It's Not Easy
Random WordsA 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.
- 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.
- 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?
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.
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.
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.
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
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.
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
aa. And if
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?
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.
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.
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.