# Thread: Trefoils in Genesis 1.1

1. Originally Posted by thebluetriangle I'm glad I came back to this. I can't understand how you arrive at the 1 in 8.6 probability. Bear in mind too that my own estimation of probability, which I readily admit is likely too pessimistic and very rough, does not take into account factors like the fact that the inner trefoil in each case can be derived from the self-intersection of the parent G-triangle of the larger trefoil. That reduces the odds even further, in the same way that it is less likely to find an encoded G-triangle within Genesis 1.1 that just happens to be the one that fits snuggly inside triangle 2701 than one of several other possibilities. And it has happened four times here! This is a miracle!

My calculation is simplistic but based on a simple ball-in-a-bag problem. Numerating the four trefoil sequences up to as close to 3000 as possible, gives a set of numbers that could be randomly picked from a bag containing the numbers 1 to 3000. The ten numbers I chose, which would be top of a list of any Genesis 1.1 derived numbers, is equivalent to picking ten numbers out of that bag of 3000 balls, only 114 of which are trefoil numbers, as defined.

I cannot understand how you conclude there are 40 choices. There are only ten as far as I can see - the ten numbers deriving from the standard, ordinal and reduced values and the number of words and letters, both in the verse and in the last two semantically-distinct words.

Sorry, Richard, but I think you've taken a wrong turn here.
Hey there Bill,

I'm glad you are pursuing this. It seems to me that your "ball-in-a-bag" calculation is not merely "simplistic" - it is fatally flawed and extremely misleading. As you know, it would be absurd to suggest that the number of words in a Bible verse has an equal probability of being any number between 1 and 3000. The longest verse in Genesis has only 32 words! The average verse has about 13 words. So if you wanted to calculate the probability of randomly getting a specific value, say 7, then you would have to look at the distribution like this: If we assume this sample of verses from Genesis is a sufficiently accurate representation of the a priori probability distribution, then the probability that a random verse would have 7 words is 4.6% which is about 140 times larger than the number 0.033% = 1/3000 x 100% which you assumed.

We have the same problem with the probability you assumed for each of the features. Each has a very different range of possible values, so the real probability is nothing like your "simplistic" estimation.

And there is really big problem with your use of the Binomial Probability Calculator because your "experiment" is not a Binomial Experiment as defined on the page you linked. Here is the definition:

A binomial experiment has the following characteristics:

1. The experiment involves repeated trials.
2. Each trial has only two possible outcomes - a success or a failure.
3. The probability that a particular outcome will occur on any given trial is constant.
4. All of the trials in the experiment are independent.

Point 3 is violated because, as shown above, the probability for each of the features (number of words, number of letters, various numerical values calculated with different forms of gematria) are most certainly NOT constant! On the contrary, each "feature" has a different probability, and the probability of an individual feature itself is not even constant but follows a distorted Bell curve. A constant probability would be like flipping a coin. You have two choices, and each has a constant probability of 50%.

Likewise, point 4 is violated because the trials are NOT independent. For example, there is a strong correlation between the number of words and the number of letters. Case in point: If you "just happened" to get a verse with 7 letters by chance, then the most likely number of letters would be around 27 or 28! They are not independent because there is an average of around 4 letters per word in Genesis. Now as for the number of "trials" - I said there were 40 trials because you compared each of the 10 "features" with each of the four possible patterns you were looking for. So there were a total of 40 opportunities for a "match". But now that I think of it, I see you were looking for "correlated matches" in which the pair of numbers derived from the pair of 7|2 words both fit the same pattern, which reduces the set of "features" to 5 pairs, rather than 10 independent features. This means you had 20 = 5 x 4 opportunities to find matches because you could compare each pair with the numbers generated by each of the 4 patterns. But this doesn't really matter because you can't apply the Binomial Calculator to these 5 paired features because they all have different probability distributions and the calculator is based on the assumption that they all have exactly the same probability, and that that probability was constant (which is most certainly is not).

Bottom line: If you want to support your case with statistics, you are going to have to do a real statistical analysis.

Great chatting!

Richard  Reply With Quote

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230 Originally Posted by Richard Amiel McGough Hey there Bill,

I'm glad you are pursuing this. It seems to me that your "ball-in-a-bag" calculation is not merely "simplistic" - it is fatally flawed and extremely misleading. As you know, it would be absurd to suggest that the number of words in a Bible verse has an equal probability of being any number between 1 and 3000. The longest verse in Genesis has only 32 words! The average verse has about 13 words. So if you wanted to calculate the probability of randomly getting a specific value, say 7, then you would have to look at the distribution like this:
Thanks for the effort you've put into your reply. It's always appreciated! I agree that the chance of getting the number 7 out of a word count is much higher than the odds I was working with (although I did another calculation in an earlier reply based on your probability and it was still very unlikely, nothing like 1 in 8.6.) On the other hand, though, the chances of 2701 being a trefoil number are much less than the odds I worked with.

So, as it stands, the probability I worked out, which, after I found a powerful enough binomial calculator, was 2 in a trillion, gives an initial ball-park estimate of the probability of finding 9 trefoil numbers out of ten numbers. You seem to be looking at the problem in a way that creates needless complexities (for a ball-park estimate, that is - I know you're aiming for accuracy here). If you look at the ten numbers purely as numbers you have 2, 7, 7, 28, 28, 73, 82, 298, 703, 2701. If we were to randomly pick 10 numbers between 1 and 3000 we would in most instances get higher numbers. The Genesis-derived numbers are therefore skewed towards the lower end, where the probabilities of hitting a trefoil number are higher, since the distance between members of each of the four sequences gradually increases. It's obvious that although the final probability will be nothing like 2 in a trillion, it will be high. Why? Because if the Genesis-derived numbers were not deliberately chosen, they would be blind regarding figurate properties. So the fact that all but one of them (2) are trefoil numbers and that 8 out of these 9 numbers make trefoil pairs, directly related to the prevailing G-triangle geometry within Genesis 1.1, is obviously of great significance if it can be shown to be improbable. Any set of numbers is equally improbable, but most of them are no little or no significance with regards to having related properties both to each other and to other numbers derived from the verse. That is where the significance of the Genesis-derived numbers lies.

Probability theorists will have ways of accounting for this skew towards lower numbers in the 10 values I 'picked' out of the bag of 3000 balls, but it seems obvious to me that you can obtain a very approximate answer to the question "What are the odds against 9 of 10 numbers randomly picked out of a bag of balls numbered 1 to 3000 (with replacement), happening to be trefoil numbers?" You can get an idea of the range of possible probabilities by taking the individual probabilities for the highest and lowest numbers in the set. The highest possible probability is based on the lowest value, 2. For the natural numbers up to 2 (1 and 2) there is a 50% probability of one of them being a trefoil number, 1 being a trefoil number. So if we assume there is a 50% probability of each of them being a trefoil the binomial probabilty of 9 out of 10 being a trefoil (equivalent to tossing a coin 10 times and getting 9 heads) is about 0.01, or 1 in 100. The lowest possible probability will be much lower than 2 in a trillion, maybe 1 in a quadrillion or thereabouts. It's obvious that the overall probability will be way below 1 in a 100, therefore, and easily below 1 in a million, I would guess. That's before we look at the extraordinary fact that the ten numbers are in pairs, the number from the verse being paired with the number from the last two words in the verse, and that four of the five pairs are trefoil numbers related to each other via G-triangle geometry! That itself is extraordinarily unlikely to have occurred by chance.

A separate calculation for each variable would be more accurate, and if I get time I'll do one. The separate probability would then have to be manipulated to get an overall average probability, but I'm not sure how to do that. Take the 10th root of the products of the 10 averages? I've already dipped my toes in the waters of probability theory and I'm not sure I'm capable of going further, not without a lot of training. Even then it might not be of much value, as some of the world's top statisticians and probability theorists disagree entirely about the reality of the Torah codes.

No, I'll stick to the kind of back-of-an-envelope maths I've always done. It has served me well and it is, I believe, good enough to give a very rough idea of how unlikely this phenomenon is. Remember, all I am calculating is the probability of 9 out of those 10 numbers having the properties of rhombic and triangular trefoils, based on numerical triangles and centred triangles. Yes, there is a relationshi between the number pairs, because a small number of letters, for example, must yield a small number of words. But there is zero relationship between any of the derived numbers and the properties of figurate numbers. It simply CANNOT be as high a probability as 1 in 8.6. It MUST be far lower than that. As a working estimate, I would go for 1 in a million, but I bet even that is conservative.

There are other types of trefoils, of course. You might like to see this one, which I derived from Vernon's Creation triangle. Here we see the name and title of Jesus in Hebrew, Yehoshua HaMashiach, related to the Creation triangle, the Star of David and the threeness of trefoils.  Reply With Quote