I was just reading where the pyramids were made of 2.3 million blocks, yet they were only 1/4" off at the top of the pyramid. Would the large numbers of block account for more accuracy? Kind of like rolling the dice 2 million times and seeing how close they come to predicted odds?
Just some thoughts on randomness, if I were to mix a few different chemicals that would dissolve in liquid I would expect a very even distribution. Would the same hold true for a powder? For example, I might have 2 cups of flower and mix in 2 tsp of cinnamon while it is dry. Use my beaters for a few seconds and to the naked eye it appears very evenly distributed. If I were to divide that mixture into 12 groups, I wonder how it would check out if there were a way to count it? And then repeat that test with 2 million cups of flower and 2 million tsps of cinnamon? Would the larger number be more precise statistically?
They had plumb lines to level each tier as it went up so no significant error would accumulate.
So, is the notion in the OP that, when piling a lot of stones to make a giant pyramid any errors will sort of even out? A little too big here, a little too small there. In the end it’s a wash and it all evens out into a well formed pyramid?
Not at all, I know they are being skillfully carved
If the four corners of the base level are properly surveyed to form a perfect square (which being at ground level can be easily verified by different and independent methods), then its easy to intersect the diagonals for an exact centre point.
Provided that the four corners of each subsequent layer are inset the same distance from the previous one, them you should be able to maintain your desired level of accuracy, no matter how many layers or blocks are used.
How they actually surveyed as they built the pyramids is unknown, but one of geometry’s superpowers is that simple methods are scaleable.
To your original question, I don’t think that randomness contributes to accuracy, but deciding explicit measuring points when you start building means that the rest of the build can be less reliant on accuracy. For example, for layer 27 spending lots of time setting the four corners exactly relative to layer 26 then, once they are fixed, all the other stuff can be shovelled in quickly, knowing they are within acceptable limits of accuracy.
1/4" off in what dimension?
What the OP is asking about is essentially a random walk.
And if you read the article, the answer is no, it doesn’t even out.
The OP may find this interesting too. There is a sense in which certain things do converge better with larger quantities:
As to the pyramid accuracy thing, that is classic techo-babble geewhiz writing. The sort that both Discovery channel and CT theorists use to create false erroneous thinking in the audience.
Emphasize the ginormous number - 2.3 milliom!!! - of blocks, when the number of blocks is totally immaterial to the accuracy. But it sets the audience up to think along the lines of “What are the odds of success against 2.3 million chances to screw up?” thought process. Which thinking has no basis in fact but folks unused to critical analysis or thinking will fall for it every time.
Mixing of powders, and of liquids, to very high tolerances of uniformity is a non-trivial problem. The folks that manufacture pharmaceuticals deal with this all the time. “It looks good by eye” may be orders of magnitude less good than is necessary. Depending on the details of the substances involved, liquids may be easier than powders or harder.
Is this (incomplete mixing) a/the primary cause of fentanyl overdoses? That is to say, when drug makers are mixing a small amount of fentanyl into a large batch of some other drug, are the ensuing overdose incidents mostly due to a few portions of the whole batch containing most of the fentanyl, or are they more usually due to simply adding way too much fentanyl in the first place, rendering the entire batch toxic no matter how well-mixed?
Mixing up a bunch of different drugs is already dangerous (e.g., what happens if you take fentanyl, flubromazepam, and 3,4-dichloro-N-[2-(dimethylamino)cyclohexyl]-N-methylbenzamide at the same time?), and the main problem with shooting up an unknown mixture of random synthetic opiates cooked up by who-knows-whom in their bathtub is that you have absolutely no idea how strong it is going to be or the pharmacokinetics of whatever happens to be in there, so it is pretty easy to overdose if you are not careful. Of course, if the dealer cannot even turn out consistent batches it is going to be that much worse, but I do not know if that is a worse problem with fentanyl than with anything else that might be in there.
Agree w @DPRK just above. Once you’re talking random crap in a mixture, you’re on the experimental frontier with each dose you take. Lotta ways for that to end very badly very quickly.
As to fentanyl specifically, the problem is the LD50 is a very small amount. Compared to e.g. heroin or morphine. When it was invented, it was spectacularly more potent than anything before. Subsequent legit opioid synthetics are even more potent.
So yeah, sloppy mixing in homebrew fentanyl produces hot spots in the batch which produces all-but guaranteed ODs for somebody. The same thing was true for street heroin 50 years ago, but the amount of “close enough was still good enough” was larger, so ODs were a lower percentage of all doses.
IANA expert, but some non-trivial fraction of fentanyl ODs are folks consuming legit professionally manufactured pharmaceuticals, but in illegit quantities for illegit reasons. And that just comes down again to the idea that some is fun, a bit more is OK, and a wee bit more is way too much and now you’re doomed absent Narcan or whatever. Couple that with increasing tolerance to the psychoactive effects, and the typical incompetent lousy judgment of addicts in general, and you’ve got a recipe for a lot of inadvertent suicides.
My late first wife spent 8 years wearing a fentanyl patch for her ever-increasing cancer. Worked great for pain relief and didn’t slow her mental processes down much. No high there. But I recall a convo with the oncologist at a time she was on a pretty hefty dose even by their standards. He said “You or I would be on the floor with that much drug in our system, and here she is sitting upright talking with us normally.”
+1
IOW, the precisión is a result of the BUILDING PROCESS and not of the RAW MATERIALS …
on a smaller scale, just look at ol’ time bricklayers that were setting some “not-so-square” bricks aside, to be used later in some conditions that needed correction to get back to plumb.
Thanks, HoneyBadgerDC. At first, I wondered if the OP thought the builders got a big pallet of ACME Pyramid Blocks from their local Home Depot.
It’s a lot easier to build a house that’s plumb if you can measure and cut the lumber as you proceed.
Not only did the Egyptians learn to measure accurately, they learned to build accurately. It didn’t just happen the first try.
If just using more materials produced perfection, then why did so many ancient buildings collapse in ancient times?
The odds are astronomical that a random assortment of variables would be that close to being perfect at the end. Those blocks were super heavy and their technology limited. It’s not like they could stack a few, decide it was off, UNstack them, and do it all over again.
I was actually thinking fairly close tolerances, with a million blocks even close tolerances could go way off without constant adjustments. I sometimes wonder if they were just not poured instead of cut.
You can stop wondering. All modern archaeology says they were blocks hauled up ramps.
One factor I read of was that the crystals are very hard (and presumably, the people doing the dilutions are less than concerned about issues). As a result, because of the tiny threshhold amounts (LD50?) an error with a bit too much due to a large crystal can be fatal. The mix result is intensely variable.
One theory says the close fit of the pyramid structure is because before a block went up, it was “finished” to match the neightbour block(s) at the bottom of the ramp. Presumably at that time thy could also do any height adjustments to a block to make that layer stay level.
The bent pyramid was a learning experience in a different way - they started to built at steep angle and part way up, realized they had made it too “pointy”. Things were starting to shift. So they corrected by making the rest of the pyramid a less sharp angle. They 3 main pyramids at Giza however have the distinction of being built on a limestone base, so they were very resistant to shifting - and they were built with the experince of the Bent Pyramid indicating the apppropirate 'safe" angle.
FYI - the commonly suggested method of building the pyrmid was that a mud brick ramp was built on the blocks, spiraling the pyramid as it went up. The article is confusing, since the top was a nice pretty smoothed-off limestone cap - some speculate the last foot or more was topped with gold leaf. (None of these caps survives, so who knows?) Then as they removed the mud-brick ramp, they worked their way down and around and covered the block construction with nice smooth limestone sides, which have now mostly fallen away or been “repurposed” in other buildings. At the time however, these would have been polished shiny white limestone perfect pyramids. (You can see the remnants of this smooth cover near the top of the center Giza pyramid.) So what is the article talking about, since the exact pinnacles of the pyramids are long gone? IIRC from assorted photos, all that is left at the top of the Giza pyramids is now a small flat platform of blocks.
A straight gravel ramp as high as the pyramid, as envisioned by some artists, would have required more volume of fill than the pyramid itself and there is no evidence of such ramps or the debris from them. Mud bricks would have been re-used.
just a tiny tangent:
Paul Horn plays flute inside the great pyramids in gizah (about 1970ies)
