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le_bebna_kamniTwo days ago, I was a firm agnostic (or at least wavering equally between the two sides). In fact, my original intent was to post my frustrations in regards to George H. Smith’s Atheism: The Case Against God. Namely, I was perturbed by his rather narrow definition of agnosticism and his insistence that you must be either a theist or and atheist – there is no middle ground.
While I may later post the rant on this topic (before the scrawled thoughts get lost in my “organization” system), my current post regards a book that has decidedly shifted me from agnostic to nearly atheist, or at least anti-theist.
This particular book, The G.O.D. Experiments by Gary E. Schwartz, was not some scathing diatribe against theism. On the contrary, this book was designed to encourage the readers to believe in a "Guiding, Organizing Designer" (G.O.D. – a.k.a. intelligent design).
I've been reading a lot of atheistic arguments of late, and I was not particularly impressed. So I decided to try the other side of the coin. I came into the book fairly open-minded, and in fact after the first two chapters was quite willing to listen to what he said.
The first two chapters are about an experiment with a psychic called "Christopher". Normally such studies are ignorable, because they're poorly controlled and often run by people with little or no scientific background. However, the author's credentials seemed reasonable (previous faculty position at Harvard, tenured position at Yale, and is now currently a professor of psychology, surgery, medicine, neurology, and psychiatry at the University of Arizona – his credentials, by the way, appear to check out). And his claim to initially be an agnostic meant, in theory, that his research should be somewhat unbiased.
This psychic, Christopher, hailed from England and worked with the local police force to solve various crimes and disappearances. Christopher called Dr. Schwartz and asked to have his talent empirically tested. The psychic even offered to pay his own way out to the University of Arizona. The experiment for Christopher was as follows: Dr. Schwartz selected 20 specific locations in Arizona (not just cities, but particular buildings), wrote them on pieces of paper, and put each one into an individually sealed envelope. He then shuffled the envelopes, sent them to a colleague, who shuffled them again and passed them on to a third party for safe keeping. When Christopher arrived in Arizona, it was agreed that he would stay for ten days, and each day a single location would be selected randomly from the 20, and Christopher would give predictions as to where they would go that day and what they would see.
Before the envelope was opened (at a location separate from where Christopher was), Christopher would be videotaped showing his dream diary (from whence his predictions came) and explaining his overall impressions of the day to come. Then the envelope would be opened, its contents videotaped, and then the paper read aloud by the third party over the phone. And, remarkably, his predictions were incredibly correct. So much so, that I might be willing to consider a belief in the paranormal, especially if he took his findings to a peer-reviewed journal.
Dr. Schwartz claimed this as evidence for a divine hand. While I didn't necessarily agree this was the only interpretation – for example, Jung's collective unconsciousness is another alternative – I was intrigued, and more than willing to hear what other evidence he had to offer.
Unfortunately, his scientific credibility took a nose dive in the third chapter and continued to fall. Not only did he prove that he isn't a man of science, but he also showed beyond a reasonable doubt that he doesn't know how to do math. Let me give you an easy example:
I'm not sure how math savvy the average person is, but I've known since sixth grade that pi is the circumference of a circle divided by its diameter, not its radius. If all his evidence rests on math (statistics – which it does), he needs to prove that he at least knows the basics.
The foundation for his book is this: that the whole universe can't possibly be the work of chance, and that all randomness is really evidence for order. According to him, this is best demonstrated by the number pi. He claims that the digits of pi are completely random, but because they are the same for every circle, it's obvious that some G.O.D. is bringing order to randomness. However, pi is not random. It's a fixed ratio that has non-repeating digits. Scientists have not been able to find a repeating pattern to those digits, but that's not the same as being random. If pi were actually random, you wouldn't get the same number every time you calculated it. Another good example of a non-random, non-repeating decimal is the square root of two. There is only one number that can be the square root of two – it's just too long (in fact, infinite) to calculate it using finite computer memory. Can we say, "Baka desu ne"1?
This idea of pi being random (which it isn't) is the basis for his claim that other data that scientists say is random is really not:
(I repeat, scientists know that pi isn't random.)
So in other words, if it looks random, it really isn't? Hmmm....doesn't that invalidate all scientific research if we can't trust our own data? What's the point of even doing statistical analysis on data, if we already know it can't be random even if it says it is? I have the distinct feeling that these words will come back to haunt him at a later date, because it also invalidates any reasearch he might choose to do.
Gary Schwartz obviously believes that physicists/mathematicians who have done the advanced math are simply deluding themselves about their "random" data. Well, Dr. Schwartz, how does your math compare?
Clearly when it comes to the realm of statistics, Dr. Schwartz is a floundering ignoramus. He claims to be a "show-me" kind of guy, and proceeds to give experiments that "prove" the existence of G.O.D. that even the average reader can do in their own homes. Intrigued? Yeah, so was I until I read the experiments.
His first experiment revolves around sand paintings. You know all those cute little glue and sand paintings you might have done as a kid? For this experiment, take a closeable container and fill it with pretty colored sand (and feel free to make pretty designs with it, he says). Now close the lid and shake it. If you shake it long enough, the designs will disappear and all the colors will mix together. It will never spontaneously reform into a coherent design.
Common sense says he's right, but statistics say he is wrong.
Note the use of the word "never". He uses it a lot in his book, along with the phrase "100% replicable". Now, in my opinion this is a cardinal sin in statistics. While the probabilities may be so exceptionally small as to make something exceedingly unlikely during this particular expansion-contraction of the universe, saying something is absolutely 100% impossible is a blatant falsehood.
Let's take for example a coin toss. Anyone with basic statistics knowledge knows that the probability of getting a head is 1/2, or 50%. In two coin tosses, your chance of getting all heads is 1/22, or 1/4 (25%). In five coin tosses your chances are 1/25 (1/32), and so on. The more coin tosses a person intends to do, the chances of them all coming out heads gets exceptionally smaller. But it can never reach zero2
The problem with his home experiments is that two or five or ten trials won't cut it, because the probability of a spontaneous sand painting forming is very small. If you told a person to take 3d103 and randomly roll a pre-determined number between 1 and 1000, your chances of rolling that number are very slim if you only get one try. But given 500 tries to get that number, the odds are significantly greater. If you had everyone on the planet shaking their containers for a billion years, there's a much better chance that a sand painting will occur4.
I might be able to forgive Dr. Schwartz's unacceptance of low probabilities, if he hadn't gone on to say this:
Wait a second. He says sand paintings can't occur by chance (because his inadequate handful of "experiments" says so), so if you do happen to see a sand painting that appears to have been made by chance, it really wasn't. But why is this "chance sand painting" evidence of a divine being, and not simply evidence that his original hypothesis was wrong? It's like a Freudian psychoanalyst who says that you have to have sexual feelings for your mother, and if you prove that you don't, that's clearly evidence that you do since it demonstrates that you're repressing your desire. This man obviously has no scientific integrity.
He has already come to the conclusion that statistical anomalies cannot exist (which they can), but if you find any to contradict that statement, then they must be the work of a divine being. He then goes on to say – and I have to quote this because I think you'll find it amusing –
I don't know if anyone else found that profoundly hilarious, but I thought the definition of "pure chance" was, in fact, randomness. If it's not random, it's not pure chance.
The computer experiment is simple: he writes a computer program to use randomness (or an algorithmic simulation of randomness, since computers can't be truly random) to generate numbers from 1 to 100. These numbers are then averaged, and the average is graphed. This is done multiple times, until a sufficient number of these averages have been computed. The result is what statistics have always predicted: a bell curve with it's mean around 50, which happens almost every time. Sometimes the average of an individual series will be 49 or 52 or even 47. But they all fall more or less around 50, and the farther out you get from 50, the less likely you are to get an individual series that has that average (for example, to get a series that has an average of 1, all numbers that were selected would have to be 1, which is highly unlikely). This "evidence" is not surprising -- in fact, it's exactly the way mathematics predicts random numbers to fall.
Where he fails in his statistics is this: he claims that anomalies like having a mean of 30 or a mean of 75 are completely impossible. They will never happen (see, there's that word again). But if they do happen to show up, they must be divine interference. Even more so, he uses these really good, really predictable bell curve graphs created from random numbers to show that – get this – order can't possibly come from randomness!
His statistical ignorance is once more revealed in his assertions about statistical analysis:
1) to measure randomness, each event must be independent of every other event, and
2) the event must be unchanging over time. (my paraphrase)
He then comes to the fallacious conclusion that because the universe does not have any events that occur in isolation (and hence are not independent), and because the universe is constantly changing, there can be nothing in the universe that is random.
My first statement is this: if there can be no randomness in the universe, then his randomness "experiments" are completely meaningless – including the sand painting experiment. Bye bye, supporting evidence! He has just invalidated everything he has so far discussed.
Secondly, where in the hell did he get those statements? Those principles might be good to ensure unbiased coin flipping, but don't match up to other statistical analysis.
The best I have been able to figure (as far as how he came up with those statements) is that certain types of analysis (like chi-square) can only be done on independent events – but obviously there are ways of analyzing dependent events as well. For example, if you select cards from a well-shuffled deck, that's random. If you draw cards in succession from the same deck, that's still random, but the probability becomes dependent on the previous card drawn (because you can't draw the same card again once you remove it from the deck). It's obviously not an independent event, but it's a still random event that can easily be modeled using probability.
As for the second criteria, I'm surprised that Dr. Schwartz hasn't encountered this with his psychology background. Many psychological experiments are designed to test change over time (especially in learning experiments). Let's say you have someone try to psychically guess a card that is drawn, and you have the hypothesis that people can get better at guessing the card if they exercise their "psychic muscle". The analysis is done to show whether changes in guessing come from actual improvement (or perhaps the numbers show working your "psychic muscle" actually decreases performance). More likely, the change is performance is just random (maybe your test subjects had a lucky day). But randomness can still occur when the results aren't identical (i.e., you think you see change over time)5.
Before I strangle this guy for his stupidity, I'm going to end my rant. Let's just say that I haven't listed all his scientific (and mathematical) errors. And I haven't listed his physics errors (which a friend has assured me there are). I certainly wasn't able to stomach the book to completion (which, as far as I could tell, gave no new evidence, but simply built on previous faulty assumptions).
So why did this change my mind about being agnostic? Normally I read moronic arguments from either side and discard them (well, I usually complain about the stupidity and then discard them). But as I was reading, I realized that I could do much better defending the "pure chance" camp than I camp than I could defend the "intelligent design" camp. Of course, this doesn't rule out a god (not a G.O.D., but a god – an all powerful being that could at least potentially fuck with the universe). But perhaps this god really doesn't care, and has no desire to deal in the affairs of humans or galaxies or atoms. But a god like this isn't scientifically testable, so why worry if this god exists?
I now understand why many intelligent people turn atheist. I went online to do a search for "reasons why God might exist". The most intelligent arguments eventually boiled down to this:
1) chance can't possibly explain the universe.
2) we haven't come up with any better idea for how the universe exists.
3) therefore, god must have done it.
It's the "god of the gaps" philosophy that I detest so much. "We don't know how the universe began, so we'll just say god created it, and everything's answered." "We don't know what creates lightning, so it can only be Zeus" – at least back then it was excusable. While we're on the subject of erroneous explanations, I've got a few more to add:
(By the way, now that we must worship the spaghetti monsters, my significant other and I realized that we can take Holy Communion every time we visit Olive Garden. Catholics take their communion wafers as the body of Christ; and we take our pasta in remembrance of those who created us all.)
_______________________________________
1Japanese for "he's dumb, huh?" By the way, does anyone else have the urge to say..."ah, I see your Schwartz is as big as mine"?
Back
2The limit as n approaches infinity of 1/n is zero – which means that the larger the bottom number gets, the closer it gets to zero – but as 1 can't be divided by infinity it can never actually reach zero.
However, my statistics professor was fond of pointing out that statistics don't tell you what has happened, only what is likely to happen in the future. If you plan on doing 32 coin tosses, you can guess that the chance of you getting 32 heads is very, very, very slim (1/232). But if you've already done 31 coin tosses, and they all turn out to be heads, what is the chance that the next one will be heads? If you guessed 50%, not 1/232, you'd be right. Every time you flip the coin in the future, the probability is always 1/2 for each individual flip. You have an equal chance of getting a head or a tail, regardless of the last 31 or 99 or 10,003 flips.
Back
3Gamer speak for three 10-sided dice, as opposed to the usual 6-sided dice you use for parcheesi. An explanation for non-gamers: three different colored dice are used, with each die representing the 1s, 10s, and 100s place, respectively and 0 representing either 10 or zero. For example, to roll 1000, you would have to get 0,0,0 on all three dice. To roll a 1 you would need to get zeros on the 10s and 100s dice, but a 1 on the 1s dice (since it can't be read as 1,101 in a 1 to 1000 number system).
Back
4I once attended a physics lecture on a similar subject – the probabilities of all the gas molecules in a small region of space spontaneously crowding together in one corner of that space. While almost completely unlikely to occur (especially on our small planet), when all the gaseous regions of the universe are taken into account, the probability becomes much higher.
Back
5Technically speaking, you can't ever "prove" something is random, just as you can't prove that it isn't random. However, you can find that something is statistically so insignificant as to be not any better than chance. If a person doing these psychic experiments got one more card right out of several hundred tries, that probably would not be significant to conclude that they had "improved their psychic performance". Simply getting one more card right could easily be attributed to a lucky guess, since they're still not doing any better than mere chance.
Back
While I may later post the rant on this topic (before the scrawled thoughts get lost in my “organization” system), my current post regards a book that has decidedly shifted me from agnostic to nearly atheist, or at least anti-theist.
This particular book, The G.O.D. Experiments by Gary E. Schwartz, was not some scathing diatribe against theism. On the contrary, this book was designed to encourage the readers to believe in a "Guiding, Organizing Designer" (G.O.D. – a.k.a. intelligent design).
I've been reading a lot of atheistic arguments of late, and I was not particularly impressed. So I decided to try the other side of the coin. I came into the book fairly open-minded, and in fact after the first two chapters was quite willing to listen to what he said.
The first two chapters are about an experiment with a psychic called "Christopher". Normally such studies are ignorable, because they're poorly controlled and often run by people with little or no scientific background. However, the author's credentials seemed reasonable (previous faculty position at Harvard, tenured position at Yale, and is now currently a professor of psychology, surgery, medicine, neurology, and psychiatry at the University of Arizona – his credentials, by the way, appear to check out). And his claim to initially be an agnostic meant, in theory, that his research should be somewhat unbiased.
This psychic, Christopher, hailed from England and worked with the local police force to solve various crimes and disappearances. Christopher called Dr. Schwartz and asked to have his talent empirically tested. The psychic even offered to pay his own way out to the University of Arizona. The experiment for Christopher was as follows: Dr. Schwartz selected 20 specific locations in Arizona (not just cities, but particular buildings), wrote them on pieces of paper, and put each one into an individually sealed envelope. He then shuffled the envelopes, sent them to a colleague, who shuffled them again and passed them on to a third party for safe keeping. When Christopher arrived in Arizona, it was agreed that he would stay for ten days, and each day a single location would be selected randomly from the 20, and Christopher would give predictions as to where they would go that day and what they would see.
Before the envelope was opened (at a location separate from where Christopher was), Christopher would be videotaped showing his dream diary (from whence his predictions came) and explaining his overall impressions of the day to come. Then the envelope would be opened, its contents videotaped, and then the paper read aloud by the third party over the phone. And, remarkably, his predictions were incredibly correct. So much so, that I might be willing to consider a belief in the paranormal, especially if he took his findings to a peer-reviewed journal.
Dr. Schwartz claimed this as evidence for a divine hand. While I didn't necessarily agree this was the only interpretation – for example, Jung's collective unconsciousness is another alternative – I was intrigued, and more than willing to hear what other evidence he had to offer.
Unfortunately, his scientific credibility took a nose dive in the third chapter and continued to fall. Not only did he prove that he isn't a man of science, but he also showed beyond a reasonable doubt that he doesn't know how to do math. Let me give you an easy example:
Pi is a remarkable number. It is, on the one hand, so simple – it is the circumference of a circle divided by its radius.
I'm not sure how math savvy the average person is, but I've known since sixth grade that pi is the circumference of a circle divided by its diameter, not its radius. If all his evidence rests on math (statistics – which it does), he needs to prove that he at least knows the basics.
The foundation for his book is this: that the whole universe can't possibly be the work of chance, and that all randomness is really evidence for order. According to him, this is best demonstrated by the number pi. He claims that the digits of pi are completely random, but because they are the same for every circle, it's obvious that some G.O.D. is bringing order to randomness. However, pi is not random. It's a fixed ratio that has non-repeating digits. Scientists have not been able to find a repeating pattern to those digits, but that's not the same as being random. If pi were actually random, you wouldn't get the same number every time you calculated it. Another good example of a non-random, non-repeating decimal is the square root of two. There is only one number that can be the square root of two – it's just too long (in fact, infinite) to calculate it using finite computer memory. Can we say, "Baka desu ne"1?
This idea of pi being random (which it isn't) is the basis for his claim that other data that scientists say is random is really not:
The proponents of the chance universe hypothesis cite veritable mountains of data that seem to be consistent with the existence of randomness in the evolution of the universe. I emphasize the word "seem" because to accept the chance hypothesis requires that one assume that if something appears random – like the sequence of numbers in pi – then the order must be random (a very shaky assumption).
(I repeat, scientists know that pi isn't random.)
So in other words, if it looks random, it really isn't? Hmmm....doesn't that invalidate all scientific research if we can't trust our own data? What's the point of even doing statistical analysis on data, if we already know it can't be random even if it says it is? I have the distinct feeling that these words will come back to haunt him at a later date, because it also invalidates any reasearch he might choose to do.
Gary Schwartz obviously believes that physicists/mathematicians who have done the advanced math are simply deluding themselves about their "random" data. Well, Dr. Schwartz, how does your math compare?
Clearly when it comes to the realm of statistics, Dr. Schwartz is a floundering ignoramus. He claims to be a "show-me" kind of guy, and proceeds to give experiments that "prove" the existence of G.O.D. that even the average reader can do in their own homes. Intrigued? Yeah, so was I until I read the experiments.
His first experiment revolves around sand paintings. You know all those cute little glue and sand paintings you might have done as a kid? For this experiment, take a closeable container and fill it with pretty colored sand (and feel free to make pretty designs with it, he says). Now close the lid and shake it. If you shake it long enough, the designs will disappear and all the colors will mix together. It will never spontaneously reform into a coherent design.
Common sense says he's right, but statistics say he is wrong.
Note the use of the word "never". He uses it a lot in his book, along with the phrase "100% replicable". Now, in my opinion this is a cardinal sin in statistics. While the probabilities may be so exceptionally small as to make something exceedingly unlikely during this particular expansion-contraction of the universe, saying something is absolutely 100% impossible is a blatant falsehood.
Let's take for example a coin toss. Anyone with basic statistics knowledge knows that the probability of getting a head is 1/2, or 50%. In two coin tosses, your chance of getting all heads is 1/22, or 1/4 (25%). In five coin tosses your chances are 1/25 (1/32), and so on. The more coin tosses a person intends to do, the chances of them all coming out heads gets exceptionally smaller. But it can never reach zero2
The problem with his home experiments is that two or five or ten trials won't cut it, because the probability of a spontaneous sand painting forming is very small. If you told a person to take 3d103 and randomly roll a pre-determined number between 1 and 1000, your chances of rolling that number are very slim if you only get one try. But given 500 tries to get that number, the odds are significantly greater. If you had everyone on the planet shaking their containers for a billion years, there's a much better chance that a sand painting will occur4.
I might be able to forgive Dr. Schwartz's unacceptance of low probabilities, if he hadn't gone on to say this:
This is a fact. Sand paintings never spontaneously occur...If you happen to come upon a detailed, multicolored sand painting...you will know for certain that some highly intelligent, Guiding, Organizing Designer – or intelligence of another sort...carefully put it there.
Wait a second. He says sand paintings can't occur by chance (because his inadequate handful of "experiments" says so), so if you do happen to see a sand painting that appears to have been made by chance, it really wasn't. But why is this "chance sand painting" evidence of a divine being, and not simply evidence that his original hypothesis was wrong? It's like a Freudian psychoanalyst who says that you have to have sexual feelings for your mother, and if you prove that you don't, that's clearly evidence that you do since it demonstrates that you're repressing your desire. This man obviously has no scientific integrity.
He has already come to the conclusion that statistical anomalies cannot exist (which they can), but if you find any to contradict that statement, then they must be the work of a divine being. He then goes on to say – and I have to quote this because I think you'll find it amusing –
As you will soon see, you can use a home computer to show that even randomness itself does not occur by chance.
I don't know if anyone else found that profoundly hilarious, but I thought the definition of "pure chance" was, in fact, randomness. If it's not random, it's not pure chance.
The computer experiment is simple: he writes a computer program to use randomness (or an algorithmic simulation of randomness, since computers can't be truly random) to generate numbers from 1 to 100. These numbers are then averaged, and the average is graphed. This is done multiple times, until a sufficient number of these averages have been computed. The result is what statistics have always predicted: a bell curve with it's mean around 50, which happens almost every time. Sometimes the average of an individual series will be 49 or 52 or even 47. But they all fall more or less around 50, and the farther out you get from 50, the less likely you are to get an individual series that has that average (for example, to get a series that has an average of 1, all numbers that were selected would have to be 1, which is highly unlikely). This "evidence" is not surprising -- in fact, it's exactly the way mathematics predicts random numbers to fall.
Where he fails in his statistics is this: he claims that anomalies like having a mean of 30 or a mean of 75 are completely impossible. They will never happen (see, there's that word again). But if they do happen to show up, they must be divine interference. Even more so, he uses these really good, really predictable bell curve graphs created from random numbers to show that – get this – order can't possibly come from randomness!
His statistical ignorance is once more revealed in his assertions about statistical analysis:
1) to measure randomness, each event must be independent of every other event, and
2) the event must be unchanging over time. (my paraphrase)
He then comes to the fallacious conclusion that because the universe does not have any events that occur in isolation (and hence are not independent), and because the universe is constantly changing, there can be nothing in the universe that is random.
My first statement is this: if there can be no randomness in the universe, then his randomness "experiments" are completely meaningless – including the sand painting experiment. Bye bye, supporting evidence! He has just invalidated everything he has so far discussed.
Secondly, where in the hell did he get those statements? Those principles might be good to ensure unbiased coin flipping, but don't match up to other statistical analysis.
The best I have been able to figure (as far as how he came up with those statements) is that certain types of analysis (like chi-square) can only be done on independent events – but obviously there are ways of analyzing dependent events as well. For example, if you select cards from a well-shuffled deck, that's random. If you draw cards in succession from the same deck, that's still random, but the probability becomes dependent on the previous card drawn (because you can't draw the same card again once you remove it from the deck). It's obviously not an independent event, but it's a still random event that can easily be modeled using probability.
As for the second criteria, I'm surprised that Dr. Schwartz hasn't encountered this with his psychology background. Many psychological experiments are designed to test change over time (especially in learning experiments). Let's say you have someone try to psychically guess a card that is drawn, and you have the hypothesis that people can get better at guessing the card if they exercise their "psychic muscle". The analysis is done to show whether changes in guessing come from actual improvement (or perhaps the numbers show working your "psychic muscle" actually decreases performance). More likely, the change is performance is just random (maybe your test subjects had a lucky day). But randomness can still occur when the results aren't identical (i.e., you think you see change over time)5.
Before I strangle this guy for his stupidity, I'm going to end my rant. Let's just say that I haven't listed all his scientific (and mathematical) errors. And I haven't listed his physics errors (which a friend has assured me there are). I certainly wasn't able to stomach the book to completion (which, as far as I could tell, gave no new evidence, but simply built on previous faulty assumptions).
So why did this change my mind about being agnostic? Normally I read moronic arguments from either side and discard them (well, I usually complain about the stupidity and then discard them). But as I was reading, I realized that I could do much better defending the "pure chance" camp than I camp than I could defend the "intelligent design" camp. Of course, this doesn't rule out a god (not a G.O.D., but a god – an all powerful being that could at least potentially fuck with the universe). But perhaps this god really doesn't care, and has no desire to deal in the affairs of humans or galaxies or atoms. But a god like this isn't scientifically testable, so why worry if this god exists?
I now understand why many intelligent people turn atheist. I went online to do a search for "reasons why God might exist". The most intelligent arguments eventually boiled down to this:
1) chance can't possibly explain the universe.
2) we haven't come up with any better idea for how the universe exists.
3) therefore, god must have done it.
It's the "god of the gaps" philosophy that I detest so much. "We don't know how the universe began, so we'll just say god created it, and everything's answered." "We don't know what creates lightning, so it can only be Zeus" – at least back then it was excusable. While we're on the subject of erroneous explanations, I've got a few more to add:
A) Invisible dragons hold the universe together by flying around and manipulating things. Spiral galaxies are created by their wings as they fly in circles. Entropy will be kept in check by their fiery breath.
B) Our universe is a giant hairball coughed up by some ever-present cosmic cat.
C) A herd of giant spaghetti monsters rules the universe. The planets are made to be meatballs, which will be gathered up at the end of the universe. All unbelievers will be thrown into a vat of sauce, where they will be struck down with a horrendous form of "pastaplegia".
(By the way, now that we must worship the spaghetti monsters, my significant other and I realized that we can take Holy Communion every time we visit Olive Garden. Catholics take their communion wafers as the body of Christ; and we take our pasta in remembrance of those who created us all.)
_______________________________________
1Japanese for "he's dumb, huh?" By the way, does anyone else have the urge to say..."ah, I see your Schwartz is as big as mine"?
Back
2The limit as n approaches infinity of 1/n is zero – which means that the larger the bottom number gets, the closer it gets to zero – but as 1 can't be divided by infinity it can never actually reach zero.
However, my statistics professor was fond of pointing out that statistics don't tell you what has happened, only what is likely to happen in the future. If you plan on doing 32 coin tosses, you can guess that the chance of you getting 32 heads is very, very, very slim (1/232). But if you've already done 31 coin tosses, and they all turn out to be heads, what is the chance that the next one will be heads? If you guessed 50%, not 1/232, you'd be right. Every time you flip the coin in the future, the probability is always 1/2 for each individual flip. You have an equal chance of getting a head or a tail, regardless of the last 31 or 99 or 10,003 flips.
Back
3Gamer speak for three 10-sided dice, as opposed to the usual 6-sided dice you use for parcheesi. An explanation for non-gamers: three different colored dice are used, with each die representing the 1s, 10s, and 100s place, respectively and 0 representing either 10 or zero. For example, to roll 1000, you would have to get 0,0,0 on all three dice. To roll a 1 you would need to get zeros on the 10s and 100s dice, but a 1 on the 1s dice (since it can't be read as 1,101 in a 1 to 1000 number system).
Back
4I once attended a physics lecture on a similar subject – the probabilities of all the gas molecules in a small region of space spontaneously crowding together in one corner of that space. While almost completely unlikely to occur (especially on our small planet), when all the gaseous regions of the universe are taken into account, the probability becomes much higher.
Back
5Technically speaking, you can't ever "prove" something is random, just as you can't prove that it isn't random. However, you can find that something is statistically so insignificant as to be not any better than chance. If a person doing these psychic experiments got one more card right out of several hundred tries, that probably would not be significant to conclude that they had "improved their psychic performance". Simply getting one more card right could easily be attributed to a lucky guess, since they're still not doing any better than mere chance.
Back
