|
About This Author
Come closer.
|
Complex Numbers
Complex Numbers
A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.
The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.
Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.
Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.
February 13, 2025 at 7:01am February 13, 2025 at 7:01am
| |
Kinda-sorta still technically a Full Moon this morning (not that I could see it last night through all the clouds), and then this NPR article comes up at random from my queue:
The Grand Canyon in Arizona got carved by water over millions of years of slow but steady erosion.
Or, if you believe bullshit, it got created that way about 6000 years ago, specifically to fool us.
Two similarly-sized canyons on the moon got carved by flying rocks in about ten minutes.
Also way more than 6000 years ago.
"This was a dramatic impact that was followed by a series of smaller impact events that excavated these canyons in, you know, roughly 10 minutes," says David Kring with the USRA Lunar and Planetary Institute in Houston.
Translation: The Moon's shit got fucked up.
The two canyons, called Vallis Schrödinger and Vallis Planck...
So, one of them may or may not actually exist, and the other is as small as it's possible to get?
If you don't know anything about the history of physics, just take my word for it: that's a really, really funny joke.
...are located on the far side of the moon...
Hm. Most far side features are named for Russians, because they were first mapped by a Soviet probe. I guess there are exceptions, and I'm too lazy to look to see if there are other exceptions.
...so they can only be seen from orbit—not from Earth.
As this is unclear, I'll jump in to say that they mean either lunar orbit, or an Earth orbit that's so far out that it takes you around the butt side of the moon.
Butt Side of the Moon is, by coincidence, the name of my Butthole Surfers style cover of Pink Floyd's greatest album.
Each canyon is over 165 miles long and over 1.5 miles deep.
Oh, so they're American canyons?
The canyons look like remarkably straight lines that extend outward from a circular crater that is the Schrödinger impact basin, the result of a large impact that occurred around 3.8 billion years ago.
Or maybe it didn't occur.
Look, Schrödinger jokes never get old. Unlike these canyons.
When the impactor hit the moon, it was moving at roughly 38,000 miles per hour, says Kring, and would have penetrated to a depth of about 15 miles.
And the impactor was also American, it seems.
The amount of energy needed to produce these grand canyons on the moon is 1200–2200 times larger than "the nuclear explosion energy once planned to excavate a second Panama Canal on Earth, more than 700 times larger than the total yield of US, USSR, and China's nuclear explosion tests, and about 130 times larger than the energy in the global inventory of nuclear weapons," the researchers write in their report.
How much is that in gridiron football fields? You know, since we're measuring everything else with American units.
Even though these particular lunar craters aren't visible from your backyard, Kring says there are similar, but smaller canyons on the near side of the moon that's visible in the night sky.
Might need binoculars or a telescope, but those are a bit cheaper than hitching a ride on the next lunar orbiter. |
© Copyright 2025 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.
|
Comment 
![Merit Badge in Quill Award
[Click For More Info]
Congratulations on winning Best Blog in the 2021 edition of [Link To Item #quills] !](https://images.Writing.Com/imgs/writing.com/writers/badges/group-Quill_Award-1375927_6.gif)
![Merit Badge in Quill Award 2
[Click For More Info]
2022 Quill Award - Best Blog - [Link To Item #1196512] . Congratulations!!!](https://images.Writing.Com/imgs/writing.com/writers/badges/group-Quill_Award_2-1375927_6.gif)
![Merit Badge in 30DBC Winner
[Click For More Info]
Congratulations on winning the Jan. 2019 [Link To Item #30dbc] !!](https://images.Writing.Com/imgs/writing.com/writers/badges/group-30DBC_Winner-2064535_14.gif)
![Merit Badge in Blogging
[Click For More Info]
Congratulations on winning an honorable mention for Best Blog at the 2018 Quill Awards for [Link To Item #1196512] . *^*Smile*^* This award was sponsored by the blogging consortium including [Link To Item #30dbc] , [Link To Item #blogcity] , [Link To Item #bcof] and [Link To Item #1953629] . For more details, see [Link To Item #quills] .](https://images.Writing.Com/imgs/writing.com/writers/badges/type-Blogging-2180.gif)
![Merit Badge in Highly Recommended
[Click For More Info]
I highly recommend your blog.](https://images.Writing.Com/imgs/writing.com/writers/badges/Kudos-Highly_Recommended.gif)
![Merit Badge in Opinion
[Click For More Info]
For diving into the prompts for Journalistic Intentions- thanks for joining the fun!](https://images.Writing.Com/imgs/writing.com/writers/badges/genre-Opinion-1150.gif)
![Merit Badge in High Five
[Click For More Info]
For your inventive entries in [Link To Item #2213121] ! Thanks for the great read!](https://images.Writing.Com/imgs/writing.com/writers/badges/Kudos-High_Five.gif)
![Merit Badge in Enlightening
[Click For More Info]
For winning 3rd Place in [Link To Item #2213121] . Congratulations!](https://images.Writing.Com/imgs/writing.com/writers/badges/general-Enlightening.gif)
![Merit Badge in Quarks Bar
[Click For More Info]
For your awesome Klingon Bloodwine recipe from [Link to Book Entry #1016079] that deserves to be on the topmost shelf at Quark's.](https://images.Writing.Com/imgs/writing.com/writers/badges/group-Quarks_Bar-2046190_12.gif)
