Some notes on the "25 trees experiment"

One of the earliest and most famous Torah codes "experiments" concerned the appearance of the names of 25 trees encoded in a portion of Genesis that describes the Garden of Eden. In this article we demonstrate that the claimed amazing result was artificially manufactured by manipulating both the data and the method of analysis.

We will write Hebrew words using the Michigan-Clairmont transliteration scheme.

The Claims

The first published report of this experiment appeared in the article "Codes in the Torah, Reading with Equal Intervals" by Daniel Michelson, published in B'Or HaTorah, Volume 6, 1987:

The text in Figure 15 consists of Genesis 2 (this is an enlargement of the third page of Figure 10). Verse 9 reads: "And from the earth G-d caused to grow every tree that was pleasing to the sight and good for food, and the tree of life in the middle of the garden and the tree of knowledge of good and evil". As names of the trees are not mentioned explicitly in this chapter, Rips suggested that perhaps they are hidden there at equal intervals. He took all the 25 trees named in the Torah (as listed in "The fauna and flora of the Torah" by Yehuda Feliks) and found them in the above chapter! Before the reader jumps out of his seat, let us explain that three or four letter words would normally appear with some intervals in a segment as long as ours (about 1000 letters). What is so exceptional here is that most of the intervals (except for @RMN and LBNH) are very short. There is no other segment in Genesis of such length which contains so many trees with intervals less than 20. Based on the density of the letters in the chapter one could estimate the probability of the "orchard" phenomenon the number is about 1 in 100,000!

Consulting Figure 15 of Michelson's article, we don't find Chapter 2 exactly, but rather the passage from Gen 2:7 to Gen 3:3. We also see there a list of the 25 "trees". We will refer to that portion of Genesis as GT.

The Data

In order to check the objectivity of the data, we compared the list of trees in Michelson's paper to the list in Feliks' book, with the kind assistance of Prof. Feliks. We were surprised to discover some significant differences, which we display in the following table. In each case, the minimum skip of the word in GT is indicated. The notation "np" means "not present as an ELS".

```     Rips         Feliks         Notes

X+H   5  *      -        Wheat is not a tree (see note)
GPN  18       GPN  18    Vine
@NB   6  *      -        Grape is not a tree (see note)
@RMN  44  *  @RMWN  np    Chestnut, @RMWN in the Torah
@BT   3  * @C @BT  np    Dense forest
TMR   5       TMR   5    Date
\$+H   3       \$+H   3    Acacia
A+D   7       A+D   7    Bramble
ARZ   5       ARZ   5    Cedar
B+N  13  *   B+NH  np    Nut
TANH  14      TANH  14    Fig
@RBH  15      @RBH  15    Willow
RMWN   8      RMWN   8    Pomegranate, RMN and RMWN in the Torah
AHLYM   6     AHLYM   6    Aloe
A\$L   2       A\$L   2    Tamarisk
ALWN  17      ALWN  17    Oak
LBNH  85      LBNH  85    Poplar
QDH   7       QDH   7    Cassia
\$QD   5       \$QD   5    Almond
ALH   2       ALH   2    Mastic
SNH   9       SNH   9    Thorn bush
LWZ  13       LWZ  13    Hazel
ZYT   3       ZYT   3    Olive
HDR   3  * @C HDR  np    Citron
GPR   8       GPR   8    Fir
-       *   BDLX 158    Comiphora Africana
-       *   NKAT 107    Astragalus
-       *   QNMN  np    Cinnamon
```

Here we can see 9 differences between the original list and the list that, according to Michelson, Rips used.

Note that a midrashic argument can be advanced that wheat is a tree, but Prof. Feliks used the botanical classification and did not list it as such. Also, he listed the grape vine under GPN, not under @NB (which is the name of its fruit). In each case the only scientific choice was to follow the given source, not to look for excuses for violating it.

Analysis

Recall from Michelson's article that the "real" claim about the 25 trees is not their mere appearance as ELSs but the smallness of their skip.

Indeed, the odds are about 50% that all 25 trees of Rips' list appear as an ELS with some skip in GT, so that by itself is uninteresting.

The smallness of the skip might be measured in a number of different ways. First consider the measure used: the number of trees with skip less than 20. Let us see whether "20" was a fortuitous choice. The following table shows the number of trees in each list which appear with a skip less than the bound indicated.

```      Skip         Rips     Feliks

At most 10       17        13
At most 20       23        18
At most 30       23        18
At most 40       23        18
At most 50       24        18
```

We can see two things. Firstly, 20 is the optimal cutoff. Secondly, the original list of Feliks does much worse than Rips' modified list.

Michelson does not state precisely what method was used to compute the "1 in 100,000" he claims, but we can infer it was probably similar to this: permute the text at random, and find the probability that the number of trees with an ELS of skip at most 20 is as great as it is for the real text.

Such a method for computing probabilities is well established to be invalid, as meaningful texts have a fundamentally different structure from randomised texts, but we will use it here since Rips used it. Using 100,000 random permutations of the text, we find that a cutoff of 20 does very much better than other natural cutoffs, and also (again) that Rips' list of trees does much better than Feliks' list. The following table gives the rank out of 100,000 random permutations for each list and each cutoff.

```      Skip         Rips      Feliks

At most 10       187       1050
At most 20         4        163
At most 30       438       3199
At most 40      3534      14035
At most 50      2953      31540
```

To avoid the arbitrariness of the cutoff value, we considered other ways to measure the claim that the skips are unusually small. The most obvious is to measure the average minimum skip of those trees in the Feliks list which appear as an ELS. For GT, this average is 23.6667. For 1000 random permutations of GT, an average that small or smaller occurred 97 times. So, by this way of measuring, a result of around 10% is obtained. A similar result is obtained if we restrict our attention to those permuted texts containing the same number of trees (21) as GT contains.

In addition, we have to ask whether the smallness of the skip was predicted, or noticed afterwards. Unless it was decided in advance to use the smallness of the skip, with a cutoff of 20, as the measure of success, the probability is invalid. The other experiments from around the same time-period (such as the Aaron experiment) usually focused on the number of ELSs rather than the size of the smallest skip. The total ELS count for the Feliks list is 1163. Looking again at 1000 randomly permuted texts, we find that they have total ELS counts ranging from 921 to 1239. Altogether 32 have 1163 or more ELSs, so this method gives a score of 3%, which is completely insignificant statistically.

The Text

Perhaps the most arbitrary choice in the design of Rips' experiment was the choice of text passage. Although the verse Gen 2:9 is highly relevant, there is nothing about the content of the surrounding verses to indicate a natural boundary at Gen 2:7 or Gen 3:3. The smallest surrounding natural division in the Hebrew Bible runs from Gen 2:4 to Gen 3:15, but that performs over 100 times worse (for Rips' list of trees).

So where does the choice of Gen 2:7 to 3:3 come from? Out of the 9 possible combinations of starting at Gen 2:6, 2:7 or 2:8, and ending at Gen 3:2, 3:3 or 3:4, the choice giving the strongest result is the one Rips used.

Conclusions

In order to achieve the strong result report by Michelson, we need all the following choices:

1. The list of trees modified from what is in Feliks' book.
2. The criterion of minimal skip.
3. The cutoff of 20 for the minimal skip.
4. The text boundaries set at Gen 2:7 and Gen 3:3.

It should be obvious that all those choices cannot have been merely fortuitous. No, they were adjusted to make the result as strong as possible. Such adjustment completely invalidates the computed probability.

There is no evidence whatever that there are trees encoded into the Bible to a degree unexplainable by reasonable chance.

Note that this early experiment probably illustrates an ignorance of correct experimental procedure rather than any specific desire to deceive.