Clive Wrote:
-------------------------------------------------------
> MJ:
>
> I didn't realize you were concerned about decimal
> inches...I had the impression from previous posts
> that you never stressed such measures.

You asked for confirmation of Petrie’s measurements of certain features.
Petrie gives measurements often to a hundredth-of-an-inch.
I quote Petrie’s measurements either exactly as he gives them or, for convenience (although only occasionally), to the nearest one-tenth of an inch.


> One thing I didn't mention regarding AutoCAD...you
> can decide to what accuracy the measures are
> taken...up to eight decimal places...but that's a
> ridiculous accuracy for measuring hand cut stone
> blocks...don't you think?
> I selected the closest inch...as the results
> indicate.

The smallest known part of a royal cubit is one-sixteenth of a digit or 1/448th of a royal cubit, which is equivalent to 0.05”/1mm.
I find working to 0.001/ royal cubits, which is equivalent 0.02”/0.5mm) more than adequate, and it is easier to round up or down to the nearest 0.001rc than the nearest 0.002rc.


> Well...I gave these measures some thought and
> since Petrie always adds his +/- decimal inches
> then I thought why not forget about this precision
> because it's no more than slicing hairs and that's
> not the intent since it's impossible to build to
> that accuracy.

For the Pyramid’s builders it might well have proven impossible to work core and facing blocks to less than, say, 0.002rc/0.05”/1mm.
However, we are concerned here with the measurements taken by Petrie.


> So...I then thought +/- several inches per
> thousand would not be too bad considering the
> computations required for construction.

That’s your choice, Clive.
I choose to go by what is, not what I think it should be.


> That's
> what Petrie had to face, but he was determined to
> calculate to the closest decimal of an inch...a
> stubborn man…yet he succeeded.

I see his approach to measuring the Pyramid and its passages and chambers as exacting.


> As you have confirmed...my measures look
> satisfactory to me. You don’t get away free on
> this one…I've added some discrepancies of yours,
> however, I will not make such a bold statement as
> this...
>
> "...the measurements that produce your imaginary
> slope of 4139” are mostly incorrect..."

There is nothing bold in my statement, Clive.
You give the measurements to the nearest inch, I give them as recorded by Petrie (occasionally corrected by me to the nearest 1/10”).
By this standard the measurements you give are mostly inaccurate.


> > Starting at the left side of your drawing:
> > 1693 - 1691.6... (Petrie 1693.7-1694.6 after adding wear of step)

I disagree because 1691.6 is allowing for the wear and tilt E-W and N-S of the Great Step.


> > 4534 - 4537.2...east side divided by 2 = 9067.7/2 = 4533.6...mine correct

Cole’s 1925 survey says otherwise, i.e. length of east side at base divided by 2 = 4535.71” to 4537.28” – but I remind myself that you are not concerned with any of Petrie’s errors.


> > 524 - 525.6 to 527...Petrie 524.1...don't recognize yours. It's probably the reason why yours above is also different. Distance "along" the descending passage should be 1110 inches

Petrie’s 524.1 is a calculation based on mean linear and gradient measurements.
Petrie made it 1110.64", Edgar has it as (I think) 1110.8", I make it 1110.9"


> > By Petrie’s measurements: vertical = 1691.6” –
> > 668.2 = 1023.4; horizontal = 4537.2” – 525.6 to
> > 527 = 4010.2 to 4011.6; slope therefore 4138.7 to
> > 4140”.
>
> Incorrect.

Please point out where the error is.


> > Now, as Jon_B has already rightly pointed out...
>
> You don't need Jon ...I have been stating that
> fact from the start. Soooo...what's the issue
> MJ..?
>
> > But if they are for use in a theory about the
> > significance of certain measurements, then one
> > runs immediately into complications.
>
> No you don't, because the average mathematician
> works on tolerances otherwise you are fooling
> yourself.
> I've worked on the finest of equipment with their
> base frames cut to +/- 1/2" yet other aspects of
> the machine are critical and measured to the
> closest 1/2 tho.
> Practicality is the word...not precision. There is
> no way any builder of monuments of this magnitude
> can dictate the accuracy you are calling for. That
> is also true of the KC...there are too many
> variations in measure to dictate which one is
> correct.

IMO, you are trying to justify your basing your theories on what you think the measurements involved should be in preference to what they actually are.
I go by what is, not what I think it should be.


> > The length of the Descending Passage floor is
> > 4148”.
>
> Nope...I told you before...Produce all of the
> man's calculations, similar to what you have asked
> from me, then we will determine why the 8"
> discrepancy...if it exists.
> If you cannot produce that information then it is
> a pointless situation that you are creating...it's
> a rubber duck...it's all yours and you can play
> with it as long as you wish...!

You are being truly preposterous, Clive!
It has been pointed out to you several times that Petrie explains in his work why his measurement of the Descending Passage floor from the Descending Passage/Ascending Passage floor line intersection is inaccurate.


> > just consider...undoubtedly have recorded the
> correct measurement of 4148”..."
>
> No he wouldn't because Petrie allowed for the
> rubble and stated a +/- 3" to compensate...but you
> are stating it is 8" longer +/- nothing...!

I am not stating, I am quoting.
You really do need to read the full accounts by Petrie and J & M Edgar for yourself.


> > Now, is there any significance in these two
> > measurements being, within 8”, the same length?
>
> MJ:
> They are both approximately 4140" and there is a
> reason for this value, but...I told you that first
> things first. I show you the simple correlations
> then we work toward the part that requires some
> thinking.
>
> > Well, with the entrance to the top of the face of
> > the Great Step measurement we have a 90deg
> > triangle: height 1023.4”, base 4010.9” ± 0.7”,
> > hypotenuse 4139.4” ± 0.6”.
>
> > If the intent was for a slope measuring 4139.4”,
> > then what was the other determining factor?
>
> MJ:
> Make it simple for all to read...it's 4139 and
> 4140...no decimals.

I’m all for simplicity, but not at the expense of accuracy.


> > Was it the height @ 1023.4”, or was it the
> > horizontal length @ 4010.9”?
>
> Neither.

I look forward to reading what you think the determining factors were.


> > And in both cases, how were the vertical and
> > horizontal dimensions of the upper Descending
> > Passage, Ascending Passage, Grand Gallery and
> > Great Step each fitted in?
>
> They lead you to finer details within the design.
> You have witnessed the "imaginary" line as you
> call it...you needed intelligence and imagination
> to discover it...

“intelligence and imagination”???
I thought it was all down to your inputting into AutoCAD carefully-selected-by-you-rounded-up-down-to-the-nearest-inch measurements …


> there are lots more hidden within
> these passages.

And most of it is purely coincidental … IMO …


> Think...why are two of the three
> chambers offset from the centre of the pyramid?

IMO, choice by Khufu (and or his architect) and practical considerations put the chambers generally where they are, and basic arithmetic and rectilinear geometry determined their precise vertical and horizontal locations.


> Why is one formed from bedrock, one comprised of
> limestone and one of granite?

How could the Subterranean Chamber be anything but bedrock?
Limestone was the usual choice for chambers inside a pyramid.
The choice of granite for the King's Chamber – presumably the intended burial chamber – is most likely down to symbolism and a very human desire for the best material available.


> You may recall and I'll say it again...if you lack
> understanding the total pyramid site then you will
> never understand their interior.

I doubt we can ever fully understand the pyramids.
However, when it comes to theorising about the pyramids (not just Khufu’s) then it is, I feel, essential to learn as much as one can not only about the physical structures themselves, but also the culture that built them.
I can’t help feeling that you have no interest in the latter.


> > Or could it be that the determining factor was the
> > gradient (seked) of the slope?
>
> Believe me...the designers of this structure cared
> less about rudimentary sekeds.

My finding is that the architect was concerned only with vertical rise and horizontal run, making the hypotenuse incidental to them.


> > But, then, even this does not explain how the
> > Descending Passage, etc., were fitted into the
> > triangle.
>
> Big puzzle isn't it? Big story goes with it.

I think the solution to ‘the puzzle’ is very simple and extremely mundane.


> > Another possibility is that the vertical and
> > horizontal locations of the entrance and the Great
> > Step were the determining factors – but how did
> > they get to be where they are?
>
> About six months ago I posted one reason why the
> entrance is at this height...there is one more,
> but you would never believe it...Don Barone
> would...but you and most others wouldn't.

If it involves– which no doubt it does – astronomy, geodetic data, higher mathematics, etc., for which there is no evidence of the AEs knowing then I can guarantee I won’t believe it.


> > The point is, one cannot say that there is
> > significance in the Descending Passage floor
> > length (regardless of the 8” difference) being
> > almost the same as the imaginary
> > entrance-to-Great-Step sloping line without
> > explaining the vertical and horizontal
> > measurements of and associated with the upper
> > passages and the Great Step.
>
> Actually...the passages and chambers relate to
> astronomy...the "imaginary triangle" relate to
> higher math and also astronomy.

I disagree.
The entire Pyramid plan can be reproduced accurately without recourse to astronomy, geodetic data, higher mathematics, etc., etc.


> But do not rule out the sub passages...they also
> have an important contribution to the design.

I don’t know of anybody who ignores the Subterranean Chamber, etc.


> Perhaps you can now realize why one drawing with
> all information included would be mind-boggling to
> analyze.

Which probably explains why I have the plan of the entire Pyramid broken down into a series of 200+ carefully scaled diagrams.


> Every aspect of this structure is an
> intentional design feature...

Well, certainly most, but some must be by-products


> they didn't miss a
> single trick...

Such as?


> and never overlook what others have.
For example?


> I erred by assuming Petrie's assumed
> measures of the Grotto to be close
> enough...bad...bad...egg on my face...it’s
> embarrassing…!

With this in mind, along with other errors you have made, I once again suggest that when it comes to analysing the measurements you not only ditch the AutoCAD but also use Petrie’s and others’ measurements to at least 1/10” (calculations based on measurements rounded up or down to the nearest inch will invariably give a misleading result – I know because I’ve tried it many, many times).

MJ

We can't all be right, but we could all be wrong ...