432 shows harmony of Sun, Moon, Earth Design

[ReligionStudent]

tIve edited the code so it is running as fast as it can and its already hundreds of thousands

Up to millions now

Just a note: This is really a pretty brute force counting program, and it appears that it will take a bit of time to finish.

 

[jsfisher]

Currently running the program... May take a while did not get fancy with math so there are just 13 loops and two if statments with lots of itterations.

If you are trying to enumerate all possible "sets", I predict you program will not complete in your lifetime.

 

[ReligionStudent]

after about an hour (a little less than 1 hour) I am at roughly 9847851562500 comparisons, that is still quite a few lifetimes

 

[ReligionStudent]

If you are trying to enumerate all possible "sets", I predict you program will not complete in your lifetime.

I am attempting to emulate all sets that are fit the 1000/somthing else option. I am concerned with finishing time, not having thought of it, but since I have done programming more recently than the math that would be involved, I thought I might as well try.

Also, however far I get should give us a better room for estimation.


Unfortunatly the power needs were starting to overtax my poor laptop, and I had to unplug the brick so as to not fry it. my last like of output was this

Total count of valid sets 13505197
most recent succesful set {16,16,16,16,16,16,16,62,172,154,171,173,163}

It was a simple algorythm that incremented from right to left in the set and counted successes (with some elimination statments to keep from testing obviously false areas of data).

Now there is certainly a way to do the math, so I hope someone does it, but perhaps there is some extrapolation possible from this.

 

[JonnyFive]

Well, I've been doing some thinking about this.

Any set with more than 8 16's can be tossed, because that is the maximum number that can result in a set that exceeds the minimum value of 1000.

Similarly, any set with more than 7 175's can also be tossed, as this is the maximum number that can be in any set that falls under 1452.

That allows us to discard only 16,988,250,163,520 results off-hand, without having to do further calculations.

However, the number of cases that aren't simply excluded ones is massive (one might say... astronomical).

Perhaps a simpler approach would be to approximate using percentages. The maximum possible value is 2,275 (175*13), and the minimum possible is 208 (16*13). Therefore, approximately 38% of the possible values are under the minimum, and 40% are over the maximum. That leaves us with approximately 22% of the total values remaining within the acceptable range.

Thus, we should see roughly 9,907,919,180,215,100,000,000,000,000 combinations within the acceptable range.

ETA: This is a naive model, so to approximate the distribution curve I'm just going to multiply by two and assume roughly 1.8 x 10^27 possible combinations that fall within the acceptable range.

Mathematicians and other assorted math geniusi: please let me know if my reasoning is in error.


ETA: I just realized I made a stupid mistake, so I fixed the numbers (you can see the originals in jsfisher's post below). This estimate is using basic percentages only, and so should be considered a very rough approximation. The geometric approximation that jsfisher used is considerably more accurate.

 

[jsfisher]

Well, I've been doing some thinking about this.

Any set with more than 8 16's can be tossed, because that is the maximum number that can result in a set that exceeds the minimum value of 1000.

Similarly, any set with more than 7 175's can also be tossed, as this is the maximum number that can be in any set that falls under 1452.

That allows us to discard only 16,988,250,163,520 results off-hand, without having to do further calculations.

However, the number of cases that aren't simply excluded ones is massive (one might say... astronomical).

Perhaps a simpler approach would be to approximate using percentages. The maximum possible value is 2,275 (175*13), and the minimum possible is 208 (16*13). Therefore, approximately 35% of the possible values are under the minimum, and 36% are over the maximum. That leaves us with approximately 29% of the total values remaining within the acceptable range.

Thus, we should see roughly 13,060,438,919,374,400,000,000,000,000 combinations within the acceptable range.

Mathematicians and other assorted math geniusi: please let me know if my reasoning is in error.

If I counted correctly (which I only occasionally do), I get that there are 8,544,668,310,043,540,000,000,000,000 "sets" that sum to less than 1,000 and 14,245,494,044,045,800,000,000,000,000 "sets" that sum to more than 1,452. That leaves 22,245,833,919,615,600,000,000,000,000 that qualify (plus or minus 10db).

JonnyFive's estimate is in the same ball park, so, I'd say we are both near enough. Regardless, the true number of "sets" is slightly larger than a metric boat load.


{ETA: For those that care, the way I counted was via a geometric strategem. If you were considering sets of size two, you could imagine the sets as coordinates on an X/Y plane. The sets with elements that sum to N are all represented on the line (0,N) to (N,0). The concept can be generalize to 13 dimensions with the corresponding hyperplanes replacing simple lines. Finding a formula for the number of "sets" in a given hyperplane isn't terribly difficult.}

 

[JonnyFive]

jsfisher, thanks for posting a much more accurate estimate.

For the interested, my modelling on the problem was too naive. I assumed an even distribution of values, but the actual sum distribution would tend to concentrate around the middle values more than the ends.

In fact, it would basically form a bell curve, if I am not mistaken. So my estimate is off by a factor of approximately 2 or more.

 

[Belz...]

So, Jiri. Where are those lineholders ?

 

[ReligionStudent]

Well, I've been doing some thinking about this.

Any set with more than 8 16's can be tossed, because that is the maximum number that can result in a set that exceeds the minimum value of 1000.

Similarly, any set with more than 7 175's can also be tossed, as this is the maximum number that can be in any set that falls under 1452.

That allows us to discard only 16,988,250,163,520 results off-hand, without having to do further calculations.

However, the number of cases that aren't simply excluded ones is massive (one might say... astronomical).

Perhaps a simpler approach would be to approximate using percentages. The maximum possible value is 2,275 (175*13), and the minimum possible is 208 (16*13). Therefore, approximately 38% of the possible values are under the minimum, and 40% are over the maximum. That leaves us with approximately 22% of the total values remaining within the acceptable range.

Thus, we should see roughly 9,907,919,180,215,100,000,000,000,000 combinations within the acceptable range.

ETA: This is a naive model, so to approximate the distribution curve I'm just going to multiply by two and assume roughly 1.8 x 10^27 possible combinations that fall within the acceptable range.

Mathematicians and other assorted math geniusi: please let me know if my reasoning is in error.


ETA: I just realized I made a stupid mistake, so I fixed the numbers (you can see the originals in jsfisher's post below). This estimate is using basic percentages only, and so should be considered a very rough approximation. The geometric approximation that jsfisher used is considerably more accurate.

Seems reasonable enough to me, especially because there apears to be no reason to ask the question as of yet.

 

[ReligionStudent]

jsfisher, thanks for posting a much more accurate estimate.

For the interested, my modelling on the problem was too naive. I assumed an even distribution of values, but the actual sum distribution would tend to concentrate around the middle values more than the ends.

In fact, it would basically form a bell curve, if I am not mistaken. So my estimate is off by a factor of approximately 2 or more.

Factor of two not so bad, we're looking for more of a big O type value here I would think.

 

[jsfisher]

jsfisher, thanks for posting a much more accurate estimate.

As it turns out, I over counted by a little. The final count of the number of Jiri-sets is just a bit larger than I'd posted. Still a metric boat load, however.

 

[Jiri]

Originally Posted by Jiri
One semi-circle suffices, and we have the makings of at once two Golden Rectangles, so you are indeed right. The diagonal of the 2:1 rectangle will be the circle's radius (2.236..).
When we swing it to the left, for example, the resulting distance is now divided into 1 and 1.236. The extension of the square's base gives Phi with the height of the rectangle - they represent two sides of a Golden Rectangle.
2 / 1.236.. = 1.618..

Swing it to the right (Square dancing to get 1 + 2.236 = 3.236.. Now, the height of the old rectangle (2) forms the short side of a Golden Rectangle with the new distance of 3.236.. - two sides of four needed for a Golden rectangle. To see this done in the context of the engraving's square:
http://www.vejprty.com/seat3.htm

Add, or subtract a square from any Golden Rectangle, get a new Golden Rectangle. Repeating the process will lead to a spiral. But, you still did not get around to constructing a 36 degree angle from this position, not to mention construction of the regular 5-pointed star.
More steps would be needed. So, your small example doesn't work. It does not take you past the simple repetitive and decorative stage at best as the intention of the artist.

.

Why would you do this unless you're trying to force golden ratios to appear? That web page fails to clearly explain why you chose to do any of this. You planning to answer my various questions posted here, or are you just one of those people that wants us all to accept what you say without question?

Please let me know if you are, so I can stop wasting my time with trying to get a serious answer out of you.
.

"trying to force golden ratios to appear? " - Exactly, I am forcing golden ratios to become visible for the Square, which is already there, in order to see, how other things already engraved there integrate into this overall inner order. Example: the Torso lines, which everybody pooh-poohed so intensely, because of my method of extrapolation. At the same time, this relates to all the articles, which maintain that it is easy for such (simple) ratios to appear accidentally in any given line-art, and of course, all the articles, which maintain that it is easy to force a higher preconceived order onto any line-art...

.

Back to our discussion, I bet you couldn't come up with a number for the following: the number of sets of thirteen numbers in the range of 16 to 175..

..

I can:

You care to refine your definition of "numbers" a little more? You want to know the number of unique sets of 13 natural numbers using the whole numbers 16 to 175, including both 16 and 175 and allowing for repetition?

Therefore you're looking for all possible sets of 13, drawing from a possible source of 160 unique numbers..

.
Yes, whole numbers (self-understood), and including both 16 and 175, because that is the Frame's range.
.

Number of permutations with repetition is where n is the number of possible "things" (natural numbers) and k is the number put into the set.

If I do my math correctly (or, rather, if Excel does its math correctly), it should be:

45,035,996,273,705,000,000,000,000,000. .

Thank you, so you propose a rather low number (only octillions) as the answer, but as I saw below from all the posts, the answer is not all that simple.

.

Quote:
Eliminate all the sets totalling less than a 1000, and more than 1452 (a realistic range for engraving sizes). I'm sure you can put it into numbers, but not words, since you probably don't know the name of that particular astronomical number.
unquote
.
The easiest way to eliminate that range would probably be through computer simulation. You're looking to eliminate everything where the average value is less than about 77, and more than about 111, but it isn't that simple because those are average values, so a permutation using, say, 91, is fine as long as the other values pull the average down to that range.

It would probably be simplest to program a computer to just check all the values, as it could do it quickly and without having to develop some god-awful formula for the problem.

Since the number is going to be less than 45 octillion (because you're restricting the problem further), I think naming it would be no problem.

But as you didn't say natural numbers, the answer is still infinity. .

Sorry, of course, I meant whole numbers. But, as I saw, having a computer run through every permutation would take considerabe time.

 

[Macoy]

Back to our discussion, I bet you couldn't come up with a number for the following: the number of sets of thirteen numbers in the range of 16 to 175.

how much did you lose?

 

[ReligionStudent]

.
"trying to force golden ratios to appear? " - Exactly, I am forcing golden ratios to become visible for the Square, which is already there, in order to see, how other things already engraved there integrate into this overall inner order. Example: the Torso lines, which everybody pooh-poohed so intensely, because of my method of extrapolation. At the same time, this relates to all the articles, which maintain that it is easy for such (simple) ratios to appear accidentally in any given line-art, and of course, all the articles, which maintain that it is easy to force a higher preconceived order onto any line-art...

.
..
.
Yes, whole numbers (self-understood), and including both 16 and 175, because that is the Frame's range.
.
Thank you, so you propose a rather low number (only octillions) as the answer, but as I saw below from all the posts, the answer is not all that simple.

.Sorry, of course, I meant whole numbers. But, as I saw, having a computer run through every permutation would take considerabe time.

First, why would whole real numbers be self understood? I thought this was some sort of measure having to do with an engraving, then there should be a clear understanding of decimals

Octillions is not a low number, 45 octillion is the maximum number of permuations of thirteen numbers where the choice ranges from 16-175. The actual count would be lower than this, as this is all permutations possible.

 

[Jiri]

First where do you get the satement "a realistic range for engraving sizes"? What science, study, or example to you have to support this or is this just something you pulled from your assumptions (and what exactly is the range 1000 to 1452 pixels?, inches? and is this a side length or the area? How does it define the picture?)

.
I am just trying to account for factors, which narrow the range of variations we work with. We are talking about engravings on tablets. So, once we have another artist drawing a comparable engraving on the same tablet i.e., it must have thirteen peripheral points in its perimeter, or frame (the Outer Limits ), we can expect some variation in where those points will be, and in the particular distances between particular points. The Frame, a set of those peripheral distances totals 1226 millimeters (in double the lifesize). Of course, the total length of each perimeter in other such engravings would tend to vary, mostly falling into a range. So, an equal distance from 1226 gives an even 1,000 and 1,452. I think this is a fairly realistic range.

Some of the tablets are comparable to the high quality limestone tablets students used back in the 18-th or 19-th century. I don't know if this particular Athena engraving is on such a limestone tablet, or a quartzite one, a type also found at the site. I do see the hand of a genius, though. The perfection in the line-art often works even under serious magnification in CAD (perfection in the circle-arcs, when following line edges).

The number of sets by the way, is clearly infinite

Set 1. 77 repeated 13 times
Set 2 77 repeated 12 times followed by 77.1
Set 3 77 Repeated 12 times followed by 77.11
Set 4 77 Repeated 12 times followed by 77.111

Well I demonstrate it obviously with my example, but I think I can do a real proof here:

Any Set of 13 numbers containing {77,77,77,77,77,77,77,77,77,77,77,77,77} Has a sum greater than 1000 but less than 1452. ====> 77 * 12+ 77 = 1001

Any Set of 13 numbers containing {77,77,77,77,77,77,77,77,77,77,77,77,78} in any order has a sum greater than 1000 but less than 1452======> 77*12+78=1002

Their are infinate numbers X, where 77<=x<=78

Therefore there are infinite lists containting {77,77,77,77,77,77,77,77,77,77,77,77,X} where 1001<=77*12+X<=1002

Therefore there are infinite lists of 13 numbers where the sum of the numbers greater than 1000 and less than 1425

QED
​

Now maybe you meant whole real numbers, but I would just say any measurment you make would likely not consist of such numbers.

.
To the contrary, it would consist of such numbers, because we still measure in millimeters even when we can and do measure in angstroms, as well. In other words, you can play in sets of rounded numbers for each perceived level of accuracy. (off topic: My impression is that the designer knew limits of accuracy for the unaided human eye. At those levels, millimeter like units seem like the finest an average human can see and work with. The Frame operates on this accuracy level, when blown up to two-times, so the image had been probably reduced to half-size by the ancients. I say this, because of the difficulties involved in using the classic tools of geometry in exploratory work on the image in its present life-size. The compasses, and pencils make lines too thick for accurate drafting to match the ancient designer in his work.

If all your measurments were somehow comming out to such miracoulous numbers, it would still be on you to verify this by actually using the real object instead of measuring a copy which in and of itself makes your work less acurate.

The concept of whole numbers is not as miraculous to come up with as you say, thanks God. Rounding to whole numbers is one way of controlling damage done by the above factors. You get pretty good preliminary results, your values fall smack in the middle of acceptance ranges, and when you get the object into a lab, you can also check out if the designer's level of accuracy on the Frame stops at millimeters, or goes much deeper. The Frame, however, is already complete for this level.

 

[ReligionStudent]

.
I am just trying to account for factors, which narrow the range of variations we work with. We are talking about engravings on tablets. So, once we have another artist drawing a comparable engraving on the same tablet i.e., it must have thirteen peripheral points in its perimeter, or frame (the Outer Limits ), we can expect some variation in where those points will be, and in the particular distances between particular points. The Frame, a set of those peripheral distances totals 1226 millimeters (in double the lifesize). Of course, the total length of each perimeter in other such engravings would tend to vary, mostly falling into a range. So, an equal distance from 1226 gives an even 1,000 and 1,452. I think this is a fairly realistic range.

So this is all based on your feelings and not any sort of study or comparison, and not anything in a real journal or book? So its completely not valid.

Some of the tablets are comparable to the high quality limestone tablets students used back in the 18-th or 19-th century. I don't know if this particular Athena engraving is on such a limestone tablet, or a quartzite one, a type also found at the site. I do see the hand of a genius, though. The perfection in the line-art often works even under serious magnification in CAD (perfection in the circle-arcs, when following line edges).

You propose to study it but do not know what it is made of, and you simply apply your own aesthetics to it?

To the contrary, it would consist of such numbers, because we still measure in millimeters even when we can and do measure in angstroms, as well. In other words, you can play in sets of rounded numbers for each perceived level of accuracy. (off topic: My impression is that the designer knew limits of accuracy for the unaided human eye. At those levels, millimeter like units seem like the finest an average human can see and work with. The Frame operates on this accuracy level, when blown up to two-times, so the image had been probably reduced to half-size by the ancients. I say this, because of the difficulties involved in using the classic tools of geometry in exploratory work on the image in its present life-size. The compasses, and pencils make lines too thick for accurate drafting to match the ancient designer in his work.

Ok, quick miracle here, there are units smaller than millimeters and there can be fractional millimeters. Also, if you really want to study this you should be using tools that do not cause you to complain about their accuracy.

The concept of whole numbers is not as miraculous to come up with as you say, thanks God. Rounding to whole numbers is one way of controlling damage done by the above factors. You get pretty good preliminary results, your values fall smack in the middle of acceptance ranges, and when you get the object into a lab, you can also check out if the designer's level of accuracy on the Frame stops at millimeters, or goes much deeper. The Frame, however, is already complete for this level.

No rounding to hole numbers is a way to throw your validity out the window, down the street, and then have it crash the Mars lander. You have to deal with the fact that in real life there are infinite measurable possibilities.

 

[Jiri]

Johny, are you a she?

his stupid limit on the sum
his innane limits (why 1452? Why 1000?).

I don't know why he (presumption on my part: might be a "she") chose those numbers.

.
Why not presume you're a "she", Jonny-boy?

[/QUOTE]

ETA: ZOMG! Neither 1452, 1000, nor 175 are Osiris numbers! Jiri, you're slipping! I suggest you choose 16 and 180 as your range of numbers, and accept 1080 and 1758 as your limits! That will make your numbers look more magical more harmonious.[/QUOTE]

 

[Jiri]

So this is all based on your feelings and not any sort of study or comparison, and not anything in a real journal or book? So its completely not valid.

You propose to study it but do not know what it is made of, and you simply apply your own aesthetics to it?

Your conclusions really surprize me, as well as the fake air of indignation (you do not know if the engraving is limestone or quartzite, and yet you dare to study some visible aspects of it? ) Disingenuous at best, on your part.
.

Ok, quick miracle here, there are units smaller than millimeters and there can be fractional millimeters. Also, if you really want to study this you should be using tools that do not cause you to complain about their accuracy.

.
Same thing, by the way I am using CAD nowadays,

No rounding to hole numbers is a way to throw your validity out the window, down the street, and then have it crash the Mars lander. You have to deal with the fact that in real life there are infinite measurable possibilities.

.
I can't believe, you still are missing the concept. The whole numbers are the intended numbers, rounding is part of it. This is the level of accuracy the Frame sets for its particular objective. The proof is in the pudding.

 

[Jiri]

The bet - a summary

Now that we established that the Frame is one of octillions of possible frames it is easy to draw a couple observations:
If the Frame is accidental then there must be a large number of other frames, whose meaning is more intelligent, and more extensive regarding its perceived objectives.
If so, no one should have any difficulties in defeating blind accident and using human intelligence to compose some such superior frames and presenting them here in order to disprove my contention that the Frame is the best possible one out of all those octillions of permutations available for the purposes. Conversely, realizing this we might be a bit more appreciative of what the Frame has to offer.
The same could be said for the thirteen numbers as they are. Again, it should be possible to rearrange them, so they make better sense regarding the stated objectives. There are quite many such arrangements, why should the Frame be the best of all?
If the "accidental" Frame is the best and it beats best efforts of human intelligence then it must be deliberately created.

 

[Jiri]

Levels of accuracy

.
I can't believe, you still are missing the concept. The whole numbers are the intended numbers, rounding is part of it. This is the level of accuracy the Frame sets for its particular objective. The proof is in the pudding.

I forgot to point out that the Frame already sets a number of precedents in working with different levels of accuracy. It quotes various approximations of Pi, and Phi (different levels of accuracy), and works with three levels of accuracy in stating the duration of equinoctial precession.