A news story broke there's massive structures beneath the Pyramid of Khafre, something far beyond the tech level assumed of ancient Egyptians.
What can back these claims? Extraordinary technology: Synthetic Aperture Radar🧵
First lets start with optics - in general a larger lens lets your resolve finer and finer details.
Roughly, the angular resolution goes like wavelength/diameter.
This makes sense if you think about how waves are diffracted - smaller waves or larger opening, less diffraction
But optics just uses a range of radio frequency spectrum we call visible light. The exact same physics applies for radar systems.
But radar uses far far larger wavelengths, on the scale of meters versus nanometers for visible light. What can we do?
Make the aperture massive
Synthetic Aperture Radar does exactly this by forming an 'imaginary' lens by sweeping the radar system across the sky, taking a succession of radar snapshots that are then reconstructed into a single image.
The mathematical framework for this was developed first in the 1950s and applied to airplanes through the 1950s - 1960s. At the time these tested the limits of both radar power and computational image processing.
These days the SAR market is exploding - thanks to decreasing launch costs, higher performance computing, solid-state RF amplifiers, the resolution for SAR systems in orbit.
Now enter @capellaspace and the Pyramids of Giza
These systems provide the best commercial SAR resolution in the world, well actually, in space. @capellaspace latest platform upgrades bring the azimuthal resolution down to 5cm
But, radar can't penetrate pyramids. How do you image the inside to find hidden structures?
This is where it gets insanely cool. SAR doesn't just give pixel-by-pixel angular resolution, but by looking at each component of frequency they can also find the doppler shift from each pixel.
Doppler shift comes from the movement of the imaging surface relative to the wave
The exterior surface of the Pyramid is slightly vibrating from seismic tremors in the Earth and atmosphere, and exactly how it shakes reveals information about its interior structure.
There is a lot of math I'm skipping here but - you can reconstruct interior features
The feature reconstruction is extremely impressive - you can make out individual roof segments in the King's chamber
By performing this process all over the exterior sides you can start reconstructing interior passageways, vaults, hidden chambers, things completely buried and otherwise unobservable
In the original publication the authors reach a fairly profound conclusion - that the Pyramid of Khafre acted as a giant hydro-acoustic device designed to produce very specific and concentrated fields of acoustic resonance in the Kings and Queens chamber
This more recent press release is from subsequent work by the same team - finding now that there are massive cylindrical wells beneath the pyramid claimed to extend 600 meters below the surface.
This is totally beyond anything conceived of as 'engineering ability' at the time
Any indication of this from other sources? Incredibly, yes.
Herodotus claimed that in the construction of the Pyramids, 10 years were spent on the passageways and caverns beneath the Giza plateau, while 20 years spent on the Pyramid itself.
The SAR team also claims, like Herodotus, that there are passageways underground extending across 2km of distance underneath the Giza Plateau.
This is all utterly insane and cool so I'll just say this:
Civilizations is likely way older than we think
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Up until Minnesota the largest medicare fraud in history was run by....
A guy who used oxycontin and fentanyl to get patients addicted so they remained in his nursing homes.
Trump pardoned him in 2020.
$1.3 billion in fraud by one person.
Presidential Pardon.
People who think this is 'whataboutism' are too partisan-addled by years of divisive thinking. Fraud is everywhere, supported by all political parties, that you will not get justice for these crimes against the public unless we investigate and expose them ourselves.
*sentence commuted. I don't know why you'd commute this sentence. Seems like a pretty horrible person.
What looks to be a bug in a video game making a person hold the pistol sideways - like a gangster - actually reveals something subtle about the shape of space.
It has implications from CAD design to Black Holes + anti-gravity. Differential geometry + parallel transport 🧵
Differential geometry is the mathematics of curved surfaces. Euclidean geometry is the 'nice' flat space - where moving along a direction doesn't change the absolute orientation of your perspective.
In curved space, however, this changes.
In both CAD design programs and first-person shooters, the view is inscribed on the surface of a sphere. In CAD its looking inwards, for an FPS its looking outwards.
Yet our mouse controls are Euclidean vectors mapped onto the surface
The Blight shields itself from direct criticism by installing hair trigger victim complex in it's adherents, who decry any deviation from it's central narrative of mandated equality of outcomes
Beauty, success, pride, are all immediately equated to Fascism
Strength is a crime
The primary tactic to hijack empathy is, like a shitty LLM, endless semantic inversion.
The Patriot Act defends the constitution by defiling your constitutional rights.
The UK Online Safety Act protects children by banning talking about pedophile Pakistani rape gangs.