Reality Game Comentary From Experts
A number of mathematicians and theologians have commented on the
Reality Game. Do you agree
with their analyses? How do they make you feel on an emotional level?
What are the odds that these are the only verses in the King James Bible to converge
to God in such a manner?
In your list of words (the verses from Genesis), replace each
word by its length, obtaining a sequence of positive integers
s(1), s(2), ...
Now define the "chain" of terms beginning with any term s(i):
s(i), s(i+s(i)), s(i+s(i)+s(i+s(i))), ...
(These are the lengths of the "chain" of words you get by
choosing the ith word and skipping from it through the list
as you describe.)
The question is:
Is it extraordinary for all chains starting among the first
ten words, to pass through the 41st word, and for that word
to be "God"?
It seems clear that for any reasonable probability model,
all chains passing through any finite number of terms will
almost surely merge eventually. And once they've all merged,
the common chain can be followed until an "interesting" word
In your case, if I haven't miscounted (see below), the first
word common to all chains starting among the first *35* words
(not only the first 10) is not the 41st word "God", but the
less interesting 38th word "the", in the 2nd verse. So it
seems that the reason for going into the 3rd verse is merely
to find a word more interesting than "the" ;o)
I think the basic question can be formulated as follows:
Assume some reasonable probability model for s(1), s(2), ...
and consider all the chains starting among the first n terms.
Let K_n be the index of the first term common to all of these
What is the value of E(K_n)? pr(K_n <= k)?
In particular, is E(K_10), or E(K_35), anywhere near 38?
Is pr(K_10 <= 38), or pr(K_35 <= 38), more than 50%?
This would be interesting even for the (unrealistic?) model
of s(1), s(2), ... being iid uniform.
For reference, here's what I find for the Genesis verses,
replacing the words by their lengths (each chain is labelled
with a distinct letter until it merges with a previous chain):
...................................N...N..N..N.... < not yet A
....................................O.O.....O.O..O < not yet A
.........................................P...N.... < not yet A
...............................................Q.. < not yet A
All the chains starting among the first 35 words (not just the
first 10) are seen to merge on or before the 38th word ("the",
marked with "t"). The next word after "the" in that common
chain is "God" (marked with "G").
Chip E. says:
It's a cute observation, more in the vein of recreational math.
Stripped to its mathematical essence, Cliff defines certain "paths"
(subsequences of a particular sequence) by a rule of jumping ahead
from a term in the sequence a number of positions given by the
(positive integer) value of that term.
His claim is basically that by this rule paths from the first ten
terms will all pass through a certain common point not too far from
the beginnings of those sequences. Actually these paths coalesce
slightly before the point indicated in Cliff's puzzle. Of course a
player following a particular path will be unaware that "his" path is
being crossed by other paths.
By the construction of his rule, once two paths "meet" in a common
point, they continue along the same sequence thereafter. Given the
shortness of jumps in these paths, it becomes quite likely that two
paths which start close to one another will quickly merge.
For example, any two consecutive terms of the form n, n-1 will cause
all paths that hit either term to combine at the next term. Four such
pairs occur within the first twenty terms following the starting
points of the ten paths, and are quickly followed by a triple
"trapping" pattern of the form n, n-1, n-2.
It seems that the nature of the sequences plays an important roll here. In
the case of a book with consecutive words having different numbers of
letters there is a certain degree of randomness. But it is easy to have a
sequence (1 2 3 1 2 3 1 2 3 ... ) where two paths will never cross.
So what specific properties must the sequence have? (I hope I am
interpreting this problem correctly).
Spike A. says:
Obvously the page makes a much bigger deal out of it than is necessary.
Also, this isn't really mathematical at all, it's just a coincindence,
albeit an impressive one. Or it's a sign from God procaiming that King
James got it right and that all other translations are bo****ks. Yeah,
that's probably it.
Robert I. says:
Actually, this sort of thing works with many books in most languages
(changing "verse" to "sentence") - best with a text that has fairly short
words and a fairly long second sentence. For example, you might take
1. In a hole in the ground there lived a hobbit.
2. Not a nasty, dirty, wet hole, filled with the ends of worms and an
oozy smell, nor yet a dry, bare, sandy hole ...
If my counting is correct, no matter what word you choose in the first
sentence, you will come to the word "dry".
It's more often done as a card trick.
I would imagine this would only work with the particular
version/translation/language-version that _you_ happen to have?
In either case, you are a nut if you think my "... view of reality will
change as you embark on this shattering odyssey of self-discovery" because
Phil C. says:
Being Nietzsche reincarnate, I simply point the so-called Angel to get
back on his pinhead, and do the same to 1 Samuel.
Sorry Cliff, your guess is wrong. (I didn't land on "God.")
Better luck next time.
Cliff, what is exciting about this problem is that it also appears to
work when using a Hebrew version of the Bible. Now, tell me, what are
the odds of that!
Graham C. says:
1 Au commencement, Dieu créa le ciel et la terre.
2 Or la terre était vide et vague, les ténèbres couvraient l'abîme,
un vent de Dieu tournoyait sur les eaux.
3 Dieu dit : Que la lumière soit et la lumière fut.
It works - but only if you take "l'abîme" as one word, whereas
logically it is two.
In German, Luther's version
1 Am Anfang schuf GOtt Himmel und Erde.
2 Und die Erde war wüst und leer, und es war finster auf der Tiefe;
und der Geist GOttes schwebete auf dem Wasser.
3 Und GOtt sprach: Es werde Licht! Und es ward Licht.
German, the Elberfelder version:
1 Im Anfang schuf Gott die Himmel und die Erde.
2 Und die Erde war wüst und leer, und Finsternis war über der
Tiefe; und der Geist Gottes schwebte über den Wassern.
3 Und Gott sprach: Es werde Licht! Und es wurde Licht.
It works - unless you take 'Erde' in the first verse, when it
Latin, the Vulgate
1 in principio creavit Deus caelum et terram
2 terra autem erat inanis et vacua et tenebrae super faciem abyssi
et spiritus Dei ferebatur super aquas
3 dixitque Deus fiat lux et facta est lux
Doesn't work at all. Mostly you end up on 'et', sometimes on 'lux'.
So it seems to work for Protestants, not Catholics, although the
French confuse the issue. I may look further afield. If I find out
anything interesting I'll report back. Notify my next of kin if you
don't hear anything.
Avi G. says:
If you look at the original (Hebrew) version, you find a similar effect.
Starting at any word in the first verse, you eventually end up at the
word 'elohim' (god) in verse 7, as well as the word 'or' (light) in the
Because of the structure of the hebrew language--words like 'in', 'and',
and 'the' are prefixes rather than separate words--there are only 7
words in the first verse (instead of 10) and 27 words in the first three
verses (instead of 50). Elohim in the 7th verse is the 65th word. Elohim
in the 5th verse is number 41.
Olly H. says:
First of all, I am not moved by the result,and I really don't think
there is anything to be explained here, but I'll be game and offer two
explanations just the same. The first and most likely is that it's simply a
coincidence. The effect would disapear if you simply used another language.
In fact, if the 3 verses weren't stated so awkwardly, you wouldn't even have
the effect in this translation. Is there something "Holy" or "Sacred' or
"magic" about lousy writing and poor syntax? I don't think so.
This brings us to possible explanation two. At the time the KJV was
produced, I've no doubt numerological ideas were probbably fairly popular.
The fact that the "effect" occurs only in the first three verses would make
sense if it was done on purpose. It's a cool way to begin- but you would
never want to have to write the whole thing that way(they'd probably still be
translating the first copy today!)
It is rather tortuously written- full of strange choices of word and
sentences that begin with "And" and so forth- just the sort of thing you'd
expect if it was "tweaked" to achieve a cheesy numerological effect. It seems
Anyway, there's no magic here.
Nice little diversion though. (Don't show it to any Creationists
An even simpler explanation of the "Genesis Effect" which doesn't
require any vague speculations about KJV translators being interested in
numerology or writing it off to coincidence would be as follows: If you take
an arbitrary string of words (the words in the first verse suffice), and play
the game (pick a word, count the letters, find the word that many words away,
count the letters, find the word that many words away, etc), now matter what
word you originally pick, given the length of the text and the preponderance
of words with the same number of letters, any sequence will inevitably
eventually converge to a target word long before the end of the text,
vided the target word appears often enough.
In the Genesis example, I observed the following:
Picking "In" would yield the same result as picking "beginning"
Picking any "the" would yield the same result as picking "beginning" by the
time you got to the 12th word.
Picking "Earth" would yield the same result as picking "beginning" by the
time you got to the 15th word.
Picking "heaven" would yield the same result as picking "beginning" by the
time you got to the 18th word.
Picking either "and" would yield the same result as picking "beginning" by
the time you got to the 38th word.
The first time all paths converge to an instance of "God" is early in
the the third verse, so, we stop there ( note that there are two earlier
instances of God that all paths do not converge to!).
Now if we were bored enough to continue through the bible like this, I
have no doubt that we would find other instances where all of the series of
words converged on "God", as well as any other number of words. For example,
regardless of which of the first 10 words we start on, we converge at the
word 38th word, "the".
You could play this same game with any text, provided that it was long
enough and the target word appeared often enough.
So, as I said earlier, I don't think there is really anything to
explain. Given the length of the Bible and the frequency with which the word
"God" appears, particularly in Genesis, something like the "Genesis effect"
will inevitably be seen if you look for it- it doesn't require numerological
tweaking or coincidence- it's essentially a matter of statistical
Just one final thought about the Reality Game. Just to confirm my
suspicions, I tired it using an email that I selected randomly from the ones
I posted to your discussion group earlier today. I think it illustrates
fairly well the generality of the phenomenon responsible for "the Genesis
Effect" in the Reality Game, which I discussed in my last email.
Consider the first 8 words from the text of the this email I sent to
your discusison group earlier today (text below):
Is our language as complex as our brains
2 3 8 2 7 2 3 6
All of these words "converge" by the 33rd word. That is to say, when we play
the "Reality Game" using the text from this email, regardless of which of the
first 8 words we choose to start from, from the 33rd word on, all of these
words will converge on the same word in the text. If I made liberal
references to God from the 33rd word onward, inevitably we would land on the
word "God", as well as any other number of words. In this case, at the 33rd
word in my email, they all converge to the word "our"- should this be
interpreted as some sort of divine message from the universe? Nah!
Obviously, we can play the reality with any ordinary text, and it
probably doesn't even have to be all that long. Genesis converges after 38
words. This email converges after 33. I suspect any text would converge by
the 50th word, and that really is not very long!
You may contact me if you believe you have
a theory as to why we find this "Genesis Effect," or if you have any comments about this effect.
I'm especially interested in hearing from those of you who did
not finally land on the word "God" or if you have discovered
similar effects in other Biblical passages.
Note that this kind of textual enigma
was discussed by Martin Garder in Scientific American.
The idea of applying Kruskal's principle to a holy text
appears in John Paulos's book Once Upon a Number.
I discuss their work in Wonders of Numbers.
Web page copyright Cliff Pickover.