Writing 1/3 in binary (2014) [video] | Hacker News Reader

Writing 1/3 in binary (2014) [video]

mikesmathpage.wordpress.com

72 pointsvo2maxer28 comments

Loved seeing this video, just gotta quibble with this part of the blog post:

> “I think the fun of topics like this can draw kids into math …”

Nope, it can't! There is no generally applicable lesson about building math enthusiasm here! “The fun of topics like this” is only legible to kids who are already into math!

One thing you’ll notice if you look at more of Mike Lawler’s blog is that he is consistently very optimistic and upbeat. Trying to cut that down with pedantic cynicism based on your own projected idea of his intent is pretty sad.

The context here is one dad who does frequent (weekly?) Socratic-style math lessons with his kids as a long-term family ritual, where they explore a broad range of topics both inside and outside the usual math curriculum.

This is not supposed to be an isolated example problem you can just drop down on a completely unprepared student and forever change their life in 10 minutes, and nor is he suggesting that.

You're absolutely right. My favorite illustration of this is history. A lot of Americans learn about things like the history of U.S. colonial rule in the Philippines and say, "OMG! If only they taught us things like this in high school, I would have been so fascinated and engaged! But my stodgy old teachers didn't want to teach us the controversial stuff that might have challenged our naive views about our country and our government."

But... they did, for precisely that reason. And you probably wrote down the right answers about U.S. colonial rule in the Philippines on quizzes and tests, but at age fifteen you weren't ready to care. "People a long time ago did stuff that my teacher thinks is sooooo interesting, blah blah blah." Those stodgy uptight teachers, the reason you thought they were so stodgy and conservative was because they tried to make you learn about U.S. colonial rule in the Philippines.

That's the way our minds work. We can overlook something right under our noses a thousand times if we aren't ready to see it, and then as soon as we're ready, it blows our minds.

There was very little discussion of US actions in the Philippines in my middle school / high school history courses. There was some coverage in 10th grade world history, but the 11th grade US history course pretty much skipped it.

I can remember as a 15–16 year old high school student having a discussion about this with the teacher and other students, because we (the students) thought it was a serious oversight which left a whitewashed impression of the history of US international relations.

In general, the US and its military are consistently treated as “good guys” in American high school history courses, even when discussing events where that summary is insupportable by dispassionate analysis.

I can believe that it was different in other places. In fact, it's probably different at my old school now that conservative parents have been taught to be vigilant and constantly enraged about what their children are learning. Still, I think it's noteworthy that my old classmates remember our teachers as being uniformly conservative and narrow-minded when in fact we were reading bell hooks and examining John Donne's religious poems for sexual imagery, and that they have conspiratorial notions of teachers hiding information from us that they in fact tried very hard to teach us. (Tuskegee airmen, boarding schools for Native Americans, etc.) Science, too, I remember every single science teacher drilling into us that all scientific theories are incomplete, provisional, often based on limited data, and likely to be improved or even disproved in the future, and the students who sat in those classes with me remember us being brainwashed to think scientists are omniscient and infallible.

I'd have to agree here. Show this to a classroom of students and half wouldn't even give attention to an introduction.

That probably has more to do with the classroom setting than the material. This boy is engaged because he’s learning from his father, one on one. The classroom disengages kids because they don’t get enough attention.

He's probably also one of the minority of students who are interested in maths. Most students have very little interest in it.

I homeschooled my son in math and I found he was fascinated by the way repeating decimals formed cycles. I'm sure that this reinforced his skill at long division.

I think may be more fun to do than to watch somebody else do it.

In my experience some people just love numbers, myself included. I could spend all day looking at various patterns of prime numbers, server metrics, etc.

Other people just.... don’t care numbers at all. Which is really disheartening when you find something really cool and everyone else doesn’t even listen. :(

Gauss, too, was excited by the way decimals formed cycles as a kid, and he went on to invent modular arithmetic to completely explain the phenomenon!

Seeing how that kid went about that problem, seeing how interested he seems, makes me want to teach. It's impressive how natural the discussion was with the kid, the two were on exactly the same page throughout the entire discussion. This video doesn't really show that all kids can get this interested in math, but it does show that for the right kids, of which I suspect there are a substantial number, we can be teaching concepts much much earlier.

Perhaps an easier way would be to just do normal long division just in base 2.

An easier easier way:

  1/3   =   0.3333...   =      0.????...b
   *2   =   0.6666...   0 ->   0.0???...b
   *2   =   1.3333...   1 ->   0.01??...b
   -1   =   0.3333...
   *2   =   0.6666...   0 ->   0.010?...b
  etc.

This is insightful, but hard to read.

Essentially:

  1/3 * 4 = 4/3
  4/3 = 1 + 1/3

So, working backwards, our number can be more and more closely approximated by repeatedly adding 1 and dividing by 4 - or in binary, prepending a 1 and shifting two places right: 0.01010101...

Nice. Maybe an easier^3 could be: 1/3 = 0.xyz 4/3 = 1.xyz Meaning (shl,2) leaves the same digits after the decimal point. So it must be 0.010101...

This actually is the long division algorithm. Usually the positional system hides away the powers of 10 (or 2 in this case) so we can do it mechanically and fast. He is just going through the algorithm explicitly.

Flagging as I was redirected in Safari to a malware fake Flash download.

I’m not redirected when I open it in Safari, FF, or Chrome.

I'm not getting it now either. Probably got hit with a rotten ad. Unflagged.

Same here, for what it's worth -- I got redirected to a fake antivirus download (also in Safari), but only on the first load.

Thank you for update.

That guy knows how to teach.

He's a great dad. Gives me warm feelings

I loved seeing the kid do this. When I was 12 my dad gave me math problems (including long division) in all sorts of bases (he started with hex, octal, and binary but went on to 3, 7, 27, etc). Sadly this was pre IEEE 754 -- I could really have benefitted from that!

1/11?

Exactly, I thought the same thing myself.

See, that wasn't so hard!!

I'll be here all week, try the lamb.

If this kid pursues a career in tech, he's going to crush his whiteboard interviews.

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