# one divided by none just isn't fucking done **URL:** \ **Category:** The BBQ Pit\ **Created:** [February 15, 2011, 4:24am UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413 "2011-02-15T04:24:32Z")\ **Posts on this page:** 20\ **Page:** 4
**Author:** ![The\_Tao\_s\_Revenge](https://avatars.discourse-cdn.com/v4/letter/t/73ab20/32.png) [@The\_Tao\_s\_Revenge](https://boards.straightdope.com/u/The_Tao_s_Revenge)\ **Post date:** [February 16, 2011, 7:57am UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/61 "2011-02-16T07:57:03Z")
> [@Thudlow\_Boink](#): > > For that matter, does negative one exist? What does it mean for a number to “exist,” anyway? Well if you’re overdrawn try telling the bank it doesn’t exist. -1 exists as an integer on the number line. Where is _i_ on the number line? It’s variable that can’t be solved. Further it’s poetic license to call it a lie. Although if you want to nitpick something juicy I’d pick my usage of square when I meant squareroot.:smack: I should have waited until after I got some sleep before posting. ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [February 16, 2011, 9:53am UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/62 "2011-02-16T09:53:15Z")
> [@The\_Tao\_s\_Revenge](#): > > Well if you’re overdrawn try telling the bank it doesn’t exist. -1 exists as an integer on the number line. Where is _i_ on the number line? The number line has just shown you its fundamental limitation: It can’t be used to model rotation, or anything that works like rotation (like, for example, alternating current). It’s the fault of that particular model, nothing else. I can make the same dumb argument by insisting the number line begins at zero and extends off to positive infinity, so therefore negative numbers don’t exist. Or I can say that a trillion is _ultima thule_, chop my number line off there, and therefore bigger numbers are the product of a deranged imagination. Ultimately it doesn’t matter: A given model can be useful and interesting or it can be worthless. That doesn’t invalidate the utility and interest of other models. ---
**Author:** ![Kobal2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kobal2/32/20_2.png) [@Kobal2](https://boards.straightdope.com/u/Kobal2)\ **Post date:** [February 16, 2011, 11:01am UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/63 "2011-02-16T11:01:02Z")
> [@The\_Tao\_s\_Revenge](#): > > What really pisses me off too is the way it’s presented. Occasionally the clouds part and I see an intuitive glimpse into how algebra works and it’s elegant and wonderful. Then I get drug back to the fog of arcane voodoo steps written in what sub vocalizes to a monotone Ben Stein voice. > > Why can’t this stuff be written with passion and personality? I once had a teacher who was like that 24/7. I never really figured out maths myself, or the difference between an “elegant” proof and an inelegant one (it’s a proof, it works, it solves the problem, fuck it end of story, amiright ?) but listening to him talk about math was really something. He talked about Gauss the way other men talk about Sharon Stone. Again, I never grokked that myself, but at the time he made me wish I would. I felt like I was missing out on something glorious. Then the next year I had one of those “I hate it here and I loathe every last one of you” kind of teachers. There went my brief enthusiasm for (failing at) maths, never to come back. ETA: now that I think about it, I owe him one of the very few things I remember about college maths: how to calculate SUM(1 to x) instantly. ---
**Author:** ![Martini\_Enfield](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/martini_enfield/32/11123_2.png) [@Martini\_Enfield](https://boards.straightdope.com/u/Martini_Enfield)\ **Post date:** [February 16, 2011, 12:38pm UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/64 "2011-02-16T12:38:09Z")
> [@Norse](#): > > This statement holds true if, and only if, engineers don’t have a real life when they’re working. : The statement is absolutely true, IME, for people who aren’t Engineers. Which is most people. ---
**Author:** ![Chefguy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chefguy/32/138_2.png) [@Chefguy](https://boards.straightdope.com/u/Chefguy)\ **Post date:** [February 16, 2011, 2:44pm UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/65 "2011-02-16T14:44:00Z")
While in school, I found math to be boring and somewhat pointless. As a surveyor, and later as an electrician, I found algebra and trigonometry to be indispensable tools with nearly every-day applications. The beauty of math for me is in the relevant applications to the real world. Something as simple as ratio and proportion is a powerful tool. ---
**Author:** ![The\_Tao\_s\_Revenge](https://avatars.discourse-cdn.com/v4/letter/t/73ab20/32.png) [@The\_Tao\_s\_Revenge](https://boards.straightdope.com/u/The_Tao_s_Revenge)\ **Post date:** [February 16, 2011, 3:42pm UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/66 "2011-02-16T15:42:38Z")
> [@Derleth](#): > > The number line has just shown you its fundamental limitation: It can’t be used to model rotation, or anything that works like rotation (like, for example, alternating current). It’s the fault of that particular model, nothing else. > > I can make the same dumb argument by insisting the number line begins at zero and extends off to positive infinity, so therefore negative numbers don’t exist. Or I can say that a trillion is _ultima thule_, chop my number line off there, and therefore bigger numbers are the product of a deranged imagination. Ultimately it doesn’t matter: A given model can be useful and interesting or it can be worthless. That doesn’t invalidate the utility and interest of other models. Look I’m not flaming math. I was trying to explain to another poster why _i_ is cool. Someone who is into music but doesn’t get math might connect with it better if it’s shown how it can affect music such is in the design of guitar amps. Yes _i_ exists as much as any nonphysical logical symbol exists, however it does not have a real numerical value because there is no real number that times it’s self is negative one. However if we operate under the fiction that there is, and give it the the variable _i_ we can do some cool stuff with complex numbers. So I took a little linguistic license of a double entendre on the classification of _i_ (that it isn’t [real](http://en.wikipedia.org/wiki/Real_number), therefore you could call it fake, or a lie) to try to explain the much more important concept of why it’s such a cool thing to someone, and why they might already be using it (if that person has ever played electric guitar then _i_ is used controlling the amp) and I get jumped on for the little thing. However maybe my tone came off as criticism of _i_, or the real number line, and not hey look how fun and whimsical _i_ is. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [February 16, 2011, 3:52pm UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/67 "2011-02-16T15:52:06Z")
Oh, I totally get that. But I think it may be worth pointing out (not to you, specifically) that words like “real” and “imaginary,” when applied to numbers, are just technical terms. So, talking as if the real numbers “really exist” but imaginary numbers like _i_ don’t really is a play on words or double entendre. ---
**Author:** ![The\_Tao\_s\_Revenge](https://avatars.discourse-cdn.com/v4/letter/t/73ab20/32.png) [@The\_Tao\_s\_Revenge](https://boards.straightdope.com/u/The_Tao_s_Revenge)\ **Post date:** [February 16, 2011, 4:16pm UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/68 "2011-02-16T16:16:29Z")
> [@Thudlow\_Boink](#): > > Oh, I totally get that. But I think it may be worth pointing out (not to you, specifically) that words like “real” and “imaginary,” when applied to numbers, are just technical terms. So, talking as if the real numbers “really exist” but imaginary numbers like _i_ don’t really is a play on words or double entendre. That’s true, for realz.😛 ---
**Author:** ![Sattua](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sattua/32/11906_2.png) [@Sattua](https://boards.straightdope.com/u/Sattua)\ **Post date:** [February 16, 2011, 4:20pm UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/69 "2011-02-16T16:20:07Z")
What we need is for Apple to publish a curriculum of math-teaching apps that are instantly adopted by schools everywhere. Steve Jobs could make math sexy. ---
**Author:** ![Really\_Not\_All\_That\_Bright](https://avatars.discourse-cdn.com/v4/letter/r/e8c25b/32.png) [@Really\_Not\_All\_That\_Bright](https://boards.straightdope.com/u/Really_Not_All_That_Bright)\ **Post date:** [February 16, 2011, 4:24pm UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/70 "2011-02-16T16:24:15Z")
> [@Dr.Love](#): > > But literal notation (using x,y,z to represent variables, writing equations) hasn’t. Diophantus made some early steps towards literal notation in the 3rd century, which was promptly abandoned for over a millennium. A few mathematicians started toying around with notation in the 1500s, until Rene Descartes invented the modern notation (more-or-less) in the 1600s. That statement is only true if things that happen east of Greece don’t count. The Indian mathematician and philosopher Abhayanta was using literal notation (obviously, with different characters) in 500 BC. Not everything was reduced to symbols - the world _equals_ was still written longhand (actually, the word used was something like _begets_) but the system was there. ---
**Author:** ![Cheshire\_Human](https://avatars.discourse-cdn.com/v4/letter/c/5f8ce5/32.png) [@Cheshire\_Human](https://boards.straightdope.com/u/Cheshire_Human)\ **Post date:** [February 16, 2011, 4:36pm UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/71 "2011-02-16T16:36:16Z")
> [@Heyoka13](#): > > It is my opinion, and it is very true.😃 I worked as a construction inspector (including lab work) for over a decade, and used algebra almost daily. I’ve also done many of the other things you mentioned. While they don’t _ **require** _ algebra, algebra makes some of those things _ **easier** _ and more productive. I respectfully disagree with your opinion. ---
**Author:** ![Martini\_Enfield](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/martini_enfield/32/11123_2.png) [@Martini\_Enfield](https://boards.straightdope.com/u/Martini_Enfield)\ **Post date:** [February 16, 2011, 10:58pm UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/72 "2011-02-16T22:58:09Z")
> [@Cheshire\_Human](#): > > I worked as a construction inspector (including lab work) for over a decade, and used algebra almost daily. I’ve also done many of the other things you mentioned. While they don’t _ **require** _ algebra, algebra makes some of those things _ **easier** _ and more productive. I respectfully disagree with your opinion. And like I said before, most people _aren’t_ engineers, scientists, electricians, or lab assistants, and therefore have absolutely no use for algebra at all. I honestly feel High School Maths would be a _lot_ more useful if it focused entirely on “Real-world”, practically applied stuff. Money, percentages, how interest works, probability, working out speed/distance and travel times, and so on. If there’s any Sheldon Coopers in the year they can have an “Advanced Maths” class for them to go and learn algebra and calculus and quadratic equations and all that other stuff 99% of people don’t give a shit about or need to know and hate so much it makes them less interested in learning the “Useful” maths stuff. I’ve _never_ used Algebra or Calculus (or Long Division, for that matter) in my adult life. ---
**Author:** ![Crackrat](https://avatars.discourse-cdn.com/v4/letter/c/919ad9/32.png) [@Crackrat](https://boards.straightdope.com/u/Crackrat)\ **Post date:** [February 16, 2011, 11:11pm UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/73 "2011-02-16T23:11:03Z")
> [@Martini\_Enfield](#): > > And like I said before, most people _aren’t_ engineers, scientists, electricians, or lab assistants, and therefore have absolutely no use for algebra at all. > > I honestly feel High School Maths would be a _lot_ more useful if it focused entirely on “Real-world”, practically applied stuff. Money, percentages, how interest works, probability, working out speed/distance and travel times, and so on. If there’s any Sheldon Coopers in the year they can have an “Advanced Maths” class for them to go and learn algebra and calculus and quadratic equations and all that other stuff 99% of people don’t give a shit about or need to know and hate so much it makes them less interested in learning the “Useful” maths stuff. > > I’ve _never_ used Algebra or Calculus (or Long Division, for that matter) in my adult life. I learned every single one of your examples in Algebra class (except, I suppose for money. Making change would probably fall under arithmetic. Unless you bought multiple items. ---
**Author:** ![Martini\_Enfield](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/martini_enfield/32/11123_2.png) [@Martini\_Enfield](https://boards.straightdope.com/u/Martini_Enfield)\ **Post date:** [February 16, 2011, 11:13pm UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/74 "2011-02-16T23:13:05Z")
> [@Crackrat](#): > > I learned every single one of your examples in Algebra class (except, I suppose for money. Making change would probably fall under arithmetic. Unless you bought multiple items. I was taught the exampled stuff in the “General Mathematics” units. There were separate units for Algebra and Calculus, which were an utter waste of time IME. ---
**Author:** ![Dr.Love](https://avatars.discourse-cdn.com/v4/letter/d/e8c25b/32.png) [@Dr.Love](https://boards.straightdope.com/u/Dr.Love)\ **Post date:** [February 17, 2011, 3:09am UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/75 "2011-02-17T03:09:37Z")
> [@Really\_Not\_All\_That\_Bright](#): > > That statement is only true if things that happen east of Greece don’t count. The Indian mathematician and philosopher Abhayanta was using literal notation (obviously, with different characters) in 500 BC. Not everything was reduced to symbols - the world _equals_ was still written longhand (actually, the word used was something like _begets_) but the system was there. And what happened after Abhayanta died? Did his literal notation become commonly used, or did it vanish like Diophantus’ notation? > [@Martini\_Enfield](#): > > I honestly feel High School Maths would be a _lot_ more useful if it focused entirely on “Real-world”, practically applied stuff. Money, percentages, how interest works, probability, working out speed/distance and travel times, and so on. If there’s any Sheldon Coopers in the year they can have an “Advanced Maths” class for them to go and learn algebra and calculus and quadratic equations and all that other stuff 99% of people don’t give a shit about or need to know and hate so much it makes them less interested in learning the “Useful” maths stuff. But all those things are algebra! Or, at least, using algebra to understand them is much simpler than the alternative. Consider two questions: 1. If you invest $10,000 at 4%, how much will you have after 30 years? 2. If you want to have $50,000 after 30 years, how much should you invest in an account earning 4% interest? If you use algebra, you understand that both of these questions are solved using the same formula, P(1+r)[sup]t[/sup] = V. Put another way, algebra is the set of skills that allow you to solve problem 2 given that you already know how to solve problem 1. If you teach about interest without algebra, you’ll be forced to tell the students that problems 1 and 2 are solved by two different, unrelated methods. ---
**Author:** ![The\_Tao\_s\_Revenge](https://avatars.discourse-cdn.com/v4/letter/t/73ab20/32.png) [@The\_Tao\_s\_Revenge](https://boards.straightdope.com/u/The_Tao_s_Revenge)\ **Post date:** [February 17, 2011, 3:29am UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/76 "2011-02-17T03:29:53Z")
So I got to thinking about the situation. Basically what I have here is a really hard class. Growing up classes came in two varieties, easy and boring, and easy and interesting. In college they’re a bit more work but generally easy. As a result I’ve never had to develop effective study habits. I read the text and bam it’s known now. Usually I’ll do 3rd party research if the text doesn’t make much sense, or isn’t satisfying as going far enough, which I’ll incoporate into any class work. Sometimes I’ll disagree with class textbook, and so I’ll end up doing things like answer a true/false question with the “book says” follow by a paragraph with citations about why the book is wrong, or rewrite some code I’m supposed to incorporate into a homework project so it’s better. This I’m not doing anything like that. I’m too busy trying to keep up, let alone do extra. So this is a chance to practice and become better at learning things that don’t come easy. ---
**Author:** ![Kimstu](https://avatars.discourse-cdn.com/v4/letter/k/ecd19e/32.png) [@Kimstu](https://boards.straightdope.com/u/Kimstu)\ **Post date:** [February 17, 2011, 3:58am UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/77 "2011-02-17T03:58:52Z")
> [@Really Not All That Bright](#): > > That statement is only true if things that happen east of Greece don’t count. The Indian mathematician and philosopher Abhayanta was using literal notation (obviously, with different characters) in 500 BC. Not everything was reduced to symbols - the world equals was still written longhand (actually, the word used was something like begets) but the system was there. > [@Dr. Love](#): > > And what happened after Abhayanta died? Did his literal notation become commonly used, or did it vanish like Diophantus’ notation? Not your fault, but this information is pretty garbled and largely erroneous; unfortunately, there is a lot of garbled and erroneous information on pre-modern Indian mathematics out there. The Indian mathematician you’re talking about is probably [Aryabhata I](http://www-history.mcs.st-and.ac.uk/Biographies/Aryabhata_I.html), who lived about 500 CE/AD, not BC. He was a mathematician and astronomer, but we have no evidence for considering him a “philosopher” except in the classical Greek sense where anybody who studies abstract or natural sciences is a philosopher. Aryabhata was not the first Indian mathematician to employ a sort of syncopated symbolic (not quite “literal”) notation for algebra equations, but his is the first surviving work to clearly attest to it. So we don’t know exactly when Indian algebra symbolism developed, but it was probably nearly contemporary with although independent of Diophantus. There were various forms of notation, but a typical example would stack the two sides of an equation one above the other, with no equals-sign symbol or word between them. The degree of a variable would be indicated by a syllable abbreviating an appropriate word. For instance, a standard term for the unknown was “yavattavat”, Sanskrit for “as much as so much, some amount”, abbreviated “ya”. The square of the unknown was called “yavattavat-varga”, abbreviated “yava” and constants were identified with the word “rupa” (“form”, “number”), abbreviated “ru”. Negative quantities had special markers such as a dot above them. So to write an equation that we would denote 2x^2 - 4x + 3 = 6x - 5, a Sanskrit algebra text might put yava 2 ya 4o ru 3 ya 6 ru 5o And yes, this sort of symbolic notation was used in Sanskrit algebra right up until the 19th century or thereabouts when modern Western mathematics came to dominate the Indian educational system. Islamic algebra, although somewhat influenced by Indian sources, was originally purely verbal until some second-millennium mathematicians began to devise a similar kind of abbreviated notation. Renaissance “cossists” or authors of texts on practical computations reinvented various semi-symbolic conventions for expressing equations, which were standardized into complete systems by later mathematicians like Viete and Descartes. Descartes’ system of algebra notation is more or less what we use today. ---
**Author:** ![Martini\_Enfield](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/martini_enfield/32/11123_2.png) [@Martini\_Enfield](https://boards.straightdope.com/u/Martini_Enfield)\ **Post date:** [February 17, 2011, 5:36am UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/78 "2011-02-17T05:36:15Z")
> [@Dr.Love](#): > > But all those things are algebra! Or, at least, using algebra to understand them is much simpler than the alternative. > > […] > > If you use algebra, you understand that both of these questions are solved using the same formula, P(1+r)[sup]t[/sup] = V. Put another way, algebra is the set of skills that allow you to solve problem 2 given that you already know how to solve problem 1. If you teach about interest without algebra, you’ll be forced to tell the students that problems 1 and 2 are solved by two different, unrelated methods. Or, I could use a calculator. Seriously, Algebra is _never_ simpler for me. It’s complicated gibberish to me, and always has been, no matter how much effort I put into trying to understand it. I gave up years ago, especially since I’ve never needed it anyway- I think it’d actually be a more productive use of my time to learn Swahili. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [February 17, 2011, 5:51am UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/79 "2011-02-17T05:51:27Z")
> [@Martini\_Enfield](#): > > Or, I could use a calculator. How do you know what to plug in? ---
**Author:** ![Norse](https://avatars.discourse-cdn.com/v4/letter/n/a9adbd/32.png) [@Norse](https://boards.straightdope.com/u/Norse)\ **Post date:** [February 17, 2011, 6:37am UTC](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413/80 "2011-02-17T06:37:04Z")
> [@Martini\_Enfield](#): > > Seriously, Algebra is _never_ simpler for me. It’s complicated gibberish to me So, what you’re really saying is that since _you_ don’t understand algebra, real world people _in general_ have no use for algebra? OK… :dubious: [Previous page](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413.md?page=3) [Next page](https://boards.straightdope.com/t/one-divided-by-none-just-isnt-fucking-done/571413.md?page=5)