The Canonization of Maccabees

[AngCath]

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?

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.
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]

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?

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.

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?

Hi AngCath,

I'm sorry to have to say this, but all your statements are false. "I" did not take out Tobit, Maccabees, etc. The Reformers excluded those books long before I was born. Neither did "I" choose "to make the Minor Prophets 12 books instead of 1." That was done many centuries ago by the translators of the Septuagint. And neither did "I"exert an "influence on the pattern" by merely pointing it out! Furthermore, at no point does my argument ever depend upon the assumption that the Reformer's Bible is "true."

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.

Richard

 

[Philip]

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.

We shall see. However, I notice a potential problem already. Are you going to calcutate the odds of having any 'three-level symmetry' or the of having the specific 'three-level symmetry' you claim?

EDIT: After reading the rest of your post, it is clear that you are attempting to compute the odds of the specific symmetry you observe. If you want to argue the uniqueness of the symmetry suggests design, you need to examine the odds of there being any symmetry present. Actually, I am not sure this can be done. It is more likely that you will need to compute the odds that there is no symmetry present and then infer the odds of the being any symmetry.

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.

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) ] combinations.

This is basic combinatorics.

Yes, and you made a freshman mistake.

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.

This is overkill, but okay. It suffices to observe that the position of the first divider uniquely determines the position of the second divider.

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.

Actually, 19/703 = 1/37.

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.

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 are

C(38,4) = 38! / (4! 34!) = 73,815​

ways to divide 39 books into 5 groups.

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 ]

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.

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.

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.

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

Again, this is overkill. It suffices to notice that the position of the third divider uniquely determines the position of the fourth divider.

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.

Not really. Given that the first level of symmetry exists, the odds that this second level also exists are, at worst, a mere 6/6,156.

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.

Coincidences like this are meaningless. The Bible is full of numbers, and you can always find one to match. If the number 1 came up, you would note that there is 1 God. If the number 2 came up, you would note that God created 2 humans, Adam and Eve. If the number 3 came up, you would note that God is 3 Persons. If the number 6 came up, you would note that God created the world in 6 days. If the number 7 came up, you would note that the creation story covers 7 days. We can find all kinds of connections like this. I've covered 1,2,3,6, and 7, and I am still in the first couple chapters of Genesis.

Have you ever read St Irenaeus's Against Heresies? He takes great pleasure in denouncing the Gnostics for supporting their doctrines with exactly these kinds of observations.

Moving on to the third level of symmetry, we do the same math as above and drop in two more divisions.

And more of the same mistakes. I will skip the details. However, I will take the time to ask if you have done any hypothesis testing on the significance of your findings.

No other form of the Christian Canon (RCC, GO, or any other) shows the same evidence of design.

This is a blank claim. You have not demonstrated it to be so.

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.

This is a false dilemma.

 

[Philip]

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.

Let's try an analogy from QT. Let &#936; 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 &#936;. 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 &#936; 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?

Do you see the connection with your claim about symmetry?





* Okay, the form of &#936; can be important. If &#936; is a dirac delta or similar distribution, the probability will be nonzero. However, this is an extremely special case. To my knowledge, it does not coorespond to any real world situation. For the sake of this analogy, let us assume that &#936; is a Schwartz test function.

 

[Philip]

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?

You are choosing a specific combination, the Jewish canon in the Vulgate order, and looking for symmetries in it. You admit that you are choosing a specific case to study. Rather than look for patterns in a general case, you deal with a specific case. A proper study would look at the general case and determine the probabilty that no symmetry should exist.

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.

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.

 

[Philip]

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.

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'.

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.

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.

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.

Of course you assume your theory is correct. How can you study a symmetry without first assuming that symmetry is present?

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.

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.

It was not an appeal to authority. It was an merely an example that others have seen a relation between symmetry and design.

As I noted before, you have not established that these others who have seen a relationship between symmetry and design have any expertise in the area. You did, however, hold up an irrelevent expertise (authorship of a large dictionary). Tell me, why should I accept their opinions on a relationship 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.

That is the beauty of mathematics and logic. Mathematics is not a matter of charity. Either something is logical or it is not. Indeed, I consider it to uncharitable to not point out errors in logic when I see them.

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.

Then you have fail to meet your goal. The use of literary styles such as chiasic structure can be seen across many texts, both Scriptural and secular. When an author follows an established pattern, there is reason to look for design. You claim that the symmetry of the OT is unique, that it does not follow an established pattern. I renew my assertion that you have made a false association.

It does extend to an infinite depth. I just haven't shared the rest with you yet.

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.

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 await proof of this claim as well.

 

[Philip]

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.

Please post you analysis. I would be interested in seeing method by which you prove the 'Sign and Seal of being designed by the Lord God Almighty' is not present. Indeed, proving that there is no pattern is a difficult, if not impossible, task. The fact that we can not discern a pattern is not evidence, much less proof, that a pattern does not exist.

 

[BibleWheel]

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.

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) ] combinations

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.

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.

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 are
C(38,4) = 38! / (4! 34!) = 73,815
ways to divide 39 books into 5 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.

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 ]

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.

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).

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.

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).

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.

It seems like you are confusing the sample space with the solution space.

The sample space is the set of all possible 5-group canonical structures, which we agree has 73,815 elements.

The solution space is the set of all possible 5-group canonical structures that satisfy the following constraints:

n-m : m : 39-2n : n-m : m with 1 < n < 20 and 0 < m < n

These constraints select all 5-group canonical structures that exhibit both the top and the second levels of symmetry without the constraint that the first division on the second level is the same size as the second division on the first level (this will be discussed below).

Given that the first level of symmetry exists, the odds that this second level also exists are, at worst, a mere 6/6,156.

This is incorrect. The error is that you confused the sample space with the solution space.

Now we need only to count the number of solutions that satisfy the constraints listed above. This is easy. For each n, there are exactly n-1 possibilities for m (as you correctly noted above), and n runs from 2 to 19, so the answer is .....

Sum[n=2 to 19](n-1) = 171

This number is larger than the six solutions found in the previous post because I did not apply the constraint that links the second level symmetry to the first level. This constraint demands that n-m = 39-2n (discussed below).

Therefore, the correct probablitiy (assuming I haven't made any more silly mistakes) is given by:

171/73,815 x 100% = 0.23%

That's about one chance in 431.

This is the chance that a 5-group canon would exhibit the symmetry of the Protestant OT without the constraint that the first group of the second level is the same size as the middle group of the first level. This constaint is expressed by writing n-m=39-2n. Solving for m we have m = 3n-39, which implies 13 < n since 0 < m. Substituting this in the formula above yields:

39-2n : 3n-39 : 39-2n : 39-2n : 3n-39 with 13 < n < 20

Obviously, there are exactly six solutions, and we have the final result:

6/73,815 x 100% = 0.0081%

Alternately, we can write this as one chance in 12,302.5

And that is only for the second level symmetry. What if we add the third? As far as I can tell, the only error in my previous calculation of this number was my use of P(38,6) rather than C(38,6) = 2,760,681 for the sample space. So the answer is:

57/2,760,681 x 100% = 0.0021%

That's one chance in 48,433

Now lets consider what this means. All the math was really unnecessary. It should have been intuitively obvious to you, with your knowledge of combinatorics, that a three-level symmetric structure was much less likely than a non-symmetric structure. The actual number itself is not particularly significant for the argument.

My original point stands. The three-level symmetric stucture of the Protestant OT is very rare indeed. It also is unique amongst all forms of the OT canon ever produced. Lets look at the Catholic OT as an example. It has 46 books:

5 Books of the Torah
14 Books of History (Joshua-Nehemiah, Tobias, Judith, Esther)
7 Books of Wisdom
6 Books of the Major Prophets
12 Minor Prophets
2 Books of Maccabees (the topic of this thread!)

First note that this canonical structure doesn't even display a consistent pattern of categorization. Maccabees is historical, and so is out of place with the rest of the historical books. As similar problem is seen in the Tanakh, where Chronicles is placed anachronistically at the end after Ezra/Nehemiah!

But lets try to lay out the Catholic canon to see what we get:

Top-level 19 History : 7 Wisdom : 18 Prophets : 2 History

This exhibits no symmetry and a broken categorical order.

Second-level 5 Torah : 14 History : 7 Wisdom : 6 Maj Proph : 12 Min Proph : 2 History

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.

Third level - why bother? Its not there!

I assert that there is no other OT canon on the planet that exhibits any symmetry like that of the Protestant OT. I don't need to go through every canon for you. If you want to challenge my assertion, all you need to do is go find one that is comparable in any way to the divine beauty of the Canon God gave us in the Protestant OT.

I really want to thank you for reviewing this with me. Iron sharpens iron!

Richard

 

[AngCath]

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]

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.

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'.

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 was just following your lead - IF there is any universal testimony of the whole body of Christians, it testifies to the 39 Books. Yes, some of them were contested at various times, but the protos are now all accepted. The same can not be said for the various Orthodox deuteros, some of which are rejected by other Orthodox groups, others by the Catholics, and all by the Protestants.

As for your second point: there was no confusion there at all. My whole point is that there is no agreement amongst RCC, GO, and Prots about the "entire extent of the canon." The only agreement is that the protocononical subset is 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.

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.

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.

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? And since you are Orthodox, why not limit the discussion to the what you know best? Just present the Orthodox OT and we can discuss it.

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.

Of course you assume your theory is correct. How can you study a symmetry without first assuming that symmetry is present?

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.

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.

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.

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.

It does extend to an infinite depth. I just haven't shared the rest with you yet.

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.

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.

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 await proof of this claim as well.

I believe I proved the claim in the last post. I await your evaluation.

Richard

 

[BibleWheel]

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.

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 &#936; 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?

I changed your character to "Psi" because it showed up as a "?" on my screen.

Your suggestion has a couple errors. First, no one has ever measured the exact space-time point (x,y,z,t) of any particle in any experiment. To use your language, this is a "freshman mistake." All measurements are inexact.

Second, you have presented a semi-classical view of QT, which is ok for a freshman class, but completely inadequate for any really meaningful discussion. You asserted that "the probability that the particle is at any specific point is 0." This is meaningless in QT. The theory makes no predictions about where a particle "is." It only predicts the range of readings you will find on your instrument when you measure it. This all falls under the rubric of "The Problem of Measurement" which is a fundamental issue in the foundation of QT. I had the good fortune of studying under a professor who specialized in this very topic.

Do you see the connection with your claim about symmetry?

No.

Richard

 

[BibleWheel]

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.

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.

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!

Just like the equation F(n) = F(n-1) + F(n-2) with F(0)=F(1)=1 generates the Fibonacci sequence.

A second error is your assertion that there is "no reason why" the symmetries of the Julia set exist. Of course there is a "reason." The graphical display of the data reveals the underlying patterns that exist in the set selected by the iterative function. Your statement is like saying that the equation y = x^2 doesn't "explain" why a hyperbola is minimized at x = 0.

But none of this has anything to do with the topic at hand. I NEVER said or implied that every symmetric structure always implies design. That would be a ludicrous statement. Look at a snowflake. Their symmetry reveals the action the underlying physical laws. It has nothing to do with intentional design.

The topic at hand is nothing like a snowflake. We are talking about literary works here that were intentionally designed (to a greater or lesser extent, there certainly appears to be some random elements) by intelligent agents.

My assertion is that the symmetry of the OT can not be attributed to the humans that God used in its design, and that it didn't happen by chance nor by natural law, and so we have evidence of its divine origin.

Richard

 

[BibleWheel]

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.

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.

But the "jump" from the symmetry of the OT to the "Sign and Seal of God" will require a larger view that takes in the whole 66 Book canon. I will share that when we finish up the review of the OT.

Richard

 

[Philip]

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 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. 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.

I never meant to imply that there were no other canons with any symmetry of any kind.

Then what, exactly, did you mean by these statements.

In Post 39, you wrote

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.

In post 42, you wrote

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.

Finally, in post 48, you state

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]

In post 48, you explicitly stated that 'there is no symmetry whatsoever'. But now you want to claim that 'I never meant to imply that there were no other canons with any symmetry of any kind.' Come, on. Which is it? Is it your position that the RC and EO canons have no symmetry?

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.

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.

When I spoke of "no symmetry" it was obviously in the context of the symmetry "like" what we see in the Protestant OT.

It was not obvious to me. But the fact that you think it was obvious suggests that you have not consided the possibilities of other, perhaps more subtle or intricate, structures in other canons.

My assertion is that the symmetry of the Protestant OT implies design,

An assertation that still remains unproven.

and that its symmetry is unique amongst all OT canons ever compiled.

But, you admitted above that you do not know if other canons have structures built into them. Without knowning whether or not they do, all you can conclude is that the Protestant canon has a unique structure. You have no basis for saying its structure is more unusual, more symmetric, more beautiful, or anything else since you do not know what structures to compare it to.

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.

Okay, so they don't exhibit your special pet pattern. You, by your own admission, do not know what patterns they might have. These patterns might be substantially more intricate than the one you are so proud of.

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?

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.

That's a really odd question Philip! I don't have to assume a square is symmetric to study its symmetry.

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.

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.

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?

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.

Okay.

I believe I proved the claim in the last post. I await your evaluation.

You did not. I will respond to your claims about the sample space once I have had time to examine them. However, even if we assume you are correct, all you have demonstrated is that your particular pet symmetry is rare. You have not proven that all 'three-level symmetries' are rare. It may be the case all arrangements have an equally rare symmetry. If this is so (and the burden of proof rest on you to show it is not so), then we should not be surprised if one particular symmetry shows up in a random process.

 

[Philip]

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.

 

[BibleWheel]

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 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.

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.

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 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.

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.

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.

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.

The important thing to understand is that the discovery of the Divine Design of the Protestant OT does not in and of itself necessarily imply the invalidity of larger structures in other canons that include the deuteros. That is an entirely different issue. The truly wonderful discovery of the design of the Protestant canon is that all christians everywhere can delight in what God has done. This should be a point of unity, not division.

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?

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.

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.

That's a really odd question Philip! I don't have to assume a square is symmetric to study its symmetry.

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.

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.

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.

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?

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.

As it stands, there's no reason to belabour the point of uniqueness. That is not part of the fundamental argument. The fundamental argument is as follows:

1) The Protestant OT exhibits an extremely unlikely three-level symmetry (1 chance in 48,433).
2) The natural history of the formation of the Protestant canon can not account for this symmetry.
3) Since neither chance nor intentional human activity can account for this symmetry, God did it.

For unbelievers, I would probably need to nuance my final clause "God did it," but amongst brothers, I think the conclusion is obvious engough.

Richard

 

[BibleWheel]

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.

Ok- first, I am thinking of probabilitity in terms of "configurations" rather than "events."

Very simple. How many configurations possible with no constraints? That is the sample space .

How many configurations possible given the constraints? That is the solution space.

Edit to add: I reread your question, and think there is more to say. Consider the second-level constraints:

n-m : m : 39-2n : n-m : m with 1 < n < 20 and 0 < m < n

All the dependence is in the constraints. When we do the calculation, we have to keep 0 < m < n. That's all. That's why the calculations are so easy. The same thing goes for the third level. Specify the structure in terms of constraints, not in terms of "dependency" on previous actions.

Hope that helps,

Richard

BTW - I'm loving the conversation!

 

[BibleWheel]

To really "get" the significance of the calculations, I think it is important to reverse the numbers, and list how many of all possible canonical structures do NOT show the symmetry of the Protestant OT:

97.297% do not exhibit the Top-Level n:39-2n:n

99.768% do not exhibit the Second-Level n-m:m:39-2n:n-m:m

99.997% do not exhibit the Third-Level 39-2n:3n-39-k:k:39-2n:39-2n:3n-39-k:k

Assuming no one finds any errors in my corrected calculations, these numbers seem to leave no doubt that "chance" can be conclusively eliminated as an explanation of the symmetry found in the Protestant OT.

Richard

 

[BibleWheel]

Here is a little something I found a couple years ago when I was studying the Orthodox canon of Scripture. It was written by Orthodox Priest Father Demetrios Serfes. It can be found here.

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.

It would seem that the idea of an "order" of the books in the Orthodox tradition is not even a well-defined concept.

Richard

 

[thereselittleflower]

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

Richard, actually, that's not correct.

They were offically canonized as scripture when the books in your New Testament were canonized as scripture, by the same people - over 1600 years ago!

At the council of Trent the canon of both the Old and New Testaments was elevated to the level of DOGMA . .


Just because some individuals thought they knew better than the Church at various times doesn't mean diddly sqwat.

luther tried to take out Hebrews, James, Jude and Revelaiton. . . so what?


If those Bishops were guided at the end of the 4th century and beginning of the 5th century by the Holy Spirit to canonize the NT scriptures, they were equally guided in their canonization of the OT scripture (including the so-called deuterocanonicals) which were done in the SAME canon at the same time.


Why do you accept their determination of the NT and not the Old?

It is a very pertinent question. . . .



Peace