# should schools stop teaching the 3 4 5 triangle? **URL:** \ **Category:** Great Debates\ **Created:** [November 17, 2009, 4:46am UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886 "2009-11-17T04:46:38Z")\ **Posts on this page:** 8\ **Page:** 4
**Author:** ![gonzomax](https://avatars.discourse-cdn.com/v4/letter/g/e8c25b/32.png) [@gonzomax](https://boards.straightdope.com/u/gonzomax)\ **Post date:** [November 18, 2009, 5:36pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/61 "2009-11-18T17:36:31Z")
Indian chief has 3 pregnant women. He puts 1 in a teepee with a deer skin He puts the 2nd in a teepee with an elk skin He looks about and all that he has left is a hippopatamus skin for the 3rd one Next day they all gave birth. The last one had twins others had singles The chief observed The squaw on the hippopatamus hide is equal the the sum of the squaws on the other two hides. ---
**Author:** ![Marley23](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Marley23](https://boards.straightdope.com/u/Marley23)\ **Post date:** [November 18, 2009, 6:29pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/62 "2009-11-18T18:29:12Z")
> [@Kobal2](#): > > I think most of us are beginning to doubt the reality of yours, so you’ve got a point there. Personal insults aren’t allowed in this forum. ---
**Author:** ![begbert2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/begbert2/32/3357_2.png) [@begbert2](https://boards.straightdope.com/u/begbert2)\ **Post date:** [November 18, 2009, 10:00pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/63 "2009-11-18T22:00:29Z")
> [@Keweenaw](#): > > The op’s mathematical premise is not a unique one. It’s essentially [Intuitionism](http://en.wikipedia.org/wiki/Intuitionism). It could certainly be considered that [L. E. J. Brouwer](http://en.wikipedia.org/wiki/Luitzen_Egbertus_Jan_Brouwer)was misguided, but probably not a complete moron. No, it’s _denial_ of intuitionism. It’s a statement that the math that is correct based on proofs and internal logic is _wrong_. It’s a ratinalle-less rejection of mathematics itself. It’s kind of like what it takes to get creationism into a science class, actually. > [@Keweenaw](#): > > Is there is the connection between consideration of the abstract 3 4 5 triangle, which does not exist in the physical world, and the consideration of supernatural to explain the source of goodness? No. Triangles exist in the abstract model called “mathematics/geometry” which does not exist in reality, but is useful because when reality is found to match the model to some degree, the model can be used to infer additional useful data that is accurate in proportion to the degree that the chunk of reality you are observing matches the model. The supernatural is also an abstact model that does not exist in reality, but unlike math it is useless - you cannot match the supernatural elements with reality directly, since we can’t find anything resembling actual ghosts and gods running around, and attempts to use observed “results” to infer the presence of the supernatural consistently fail to yeild better predictive power than chance, once you correct for observer bias. Using the supernatural to “infer” the souce of goodness is like “inferring” that ((334 \* 999 + 1) \* 37 - 12345678) happened just because you run across the number 1. In theory that _might_ have been the math that led to the answer you see, but there’s no real reason to think so. > [@Keweenaw](#): > > Don’t both atheism and intuitionism have a some connection in the form of anti-realism? I looked up anti-realism, and atheism doens’t qualify. Quoting [wikipedia](http://en.wikipedia.org/wiki/Anti-realism), “In philosophy of science, anti-realism applies chiefly to claims about the non-reality of “unobservable” entities such as electrons or DNA, which are not detectable with human senses.” Which is to say, it disregards _all_ secondary evidence - no matter how consistent or compelling the secondary evidence is. This is not something atheists generally do - atheists not only almost universally believe in electrons and DNA, they also would accept sufficently compelling secondary evidence for God. The problem is, of course, that all the so-called evidence for god is the crudest level of misinterpretable personal anecdotes - and it’s wildly inconsistent across varying populations besides. Though this is just the crap argument that skepticism isn’t justifiable repeated again, I will say that this is one of the most intellectually complex phrasings of it I’ve ever seen. Kudos. ---
**Author:** ![begbert2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/begbert2/32/3357_2.png) [@begbert2](https://boards.straightdope.com/u/begbert2)\ **Post date:** [November 18, 2009, 10:52pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/64 "2009-11-18T22:52:16Z")
I’m going to give you better answers than your rambling questions deserve. > [@confission](#): > > but what’s the difference between reality and mathematics? Reality is real. Mathematics is an abstract model - it’s all in your head. However, if you find things in reality that approxomate things in mathematics, the math can tell you additional facts about the real things, to the degree that reality matches the math. > [@confission](#): > > “reality” is what i see and measure outside of myself? and mathematics is at the core of where who i am actually touches reality head on? Yes to the reality part. The math stuff here is gibberish. > [@confission](#): > > mathematical logic is in my being? Apparently not - and even those of us who have it, had to learn it; it’s not inherent, not any more than the Klingon language is. > [@confission](#): > > mathematical logic is what i know for sure, but “reality” is what i can only make approximations of? Mathematical knowledge _can_ be known for sure, though _you_ might not know it. However, the only thing that math is sure about is other math. When you start to talk about the bits of reality that resemble the things in the abstract math, then errors will exist between the abstract math results and the actual reality, because the reality doesn’t precisely match the model. That said, reality can be known directly, to the limits of your sensory apparatus. Those aren’t perfectly accurate, but that’s not math’s fault. > [@confission](#): > > if the point in which whatever i truly am touches reality is not itself part of reality, then what is it? Math isn’t where you “touch reality” (with me, that’s my skin), so this is gibberish. > [@confission](#): > > what do you make of the electrical light energy that makes up logic in a human’s head? is there any reality to it, or is it all complete fiction? Electricity isn’t fictional. (Dunno about “light” energy.) There is as much reality to your mind as there is to your computer browser; both are things that exist due to and created by the organized behavior of electrons operating within and interacting with a material substrate. > [@confission](#): > > where does our idea of the number 1 come from? what is the explanation of our idea of the number 1? Most humans learn very early on how to distinguish between separate objects - the awareness that distinct objects exists gives rise to the notion of the number 1 - each distinct object that you can recognize is 1 object. > [@confission](#): > > what does the number 1 mean, on its own, without any units put to it? what does it mean that we can use the number 1 without ever assigning any units to it? if the number 1 does not have any real existence in the “real world” without units, where does the number 1 come from? does it not come from reality? is it not real? how can we talk about it if it’s not a real part of reality? The number 1 without units is an abstraction from individual objects ‘with’ units - which is to say, you go from “an orange” to “1 orange” to “1”. The abstraction exists because there are common properties of things that all can be describes as “1”: for example, when you have two of them together, you get “2”. Between when you abstract it (take the units off) and when you later use it as a model of some part of reality (put the units on), it does not exist in reality; it’s just part of the mathematical model. You can do things with it, but all the things you do are still part of the abstract mathematical model. > [@confission](#): > > how do you explain the mapping of the 3 4 5 triangle on a real sheet of paper using real ink (even if it’s not exact, it’s close enough that it appears amazing, because it maps to something real in our heads) Err, it’s ink on paper. That’s my explanation. It’s usually done to help other people learn things about the abstract thing called “math”, the same way that books exist to help people learnd about the abstract thing called “Klingon”. And it’s mostly cool because integers unexpectedly popping up is cool in math like this. It’s not cool because it maps to something “inside year head” (in the abstract model called “math”) - there’s lots of boring things that are equally mathematical. 13 + 2 = 15, for example. > [@confission](#): > > are the light particles that are bouncing in our heads not real? what are they? and how do you explain them? how on earth would the real world.. the sun and the earth, go about putting light particles in your head so that you can think of a 3 4 5 triangle? I dunno about you, but I don’t have a big hole in my head to let light in. And electrons are everywhere, and the beasties that stumbled on putting them in clever patterns outcompeted enough other beasties to survive. That’s all there is to it. > [@confission](#): > > why would the universe create a human through evolution and place the thought of a 3 4 5 triangle in its head? The universe didn’t put 3 4 5 in my head. Some human figured it out, based on math which humans made up from their ability to tell one thing from another, and then eventually some teacher tought it to me. That’s how it got in my head, and the universe couldn’t care less. > [@confission](#): > > isn’t your head a consequence of real life? Yes. > [@confission](#): > > how do 3 4 5 triangles exist in real life in your head? The same way the res of my thoughs do - they’re arrangements of chemicals and electrons that are meaningful when interpreted according to rules encoded in the electrochemical arrangements in the other parts of my head. Your computer’s memory works exactly the same way. > [@confission](#): > > how do we know what a 3 4 5 triangle is if it doesn’t exist, at least in our head. and if it exists in our head, then can it be said that what is in our head is a real 3 4 5 triangle. we hold light particles in our head in the shape of a 3 4 5 triangle? Look at your screen, here: R. See that letter R? It’s held in your computer’s memory, but _not_ in an arragment of “light particles”:rolleyes: in the shape of a letter R. It’s encoded. Just like our thoughts are. > [@confission](#): > > how can we form light particles in our head in the shape of an exact 3 4 5 triangle when we don’t even know the exact angles of the 2 non-90 sides? We can’t, but we don’t have to, because our thoughts are encoded. And further, all we encode are the things we actually know, which is untroubled by the fact we don’t know the other angles (or at least, we’re not usually taught them when we learn the 3-4-5 triangle thing.) > [@confission](#): > > how can a real 3 4 5 triangle exist in my head (i know what it is) and not exist in my head (i don’t know the exact angles) at the same time? No “real” 3 4 5 triangle exists in your head. > [@confission](#): > > and if the real 3 4 5 triangle does not exist in my head, then shouldn’t it be said that there is no truth at all to a 3 4 5 triangle? and nobody should even mention them or use them, because they are a myth? Nonsense. The 3 4 5 triangle is an emergent behavior of the abstract system called mathematics/trigonometry. This system is useful because it gives us approxomately accurate information when applied to things in real life that approxomately line up with it. Because it is useful, it should be mentioned and used when it is useful to do so. > [@confission](#): > > if what’s happening inside my head is not real life, then what is it? why would evolution go through millions of years of struggling just to create something that’s not real? why is the brain not real? Evolution doesn’t struggle, any more than 1 and 1 struggle to make 2. Evolution is just the way things happen in certain circumstances - just like in the circumstances when you have 1 and 1, they make 2. And math didn’t evolve anyway; it was deduced by humans independent of their evolution. And as for what’s going on in your head, it’s as real as what’s going on in your computer case. There are no browsers floating around in there, but you can get on the internet just the same. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [November 18, 2009, 11:02pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/65 "2009-11-18T23:02:22Z")
A weird coincidence: I had been planning myself to use the abstract concept of the letter ‘R’ as an example to illustrate a point, and then **begbert2** went and did it independently, same letter and everything. ---
**Author:** ![ToeJam](https://avatars.discourse-cdn.com/v4/letter/t/dfb087/32.png) [@ToeJam](https://boards.straightdope.com/u/ToeJam)\ **Post date:** [November 19, 2009, 12:04am UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/66 "2009-11-19T00:04:20Z")
Pffft… the 3-4-5 Triangle? I always preferred the 30-60-90 Triangle. And who could forget it’s unloved stepchild, but infinitely more likable 45-45-90 Triangle. Screw the evolutionary distance, man, it’s all about the \*angels \*in the **angles**! _edit_ whoops, just noticed this was by the sperm guy. I’ll quietly slink away and come back in a few days to see where this train of discussion actually goes. ---
**Author:** ![BunnyTVS](https://avatars.discourse-cdn.com/v4/letter/b/977dab/32.png) [@BunnyTVS](https://boards.straightdope.com/u/BunnyTVS)\ **Post date:** [November 19, 2009, 12:19am UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/67 "2009-11-19T00:19:16Z")
> [@confission](#): > > if what’s happening inside my head is not real life, then what is it? From many minutes of rigorous masturb… calculation, I have calculated 2(two) equally proble results. 1: **Frickin’ Frightning** 2: **What happens when you smoke a full 1/4oz of prime grade skunk** Strangely enough **Frickin’ Frightning** [sup]2[/sup] + **What happens when you smoke a full 1/4g of prime grade skunk** [sup]2[/sup] = **confission** [sup]2[/sup] ---
**Author:** ![tomndebb](https://avatars.discourse-cdn.com/v4/letter/t/b9e5f3/32.png) [@tomndebb](https://boards.straightdope.com/u/tomndebb)\ **Post date:** [November 19, 2009, 12:47am UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/68 "2009-11-19T00:47:15Z")
If confission wants to post this, again, in MPSIMS or a Joke forum on another board, that is fine, butr it is not funny enough to be left here and it is certainly nothing resembling a legitimate debate. Closed. [/Moderating] [Previous page](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886.md?page=3)