Tickle My God Spot!

A few weeks back during my pilot broadcast, I discussed the article Hopkins Scientists Show Hallucinogen In Mushrooms Creates Universal 'Mystical' Experience. The article describes a study done at Johns Hopkins by Roland Griffiths. In the study, 36 subjects were given either psilocybin (the active ingredient in "magic" mushrooms) or the placebo methylphenidate (th active ingredient in Ritalin -- it has similar physiological effects to psilocybin, but without the hallucinagenic ones). Most of the subjects who took the psilocybin reported having mystical experiences and furthermore reported that they were happier and more satisfied in the two months following the exposure.

I'm all for this type of research. For one, the taboo against doing serious research with illegal psychoactive drugs is counterproductive. To not be able to even investigate certain substances just because some non-medical authority says they have no medicinal value is plainly irrational. For another, I'm personally fascinated with the human "mind" and would love to know more about how the devoutly religious mind works. It appears to work like it's high on shrooms.

But there were a couple things that bothered me.

In the study, more than 60 percent of subjects described the effects of psilocybin in ways that met criteria for a "full mystical experience" as measured by established psychological scales.

What exactly is a "full mystical experience" and what "established phychological scales" were used to measure it? I just don't know what that means. Does it mean that the vocabulary used to describe it is very similar to the way people have been describing these experiences for centuries? I don't know. Perhaps the actual paper describes this to my satisfaction--I haven't read it yet.

In the present work, 36 healthy, well-educated volunteers-most of them middle-aged-with no family history of psychosis or bipolar disorder were selected. All had active spiritual practices. "We thought a familiarity with spiritual practice would give them a framework for interpreting their experiences and that they'd be less likely to be confused or troubled by them," Griffiths says.

So I guess an atheist who took psilocybin would be utterly confused due to his lack of proper framework. Methinks that the purpose of this study was to prove how safe and helpful psilocybin-like substances are; that way their sponsors could market their own version at some point down the road. So naturally they recruited volunteers who were predisposed to see delusional experiences as positive events in ther lives.

Personally, I would have done it all differently: I would've included atheists as controls. I would've compared the descriptions of the believers and non-belivers to see how they differed. Finally, I would have had the subjects monitored by fMRI during their "experiences" to see exactly what was going on, and if believers and non-believers were having actually different mental experiences, or just interpreting them differently.

Then yesterday, I saw this other article about another study that did (some) of that. Okay, no psilocybin and no atheist controls, but si to "mystical experiences" during fMRI. In No 'God Spot' in the Human Brain, a University of Montreal study involving 15 cloistered Carmelite nuns was described.

The nuns were not asked to try and actually achieve a state of spiritual union with God during the experiment because, as the nuns put it, "God cannot be summoned at will."

Nevertheless, the researchers believe their method was justified because previous studies have shown that actors asked to enter a particular state activated the same brain regions as people actually experiencing those emotions.

Gee, didn't they know that a little psilocybin would've done the trick? Seriously though, here's the kicker.

The study found that mystical experiences activate more than a dozen different areas of the brain at once.

So it seems that the magical "God Spot" is just a myth. The brain actually has quite a few religenous zones. (Yes, I did just make up that word)

Which Muppet Am I?

I noticed that some bloggers over at Scienceblogs have taken The Muppet Personality Test, so I thought I would too. A few weeks ago I was really into taking those blogthings tests (I'm 52% Evil), so I don't know how I missed this one; maybe it's a new test.

The reason I really wanted to take this particular test is that the subject of which muppet I am came up just last weekend. I was talking to a fellow member of my neighborhood association who told me that I reminded him of a particular muppet. I naturally asked "Is it Beaker?" You see, Beaker and I have the same profession (lab assistant, not experiment victim -- I think). I also really enjoyed Beaker's attitude. He always started each skit layed-back and calm. Then the intonation of his "meems" would (hilariously) change right when Dr. Honeydew got to the part of his description where he describes exactly what his assistant's participation in the experiment would entail. I loved Beaker.

But that's not the muppet he had in mind. It seems I reminded him of Sam the Eagle. At first I thought he was making fun of my scalp, but the more I thought about it and the more I heard his reasoning, the more it made at least some sense. Could it be?

Okay, he might be onto something. I can kind of see it. It's by no means a perfect match, but hmm... So the big question is "Which muppet would I be when I took the test?" Would I be Beaker? Would I be Sam the Eagle? Only the test would reveal the true muppet trapped inside of me.



So I took the test.

You Are Dr. Bunsen Honeydew

You take the title "mad scientist" to the extreme -with very scary things coming out of your lab. And you've invented some pretty cool things, from a banana sharpener to a robot politician. But while you're busy turning gold into cottage cheese, you need to watch out for poor little Beaker! "Oh, that's very naughty, Beaker! Now you eat these paper clips this minute."

The Muppet Personality Test

I'll take it!

Katrina remembered

This Monday, August 28th is the 1 year anniversary of hurricane Katrina hitting New Orleans. Since our President has warned us against placing too much importance on this, I thought I would join Shakespeare's Sister (via Coturnix) in blogging on this date.

For starters, let's review the entire 2005 Atlantic hurricane season.



My view a year later is:

• The administration castrated FEMA.
• They responded poorly when they very well should've known better.
• And they still haven't done what they promissed.

Besides the above video, I am also including footage shot by my sister when the eye passed over Hollywood, FLA. This was back when Katrina was still a cat. 1 storm--before it morphed into the mass killer it would eventually become. I realize that the idea of the blogswarm is to remember the tragedy in New Orleans, but what can I really add that all the other blogswarmers won't have already said? My sister's video is definitely original. Enjoy!

Seeing Ghosts in Space

One of the best layman’s responses I’ve seen to Intelligent Design’s “problems with Evolution” argument is

Every time you hear them say the word “evolution,” substitute the word “gravity.”

This statement is concise and doesn’t get into the nitty-gritty biological details. It points out the absurdity of the ID argument by drawing a parallel to something we all can understand: gravity. We all can see an apple falling from a tree; we all can (sort of) see the Moon orbit the Earth; we can all feel gravity’s effects when we ride a roller-coaster (well, all the time really). The above statement basically says that we can in fact see evolution happening, just as clearly as we see the effects of gravity. No serious biologist doubts that evolution is real just as no serious physicist doubts that gravity is. The devil is in the details.

What I always found ironic about that statement is that biologists actually know more about the workings of evolution than physicists know about the nature of gravity. Ask ten different physicists to explain the nature of gravity and you might get less than ten different answers only if more than one admits that they don’t really know.

Among the fundamental forces in nature, gravity is the rogue oddball. It doesn’t want to play by the same rules as everyone else. For decades, physicists have been searching for a grand unification theory that will unite all the fundamental forces under one umbrella. Many consider it the last great frontier of science. Michael Faraday made the first move in this direction when he showed the relationship between the electric and magnetic forces. Over the years physicists have been able unite them all, except for one: gravity. They have been able to quantize them all, except for one: gravity. It just wants to be different—so different that astronomers have discovered a type of matter that seems to be impervious to all the fundamental forces, except for one.

Dark matter is a funny animal. We know it’s there because we can see it’s gravitational effect on regular matter. You see, galaxies don’t have enough regular matter in them to keep them from flying apart. So there must be some other type of matter out there (in huge quantities, it turns out) that’s supplying the extra gravitational force to keep things together. Yet, apart from gravity, this dark matter doesn’t seem to interact with regular matter. It doesn’t come together to form atoms, or molecules or stars. It’s just there.

That’s why many physicists feel that it might not exist at all. Perhaps there’s another explanation for this observed gravitational effect. One of the more popular alternative explanations is MOND (Modified Newtonian Dynamics). MOND says that the laws of gravity (i.e. Newton’s and Einstein’s formulae) are wrong and that at galactic distances, gravity is proportionately stronger than the reciprocal of the square of the distance. These hypotheses have recently been dealt a blow by a new discovery made by astronomers around the world.

This discovery relies on the hypothesis that dark matter only weakly interacts with regular matter. One way to think about this is that dark matter only interacts with regular matter gravitationally. This would be like a movie ghost that walks through walls but is gravitationally bound to the earth. (However, most movie ghosts that can walk through walls can also fly, so perhaps ghosts aren’t made of dark matter after all.) But there’s another school (we don’t know who’s right—another mystery of dark matter) that says that dark matter can interact with regular matter if there’s a direct collision between particles of dark and regular matter. These collisions, however, should be so rare as to be practically ignored. Imagine an atom as filling an area the size of a soccer stadium, with a soccer ball sized object at roughly mid-field, several marble sized objects racing around the stands, and all the empty space in between filled by a powerful force field holding it all together. Now imagine trying to hit this atom with a pistol shot. If the bullet is affected by the force field, then hitting the atom is like hitting a stadium-sized target. However if the bullet is made of some dark material which is completely unaffected by the force field, then the atom becomes a soccer ball sized target—almost impossible to hit.

Therefore if two large objects (such as galaxy clusters) should collide, then the regular matter from the objects should interact, slowing down each object’s momentum, while each object’s dark matter, which doesn’t interact, should initially overshoot the collision before being brought back into the fold by gravity, like a stretched spring. If this indeed happens, then the effect should be observable using a technique called gravitational lensing. This method works because light is affected by gravity. Therefore light passing near a massive object—say, the dark matter from a galaxy cluster—will be bent (according to General Relativity) and focused, just as if it were passing through a lens. We should be able to observe this effect from earth, and we did! Furthermore, this observation is incompatible with MOND.

Does this finally prove that dark matter exists? Not quite. Can there still be another explanation for what we’re seeing? Yes, but that is becoming increasingly remote. Are we any closer to actually knowing what dark matter is? No, but I think we’re headed in the right direction.

And if that doesn’t satisfy you, then you can always just chalk it up to the designer.

Raglan's Scale and the Hero of Star Wars

Joseph Campbell's The Hero with a Thousand Faces was a very influential book for me. It helped me see how Myth pervades all human cultures--including my own. I found it all utterly fascinating. I was glued to the television when Bill Moyers interviewed Campbell for The Power of Myth. (side note: I remember during that interview, Campbell said the he thought Judas was given a bad rap because he also fit the Hero profile--the one that "kills the beast." I wonder if he would have felt vindicated by the recent discovery of the Gospel of Judas?)

The Bill Moyers interview of Joseph Campbell was filmed at George Lucas' Skywalker Ranch. Lucas himself has always said that Campbell's Hero was one of his greatest influences. And my copy of Hero had Luke Skywalker on the cover. It was plainly obvious to me that Luke was an example of the hero. He was the hero of the Star Wars trilogy.

When the prequel trilogy came out we had a new hero. Anakin was the hero of the new trilogy, while Luke was the hero of the original trilogy. There was one small problem, though. When viewed as a six-part epic (in other words, pretend you saw Phantom Menace first and Return of the Jedi last), Anakin never really ceases to be the hero. I had noticed this, but never really gave it too much thought until recently when I had a conversation with my brother on the topic. He said he saw an interview with George Lucas where Lucas said that Anakin was always supposed to be the hero and the reason he made the prequel trilogy was to drive that point home.

To put this to the test, we used Raglan's Scale. I remember reading about Raglan back when I was on my big mythology kick. But I've been recently reintroduced to him thanks to an interview with the late Alan Dundes in Brian Flemming's movie. Lord Raglan came up with a list of 22 common traits that heroes tend to have.

LORD RAGLANS SCALE

1. The hero's mother is a royal virgin
2. His father is a king and
3. often a near relative of the mother, but
4. the circumstances of his conception are unusual, and
5. he is also reputed to be the son of a god
6. at birth an attempt is made, usually by his father or maternal grandfather, to kill him, but
7. He is spirited away, and
8. Reared by foster-parents in a far country
9. We are told nothing of his childhood, but
10. On reaching manhood he returns or goes to his future kingdom.
11. After a victory over the king and or giant, dragon, or wild beast
12. He marries a princess, often the daughter of his predecessor and
13. becomes king
14. For a time he reigns uneventfully and
15. Prescribes laws but
16. later loses favor with the gods and or his people and
17. Is driven from from the throne and the city after which
18. He meets with a mysterious death
19. often at the top of a hill.
20. his children, if any, do not succeed him.
21. his body is not buried, but nevertheless
22. he has one or more holy sepulchres.

We compared how many applied to Luke, and how many applied to Anakin. Some attributes are negotiable (Does Sith Lord = King? I say yes.) The ones I thought were a yes are in green, and the no's are in red.

Hero Attribute	Luke	Anakin
1	possibly	yes
2	yes	yes
3	no	no
4	no	yes
5	no	yes
6	no	unknown
7	yes	yes
8	yes	arguably
9	no	yes
10	yes	yes
11	yes	yes
12	no	yes
13	no	yes
14	no	yes
15	no	yes
16	no	yes
17	NA	yes
18	no	maybe
19	NA	Death Star = hill?
20	NA	yes
21	NA	yes
22	NA	yes
Total	6	18

Luke doesn't even break into double digits (of course, he didn't die) but Anakin gets a whopping 18! Thet puts him right behind Oedipus, Theseus and Jesus, and just ahead of Romulus, Hercules and Perseus. Now that's some good hero company!

But now to test the final part of the theory, let's figure out Anakin's score based only on what we know from the original Star Wars trilogy. By my reasoning, I'm giving him numbers 9 through 22 except for 18 (since I didn't give it to him in my original calculation). I'm not sure about number 12, but I seem to remember that at some point in the original trilogy it was revealed that Luke and Leia's mother was a princess, so I'll give him that one. That makes a total of 13 -- more than twice Luke's score.

Therefore, according to the Raglan scale, the hero of Star Wars is unquestionably . . .
Anakin!

John Von Neumann and the Mathematician's Trap

This little story about the great mathematician John Von Neumann has always been one of my favorites. I will tell it the way I first heard it. I have since heard a few variations on the story, leading me to think that there may be a component of Urban Legend to it. But I really don't care, because I think it's such a great story that it's worth retelling.

John Von Neumann was considered by many to be one of the most brilliant minds of the twentieth century. He reportedly had an IQ of 180. He was a pioneer of Game Theory, which was very important during the nuclear arms race. (Because GT assumes that all players act in their own best enlightened self-interest, GT turned out to be a much better model for evolutionary biology than for human behavior.) He was also one of the two people (Alan Turing being the other) who is credited with being the father of the modern computer.

The story goes that someone once posed to Von Neumann the following problem:

Two trains are 20 miles apart on the same track heading towards each other at 10 miles per hour, on a collision course. At the same time, a bee takes off from the nose of one train at 20 miles per hour, towards the other train. As soon as the bee reaches the other train, it bangs huwey and heads off at 20 miles per hour back towards the first train. It continues to do this until the trains collide, killing the bee.










The question is, how far does the bee fly (d) before the collision?

This is a pretty staight-forward problem for anyone who has studied Mathematical Analysis or Pre-Calculus. The initial separation is D = 20 miles (from here on out I will use the variable D, then substitute the value of 20 miles at the end. I think this makes it easier to follow the steps.) The bee is traveling twice as fast as each of the trains, therefore covering twice the distance as the approaching train before the first turn-around. So the distance d1 that the bee travels on the first leg, plus the distance the approaching train travels (one half d1) equals D.
Therefore d1 = 2/3 D.

As the bee begins leg #2, not only has the turn-around train covered the distance 1/3 D, but so has the train the bee is now heading towards. That means the remaining free distance D' = 1/3 D. By the same argument as above, the bee covers two thirds of this distance on his second leg.
Therefore d2 = 2/3 D' = (2/3)*(1/3)*D.

For leg #3, by the above argument, the remaining distance D'' = 1/3 D', which the bee covers two thirds of.
Therefore d3 = 2/3 D'' = (2/3)*(1/3)*D' = (2/3)*(1/3)*(1/3)*D.

I hope you all can see the pattern that's developing. Each trip gets one third shorter. Symboically speaking, if we move the 2 and the D out to the begining, we get 2D*(1/3)*(1/3)*... with the number of 1/3's being equal to the leg#. Since this is the same as raising (1/3) to the exponent equal to the leg#, we get
dn = 2D/3^n.

This means that on the nth leg of its journey, the bee flies 2D times one third raised to the power n (or conversely, 2D divided by three raised to the power n). Now that we know how far the bee travels on each leg, it's time to find out the total distance. The distance the bee travels after n legs (d'n) equals
d'n = d1 + d2 + ... + dn, which equals
d'n = 2D/3 + 2D/3^2 + ... + 2D/3^n, which when we factor out the 2D we get
d'n = 2D*(1/3 + 1/3^2 + ... + 1/3^n), which in mathematical notation is written as

(note: I've been having trouble with my free Math graphics software. The formulas look neat when I compose them, but when I go to export them, the software keeps changing the capital Sigma "Σ" to a capital Ess "S" which is begining to frustrate me. When I work out the prblem, I will edit this post to add the cool mathematical graphics. In the meantime, please bear with my poor man's notations.)

d'n = 2D * (x=1 --> n)Σ[1/3^x]

Let me take a moment to try to explain my rigged notation. Σ means "summation." The expression inside the brackets is what is being summed. The expression inside the parenthesis tells you over what values you perform the summation. So for the above expression, that means we will be adding up the values of 1/3^x for the values of x=1 through x=n. In other words, 1/3^1 + 1/3^2 + ... + 1/3^n.

There may be a formula for solving that sum; I may even have been taught that formula. But unfortunately, that's not the kind of knowledge that I tend to retain. Therefore we will solve this using the algorithm I remember and can (kind of) explain. What I will do is sum up the first few terms, look for a pattern, then use induction to prove it. Hopefully my explanation will at least make an inkling of sense to those of you who are completely lost right now. So here we go.

1/3 =1/3
1/3 + 1/9 = 4/9
1/3 + 1/9 + 1/27 = 13/27
1/3 + 1/9 + 1/27 + 1/81 = 40/81
. . .

The pattern I see here is that the numerator (top part of the fraction) is half of the denominator (bottom part of the fraction) minus one. In other words,
1/2*(3-1)=1
1/2*(9-1)=4
1/2*(27-1)=13
1/2*(81-1)=40
Since the denominator is just 3^n, then the numerator is 1/2*(3^n - 1).

So the formula that I need to test with induction is
(x=1 --> n)Σ[1/3^x] =? 1/2*(3^n - 1)/3^n

Before I proceed further, let's do a quick refresher on mathematical induction. The basic idea is that you prove a general expression by first proving that it is consistent, ie. IF it's true for some specific case, then it must necesarrily be true for some general case. Then prove that it's true for that specific case, and you're done.

The normal route is to assume that an expression is true for some value x=n, then attempt to prove that it must necesarrily be true for x=n+1. Which of course means it's also true for n+2 (substitute n+1 for n), n+3 and all x greater than n. Now if you prove it's true for x=n=1, then it must be true for all n. Since we've already proven our formula true for n=1 (and 2 and 3 and4), we only need to prove that if it's true for x=n, then it must also be true for x=n+1.

We have
1. (x=1 --> n)Σ[1/3^x] = 1/2*(3^n - 1)/3^n
which we are assuming to be true for x=n, and trying to see if
2. (x=1 --> n+1)Σ[1/3^x] =? 1/2*(3^{n+1} - 1)/3^{n+1}
is also true.
If we recall that adding 1 to an exponent is the same as multiplying by the base
3. 3^{n+1}=3*3^n, we get
4. (x=1 --> n+1)Σ[1/3^x] =? 1/2*(3*3^n - 1)/3*3^n
Going back to the meaning of Σ as summation, summing up to x=n+1 is the same as summing up to n, then adding the next term where x=n+1. In other words,
5. (x=1 --> n+1)Σ[1/3^x] = (x=1 --> n)Σ[1/3^x] + 1/3^{n+1}
Substituting statements 1. and 3. into 5. we get
6. (x=1 --> n+1)Σ[1/3^x] = 1/2*(3^n - 1)/3^n + 1/3*3^n
= 3*(3^n - 1)/2*3*3^n + 2/2*3*3^n
=(3*3^n - 3 +2)/2*3*3^n = (3*3^n - 1)/2*3*3^n = 1/2*(3*3^n - 1)/3*3^n
which is the expression we were trying to prove in statement 4.

Since we've already proven it for n=1, then expression 1. has now been proven true for all n.
1. (x=1 --> n)Σ[1/3^x] = 1/2*(3^n - 1)/3^n

Back to our friend the bee. We now have an expression for how far the bee flies after n legs
7. d'n = 2D * 1/2*(3^n - 1)/3^n = D*(3^n - 1)/3^n
and we need to solve it for how far the bee flies before dying. In actuality, the bee will stop flying (okay, "in actuality" this would never happen) when the distance between the trains is less than the body length of the bee. However, since the summation quickly converges on the solution, we can assume that the bee is a point, ignore the famous paradox, and do the summation up to n=infinity.
7. d'n = D*(3^n - 1)/3^n = D*(3^n/3^n - 1/3^n) = D*(1 - 1/3^n)
Quick refresher on infinite limits: as we let n get infinitely large, 3^n approaches infinity, and 1/3^n approaches zero. Therefore the limit as n approaches infinity is
d = limit(n-->infinity)[D*(1 - 1/3^n)] = D*(1-0) = D = 20 miles!
Woo-hoo!!

We have just solved this problem by the infinite series method. Infinite series are very important in Mathematical Analysis and Pre-Calculus as they form the basis for derivatives and integration and everything which is Calculus and Differential Equations. That's why all students of Math, Physics and Engineering get to do a ton of infinite series problems before they graduate. The reason I call this problem the "Mathematician's Trap," is because virtually all mathematicians who see this problem will try to solve it the way we just did.

However, if you were to give the problem to someone who's only had basic Algebra, they might solve it differently. The trains crash at the midway point which is at 10 miles. Since each train is going 10 mph, this takes one hour. During that same hour, the bee is flying at 20 mph, therefore the bee flies 20 miles! Wow, that was a lot easier!

(note: Some of you may have noticed that for the infinite series solution, I didn't use the respective speeds of the bee and the trains, but only their ratio. This would also work for the algebraic solution, but it would make the math a little more complicated, which rather defeats the purpose of what I was trying to prove. In fact, as a general case, as long as the speeds of the two trains adds up to the speed of the bee, the distance traveled by the bee will always be the initial separation of the trains, ie. d=D. You can see this in the following thought experiment. Since the speeds of the trains added together equals the speed of the bee, at any given moment in time, the distance covered by the two trains together is equal to the distance covered by the bee. That means that at any given moment in time, the available flying space left is equal to what would be the remaining distance if the bee were flying unimpeded from point A to point B. Therefore d=D. Think about it.)

The moral of the story is that being smarter or better educated can often times put you at a disadvantage. When someone is trained at doing something a certain way, that action is virtually automatic. It takes great insight to be able to "step outside of the box" and ask if there's an easier way to do it. (I'm currently working on another post on just this subject which should hopefully be up soon.) Even brilliant mathematicians will fall into the trap, which brings us back to John Von Neumann.

When posed with the above problem (or some variation of it), JVN took all of five to ten seconds to come up with the correct solution. This floored the questioner who said "I'm impressed that you didn't fall for the Mathematician's Trap." After getting a perplexed look from our genius, he asked "How did you solve the problem?"

"By infinite series, of course!"