Proof of Divine Providence

[Jason R]

"The chances are exactly the same as those letters/cards/squares/whatever adding up to something different, and that "something different" would have exactly the same chance of you being able to manipulate it to yield some result that strikes your mind, subjectively, as impressive."

Los,

I tell you what, I am completely and utterly disappointed in you here. I actually expected something a LOT better than this!

Your answer is blatantly rediculous, and goes on without really explaining anything in particular, other than ramble about "chance". You forget, it added up that way exactly how the riddles described. MAYBE I would agree with JUST the 666 or a 418, but there is multiple areas of cohesion. EVERYTHING lines up.

I highly doubt you even truly READ what I wrote on the post! I'm convinced you glanced at it, saw some numbers, and rolled your eyes and wrote that lazy reply.

You HAVE to be insane to think that out of the NATURAL sequence of 0 thru 25, bending them in half, and reducing, could add up to half of foursquare 666, FOUR 36 squared quadrants of 6 x 111, and a CENTRAL cross of 418 just randomly.

Sure.

Lol, if your right, should be EASY for you to demonstrate such a random mentally created pattern! Yeah, I simply MANIPULATED the sequence by folding in half and reducing and adding? Show me by your mental powers such a feat! You cant! Its impossible!

How do you explain the 5,14,23 being compared to the Greek letters and Hebrew to 666?

Lame explanation, and you know it!

[Los]

@Jason R said

"You HAVE to be insane to think that out of the NATURAL sequence of 0 thru 25, bending them in half, and reducing, could add up to half of foursquare 666, FOUR 36 squared quadrants of 6 x 111, and a CENTRAL cross of 418 just randomly."

Your story demonstrates only that if you play with numbers long enough, you'll eventually find numbers that are meaningful to you. Big surprise.

What's really ridiculous is the idea that there is some oogity-boogity goblin man who decided to dictate some magical book, and he decides that he wants to leave "proof" that he really is a "preterhuman intelligence" with far advanced knowledge that represents the one and only chance for mankind to advance as a whole and yadda yadda yadda....

So what kind of "proof" does he give? Does he provide specific, unambiguous, and incotrovertible prophecies of the future? Does he actually give people useful knowledge, like, say, the plans for technology that would vastly improve life as we know it? Does he provide unambiguous solutions to serious problem plaguing humanity? Does he bother telling us about climate change?

No, of course not. He leaves a bunch of obscure number games in some little-known text, games that can only be solved by using the most convoluted methods possible to "find" numbers that add nothing to the meaning of the Book.

Honestly, if this is the best that such a being can do, he's welcome to keep his super-duper number games. I think humanity is going to get along just fine without them.

[Jason R]

@Los said

"
@Jason R said
"You HAVE to be insane to think that out of the NATURAL sequence of 0 thru 25, bending them in half, and reducing, could add up to half of foursquare 666, FOUR 36 squared quadrants of 6 x 111, and a CENTRAL cross of 418 just randomly."

Your story demonstrates only that if you play with numbers long enough, you'll eventually find numbers that are meaningful to you. Big surprise.

What's really ridiculous is the idea that there is some oogity-boogity goblin man who decided to dictate some magical book, and he decides that he wants to leave "proof" that he really is a "preterhuman intelligence" with far advanced knowledge that represents the one and only chance for mankind to advance as a whole and yadda yadda yadda....

So what kind of "proof" does he give? Does he provide specific, unambiguous, and incotrovertible prophecies of the future? Does he actually give people useful knowledge, like, say, the plans for technology that would vastly improve life as we know it? Does he provide unambiguous solutions to serious problem plaguing humanity? Does he bother telling us about climate change?

No, of course not. He leaves a bunch of obscure number games in some little-known text, games that can only be solved by using the most convoluted methods possible to "find" numbers that add nothing to the meaning of the Book.

Honestly, if this is the best that such a being can do, he's welcome to keep his super-duper number games. I think humanity is going to get along just fine without them."

Yawn. Like I said, you gave it no thought, you didn't even read it really. I explained it. I truly think the idea of something more to life scares you, or you have some problem with that idea. You refuse to see anything at all contrary to your views. I'm sorry, if you take all the factors its beyond chance, and I did not "toy" with it. Did you try it on paper? Nope. Id like you to show me just how much toying I did. Not much more than is described easily in Liber L.

Toy with numbers, show me. Demonstrate it for me, your theory. I dare you lol. Same ease as mine, as straight forward and resulting in the same amount of related symbols. For example 666 derived from 6 x 111, and another example of cohesion, a central cross of 418, four solar gates composed "randomly" of 36 squares summing to 666. Do it or shut up.

[Knowledge + Delight]

VERY interesting........

Can you sketch up the FULL table of numbers for us, just so there's no ambiguity ?

Now, if such 'number games' can 'easily be made to pull out whatever number you desire', it should be simple then, to pull 111,418, and 666 out of a similar-but-different 'game' of your own devising? I've played around a bit with my own theories and 'games'. It's not as easy as you'd think. Sure, you can maybe get one thing to add up here and another there, but more often than not, things DON'T just 'line up' on their own.

I think your method makes sense (somewhat), you seem to have started with an insightful idea, 0-25 for the 'order and value of the english alphabet', and the results look promising.

"But what can you do with it"?

[Jason R]

@Knowledge + Deligh said

"VERY interesting........

Can you sketch up the FULL table of numbers for us, just so there's no ambiguity ?

Now, if such 'number games' can 'easily be made to pull out whatever number you desire', it should be simple then, to pull 111,418, and 666 out of a similar-but-different 'game' of your own devising? I've played around a bit with my own theories and 'games'. It's not as easy as you'd think. Sure, you can maybe get one thing to add up here and another there, but more often than not, things DON'T just 'line up' on their own.

I think your method makes sense (somewhat), you seem to have started with an insightful idea, 0-25 for the 'order and value of the english alphabet', and the results look promising.

"But what can you do with it"?"

Knowledge + Delight 93,

Thank you! Yes, I realize its hard BTW to have many points align, and that's my main reason for my claim. While it may be true we can toy with numbers all day, and find patterns - rarely do so many tally on so many PROPER points. Like I had explained; if for example, I was saying things like "well if you take the 5 A's out of Abrahadabra, and arrange them as 0's, and take the consonants and value them as Hebrew.." THAT is manipulating things, and taking them out of order, or toying. It would also be toying if I told everyone to pick out all the "odd" numbers, and add them together and viola - it totalled 666!

Instead, this situation does maybe 3 "manipulations", four if you count "finding" the divisions, yet that is already there. The manipulations then are VERY limited:

**1. Arranging 0 thru 25 left to right and top to bottom, folded in half. (coincidentally at the micro/macro division)

2. Reducing these numbers. (Is that really manipulation though? How could you really control THAT result?)

3. Adding them all together. Done.

4. Realizing the sums in the divisions are half those for 666,418, and 111. (In addition to many more, like 56)*

So, basically in the above, simple four steps all these significant results are generated. Manipulation to "find" what you want is sort of difficult in such a limited method. THEN, if you use the same steps, but this time do not reduce the factors, and add one or two sets etc., you generate even more results, all of which, again tie in and make symbolic sense, they all have an inherent harmony.

So, anyone claiming its just pulling out "random patterns" is missing the argument that those with complete SYMBOLIC harmony push it well beyond chance, in my opinion (Id like Simon's input here, knowing he has knowledge of statistics). That symbolic consistency, arrived at by such a simple process, to me, is another valid point.

Anyway, I will try to give the full tables here, yet it's difficult because the typed numbers don't align right on here (I tried). In my other post (Liber Al Cipher 666), I do provide a few charts, but not the half results for 666 result. I don't have access at the moment to work up a new graphic, so ill try to provide it here through typing.

Ok, and I almost forgot, and its something I really need to explain more because it is important, and that is "ok but what the hell IS it? What does it DO?" I'm sorry, I did focus more on the number evidence and not what it was.

I believe it is a new Enochian style Thelemic Tablet. Now realize, I am not as knowledgeable as Jim, or many of those here, and so I'm not even sure of exactly "how" or "what" it does, but I do know enough about magick, and Enochian to have an educated guess. My analysis is that it is a magical "House", or symbolic "Solar-martial temple", with "four gates", or solar quadrants, like the Enochian scheme. This sort of thing is hinted at within Liber L, as I'm sure you know. Stands to reason we would use it very similar to the way we use the Enochian system, travel into these squares which actually blend the Tarot cards in a 5 & 6 fashion. There are elemental attributes given to each square as well, and Hebrew, Greek, and English letters blended for each square. There are letters upon these squares just as there are on the Enochian, which obviously give us particular names to be used in this new system.

I'm thinking this Tablet, like Liber Tav, gives us a unique combination of Tarot, within an elemental arrangement, which adds to it, that provides new insights into Thelemic ideas, and a workable Thelemic system of magick. I'm sure, there are a lot of similarities of uses to the Enochian, of which it is obviously suggesting. BTW, I have not revealed the "letters" that go upon these squares, what is shown in these numbers, is simply the numerical skeleton, that is the Books way of pointing out this whole scheme, a way to point us in the right direction for putting it all together.

I hope this helps clear up the point of it. Of course this is a real quick sketch, but I think its enough for you to look onto it with this idea in mind, and see for yourself if it makes sense in the results. Look at how the cards and elements and numbers align and you'll see what I mean, AND how, with this scheme in mind, the verses in Liber L seem to confirm it.

[Jason R]

The first Tabulation

1. Step one. "Paste the sheets from right to left and top to bottom"

__12 11 10 9 8 7 6 5 4 3 2 1 0
13
14
15
16
17
18
19
20
21
22
23
24
25

2. Reduce these.

__3 2 1 9 8 7 6 5 4 3 2 1 0
4
5
6
7
8
9
1
2
3
4
5
6
7

3. Add them into a graph.

This produces a graph giving us half the results for four quadrants of 36 squares, totalling 666, and a central cross of 418. Excuse the sloppy alignment of the numbers, its the best I can do for now. I suggest taking a piece of graph paper and adding them line by line.

7 6 5 13 12 11 10 9 8 7 6 5 4
8 7 6 14 13 12 11 10 9 8 7 6 5
9 8 7 15 14 13 12 11 10 9 8 7 6
10 9 8 16 15 14 13 12 11 10 9 8 7
11 10 9 17 16 15 14 13 12 11 10 9 8
12 11 10 18 17 16 15 14 13 12 11 10 9
4 3 2 10 9 8 7 6 5 4 3 2 1
5 4 3 11 10 9 8 7 6 5 4 3 2
6 5 4 12 11 10 9 8 7 6 5 4 3
7 6 5 4 13 12 11 10 9 8 7 6 5 4
8 7 6 14 13 12 11 10 9 8 7 6 5
9 8 7 15 14 13 12 11 10 9 8 7 6
10 9 8 16 15 14 13 12 11 10 9 8 7

If we take step 2, and reverse the numbers for each side, like this:

__3 2 1 9 8 7 6 5 4 3 2 1 0
4____________________________7
5____________________________6
6____________________________5
7____________________________4
8____________________________3
9____________________________2
1____________________________1
2____________________________9
3____________________________8
4____________________________7
5____________________________6
6____________________________5
7____________________________4
__0 1 2 3 4 5 6 7 8 9 1 2 3

Then add for every square right and left, and top and bottom. You get:

14 14 14 23 23 23 23 23 23 23 14 14 14
**14 14 14 **23 23 23 23 23 23 23 14 14 14
14 14 14 23 23 23 23 23 23 23 14 14 14
14 14 14 23 23 23 23 23 23 23 14 14 14
14 14 14 23 23 23 23 23 23 23 14 14 14
14 14 14 23 23 23 23 23 23 23 14 14 14
05 05 05 14 14 14 14 14 14 14 05 05 05
14 14 14 23 23 23 23 23 23 23 14 14 14
14 14 14 23 23 23 23 23 23 23 14 14 14
14 14 14 23 23 23 23 23 23 23 14 14 14
14 14 14 23 23 23 23 23 23 23 14 14 14
14 14 14 23 23 23 23 23 23 23 14 14 14
14 14 14 23 23 23 23 23 23 23 14 14 14

(Note how the numbers seem to draw the figure of an** H,** or** X**?) "H" is HEH = "Behold"

Four quadrants then of 36:

14 14 14 23 23 23 = 111
14 14 14 23 23 23 = 111
14 14 14 23 23 23 = 111
14 14 14 23 23 23 = 111
14 14 14 23 23 23 = 111
14 14 14 23 23 23 = 111

Total 666

Horizontal arm of cross = 128
Vertical arm of cross = 290
Total = 418

Central number 14 (in cross of 25 squares)

Adding each opposite number of cross 23+23+5+5=56

Three numbers only 5,14,23 = 42 = 6
Each reduce to 5.

PART TWO 2nd TABULATION

If we do the same double arrangement as above, but DO NOT reduce, we get:

50 50 50 50 50 50 50 50 50 50 50 50 50
50 50 50 50 50 50 50 50 50 50 50 50 50
50 50 50 50 50 50 50 50 50 50 50 50 50
50 50 50 50 50 50 50 50 50 50 50 50 50
50 50 50 50 50 50 50 50 50 50 50 50 50
50 50 50 50 50 50 50 50 50 50 50 50 50
50 50 50 50 50 50 50 50 50 50 50 50 50
50 50 50 50 50 50 50 50 50 50 50 50 50
50 50 50 50 50 50 50 50 50 50 50 50 50
50 50 50 50 50 50 50 50 50 50 50 50 50
50 50 50 50 50 50 50 50 50 50 50 50 50
50 50 50 50 50 50 50 50 50 50 50 50 50
50 50 50 50 50 50 50 50 50 50 50 50 50

If we reduce of course we get 5 in every square. If we add the numbers then in each of the divisions as before we get:

50 50 50 50 50 50 = 300 (Shin)
50 50 50 50 50 50 = 300
50 50 50 50 50 50 = 300
50 50 50 50 50 50 = 300
50 50 50 50 50 50 = 300
50 50 50 50 50 50 = 300

Total 1800 reduces to 180 number of the Moon (from quadrant that produced number of the Sun)

13 x 50 = 650 for vertical & horizontal arm of cross (or ANY row or column)

650 + 650 = 1300 (13 Achad "one", as in "One Palace" Palace = 65)

50 of course is the 13th Key of the Tarot, Death.

It goes on and on and on.

[Jason R]

The Tarot Order applied to English Alphabet
(With corresponding Greek)

0. A. Alpha 1
1. B. Beta 2
2. C. Gamma 3
3. D. Delta 4
4. E. Epsilon 5
   5. F. Stau 6
5. G. Zeta 7
6. H. Eta 8
7. I. Theta 9
8. J. Iota 10
9. K. Kappa 20
10. L. Lambda 30
11. M. Mu 40
12. N. Nu 50
    14. O. Xi 60
13. P. Omicron 70
14. Q. Pi 80
15. R. Koppa 90
16. S. Rho 100
17. T. Sigma 200
18. U. Tau 300
19. V. Upsilon 400
20. W. Phi 500
    23. X. Chi 600
21. Y. Psi 700
22. Z. Omega 800

Now, looking at the above, if we look at the corresponding letters for the three repeating numbers that generate the 666 & 418 results, we get:

**5. F, Greek Stau = 6

14. O, Greek Xi = 60

15. X, Greek Chi = 600

Total = 666**

[Takamba]

FOX = 666. I've seen this Qabalah before. Can't remember where, but at least it demonstrates this has been discovered before.

[Jason R]

@Takamba said

"FOX = 666. I've seen this Qabalah before. Can't remember where, but at least it demonstrates this has been discovered before."

Well I did put this in my other post as "FOX English Qabalah". I made that up lol. Look at my other post, maybe that's where you remember it from. Ive never heard of it before otherwise, and love to see it if it was done before!

[EDIT] I should clarify here a point. I believe the values of the English are the REDUCED order numbering. This means Z = 7, T = 1 etc. An example of this is ABRAHADABRA = 28, which is fitting, since in Hebrew Gemetria 28 is "Power", and Abrahadabra is the "Double word of power" (28 + 28 = 56)

[Takamba]

@Jason R said

"
@Takamba said
"FOX = 666. I've seen this Qabalah before. Can't remember where, but at least it demonstrates this has been discovered before."

Well I did put this in my other post as "FOX English Qabalah". I made that up lol. Look at my other post, maybe that's where you remember it from. Ive never heard of it before otherwise, and love to see it if it was done before!"

Turns out there's more than one way to make FOX=666, I probably saw it the other way years ago - which is why I don't remember it, I tend toward dismissing certain silliness (not your topic, the FOX = 666 from before).

[Jason R]

@Takamba said

"
@Jason R said
"
@Takamba said
"FOX = 666. I've seen this Qabalah before. Can't remember where, but at least it demonstrates this has been discovered before."

Well I did put this in my other post as "FOX English Qabalah". I made that up lol. Look at my other post, maybe that's where you remember it from. Ive never heard of it before otherwise, and love to see it if it was done before!"

Turns out there's more than one way to make FOX=666, I probably saw it the other way years ago - which is why I don't remember it, I tend toward dismissing certain silliness (not your topic, the FOX = 666 from before)."

Hmmm interesting, never heard of it. Thanks though, I still may peek at it, yet I trust your judgement.

[Mephisto]

Thank you for elucidating your system in more detail. I'm still digesting the material; I'll give a longer critique later. So far my thoughts are: interesting and impressive, but inconclusive.

The Book, as I understand it, has a subtlety that corresponds to that of the reader. While I feel that your findings are interesting and thought-provoking, I feel that there is still a great deal left unanswered. What I see is an intelligent mind working sincerely on the problems presented by the Book of the Law. I don't think that you've answered any questions conclusively, however. Nor am I certain your findings establish "proof of divine providence."

I'll give my final analysis later. But whatever the case, I can encourage you to keep working in the same direction. "A tree will be known by its fruits."

[Jason R]

@Mephis said

"Thank you for elucidating your system in more detail. I'm still digesting the material; I'll give a longer critique later. So far my thoughts are: interesting and impressive, but inconclusive.

The Book, as I understand it, has a subtlety that corresponds to that of the reader. While I feel that your findings are interesting and thought-provoking, I feel that there is still a great deal left unanswered. What I see is an intelligent mind working sincerely on the problems presented by the Book of the Law. I don't think that you've answered any questions conclusively, however. Nor am I certain your findings establish "proof of divine providence."

I'll give my final analysis later. But whatever the case, I can encourage you to keep working in the same direction. "A tree will be known by its fruits.""

In the end, no matter what, I am not here to shove it down throats. Do what thou wilt. However, realize of course the above is a brief sketch, enough I figure, to show something higher at work. The proof being in the statistical unlikeliness of these consistent symbolic results.

I accept your findings, but with the point that you have not proven me wrong either. Of course the verses hold personal meaning, however, I feel they have an ingenious magical quality to have layers of potential meaning. I again say, my conclusion for proof rests in these results not being the product of chance. My demand is to be shown a comparable example of such findings. Can you demonstrate something like this that provides similar numbers in the same amount of steps and just as relevant to the riddles?

Anyway, thank you for your opinion, and taking the time! That alone is awesome of you and appreciated!

[Jason R]

P.S.

A further tid-bit, I believe the TRUE arrangement for these numbers are "left to right and top to bottom", which is a secret hidden in the line drawn clue. This changes the cards blended within certain elements, for example, 0 & 13 (Aleph & Nun 51) at the then top left corner, which is then in "Air of Air". Like the Enochian, there were some blinds I believe. There really is a lot to share, more results, but ANYONE with a basic knowledge in Qabalah & magic can find these, IF they truly take the time to investigate. That's the problem however, not many are motivated with some "nobodys" apparent "idea" lol.

[Faust]

Once I`ve read something from a shaman that I find amazing.

“Everything has a spirit, but not all spirits have power”

Since a do not take riddle stuff seriously (as I do not take most thinks seriously), the question I believe that should be asked is:

Does it have power?

If yes, you got something.

[Jason R]

@Faus said

"Once I`ve read something from a shaman that I find amazing.

“Everything has a spirit, but not all spirits have power”

Since a do not take riddle stuff seriously (as I do not take most thinks seriously), the question I believe that should be asked is:

Does it have power?

If yes, you got something."

Try it. My own answer, and here I can only talk about MY experience, is an emphatic YES! I know (for me at least) it has power. However, of course one can give anything power for themselves if they believe in it. The question here is, does it have objective power? I say TRY IT! Look into it, study it, and see for yourself. Speaking for myself only, I have MY proof of providence and its relevence, but I feel it goes beyond just my own sphere.

[Faust]

@Jason R said

"
my own answer, and here I can only talk about MY experience, is an emphatic YES! I know (for me at least) it has power. "

So harness the power of your discovery and be the living example of its power. Success is my proof.

@Jason R said

"I say TRY IT! Look into it, study it, and see for yourself. Speaking for myself only, I have MY proof of providence and its relevence, but I feel it goes beyond just my own sphere."

Already tried scrying at it? Calling its power? What new knowledge comes from this new table? What heavens and hells are commanded by its power?
Mathematic tricks are cool, but some interesting answers for these questions would it make worth investigating. Otherwise, why bother?

[Jason R]

@Faus said

"
@Jason R said
"
my own answer, and here I can only talk about MY experience, is an emphatic YES! I know (for me at least) it has power. "

So harness the power of your discovery and be the living example of its power. Success is my proof.

@Jason R said

"I say TRY IT! Look into it, study it, and see for yourself. Speaking for myself only, I have MY proof of providence and its relevence, but I feel it goes beyond just my own sphere."

Already tried scrying at it? Calling its power? What new knowledge comes from this new table? What heavens and hells are commanded by its power?
Mathematic tricks are cool, but some interesting answers for these questions would it make worth investigating. Otherwise, why bother?"

Yes and no. I admit I'm not as skilled in skrying as I would want, but I have tried. Yes, I received "results", but again, this is subjective. Does it provide anything new? Good question, again I say yes, but I am not in a position to declare these, or understand them fully myself. Part of the reason I am Sharing it, is to get help in understanding it. Some of those here have a lot more knowledge and insight AND experience to decide this than me. That's part of why I ask everyone to look themselves. I'm sure, for example, Jim could get a LOT more out if it than me, or easily catch problems. But, whatever I get out of it isn't "evidence" really, because it is just "subjective" opinion, and MY take on it. I could be totally wrong, and yet this may not be proof either way, because it is MY subjective interpretation. This is why, I stuck to the numbers, and the symbolic consistency, since that is at least something objective we can agree on, since say "666" has meaning to us all according to our being magicians and of course Thelemites.

[Faust]

Well, I understand your position. I see no reason to worry to get confirmation. It is like what was once suggested about learning the name of your Angel, you simply keep doing the work assigned to your grade. There will be a time when you will be able to access this table and validate it.

I also understand why most people won’t bother to spend energy with it. The other tables we have do the job just fine, why should we need a new one? Can it be a better table? Sure! But it can be just a huge waste of time. Probably it won’t be a priority for them.

About the numbers, I never understood why Crowley spent so much time playing with them and saying that they prove something. They are the kind of thing that only makes sense inside the symbolic system he is using.

For example, I use the French set of attributions of Hebrew letters to the tarot. As a result of it I get some really cool ideas that those using thelema-golden dawn attributions do not. Are they proves that my set is better?

[Jason R]

@Faus said

"Well, I understand your position. I see no reason to worry to get confirmation. It is like what was once suggested about learning the name of your Angel, you simply keep doing the work assigned to your grade. There will be a time when you will be able to access this table and validate it.

I also understand why most people won’t bother to spend energy with it. The other tables we have do the job just fine, why should we need a new one? Can it be a better table? Sure! But it can be just a huge waste of time. Probably it won’t be a priority for them.

About the numbers, I never understood why Crowley spent so much time playing with them and saying that they prove something. They are the kind of thing that only makes sense inside the symbolic system he is using.

For example, I use the French set of attributions of Hebrew letters to the tarot. As a result of it I get some really cool ideas that those using thelema-golden dawn attributions do not. Are they proves that my set is better?"

Of course, really, your right. In the end it only matters for the individual, and as you wisely say, later if it is to be it will be validated. But, if you discovered something (at least to you) that seemed to have value for your fellow Thelemites, and objective truth, what would you do? I chose to share it, if someone else also finds it helpful, useful in their work, or if by some chance it DOES have objective truth then its worth it. If no one cares, fine. Of course it bothers me that others may see me as some kook, or moron or whatever else they may say, but I cant be afraid of that, I truly believe in it. I truly, honestly believe it has something to it, so in that personal belief I bravely offer myself up. I believe in Thelema, if there's a chance I have anything to give our cause, then I'm going to give it regardless. No one has to accept it, we all know the Law.

As for the numbers etc., my only input is that I stick with what the Master Therion saw fit. It stands to reason he would know and use what worked and what was in alignment with that system. Yes, to some degree the numbers meanings are subjective, yet we ALL (even Bible thumping xtians) HAVE to nod to these numbers significance, historical significance, that by now are well known. These numbers and their relationship themselves stand to impress in themselves devoid of our subjective ideas.