Triangles are the new front in the culture war and are possibly being controlled by demons

Imagine, if you will, a triangle. I’ll make it a very specific one. It has a base of 18 centimetres and a perpendicular height of 9 centimetres. It even has a specific orientation with its base horizontal on a grid. Here it is (or at least a version of it)

Am I being wholly honest? The actual picture I’m showing you is a .png file and you are viewing it on a computer screen. The image is made of tiny squares (visible with a magnifying glass) and the file itself, the more abstract description of the image, is a .png i.e. in principle a set of coordinates of colour information for a grid of data. Does that matter? The answer is “It depends”.

Here’s the image again and superimposed a set of largeish squares. They are there to represent a low-resolution version of the pixelated triangle.

Make the squares a bit smaller and our shpae made from squares begins to look a lot more akin to a triangle:

You get the picture. Smaller and smaller squares make for a smoother image. The first set of stacked squares really doesn’t look much like a triangle but with smaller and more squares the image gets more and more like a triangle. How small do the squares have to be for it to be REALLY a triangle? Trick question.

Here’s a different way of looking at it. As I make the squares smaller the area of the stacked squares gets closer and closer to the are of the triangle we would find from the classic half-the-base-times-the-perpendicular-height formula. Our stacked squares shape literally gets more triangular as far as area goes as we improve the resolution.

But what about the perimeter? Well that’s a mess. It’s not even clear whether perimeter is meaningful. We could define it taking into encounter the edges of the nominal squares. If we do that then (I think, correct me if I’m wrong) the perimeter would tend towards the perimeter of a 9 by 18 rectangle. Ooops. My pixelated triangle is getting more rectangular. However, if I treat the perimeter as meaning “number of pixels on the outside of the shape” then I get a different limit.

Yeah but make them small enough and it is basically a triangle right? Sure, unless you really care about counting pixels, in which case not so much. Every real, physical manifestation of a geometric entity is a messy, not entirely correct compromise. Doing actual useful maths with real things requires understanding the extent to which a thing is and isn’t the “pure” mathematical entity it resembles.

This is a basic fact about the universe. It’s true whether you take a strong Platonic realist view of mathematical entities (i.e. they really are really real, maybe even more real than other things) or not (i.e. they are essentially fictional abstractions that are useful but less real than physical stuff that you can bump your head on).

Too cut a long story slightly shorter I sort of maybe tried to engage our old pal and the inaugural Dragon Award Winner for Best Horror Story That Is Actually A Space Opera Brian Niemeier about this. My excuse is that he said that “necessary being is what theologians mean by God.” and logically necessary things are to me like a flame is to a moth. Brian’s going to be doing the ontological argument for the existence of god and by golly if there’s one think I have opinions on it’s that. Then he used the necessary properties of a triangle as an example…

Anyway, the guy thinks I’m a demon anyway, so if he does the equivalent of drawing a summoning circle for me, I really have no choice but to manifest in a puff of sulphur.

The discussion ended with this:

“You have two choices.
1) Confess that Jesus is the Christ, and God has raised Him from the dead. I shall forgive your violation of my hospitality, and you may continue commenting here.
2) You decline to make this just and logically irrefutable profession, and you cease commenting here. Persist in commenting without meeting my terms, and you get spammed.”

Point 1 apparently is how he expels demonically controlled beings from his blog. Which worked because I then vanished back to my demonic lair without even once twisting my head around 360 degrees. Brian then followed it up with an additional rant about the left being controlled by demons, in particular Doris:

Anyway, how was your day?

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61 responses to “Triangles are the new front in the culture war and are possibly being controlled by demons”

  1. Hahahahahahahaha hahahahahahahaha hahahahahahahaha hahahahahahaha

    So it’s not enough for us to be immoral liars anymore — we have to be demon-controlled. And your unwillingness to progress a faith you don’t believe … proves your demonic involvement.

    I wonder what he would have done if you *had* professed your belief?

    Liked by 1 person

  2. This has got me thinking whether you could build an “I am not a demon” reCAPTCHA-type service for stuff like commenting on his blog. Possible implementations might be:

    * The traditional “Enter the letters as they are shown in the image above” CAPTCHA, but the letters always spell out JESUS, CHRIST, etc
    * Instead of the ones that ask you to perform a simple sum, ask you to enter “I confess that Jesus is Lord, etc”
    * Click on all the pictures with crosses that aren’t inverted

    Liked by 6 people

  3. I don’t really get his logic. Was it something in the style of “if things exist, there must be a supreme being”? Why not hundreds? Or an infinite number?


    • That is one of the standard arguments for the existence of god, yes. Basically the idea goes that everything has a cause, and if you trace those causes back far enough there is a single ‘prime cause’ that started everything off, and that is god. There is not, as far as I know, a satisfactory reason why you can’t just keep going back forever; but there are also lots of things that don’t (or can’t) have a single cause, and there’s no reason to suppose that the cosmos is not one of these things.

      Liked by 2 people

      • I think the largest hole in this reasoning is not the argument for a “prime cause” itself, but the (implicit) leap that follows from saying there’s a “prime cause” to saying that this “prime cause” is a conscious entity, that this entity has Opinions on how we conduct our lives, and that we can gain insight into these opinions by reading the Bible. (Or as Brian N says, that “Jesus is the Christ, and God has raised Him from the dead.”)

        Liked by 2 people

      • Not to say the problem with also trying to prove that the creator still exists. They could have committed suicide.

        Liked by 1 person

        • Ah, I’ll defend the point here. It’s not a creator as such and more of an active principle. “Cause” is a tricky word here and in the sense of “first cause” means something more like “the primary reason why things are rather than are not” on an ongoing basis. In other words, if the first cause had gone then everything just stops happening. It’s like the existential power supply keeping the existential light on.


      • As for why you can’t keep going back infinitely, I think the argument is that you can’t rely on a chain of infinite points to get to this point.
        The way it was explained to me is The vending machine analogy.
        Basically, your standing in front of a sandwich machine and you want to buy a sandwich for a dollar, only to find out that you don’t have any money with you.
        So you ask your friend for a dollar, but he also doesn’t have any money so he asks his friend and so on, the belief is that if there is an infinite amount of this going on you’ll never be able to get the dollar to buy the sandwich.


      • “the belief is that if there is an infinite amount of this going on you’ll never be able to get the dollar to buy the sandwich.”

        Or you might get it immediately. The problem with “infinity” (and a lot of other concepts that people trying to “prove” the existence of God throw around), is that it almost defies human understanding, because it doesn’t work like anything that anyone is ever likely to encounter.

        For example, imagine you have a hotel with infinite rooms, and the hotel is completely occupied by an infinite number of guests. A family drives up with an infinite number of rooms asking for a room for each of them. Each current guest simply moves over to another room and there is plenty of space for them. The fact that the hotel was entirely full before is no impediment to housing an infinite number of new guests.

        Or take an infinite number line. Pick a point to cut it off so that you have a new line stretching “up” in value, and another line stretching “down” in value. Each of these new number lines is still an infinite sequence. Take an infinite sequence of counting by two (2, 4, 6, 8, 10, and so on). Multiply it by two. You now have an infinite sequence that is both twice as large and exactly the same size as the number sequence you started with. The point is, none of this makes “sense” in the normal way people expect, so trying to make arguments based on what is “within reason” is kind of a fool’s errand.

        Fortunately for us, we don’t actually have to go back to an infinite regress. We only have to go back to the Big Bang event, because in the equations leading to the Big Bang, if you go back far enough, time drops out of the calculations. In other words, if you get “close” enough to the Big Bang, there is no time. But if there is no time, then how do you have a causal sequence? Without time, the concepts of “before”, “after”, and “now” have no meaning. You could say that causes have to precede effects, but without time that’s a meaningless statement. Even saying that effects could precede causes is a meaningless statement without time, because “precede” is a temporal concept. Without time, all effects are effectively neither caused or uncaused.

        Another concept that gets abused by those seeking “proofs” of God is “nothing”, as in many people will try to claim that “nothing can’t produce anything – therefore some prime cause must have caused everything”. But if you are claiming that nothing can come from nothing, have you really described nothing? Or have you described something that can’t produce anything else – but that means you’ve described something rather than nothing. You’ve put attributes on it, which makes it a thing, and therefore not nothing.

        I have seen the physicist Lawrence Krauss posit that the Big Bang could have been caused by quantum fluctuations in a zero-point field. He was criticized for this by some of the usual theological Aquinas-proponents on the grounds that he wasn’t describing nothing, but was rather describing something – a zero-point field. But what they failed to notice is that their nothing is just as defined as “something” – because their nothing is actually “something that can’t have quantum fluctuations or be a zero-point field”. In fact, I would argue that it is almost impossible to think about the concept of “nothing”, because once you do, you are thinking of something, and not nothing.

        The point here is that a lot of the concepts at the heart of the various “arguments for God” are much weirder and more amorphous than the apologists who make these arguments are willing to admit (and I’m pretty sure that many of them don’t even understand this). None of the arguments for God work because they all rely on taking almost incomprehensible concepts and making a huge load of unwarranted assumptions about them.


    • Well he hadn’t quite got to the punchline of the ontological argument, he was more setting the scene. However, the multiplicity issue is an important one – for example is the whole number 2 a single thing or are there lots of them? Both are true, even in the abstract because 2 is unique (as in it’s properties define a specific number uniquely) but 2+2+2 is meaningful.

      tl;dr There’s lots wrong with the ontological argument but one thing wrong with it is that makes God ‘exist’ in the same mathematical abstractions exist.


  4. Isn’t describing god as a necessary being (as opposed to a contingent one) essentially the cosmological argument, not the ontological argument?

    Liked by 2 people

    • He’s using the cosmological argument as well. Ontological to say what God is (a being that has existence as a necessary property) and cosmological to say why everything depends on God (if most things need something else to exist then there must be something that doesn’t need something else to exist) [I think]


  5. As a card-carrying Christian myself – I can say the Apostolic Creed with a straight face and everything – can I just point out that we’re not all like that, honestly?

    Also, what happens when you use vector graphics for your triangle instead of raster? I suppose, on a monitor screen, you’re still constrained by the physical size of the phosphors or whatever….


    • Don’t worry – I know he’s an outlier 🙂

      But yes! There’s an interesting distinction in file format there. triangle.svg is still rendered in pixels but the file defines the shape in terms of its geometry – although the contents of a file don’t “look” like a triangle and look like a bunch of words instead. Of course looking like a triangle is what Brian and his followers are going off – which is even more hilarious when you think this is going to be a lead into an argument about god.


      • By the way, I saw where one guy on his site posted that “a triangle has three side by definition, which means if and only if. If it has three sides, it’s a triangle, and if it’s a triangle, it has three sides.”

        I just wanted to point out that that’s not true: Take a rectangle. Remove one side. You now have a figure with three sides that is not a triangle. A triangle is a polygon that has three sides.

        Liked by 2 people

      • I’d say it also depends on how you define “side”, etc. I mean, a sphere (well, I guess I mean “ball”?) that’s been cut in half, then that half cut in half again, arguably has three sides (two flat, one curved) and is not remotely like a triangle. For one, it only has two corners.


        • Well yes. Non-euclidean geometries start from taking a straight line as the shortest distance between two points, which opens up a plethora of possibilities for what might be straight.


  6. This is something I’ve always said. If your faith can’t stand being challenged, or if you as a believer can’t cope with people who don’t believe as you do, then your faith isn’t worth much.

    In Brian’s case, he might as well have said, “Confess that Jesus Christ is the Triangle, and God raised Him from the pixels.” That makes about as much sense, and has as much to do with his original assertion.

    Liked by 6 people

  7. Whatever he’s been smoking, I think I’ll stay away from it because I like my brain to not melt and run out of my ears.

    Liked by 1 person

  8. Good, god-fearing maths. None of that witchcraft of non standard topologies or the demon-spawned mess of hyperreal numbers. No *R here!

    Liked by 2 people

  9. OMG. Is that ever a “when did you stop beating your wife” standard or what? They’re all patting each other on the back about how wonderful a test it is. Shoot, you either profess or you get spammed/banned. That’s no religious proof of demonic activity, and if I had time to play, I’d come back on them with the line that they are all heretics (welp, if I want to be picky as a lapsed Catholic, I sure could make that claim). Or start proof-texting right back at ’em….but damn, that takes a lot of effort–and yes, there are counter verses out there. Even the Devil acknowledges the divinity of Christ, according to traditional theology.

    Nonetheless, I think the appropriate comeback is to demand that they recite the Nicene Creed in response.

    Liked by 1 person

    • Actually, a good reply to that is, “Okay, I’ll confess Jesus Christ to be my savior and God raised him from the dead. I say that while lying through my teeth and crossing all ten fingers behind my back, and I haven’t been struck dead. So what does reciting those words prove, precisely? It proves that your litmus test for demons is meaningless.”

      Liked by 1 person

    • Considering Niemeier sounds like one of those loud U.S. evangelical/non-denominational Protestants that insists that they ‘don’t have a creed’ because they consider that a Catholic thing, asking him to recite the Nicene Creed would probably get a reaction, yes. (Which is presumably what you were talking about.)

      The same sorts of people who insist they’re reading the ‘plain language’ of the bible without interpretations, which really means they’re imposing their own interpretations while insisting they’re not doing so, and then making that part of their identity; any challenge to those interpretations (including pointing out that they ARE just interpretations) thus becomes a personal attack.

      Sometimes I think that the inconsistencies in the evangelical worldview are just like the common misspellings and such in spam email… a way of making sure that anybody with any real common sense just walks away and you’re guaranteed that anybody in the inside will be gullible enough to swallow everything and invested enough in the worldview to treat any challenges as personal attacks.

      Liked by 2 people

      • Well, yeah. The inconsistencies in the evangelical worldview are supposed to be papered over by faith, not logic. And yes, I’m guessing that Niemeier is one of those sorts that consider Catlicks to be eeeevill, I tell you, EEEEVVVILLL. I have heard it said just that way once while selling jewelry–an older woman with her hair pinned up on her head (stereotypical presentation of the loud-mouth sort) who looked over the selection of religious jewelry I had, poked out her lower lip, and said in a condemnatory tone: “That’s Catlick. I’m Babtist.” Then she marched away before I could engage my seriously dropped jaw. I’d always thought the Catlick/Babtist thing to be a stereotype. Hadn’t expected it to manifest in real life.

        And as for the reaction…personal experience. Husband got hit up by one of those sorts in a door-to-door evangelism thing. Not Jehovah’s Witnesses…but the local born-again fundy crowd. He’s lapsed Lutheran, but at the time I was practicing Catholic. He told the fundy that we were a Catholic household, and reported that he had a hard time keeping a straight face at the speed at which the fundy retreated. It *has* worked for me with Jehovah’s Witnesses, just not as dramatically.


        • Half a century ago, when I was a teen in Chattanooga, TN, my friends and I used to talk about how to handle the ultra-religious folks on the street who’d try to rope you in. “Are you saved?” was the line they used at at the time.

          Now we were all born-again, evangelical protestants ourselves (or raised that way, anyway), but even we couldn’t cope with those folks. Just saying, “Sure, I go to First Baptist downtown” wouldn’t work. Either they’d offer reasons why First Baptist wasn’t a “real” Christian church (e.g. “that’s the rich people’s church”) or, much worse, they’d demand you prove it by joining them in haranguing people on the sidewalk.. Whatever you did, short of just ignoring them and walking away, you could end up spending hours talking to them. It was rude, but it was the least rude thing to do.

          We did fantasize about other ideas, but no one (to my knowledge) ever had the guts to try any of them. E.g. “Gosh, you’re cute; can we go somewhere private to talk?” (Obvious problem: what if they say yes?)

          Liked by 1 person

      • Brian Niemeier actually is a Catholic of the ultra-conservative sort, though he probably thinks that all Catholics who are not ultra-conservative like him are evil.


  10. As far as the perimeter goes, your triangle has a perimeter of 18(1+sqrt(2)) but the perimeter of your approximation will be 36 in the limit. Filling it with smaller and smaller squares definitely lets you approximate the area, but it won’t work for the perimeter.

    Pretty much all the methods for approximating the length of a curve depend on us having a formula for the length of a line, so I don’t see any good way to fix this for you. Pythagoras rules! 🙂


    • Oops. The perimeter of the approximation is going to be, as you said, the same as the rectangle that’s 9 x 18. I probably shouldn’t try to do math when I’m sick . . .


    • 54 in the limit (I think) if we are counting the *steps* in the squares. Base is a straight path of 18. Going up one side of the blocks is 9 cm worth of verticals and 9 cm worth of horizontals and going back down again is the same. So 54.

      But yes, if I treat the perimeter as counting external edge tiles then 18 cm worth as the base and 9 cms worth of rows up and 9 cms worth back down, so 36 cms. Like traveling around an inverted T shape.


  11. While I also find the subject of real interest, I don’t see much point in trying to discuss it in a forum where truth and reason are obviously going to be unwelcome.

    Liked by 1 person

  12. I took a peek at Niemeier’s article, and it reminded me of something from a linguistics class on ontologies. If we define a cat as a mammal with whiskers that purrs, does that mean it stops being a cat if we shave off the whiskers? Is a dead cat not a cat? Is a lion a cat? To address Niemeier’s example that a triangle must have three sides, I’ll note that in math it’s useful to treat a degenerate triangle (where one of the angles is zero degrees or 180 degrees, so the thing just looks like a line segment) still be a triangle so that things like the law of cosines are valid for all angles.

    What we learned in my class was that we use different conceptualizations for words based on the context of the conversation we’re having. So when I ask, “Have you got a cat?” my conceptualization definitely excludes dead cats and lions, and if I cite the law of cosines, my conceptualization of triangles does include some that only have two sides (visually, at least). We call a set of conceptualizations an ontology and one of the marvels of natural language is the way a speaker and listener negotiate a shared ontology and update it on the fly. “I’m surprised your apartment lets you keep a cat.” “It’s ceramic; most places let you keep that kind.”

    Likewise, I can happily conceptualize a triangle as any real-world object that’s got three reasonably-straight sides. When that’s not sufficient for conversation, we can start talking about pixels and/or tolerances, but as a general rule, people use the simplest conceptualization that works in a given conversation. We get annoyed if someone insists on one that unnecessarily precise, often making the comment “you’re arguing semantics.”

    We can also conceptualize things that don’t exist. Elves, for example. Note that we use a very different conceptualization for Santa’s elves than we do for Tolkien’s, yet we’re easily able to hold a conversation about either one. That doesn’t mean either one is real, though, and that’s where all the ontological proofs of the existence of God fall down.

    Liked by 2 people

  13. Okay, lots of things to talk about here, but I’d like to point out something that’s easily missed: he’s making a serious ethical lapse as a creator. In that 2017 rant about me he links to, he came out in support of the known plagiarist Douglas S Taylor, hailing him as a “hero” and “a man who’s actually accomplished something”.

    I’m one of the people who called out Taylor for his theft (hence why he hstes my guts) but I’m not the only one. There’s a whole parody Twitter account that logs his plagiarised art:

    As far as I know, Niemeier is the only author to support Taylor. Note that this isn’t even an ideological partnership: Taylor, like any edgelord metalhead worth his salt, is rabidly anti-Christian. So, what we have here is an author throwing ethics to the wind by supporting a plagiarist, purely to score points against a single detector. That’s the level of pettiness we’re dealing with.

    When Niemeier rambles about “cyberstalking”, he seems to be referring to the fact that I posted Taylor’s book covers into Google images to find the sources of the art he’d stolen. I wasn’t aware that “stalking” a book cover was possible, let alone a felony. But hey – if those covers press charges, I suppose can say the Devil made me do it.

    Liked by 1 person

  14. Wut?

    His “write this or I ban you” demands make Dave’s look like a model of rationality.

    (Also, and I can’t believe I only just thought of this, his space-opera-in-hell novels become a lot more disturbing when I’m reminded he thinks demons are literally real)

    Liked by 1 person

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