Problems

Cantor’s infinities are meaningless and stupid

Overall, this video provides a good intro to some important math ideas:

Here are some random thoughts on the video:

I don’t think principles like undecidability necessarily imply a “hole” or “flaw” in mathematics. It only appears to be a “hole” if you’re assuming something should be there, like decidability. But that’s based on your assumption that it should exist in the first place.

The video soon turns to Cantor, giving me the perfect opportunity to finally rant about how foolish he was! (I’ve been intending to do so for some time.)

Cantor’s infinities are a bit of a pet peeve of mine. His foolishness, and the foolishness of those who nod in bedazzled wonder and agreement with his nonsense, stem from a lack of understanding the implications of infinity. Infinite size means no size. That can be confusing, because in this instance “no size” does not mean a size of 0. So how can something have no size without the size being 0? By being infinity. One must stop thinking about infinity as a number, but as a concept parallel to that of number.

So when Cantor asks (at 4:30 in the video): “Are there more natural numbers or more real numbers between 0 and 1?”

Woah, back it up, back it up, beep, beep, beep!

That is a nonsense question. It’s like asking: “What is five divided by green?” By definition, there cannot be “more” or “less” of something that has no amount to begin with. There are infinite natural numbers. There is not an amount of natural numbers, because there are an infinite amount, which means there is no amount. So there cannot be more, or less, or the same. There can be no comparison whatsoever because what you’re trying to compare is the amount, which does not exist.

Does infinity equal infinity? If you’re intending to compare amounts, the question is again meaningless nonsense. Infinity cannot, in this sense, equal or not equal infinity because you cannot compare them like finite amounts.

As the video shows, Cantor goes on to (rather stupidly) compare two lists. His methods are meaningless because his premise (that infinities can be compared) is already flawed. He then finds with his “diagonalization proof” that you can’t logically define a pairing between every natural number and every real number between 0 and 1, and in the depths of his infinite stupidity thinks that this somehow proves that there are “more” real numbers than natural numbers.

Uh, no it doesn’t, Mr Georg without an “e”. All you’ve shown is that you didn’t actually succeed in defining a pairing. You haven’t proven anything about sizes because infinite sets do not have sizes. Whether or not you can rigorously define a pairing (a one-to-one corresponce) implies nothing at all about sizes. It only proves your definition of the pairing to be paradoxical nonsense. You can’t say “let’s assume we’ve paired all natural numbers to real numbers between 0 and 1” and then say “here’s a real number that can’t be in the list!” That just means we didn’t actually pair the sets to begin with!

The crux of the paradox doesn’t lie in the “sizes” of the sets anyway (which don’t exist). It lies in the inability to express all real numbers with finite decimal places in the decimal system. If we take for granted that we could instead express some otherwise undefined real number with an arbitrary symbol (like, gee I don’t know, a natural number), the paradox is completely resolved. There is nothing to “diagonalize” and the one-to-one corresponse is complete. Logic 1, Cantor 0.

At 6:45: “Cantor’s work was just the latest blow to mathematics…” Perhaps more of a blow to mathematical philosophies than to math itself. Aside from being complete nonsense, it had no implications aside from morons thinking “oh wow, different size infinities sure is amazing, derp!” which is about as meaningful as thinking, “oh wow, five sure is colorful, derp!”

At 7:27: “On the one side were the intuitionists who thought that Cantor’s work was nonsense. They were convinced that math was a pure creation of the human mind and that infinities like Cantor’s weren’t real.”

Perhaps, but whether or not an infinity can be “real” is really not the issue with Cantor’s illogic. Also, his lack of logic in this particular area does not necessarily imply inherent weakness with set theory in general.

The video goes on to speak of set theory’s self-reference paradox. It is indeed a paradox, but is by itself really no weakness of set theory anymore than the existence of paradox itself is somehow a weakness of the human mind that conceives of them. In fact, one could say the ability of a system to define a paradox is actually a strength.  It’s like trying to make a programming language that doesn’t allow for infinite loops by taking out the ability to have any loops at all.

I really like the video’s explanation of Gödel’s work with using; actually, perhaps because it’s visual and tangible, I think it may be the best explanation I’ve seen!

At 31:34: Haha, what is this artsy-fartsy shot? “Look at my back as I gaze at the sky and ponder the deep thoughts of the world…”

The video ends by circling back to the “hole” in math, which is now defined as not being able to know everything with certainty, which seems a rather imprecise way of summing up undecidability and incompleteness as it takes for granted the meaning of “certainty”. I guess we could say: “Hey, Gödel, if math is incomplete, then your proof is incomplete and therefore not a proof! Hyuck hyuck!”

By S P Hannifin, ago
Interesting things

UFOs: Are they projections?

I was just randomly thinking about the strange ways in which UFOs seem to defy the laws of physics:

  • Anti-gravity
  • No visual propulsion system
  • Maintain insane speeds
  • Accelerate with insane force
  • Observed in air and water

But what if we’re taking it for granted that the UFO is a unit unto itself?

This isn’t a perfect analogy, but think about shining a laser pointer on the wall. With the rotation of the wrist, we can give the dot of light similar physics weirdness, albeit limited to two dimensions. The point of light doesn’t propel itself, so it doesn’t need a propulsion system. Likewise, insane speeds and accelerations are actually derived from magnified wrist rotations, and so are not nearly as insane as they seem.

Granted, this doesn’t quite explain the anti-gravity. Gravity’s effect on light is negligible from our typical standpoint; it’s generally not until we’re studying blackholes or light across galactic distances through telescopes that gravity’s effect on light becomes measurable. Assuming UFOs are not just light, it seems they’d still have to contend with gravity. Still, maybe whatever is “projecting” them provides the force needed to hold them aloft.

The analogy also breaks down dimensionally. The dot of light from a laser pointer projects onto a wall and bounces to our eyes. Without the wall, the light would just keep travelling and disappating into space. If UFOs are projections, what are they projecting onto? (This is also the obvious challenge of developing the sort of 3D hologram systems often seen in movies like Star Wars. How can we seemingly get light to reflect at a specific point in empty space?) And, for that matter, how can one project actual physical matter rather than just light?

I have no clue, I just thought it was an interesting idea.

Regardless, I’d love to know what their weird UFO things are and what exactly they’re doing out there.

By S P Hannifin, ago
Movies

Movies watched in April 2021

I haven’t done a “movies I watched” post on this blog in something like 8 or 9 years. But let’s get back to it, shall we? So here are the films I watched for this first time in April 2021:

The Sign of Four

This is a made-for-British-TV Sherlock Holmes film, based on the Arthur Conan Doyle story of the same name. The mystery itself was not very deep or engaging, but the film was entertaining mostly because of its dated cheesiness. A digression: I’ve never been quite impressed with Holmes as a character, as his deductive powers mostly rely on the author giving him the power to correctly guess what the author wants him to based on the clues the author gives him for that exact purpose; that is, it’s all what I call a “cleverness cheat“; making successful deductions in the real world is hardly so convenient. Anyway, they also filmed The Hound of Baskervilles the same year with the same actor playing Holmes, so I hope to watch that at some point as well. (According to Wikipedia, they originally intended to film six Sherlock Holmes stories, but I guess that didn’t work out for complicated business reasons.)

Greyhound

This 2020 war film starring Tom Hanks is based on the 1955 novel The Good Shepherd by C.S. Forester (best known for his other book The African Queen, the classic movie adaptation of which I still haven’t seen). The film is about a bunch of ships fighting in the Atlantic during World War II. And “fighting in the Atlantic” is really all the plot consists of. The screenplay was written by Tom Hanks himself, and I guess it shows, because it’s really not that great; no change in pacing, no character development, no subtext. Just a bunch of commands from military people and boats fighting.

One Hundred and One Dalmations

I of course have seen this 1961 Disney animated classic before, but it’s been a long time. If I recall my Disney animation trivia correctly, this was their first film to use Xerox machines to transfer the animators’ line drawings to cel sheets for coloring, a process which had to be done by hand before. This saved them a lot of time and gave the drawings a bit more of an organic look, which of course blends well with the film’s jazzy blocky-colored backgrounds. Everyone probably knows the story: a bunch of puppy dalmations are kidnapped by Cruella de Vil (you know you’re asking for trouble when you name your kid something like that), who wants their fur. They are then rescued, along with a bunch of other puppies that had been stolen. By the way, why does Roger assume he gets to keep so many stolen puppies? One thing I noticed that I never had before was the What’s My Line? parody that the puppies watch on TV while kidnapped, called What’s My Crime? That must’ve been completely over my head as a kid.

Rat Race

This 2001 comedy, very obviously inspired by the star-studded 1963 comedy It’s A Mad, Mad, Mad, Mad World, features a bunch of people racing from Nevada to New Mexico in hopes of being first to nab some treasure for the entertainment of a bunch of wealthy people betting on them. Nothing profound, but a fun comedy.

Godzilla vs Kong

This is the first film I’ve watched in theaters since the beginning of 2020. I mostly wanted to see it in theaters because it was in 3D, and there have been hardly any releases in 3D for the past year, thanks to both the pandemic and dwindling interest in 3D movies in general. Unfortunately the 3D conversion was not great, nor was the weird story, which involved taking Kong to the mystical realm deep inside the earth to find a mystical weapon to defend the world from Godzilla’s destruction. It really made no sense, but I suppose one must not think too much with a movie like this.

WeWork: or The Making and Breaking of a $47 Billion Unicorn

This 2021 documentary tells the bizarre tale of the company WeWork, whose phenomenal valuation came mostly from a bizarre CEO’s ability to convince investors of it. As far as I can tell, nothing illegal actually happened; a lot of people just got drunk on the promises, perception, and larger-than-life energy of a CEO, only to realize the company wasn’t nearly as valuable as it seemed. Interesting story, but I still get the sense there’s a lot more to the over-valuation than just what the documentary presents. What really made people believe the company’s crazy valuation without solid verification?

Note by Note: The Making of Steinway L1037

This 2007 documentary chronicles the creation of a Steinway piano from start to finish. Unfortunately it’s not very informative in terms of the how’s and why’s of piano building. Instead we just watch the workers doing random work while listening to them talk about their backgrounds and how they got into piano building. This is spliced with interviews of famous musicians waxing poetic about how pianos have their own personalities, as though anyone willing to watch a documentary on piano creation would think otherwise. I don’t think I learned anything interesting from this film.

Boss Level

This 2021 action-comedy is about a man who’s stuck in a time loop. Everytime he dies, he wakes up to start the same day again. The day mostly consists of assassins trying to kill him as he in turn tries to figure out why they want him dead, and why he’s stuck in a time loop. It’s a bit like Edge of Tomorrow, but without aliens. It’s a fun popcorn movie, but don’t expect anything deep or profound.

Suspiria

This 1977 Italian horror (though it’s in English) is considered a classic among horror fans, though it was too cheesy for me. It’s about a girl who enters a ballet school and slowly discovers its sinister (albeit chiché) secrets. Not sure why it’s considered such a classic; nothing about it seemed all that interesting to me.

Grand Isle

In this 2019 drama, a young man has the misfortune of being stuck with a creepy crazy Nicolas Cage and his crazy wife during a storm. Hilarity ensues. Actual, a rather dull and bland story ensues. This one’s pretty forgettable.

The Darkness

This 2016 horror is also bland and forgettable. A young autistic boy finds some weird stones in the wilderness. When he brings them home, the spirits of evil Native Americans begin to haunt the house. It follows the standard horror movie template. Not much of interest here.

Captain Phillips

“I am the captain now.” This 2013 action drama starring Tom Hanks tells the true story of how Captain Phillips narrowly survived his cargo ship being hijacked by Somali pirates. Things get especially tense when, having failed to steal much of value from the ship itself, they take Phillips hostage and wind up in a long stand-off with the US military. An interesting story but a mostly average film. Not bad, but not great.

Agenda: Payback

This 2018 action drama mostly consists of an unsavory Sean Patrick Flanery getting tied up and tortured by various figures in his life who seek vengeance on him for past misdoings. There’s a lot you can do with a minimal set and cast. Misery for example. But you’ve gotta pace yourself, vary the dramatic arcs, give it space to rise and fall. This movie is a great example of how not to do it. It’s bland, boring, and forgettable.

The Boys from Brazil

This 1978 thriller follows an old Laurence Olivier as a Nazi hunter investigating some Nazi activity and uncovers a shocking and horrible Nazi plot! I won’t spoil it, but the plot turns out to be more ridiculous, silly, and convoluted than it is all that shocking or horrible. Laurence Olivier and Gregory Peck don some rather silly-sounding German accents as well.

Dolphin Tale

Watched this in my search for family friendly films. This 2011 drama is loosely inspired by the true story of a dolphin being rescued and given an prosthetic tail after being found trapped in ropes on the shore. A rather low-stakes cheesy story, but a nice family film I suppose. It’s also a rare film that was actually filmed in 3D, and so offers a very good 3D picture. The extra dimension doesn’t add much to the story here, but I still love 3D movies, especially ones actually filmed in 3D (rather than cheap conversions, like Godzilla vs Kong).

Awakenings

This 1990 drama stars Robin Williams as a doctor and Robert De Niro as a catatonic patient in a New York City hospital. After an experimental treatment, De Niro gains control over his body again and is eager to explore the world after decades stuck in the hospital. It’s based on a book by Oliver Sacks, so is supposedly a true story, yet it’s very obviously Hollywood-ized. Also, De Niro did not seem right for the role. Not sure if it was his acting or just the association of his persona with his more famous roles, but I just couldn’t see him as the character he was trying to portray. (Robin Williams, on the other hand, always seems to play doctors very well.)

By S P Hannifin, ago