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Your persistent assertion that I had "an influence on the pattern" baffles me. Is it not obvious that I had nothing to do with the formation of the 39 Book canon? Exactly how does the fact that I chose to study it have anything to do with any patterns it may or may not contain?
Hi AngCath,AngCath said:Well you say the Vulgate chose the order... except that you took out Tobit, Maccabees, etc. and you say the Tanach chose the content... except that you chose to make the Minor Prophets 12 books instead of 1.BibleWheel said:Your persistent assertion that I had "an influence on the pattern" baffles me. Is it not obvious that I had nothing to do with the formation of the 39 Book canon? Exactly how does the fact that I chose to study it have anything to do with any patterns it may or may not contain?
Your influence on the pattern is your very assumption that the Canon as laid out by the Reformers is true. Have you done the same analysis with the Roman Canon? any of the various Eastern Canons?
BibleWheel said:Actually, statistical theory shows that the organization of the Old Testament as we have it in the Protestant Bible is extremely unlikely. There is exactly one chance in 34,871,760 that a three-level symmetry like what we find in the OT happened by chance.
The math is elementary. Consider a list of 39 objects. How many ways is there to divide them into three groups? The answer is easy to calculate. We need to just drop two "dividers" ^ in the list below.
1 2 3 4 ^ 5 6 7 8 ... 35 36 ^ 37 38 39
How many ways can we do this? Well, there are 38 slots to drop the first divider, and then there will be 37 slots to drop the second divider. Thus, there are 38 x 37 = 1406 ways to divide the 39 books into three groups.
This is basic combinatorics.
And how many of these will show the symmetry like the 17 : 5 : 17 of the OT? That too is easy to calculate. Suppose the first divider is dropped between books n and n+1. To achieve the symmetry, the second divider must be dropped between books 39-n and 39-n+1. This symmetry can be written in terms of "n" as n : 39-2n : n. Since n can range over 1 to 19, we have exactly 19 possible ways to divide the 39 books into three symmetric groups.
So what is the probability that we would find a canon with the top-level symmetry of the OT "by chance"? It is simply the ratio 19/1406 = 1/74. Not too rare really. The top-level symmetry is not by itself proof of design.
But now lets consider the second level of symmetry. We do the same calculation as above, only now we drop in two more dividers.
38 x 37 x 36 x 35 = 1,771,560 ways to divide 39 books into 5 goups.
How many of these will show the second-level symmetry of the OT? To see this, we need to write it abstactly as follows:
Top-level n : 39-2n : n [OT has n=17 to give 17 : 5 : 17]
Second-level n-m : m : 39-2n : n-m : m [OT has n=17, m=12 to give 5 : 12 : 5 : 5 : 12 ]
Now to achieve a symmetry for all m like the second level of the OT, the size of the first, the third, and the fourth divisions must all the same. In the existing Canon, these groups all have 5 Books. Mathematically, this demands that n-m = 39-2n. This gives a restraint on both m and n:
m = 3n-39, and since 0 < m < n-1, we also have a restriction on n such that 13 < n < 20.
Therefore, second-level symmetry demands a structure that can be represented by a single variable "n" that ranges from 14 to 19:
39-2n:3n-39:39-2n:39-2n:3n-39 with 13<n<20
The are only six solutions that match the constraints. Here they are:
n=14 11:3:11:11:3
n=15 9:6:9:9:6
n=16 7:9:7:7:9
n=17 5:12:5:5:12
n=18 3:15:3:3:15
n=19 1:18:1:1:18
So there are six symmetric solutions out of 1,771,560 possibilities. Thus, there is one chance in 295,260 =6/1,771,560 that this structure would appear by accident. The numbers are starting to look pretty persuasive, and this is only at the second level of symmetry.
But there's another thing to consider before moving on to the third level. I speak of the self-witness of Scritpure to the meaning of the numbers God used in the design of the Old Testament. How many loaves fed the five thousand? FIVE. How many baskets left over? TWELVE. What is the symbolic meaning of BREAD in the Bible? It is the WORD OF GOD that feeds the disciples. There is much more to say on this, but now is not the time.
Moving on to the third level of symmetry, we do the same math as above and drop in two more divisions.
No other form of the Christian Canon (RCC, GO, or any other) shows the same evidence of design.
Either I have made an error in the calculations, which I trust you will point out, or we are beholding a mathematical proof of the Divine Design of the Old Testament Canon.
BibleWheel said:Hey Philip - this is cool! I didn't see this post before I posted my analysis. I myself have degrees in math and physics. I worked on a PhD in Quantum Theory, though I never completed it.
BibleWheel said:Your persistent assertion that I had "an influence on the pattern" baffles me. Is it not obvious that I had nothing to do with the formation of the 39 Book canon? Exactly how does the fact that I chose to study it have anything to do with any patterns it may or may not contain?
The symmetries of the Julia set derive inevitably from a MATHEMATICAL LAW. The structure of the 39 Book OT Canon derives from (seemingly) free choices made by the many people that God used in the process of its formation. To compare the two seems to me to be utterly meaningless.
BibleWheel said:I do not "reject the testimony of the Church through the ages." As I see it, there is only one universal testimony of the Church through the ages. All Christians agree that the 39 Books of the Protestant OT are canonical.
No, I do not "pick and choose" the evidence. I have compared all forms of the OT canon and concluded that the Protestant form is unique in its structure. I have not ignored any evidence whatsoever.
I need assume no such thing. My point is that the natural history of the Protestant Bible prohibits the conclusion that is was deliberately designed by humans to fit a fancy pattern. There is no assumption whatsoever about which is the "correct" canon or that my "theory" is correct.
You twice highlighted the pronoun "you." This is misleading. "I" had nothing to do with the formation of the canon. I was talking about what the REFORMERS did when they rejected the deuteros. "I" had no hand in their decision.
It was not an appeal to authority. It was an merely an example that others have seen a relation between symmetry and design.
It would help if you didn't characterize every point of disagreement as a "logical fallacy" on my part. A little charity goes a long ways in forums like this.
You erred in evaluating my intent when I made this point. My intent was to show that many people infer that structure implies design. I thought it would be obvious that I was not applying this particular example to the structure of the OT.
It does extend to an infinite depth. I just haven't shared the rest with you yet.
But even if the symmetry only went three levels deep, you conclusion would still be invalid because the three levels of symmetry by themselves are extremely rare.
BibleWheel said:And yes, I have analysed every variation of the OT that I know of - Jewish, RCC, GO, Protestant, and others - and the PROTESTANT OT CANON stands out as unique amongst all forms ever produced on planet earth. It bears the Sign and Seal of being designed by the Lord God Almighty.
Thanks for the correction! That was a silly mistake. I forgot to divide by the number of ways to arrange the dividers, something everyone learns in introductory courses on combinatorics. Like I said in a previous post, I, like all humans, make mistakes. I hope that everyone in this forum will be charitable with each other in this regard. So you are correct, the number of possible canonical structures divided into three groups is 703.Philip said:Mistake #1. The grouping of books is independent of the order in which the divisions are made. Placing the first divider in slot 1 and the second divider in slot 2 yields the same result as placing the first divider in slot 2 and the second divider in slot 1. There are 703 [ C(38,2) ] combinationsBibleWheel said:The math is elementary. Consider a list of 39 objects. How many ways is there to divide them into three groups? The answer is easy to calculate. We need to just drop two "dividers" ^ in the list below.
1 2 3 4 ^ 5 6 7 8 ... 35 36 ^ 37 38 39
How many ways can we do this? Well, there are 38 slots to drop the first divider, and then there will be 37 slots to drop the second divider. Thus, there are 38 x 37 = 1406 ways to divide the 39 books into three groups.
Correct again, for the same reason. I like the way you noted it as "Mistake 1b" since it was a silly repetition of Mistake 1.Philip said:Mistake #2. (Or at least Mistake 1b.) Again, the divisions are independent of the order in which the dividers are placed. The value we want here is C(38,4), not P(38,4). There areBibleWheel said:But now lets consider the second level of symmetry. We do the same calculation as above, only now we drop in two more dividers.
38 x 37 x 36 x 35 = 1,771,560 ways to divide 39 books into 5 goups.
C(38,4) = 38! / (4! 34!) = 73,815
ways to divide 39 books into 5 groups.
I paramaterized the second level symmetry to impose the constraint that every solution will show both the top and second level symmetry. This does not limit the sample space of all possible 5-group canonical structures - it limits the solution space (see below).Philip said:Mistake #3. Your calculations assume that the first and second level of symmetry are independent events. I see no reason to assume that they are independent. Further, since you speak of a 'three-level symmetry', I doubt that you believe that they are independent.[BibleWheel said:How many of these will show the second-level symmetry of the OT? To see this, we need to write it abstactly as follows:
Top-level n : 39-2n : n [OT has n=17 to give 17 : 5 : 17]
Second-level n-m : m : 39-2n : n-m : m [OT has n=17, m=12 to give 5 : 12 : 5 : 5 : 12 ]
That's why the symmetry exhibited in the Protestant OT is so rare. The constraint selects a subset (the solution space) of all possible 5-group canonical structures (the sample space).Philip said:If you want the specific symmetry you describe, not all of the 73,815 combinations we calculated above are valid. Once you've fixed the first two dividers to get your first level of symmetry, you limit the places where the third and fourth dividers can be placed.
It seems like you are confusing the sample space with the solution space.Philip said:We are dividing the sets of size n into sets of size n and n-m. Assuming we do not want any null sets, there are exactly n-1 ways to do this. So, while there are indeed 73,815 ways to make five sets out of 39 books, not all of those are valid members of your sample space. The sample space for your second level of symmetry is only 19 * (n-1) * (n-1)since there are 19 combinations valid for the first level of symmetry and n-1 slots in which you can place the third and fourth dividers. As you noted above, n is bounded from above by 19. So, given that the first level of symmetry is present, the cardnality of your sample space for the second level is at most 19*18*18 = 6,156. That is a far cry from the nearly 2 million you claimed above.
This is incorrect. The error is that you confused the sample space with the solution space.Philip said:Given that the first level of symmetry exists, the odds that this second level also exists are, at worst, a mere 6/6,156.
That's actually pretty funny Philip! You asserted that I rejected "the testimony of the Church through the ages" and now you admit that some canonical books were contested, meaning there was no single "testimony of the Church through the ages" in the first place, and that voids your original assertion.Philip said:There are two errors here. First, many Christians, ancient and modern, have questioned the canonicity of Esther, Canticles, and others. Second, it seems that you are confusing the concept of 'agreeing that a set of books is canonical' with 'agreeing that a set of books is the entire extent of the canon'.BibleWheel said:I do not "reject the testimony of the Church through the ages." As I see it, there is only one universal testimony of the Church through the ages. All Christians agree that the 39 Books of the Protestant OT are canonical.
I never meant to imply that there were no other canons with any symmetry of any kind. There could be some other pattern that I know nothing of that might suggest design. But that is not relevant to the question at hand. When I spoke of "no symmetry" it was obviously in the context of the symmetry "like" what we see in the Protestant OT. My assertion is that the symmetry of the Protestant OT implies design, and that its symmetry is unique amongst all OT canons ever compiled.Philip said:Please provide proof of this. Post your analysis that neither the Roman not the Greek canon contain any symmetry. It is not sufficient to show that they do not contain the same symmetry you see in the Protestant canon. You need to prove that they have no symmetry.BibleWheel said:No, I do not "pick and choose" the evidence. I have compared all forms of the OT canon and concluded that the Protestant form is unique in its structure. I have not ignored any evidence whatsoever.
That's a really odd question Philip! I don't have to assume a square is symmetric to study its symmetry. I just take the object and analyse its behavior under rotation and reflection and note what I see. Then I take a triangle and do the same thing, and find different symmetries. Then I take an arbitray irregular closed polygon and find no symmetry. In no case do I assume that the object of my study has any symmetry at all.Philip said:Of course you assume your theory is correct. How can you study a symmetry without first assuming that symmetry is present?BibleWheel said:I need assume no such thing. My point is that the natural history of the Protestant Bible prohibits the conclusion that is was deliberately designed by humans to fit a fancy pattern. There is no assumption whatsoever about which is the "correct" canon or that my "theory" is correct.
Yes, in my personal devotion I "choose to use the canon they set out." But for the sake of my argument that I am presenting here, I have chosen nothing. I am discussing all forms of the OT canon. Their's just happens to stand out as uniquely symmetric, amongst other things.Philip said:You most certainly do have a hand in accepting their decision. You may not have participate in their decision, but you did choose to use the canon they set out.BibleWheel said:You twice highlighted the pronoun "you." This is misleading. "I" had nothing to do with the formation of the canon. I was talking about what the REFORMERS did when they rejected the deuteros. "I" had no hand in their decision.
Oh, I will share it when we finish with these preliminaries. You may recall my desire to narrow down the discussion until we can find true agreement on points of fact. If we can't do that, further discussion would be futile because it would mean one or both of us is not dealing with reality.Philip said:Please do share it. This should be quite interesting. Am an intrigued by the possibility of a finite structure such as the OT ever having an infinite depth. The idea that there is a structure across the entire depth is just icing.BibleWheel said:It does extend to an infinite depth. I just haven't shared the rest with you yet.
I believe I proved the claim in the last post. I await your evaluation.Philip said:I await proof of this claim as well.BibleWheel said:But even if the symmetry only went three levels deep, you conclusion would still be invalid because the three levels of symmetry by themselves are extremely rare.
I changed your character to "Psi" because it showed up as a "?" on my screen.Philip said:Let's try an analogy from QT. Let Psi by the wave function of a particle. Observe the particle's position in spacetime. This yields a specific point, say (x,y,z,t). Now, look back at Psi. Compute the probability that the particle will be found at the specific coordinates (x,y,z,t). Since (x,y,z,t) has a Lebesgue measure of 0, it doesn't matter* what form Ψ has, the probability of particle being at (x,y,z,t) is precisely 0. Not near 0. Not infinitesimally small. It is 0. In fact, the probability that the particle is at any specific point is 0. Yet, when we observe the particle, it is somewhere. How can this be? How is it possible for the particle to be at a specific location when the probability of it being there is 0?BibleWheel said:Hey Philip - this is cool! I didn't see this post before I posted my analysis. I myself have degrees in math and physics. I worked on a PhD in Quantum Theory, though I never completed it.
No.Philip said:Do you see the connection with your claim about symmetry?
I didn't say the symmetries were "built into the equations that describe them." Besides, that's a meaningless statement anyway. The equations don't DESCRIBE what the two-dimensinoal represention of the Julia set looks like, the equations GENERATE the pattern!Philip said:The symmetries of a Julia set are not built into the equations that describe them. The symmetries are just there. There is no reason 'why'. They are not designed to be there. This exposes the error in your thinking about symmetry implying design.BibleWheel said:The symmetries of the Julia set derive inevitably from a MATHEMATICAL LAW. The structure of the 39 Book OT Canon derives from (seemingly) free choices made by the many people that God used in the process of its formation. To compare the two seems to me to be utterly meaningless.
Actually, there is a very strong link on multiple levels. First there is the beauty of God's great and wonderous creation of His Word. People have noticed all kinds of symmetry in it. For example, many things lost in Genesis are regained in Revelation. There is a kind of "closure" to the whole Divine Drama even as it opens unto Eternity. This is an example of thematic symmetry.AngCath said:I don't know about the math. I care about the fact that you link patterns/symmetry with "divine beauty." you can prove and reprove all the symmetry you want, but nowhere in all that math does the link from pattern to God emerge.
BibleWheel said:That's actually pretty funny Philip! You asserted that I rejected "the testimony of the Church through the ages" and now you admit that some canonical books were contested, meaning there was no single "testimony of the Church through the ages" in the first place, and that voids your original assertion.
I never meant to imply that there were no other canons with any symmetry of any kind.
I have compared all forms of the OT canon and concluded that the Protestant form is unique in its structure. I have not ignored any evidence whatsoever.
And yes, I have analysed every variation of the OT that I know of - Jewish, RCC, GO, Protestant, and others - and the PROTESTANT OT CANON stands out as unique amongst all forms ever produced on planet earth. It bears the Sign and Seal of being designed by the Lord God Almighty.
Look at that. Each division has its own distinct number of books. There is no symmetry whatsoever. Exactly what we would expect from a chance distribution.[Emphasis mine]
There could be some other pattern that I know nothing of that might suggest design. But that is not relevant to the question at hand.
When I spoke of "no symmetry" it was obviously in the context of the symmetry "like" what we see in the Protestant OT.
My assertion is that the symmetry of the Protestant OT implies design,
and that its symmetry is unique amongst all OT canons ever compiled.
I did a quick review of the RCC OT canon in the previous post. Pretty much the same thing holds for the various Orthodox canons, since they are all just variations on the deuteros.
Now if you really want to challenge my assertion, why not present counter-example that you think has any chance of competing with the Protestant version?
That's a really odd question Philip! I don't have to assume a square is symmetric to study its symmetry.
Yes, in my personal devotion I "choose to use the canon they set out." But for the sake of my argument that I am presenting here, I have chosen nothing. I am discussing all forms of the OT canon. Their's just happens to stand out as uniquely symmetric, amongst other things.
Oh, I will share it when we finish with these preliminaries. You may recall my desire to narrow down the discussion until we can find true agreement on points of fact. If we can't do that, further discussion would be futile because it would mean one or both of us is not dealing with reality.
I believe I proved the claim in the last post. I await your evaluation.
Well, since you are Eastern Orthodox, I am guessing you actually mean "Easter Orthodox" when you write "the church as a whole." The discussion on this point is thus reduced to an absurdity. You knew perfectly well that I was speaking of all christian churches - Catholic, Protestant, and all varieties of Orthodoxy with their different deuteros - when I made the statement about the universal Christian acceptance of the protocanon. Your response, therefore, does not relate to my point.Philip said:You reveal your ignorance of Orthodoxy. I do not claim that any book has universal support. I claim that the Church as a whole (but not each and every individual) supports a particular canon.BibleWheel said:That's actually pretty funny Philip! You asserted that I rejected "the testimony of the Church through the ages" and now you admit that some canonical books were contested, meaning there was no single "testimony of the Church through the ages" in the first place, and that voids your original assertion.
You have mischaracterized my claim. I've never suggested that an entire OT canon was universally accepted. My my claim is and has been that the only set of OT books 'universally accepted by all Christians' as canonical are the 39 books of the Protestant OT. Excluding possible fringe groups that still reject some of the protocanonical books and the history of various disputes that have long been settled "in the church as a whole," my statement stands as self-evident to anyone familiar with the issues at hand.Philip said:It is you that claim a universally accepted canon. Can you demonstrate such a canon that is, in your own words 'universally accepted by all Christians'? I doubt it.
You are correct about my use of the word "unique" - even with the success of my argument, the question of uniqueness will still have to be addressed. But at this stage, the question of uniqueness is not the "center of the discussion." The center of the discussion is whether or not the Protestant OT was designed by God. If this is settled in the affirmative, then there is reason to discuss its implications and the possibility of as yet undiscovered patterns in other canonical structures. If in the negative, the point would be moot, so it is not relevent to the discussion at hand.Philip said:Incorrect. It is at the very center of the discussion. Let us suppose for the moment that the RC canon does have a (yet undiscovered) symmetry equal to that you claim is in the protestant canon. If this is the case then, according to your argument, both of them were designed by God. For you to argue that the Protestant canon uniquely bears the stamp of God, you must eliminate the possibility that any other canon likewise bears such a stamp.BibleWheel said:There could be some other pattern that I know nothing of that might suggest design. But that is not relevant to the question at hand.
Sure, I make the claims, I provide the evidence. I was just trying to help. One of the fastest and most effective methods of proving someone wrong is to give a counter-example to their assertions. But of course you won't attempt this, because you know I am correct on this point. There is no known pattern in any other canonical structure that is anything like the three-level symmetry we see in the Protestant OT.Philip said:Nice try. You claim that the Protestant canon uniquely has a non-random structure. It is up to you to demonstrate that is the case. It is not up to me or anyone else to disprove your claim. The burden rests on you to demonstrate that your claim is true.BibleWheel said:Now if you really want to challenge my assertion, why not present counter-example that you think has any chance of competing with the Protestant version?
I think I get what you mean. For example, in my analysis I didn't think about other forms of symmetry like the second half mirroring the first rather than repeating it, or some such subtlety. So you are right, but the calculations we did seem sufficient to establish the fundamental point that the symmetry is indeed rare.Philip said:You misunderstand. In order to preform the calculations you want to use to show that this symmetry is rare, you must first assume not only the existence a symmetry, but also its particular form.BibleWheel said:That's a really odd question Philip! I don't have to assume a square is symmetric to study its symmetry.
Yes, I asserted it is uniquely symmetric. And so it is to my knowlege, which means I spoke the truth as I know it. If you know about some other "even more unusual structures" in some other canon, let me know! It sounds interesting.Philip said:There you go again claiming that it is uniquely symmetric. Is it your belief that the Protestant canon is uniquely symmetric? Sure, it may be the only one with your pet symmetry, but you have yet to demonstrate even the slightest evidence that other canons do not have even more unusual structures?BibleWheel said:Yes, in my personal devotion I "choose to use the canon they set out." But for the sake of my argument that I am presenting here, I have chosen nothing. I am discussing all forms of the OT canon. Their's just happens to stand out as uniquely symmetric, amongst other things.
Ok- first, I am thinking of probabilitity in terms of "configurations" rather than "events."Philip said:Okay, I've looked over your explanation again, and I don't understand the process you are trying to model. At some points, it seems like you treat the placement of the dividers as independent events. At other times, it seems you want the placement of dividers to be dependent on the placement of previous dividers.
Can you explain the process you are trying to model? Which events are independent, and which are dependent? Don't worry about any calculations, we'll get to those latter. Just describe the random process you are trying to model.
Father Demetrios Serfes said:Strictly Speaking, there never was a "Bible" in the Orthodox Church. At least not as we commonly think of the Bible as az single volume book we can hold in our hand. Since the beginning of the Church, from the start of our liturgical tradition, there has never been a single book in an Orthodox church we could point to as "the Bible".
Instead the various "Books" of the Bible are found scattered throughout several service books located either on the Holy Altar itself, or at the chanter"s stand. The Gospels (or their pericopes) are complied into a single volume -- usually bound in precious metal and richly decorated -- placed on the Holy Altar.
The Epistles (or, again, their pericopes) are bound together in another book, called the Apostolos, which is normally found at the changer"s stand. Usually located next to the Apostolos on the chanter"s shelf are the twelve volumes of the Menaion, as well as the books called the Triodion and Pentekostarion, containing various segments of the Old and the New Testaments.
The fact that there is no "Bible" in the church should not surprise us, since our liturgical tradition is a continuation of the practices of the early Church, when the Gospels and the letters from the Apostles (the Epistles) had been freshly written and copied for distribution to the Christian communities.
The "Hebrew Scriptures" (what we now call the "Old Testament", comprising the Law (the first five books) and the Prophets, were likewise written on various scrolls, just as they were found in the Jewish synagogues.
BibleWheel said:Hi AngCath,
As I'm sure you know, the Prots would see things in exactly the opposite light - namely that the deuteros were contested throughout the history of the church and only officially established as canonical at Trent (1545 AD) in response to the Reformation.
I imagine this has been discussed here quite a bit. I'm new here, so could you point me to a thread that discusses this?
Thanks!
Richard
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