I've been busy today, but i'll be working on it tomorrow. It shouldn't be too hard to figure out the percentage of numbers within a given range that can be expressed as trefoils, triangular trefoils and their centred-triangle equivalents.
I'm curious about your claim that this is inconsistent though. There seems to me to be a great deal of consistency here. Remember, the words in the text had to be meaningful and grammatically correct, so there was relatively little wiggle room for encoding mathematics. Yes, they are three different kinds of trefoil, but as always they are the simplest, most natural trefoils, analogous to the Star of David, all deriving from G-triangles. There is your consistency. It's G-triangle geometry that holds it all together. The fact that so much mathematics has been found in there, some of it by yourself, is evidence not of some trivial number game but of the playful Mind of our Creator at work. But again, if it can be shown that any old piece of text could produce such numbers then it really is trivial.
By the way, what did you think of the encoding of the Star of Stars in Genesis 1.1? Here it is again.
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I used a binomial probability calculator to work out how many numbers in the first 3000 are either rhombic trefoils, triangular trefoils and their centred-triangle equivalents.
There are
a) 31 rhombic trefoils
b) 44 triangular trefoils
c) 19 centred rhombic trefoils, and
d) 26 centred triangular rhombic trefoils (sorry, can't think of better terminology at present)
in the first 3000 natural numbers.
The sum is 120 and since some of the numbers are shared this reduces to 114 (at least, I only calculated up to 1000 or so).
114/3000 = 0.038, which is the probability of success on a single trial.
I derived 10 numbers from Genesis 1.1: 2701/703, 298/73, 82/28, 28/7, 7/2.
Of the ten numbers 9 gave trefoils, so the number of successes was 9.
Plugging in the numbers gives a probability of success of <0.00000001, or less than 1 in a 100 million. However, it is much less probable even than that, because even 7 out of 10 hits has a probability of success of less than 1 in 100 million. I think we're talking many billions to one against it being chance, based on that calculation. Of course, it's an after-the-fact calculation, and there are many other geometric figures that could have been found. Taking these facts into account would increase the odds considerably. But these trefoils are the simplest of their kinds and they all derive from G-triangles and G-triangle geometry has already been shown to be prominent within Genesis 1.1. These mitigate against it being chance, because the trefoils are part of a larger theme involving basic G-triangle geometry. The triangle itself is the simplest 2D figure and its preeminence within the numbers underlying Genesis 1.1 points to the Christian concept of the Trinity.
The accumulated geometric evidence points to design, using G-triangle geometry as the principle unifying theme.
Here's the calculators I used https://www.stattrek.com/online-calc.../binomial.aspx
https://www.danielsoper.com/statcalc...tor.aspx?id=69
Thanks for the analysis, but I think there are some serious flaws in it. I'll explain more this evening after work when I have time and access to some data I need.
In the meantime, perhaps you could address a problem with your approach. You are treating this question as if it could be answered by a simple statistical test, but you have not explained the details or shown that any statistical scientist has ever used your method to prove that a small isolated text contained "evidence of design." If your method is valid, I would think you should be able to find examples in the scientific literature that use it.
Well, gotta get back to work. Talk more soon.
- Skepticism is the antiseptic of the mind.
- Remember why we debate. We have nothing to lose but the errors we hold. Who but a stubborn fool would hold to errors once they have been exposed?
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Hey there Bill,
As I mentioned before, statistics can be very tricky and neither you nor I are professional statisticians. So it's not surprising that your "analysis" is filled with fatal flaws and that it took me most of the day to begin to understand your errors.
Rather than explaining your errors, I've decided to start with a couple facts and four hints in the hope that you will be able to figure it out for yourself.
Fact 1: This is the distribution of the Word Count for each verse in Genesis.
Hint 1: The number that caught your attention, 7 words, accounts for 4.69% of the 1533 verses in Genesis.
Hint 2: The distribution spans only 30 numbers, which is only 1% of the range you assumed in your statistical analysis.
Fact 2: This is the distribution of Letter Count for each verse with 7 words in Genesis: Note that the twin peaks center on 27 and 28, the latter number you treated as "random" in your analysis.
Hint 3: The number of letters is not statistically independent of the number of words.
Hint 4: The distribution spans only 13 numbers, which is about 0.4% of the range you assumed in your statistical analysis.
Hope that helps!
Looking forward to discussing this more with you.
- Skepticism is the antiseptic of the mind.
- Remember why we debate. We have nothing to lose but the errors we hold. Who but a stubborn fool would hold to errors once they have been exposed?
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I'll quickly answer both of your replies here.
I wasn't promoting my result as definitive - far from it. It's very much a back-of-an-envelope calculation and I am aware that there are serious flaws in modelling the numbers derived from Genesis 1.1 as a balls-in-a-bag problem. But I think it indicates to the reader that this is not something you would normally expect to have happened. I think you would agree that it is a very unlikely event. Yes, every single set of numbers derived in this way is unlikely, but this is unlikely and mathematically significant, which nearly every other set of numbers would not be.
It would certainly be possible to refine the model, perhaps by working out the likelihood of trefoils within the likely range of each number (so for the number of words it might be something like 2 to 35, for the number of letters 10 to 70, for the standard value 1000 to 5000, something like that), then calculate the overall probability. That would still be pretty inaccurate, I suspect, but it would be closer to the truth. With effort a much better method could be developed, but I have never seen anything like this attempted. That scientific method of analysing textual features you were asking about may not exist.
One thing I would say though is that it is clear even to a non-statistician like me that something very unusual is going on in Genesis 1.1.
Here's another very back-of-an-envelope calculation. The number of words is 7, which is a trefoil. In the range 3 to 30 your analysis of word counts showed, five numbers are trefoils of the four types I mentioned - 7, 10, 16, 25 and 28. This gives p = 5/28 for the number of words being one of those trefoils. Compared with the number of letters and the three numerical values, 5/28 will be the highest probability. In other words, the number of words is most likely of all the variables to be a trefoil. We already know that the last two words can never be a trefoil, but let's keep it in anyway. Let's also be very conservative and assume that all of the other probabilities are 5/28, or 0.18. So we have 9 successes out of ten 'trials' with p = 0.18 for each trial. The probability of 9 out of 10 hits is then 1 in 600,000. So it is still fabulously unlikely! Since this is the most probable it could be, the real probability of finding trefoils of these types is surely much less than that.
As I said before though, it's an after-the-fact calculation and there are many other geometries that could have been found. But the common triangularity of these figures, their G-triangle origins, the fact that G-triangle geometry is so prevalent in Genesis 1,1 and so meaningful in representing life, fecundity and our fractal universe, along with the fact that triangles and trefoils are such simple uncontrived figures anyway, all point the other way: towards deliberate design!
Hello again Bill,
There is another critical error in your calculations that we must correct before we can get an accurate estimate of the probability.
Your count of "trials" is off by a factor of four. Each of the ten features was tested against each of the four patterns, so the number of trials was 40, not 10.
This is easy to see. Consider one hypothesis at a time, such as the hypothesis that all 10 features would match the first pattern. How many trials? 10. How many successes? 2.
You must test each of the 10 features against each of the four patterns - that's how you got your 9 successes. So the total number of trials was 40, not 10.
This means that your real "success rate" was only 22.5% rather than the 90% that you claimed.
I'll see if I can get an accurate estimation of the probability when I get home this evening. I'm at work.
- Skepticism is the antiseptic of the mind.
- Remember why we debate. We have nothing to lose but the errors we hold. Who but a stubborn fool would hold to errors once they have been exposed?
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Hey there Bill,
Using your estimation of 0.18 for the probability, and using the correct number of trials (40) and successes (9) we get a probability of about 1 in 8.6!
In other words, it seems that there's nothing about your trefoils that indicate "something very unusual going on in Genesis 1:1."
Of course, this was obvious to me before plugging the numbers into the binomial calculator because you had to invent four different patterns just to get a 22.5% success rate.
I think it is extremely important for you to ponder what has happened here. You went from claiming a chance of "1 in a 100 million" followed by a claim of "1 in 600,000" when in fact the real chance is around 1 in 9!
Like I said, statistics can be very tricky, especially when your intuition is biased and you are trying to use them to prove something like numerology.
- Skepticism is the antiseptic of the mind.
- Remember why we debate. We have nothing to lose but the errors we hold. Who but a stubborn fool would hold to errors once they have been exposed?
Check out my blog site
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.
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