Math of General Relativity Part 14
Albert Einsten, with the stealth help of Berhard Riemann, showed how to construct a 4D Space with a one-to-one correspondence with real Space-Time. To keep it real and specific:
Consider a certain volume of space, like the inside of Madison Square Garden (MSG), but only during a certain interval of time, from midnight tonight to the midnight the night after that. That's 24 hours, which contains 86,400 seconds. At midnight tonight, we set a "Seconds" Clock at zero. So the Space-Time (call it S4) that we are visualizing is the inside of MSG from time zero to time 86,400. This is S4.
Net, we will create a Riemann 4D "space" R4 that is given a one-to-one correspondence with S4. To keep it real, you can completely think of R4 as a surface. It is a 4D surface, whereas you can really only "picture" 2D surface, but when I talk about R4, just think of a surface R2 and then push your mind out from there.
At this scale, it is easier to see that the trees are not under the influence of "artificial" gravity. It is real.
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The gravitational field around each blade of grass and tree is the same as the field around each blade of grass and tree on the surface of Earth.
Notice that if you drive on a road perpendicular to the cylinder axis, you will increase gravity driving one way and decrease it driving the other. If you drive opposite to the spin and at the radial speed, your gravitational field turns Minkowskian, and you are in a "free fall" or inertial coordinate system. That is, you and the car become "weightless."
That means this: The value of a gravity field can go from a surface-of-a-planet value to a free-fall value by a coordinate transformation among systems that are moving at a constant velocity with respect to each other.
At any instant of time, a car moving at the radial speed is in a Minkowski field, and a system at rest on the cylinder is in a planet-surface field. A ...
"Aja" is the title track of Steely Dan's 1977 album, and its meaning has been a subject of interpretation rather than a straightforward explanation from the band themselves, Walter Becker and Donald Fagen, who were known for their cryptic and layered lyrics. The song doesn’t tell a linear story but evokes a mood and imagery that fans and critics have analyzed over the years.
The word "Aja" is often speculated to refer to a person, place, or concept. One popular theory ties it to the name "Aja," which Becker and Fagen reportedly chose after learning of a Korean woman named Aja who married a friend of theirs. This fits Steely Dan’s tendency to draw inspiration from real-life fragments and transform them into something abstract. The lyrics—"Up on the hill / People never stare / They just don’t care / Chinese music under banyan trees"—suggest an exotic, serene escape, possibly a romanticized or imagined refuge from the complexities of modern life.
Musically and lyrically, "Aja" ...
"Deacon Blues" by Steely Dan, released in 1977 on their album Aja, is a richly layered song that invites multiple interpretations, blending the band’s signature irony, cynicism, and romanticism. Written by Donald Fagen and Walter Becker, the lyrics follow a narrator who seems to embrace a life of reckless abandon, yearning for a kind of mythic, self-destructive freedom often associated with jazz musicians or countercultural figures. Let’s break it down:
The title "Deacon Blues" itself is intriguing. It’s been suggested that it references football—the "Deacon" could nod to Wake Forest University’s Demon Deacons, a team whose colors are black and gold, though Fagen and Becker have said it’s more about vibe than a literal connection. "Blues" ties it to the musical genre, evoking a sense of soulful melancholy. In a 2003 interview, Fagen described the song as being about "a broken dream of a broken man living a broken life," but delivered with a sardonic twist typical of Steely Dan’s ...
