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.
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.
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.
The statement is absolutely true, IME, for people who aren’t Engineers. Which is most people.
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.
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, 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.
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.
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.
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.
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.
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.
And what happened after Abhayanta died? Did his literal notation become commonly used, or did it vanish like Diophantus’ notation?
But all those things are algebra! Or, at least, using algebra to understand them is much simpler than the alternative. Consider two questions:
If you invest $10,000 at 4%, how much will you have after 30 years?
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.
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.
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, 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.
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.
How do you know what to plug in?
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: