Is Algebra necessary?

General Discussion
421

As a programmer, I use algebra constantly. I love math. I also feel that basic algebra and even trig are useful later in life. Inverse proportions are useful with gas mileage, probability is often a good tool for decisions. As a student, I find that my peers fail because all they do is piss around. Any student can pass math courses if they try. The problem isn’t the education system, it’s the students.

I know how hard it is to deal with a class you hate, but if you really try, you can’t fail a course. It’s impossible.

422

I don’t know about “anything goes”, but there are problems when you try to imagine a real object with all the properties of certain mathematical objects. Of course there would be a problem if mathematicians were to say that you can have an actual horn with infinite surface area and finite volume, but nobody is saying that. The fact that it’s possible for a mathematical object shouldn’t be considered a paradox because it doesn’t present a logical contradiction and it’s beyond the scope of human intuition.

A though experiment is never pointless if you understand its limitations and don’t try to get more out of it than you should. If assuming that “infinity” exists, whatever that may mean, helps you understand something, then that’s fine with me. But it should be understood that that’s a big assumption and might lead to incorrect conclusions.

I don’t think it’s an argument against calculus because infinity isn’t really a concept in calculus. Anytime you see the infinity symbol or someone talks about “infinitely many”, you can always trace it back to some finite number of terms. 1+1/2+1/4+…=2 doesn’t really mean that you somehow add infinitely many terms and somehow get exactly 2. It’s shorthand for “I can add some finite, possibly very large number of terms, and get as close to 2 as you wish”. No mention of infinity at all. The early users of calculus were rightfully questioned about their sloppy reasoning with infinitely small things (thankfully, they didn’t let that stop them and mostly got all the right results anyway because they were so smart).

I don’t think it is.

Exactly. If you think every mathematical object must exactly correspond to some physical object, instead of maybe being just a convenient model for it, then you’d think almost everything is a paradox. I don’t think it’s a waste of time to think about these things, but it is going too far to say that a mathematical object having certain properties presents a genuine physical paradox.

You don’t have to use something fancy like Gabriel’s horn either. A simple line segment is a physical impossibility, but not many people would consider that to be some sort of paradox.

423

We’re going to have to agree to seriously disagree there when it refers to the educational system in its totality.

424

Nah, the US education system is trash. Saying it’s not is like a scrub saying Q is god tier in 3S because Kuroda destroys people with him. I do agree that there are a ton of students who don’t care about education and schools shouldn’t pander to these scrubs and schools should offer more advanced classes for people who actually want to learn or finish school faster. A decent education for my kids is one of the reasons why I’m considering moving out of the US.

Also grades aren’t the only thing that matters, the college you go to matters as well. Someone from a community college like Brooklyn College can easily get a perfect GPA while partying every day and chilling (shout outs to my friends, you know who you are). Meanwhile, someone from MIT might be studying 24/7 and only pull off a B-. If both of these students came to me for a job, I would value the MIT student with a B- far beyond the Brooklyn College student with a perfect GPA.

425

I would value the ones with praticle experience more because GPA to me is a nice number to make you feel bad about your life.

I’ve known 4.0 students who couldn’t think their way out of a paper bag.

426

So far we dropped diet and now we are going to drop Algebra. Lets just quit on everything we struggle on. Lazy asses!

427

A. Teachers has to care and want to teach
B. Student wants to learn
C. Parents giving a dayum.

Unfortunately at times there are too many factors at play and all 3 parties want to blame each other.

There are plenty of those and many of them are working for the federal government cuz you have to have at least a 3.5 or so depending on the “middle tier” position which is nothing more than a GS9 auditor for the IRS.

428

Saw this and thought of you guys:

[LEFT]

Full article here:
http://boingboing.net/2012/08/07/what-do-christian-fundamentali.html[/LEFT]

429

It’s necessary for the ones that need it. The ones not good at it will ask the ones that are for help, and that’s how the world turns.

430

I read it and never knew that set theory was an enemy of religion, but nothing surprises me anymore. I’ll be the first to admit that I don’t know all that much about the mathematical results of Cantor’s work beyond the basics learned in undergrad courses, but I think people are really reaching when they see deep philosophical implications in infinite sets, let alone something like the (non)existence of God. Anytime someone claims that math proves or disproves God then you can immediately ignore them, or try to educate them if they’re simply ignorant and you have the patience.

An infinite set is one which can’t be mapped injectively into {1,2,…,n} for any integer n. In other words, an infinite set is a set which isn’t finite. Furthermore, the existence of an infinite set is an axiom. We assume that one exists right from the start. A set A is “bigger” (not the technical word for it) than a set B if B can be mapped injectively into A but A can’t be mapped injectively into B. The power set of A is always bigger than A itself, so from any infinite set you can keep making bigger and bigger sets forever.

I’d be happy if someone who knows more about it would help me out, but I truly think that if we stick to this language and don’t delude ourselves into seeing more than what’s there, we just end up with some nice math but nothing philosophically groundbreaking.

Yeah, I’m basically using this thread as the new math thread at this point…

431

Math can be used to disprove the christian god who has “omnipotence” as one of his attributes.

It goes back to the pedantic question, can god create a rock so heavy that even he cannot lift it? which directly shows that omnipotence is a logically impossible trait, thus a god who possesses it by definition cannot exist.

This involves set theory because the definition of both sets, omnipotent deities and unliftable rocks are contradictory. There cannot be a member in both sets at the same time. Canonical example - a barber has a sign that says: “I’ll cut the hair of anyone who does not cut their own hair”. So does he cut his own hair? Does he belong to the set of people who cuts their own hair? If so, he cannot cut his own hair. If he doesn’t belong to that set of people who cuts their own hair, he belongs to the set of people who does not cut his own hair, so he must cut his own hair. My math speak is very rusty, but you get the idea.

Likewise omniscience is similarly logically impossible. If you know everything, then you have a mental representation of everything in your mind. Think of a map of the world. A map of the world that is “omniscient” would have every single detail mapped out. Every gas station, every tree, every rock. This map would also contain itself on it, rendered in perfect detail. Which would mean that map would contain a map of itself, and so on.

You basically get infinite recursion, and if god were omniscient he’d run out of memory and blow his stack. Its illogical.

So yes you can disprove god with math, or at least neuter his so that he’s no longer omnipotent or omniscient. at best god is a powerful alien.

you can try to prove god exists via weak logic arguments like the ontological argument:

Define god as the most powerful being, that no other being can be more powerful than it.

a being that exists is more powerful than one that does not.

so by definition god does not exist.

this logic falls apart, because it can be used to prove anything. replace god with “best awesomest ice cream sundae” and you can prove a 100 lb ice cream sundae that gives you orgasms is defined to exist. meaningless.

edit: my bad i didnt even realize the article mentions the barber paradox

best paradox EVAR!!!111 math is awesome

432

Yeah but God can do anything, or at least anything that several councils of Roman politicians hundreds of years after the supposed events of the Bible decided he can do, so there must be a problem with the math. Unless the math can be used to prove that God is real, in which case you can’t argue because it’s MATH! And I think the proof is actually the existence of bananas if youtube has taught me anything.

edit: But seriously, I think the counterargument to the rock problem is just to basically say the question is meaningless. Which sounds suspiciously like cheating, although the solution to the barber problem is pretty much the same lol. The difference is that in math, it’s not a bad thing to tweak some axioms to make the resulting theory contradiction free.

433

Maybe the ship has sailed on this topic, but just wanted to chime in that math is a self-contained human construct. We start with axioms and rules, and then build theorems based on those rules. The concept of “perfect math” is silly, because I assume you mean math will never be able to perfectly estimate/simulate some real-life system or something? Math doesn’t care about that. Math’s goal is to be perfect within itself (and it is). You try and mold math to be useful for estimating real-life phenomena, but if it can’t that doesn’t mean math isn’t perfectly correct.

Of course, we choose the axioms we build the mathematical model on such that we can draw real world parallels easily. That way it can be used pragmatically. But this talk of “math is based on logic, which is made by imperfect humans” is silly. Math is nothing more than a giant if statement. “If we assume these axioms and rules, we can derive all these wonderful things.” The fact that fallible humans are behind that is irrelevant. Math as a system is self-contained and flawless.*

  • (Occasionally, we have to re-examine our axioms, like early 20th century set theory stuff)
434

I don’t think Algebra is all that necessary to everyday life.

Don’t get me wrong, basic-to-moderate math skills are crucial to everyday stuff. However, i don’t need to create & plug-in a complex algebra equation just to calculate something like the approximate amount of gas i’ll need for a trip and back. Or which two products are the better deal.

Much simpler ways i can go about doing that with basic Math.

435

We’ve been over this several times though, you DO need that for loans or savings, which you are going to need no matter how poor/rich you are. It’s also useful to understand data that’s given to, IE politics, scientific advancement etc… Lots of numbers and math are thrown around and you’ll be better off and better for society if you understand it all.

436

oh boy are people seriously debating the importance of algebra?
no wonder the rest of the world see united states as a country full of dumb people :confused:

437

I just saw this article the other day after reading some comments on Good Math, Bad Math. Whether math teaching is really a big factor in racial equity or not, everything about poor teacher knowledge is true. Elementary school teachers not knowing how to find the area of a rectangle doesn’t surprise me at all. It’s hard to actually understand how bad it is unless you’ve seen it with your own eyes, time and time again.

438

I like how somewhere along the line the subject of this thread went from “Is Algebra Necessary?” to “Is Matriarch Necessary?”

(Apparently the answer is no)

439

I would like to point out, while people bash U.S. education’s system, that everyone is included, regardless of background, disability, or even citizenship.

Where I live in California, there is a high percentage of children who get out of elementary school who cannot speak or read english, whose parents cannot speak or read english, and who suffer poor results for obvious reasons.

I am proud everyone is included, but I expect and respect the difficulties of raising literally everyone, including those from other countries and those with disabilities, such as dislexia or retardation.

Now to get back to the ignorance of math, if a person doesn’t understand english, the teaching of math is unlikely in our country.

Random fact: 75% of prison inmates are dyslexic.

440

source please? I would like to make further incury to this