I don’t know why I’m so fascinated that the rational numbers are countable even though they’re a dense subset of the uncountable real numbers. A rational number can be arbitrarily close to any real number, making you think they’d be infinite like the reals, but in fact, nearly all numbers are irrational (and an uncountable subset of the reals).
So, the rational numbers — good old p/q fractions — though still infinite are countably infinite (see this post for details).
More to the point here, a common way of enumerating the rational numbers, when graphed results in some pretty curves and illustrates some fun facts about the rational numbers.
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3 Comments | tags: charts, fractions, graphs, rational numbers | posted in Brain Bubble, Math
The previous two posts (this one and this one) each discussed an aspect of Sapiens: A Brief History of Humankind (2011), by Yuval Noah Harari. While those aspects grabbed my attention and got me thinking, I took very little from the rest of the book.
In fact, reading the latter two-thirds got to be something of a chore. It had many examples from comparatively modern history (given the full breadth of our existence) but they didn’t seem to amount to a unified whole. The author seems not to connect dots his own text presents.
Final score: two bits I liked and took away (and posted about) but the rest of the book I left behind. I give it a Meh! rating and a thumbs down.
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3 Comments | tags: history, homo sapiens, humanity | posted in Books, Society
The previous post focused on a single, to me key, aspect of Sapiens: A Brief History of Humankind (2011), by Yuval Noah Harari. This post focuses on the other aspect of the book I found compelling. The last one was about the power fiction gave homo sapiens. This one is about the Agricultural Revolution (the AR).
And other important Revolutions that followed, but the AR wrought a profound change on the human race. It was our first step towards societies and civilization. It ushered in the first cities and led to kingdoms and empires.
It also led to materialism, greed, health issues, theft, and war.
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14 Comments | tags: history, homo sapiens, humanity, storytelling | posted in Books, Society
While not usually my cup of tea, Amazon Prime offered Sapiens: A Brief History of Humankind (2011), by Yuval Noah Harari, and I thought I’d give it a try. I’d never heard of the author, and don’t usually read anthropology or sociology books, but the blurb made it sound interesting (don’t they always).
I did enjoy the first third. The author discusses two aspects of our ancient past that really grabbed my attention. Unfortunately, he went on to lose it. In a big way. For me, the latter two thirds of the book added little and missed what seemed some key connections.
So, three posts (at least): one each for the two attention grabbers; one more for the book overall. This first one is about our special ability as storytellers.
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19 Comments | tags: history, homo sapiens, humanity, storytelling | posted in Books, Society
I’ve been a fan of Japanese anime since the 1980s, but in the last decade or so I’ve come to appreciate it even more (because what’s been coming out of Hollywood lately so often has little redeeming value). As fans of the genre know, anime can be as creative and engaging as any form of storytelling you care to name.
Lately, I’ve begun exploring the Japanese media franchise, Lupin the Third (aka Lupin III or Lupin the 3rd). It began back in 1967 and comprises multiple manga, at least six anime TV series, over a dozen films, and other related media.
It taps into our love of master thieves. The fictional monkey-faced Lupin III is acknowledged worldwide as the greatest (and most fun) thief in the world.
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13 Comments | tags: anime, Japanese anime, Lupin III, Lupin the Third, thieves | posted in Books, Movies, TV
It’s hard to believe I haven’t yet posted about the Robert Burns (1759-1796) poem, “To a Mouse, on Turning Her Up in Her Nest With the Plough, November, 1785”. Written, obviously, in 1785. It’s one of my favorites, and as with some of my other favorites, due in part to one line, the immortal words: “The best-laid schemes of mice and men; Go oft awry.”
And don’t they indeed. God (or fate or chance or whathaveyou) laughs at our puny plans.
It’s a short poem, and I don’t have all that much to say about it, so I’ll also tell you about an interesting bug in the new WordPress Jetpack app that lets you game your own stats.
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6 Comments | tags: Jetpack app, Robert Burns, To A Mouse, WordPress | posted in Quotes, Writing
I don’t usually write two Friday Notes posts in one month, but I was dog-sitting my funny little “nephew” Bentley for a week, and every time I don’t post for a while it’s hard to get back into blogging mode. In fact, it’s harder each time. I increasingly find social media less and less interesting or rewarding.
Some of that is on me, but more of it is disappointment and disgust with social media and technology companies in general. A bit more on that below.
Mostly, though, I wanted to — at long last — post the last two notes that have been lingering on my Apple Notes app for years (in one case, since 2018).
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17 Comments | tags: Bentley, Donnie Yen, entropy, gravity, Ip Man, Major League baseball, MLB | posted in Friday Notes, Movies
Back in February I posted about how I was starting to explore murder mystery author P.D. James (1920-2014). As it turned out, I decided she wasn’t really my cup of tea. I’ll say a bit more about that later in this Mystery Monday post, but the main topic today is Ngaio Marsh (1895-1982), a murder mystery author from New Zealand who definitely is my cup of tea.
She’s a close contemporary of Agatha Christie (1890-1976), born just five years later and dying just six years after Christie did. She lived 86 years compared to Christie’s 85.
More relevant to me, she’s a close contemporary in terms of her writing. I’ve read 15 of her novels so far and have thoroughly enjoyed each one.
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12 Comments | tags: Agatha Christie, detective books, murder mysteries, Ngaio Marsh, P.D. James | posted in Books, Mystery Monday
It’s not often that a modern movie really grabs me. Especially a modern science fiction movie. Extra especially any science fiction movie involving time travel (because time travel makes no sense at all). When that movie is a first-time directorial effort with almost zero budget and shot on iPhones, it’s really something very special.
And when the story, despite time travel making no sense at all, exudes a sense of sheer joy and fun to carry it along (despite time travel making no sense at all), and delights even on a second viewing — where one can pay attention to how it was shot to appear as one long 70-minute take — it gets an enthusiastic Wow! rating from me.
I’m talking about Beyond the Infinite Two Minutes (2020).
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2 Comments | tags: science fiction, science fiction movies, SF, SF Movies | posted in Movies, Sci-Fi Saturday
In the last edition of Friday Notes my long-winded story about a problem filing my state taxes and the unexpectedly (but very welcome) positive experience of dealing with support from H&R Block, my bank, and the Minnesota Department of Revenue used up the bulk of my word count. But, in contrast to the negative experiences with most tech companies (cough, Apple, cough), it was a good story to tell.
I didn’t have room for all the notes accumulated in my Apple Notes app. This time I’ll try to fit in the rest of them.
But I want to record a dream I had, so (once again) there might not be room.
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5 Comments | tags: dreaming, dreams, music | posted in Friday Notes
Logos con carne 