- These three guys go to a hotel (back in the old days) and rent a room.
The desk clerk charges them $10 apiece. Afterwards, the clerk decides
that he has charged too much and gives the bellhop $5 to return to the
guests. The bellhop, being unusually savvy, realizes that the $5 will
not divide evenly and decides to solve the problem by keeping two dollars
for himself. Which is what he does. He gives each guest $1, which means
that they each have paid $9 for the room, or $27 altogether.
- But wait a minute, the bellhop kept $2 and the guests paid $27, making
a grand total of $29. What happened to the other dollar?
the Null Hypothesis of Personal Mortality
(A Road Less Traveled)
Say that you find a deck of cards in the closet and decide
to play some solitaire or something.
You sit down at the table and turn over the first card. It's an ace of
spades. You place the ace back in the deck, shuffle the cards and once
again, turn over the first card. This time, it's the ace of diamonds.
Hmm. So, you try the same thing again. This time, you get the ace of spades
'Wait a minute…' You do it one more time, and this time, you get
the ace of hearts.
If you’re paying attention, you’re growing suspicious about
this deck you found in the closet. You’re starting to suspect that
you don’t have the ordinary deck that you had assumed. But, why
is that? Why are you suspicious?
You’re suspicious because the probability of drawing that 'hand'
is so small if the deck is a normal deck.
Let’s try that again. But, this time, the first
card you draw is a 3 of diamonds, the second is a
Jack of spades, the third is a 9 of clubs and the fourth is a 9 of hearts.
In this case, you probably are not suspicious.
But, of course you realize that the prrobability of drawing that hand,
given a normal deck, is just as small as the probability of drawing that
So, what’s the problem here? Why are you not suspicious of this
deck, when you were suspicious of the first
It turns out that there are two factors causing you to
be suspicious of that first deck -- and one is missing in regard to the
second deck. There is nothing about the second hand that sets it apart
in such a way as to suggest another plausible hypothesis… If there
were, you’d be suspicious of that second deck as well. It’s
as simple as that…
If, for instance, you were to remember that a few years back you had assembled
a deck of 3’s, jacks, and 9’s (for some weird reason), the
second hand would also stand out and would also
make you suspicious. And, again, your suspicion would be mathematically
Any time that new information
you receive causes the overall information you have
to logically favor a new ‘worldview,’ you are justified in
revising your expectations accordingly. Who could argue with that?
And, that’s what happened when you drew the 4 aces, but did not
happen when you drew the other hand.
The nature of a random "sample" has mathematical (probabalistic)
implications about the
population the sample was taken from. The 4 aces, by being so improbable
under your preexisting worldview regarding the deck, and by being so probable
under a different, plausible, worldview about the deck, caused the overall
information you had to logically favor the new worldview.
The "nondescript" hand, by not being
especially probable under any other plausible worldview about the deck
(that we can think of), even though it was specifically so improbable
under the old worldview, does not cause the
overall information you have to logically favor a new worldview.
By not suggesting another worldview, and thereby not setting itself apart
from most other
possible hands, the nondescript hand "blends" with most other
possible hands and effectively takes on the combined probability of most
So as to better understand the math for this kind of
situation, let’s try something where the
numbers are easier to nail down.
Say that you have 50 decks of freshly shuffled playing cards on the table
in front of you. You
know that 49 of these are normal decks, but that the other deck has only
aces. You don’t know which deck is the aces deck. You randomly select
a deck. At this point, the probability that you selected the aces deck
is 1 in 50.
Now you select the top card from the deck you chose and it’s a 3
of hearts. With that new
information, your probabilities have changed. The probability that the
deck you chose was all aces has just dropped to zero.
Backing up, say that instead of getting the 3 of hearts, you got an ace
of hearts. The probability that you chose the aces deck just got a nice
boost. Specifically, the probability is now 1/50 times 1, divided by 49/50
times 1/13, or a little better than 1to 4, or 25%.
The logic here is that the probability of drawing an ace if you had chosen
the ace deck is 1, so the “composite” probability of drawing
the ace deck and then drawing an ace from it is 1/50 times 1, or 2%. The
probability of drawing an ace if you had chosen a normal deck is 1/13,
so the “composite” probability of drawing a normal deck and
then drawing an ace from it is 49/50 times 1/13, or .075385.
So, once you draw the ace, to determine what the probability is that you
drew from the ace
deck, you need to compare the two composite probabilities, and ultimately
you end up being about 4 times as likely -- .075385/.02 -- to have drawn
from the normal deck…
One more detour before we get to the good stuff.
In the behavioral sciences, our research takes on meaning through statistics.
Say we’re trying to compare one method of teaching to another. We
find that the mean (average) test score received by students being taught
by method A is 5 points higher than that received by students being taught
by method B. We want to know if this difference is “significant”
-- and indicates that A is a better method than is B -- or is small enough
to fit within the range we would normally expect by chance.
To do that, we select an arbitrary probability – usually .01 –
and figure that if the probability of getting the results we did, under
the hypothesis that neither method was better than the other, is less
than .01, we are mathematically justified in “rejecting” that
hypothesis. That particular hypothesis is called the “null hypothesis,”
and we say that we can reject the null hypothesis at the .01 significance
We can do something analogous with the 50 decks of cards above. Say we
continue where we left off above and draw another ace from the same deck.
At this point, the probability is in favor of the aces deck -- but is
it sufficiently in favor of the aces deck in order to "reject the
normal deck hypothesis"?
No. With 2 straight aces, the probability that you selected a normal deck
becomes 49/50 times 1/13 times 1/13 divided by 1/50, or about .29. Again,
we're looking for .01 or less, so we can't reject the normal deck hypothesis
just yet. Keep in mind that the .01 significance level is intended to
be very conservative and if you had to BET one way or the other, you'd
be significantly better off betting against the normal deck in such a
case. You'd win almost 4 times more than you'd lose.
In order to reject the normal hypothesis in this case, under the typical
behavioral science standard, we'd need to draw 2 more times and get aces
each time. That would give us 49/50 times 1/13 times 1/13 times 1/13 times
1/13 divided by 1/50, or about .0017. If we bet against the normal deck
every time we got these results, on the average, we'd win 998 times out
of every 1000 times we bet.
I'm sorry, but I lied before. We have one more, short,
detour. I haven't shown how the 5 points better average of Teaching Method
A, above, suggests another plausible hypothesis. But that's obvious –
which is why you won’t get anywhere asking most statisticians about
this second factor. In our work, the other plausible hypothesis is always
a given. The other plausible hypothesis suggested by our results is that
Method A is better than method B.
You might want to take a break now, but otherwise, I think you’re
ready for the big time…
According to the typical non-religious hypothesis of
personal existence, YOU are a random and one short-lived accident (at most), and would
never exist if your parents had never met. The same would be true if your
grandparents had never met – on either side of the family. This
can be traced back for … a long time. And if just one of these chance
meetings had not taken place, you would never exist. It gets worse. Not
only did your parents have to meet, the right sperm cell had to meet the
right ovum. Otherwise, the results wouldn’t be you – it would
be your brother or sister. And, as it turns out, your father probably
produced quadrillion sperm cells in his lifetime and your mother was born
with several hundred ova. You happen to be the specific combination of
just one of those sperm cells and just one of those ova – no other
combination would do. And, just think of all those potential offspring
from your Dad and Cleopatra -- they never had a chance!
And worse. Since you will only live for about 100 years, there is another,
probability that has to be factored in – the probability that now
would coincide with your existence. It is much more likely that now would
be some other time altogether, along this infinite continuum of time…
In other words, given the typical non-religious hypothesis of personal
existence, the probability of your current existence
is incredibly small. So, the fact that you exist
casts serious doubt upon the typical non-religious hypothesis…
Or, does it? Well, is YOUR current existence analogous
to the 4 aces, or is it analogous to the 3, jack and 9s? That’s
the question. Is there, or is there not, a dollar missing?
But then, it would appear to be an easy question to answer
– much easier than, “What happened to the other dollar?”
Here, you don’t need to ‘feel’ the appropriate mathematical
logic – you have a rule to which to refer
First, does your current existence suggest another plausible hypothesis?
I don’t know about you, but I can think of at least four somewhat
plausible alternatives. Each requires a little explanation, but each is,
indeed, somewhat plausible. 1) Our understanding of time, and our existence
in it, is all screwed up. 2) You are ‘basic’ – a basic
part of reality. 3) Life is analogous to a dream. 4) You were, somehow,
intentionally created. And, it’s their total
probability (at least) that counts -- not just one of their probabilities.
We’re not quite out of the woods yet, however. We’ve got to
do the math. Does the OVERALL probability of one of these new hypotheses
being true outweigh the OVERALL probability of the old, typical, NR hypothesis
Because the probability of your specific existence is so incredibly small
under the non-religious hypothesis, the overall probability of your new
hypothesis (and remember, we can add the three probabilities together)
need not be much at all in order to validly reject the non-religious hypothesis.
While the probabilities to be added and multiplied are amorphous at best,
in search of a more
concrete understanding, we are justified in suggesting specific values
towards the morphous ranges and apply the appropriate math.
Giving the NR hypothesis the benefit of the doubt on both of the following
counts, we might
suggest that its ‘background’ probability (analogous to the
probability of a normal deck before you turned over the first card) is
9/10, whereas the probability of you existing given the NR hypothesis
(analogous to the probability of drawing an ace from a normal deck) is
1/1,000,000. And so, its overall probability given the new info of your
existence is therefore 9/10,000,000. Let’s place the ‘background’
probability of one of the other hypotheses being true at 1/100 and the
probability of you existing given one of the three other hypothesis at
9/10. If these are somewhat accurate, their overall probability comes
out to be 9/1000! Comparing the two, we get .0000000001!
So, even being grossly conservative, the overall probability of one of
the alternative hypotheses being true is MUCH greater than the overall
probability of the typical non-religious hypothesis being true, and we
are mathematically justified in rejecting the latter…
In other words, you’ve got GOOD REASON to believe that you are either
not accidental or you are not temporary – at least, one or the other.
But also, if you look closely at what we’ve done here, you’ll
see that you actually have good reason to believe that you are NEITHER
-- and that both appearances that you ARE, are illusions… How’s
Though the typical NR hypothesis is probably the road
more traveled by the intelligentsia these days, it doesn’t really
make sense, is analogous to thinking that a dollar was missing, and can
be mathematically rejected. Hallelujah! Scene2