# Testing the prophecy of Babylon

Some days ago it came to my attention the fact that there is a religious group that considers the presence of propositions within the Old Testament that seem to describe events that have happened after the propositions were written as proof of the divine origin of such a text. Not only that: to my understanding, they seem to infer from those successful prophecies that also the other predictions present in the Bible must turn out to happen somewhere in the future.

Now, in these statements, there are several problems. One can note, for instance, that successful scientific theories like the Newtonian gravitation continuously predict with great accuracy the future, and yet this doesn’t seem to be generally considered proof that Isaac Newton had a divine nature. On the other hand, the fact that his gravitational law predicts the orbits of the Earth, of Mars, of the modules of the Apollo missions, etc., doesn’t prevent the same theory to fail when it comes to the orbit of Mercury. So, this single counter-example might be considered enough to prove that the first paragraph of this article contains false statements.

But then there is another problem. How do I evaluate whether a prophecy is true or false? Despite the obvious difficulties due to the fact that this kind of predictions are expressed in a human language (translated from one tongue into another) and not in mathematical language and as such ambiguous by its very nature, one can still try – I reasoned – to apply the standard method used in science. In other words, one can calculate the probability of the null hypothesis (that, in this case, is: the prophecy is true by chance) and see what kind of number he gets.

Well, I discovered right away that this calculation had in fact been attempted by Peter Stoner, a math teacher at Pasadena City College (R), and it can be found in his book, Science Speaks (freely available here). Let’s consider one of those prophecies, the one that seems to be particularly close to the heart of Marina, the Jehovah’s Witness who is currently persecuting me, the prophecy of Babylon:

And Babylon … shall never be inhabited, neither shall it be dwelt in from generation to generation: neither shall the Arabian pitch tent there; neither shall the shepherds make their fold there. But wild beasts of the desert shall lie there; and their houses shall be full of doleful creatures.

(Isa. 13:19-21 – written 712 B.C.)

And they shall not take of thee a stone for a corner, nor a stone for foundations; but thou shalt be desolate forever, saith the Lord … Neither doth any son of man pass thereby.

(Jer. 51:26,43 – written 600 B.C.)

Now, in his book, Peter Stoner translates this prophecy in the following seven events or propositions:

$E_1$: Babylon shall be destroyed. $P(E_1)=1/10$
$E_2$: It shall never be reinhabited (once destroyed). $P(E_2)=1/100$
$E_3$: The Arabs shall not pitch their tents there (once destroyed). $P(E_3)=1/200$
$E_4$: There shall be no sheepfolds there (once destroyed). $P(E_4)=1/5$
$E_5$: Wild beasts shall occupy the ruins (once destroyed). $P(E_5)=1/5$
$E_6$:  The stones shall not be taken away for other buildings (once destroyed). $P(E_6)=1/100$
$E_7$: Men shall not pass by the ruins (once destroyed). $P(E_7)=1/10$

I have added the expression within brackets, to enhance clarity. The probabilities of the single events (on the right) are those proposed by Peter Stoner, and I am not going to discuss them. Now, if we indicate the whole prophecy with E, according to Stoner the probability of the null hypothesis is

$P(E) = P(\bigcap_{i=1}^{7}E_i) = \prod_{i=1}^{7} P(E_i) = \frac{10^ { -9 } }{5}$

This is a really small probability for the null hypothesis, so we must accept that a power beyond human comprehension has… But let’s read again the prophecy: it seems articulated but, in fact, it only says that the place where Babylon once raised will be basically abandoned by human beings. In other words, it seems reasonable to say that $E_i\subset E_7$ for $i = 2, 3, 4, 6$. If that is the case, then we have

$P(E) = P(\bigcap_{i=1}^{7}E_i) = P( E_1 \bigcap( \bigcap_{i=2}^{7}E_i) ) =$

$= P( E_1 \bigcap( \bigcap_{i=2}^{6}(E_i \bigcap E_7) ) \bigcap (E_5 \bigcap E_7) ) =$

$= P( E_1 \bigcap E_7 \bigcap ( E_5 \bigcap E_7 ) ) =$

$= P( E_1 \bigcap ( E_5 \bigcap E_7 ) ) = P( E_1)P ( E_5 \bigcap E_7 )$

A further observation is that if the place is desolated with no human beings ($E_7$) then it is reasonable to assume that it becomes the reign of wild animals. In other words: $P(E_5|E_7) > P(E_5)$. Not only that, I would guess that it is safe to assume that $P(E_5|E_7)$ is about one. Then we have found

$P(E) = P( E_1) P(E_5|E_7) P(E_7) = P( E_1) P(E_7) = \frac{1}{10^2}$

In other words, the mistake that leads Stoner to a completely wrong value for $P(E)$ is the fact that he considered the events as independent one from the other, while this is obviously not the case.

Now, is this the probability of the null hypothesis? Well, it depends, because this is a case in which we have a prediction that has been got from a very long book with thousands of propositions, some of which look very much like predictions. Now, of course, when one picks a prophecy among all these propositions, he might be unconsciously tempted to pick the one that looks more like a fulfilled prophecy. In other words, we have to check for multiple comparisons in this case. So, let us consider that we have a number of N propositions similar to the one about Babylon. The probability $p(N)$ that at least one of these propositions is true purely by chance is

$p(N) = 1 - \frac{99^N}{100^N}$

The function $p(N)$ is plotted by the following code and as you can see, for N >4 we have that the null hypothesis becomes very likely. In other words, if we pick this prophecy among 5 other similar sentences, its resemblance to reality is just due to chance. In the figure below the red line indicates a probability of 0.05. A probability equal to or higher than 0.05 is associated with null hypotheses that must be considered true.

It should be added that the fact that the prophecy of Babylon has to be considered true is highly questionable. The reader can do his own research on that, for example starting from the notes collected in this text.

% file name = Babylon
% it calculates the probability that N prophecies are true by chance
clear all
% array for p(N)
N = 30;
for i=1:N
p(i) = 1-(99/100)^i;
p2(i) = 0.05;
endfor
% plotting
plot ([1:N],p(:),’-k’, “linewidth”, 2)
hold on
plot ([1:N],p2(:),’-r’, “linewidth”, 2)
xlabel(‘number of prophecies’);
ylabel(‘probability of the null hypothesis’);
grid minor
grid on

# The words in the blank spaces

If then, language does not reproduce experience with fidelity, to what does it owe its success in dealing with experience?

P.W. Bridgman, The Nature of Physical Theory

The words that are the most important are those that you never said, those written in the language that has existed for more than two hundred thousand years, long before any known human alphabet. You find them in the blank spaces between the lines of any good novel, they are that pain that is left once last page is over.

They are the ones that Michael Ventris could never decipher: the very devotion and the dreaming love he spent on a tongue spelled a long time ago by mouths closed by soil that has become rock.

They are the definition of the constant of Euler, that number that tells the story of the attempt at drawing a curve, that is never close enough, like we can never say exactly what we meant or reach what we wanted. That number that best describes, better than any novel, the hopes without a sound when you are young and sick and your recovery is not going to happen, or even worse, it will happen when it won’t matter anymore. The desires desired between four walls.

I had never seen the ocean, I was afraid of what I would have found. And you know what I discovered? My observations have shown that all those words that you were never able to say, those that chase you like a vice, a bad habit that you can’t quit, they find their way out to the ocean, like migrant snakes, or rivers. Then, only here, all mixed up, they encounter the courage to release their load of anger, fear, love. But one over the other, in all the languages we have invented, they lose any hope of being understood and become a crowd that rapes its rage against the cliffs, without relief, over and over. And yet, this giant beast, this monument to all the mistakes we made, at the end becomes only a dog that licks your feet on the shore, still afraid, powerless.

I have collected a long list of words like those and you’ll never know them because they are hidden within the pages of the books you see closed in one of my drawings. And after all the dancing of graphite on the candid lake of paper, all the formulae cherished with the point of my pencil, what I really have been trying to say, what I meant was