As someone with almost literally a life-long love of astronomy (my first word was “star”), I’ve always been vaguely intrigued by astrology. I’m fascinated by that which endures through many ages and cultures of humanity. At the very least, such things reflect an aspect of human consciousness. They’re also a shared idea, so they form community in the like-minded.
Is there magic in the stars? No, not in the astrological sense. Any “magic” is in us, in our consciousness, not in the stars. (Worldwide, on average, almost 12 million babies are born each month. That an astrological sign applies to them all is a bit of a stretch.)
And the thing is, most of us aren’t the sign we think we are!
123 × 321 = 39,483
My interest in number multiplication goes back to exploring algorithms for generating Mandelbrot plots, which can require billions of multiplication operations on arbitrary precision numbers (numbers with lots and lots of digits).
Multiplying two numbers — calculating their product — is computationally intense because of the intermediate Cartesian product. Multiplying two 12-digit numbers creates a 24-digit result (12+12), but it also has an intermediate stage involving 144 (12×12) single digit multiplications.
Recently I learned an intriguing Japanese visual multiplication method.
I’ve posted more than once regarding my view of the Many Worlds Interpretation (MWI) of quantum physics. I find its rise in modern popularity genuinely inexplicable. (I can’t help but think it’s exactly the sort of thing Dr. Sabine Hossenfelder is talking about in her book, Lost in Math.)
Hoping to find the logic that apparently appeals to so many, I read Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime (2019), by Sean Carroll. It is, in large part, his argument favoring the MWI. Carroll is a leading voice in promoting the view, so I figured his book would address my concerns.
But as far as I can tell, “there is no there there.”
For a little Friday Fun I have a logic puzzle for you. I’ll give you the puzzle at the beginning of the post, detour to some unrelated topics (to act as a spoiler barrier), and then explain the puzzle in the latter part of the post. I would encourage you to stop reading and think about the puzzle first — it’s quite a challenge. (I couldn’t solve it.)
The puzzle involves an island with a population of 100 blue-eyed people, 100 brown-eyed people, and a very strange social practice. The logic involved is downright nefarious, and even after reading the explanation, I had to think about it for a bit to really see it. (I still think it’s twisted.)
To be honest, I’m kinda writing this to make sure I understand it!
If you keep an eye on the night sky you may have noticed two bright “stars” to the south just around midnight. (To be precise: Jupiter is dead south at 11:02 pm; Saturn is dead south at 11:37 pm. By midnight they’ve moved slightly to the west.)
If you’re the type to keep an eye on the night sky, you likely already know those “stars” are Saturn (on the left) and Jupiter (on the right). What you may not know — and certainly can’t see — is that almost right smack dab between them is the former planet Pluto. All three just happen to be lined up nicely right now.
The New Horizons spacecraft is also out there, well beyond Pluto.
Four years ago I started pondering the tesseract and four-dimensional space. I first learned about them back in grade school in a science fiction short story I’d read. (A large fraction of my very early science education came from SF books.)
Greg Egan touched on tesseracts in his novel Diaspora, which got me thinking about them and inspired the post Hunting Tesseracti. That led to a general exploration of multi-dimensional spaces and rotation within those spaces, but I continued to focus on trying to truly understand the tesseract.
Today we’re going to visit the 4D space inside a tesseract.
Back in 2015, to celebrate Albert Einstein’s birthday, I wrote a month-long series of posts about Special Relativity. I still regard it as one of my better efforts here. The series oriented on explaining to novices why faster-than-light travel (FTL) is not possible (short answer: it breaks reality).
So no warp drive. No wormholes or ansibles, either, because any FTL communication opens a path to the past. When I wrote the series, I speculated an ansible might work within an inertial frame. A smarter person set me straight; nope, it breaks reality. (See: Sorry, No FTL Radio)
Then Dr Sabine Hossenfelder seemed to suggest it was possible.
Last time I started talking about entropy and a puzzle it presents in cosmology. To understand the puzzle we have to understand entropy, which is a crucial part of our view of physics. In fact, we consider entropy to be a (statistical) law about the behavior of reality. That law says: Entropy always increases.
There are some nuances to this, though. For example we can decrease entropy in a system by expending energy. But expending that energy increases the entropy in some other system. Overall, entropy does always increase.
This time we’ll see how Roger Penrose, in his 2010 book Cycles of Time, addresses the puzzle entropy creates in cosmology.
I’ve been chiseling away at Cycles of Time (2010), by Roger Penrose. I say “chiseling away,” because Penrose’s books are dense and not for the fainthearted. It took me three years to fully absorb his The Emperor’s New Mind (1986). Penrose isn’t afraid to throw tensors or Weyl curvatures at readers.
This is a library book, so I’m a little time constrained. I won’t get into Penrose’s main thesis, something he calls conformal cyclic cosmology (CCC). As the name suggests, it’s a theory about a repeating universe.
What caught my attention was his exploration of entropy and the perception our universe must have started with extremely low entropy.
Last time I started with wave-functions of quantum systems and the Schrödinger equation that describes them. The wave-like nature of quantum systems allows them to be merged (superposed) into combined quantum system so long as the coherence (the phase information) remains intact.
The big mystery of quantum wave-functions involves their apparent “collapse” when an interaction with (a “measurement” by) another system seemingly destroys their coherence and, thus, any superposed states. When this happens, the quantum behavior of the system is lost.
This time I’d like to explore what I think might be going on here.