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.

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.

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.

The Monty Hall Riddle and Atheism

The Monty Hall Riddle riddle is presented by Wikipedia thusly,

A thoroughly honest game-show host has placed a car behind one of three doors. There is a goat behind each of the other doors. You have no prior knowledge that allows you to distinguish among the doors. "First you point toward a door," he says. "Then I'll open one of the other doors to reveal a goat. After I've shown you the goat, you make your final choice whether to stick with your initial choice of doors, or to switch to the remaining door. You win whatever is behind the door." You begin by pointing to door number 1. The host shows you that door number 3 has a goat.

Do the player's chances of getting the car increase by switching to Door 2?

The problem as generally intended also assumes that the particular door the host opens conveys no special information about whether the player's initial choice is correct. The simplest way to make this explicit is to add a constraint that the host will open one of the remaining two doors randomly if the player initially picked the car.

The solution is counterintuitive but clearly correct.

Once the host has opened a door, the car must be behind one of the two remaining doors. The player has no way to know which of these doors is the winning door, leading many people to assume that each door has an equal probability and to conclude that switching does not matter (Mueser and Granberg, 1999). This "equal probability" assumption, while being intuitively seductive, is incorrect. The player's chances of winning the car actually double by switching to the door the host offers.

The chance of initially choosing the car is one in three, which is the chance of winning the car by sticking with this choice. By contrast, the chance of initially choosing a door with a goat is two in three, and a player originally choosing a door with a goat wins by switching. In both cases the host must reveal a goat. In the 2/3 case where the player initially chooses a goat, the host must reveal the other goat making the only remaining door the one with the car.

What does this oddly quirky and counterintuitive problem have to do with atheism?

Picture a thousand doors, one door for each religion as well as atheism (not strictly a religion or strictly excluding religions).

Let's suggest you choose one of these doors on some criteria, for example, your parents chose this same door. Having chosen this door, you can clearly see that the majority of remaining doors contain no prize. You can see the logical and obvious wrongness of many of these remaining doors. You are able to view them with a skeptical eye and reject them for being as absurd (as they clearly are).

Now, if the odds of each door having the prize is taken to be absolutely random. What are the odds that the initial door was the correct door?
-- 1/1000.

Now, you realize that these other doors can't have the prize. Your choices of doors has been reduced to your initial door and atheism. Either your choice has the prize or it doesn't. So what are the odds now? Two doors remain: your religion and atheism. What are the odds that your religion is the correct religion?
-- *STILL* 1/1000.
---- and the odds of atheism is now 999/1000.

The odds seem equal because you are left with two choices and all door were initially equal chances. The odds that you were right initially is 1/1000 and the odds that you were wrong were 999/1000. A critical eye, able to see the wrongness of the other religious doors, doesn't change the 999/1000 odds that you were wrong. Rather those odds are divided up between the remaining one door of atheism.

Had you chosen any other door, you would have quickly been able to dismiss the other religions, just as you are dismissing most of them now. However, the possibility that you should dismiss them all is still available.

Your newly found critical eye for other people's religion does not increase the chance that you are right. The fact that Islam is wrong because you're Christian or Baptists are wrong because you're Methodist does not increase the chances that you are right. Your chance of guessing right is the same before you dismissed other religions as it is after you dismiss them. The possibility that you were wrong is the same before you dismissed the other religions as before you dismiss them. However, that possibility is now divided by the only possibility left: they are all wrong (atheism).

If you take a look at a religionist similarly born into another door-choice using his critical eye on your religion while you are use your critical eye on his religion. You know that his door contains no prize and he is simply wasting his life. Why doesn't he switch over to your door?
-- He doesn't switch because your door is just as absurd as his door.

Now, given the choice do you switch doors?


There is certainly a Pascal's Wager objection here. Even with only a 1/1000 chance, you could make up skewed prizes. If the prize is behind atheism is only that getting to live your own life, happy and content with love, satisfaction, and joy until you die. You could say that your door has the prize: eternal bliss and infinite life.

Further, your door is quite certain that anybody who picks that any other door is going to get tortured forever. Now that poor co-religionist standing next to a clearly bogus door is really making a critical mistake! Honestly, he's going to get tortured forever and his religion is bogus. He really should switch to your door! Why doesn't he?
-- He's thinking the same thing.

Why don't atheists come over to your door?
-- Because, your door has no prize! The only thing that's even possible is living your own life, happy and content with love, satisfaction, and joy until you die.

Why don't people change to your religion? For the same reason you don't change to their religion... there's no prize there!

Sure, your door has some pretty awful threats for the unfaithful, who lack fidelity, the infidels: but that doesn't mean that your door is the correct door.

The fact that there are so many mutually exclusive religions actually increases the chance that atheism is correct. The fact that all those other religious people adhere to wrong religions doesn't increase the chances that your religion is correct.

It isn't an equal choice between your religion and no religion. The choice is slim to none that your religion is the correct religion and you would be well advised to use that critical eye on your own religion.

If you realize the real reason why you reject other people's religions, you will realize the reason I reject yours. As the saying goes, "they can't all be true, but they can all be false."