Bible Numbers 2.0

Second Experiment
It's Not Easy

Random Words

A base line has to be established first before trying experiments on finding numbers from English words.

For this, the computer uses a list of 51,000 words to generate 10,000 groups of words at random. The number of words in each group varies at random from ten to a hundred words. Each group is checked for numeric features. Below are the results from ten random generations.

          F0     F1    F3    F5   F6   F7   F8   F10  F11
Test 1:  6122   3655   190   18   9    2    3    0    1
Test 2:  6079   3658   232   17   8    2    3    0    1
Test 3:  6026   3727   218   14   9    2    4    0    0
Test 4:  6155   3601   206   24   9    4    0    0    1
Test 5:  6100   3651   221   15   5    5    3    0    0
Test 6:  6105   3648   211   18   11   4    3    0    0
Test 7:  6174   3587   210   15   7    4    3    0    0
Test 8:  6067   3666   238   14   8    2    4    0    1
Test 9:  6106   3664   204   16   1    3    5    0    1
Test 10: 6074   3675   224   13   8    5    0    1    0

Averaging the ten results, out of 10,000 phrases 61% had no feature at all (F0). 36.5% had one feature (F1). 2.2% had three features. 0.16% had five features. 0.075% had six features. 0.033% has seven features. 0.028% had eight features. And 0.005% had eleven features. This indicates it will not be easy to find numeric features in English. But how does this compare with the actual mathematical odds?

Normally in 10,000 phrases, the odds would suggest a seventh of them (approximately 1428) would be divisible by 7. But the program searches 32 different ways for totals divisible by 7, increasing the chance something would be found (10000 ÷ 7 x 32 ≅ 45714). As can be seen in the table above, only a fraction, or 8% of the 45714 is found in column F1.

Out of 10,000 phrases the odds would indicate 343 would have three features divisible by 7: 10000 ÷ 343 ≅ 29. And by searching 32 ways, this becomes approximately 933. But column F3 at most only has 238 phrases. This is about 25% of what was expected.

Column F5 lists groups that had five features diviible by 7. 75 is 16807. It is a 1 in 16807 chance. In 10,000 phrases less than one, 0.6 would be expected to be found. Searching 32 different ways raises the possibility to 19 being found. Thus column F5 is the closest match to what the odds would expect.

The results in column F6 are several times what the odds would predict (10000 ÷ 76 x 32 ≅ 2.72). And from this point on, it appears easier to have more features. The results in column F7 average out to 3.3 phrases. This is roughly 8 times what the odds would suggest (10000 ÷ 77 x 32 ≅ 0.39).

Column F8 should only have 0.056 phrases (10000 ÷ 78 x 32 ≅ 0.056), but as can be seen the average is 2.8, or fifty times what the odds predicted. Even though it is much easier than the odds would predict, everything is still relative. Test 10 found nothing, and finding nothing increases with each additional level of features checked.

Random generation of Chinese characters produces a very different result because the Chinese language has no alphabet and characters/words are numbered consecutively from one upwards.

Ten thousand groups of characters are randomly put together. Similar to the English experiment, each group ranges from 10 to 100 characters. The values of the characters are then checked for numeric features. This was done fifteen times. (N.B. Since Chinese does not have letters, the computer can only search for features in a total of sixteen ways.)

     F0       F3      F16     F20    F28
    8539     1425      33      3      0
    8647     1324      20      9      0
    8552     1419      23      6      0
    8594     1378      26      2      0
    8613     1361      24      2      0
    8599     1374      24      3      0
    8661     1305      33      1      0
    8570     1402      21      7      0
    8583     1391      22      3      1 
    8641     1338      19      2      0
    8589     1388      23      0      0
    8547     1425      23      5      0
    8581     1392      23      4      0
    8562     1411      21      6      0
    8572     1398      23      6      1 

  128850    20731     358     59      2     Total of results
    8590     1382      23.9    3.9    0.13  Averages

Practically 86% had no features. This compares with the English having only 61% without any features. In other words, it appears to be more difficult to produce numeric features in Chinese.

14% had three numeric features. This is almost half of what the English produced (25%).

From 5 features to 15 features there are absolutely no results.

Abruptly 0.24% have 16 numeric features, 0.039% have 20 features, and amazingly 0.0013% have 28 features.

Out of 10,000 phrases the odds would indicate only 0.00000000000012 would have twenty features divisible by 7 (10000 ÷ 720 ≅ 0.00000000000012). By searching 16 ways, this becomes approximately 0.000000000002, which is still an incredibly small number. But column F28 had an average of 0.13 phrases. If this is usually what happens, then this is roughly 6.4 trillion times more than what was expected.

Like the English, a higher number of numeric features in Chinese is easier to obtain than the odds would indicate, but again this is all relative. A trillion times easier does not outweigh the odds of 720 (≅ 79.8 quadrillion). It is not easy to accomplish.

Why is it more difficult than the odds would suggest to have just a few features, and easier to have more? This is because of the type of numeric feature being searched for. The numeric features the computer searches for are based on Revelation 1:8. Most of them are paired features. If the group total is divisible by seven, and one of the paired features is also divisible by 7, then the other in the pair works as well. By fulfilling two conditions, the third is automatic. This is why it appears easier to accumulate more features than the odds would suggest. But this operates only up to a certain point. The zeroes in columns F8, F10 and F11 begin outnumbering what can be found.

N.B. There are two reasons why there are no columns F2, F4, and F9.

  1. The very first search the computer checks is for the group total being divisible by 7. If nothing else is found, this result is placed in the second column F1. The next search is for a paired feature. If this succeeds, then there are two additional features, and the result ends up in column F3. There is no F2.

  2. Sometimes nothing is found at all, and this can happen anywhere in the table. If more had been checked, more columns would have been filled in.

Everything here was from random words strung together as meaningless phrases. What about actual sentences with meaning?

Meaningful Sentences

This experiment consists of six smaller tests of varying size. The smallest test generates only 270 phrases, while the largest generates up to nine hundred thousand phrases. The results are quite interesting.

Test 1

The first test is from the second paragraph of the American Declaration Of Independence. How else might the founders of America have written it?

(The pipe character | separates the sentence into sections. Within each section are character/word choices separated by a space. The computer runs through the sentence combining the various choices into a complete phrase.)

We-hold Everyone-accepts|these|truths facts|to-be|self-evident clear 
obvious undeniable|that-all|men people men-and-women women-and-men 
women|are|created made|equal-that-they|are-endowed-by-their-Creator-with 
have are-endowed-with have-by-their-God|certain basic various fundamental 
common certain-basic certain-fundamental basic-fundamental basic-common 
common-fundamental|unalienable perpetual|Rights-that-among-these-are-Life|
Liberty Freedom Self-determination|and-the-pursuit-of-Happiness
Phrases generated: 38400
Number of phrases with features:
f1: 14125; f3: 731; f5: 62; f6: 35; f7: 21; f8: 10; f11: 2;

     Expected    Found     Ratio F/E
f1   175543      14125       0.08
f3     3852        731       0.19
f5       73         62       0.85
f6       10         35       3.5
f7        1.5       21      14.0
f8        0.2       10      50
f11       0.0006     2    3333

F1 represents the number of phrases that had one, and only one of thirty-two methods finding a total divisible by 7. 14,125 of 38,400 phrases fall into this category. If only one method was used to find a feature, the expected number found would have been 38,400 ÷ 7, or 5485.7. But since thirty-two different methods were tried, this increases the chances of finding more. The number expected to be found would be 5485.7 x 32 or 175,543. The program found 14,125, which is one twelfth what was expected.

F3 represents phrases succeeding three ways. If only one method had been tried, the number expected would have been 38,400 ÷ 343, or 112. Thirty-two different methods multiplies the number possible: 112 x 32 = 3582. The program found 731, which is one fifth of what was expected.

F5 represents phrases with five features. Seventy-three were expected. The program found 62. Although this is less than expected, it is not too far from the odds.

F6 Ten were expected to be found. The program found 35, which is three times more than the odds would suggest.

F7 Only 1.5 were expected, but the program found 21. This is fourteen times what the odds would expect.

F8 0.2 were expected, but the program found ten (fifty times the odds!).

F11 0.0006 were expected, but the program found two (3333 times the odds!).

The result is similar to the base line experiment. Actual English sentences do not seem that different from random words.

Finding just one feature is more difficult than the odds would suggest, but finding several features appears easier. But this is all relative. More difficult than the odds, or easier than the odds in reality is still extremely difficult. Just because one phrase out of 38,400 succeeded doesn't mean it would be easy to find. Computers make it easy, but if you didn't have a computer, one in 38,400 would be very difficult.

Test 2

The second test is a re-writing of Truman's recognition of Israel in 1948.

This Our|government nation|has-been-informed has-been-notified 
has-received-information|that-a-Jewish|state nation|has-been-proclaimed 
has-been-formed has-been-established has-been-set-up|in-Palestine-and|
recognition acknowledgement support|has-been-requested|by-the|provisional 
temporary transitional|Government-thereof state-thereof by-that-Government 
by-that-state|The-United-States The-United-States-of-America|recognizes 
acknowledges supports accepts|the|provisional temporary transitional|
government-as-the-de-facto-authority-of-the|state-of-Israel Jewish-state 
state-of-Ysrael
Phrases generated: 248832
Number of phrases with features:
f1: 89496; f3: 4605; f5: 318; f6: 220; f7: 45; f8: 32; f10: 2; f11: 19; 
f12: 3; f13: 1;

     Expected      Found       Ratio F/E
f1   1,137,518     89,496        0.079
f3      23,215      4,605        0.198
f5         474        318        0.671
f6          67        220        3.28
f7           9.7       45        4.64
f8           1.4       32       22.86
f10          0.03       2       66.66
f11          0.004     19     4750.0
f12          0.0006     3     5000
f13          0.00008    1    12500

The results are similar to the first test. Less than expected is found for the first few categories. More then expected is found for the more difficult categories.

Test 3

The basic sentence: Jack and Jill ran up the hill to fetch a pail of water. Jack fell down the broke his crown and Jill came tumbling after.

Jack-and-Jill Jill-and-Jack Jack Jill They|ran jogged trotted sprinted 
dashed slogged|up-the|hill mountain slope|to|fetch obtain get fill|a|
pail bucket barrel|of-water of-oil of-money|Jack-fell-down-and-broke-his|
crown skull neck leg arm shoulder elbow forearm foot toe|and|Jill they|
came|tumbling barreling|after.
Phrases generated: 129600
Number of phrases with features:
f1: 48145; f3: 2760; f5: 271; f6: 207; f7: 14; f8: 13; f11: 12;

      Expected   Found   Ratio F/E
f1    592457     48145      0.08
f3     12091      2760      0.23
f5       247       271      1.09 
f6        35       207      5.91
f7         5.03     14      2.78
f8         0.72     13     18.06
f11        0.002    12   6000.0

This third test confirms the pattern noticed in the first two. Finding phrases having from one to four features is more difficult than the odds would suggest. Finding phrases with more than four features is easier than the odds would indicate. (See the conclusion for an explanation for this oddity.)

Test 4

These three fictitious phrases are from the experiment on a Chinese version of the Balfour Declaration. They are re-written from the Balfour Declaration in favour of a Palestinian state instead of Israel.

(N.B. Since the Chinese language consists only of words/characters and has no letters, for these experiments the search is only for 16 different features divisible by seven, not 32 like the English.)

皇帝陛下的政府|喜歡看見 看重 贊成|在巴勒斯坦 巴勒斯坦內|成 立 成立 建立|
一個|國 國土 家 國家 家園 國家家庭 國民之家|給巴勒斯坦|人 民族 人民族|
並將盡努力這目標|便利順行 順行 順利實現 順利成功|但它顯然明白不會作出|
侵害破犯 侵害 破犯 損害 害|猶太人 猶太民族|的 0|權和 民權和 權利和|宗教 教|
利 權 權利|或其他國家的猶太人享有的權利和政治地位
Phrases generated: 725,760

      Expected     Found     Ratio F/E
f1    1658880      295735      0.18
f2     236983      119425      0.5
f3      33855       71662      2.1
f4       4836       14391      2.98
f5        691        8913     12.9
f6         99        1295     13.1
f7         14.1       897     63.6
f8          2.0       212    106
f9          0.3        85    283
f10         0.04       28    700



皇帝陛下的政府|喜歡看見 看重 贊成|在巴勒斯坦 巴勒斯坦內|成 立 成立 立成 建立|
一個|國 國土 家 國家 家園 國家家庭 國民之家|給巴勒斯坦|人 民族 人民族|
並將盡努力這目標|便利順行 順行 順利實現 順利成功|但它顯然明白不會作出|
侵害破犯 侵害 破犯 損害 害|猶太人 猶太民族|的 0|權和 民權和 權利和|宗教 教|
利 權 權利|或其他國家的猶太人享有的權利和政治地位
Phrases generated: 907200

      Expected      Found   Ratio F/E
f1    2073600       369739  0.18
f2     296228       149009  0.5
f3      42318        89168  2.1
f4       6045        18024  2.98
f5        864        11166  12.9
f6        123         1611  13
f7         18         1144  63
f8          2.5        251  100
f9          0.36       106  294
f10         0.05        37  740
f11         0.007        2  286


皇帝陛下的政府|喜歡看見 看重 贊成 贊有利|在巴勒斯坦 巴勒斯坦內|
成 立 成立 立成 建立|一個|國 國土 家 國家 家園 國家家庭 國民之家|
給巴勒斯坦|人 民族 人民族|並將盡努力這目標|便利順行 順行 順利實現 順利成功|
但它顯然明白不會作出|侵害破犯 侵害 破犯 損害 害|
其他國家的巴勒斯坦人享有的權利和政治地位
Phrases generated: 16800

f1 38400         6807      0.18
f2  5486         2726      0.5
f3   784         1642      2.1
f4   112          384      3.4
f5    16          260     16
f6     2.3         46     20
f7     0.3         17     57
f8     0.04         8    200
f9     0.007        2    285
f12    0.00002      1  50000

(The results for the three Chinese tests are all similar. But that probably is because the basic phrase in each test was similar.)

A meaningful Chinese sentence produces results different from random Chinese characters. In the random tests above, entire categories of features were missing. With an actual sentence more of these categories are filled in. This contrasts sharply with English where random and meaningful sentences show little difference.

F1 represents the number of phrases that had one, and only one of sixteen methods coming to a total divisible by 7. In all three tests only a fifth of what was expected was found. This is more than twice what was found in the English tests.

F3 represents the number of phrases with three of sixteen methods succeeding. The three Chinese tests come up with twice what the odds would suggest. This is ten times what was found in the English tests.

For category F5 Chinese produces fourteen times the number of features compared with English. And in each category, more is found in Chinese than in English.

Finding numeric features in Chinese is much easier than finding them in English. There is a logical reason.

Chinese characters (words) are numbered consecutively from 1 to 14,000 (or more). English words are not. This is a fundamental difference. There are no gaps between the numbers from 1 to 14,000. In English there are number gaps or gaps in value, and some of those gaps could be huge and irregular. In Chinese, there is an even balance of words divisible by N (whatever N might be), because every Nth character would be divisible by N. This does not exist in English.

Consequently, if an English sentence needed only one more word to be divisible by Y, and the word required had to have the value of 2, then there would only be two possible words b or aa. And if b or aa did not fit the sense of the sentence, then the sentence would never be divisible by Y. This restriction makes it much more difficult to manufacture a numeric phrase in English. And conversely for Chinese, it is easier because there are more word choices.

How much has the consecutive nature of the Chinese language affected the odds?

Test 5

An attempt is made to have Genesis 1:1 re-written in Chinese with more features.

起初 太初 第一 起頭 首先|上帝 天主 耶和華 神 耶和華神 天主神|創造 創 造|
天地 天和地 宁宙
Phrases generated: 270
      Expected  Found    Ratio F/E
f1    617        128     0.21
f2     88         18     0.2
f3     12         27     2.25
f4      1.8       11     6.1
f5      0.26       2     7.7
f6      0.04       1    25
f7      0.005      2   400
f8      0.0007     1  1428

The same can be tried with Joshua 1:1-2.

耶和華 上帝 天主|的僕人 的手下|摩西死了以後|耶和華 上帝 天主|曉諭摩西的 向 對|
幫手 助手|嫩的兒子約書亞|說 話|我的|僕人 手下|摩西死了|現在你要起來 你要站起來|
和眾|百姓 民|過這約但河往我所要|賜給 畀|以色列 人的地去
Phrases generated: 6912
   Expected    Found     Ratio F/E
f1 15799       2751      0.17
f2  2257       1158      0.5
f3   322       668       2.1
f4    46       189       4.1
f5     6.6     75       11
f6     0.94    29       31
f7     0.13    5        38
f8     0.02    6       300
f9     0.003   1       333

The complete results of ten experiments are tabulated in the table below to get a sense of the actual odds in Chinese.

             Chinese          Recognition   Palestinian  Muslim   Chinese     Palestinian Balfour       A          B              C
  Proclamation  Balfour    I         II       State      State    State       I       II      III

    62985600    907200  6967295   83607552   6967296   6967296  13934592   725760   907200   16800 = 183986591

f1: 25725254   370209   2903430   34492360   2806723   2822320   5788165   295736   369740   6807  = 75580744  420540779          0.18
f2: 10301991   149395   1091852   13262307   1105675   1105279   2181101   119425   149009   2726  = 29468760   60077254          0.49
f3:  6161633    88963    638762    7897494    690530    677307   1294753    71662    89168   1642  = 17611914    8582465          2.05
f4:  1228295    17663    109529    1531674    176789    166907    236343    14391    18024    384  = 3499999     1226066          2.8
f5:   750951    11195     80497    1016773     98115     94940    167356     8913    11166    260  = 2240166      175152         12.8
f6:   107565     1547      9726     149551     20686     19864     22258     1295     1611     46  = 334149        25022         13
f7:    76133     1118      8249     100830      9037      8454     16849      897     1144     17  = 222728         3574         62
f8:    16571      242      1484      23915      3312      3198      3606      212      251      8  = 52799           511        103
f9:     6064       91       664       8180       800       670      1303       85      106      2  = 17965            73        246
f10:    1831       35       195       3084       469       438       446       28       37      0  = 6563             10        656
f11:     205        4        27        371        34        39        53        0        2      0  = 735               1.5      490
f12:     111        1        14        214        55        35        25        0        0      1  = 456               0.21    2171
f13:       3        0         2         10         0         0         0        0        0      0  = 15                0.03     500
f14:       2        1         0          8         6         0         1        0        0      0  = 18                0.004   4500

A: Total number of phrases generated, and phrases found for each category.
B: Number expected according to the odds.
C: Ratio (those found ÷ expected).

Like the English, the Chinese also has more difficulty than the odds would suggest in producing just one or two features. And it is easier than the odds would indicate for Chinese to produce more than two features.

From F1 to F10, the Chinese consistently produces more features than English. But this changes from F11 and up. From this point onwards, English produces more features than Chinese.

Test 6

Aside from some historical documents, much of this site is from the Christian perspective. What about something from the Islamic perspective? Islam claims to be the successor religion of Judaism and Christianity. And at times, Islam has claimed to be the original and true religion. Do the numbers have something to say about this? Or is there something that can be learned from the numbers about Islam?

The test will be carried out in English. (1. See Alphanumeric Substitutions for reasons why Arabic is not used for numbers. 2. I don't know Arabic.)

The Islamic declaration of faith is There is no God but God and Muhammad is his prophet. The phrase is very short, so it is unlikely to have any numeric coincidences. To increase the chance something will be found, words are added that do not change the basic meaning.

There
is be was will-be was-and-is is-and-was was-is-and-will-be was-will-be-and-is is-was-and-will-be is-will-be-and-was will-be-is-and-was
no no-other no-additional no-alternative no-different no-remaining no-separate
God Divinity Deity Allah
but barring except excepting save
God Divinity Deity Allah
and
Muhammad
is
his God's Allah's
0 final last closing concluding end ending latest terminal ultimate definitive most-recent
prophet seer messenger warner
There|be is was will-be was-and-is is-and-was was-is-and-will-be was-will-be-and-is is-was-and-will-be is-will-be-and-was will-be-is-and-was|no no-other no-additional no-alternative no-different no-remaining no-separate|God Divinity Deity Allah|but barring except excepting save|God Divinity Deity Allah|and|Muhammad|is|his Gods Allahs|final last closing concluding end ending latest terminal ultimate definitive most-recent 0|prophet seer messenger warner

The following data generated 887,040 permutations. The two results with the highest number of coincidences are presented below.

There is, was, and will be no other God barring Deity and Muhammad is his last prophet.

There be no Deity but Deity and Muhammad is Allah's last prophet.

Each sentence had at least 16 numeric coincidences. This is the highest number of results in all our tests because it involved the most combinations. (More tries equal more found.) But there are shortcomings with both results. Allah's name does not appear in the first sentence, but God and Deity. No other God barring Deity doesn't quite make sense. Allah appears in the second result, but separate from Deity. It could be argued the two are not the same. No Deity but Deity sounds like circular reasoning, and again doesn't quite make sense.

716 is 33,232,930,569,601, but this has to be reduced by the 887,040 permutations tried, and by the 32 features searched for. This brings it down to one in 1,170,780. The odds are nowhere near what will be seen later. While this does not prove the Muslim statement of faith to be false, it certainly doesn't engender confidence when the result is inferior to the original.

Conclusion

Why is it more difficult than the odds would suggest with what should be easier (one or two features), and easier with what should have been more difficult (several features)? Shouldn't it be easier to find phrases with just one feature, and more difficult to find those with more features? This would be true if the computer was searching for random features divisible by 7. (In other words any numeric feature.) In this case, the computer is searching for orderly numeric features, features that come in pairs. Once the basic order is established and works, it becomes easier to find something else based on it.

Manufacturing numeric features is easier in some languages than in others. English is more difficult than Chinese at the outset. This changes when searching for a higher number of numeric features. This is because English words are composed of letters. The computer can search for numeric features in words and in letters. This extra search doubles the opportunity for more to be found in English once a workable structure is discovered. In Chinese, the search ends after sixteen methods are tried in the characters.

Test 2 (English) produced one phrase with the highest number of numeric features: 13. This was 12,500 times more than the odds would suggest. A phrase with 13 features divisible by 7 is a one in 96,889,010,407 chance. 96889010407 ÷ 12500 is still one in 7,751,121. One in seven million sounds a lot easier than one in ninety-six billion. This is why it was possible something could be found. But one in seven million isn't easy if you don't have a computer.

The third part of Test 4 (Chinese) produced one phrase with 12 numeric features. Given the small number of phrases generated, this was 50,000 times what was expected. A phrase with 12 features divisible by 7 is a one in 13,841,287,201 chance. 13841287201 ÷ 50000 is still a one in 276,826 chance. This sounds even better than one in seven million.

It would appear numeric features in language are inherently better than the odds would suggest. This proves Case 2 on the previous page. But this is all relative. The last category of fourteen features tells it all. Out of the total 183,986,591 phrases generated, only 18 were found. This works out to one in 10,221,477. One in ten million is very difficult to find. Finding numeric features is easier than what math would suggest, but they are by no means guaranteed.

Just because a computer can now run through tens of millions of combinations to generate a phrase with many numeric features does not destroy the numeric features found in the Bible. The Bible was not done with a computer.

When the odds against finding something are extremely high, nothing should be found at all. If something is found against all reason, is it still coincidence or is it something else? You will have to decide that on your own.

Notes

1Scripture references are from the Revised Standard Version, Thomas Nelson Inc., New York, 1972.

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The Rational Bible

Bible Issues

presents the Bible as a rational book, as history, economics, and prophecy (with an extensive look at the book of Revelation) also covering a diverse range of topics. (Active site.)




Preaching the word is the priority. Not numbers. (Acts 6:2)