Algebra is not hard

If I were to tell you that I was taking two apples and three oranges home, you'd know what I mean.

Algebra's the same.

You'd know that if I told you that my friend Geoff (I don't have a friend called Geoff) came home with three more apples and five more oranges, that we would have a fruit party, because we're pathetically hungry.

Using algebra is just the same as having shorthand. Maybe it's not the concept, but it's the shorthand that bothers some people?

I don't know that if algebra is difficult for one person then arithmetic is also difficult, but do let me know if it is this way for you!

All algebra's doing is giving things shorter names so that they can be manipulated more quickly. Perhaps that's where the issues start?

If this therefore confuses you, it may be something deeper.

I'm going to have the letter "r" short for oranges here, as having "o" is too much like zero:

2a + 3r + 3a + 5r = ?

Is it easier if I write it in words?

Two apples, and three oranges, and three more apples and five more oranges, is how many of both?

In real life you'd know to count apples together and oranges together, and even if you do it one by one, I'm struggling to see where the difficulty is in that.

Is the difficulty having symbolic metaphors? (I have to use 🔶 for oranges because Blogger doesn't know about them).

2🍏 + 3🔶 + 3🍏 + 5🔶 = ?

Would one have to count them out to make more sense?

🍏🍏🔶🔶🔶🍏🍏🍏🔶🔶🔶🔶🔶 = ?

That's now just simple rearrangement. Is that somehow easier? So, I move some around and...

🍏🍏🔶🔶🔶🍏🍏🍏🔶🔶🔶🔶🔶 = 🍏🍏🍏🍏🍏🔶🔶🔶🔶🔶🔶🔶🔶

Ta-da!

(I wonder how much all of that costs...)

So I really struggle to understand which bit of algebra is difficult for people. Any thoughts, anyone?

Comments

Unknown (URL) said on 2019-03-09T18:47:48.136Z:

Fair enough, Daniil. I was only referring to the substitution and basic algebra that people learn in school the first time they do it. Of course there are harder parts, but I only meant the actual understanding was a letter meant a number that can be indefinite. But fair point nonetheless.

Daniil Baturin (URL) said on 2018-08-23T19:04:35.154Z:

I'm not sure if anyone is having a problem with this part. I can see how manipulating polynomials, especially the long division, can feel highly unusual to people.

Besides, algebra _is_ hard. ;) The fundamental theorem of algebra remains magical for people until much later, when they learn complex analysis, and they have to just believe it. Proving whether a number is algebraic is still a black art.

General update on the current state of my life

Permalink | Author: Dan Dart | Published: 2016-10-19 19:00:00.003 UTC | Tags: blog doctor entertainment games gnu hunting job life linux maths media podcast skyrim social software star transgender trek who wolfram

Hello everyone!

Thought I'd give something of a general overview of my current October "2016" (but is it really, etc.). Life updates are something I'm really, really bad at, and I thought it would be nice if I didn't just have 140 characters or a broken platform to play with. Not that Google isn't a total joke.

Maybe I'll move this blog over to my real website, which uses Let's Encrypt, which is a free SSL certificate vendor, and offers an automatic client to refresh (since oddly it only gives 3-month certificates).

Job hunting is sour. I had really hoped to be able to carry on getting people to contract me to make websites but I haven't had anything for going on 7 weeks now (gosh, I sound like a mother telling you the age of her child). My usual contract profession is that I build websites for people at home (If you happen to know anyone who needs it, please get in touch), but I am also an avid musician who plays the guitar and keyboard mostly, and am interested in perhaps joining a local band.

I'm making a plethora of new software (mainly because I like coding and I'm often bored, see my GitHub). I was inspired by Matt Parker in his video about letter to number relationships, so I tried to build something automated to see if I could find more. I do love maths and have made a bunch of programs to do a few maths-y things (here are some more!). I've even got myself onto the Online Encyclopædia of Integer Sequences (twice!), and made a Node.js library for accessing it.

A few things I've made that I'm particularly proud of are Project Chaplin (edit 2021: archived) (code) the first free software video sharing website, a half finished social network manager, an automated Apache vhost manager, a clever command-line Omegle client, the beginnings of a first person shooter, with its inspiration in a set of software-rendered demos. I have also made a DeviantArt and Pinterest photo scraper, and had yet another thought about how universal packages should be built.

A few more toys (I wouldn't call them big projects) I've created are a dumb wordoid generator, a Pastafarian finite state machine, a program to play cricket with the input stream to teach me a bit of C++, a few spacey gravity simulators, an equation-based synthesiser, a webcam-based tone generator, a third-party Jamendo audio player, and even a edit: 16, 32 and 64-bit OS, to teach me assembler and C.

Although hardly started, I seem to love gamepads so much, I made something that looks almost like a game (with free pictures taken from the Internet) that basically does nothing but allow you to test a gamepad.

On the useful scale, I decided I wanted to see how up-to-date a few popular GNU/Linux distributions were, so I made a little tool to find out. I might extend it with something or add automation later.

In the future, I will probably re-make my static silly Linux-based distribution into something more sensible (stay tuned), make something to do fun things with Wolfram Alpha (I haven't decided what yet), and make an automatic web page categoriser based on string matching of page structure, as I did when I used to work for an analytics platform.

Entertainment-wise, I finished marathoning most of the Star Trek (all series) episodes ever. I thought that series 3 of Enterprise was total gobshite. 4 was alright though.

I'm marathoning Doctor Who. It's fantastic stuff, I haven't yet gotten past the lost episodes, but there are plenty of clever reconstructions from photos, occasional surviving clips and the existing (I think?) audio. At least it sounds like the real Doctor (I've gotten up to Troughton, if you're interested). Maybe he's got an impersonator? Who knows.

I play computer games more than usual (which I know is an important life skill). My favourite at the moment is Skyrim. Let me know if you want more on that.

I research my family history. I've gone back about 500 years, I'm sure I could even find you. I use Ancestry for that kind of thing and have almost 1000 people in my tree. It's very interesting to me and one discovers pretty crazy things about one's own heritage!

I'm going to see if I can blog a bit more, as it gives me a bit of free reign. Maybe I should do regular segments like discoveries of the week. Yes, I'm definitely a podcast. In fact, I'd rather like to do a tech-related podcast with someone. Any takers?

Ta-ta.

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Algebra is not hard

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General update on the current state of my life

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