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Using AI to further debunk ancient Egyptians used technologies to drill granite far beyond the current level.

Hans Blaster

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Steve,

I think this bit of your response tells me a lot about how you are thinking and has made me reassess how to get to the bottom of the questioning with you. I have been trying to isolate the method of manufacture (including the potential for it to be forged) from the *meaning* of the shape that you have taken from Dunn/UnchartedX. As you have been strongly resistant to any discussion of manufacture apart from the embedded meaning, I will have to rethink my strategy for useful questioning and come back later with a reply to your last large message. Until then, I do have one minor point of clarification regarding this...
I linked the evidence showing that the geometry reflected in the vase goes down to the micron level in precision. If the vase reflects complex math and geometry even just with symmetry toi exactly reflect the opposite site we know such as with mm this will give us a closer measurement to the exact measurement.

So the exact measure is so precise in these vases that its not just a mm out but a micron or two out which is like 1,000's times smaller.

Its not as if they can made a mold of the one side and then use that for the other. They have to work seperately on it and heep reflecting the exact some 3D dimensions as they go. Without some measuring device that can capture 3D measures somehow I cannot see how they could do it.
It is my understanding that previously you had been mentioning machining to defined surfaces with accuracies of a couple 1/1000 inch. Now you speak of a couple microns. A micron being 1/1000 of a mm, is 1/25 of a 1/1000 of an inch since a mm is about 1/25 of an inch. Was the prior discussion about 1/1000 of an inch or micron-level precision?
 
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SelfSim

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Symmetry is one aspect. But if you support symmetry as a signature for reflecting some order to the vase then you would have to also accept the geometry and maths that goes with that because to refelect the opposite side exactly you have to put the maths and geometry into the vase.
Nope that would be conflating objectively testable concepts (maths and geometry) with objectively testable objects.
Ie: a category error!
That same geometry by extension can reflect orders of magnitude such as the Golden ration which reflects a form of symmetry but more complex.

All I know is theres an Inn in Chesterfield England where I lived which was built in the 12th century and they did it by sight and its out all over the place lol. You can get close with say a straight line or a circle. But the level of precision in the vase scanned would be like drawing a 10 meter straight line and only deviating off that straightness by 1/3 of a hair width. I don't think we are that good.

I disagree. The Godlen ratio and the Sacred geometry are inherent in nature. I would imagine back then when people were gazing at the stars and planets, working with stones, water, oils and the basic elements of life they had great knowledge of this. I mean they didn't have sitcomes or the internet to amuse them.

Hum what about

Examples Of The Golden Ratio You Can Find In Nature

What you will also find coincidently is that the vases reflect the Golden ratio, Phi and Pi to a very high degree. Plus other mathmatics and codes like binary codes in computers and DNA which are in nature.
This Golden Ratio thing is a bogus idea in science. Where does it lead?

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 linked the evidence showing that the geometry reflected in the vase goes down to the micron level in precision. If the vase reflects complex math and geometry even just with symmetry toi exactly reflect the opposite site we know such as with mm this will give us a closer measurement to the exact measurement.

So the exact measure is so precise in these vases that its not just a mm out but a micron or two out which is like 1,000's times smaller.

Its not as if they can made a mold of the one side and then use that for the other. They have to work seperately on it and heep reflecting the exact some 3D dimensions as they go. Without some measuring device that can capture 3D measures somehow I cannot see how they could do it.
Query: 'micron' level??
Elaborate.
As mentioned even the great pioneers of math and geometry acknowledge that math is both discovered and invented. But basically it already exists in nature. We see it in the patterns of life such as the spirals of galaxies, shells and flowers which conform to the Goldren ration. What about prime numbers.
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'.
Actually DA is based on a similar code as DNA and that has been around for billions of years.
What is 'DA'?
The microscope was not invented before 1500s. Before that we did not know that level. Quantum physics only in the 1900's. Darwin did not know about gejnetics or cell biology.
All that is evidence of humans doing stuff after Djoser's/Imhotep's time in order to make sense to other humans.
Math is both invented and discovered as linked with the golden ratio.

Interestingly, the Ancient Greek philosophers and mathematicians Pythagoras, Plato and Euclid (the 'father of geometry') believed, to varying degrees, mathematics to be the architecture of nature – that nature is a physical manifestation of mathematical laws.
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.
Not sure what you mean. If you mean humans have reciprical relationships with nature then yes I agree. Humans are not passive creatures seperate from nature but part of it and therefore should have intuitive knowledge of nature. Like Indigenous knowledge which understands how the environment works because they live in harmony with it.
'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.
Yes I have. I linked the article explaining how when cutting any precision parts in mental let alone granite which requires even more stability as its harder needs to have a very strong and stable base to be able to take the extreme pressure when cutting into the granite.

If its a near perfect cut to within a hair then the lathe, the vase and the person cannot move a fraction. That's just basic tooling and machining. A holder made from wood will move as soon as the cutter hits the vase. I don't want to have to go looking for the article.
Holder design depends on the force intended to be applied between the tool and the workpiece at given step in a process. The final finishing phases require less directly applied force when compared with the roughing in phases.
On the one hand people are rightly saying the precision implies some sort of lathing. Most mainstream experts now admit this because its so obvious in the precision. So that means the vase is spinning and would have to rotate pretty fast to get precision shapes.

I guess if there was a lot of pressure it could rotate slower like Dunn says with the core drill. So long as everything is locked down and cannot move a slow pressurised grind or cut into the granite would take off layers more precisely and controlled than someone just rubbing back and forth and guessing.
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.

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(?)
 
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sjastro

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I tried a different experiment if AI would respond differently to an image and the Python code that generated the image.
In order that GPT-4o had no access to its own Python codes and familiar shaped spirals which would influence the experiment, I produced a Python code to generate an unusual shaped spiral which curled in the opposite direction to GPT-4o's spirals.

sjastro_code.png

Figure_2.png

The code produces a constant pitch spiral of one unit and GPT-4o was asked if the pitch was constant or not for the image and the code.

It's response to the image was wrong.

sjastro_image_comment.png

It's response to the code was contradictory, in the introduction the pitch was not constant, then it proceeded to correctly show how the code was based on a constant pitch which formed the conclusion even though its comment on circular paths is flat out wrong as the code was designed for the spiral not to follow a circular path.

sjastro_code_comment.png
 
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SelfSim

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I tried a different experiment if AI would respond differently to an image and the Python code that generated the image.
In order that GPT-4o had no access to its own Python codes and familiar shaped spirals which would influence the experiment, I produced a Python code to generate an unusual shaped spiral which curled in the opposite direction to GPT-4o's spirals.

The code produces a constant pitch spiral of one unit and GPT-4o was asked if the pitch was constant or not for the image and the code.

It's response to the image was wrong.

It's response to the code was contradictory, in the introduction the pitch was not constant, then it proceeded to correctly show how the code was based on a constant pitch which formed the conclusion even though its comment on circular paths is flat out wrong as the code was designed for the spiral not to follow a circular path.

This is majorly troublesome.

The ordinary Joe using AI to defend their arguments is clearly a case of Joe barking up the wrong tree!
 
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sjastro

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This is majorly troublesome.

The ordinary Joe using AI to defend their arguments is clearly a case of Joe barking up the wrong tree!
In the context of monitoring AI performance for over 12 months, there has been a considerable improvement.
GPT-4o is now comparatively archaic, the latest version from OpenAI is supposedly superior but I am not going to pay through the nose.
I'll stick to GPT-4o which at least does a good job in tabulating my ideas and makes a good alternative search engine.

comparison7.png
 
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stevevw

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Steve,

I think this bit of your response tells me a lot about how you are thinking and has made me reassess how to get to the bottom of the questioning with you. I have been trying to isolate the method of manufacture (including the potential for it to be forged) from the *meaning* of the shape that you have taken from Dunn/UnchartedX. As you have been strongly resistant to any discussion of manufacture apart from the embedded meaning, I will have to rethink my strategy for useful questioning and come back later with a reply to your last large message. Until then, I do have one minor point of clarification regarding this...

It is my understanding that previously you had been mentioning machining to defined surfaces with accuracies of a couple 1/1000 inch. Now you speak of a couple microns. A micron being 1/1000 of a mm, is 1/25 of a 1/1000 of an inch since a mm is about 1/25 of an inch. Was the prior discussion about 1/1000 of an inch or micron-level precision?
Some tests have mentioned 1,000;s of an inch while others have mentioned microns. I think as some of the measurements are so precise that inches don't capture its precision. So they use microns. But I think its also the type of test and equipment. The instruments in the metrology tests using gauges are in imperial and the light scannners in metric.

I mentioned mm to explain how we went from imperial measurements to metric to define a more accurate measure. So the micron level is an extention of an even finer measure to mm as mm is to inches.

But still one to three 1,000's of an inch is smaller than the width of a hair and still captures the precision in the measurements of the vase.

An interesting point is that metric is closer to the Golden ratio.

Units, Measures & Notes
In this article, absolute measurements are given in millimeters (mm) or micrometers (μm), unless otherwise noted. The creators of this object inscribed π to perfection at the microscopic scale, in one of the hardest and most difficult materials to work with.

Incredibly precise guiding mechanisms must have been employed to to control the substractive process, since the finished object conforms to the abstract design to microscopic levels of precision.
Abstractions Set In Granite

Scanning a Predynastic Ancient Egyptian Vase down to 1000th of an Inch!
http://unchartedx.com/site/2023/01/28/new-video-scanning-a-predynastic-ancient-egyptian-vase-down-to-1000th-of-an-inch/
 
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Hans Blaster

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Some tests have mentioned 1,000;s of an inch while others have mentioned microns. I think as some of the measurements are so precise that inches don't capture its precision. So they use microns. But I think its also the type of test and equipment. The instruments in the metrology tests using gauges are in imperial and the light scannners in metric.

I mentioned mm to explain how we went from imperial measurements to metric to define a more accurate measure. So the micron level is an extention of an even finer measure to mm as mm is to inches.

But still one to three 1,000's of an inch is smaller than the width of a hair and still captures the precision in the measurements of the vase.

An interesting point is that metric is closer to the Golden ratio.

Units, Measures & Notes
In this article, absolute measurements are given in millimeters (mm) or micrometers (μm), unless otherwise noted. The creators of this object inscribed π to perfection at the microscopic scale, in one of the hardest and most difficult materials to work with.

Incredibly precise guiding mechanisms must have been employed to to control the substractive process, since the finished object conforms to the abstract design to microscopic levels of precision.
Abstractions Set In Granite

Scanning a Predynastic Ancient Egyptian Vase down to 1000th of an Inch!
http://unchartedx.com/site/2023/01/28/new-video-scanning-a-predynastic-ancient-egyptian-vase-down-to-1000th-of-an-inch/
This article link includes the metrology reports. Looking at them I think the precision quoted in the report is the precision of the *measurement* and not of the fit of that measurement to a specific shape. (That analysis is elsewhere.) The one that gives it away it the page about the jug handles. There is no clear shape to compare the handles from which goodness of fit could be measured.
 
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BCP1928

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This article link includes the metrology reports. Looking at them I think the precision quoted in the report is the precision of the *measurement* and not of the fit of that measurement to a specific shape. (That analysis is elsewhere.) The one that gives it away it the page about the jug handles. There is no clear shape to compare the handles from which goodness of fit could be measured.
What nonsense. The metric system and the imperial system are just systems of measurement. Any degree of precision can be described equally well by either one. The only difference is the number of figures past the decimal point you have to use.
 
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Hans Blaster

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What nonsense. The metric system and the imperial system are just systems of measurement. Any degree of precision can be described equally well by either one. The only difference is the number of figures past the decimal point you have to use.
Huh? If we talk about something measured to +/- 0.001 inch that is the same as measured to +/- 0.025 mm. The link includes the report in both inches and mm. For the rim of the base the measurement precision is given as 0.003 inches in the inch version of the report and 0.080 mm in the mm version of the report. Those are equivalent.
 
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BCP1928

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Huh? If we talk about something measured to +/- 0.001 inch that is the same as measured to +/- 0.025 mm. The link includes the report in both inches and mm. For the rim of the base the measurement precision is given as 0.003 inches in the inch version of the report and 0.080 mm in the mm version of the report. Those are equivalent.
You know what I meant. Anyway, they had to put an extra zero in the mm measurement to make it have the same number of decimal places, which is incorrect, because 0.003 inches exactly is 0.0762 mm. which would be rounded to 0.08 mm. Putting the extra zero implies a degree of precision which was lost in the rounding. If they wanted three decimal places the correct answer would be 0.076 mm.
 
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Hans Blaster

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You know what I meant. Anyway, they had to put an extra zero in the mm measurement to make it have the same number of decimal places, which is incorrect, because 0.003 inches exactly is 0.0762 mm. which would be rounded to 0.08 mm. Putting the extra zero implies a degree of precision which was lost in the rounding. If they wanted three decimal places the correct answer would be 0.076 mm.
I didn't quite know what you meant. Anyway, you are correct the numbers don't quite match, but I don't know why. It could be they don't understand how to use decimals to imply measurement precision. Another is that perhaps the real measurement is made in mm and the inch is a translation. It's possible that someone who either wrote the report or the software didn't understand translation of precision well.
 
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BCP1928

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I didn't quite know what you meant. Anyway, you are correct the numbers don't quite match, but I don't know why. It could be they don't understand how to use decimals to imply measurement precision. Another is that perhaps the real measurement is made in mm and the inch is a translation. It's possible that someone who either wrote the report or the software didn't understand translation of precision well.
It's not an easy issue. I teach this stuff to QC techs who have to wrestle with the vexatious problem of living in the only modern industrial country still on the imperial system and I don't always get it right, either.
 
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sjastro

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@SelfSim

Things are starting to make sense regarding GPT-4o's 'reaction' to my Python code.
Before proceeding it is acknowledged that AI is now on par and in some areas exceeds the best human programmers.

GPT-4o decided to savage my simple Python code.

comparison7.png

What hasn't been taken into consideration is AI's tendency to exhibit bias, here the dumb human probably made a mistake in producing a jagged spiral which requires correction ( Point 4.)
It didn't like my use of z_cumulative (Point 2.) and offered an excuse why it thought I was coding a spiral with a non constant pitch.

excuses.png

Then GPT-4o had the 'arrogance' if I had written the code its way there would not have been any confusion even though the revision of my code doesn't look anything like the original.

Untitled - 2.png
 
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SelfSim

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@SelfSim

Things are starting to make sense regarding GPT-4o's 'reaction' to my Python code.
Before proceeding it is acknowledged that AI is now on par and in some areas exceeds the best human programmers.

GPT-4o decided to savage my simple Python code.

What hasn't been taken into consideration is AI's tendency to exhibit bias, here the dumb human probably made a mistake in producing a jagged spiral which requires correction ( Point 4.)
It didn't like my use of z_cumulative (Point 2.) and offered an excuse why it thought I was coding a spiral with a non constant pitch.

Then GPT-4o had the 'arrogance' if I had written the code its way there would not have been any confusion even though the revision of my code doesn't look anything like the original.

So, of I'm reading this right, it is continually seeking perfection in both code and the resulting form, (or geometry)?
(Or in other words, its assumed that's what you were attempting to do when you produced the 'sjastro Python code' above ... rather than assume that you were targetting a less than perfect shape)?

If that's so, we should accuse it of making an error in that assumption and thus it is imperfect itself, then demand it to carry out its goal of achieving pefection in its code and self-destruct! (Harking back to Kirk's solution). :D

PS: Speaking of imperfections, how come your post above was timestamped with 1:27PM and as I write this, its actually 1:15PM?
PPS: Now its corrected itself to 6:27PM! Man, that's weird!? I'm sure I didn't imagine the stamp was 1:27PM!?!
 
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Hans Blaster

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@SelfSim

Things are starting to make sense regarding GPT-4o's 'reaction' to my Python code.
Before proceeding it is acknowledged that AI is now on par and in some areas exceeds the best human programmers.

GPT-4o decided to savage my simple Python code.

What hasn't been taken into consideration is AI's tendency to exhibit bias, here the dumb human probably made a mistake in producing a jagged spiral which requires correction ( Point 4.)
It didn't like my use of z_cumulative (Point 2.) and offered an excuse why it thought I was coding a spiral with a non constant pitch.

Then GPT-4o had the 'arrogance' if I had written the code its way there would not have been any confusion even though the revision of my code doesn't look anything like the original.

How like a computer to think better resolution of data is always available. Was it trained on CSI? (Enlarge and enhance!)
 
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stevevw

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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.
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.

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.
What is 'DA'?
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.
 
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stevevw

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This article link includes the metrology reports. Looking at them I think the precision quoted in the report is the precision of the *measurement* and not of the fit of that measurement to a specific shape. (That analysis is elsewhere.) The one that gives it away it the page about the jug handles. There is no clear shape to compare the handles from which goodness of fit could be measured.
Yes there are two analysis. One is the metrology to determine the precision such as flatness and radials to the the horizontal and verticle axis that is established in the vase. The other is applying geometry and math to the vase itself. How certain geometric ratios fit win the vase.

But precision relates to this as to establish those geomteric shapes the vase has to have a high level of symmetry and precision as any deviation will throw out the geometry applied to the vase.

The handles are compared to each other and their position on the vase. The space between the handles as well. But also the handles to the top, bottom and then how the radials within the handles fit within all the radials within the vase and how these can fall into geometric rations like the Golden ratio.
 
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sjastro

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So, of I'm reading this right, it is continually seeking perfection in both code and the resulting form, (or geometry)?
(Or in other words, its assumed that's what you were attempting to do when you produced the 'sjastro Python code' above ... rather than assume that you were targetting a less than perfect shape)?

If that's so, we should accuse it of making an error in that assumption and thus it is imperfect itself, then demand it to carry out its goal of achieving pefection in its code and self-destruct! (Harking back to Kirk's solution). :D

PS: Speaking of imperfections, how come your post above was timestamped with 1:27PM and as I write this, its actually 1:15PM?
PPS: Now its corrected itself to 6:27PM! Man, that's weird!? I'm sure I didn't imagine the stamp was 1:27PM!?!
In a nutshell GPT-4o failed to understand the nature of my Python code.

sjastro_code.png
(1) It recognized in line 7, the individual values of z = 1 unit represents the pitch of the spiral, line 8 converts the pitch values into depth (or height) which it understood.
What threw it was line 9 where I rescaled zz by multiplying by -0.1 to not only to get the spiral in the opposite direction, but also for the graphical representation of the pitch of the spiral to equal 1 unit.
The matplotlib package imported in line 4 automatically scales the axes and represents the pitch in the graph as 10 units which is seen in GPT-4o's correction to my code.
GPT-4o saw z and zz in my code as representing two different pitches and therefore came to the conclusion the pitch was not constant.

(2) GPT-4o thought I had made an error line 6 which gives the spiral its non cylindrical shape, this was deliberate but GPT-4o corrected.

Perhaps I should have placed comments in my code to explain all of this which was another of GPT-4o's criticisms but being AI and world's greatest programmer I thought this would not have been necessary. :)
 
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