/news/world/2010/07/25/14822461.html
It's the first trickle of what could end up being a really awesome waterfall of awesome.
http://www.torontosun.com/news/world/2010/07/25/14822461.html
NASA has so far formally announced only five new exoplanets -- planets outside our solar system -- but early data analysis indicates up to 140 of the 700 identified bodies are earth-like. That is, they are solid masses containing both land and water which could allow simple lifeforms to develop.
It's the first trickle of what could end up being a really awesome waterfall of awesome.
Sunday, July 25, 2010
You run across silly things on the internet.
This plagued me for a good five hours one time before I finally gave up:
The plastic bit on the end of a shoelace is called an aglet.
http://en.wikipedia.org/wiki/Aglet
The plastic bit on the end of a shoelace is called an aglet.
http://en.wikipedia.org/wiki/Aglet
Saturday, July 24, 2010
Davy Crockett was born in the state of Franklin.
How strange. Davy Crockett was born in Franklin.
Now all I need to do is bide my time for half a decade until that factoid becomes that awesome thing I say and people wonder... "How does he know this stuff."
Now all I need to do is bide my time for half a decade until that factoid becomes that awesome thing I say and people wonder... "How does he know this stuff."
Sunday, July 18, 2010
Which came first, the chicken or the good science reporting.
http://news.sciencemag.org/sciencenow/2010/07/scienceshot-how-to-make-an-egg.html
Yes, Virginia there is real science reporting! After the terrible coverage the science got previously it's good to know somebody out there is doing it right. Thank you Phil Berardelli.
Researchers used a computer simulation to track the formation of eggshells, which are composed mostly of calcium carbonate. In the simulation, the OC-17 protein (illustration, left), which is found only in the hard part of the eggshell, clamps its molecular fingers onto a microscopic particle of calcium carbonate (right).
Yes, Virginia there is real science reporting! After the terrible coverage the science got previously it's good to know somebody out there is doing it right. Thank you Phil Berardelli.
Sunday: Atheist Experience episode 666.
4:30 to 6:00 pm CST (22:30-24:00 UTC). Atheist Experience 666 is set to air. It will be a historic event, very similar to the other 665 shows.
Saturday, July 17, 2010
Cognitive Dissonance, Monty Hall, and the nature of science.
Back in 2007, a study attempted to apply the theory of Cognitive Dissonance to monkeys. It lead to a good number of comments, made the NY Times, and got a good amount of comments on Slashdot.
So a monkey was shown to eat M&Ms pretty much equally and not much care. But, when forced to make a choice between two different M&Ms say red and blue, the rejected M&M when placed against green would be rejected at greater than the expected 1/2 outcome and was rejected closer to 2/3rds of the time. Thus proving the theory that they must have needed to rationalize the rejection and therefore valued the given item less than previously. When offered another choice, they were much less likely to chose that M&M which they rationalized themselves into not wanting anyway. Much like the Aesop Fable of the Fox and the Grapes who after thinking about it and realizing the grapes were unreachable, decided that they were also unripe and bitter.
Why do I bring this silly story up? Well, it has to do with the Monty Hall riddle. By the way, if you noticed the problem with the study, mad kudos to you. If you want, try to stop reading and figure it out (if you're well versed on the Monty Hall Riddle).
Well, it turns out that the odds for the second choice aren't 1/2, they are actually 1/3rds for the rejected and 2/3rds for the other. If there's a preference hierarchy at all there are a total of 6 different ways to rank the M&Ms.
RGB, RBG, BGR, BRG, GRB, GBR
If you are asked which you'd prefer red vs blue and you take the red, there are three possible hierarchies which could exist.
RGB, RBG, GRB - These are the only times that red is better liked than blue. And in these when offered B vs G, we find that 2 rank green > blue:
RGB, GRB. So the odds really are 1/3 that they should accept the rejected M&M if we go by pure raw statistics. The Social Psychologists who ran the experiment as well as the slashdot thread about it, which had highly rated comments about color vision in monkeys and possible flaws in methodology, etc. But, they like generations of social psychologists failed to spot this mistake. However, the flaw in the study was noticed by an economist, Dr. Keith Chen who subsequently published a paper about the flaw and the series of similar flaws that are seen throughout the field of Cognitive Dissonance all the way back to the early studies in the 1950s. And that the paradigm of "Rank, Choice, Rank" is always going to skew things because the choice changes the odds, even without any rationalization at all the first choice means the odds for the second question are different.
In fact, this same research is still going on. Supposing that if you could make the choice arbitrary enough, that it should somehow prove the point, and still it holds that if you use any metric at all (in that you don't simply flip a coin, or that if given the first choice again would more often than not choose the same way), you will find that if given and choice and then made to "chose between the rejected object and a third similar object." -- anything will prefer the third similar object 2/3rds of the time and studies with amazing datapoints like: "Both children and monkeys preferred the third object" are moot and expected by random chance and statistics.
So, an economist without any formal training in Social Psychology, Psychology, Cognitive Dissonance, or the various fields thereof offered a rather stunning rebuttal that properly refuted a fair amount of research from the 1950s to the present, and is undoubtedly correct. An economist offered a scientific refutation and demolished literally thousands of studies as an outsider. Think about this next time you hear anybody claim that atheists should study religion before trying to refute it. Or that science is simply dogmatic. It really is possible for somebody from the sidelines to kick the wall and destroy an entire house of cards. Science loves this! It doesn't matter who you are, you could be a 11 year old girl disproving therapeutic touch, or a balloonist explaining geophysics. The right answer wins. Sometimes it takes a few decades, sometimes it doesn't, but if you have the right answer then everybody else be damned. This is the debunking spirit atheists are accused of applying to religion and being wrong to do so. But, really it doesn't work that way. It doesn't matter how many texts you have on the bristliness of God's beard, if he's fictional then he's fictional.
"Any man more right than his neighbor constitutes a majority of one already." - Henry David Thoreau.
It doesn't take much to overthrow lies, it takes one boy to point and laugh and say that "the Emperor has no clothes". This is the nature of not only science but of truth. Lies cannot take the heat and it only takes a gentle wind to collapse a house of cards, so why should atheists be told to not go around blowing at the cherished beliefs of others? Are we to value the belief as worth more than the truth? In reality this is exactly what we are told. And ultimately this is the bane of skepticism and the birth of dogma. If one believes that wanting something to be true, makes it one iota more likely, then that is the only step you need to take in the wrong direction and suddenly any belief becomes acceptable because we are inclined to accept it. Restricting ones beliefs to those which are true, demands that we discount a lot of nonsense the chief-most being religion.
Those who would give up Essential Truth to purchase a little Temporary Comfort, deserve neither Truth nor Comfort.
Once a monkey was observed to show an equal preference for three colors of M&M’s — say, red, blue and green — he was given a choice between two of them. If he chose red over blue, his preference changed and he downgraded blue. When he was subsequently given a choice between blue and green, it was no longer an even contest — he was now much more likely to reject the blue.
So a monkey was shown to eat M&Ms pretty much equally and not much care. But, when forced to make a choice between two different M&Ms say red and blue, the rejected M&M when placed against green would be rejected at greater than the expected 1/2 outcome and was rejected closer to 2/3rds of the time. Thus proving the theory that they must have needed to rationalize the rejection and therefore valued the given item less than previously. When offered another choice, they were much less likely to chose that M&M which they rationalized themselves into not wanting anyway. Much like the Aesop Fable of the Fox and the Grapes who after thinking about it and realizing the grapes were unreachable, decided that they were also unripe and bitter.
Why do I bring this silly story up? Well, it has to do with the Monty Hall riddle. By the way, if you noticed the problem with the study, mad kudos to you. If you want, try to stop reading and figure it out (if you're well versed on the Monty Hall Riddle).
Well, it turns out that the odds for the second choice aren't 1/2, they are actually 1/3rds for the rejected and 2/3rds for the other. If there's a preference hierarchy at all there are a total of 6 different ways to rank the M&Ms.
RGB, RBG, BGR, BRG, GRB, GBR
If you are asked which you'd prefer red vs blue and you take the red, there are three possible hierarchies which could exist.
RGB, RBG, GRB - These are the only times that red is better liked than blue. And in these when offered B vs G, we find that 2 rank green > blue:
RGB, GRB. So the odds really are 1/3 that they should accept the rejected M&M if we go by pure raw statistics. The Social Psychologists who ran the experiment as well as the slashdot thread about it, which had highly rated comments about color vision in monkeys and possible flaws in methodology, etc. But, they like generations of social psychologists failed to spot this mistake. However, the flaw in the study was noticed by an economist, Dr. Keith Chen who subsequently published a paper about the flaw and the series of similar flaws that are seen throughout the field of Cognitive Dissonance all the way back to the early studies in the 1950s. And that the paradigm of "Rank, Choice, Rank" is always going to skew things because the choice changes the odds, even without any rationalization at all the first choice means the odds for the second question are different.
In fact, this same research is still going on. Supposing that if you could make the choice arbitrary enough, that it should somehow prove the point, and still it holds that if you use any metric at all (in that you don't simply flip a coin, or that if given the first choice again would more often than not choose the same way), you will find that if given and choice and then made to "chose between the rejected object and a third similar object." -- anything will prefer the third similar object 2/3rds of the time and studies with amazing datapoints like: "Both children and monkeys preferred the third object" are moot and expected by random chance and statistics.
So, an economist without any formal training in Social Psychology, Psychology, Cognitive Dissonance, or the various fields thereof offered a rather stunning rebuttal that properly refuted a fair amount of research from the 1950s to the present, and is undoubtedly correct. An economist offered a scientific refutation and demolished literally thousands of studies as an outsider. Think about this next time you hear anybody claim that atheists should study religion before trying to refute it. Or that science is simply dogmatic. It really is possible for somebody from the sidelines to kick the wall and destroy an entire house of cards. Science loves this! It doesn't matter who you are, you could be a 11 year old girl disproving therapeutic touch, or a balloonist explaining geophysics. The right answer wins. Sometimes it takes a few decades, sometimes it doesn't, but if you have the right answer then everybody else be damned. This is the debunking spirit atheists are accused of applying to religion and being wrong to do so. But, really it doesn't work that way. It doesn't matter how many texts you have on the bristliness of God's beard, if he's fictional then he's fictional.
"Any man more right than his neighbor constitutes a majority of one already." - Henry David Thoreau.
It doesn't take much to overthrow lies, it takes one boy to point and laugh and say that "the Emperor has no clothes". This is the nature of not only science but of truth. Lies cannot take the heat and it only takes a gentle wind to collapse a house of cards, so why should atheists be told to not go around blowing at the cherished beliefs of others? Are we to value the belief as worth more than the truth? In reality this is exactly what we are told. And ultimately this is the bane of skepticism and the birth of dogma. If one believes that wanting something to be true, makes it one iota more likely, then that is the only step you need to take in the wrong direction and suddenly any belief becomes acceptable because we are inclined to accept it. Restricting ones beliefs to those which are true, demands that we discount a lot of nonsense the chief-most being religion.
Those who would give up Essential Truth to purchase a little Temporary Comfort, deserve neither Truth nor Comfort.
Friday, July 16, 2010
Which came first the Chicken or the dumbass?
There's news coverage and then there's the horrible terrible idiotic beast that is science news coverage.
The latest and greatest of these is the "Chickens came before eggs scientists say!" Wow. That's stupid. And with all things stupid P.Z. Myers gives the smart view of them but when I heard my aunt say this the other day I was taken aback, beyond the fact that it's an idiotic thing to say the question really was solved by science a long time ago. Eggs predate G. Gallus by a few hundred million years, if you reframe the question to be "Chicken or Chicken Egg" then if you draw a line at any point between proto-chicken and chicken going back in generational time, you shall at some arbitrary point have a proto-chicken laying a chicken egg (even though they are both rightly the same species).
The article in question concerns that protein that binds calcium was found in chicken DNA and expressed in eggs. So a chicken lay an egg that was slightly harder than the egg it was hatched from? If the claim is therefore the chicken came first what did it hatch from? A proto-egg? And we are talking about proteins which predate chickens rather significantly. So some dinosaurs started laying harder eggs rather softer more reptilian eggs during the move to full time land use and therefore this very early dinosaur is the first chicken? Really? So chickens predate birds by a hundred million years or so?
Because we can't report on actual science without God particles or Missing Links being found, or overturning previously established science. No, we only get fed BS by morons about things they don't understand. Worse yet, the actual study in question is really cool, but to get any play the university released a press report that read like an idiot wrote it just to get some press coverage because press = money. It's a cycle that asks for the stupidest shit and gratefully provides it.
The latest and greatest of these is the "Chickens came before eggs scientists say!" Wow. That's stupid. And with all things stupid P.Z. Myers gives the smart view of them but when I heard my aunt say this the other day I was taken aback, beyond the fact that it's an idiotic thing to say the question really was solved by science a long time ago. Eggs predate G. Gallus by a few hundred million years, if you reframe the question to be "Chicken or Chicken Egg" then if you draw a line at any point between proto-chicken and chicken going back in generational time, you shall at some arbitrary point have a proto-chicken laying a chicken egg (even though they are both rightly the same species).
The article in question concerns that protein that binds calcium was found in chicken DNA and expressed in eggs. So a chicken lay an egg that was slightly harder than the egg it was hatched from? If the claim is therefore the chicken came first what did it hatch from? A proto-egg? And we are talking about proteins which predate chickens rather significantly. So some dinosaurs started laying harder eggs rather softer more reptilian eggs during the move to full time land use and therefore this very early dinosaur is the first chicken? Really? So chickens predate birds by a hundred million years or so?
Because we can't report on actual science without God particles or Missing Links being found, or overturning previously established science. No, we only get fed BS by morons about things they don't understand. Worse yet, the actual study in question is really cool, but to get any play the university released a press report that read like an idiot wrote it just to get some press coverage because press = money. It's a cycle that asks for the stupidest shit and gratefully provides it.
Thursday, July 15, 2010
It's 11:30 PM and 85 degrees F (30 C)
Jeepers. As much as I'd like some global warming denialists to suffer through heat waves for comeuppance, I'd like to not be around when it happens. I'd also like to see creationists get eaten by dinosaurs (non-avian ofcourse), but watch from a safe distance.
Wednesday, July 14, 2010
Rio 1992, some 12 year old gives a speech.
That was around the same time as I was 10 and wrote some crappy poem about the environment. I think the part I remember was:
Air pollution, water pollution, acid rain,
all of these problems are not the same.
They hurt our Earth, they hurt our environment.
Let's stop these problems before the Earth's retirement.
Today I have a carbon footprint the size of a Hummer, and an expectation that short of machines that extract CO2 from the atmosphere at a massive rate there's very little we can do to stop some of the most staggering environmental consequences.
Friday, July 9, 2010
Friday, July 2, 2010
He he he... Math is hard!
You call up a pet shop that you know has two puppies. You ask if at least one of the puppies is a male and they say "yes", what are the odds that the the other dog is also a male? Or rather that both dogs are male?
Interestingly I asked this question today and much to my surprise my sister got it right after a really short period of time. The answer is, oddly enough, one in three. Whereas almost everybody will say 50/50 and insist over and over again even if you just told other people who said that, that they were wrong.
There's a series of problems that fall into the same paradigm which are basically Monty Hall riddles, where known information is used to make a determination that change the odds from what we'd expect. And it turns out that *any* known information changes the odds. So when you picked Door Number 1 on the Monty Hall show and he opens Door Number 2, the odds that the prize is behind Door Number 1 is 1/3 and the odds that it's behind door number 3 is 2/3s. It's a strange math problem whereby the odds change because something is known about something else. Monty Hall wouldn't open the prize door. So we are given information that changes the odds.
In science, we start with a guess and then figure out what that guess would mean for the world and then check whether or not reality agrees with that guess. The most important step is that if reality is found to not agree that guess is wrong, it doesn't matter who suggested it or how interesting, beautiful, complex, simple or clever the guess is, it is wrong.
When we've checked a lot of things and find that we just can't prove this guess wrong over a very long period of time, it really does change the odds that that guess is correct, if we found a problem with the theory, it would be rejected. So when a scientific theory has withstood the test of time even if we are unaware of the particular tests it has withstood we can be more confident that it is true because being wrong would make it rejected. And if it's rejected, we can find a Monty Hall Door that hasn't been rejected yet which is almost certainly more likely to be correct, or with regard to scientific theory less likely to be wrong. Science is simply the least wrong guess we haven't managed to prove wrong yet. And we know it's the less likely to be wrong because we tried to prove it wrong and failed to do so thus far. This is why Einstein didn't dethrone Newton when his physics was accepted during the 20th century. Because up until then, Newton was the least wrong answer we had at the time. Now we have an even less wrong answer which can explain not only what Newton explains but more. To this end I highly recommend the Relativity of Wrong by Asimov.
The idea that knowing things about things change the odds falls a bit strangely into Hempel's paradox.
Hempel's raven paradox is basically stating that if we accept that we are given evidence to the statement "all raven are black" by the existence of a black raven, we should also accept that the existence of a green apple also provides evidence to the statement "all raven are black" because said statement is the same as saying "all non-black objects are non-raven objects" and a green apple confirms this given statement. The most accepted solution to the problem is to agree with the conclusion and suggest that the weight of evidence provided by green apples is very small because of the sheer range of non-black and non-raven objects. (As an amusing aside, there are albino ravens which are white). So really everything we know that fails to prove a statement wrong makes that statement a bit more likely to be true. Just as knowing that at least one of the puppies is male makes it slightly more likely that both puppies were male (after all we had a 1/4 chance of two male puppies before we confirmed that female/female wasn't an option). Failing to prove the theory male-male wrong by confirming female/female wasn't the case made the odds just a bit higher (though we seem to take the fact that at least one puppy is male to conclude one down, one to go and a 50/50 chance on the "other" puppy.)
The same is likely true with regard to evolution. A design is made more likely to be useful because an individual doesn't die when dying is possible. This is why the genotype (the DNA itself rather than what it codes for) which is insulated within the nucleus and doesn't interact with the outside world (there's transfer RNA and various other process that move this information around) can become very usefully complex and encode for very useful and functional proteins even though it has no access anything extra-nuclear. And this is also likely how our minds work by being able to make guesses about the world and by failing to be surprised by the wrongness of those guesses manage to build an internal view of the outside world without needing the eyes to take and process information (which is the model we are usually given). It simply isn't necessary to process information coming in from the eyes, there's only the need to see if that agrees with what we think it should be and react if we're wrong. You can build models of the outside world with guesses and checking if those guesses mesh with reality. That's the essence of science, evolution, and how our minds work. The part that understands, learns, encodes, works, theorizes, and discovers need not be actually connected to reality to understand it. It can simply trudge along failing to be wrong, and as a consequence become more reliable.
As a crazy person on the Daily Show once pointed out, either the LHC blows up the world or it doesn't. So the odds are 50/50. It's logic like this that makes me wonder how I could make money off such things.
---
If I roll two 6-sided dice and say that at least one of them is a 1. What are the odds that they are both 1s?
1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6
1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6
Because we know one is a 1, the odds that the other is a 1 is different than the typical 1/6 that people would tend to believe. Because we don't know which one was the 1 and there's only one possibility of snake-eyes (1-1).
1 1 1 1 1 1 2 3 4 5 6
1 2 3 4 5 6 1 1 1 1 1
These are the only possibilities and they are all evenly likely to occur. There's 11 of them and only in 1 of them are they both 1s. So knowing that at least one die is a 1 makes the odds that "the other one" (we don't know what other is because we don't know which is the principle one, and we should rather say "both of them") a 1 in 11 chance. We'd figure the odds to be 1 in 6, but really they are far longer than that and nearly double. This makes for a pretty good idea in a gambling game. I'll get some dice roll them somewhere, look and tell the other person what "at least one of them is X" and have them make wager that pays 8 fold that the other one is the same. They should think they are getting an advantage paying a 8X on a 1/6 chance when really they are getting paid 8X on a 1/11. I'll be rich!
Update:
Strangely due to the setup there the odds are actually 1/6. Since I would have to give information about what one die is, the chance that the other die is the same as X, is 1/6 or the odds that you roll doubles. Whereas you have twice as many things to have the dice be if you roll non-doubles. So the game would have to be setup, where you ask "Is there a 1?" and then go from there. There are 10 rolls for which the answer would be yes, and only 1 where the answer would be yes and the other one is a 1 too. Whereas if I simply offer what one die is (even if you don't know which die, it makes the odds of the other die 1/6 to be anything including X).
If I tell you that there is one 1. The odds that the other is 1 is 1/6. If you ask if there's a 1, and the answer is yes, then the odds are 1/11. The odds that I'll have a die to tell you the value of is 100%. The odds that you guess a value is lower when I've rolled doubles, so when you get that question right, the odds are 1/11th. Just as if I told you as a petshop owner that I have at least one male puppy thereby negating the chance that I have female/female puppies. As if I had female/female puppies, I would have volunteered that I had a female puppy rather than a male.
Go figure, math is hard.
Interestingly I asked this question today and much to my surprise my sister got it right after a really short period of time. The answer is, oddly enough, one in three. Whereas almost everybody will say 50/50 and insist over and over again even if you just told other people who said that, that they were wrong.
There's a series of problems that fall into the same paradigm which are basically Monty Hall riddles, where known information is used to make a determination that change the odds from what we'd expect. And it turns out that *any* known information changes the odds. So when you picked Door Number 1 on the Monty Hall show and he opens Door Number 2, the odds that the prize is behind Door Number 1 is 1/3 and the odds that it's behind door number 3 is 2/3s. It's a strange math problem whereby the odds change because something is known about something else. Monty Hall wouldn't open the prize door. So we are given information that changes the odds.
In science, we start with a guess and then figure out what that guess would mean for the world and then check whether or not reality agrees with that guess. The most important step is that if reality is found to not agree that guess is wrong, it doesn't matter who suggested it or how interesting, beautiful, complex, simple or clever the guess is, it is wrong.
When we've checked a lot of things and find that we just can't prove this guess wrong over a very long period of time, it really does change the odds that that guess is correct, if we found a problem with the theory, it would be rejected. So when a scientific theory has withstood the test of time even if we are unaware of the particular tests it has withstood we can be more confident that it is true because being wrong would make it rejected. And if it's rejected, we can find a Monty Hall Door that hasn't been rejected yet which is almost certainly more likely to be correct, or with regard to scientific theory less likely to be wrong. Science is simply the least wrong guess we haven't managed to prove wrong yet. And we know it's the less likely to be wrong because we tried to prove it wrong and failed to do so thus far. This is why Einstein didn't dethrone Newton when his physics was accepted during the 20th century. Because up until then, Newton was the least wrong answer we had at the time. Now we have an even less wrong answer which can explain not only what Newton explains but more. To this end I highly recommend the Relativity of Wrong by Asimov.
The idea that knowing things about things change the odds falls a bit strangely into Hempel's paradox.
Hempel's raven paradox is basically stating that if we accept that we are given evidence to the statement "all raven are black" by the existence of a black raven, we should also accept that the existence of a green apple also provides evidence to the statement "all raven are black" because said statement is the same as saying "all non-black objects are non-raven objects" and a green apple confirms this given statement. The most accepted solution to the problem is to agree with the conclusion and suggest that the weight of evidence provided by green apples is very small because of the sheer range of non-black and non-raven objects. (As an amusing aside, there are albino ravens which are white). So really everything we know that fails to prove a statement wrong makes that statement a bit more likely to be true. Just as knowing that at least one of the puppies is male makes it slightly more likely that both puppies were male (after all we had a 1/4 chance of two male puppies before we confirmed that female/female wasn't an option). Failing to prove the theory male-male wrong by confirming female/female wasn't the case made the odds just a bit higher (though we seem to take the fact that at least one puppy is male to conclude one down, one to go and a 50/50 chance on the "other" puppy.)
The same is likely true with regard to evolution. A design is made more likely to be useful because an individual doesn't die when dying is possible. This is why the genotype (the DNA itself rather than what it codes for) which is insulated within the nucleus and doesn't interact with the outside world (there's transfer RNA and various other process that move this information around) can become very usefully complex and encode for very useful and functional proteins even though it has no access anything extra-nuclear. And this is also likely how our minds work by being able to make guesses about the world and by failing to be surprised by the wrongness of those guesses manage to build an internal view of the outside world without needing the eyes to take and process information (which is the model we are usually given). It simply isn't necessary to process information coming in from the eyes, there's only the need to see if that agrees with what we think it should be and react if we're wrong. You can build models of the outside world with guesses and checking if those guesses mesh with reality. That's the essence of science, evolution, and how our minds work. The part that understands, learns, encodes, works, theorizes, and discovers need not be actually connected to reality to understand it. It can simply trudge along failing to be wrong, and as a consequence become more reliable.
As a crazy person on the Daily Show once pointed out, either the LHC blows up the world or it doesn't. So the odds are 50/50. It's logic like this that makes me wonder how I could make money off such things.
---
If I roll two 6-sided dice and say that at least one of them is a 1. What are the odds that they are both 1s?
1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6
1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6
Because we know one is a 1, the odds that the other is a 1 is different than the typical 1/6 that people would tend to believe. Because we don't know which one was the 1 and there's only one possibility of snake-eyes (1-1).
1 1 1 1 1 1 2 3 4 5 6
1 2 3 4 5 6 1 1 1 1 1
These are the only possibilities and they are all evenly likely to occur. There's 11 of them and only in 1 of them are they both 1s. So knowing that at least one die is a 1 makes the odds that "the other one" (we don't know what other is because we don't know which is the principle one, and we should rather say "both of them") a 1 in 11 chance. We'd figure the odds to be 1 in 6, but really they are far longer than that and nearly double. This makes for a pretty good idea in a gambling game. I'll get some dice roll them somewhere, look and tell the other person what "at least one of them is X" and have them make wager that pays 8 fold that the other one is the same. They should think they are getting an advantage paying a 8X on a 1/6 chance when really they are getting paid 8X on a 1/11. I'll be rich!
Update:
Strangely due to the setup there the odds are actually 1/6. Since I would have to give information about what one die is, the chance that the other die is the same as X, is 1/6 or the odds that you roll doubles. Whereas you have twice as many things to have the dice be if you roll non-doubles. So the game would have to be setup, where you ask "Is there a 1?" and then go from there. There are 10 rolls for which the answer would be yes, and only 1 where the answer would be yes and the other one is a 1 too. Whereas if I simply offer what one die is (even if you don't know which die, it makes the odds of the other die 1/6 to be anything including X).
If I tell you that there is one 1. The odds that the other is 1 is 1/6. If you ask if there's a 1, and the answer is yes, then the odds are 1/11. The odds that I'll have a die to tell you the value of is 100%. The odds that you guess a value is lower when I've rolled doubles, so when you get that question right, the odds are 1/11th. Just as if I told you as a petshop owner that I have at least one male puppy thereby negating the chance that I have female/female puppies. As if I had female/female puppies, I would have volunteered that I had a female puppy rather than a male.
Go figure, math is hard.
Labels:
DNA,
Evolution,
Family,
hempel,
math,
mind works,
Monty Hall,
paradoxes
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