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!”

Biden’s impossible microphones

Hahaha! I’m not advocating for any elaborate conspiracy theories here, I just thought this was funny. This short video has appeared on a couple professional news feeds (The Hill, Bloomberg) and it features some blatantly obvious horrible CGI microphones:

With his hand miraculously overlapping the microphones at the 8 second mark, something is definitely fake. Who edited and released this, and why?

Someone is trolling someone with this video!

That stupid equality vs equity picture

You may have seen this sort of graphic succinctly illustrating the difference between “equality” and “equity”:

It’s actually completely unhelpful in the context of the discussions it’s usually utilized in, as it takes completely for granted the main issues with setting any sort of policy based on such a distinction, namely:

  1. Who precisely gets to determine for what disparities “equity” is needed?
  2. Who precisely gets to determine by what metrics “equity” will be measured?
  3. Who precisely gets to determine by what means “equity” will be determined, produced, and distributed?
  4. Who precisely must pay for production and distribution of these means of “equity”?

Each question is so easily corruptible that the entire distinction is, in general, of little practical value. Unless the context is defined as narrowly as illustrated, the difference between “equality” and “equity” is a frivolous point.

Propped Up Corpse

In the 2018 horror film The Nun, a young woman meets a kindly old abbess in a convent who keeps her shadowy face veiled in black. Later in the film, when the heroine returns and finds the old woman sitting eerily still, she is shocked to discover why the old lady’s face is kept veiled: the abbess is dead. The heroine’s been talking to the shriveled rotting flesh of a blackened corpse all along.

Maybe that’s not the best metaphor, but the 2020 presidential election does kind of remind me of it. Why is nobody allowed to examine the machines or audit the ballots? Why are profoundly important court cases rejected on trivial technicalities? Because not only was the last election full of fraud, but national elections have been that way for a while. The mask just slipped a bit too far this time. We’ve been living in the shadow of a propped up corpse.

As someone tweeted:

Prob the longest-lasting effect of Trump’s presidency will be that ppl saw the degree to which heretofore kinda hidden power had to reeeeally flex to oppose him. This is true whether one liked/supported Trump or not.

To which someone else replied:

We saw the sausages being made and it’s full of pig a******s and bugs.

Thanks for that lovely image. I’m reminded of the end of Sweeney Todd when Toby discovers what’s in the meat grinder.

So what now? Unfortunately I still have no idea.

Two things seem clear to me, though:

  1. You can’t vote your way to a fair election. There are a lot of politicians who seem to want to have their cake and eat it too; they want Trump out, but they want us to keep faith in elections. They suggest that we’ve just got to let the questionable results of this election slide and prepare for the next one, which will totally be more secure, for sure. Of course, if this election has taught us that it is impossible to investigate apparent election fraud and futile to try, why should the next election be any different? (This also means it’s pointless to listen to political pundits telling you what to be mad about next. What are you gonna do about it, vote?)
  2. The courts will not uphold election laws. So filing and arguing about lawsuits in regards to elections is also a waste of time and energy.

If the puppet masters care about the illusion of fair elections, perhaps investigations will continue and they’ll say, “aha, yep, there definitely was some fraud here, but not enough to change the outcome, and now we fixed it!” Perhaps there will be some “Republican” victories in the 2022 midterms. Perhaps they’ll even grant us another “Republican” president in 2024, after Biden and Harris finish whatever evil plots they’re being installed for.

And I do think they’re being installed for a reason. Four more years of Trump doesn’t seem like it should be too harsh of a price to pay for reinforcing the illusion of a fair election while sliding the slow knife further in, so something must’ve made the allowance of obvious fraud worth the risk. Maybe Trump’s anti-China policies were causing too much strife for the economic overlords. Maybe they want to get the Middle East war machine up and roaring again. Maybe they’re genuinely afraid for our national security for some secret reason.

Regardless, I don’t see the point in voting anymore. The mask slipped too far. You can’t just reposition it and make me think it’s your real face again.

I can’t blame other voters. I can’t say: “Well, you voted for this!” As I wrote in an earlier post, if an election is fraudulent, nobody’s vote counts. Voting differently would not have changed much.

The whole “storming the Capitol” stunt was a sad and evil exploitation of useful idiots1 to serve as news cycle fodder and distraction propaganda so we’d all gawk and share impassioned opinions about that instead and use it to justify preplanned political ends. Do you really think the Capitol of the most powerful nation in the world couldn’t keep out a couple hundred hooligans with flag poles if it thought it absolutely had to? I’m not saying police were in on it or that it was staged, just that there were bad actors who intentionally put the pieces in place for that to happen. The resulting propaganda is reaching North Korean levels of blatant ridiculousness. It should be glaringly obvious to everyone.

Speaking of stupid pills, I think you can abandon the preposterous “QAnon” hopium conspiracy theories, which promise shocking revelations and surprise victories just around the corner and encourage you to just keep holding your breath until you pass out.

As the execution of all power ultimately depends on the strength of the iron hand, those who are granted legal authority to use physical force to enforce the law (military, police) will have to decide from where that authority comes if not from fairly elected officials according to the US Constitution.

As for the rest of us, I’m not sure we peasants can do much at the moment. (Other than keep a level head.)

Although this election fraud is a serious issue, it is also a temporary and worldly one; our souls were made for a different world, so keep any spiritual distress in check by keeping things in perspective. The goal here is to grow in love of God and neighbor; let’s keep that our spiritual focus.

For further reading, here are a few other articles. I do not claim to agree or disagree with all their points, I just thought they were interesting:

Anomaly detected

In the first episode of the Netflix crime thriller Ozark, a drug lord tests some of his workers with a little story: His aunt worked in his father’s grocery store and one day his father caught her stealing from him. What should his father do?

The main character responds: “Fire her. It’s not the first time she stole from you. It’s the first time you caught her.”

The Anomalies

I do not claim that any of the issues listed below are smoking guns that in and of themselves prove anything, only that they deserve attention and scrutiny rather than being too quickly dismissed.

Dead people absentee ballots

Someone on Twitter pointed out:

Turns out 118 year old “William Bradley” voted via absentee ballot in Wayne County, Michigan. William Bradley died in 1984.

How long has this been going on?

Try it for yourself:

I indeed checked it for myself and the site did indeed confirm that the dead man received and sent back an absentee ballot. Politifact, which is independent and not biased (we know because they say so), has rated this false because “A city elections official said that no ballot was cast for the now deceased Bradley.” The New York Times assures us that they’re just “run-of-the-mill clerical errors.” Whew! But then, being reassured by the source of your initial distrust (“a city election official”) is hardly compelling. Imagine a murder suspect on trial. Judge: “How do you plead?” Suspect: “Not guilty, Your Honor.” Judge: “Well, that settles that; if you were guilty, you would’ve said so, so the court is adjourned! See you at home, son.” Anyway, the same thing is happening for other names of deceased. At the very least, all deceased names should be double-checked. (And why the heck don’t they, gee I don’t know, purge supercentenarians from their database?)

Software “glitches”

Dozens of Michigan counties used the same software that caused 6,000 votes in one county to switch from Trump to Biden. As a programmer, I’d love to learn how such software “glitches”? I don’t buy it; tabulating software is probably not that complicated. (Keeping the data secure is the more complicated part.) The glitch was either gross human incompetence or voting fraud. Googling around, one can find articles on machine-hacking voter fraud happening before, this from a 2018 election, Beto O’Rourke vs Ted Cruz (was it really that close?):

In essence, security protections in software (operated on voting machines throughout the country) had been purposely disabled or ‘un-activated’; penetration of the machines was possible via online access methods widely understood among reasonably sophisticated IT people; and mismatches in time-stamped dataflows suggest votes were changed.

Again, this isn’t “proof” of fraud, but it does deserve more scrutiny. (Even counties that are “red” and “go to Trump” should be scrutinized; if any totals are artificially manipulated, it would still affect the state’s total.)

Statistical surprises & stuff

Quoting writer Larry Correia here:

The massive turn out alone is a red flag.

But as for doing better…

The late night spikes that were enough to close all the Trump leads are a red flag.

The statistically impossible breakdown of the ratios of these vote dumps is a red flag.

The ratios of these dumps being far better than the percentages in the bluest of blue cities, even though the historical data does not match, red flag.

The ratios of these vote dumps favoring Biden more in these few battlegrounds than the ratio for the rest of the country (even the bluest of the blue) red flag.

Biden outperforming Obama among these few urban vote dumps, even though Trump picked up points in every demographic group in the rest of the country, red flag.

The poll observers being removed. Red flag.

The counters cheering as GOP observers are removed, red flag.

The fact that the dem observers outnumber the GOP observers 3 to 1, red flag (and basis of the first lawsuit filed)

The electioneering at the polls (on video), red flag.

The willful violation of the court order requiring the separation of ballots by type, red flag.

USPS whistleblower reporting to the Inspector General that today they were ordered to backdate ballots to yesterday, red flag.

The video of 2 AM deliveries of what appear to be boxes of ballots with no chain of custody or other observers right before the late night miracle spikes, red flag.

(Edit: Also see There is Undeniable Mathematical Evidence the Election is Being Stolen.)

What’s the major new ingredient of this election? Mail-in ballots. Never before used them at such a scale, but they’re secure and fraud is rare. They said so on the news. (Not back in 2012, but ignore that.)

As Correia says:

I am more offended by how ham fisted, clumsy, and audacious the fraud to elect him is than the idea of Joe Biden being president. I think Joe Biden is a corrupt idiot, however, I think America would survive him like we’ve survived previous idiot administrations. However, what is potentially fatal for America is half the populace believing that their elections are hopelessly rigged and they’re eternally f***ed. And now, however this shakes out in court, that’s exactly what half the country is going to think.

If you’re going to cheat, the best way to do it is slowly and subtly, not blatantly. But that’s why the Ozark quote came to my mind. It’s not a perfect analogy, but the point is to consider what information you might be missing. If you catch someone telling a lie, how many other lies have they told undetected? If you spot one person shoplifting, how many shoplifters have already flown under the radar? If you find even one stolen vote, how many more have slipped through unnoticed?

But I guess if not enough people care (or believe), it doesn’t matter? (“The emperor has no clothes!” said the child, without evidence.)

Problem is, even if you don’t care during this election cycle because it’s the outcome you hoped for, what makes you so sure it won’t be used against you? That is, if the election result is dishonest, all votes are nullified.

So what now?

For now, I guess we can only wait for the courts to weigh in. The biggest problem is that even if the voting is investigated (which is up to the courts I guess?), it’s virtually impossible to know whether or not the final count is honest or if the fraud is just dulled to a less suspicious but otherwise effective level (if at all). What election accountability can be offered to an average citizen? (What you should definitely not do is go rioting or looting, like some people like to do. And anyway, while the presidency and the right to a free and fair election may be dangerous to tamper with (if we ever really had that in the first place), the real disasters are a bit further down the domino line.)

Quick note on abortion

Only tangentially related, but a few months ago some siblings and I were discussing the issue of abortion insofar as voting Democrat vs Republican was concerned, and a quote from Sister Joan Chittister came up:

I do not believe that just because you’re opposed to abortion, that that makes you pro-life. In fact, I think in many cases, your morality is deeply lacking if all you want is a child born but not a child fed, not a child educated, not a child housed. And why would I think that you don’t? Because you don’t want any tax money to go there. That’s not pro-life. That’s pro-birth. We need a much broader conversation on what the morality of pro-life is.

This is a sentiment which I’ve heard echoed from several other Catholics, the implication being, as far as I can tell, that the issue of murdering unborn children is really of little political importance because Republicans’ pro-life stance is actually just “pro-birth”; as Chittister implies, Republicans don’t actually care about unborn children. How does she know? Because they disagree with how tax money should be spent.

Two problems with this: 1) It’s an illogical assumption of bad faith, an ad hominem. “You don’t care because you disagree on tax policy!” No, disagreeing on tax policy is not evidence of indifference. 2) Even if it were true that Republicans were indeed “pro-birth” instead of “pro-life”, so what? That still wouldn’t justify killing babies. “Killing unborn babies is wrong.” “Well, you don’t really care… so actually it’s OK.” No; whether murdering unborn babies is right or wrong should not depend on what you think someone else actually thinks.

I’m tempted to go on about how merely throwing tax money at social problems is not necessarily helpful in and of itself, and is hardly representative of the sort of charity that Christianity calls for, but maybe I’ll do that later.

Universal Basic Income is a bad idea

As the 2020 election approaches, we’ll probably hear more about the idea of “universal basic income” from politicians. And it can sound tempting for two main reasons. Reason 1: Free money! Yay! Reason 2: Technological innovations will put people out of their jobs, whatever will we do?! (Answer: Free money! Yay!) (And perhaps Reason 3: I can show compassion towards the less fortunate without having to do anything but vote! Wow, that feels good!)

But it won’t work.

Why not?

My viewpoint is this: What is money? What does it mean, what does it represent? Ultimately it represents a person’s labor1, another person’s value of that labor. (A product you buy or don’t buy is the product of people’s labor. Even if it was made in a factory. Even if that labor was in the past. That’s really what you’re paying for.) Its value is not arbitrary. It is completely psychological, and collectively psychological at that. It is determined by the countless economic exchanges people make everyday. What is a dollar worth? It’s worth whatever the holder of that dollar is willing to exchange it for, and what someone else is willing to trade to get it.

In other words: THE VALUE OF MONEY IS DEPENDENT ON ITS DISTRIBUTION. Its value cannot be dictated by some authority other than the countless economic exchange decisions people make, because the worth of a man’s labor cannot be dictated by some authority. You can’t just redistribute it with no associated exchange of labor (abstract as that may be) and expect it to retain its value.

This is the biggest and most dangerous flaw of logic so many people seem to make, thinking that money could forcibly (that is, through governmental force rather than organic economic incentive) be exchanged and retain its value. Why / how would it retain its value?!

So when money is exchanged without any associated exchange of labor, as would be the case with universal basic income, you break the game. You devalue money. It logically doesn’t work because the money no longer represents an exchange of labor (or anything at all for that matter). This means the money won’t be spent as though it is. This means the “worth” of whatever the person buys with their “free money” is warped for everyone. Ultimately you just get a rampant cycle of inflation along with the devaluation of needed labor.

This is also why minimum wage sets “by force” (law) doesn’t work2, at least not long term; because wages are not then economically organic, and you actively incentivize businesses to innovate and replace the now costly employees or go out of business. The idea that the wealthy CEOs at the top will just shrug and swallow the loss and devalue their own work is ludicrous. The idea that shareholders of profitable companies will just snap their fingers and say “ah, shucky darns!” and devalue their own investments is ludicrous.

Also note that this has nothing to do with tax (“we can tax production instead of income!”) or issues of “so where does all this free money from?!”3 It doesn’t matter. It’s the act itself that’s the problem, the act of giving people money for nothing. The exchange is meaningless and so the money is meaningless, and so every economic exchange that ripples from the spending of that free money is devalued.

Granted, it’s difficult (if not impossible) to measure this devaluation, as it’s purely psychological4. But that shouldn’t be controversial, because the value of money itself is purely psychological to begin with.

I also thought the video below was an interesting perspective. Jordan Peterson comes at it from a more personal psychological point of view. He says that the idea of “universal basic income” tries to rectify the wrong problem. The problem is not that people lack money, he says, but that they lack purpose. A person without concrete purpose will waste their money, essentially, so it doesn’t solve their problem. “Provision of money without purpose is not helpful.” Money without meaning will do more to hurt an individual than help. “You don’t want no responsibility,” he says.

Makes sense. And so I think he sees the other side of the same coin. Money is psychological. Unearned money is not spent like earned money. This creates both personal and economic problems.

Of course, economic problems already exist. Social security, welfare, government bail-outs, spending waste, national debt, forced insurance (healthcare!). They devalue money (or labor) in one sense or another. But the system doesn’t bear these “cheats” because they somehow actually work, the system works despite them. It can be like saying, well, the camel is still standing, what’s another little piece of straw? Aside from already not moving as fast as he could, the camel is doomed to collapse if you keep adding weight to his back; that he hasn’t collapsed yet is not somehow evidence that he will never do so, especially when history is full of the graves of crushed camels (that is, socialist nations). And universal basic income would not be another little piece of straw, it would be boulder.

What does your favorite genre of music say about you?

I wanted to try my hand at writing a nonsense click-bait article with little to no value whatsoever. I hope I did a good job! If this goes well, I might have a whole new career on my hands, so please email this to all your loved ones, and hated ones too.

So what does your favorite genre of music say about you? Find out below!

Bluegrass music: It means you like bluegrass music.

Broadway music: It means you like Broadway music.

Classical music: It means you like classical music.

Country music: It means you like country music.

Dance music: It means you like dance music.

Electronic music: It means you like electronic music.

New Age music: It means you like new age music.

Opera music: It means you like opera music.

Pop music: It means you like pop music.

R&B / Soul music: It means you like R&B / soul music.

Reggae music: It means you like reggae music.

Rock and roll music: It means you like rock and roll music.

Other music: It means you like that other sort of music.

Rap music: You are stupid.

Frequently asked questions about the cookie-based diet


This holiday season, I’ve been trying out a new diet that I call the cookie-based diet. It involves eating cookies all the time. Here I try to answer some questions and concerns people may have about this diet.

Q: Is it unhealthy?

A: When people hear about the cookie-based diet, they immediately assume that it’s unhealthy. After all, cookies are full of sugar and lack vitamins and nutrients. As it turns out, these concerns are well-founded. The cookie-based diet is extremely unhealthy. Risks include everything from diabetes and cavaties to an early death. But this concern also completely misses the point of the cookie-based diet, which is to throw health concerns to the wind and eat more cookies.

Q: When will I know when to stop the cookie-based diet?

A: Never.

Q: Should children try the cookie-based diet?

A: No one at all should try the cookie-based diet, but this isn’t about shoulds and shouldn’ts. This is about cookies.

Q: Should the cookie-based diet be government funded?

A: Yes. Everyone has a fundamental God-given right to cookies, therefore the government should help provide cookies to those who cannot bake cookies themselves or buy them at the store. Please write to your congressmen and elected officials, telling them how important cookies are to you. Bribe them with cookies, of course.

Q: Should I eat cookies that fall on the floor?

A: Eat all cookies.

Q: What should I do if someone else wants to eat my cookies?

A: Eat more cookies.

Q: I am concerned about cookie riots and cookie wars.

A: You are afraid of these things because you have not eaten enough cookies. Cookies will give you peace of mind.

Q: At what point does the cookie-based diet become cookie idolatry? Isn’t it immoral?

A: The All Great and Powerful Cookie doesn’t think so.

Q: Don’t they call cookies “bisquits” or something in the UK?

A: A cookie by any other name, blah blah blah.

Q: Are your answers becoming more and more insane?

A: Cookies.

Q: Are you OK?

A: Coooookies.

Q: What happens if–


Q; W;’a



Son of a bleep…

I’ve heard it asserted that the phrase “son of a *bleep*” is sexist against women because it points the insult not at the male, but at the female. I suppose the interpretation is that the man doesn’t deserve to be insulted and so the insult has to go to someone more worthy of it? But that doesn’t make sense; the insult is clearly directed at the man, and mothers are rarely even present. It’s insulting to the man because he naturally venerates his mother. So, if anything, it points to women, mothers more specifically, being venerated above men. The man knows he’s a dirty stinking rat, so the insult is directed instead at a person the man honors more than himself. That’s what makes it hurtful. (It’s like when villains take hostages in movies. If you want to threaten a man, you could point a gun to his head, but he may be more than willing to die for his cause. Instead, point a gun to the head of his loved ones. Is he willing to sacrifice someone else’s life for his cause?)

But then, does it really make sense to be offended about a manner of insulting at all? Shouldn’t the moral condemnation be directed at the intent to insult in the first place?

It’s like when people get upset about the word “retarded” being used as an insult. Shouldn’t you be upset that someone’s insulting someone else in the first place? Is there a proper way to insult people? Insults are meant to offend people; do you really think the insult-giver cares about offending a non-present third party when he’s, you know, trying to offend someone? Aren’t all insults bad? Moral priorities, please!

Speaking of moral priorities, a video was recently released revealing that Planned Parenthood sells body parts of aborted children, to which I’ve seen comments such as: “I’m pro-choice, but this is sickening.” Really? Killing an unborn child is OK, but what’s done with the body is crossing the line? If you had any respect for the child, you wouldn’t defend his or her being killed in the first place. If a conscience allows for the murder, what difference does it make what’s done with the body?