Nope that would be conflating objectively testable concepts (maths and geometry) with objectively testable objects.
Ie: a category error!
Then how would the artisan ensure that the opposite side reflects the exact measurements as the copied side.
Geometry
The golden ratio features prominently in geometry. For example, it is intrinsically involved in the internal symmetry of the
pentagon, and extends to form part of the coordinates of the vertices of a
regular dodecahedron, as well as those of a
5-cell. It features in the
Kepler triangle and
Penrose tilings too, as well as in various other
polytopes.
en.wikipedia.org
This Golden Ratio thing is a bogus idea in science. Where does it lead?
Its not bogus. Its reflected in nature and science recognises this.
The golden ratio, approximately equal to 1.61803398875, is a mathematical concept that relates to proportion and symmetry. In nature, it manifests in various forms, from the spiral arrangement of a pinecone’s scales to the elegant curves of a seashell. Even the branching of trees and the arrangement of leaves often adhere to the golden ratio.
Nature has long been a source of inspiration for designers, and one of its most intriguing mathematical phenomena is the...
orrbitt.com
Discover how the golden ratio shapes nature through simple definitions and fascinating examples, from flora and fauna to human bodies.
www.mathnasium.com
The notion of a 'DNA codes' is our invention intended for the purposes of coming to some understanding about lots of aspects about the reactions and external manipulations of DNA molecules, (aka organic bio-chemistry). There is no evidence of external deliberate design in any of that. 'Binary codes in computers', is the product of Booleen Algebra, used to succintly express operations and their outcomes and in this case, with complex switching processes.
I am not talking about design. This goes back to breaking down what we see and trying to derive a pattern and method from the signs in the stone. As humans we recognise these patterns and signatures.
The DNA code is not invented by humans. We have applied computer tech info as an analogy to DNA because it has a similar binary codes which make up information. Thats all. We recognise the code in DNA.
Query: 'micron' level??
Elaborate.
A micron is a metric unit of measurement where one micron is equivalent to
one one-thousandth of a millimetre [1 micron (1μ) = 1/1000 mm] or 1 micron (micrometer) = 1/1,000,000 of a metre.
So its much more a precise measure than 1000th of an inch or a millimeter. It can only be seen with magnification.
Yeah we see patterns which helps us discuss with consistency amongst other human observers .. that doesn't mean the patterns were deliberately embedded to enforce 'conformance'.
It does if those patterns we see in nature are reflected in a human made object. They are purposely imputted into the vase or works and not something you fluke or create freehand.
I meant to say binary code is similar to DNA code but DNA has been around for billions of years. Now did humans create binary code or was it already in nature.
All that is evidence of humans doing stuff after Djoser's/Imhotep's time in order to make sense to other humans.
The point was that the precision in the vases and other works goes down to the micron level, smaller than the width of a hair. So to achieve that precision to the micron level without magnification to be able to set that precision in the proper place at the micron level or some device preset to that precision its impossible for humans to achieve.
If we cannot see at the micron level that we are blindly having to guess or feel that precision. I don't think individual or even the same artisan could fluke many vases with such precision.
The discussion of math being invented or discovered is pure philiosohpy of the navel-gazing variety.
It doesn't matter as far as proceeding with the science.
That is not fact. Yes because if math was only invented then philosophically why and how can math match and reflect so well nature and reality. Saying its a coincidence is a philosophical question about epistemics (how do we know) ie perhaps its not a coincience but math is actually within nature and reality and we human are just using math as a way to understand this.
As well as ontology (what is reality). Because math and reality relate so well the question naturally comes up 'what is fundemental reality'. Is it the matter we see or is it some form of information, math or knowledge. This is a common area of exploration is science today.
'Intuitive knowledge of nature', eh?
That concept gives permission to completely ignore everything humans have ever done to give reliable meaning to the term 'nature'.
I reject this idea.
Not really. It is actually humans acknowledging and copying nature. Acknowledging that there's some pretty cool designed in nature that can be useful. As humans we intuit that design through recognition of patterns of meaning and math.
Holder design depends on the force intended to be applied between the tool and the workpiece at given step in a process.
I am talking about keeping the vase perfectly still to get near perfect precision. You can't get that desired precision is the vase hold, tool or worker moves. Everything has to remain perfectly still to achieve that micron level precision. Then the cutter itself can be set to cut or grind out the object with each angle, straight line and curve be set into the fixed cutter without human aid.
The final finishing phases require less directly applied force when compared with the roughing in phases.
I disagree. Its the final cut or grind that needs to be set and near perfect. The first few cuts can vary as they are cutting away stone to get to the precise shape. Its the final cuts and grinds that will home in on the perfection.
A higher speed of rotation allows for large numbers of smaller cuts in a smaller timeframe, compared with bigger cuts over the same timeframe and a slower rotation speed. Smaller cuts reduces the possibility of catastrophies too, I suppose. A faster rotation speed might also serve as a good way to establish a symmetry axis in the workpiece.
I think ,modern day lazer cutters can cut quickly through softer material. Some heavy cutting like with the old gang saws had a slow and meticulous cut that ground through the sandstone.
I think so long as the cutting point is fixed and the device is stable you could cut through a piece slowing and accurately. But there may be differences in the marks left in the material. If you notice a circular or jigsaw which have a fast rotation tend to leave a cleaner cut than a hand saw that may rip the material.
If there is a lot of time available to make an object, then I think the same precision might be achievable in either case there(?)
I think this sounds much like the Darwinist arguement for complexity of life that given enough time nature can create anything. Like Dawkins says with the Blind Watch maker where life has the appearence of design but is not designed and NS given enough time can create a watch with the appearence of design but not designed.
So what looks like maching marks, has complex geometry and math and looks designed with a plan is actually just a coincident and the result of primitive humans with primitive tools slowing bashing, chiseling and rubbing the vase into perfection.