You actually don't need to do that part in the algorithm. If you don't know the length of the list, you can just choose a threshold that seems reasonable and calculate the margin of error after you're done processing. (or i guess at whatever checkpoints you want if it's continuous)
In this example, they have the length of the list and choose the threshold to give them a desired margin of error.
It makes a lot of sense because obviously having a river there makes the transport of materials a lot easier, but i do wonder how nobody noticed this before.
> The biggest unknown with my model is whether there was a major western Nile channel at the time, as modern authorities are split on this question.
Seems like what we have now is the discovery of a natural branch, which doesn't mean they didn't dig out useful extensions too.
The Nature article calls this branch a "tributary of the nile", which is the opposite thing to a branch. The paper says distributary (a branch). The tributaries are way to the south in Sudan and Ethiopia and Kenya.
>They said also that the first man who became king of Egypt was Min; and that in his time all Egypt except the district of Thebes was a swamp, and none of the regions were then above water which now lie below the lake of Moiris, to which lake it is a voyage of seven days up the river from the sea: and I thought that they said well about the land;
Later on
>Such is this labyrinth: but a cause for marvel even greater than this is afforded by the lake, which is called the lake of Moiris, along the side of which this labyrinth is built. The measure of its circuit is three thousand six hundred furlongs (being sixty schoines), and this is the same number of furlongs as the extent of Egypt itself along the sea. The lake lies extended lengthwise from North to South, and in depth where it is deepest it is fifty fathoms. That this lake is artificial and formed by digging is self-evident, for about in the middle of the lake stand two pyramids, each rising above the water to a height of fifty fathoms, the part which is built below the water being of just the same height; and upon each is placed a colossal statue of stone sitting upon a chair. Thus the pyramids are a hundred fathoms high; and these hundred fathoms are equal to a furlong of six hundred feet, the fathom being measured as six feet or four cubits, the feet being four palms each, and the cubits six. The water in the lake does not come from the place where it is, for the country there is very deficient in water, but it has been brought thither from the Nile by a canal; and for six months the water flows into the lake, and for six months out into the Nile again; and whenever it flows out, then for the six months it brings into the royal treasury a talent of silver a day from the fish which are caught, and twenty pounds when the water comes in. The natives of the place moreover said that this lake had an outlet under ground to the Syrtis which is in Libya, turning towards the interior of the continent upon the Western side and running along by the mountain which is above Memphis.
That's higher than the Great Pyramid. Lake Moeris still exists and is not near Giza. The two pyramids are thought to be exaggerations of the Pedestals of Biahmu:
Today, King Min is more commonly known as Menes, an upper Egyptian King who ushered in 3000 years of dynastic Pharaonic history by conquering the Nile Delta and thus uniting for the first time all of Egypt. He was as ancient to Herodotus as Herodotus is to us today (2500 years each). It is humbling just how deep Egyptian history goes.
Fascinating, thanks for sharing! Makes me wonder if the great pyramid was partially submerged, and if so, by how much.
This account lends some credence to theories of the pyramids functioning as some sort of ram pump in my opinion. (Check out John Cadman’s work if you’re interested).
I looked that up, and boy was it an interesting read! For anybody who is interested in reading what John Chapman theorized about the pyramids, see here [0].
Makes a lot of sense. I did a small dive into watersheds and fluvial systems a long time ago and something that surprises layman is how quickly rivers can change in just a few decades, let alone thousands of years. Even (or perhaps especially
) large rivers love meandering and and carving new paths over time.
Humans think of rivers as static things and like to use rivers as natural "borders" and forget that these are actually organic and evolving systems.
I can't speak to "the literature" but people have been colloquially talking about the mysterious lack of a canal since at least the 90s. One of the reasons people floated was a no-longer-active branch of the nile.
IIRC it's been well-known for a while how they moved the vast majority of materials by land (similar to how the Stonehenge megaliths were moved, highly dissimilar to how the Rapa Nui moai were).
No,the best theory is they cut the stones in a slightly underwater quarry. The limestone if submerged hasn't gained co2. They used a complex system similar to a canal. They used ballast like logs or airbags to float the cut rocks while keeping them uderwater. Even the top working row was a water filled mini canal. They would drop the stones into place. Once the water was removed the limestone would absorb co2 and swell, tightening the blocks together. This would have been some serious engineering.
> For this, they said, the ten years were spent, and for the
underground chambers on the hill upon which the pyramids stand, which he caused to be made as sepulchral chambers for himself in an island,
having conducted thither a channel from the Nile.
Sounds like the same story for the Osireion, according to Strabo.
Ancient megalithic Geopolymer masonry made with electrodes and [Lingam,] electricity is apparently lost to modern day as well.
FWIU, in the Great Pyramid, there were/are copper rods in the shafts out from the King's Chamber, and the conductive gold at the top of the pyramid was added after construction over top of a perhaps more ancient well shaft (that is not as geomagnetically-aligned) that may have been a hydraulic/hydrologic water tunnel given the water erosion in the subterranean chamber.
Fairly,
Demonstrate moving and then placing an 80 ton granite stone with ancient materials and tools: copper, gold, limestone, granite, probably fulgurite (sand glass due to lightning) and/or volcanic glass, obsidian, grain dust, papyrus rope, papyrus boats, barges, [variable buoyancy] crane machines, masonry forms and jigs, chemistry in jars, large sceptre tuning forks, sand, porous cliffs by the sea
What are the dates on the outer structure, and on the oldest largest object within the structure?
Gears: Antikythera (200 BC), Watchmaking c. 1300 AD
But the boat, and things that float due to ballast or no; how old is that?
Aliens of similar height, from the tunnel and stair heights and sarcophagi.
Such as the [presumed] Sarcophagus of Senusret II - which has a pyramid built around it with perhaps newer and less precise masonry methods - which one might've hoped had contained instructions on how to produce spec granite at those tolerances back then; [1]
There is little evidence of advanced mechanical masonry tools at the time, except for the remaining megalithic stonework that later cultures built upon.
FWIU there are only a few examples of circular polishing, and the core drilling method leaves different signatures than known methods in modern day.
An n-dimensional space is just a collection of points, each defined uniquely by a set of n-numbers. The semantic meaning of those numbers doesn't really matter. It might be like actual physical space, but it could just as well be something like "time" and "the price of big macs". We have a bunch of mathematical operations that work well on 2 or 3 dimensional space that correlate nicely with our physical intuitions of 'curvature' and 'holes', and that still work perfectly well in more generalized forms in higher dimensions.
I'm not really sure it's that useful to try and visualize what it means on higher dimensions, to be honest.
It's not perfect but to get an idea of adding one more dimension on top of the three dimensions we can visualize is thinking of color as the 4th dimension. There's a game called 4D Maze created by a topolgist that's availble in iphone app store. The visualization is 3d but if you can imagine the colors taking up the same space (instead of being right next to each other in 3d space), it kinda works. At least, it's the closest I've ever come to feeling like I could visualize or understand an additional dimension.
Yeah, the "an n-dimensional vector is just a struct with n floats" way of thinking is great - until you actually want to apply geometrical operations in the vector space, such as calculating a distance or performing a rotation. Then you have a problem: You cannot visualise such a space and "pretending" to work in 2D/3D space is convenient but often extremely misleading.
So what kind of intuition could you use instead then? Or what exactly do you mean with "work perfectly well"?
“Just a struct” plus “measuring curvature and shapes” is where my mind goes into “must visualize this” mode. How does a struct have curvature/shape? Or is curvature overloaded here (with a technical math definition that is very different than the layman’s “surface of a sphere” mental model).
the technical math definition is a rigourous formulation that encapsulates exactly the same thing as what we mean when we say things are curved, but one that also extends far more generally into contexts where our old intuition fails.
The same is true for most mathematics. For example, we are introduced to multiplication as repeated addition: 3x == x + x + x or 2x == x + x and more generally nx == x + x + ... + x, for n number of times. Of course this is only defined over naturals, what would it mean if we instead took n to be fractional, negative, irrational, or even complex? We of can easily generalise multiplication over larger and more complex fields and spaces, but in doing so we must abandon our old intuitive idea that nx is x + x n-times.
No, that's not exactly a sci-fi concoction. In special and general relativity, there are three dimensions for space and one dimension for time, and this is not something that is of "incidental" importance to special / general relativity, it's a pretty essential shift in perspective to these theories to think of the universe as (curved) four-dimensional spacetime.
But "dimension" is something mathematical. I would say it doesn't quite make sense to say "is the fourth dimension time" in the same way as it wouldn't make sense to say "is the fifth an apple?" The same way that numbers can refer to different things in different contexts (including in the context of different scientific theories), dimensions can correspond to different things in different contexts. For example, statistics and machine learning heavily use "high dimensional" mathematics, but there the "dimensions" would correspond to different variables you are trying to predict or explain. E.g. if you were trying to predict chance of heart attack from 1000 different factors, then you would have 1000+1 total "dimensions," and in that case the "fourth dimension" might be "cigarettes smoked per week" (rather than time).
Contextually of dimension even exists within a specific scientific theory. In relativity, the direction you call time might contain some component of the direction I call space. This implies notions like simultaneity are not well defined in a universal context.
No, 4D spacetime is a real thing in physics, which explains things like time dilation and the speed of light. But sci-fi does tend to abuse the term "dimension" for other ideas that are not scientific.
yeah, nobody can visualize it. it's something you just get used to after a while.
there's an old joke about a mathematician teaching an engineer about thirteen-dimensional spaces. "What do you think," the mathematician asks. "My head's spinning," the engineer confesses. "How can you develop any intuition for thirteen-dimensional space?"
"Well, it's not so hard. All I do is visualize the situation in arbitrary N-dimensional space and then set N = 13."
The letters you're referring to were written in 1753 and 1755, and has he got older, his views on race softened to the point that he was an outright abolitionist by the end of his life. In 1763 he wrote the following in a letter:
This is chiefly to acquaint you, that I have visited the Negro School here in Company with the Revd. Mr. Sturgeon and some others; and had the Children thoroughly examin’d. They appear’d all to have made considerable Progress in Reading for the Time they had respectively been in the School, and most of them answer’d readily and well the Questions of the Catechism; they behav’d very orderly, showd a proper Respect and ready Obedience to the Mistress, and seem’d very attentive to, and a good deal affected by, a serious Exhortation with which Mr. Sturgeon concluded our Visit. I was on the whole much pleas’d, and from what I then saw, have conceiv’d a higher Opinion of the natural Capacities of the black Race, than I had ever before entertained. Their Apprehension seems as quick, their Memory as strong, and their Docility in every Respect equal to that of white Children.1 You will wonder perhaps that I should ever doubt it, and I will not undertake to justify all my Prejudices, nor to account for them.
---
I'm not sure that really that excuses being so racist that he thought _Germans_ weren't sufficiently white for america in his 50s, but he did change his views over time.
This is just a consequence of the inflation countermeasures working.
During the inflationary period, people were flush with cash, demand increased, there were shortages, everyone raised prices, profits surged, companies hired workers for higher wages, people got more money, etc.. Everyone was mad because they got big raises, which were obviously the result of all their hard work which corporations suddenly saw and appreciated for a large percentage of people all at once and _also_ "greedy corporations" suddenly en masse decided that they no longer wanted to be charitable enterprises and decided to raise prices to steal money from the pockets of hard working americans.
Or, you know, there was a bunch of inflation and wages and prices went up in parallel.
And now money is no longer flowing into the economy, some companies went too far raising prices anticipating more inflation, and now they're losing sales and that's hurting profits, and they're going to end up cutting prices to increase sales and maximize profits again.
Nature is healing.
I think a lot of people have the impression that inflation reduces how much stuff people can afford and generally it's fairly neutral in that respect. There's a certain amount of production and a certain amount of demand and in general it will balance out and no matter what's' going on with inflation people are gonna be able to afford the same amount of stuff. I think people had this idea that if we got inflation under control that suddenly everyone would be able to afford to buy all the stuff they wanted to buy, and they just can't.
The main reason inflation is bad for most people is instability and you have to keep getting raises to keep up with prices. You get a raise, you can suddenly buy some stuff you couldn't before -- prices go up and now you can't again. Then you get a raise, can afford to buy a bunch of stuff, and prices go up and now you can't again. (not to mention that toll it takes on saving, but even that isn't that bad if you own stock instead of holding cash, because asset prices inflate, also)
I read an article about the "unreasonable effectiveness of mathematics" that it was basically the result of a drunk looking for his keys under a lamp post because that's where the light is. We know how to use math to model parts of the world, and every where we look, there's _something_ we can model with math, but that doesn't mean that there's all there is to the universe. We could be understanding .0000001% of what's out there to understand, and it's the stuff that's amenable to mathematical analysis.
