The Itch to Explain (Everything I Know About Trigonometry)

This post has two parts, one about math and one about explaining.

Part 1: commentary on the following animation.

A friend posted this on Facebook:

This illustrates pretty much everything I remember about trigonometry. Pick a point on the unit circle. The x coordinate of that point is the cosine of the angle, and the y coordinate is the sine. It's as simple as that: cosine is the horizontal leg, sine is the vertical leg. For any point on the circle.

If I recall correctly, everything else in trig derives from that. For example, if you forget the following formula, you can use Pythagoras to re-derive it in your head:

sin2 + cos2 = 1

Granted, not all trig formulas are so easy to reconstruct off the cuff.

One other thing: angles in trig are measured in radians, which is the length of the arc that is swept out on that circle. Since the circumference of any circle is 2πr, the circumference of the unit circle is 2π*1, which is 2π. So for example by drawing the picture you can remember that sin(90°) = sin (π/2) = 1 (it's the point at the very top of the circle, with x = 0, y = 1).

Part 2: tangential thoughts (so to speak).

I swear, this is the kind of thing where I could spend hours and hours making a 5-minute explanatory slide presentation and video. Don't ask for anything more advanced math-wise; this is all I know about trig. And I'm positive you can already find this exact explanation for free at Khan Academy or Quora or Stack Exchange or a million other places. See also Vi Hart, whose videos remind me that it's not all about bells and whistles, and that clear, insightful explanation with clever use of low-tech is extremely compelling. But still, if the planets that govern my whims and impulses were to align, I'd totally do my own take on the unit-circle explanation. At least I think I would.

In my dream scenario, I'd fuss over language and graphics and pacing. I'd like some way for people to easily jump around and either skip or re-watch some portions. I know some people learn better when they hear, so voiceover would have to be part of it. I guess that means subtitles too, and if I feel really ambitious, translations to multiple languages.

Along the way, my math-y friends would say, "You know, there's a MUCH easier way to make that animation in seconds rather than hours, using Mathematica or whatnot" (or a Swift playground — ooh!), and my brain would hurt a lot learning the whatnot, and the brain pain would make me regret my initial eager impulse to share. But hopefully I'd muddle through.

During "user testing" (as we software people call it) I'd learn about areas that people commonly have trouble understanding, and I'd reframe the presentation to address those areas.

It's crazy to want to spend all that time on something people can already get elsewhere. And truth be told, talk is cheap, and I wouldn't be quite as ambitious as I claim. But I do love that I know this one cool thing, and although I often misjudge my own ability to communicate, maybe I can help you know it too. If not you, maybe your kid. Or if you are a kid, maybe your parents. Whether you're a "math person" or not, if you understand the above animation then you understand the single most important thing about the scary subject of trigonometry.

There are a few isolated nuggets of knowledge like this, not all about math, that I get the itch to explain. Some, I'm pretty confident about. In other cases, the idea would be to explain what I think I know, and I'd be looking for feedback and corrections. Maybe I'll take up "explaining" as a hobby. Maybe I'll make "explanations" the way amateur carpenters build cabinets. And just as a carpenter tries to make a better cabinet each time, maybe I'll take multiple passes at explaining the same thing if I feel the need.

By the way, I'd love to be an amateur carpenter too, and make actual physical stuff, but who has time for that?

Trying to Understand Obesity and Nutrition

I've been bugging friends in various forums about what I've been finding out about weight loss. One thing I am sure of: there is a huge amount to question, challenge, and reconsider when it comes to what we know about obesity and nutrition. We have so much to learn, and so much to unlearn, having discovered that what we already learned was bogus. Doing good studies on human subjects is very expensive, but so are the costs of health care for metabolic conditions. And confounding it all are people jockeying for political advantage of some kind, or looking to make a buck. There's always a buck to made in areas that are both deeply important to people and highly confusing.

I frequently feel overwhelmed, and I struggle with my intellectual limitations. For one thing, I want to get things right, but my biases are strong. And when I try to read about certain topics — recent ones are statistics and chemistry — the part of me that is "nerd" completely fails me. My eyes glaze over, and my brain folds its arms and says "You should have studied this stuff when I told you to 35 years ago."

For now I will keep trying to understand, and will keep spouting off and asking for correction and feedback. My attention span swings like a yoyo, but so far it seems to keep swinging back to this topic.

Biggest Loser

The NY Times article about the Biggest Loser contestants has been showing up in various places I follow. I've only skimmed it, but my preliminary reaction is "I'm surprised anyone's surprised." Which I know sounds dismissive, and I know it's annoying when people say that. But time and time again it's been shown that starvation diets don't work long-term.

It's old news that your metabolism slows down when you starve yourself. That's partly why simple calorie restriction doesn't work. That approach might be fine if calories-in and calories-out were independent variables, but they are not: reducing the former affects the latter. If you simply starve yourself using blind calorie counting, your body will change its energy budget, and now you're chasing a moving target, on top of which you feel crappy.

Another fallacy in "calories in, calories out" is that most people take that to mean calories in and out of the body as a whole. But what we care about is calories in and out of our FAT CELLS specifically, and that simple change in perspective leads to useful ways of reasoning.

We KNOW that WHAT you eat — as in protein vs. fat vs. carbohydrate — has a large effect on how your body meets its energy budget, in particular, how much energy it gets by burning fat. We KNOW that carbohydrates bump insulin, and insulin is the primary driver that tells fat cells to get fatter and more numerous. None of this comes from some recent magic discovery. It's old, boring, first-year-med-school news [1]. But I can't tell from the article how much of this knowledge was applied to the Biggest Loser contestants.

By the way, it also seems there is a lot of variation among individuals in how they respond to a given intervention, which to its credit the article does mention.

The findings about levels of leptin and other satiety hormones are interesting. My current understanding is that we still have a lot to learn about the hunger and satiety hormones, but they're a promising avenue of research. My understanding is that fat cells secrete leptin, which means it should be no surprise that huge decreases in fat caused the subjects' leptin levels to drop precipitously. I've seen a claim [2] that insulin blocks leptin from getting its message to the brain. But I hesitate to make any strong claims about hunger and satiety hormones — the research is much more recent than what we know about insulin.

My impression is that the Biggest Loser show took an approach to weight loss that has been proven to fail, and dialed it up to 11 for entertainment value. That's my impression, but I'm open to learning that I'm wrong. And if useful science can result regardless of that, then at least that's a good thing.

[1] At least that's what I've read. I'd be curious if any of you who are doctors or know doctors can confirm. One of the books I have shows a chart from a med school textbook that supposedly supports the "first-year med school" claim. I'll try to find it. But whether or not it's strictly true that any rookie med student "knows" this about insulin, I'm pretty sure it's long-established fact.

[2] The Skinny on Obesity (Ep. 3): Hunger and Hormones- A Vicious Cycle

My caveat on this video is that Lustig has been criticized for his claims about fructose. I'm not sure yet how to evaluate the criticisms. But what he says about insulin jibes with everything I've read. Again, I'm open to learning that I'm wrong.

Hurry Up and Copy Faster

[I posted this on Facebook today and felt compelled out of self-absorbedness to repurpose it as a blog post.]

From the department of "'But enough about me…' is not a phrase in my vocabulary":

You guys are killing me over here. So much fascinating stuff today, so many articles I want to read and respond to, so many interesting updates about your lives, so much plain old fun. I open my Facebook timeline and my brain is like a dog bombarded with a million amazing, irresistible scents. That dog is going to starve to death if it doesn't pick a rabbit to chase.

On top of that, my mental bandwidth is so narrow. It feels like dial-up Internet when what I need is fiber-optic. It's like in a spy movie when the spy is stealing computer files, and the bad guys are beating down the door, and you're watching the download progress bar, thinking "Argh, HURRY UP AND COPY FASTER so the spy can escape!" I feel like that during a high percentage of my waking hours. My progress bar always feels like it's moving too slow relative to the urgency of my impulses around information.

My "bandwidth" is frustratingly low in both directions. In the incoming direction — I'm not a great reader. I have to reread a lot, and it takes me more effort than your average bear to put together a mental model of what the heck the writer is saying. Maybe I should work to improve on this, to learn to read. That said, on rare occasions when that mental model interests me, I will turn it over and over in my head long past where most people would have been tired of it. I fiddle with it, critique it, boil it down. I try to think how I would communicate it to someone else. For better or worse, I am glad I do that. I value my fussiness — I think it means I care about getting things right — though I wish I could direct it more selectively and productively.

In the outgoing direction — I often struggle to express myself in words. Takes me way too long to compose simple email replies. Yes, writing is partly an act of discovery, and a certain amount of writerly squirming is necessary to figure out what I think. But sometimes, honestly, just spit it out already. No one is going to judge, remember, or necessarily even notice this thing I'm writing. And if they do judge, well hey, it's a free American country [1], I can say what I want. This is also something for me to work on, the spitting it out already.

There's a flip side, which is that I can babble at length once I do get going, which is not great in terms of having good conversations. It's both a social skill thing and a cognitive thing, I think.

All I really meant to say is, I'm trying to rush through my Facebook-skimming today — a few quick likes and shares, and then step away, and get back to various tasks I'm behind on. But you guys make that difficult.

[1] I could swear this is a line from Taxi Driver, spoken by Peter Boyle's character. Can't seem to find a reference online though, and the phrase is not in the script that I found. [Update: My sister thinks it was Archie Bunker who said "free American country", and I think she's right.]

Fresh Off the Boat: Two Women

I've liked all episodes of Fresh Off the Boat except the one mentioned in this NY Times article, in which "Eddie develops a protosexual fascination with a blond, large-breasted trophy wife who has just moved into the neighborhood". I did not like how sexuality was treated in that episode, and I can see how the real Eddie Huang would feel betrayed by how it trivialized his deep connection with hip hop. I mostly try to pretend that episode never happened — mostly. The episode has one saving grace, in that the busty blonde in question, Honey, is a refreshingly sympathetic character, sweet but not ditzy. She isn't there for other characters to take cheap shots at.

By contrast, I really dislike how the grandmother's character is written. Every time she appears I dread what she's going to say. She only speaks an occasional line, always in Mandarin with subtitles, and always something weird or offbeat. No one ever replies to anything she says. In several episodes Eddie basically uses her as a prop. To me it seems the intended humor is a combination of:

  • "Ha, crazy old lady",
  • "Ha, crazy old Chinese lady", and
  • "Actually this line is not funny at all, but she says it in Chinese, and that's funny."

In Episode 11 ("Very Superstitious") the grandmother finally gets a few reasonable lines, and one of the kids actually asks her a genuine question. I swear, a little part of me cheered when that happened. But in the same episode there's an awful moment when the parents accidentally walk in on her while she's on the toilet. Talk about a cheap shot.

I hope the lines Grandma got were a sign of better things to come. If not — if the writers aren't going to give her basic dignity or a real personality — then I'd rather she be written off the show, as brutal as that sounds.

Fresh Off the Boat: Enjoying the Book vs. Enjoying the Show

I highly recommend Eddie Huang's autobiography Fresh Off the Boat, on which the TV sitcom is loosely based (more on that in a moment). Huang's writing is raw, passionate, and funny. Just about every page of the book has got something interesting on it. In that respect, I find it's like reading Richard Feynman's collections of stories about his own life.

Among his many adventures, Huang writes about hustling sneakers on the Lower East Side and turning that into a way to support the Obama campaign. He writes about his ill-fated attempt to get hired as a beat writer for the local newspaper (I'll never hear the phrase "that face" the same way again). He writes about being stomped day after day, Rudy Ruettiger-style, playing high school football.

In a more serious vein, Huang writes about the deep influence hip hop culture had on him, and how it spoke to him as an outsider. He writes about his lifelong love of food and his passion for cooking. He also writes about his experiences with racism and about the violence he grew up with, both on the streets and at home, where Eddie and his brothers were routinely beaten by their parents.

I see loose parallels with Bruce Lee in the life stories of both Huang and his father, in that all three men started as Chinese street punks and grew up to achieve versions of the American Dream. I'm not the only one to see this connection — a friend pointed it out to me recently.

Part of what I find fascinating about Huang, in both his writing and the bits of him I've seen on YouTube, is how strikingly he differs from stereotypes of Asian males — again, a very loose Bruce Lee parallel.

At this point, if the only "Fresh Off the Boat" you know is the TV show, you may be wondering if I'm talking about the same Eddie Huang. Street fights? Domestic violence?

The TV show is indeed very different from the book. By comparison, imagine being told The Cosby Show was based on The Autobiography of Malcolm X. (Please note: I'm not comparing Huang to Malcolm X by any means; I'm just trying to give an idea of how the show might shock someone who was expecting the book, and vice versa. Also — full disclosure — I have not actually read The Autobiography of Malcolm X.)

Huang has spoken out more than once about how the show has sanitized and trivialized aspects of his life that are important to him:

I can understand his disappointment in the show, but I can also understand the question "What did you expect?" Huang admits he naively thought he could "change things" much more than he did. Perhaps this is yet another similarity to Bruce Lee, in that Huang had about as much chance of telling his story in his own way as Lee did of starring in Kung Fu. Who knows, maybe someday there will be an Eddie Huang 2.0, just as there was a Steve Jobs 2.0, who will take what he's learned from bitter experience and find new and bigger ways to change the world.

I'm glad Huang did push his way into the show to the extent he was able to. He tells a story about how one of the writers thought it would be funny to have a line about how Huang's grandfather used to castrate pigs with a stick. Huang's actual grandfather sold mantou (Chinese buns) on the street, took a factory job from a customer who admired his work ethic, and eventually took over the factory. Huang did not appreciate the Boratification (a term I just made up) of his grandfather, nor the fact that the writer could not understand why Huang was horrified. The line was eventually changed.

I enjoy the show. With one exception, I find all the characters very likable and funny. I enjoy the show separately and differently from how I enjoy the book. For better or worse, it is simply a different thing.

In the months leading up to the show's premiere I wasn't sure what to expect from an Asian family sitcom. Does that sound strange? What's so hard to imagine about a network sitcom? It just goes to show how the absence of Asians on TV had affected me. Fortunately, by the end of the pilot episode I was cured of that befuddlement. The show seems as "normal" as any other TV show, and that feels good.

Part of what feels good is not only seeing faces like mine, but seeing memes from Asian life being aired in mainstream American comedy. In one episode, the mom wants to use "white flower oil" on Eddie's broken arm. It was a passing reference, and I doubt it stuck in many non-Chinese viewers' minds, but it was there. Who knows, maybe it will be repeated enough that white flower oil will be recognized for what it is: my people's tussin, my people's Windex.

Do I see myself in the show? Not really, but I've seen comments from friends and strangers, Asian, Jewish, and black, who say they do, and I like that too.

I'm Going With Goat

There's some confusion as to whether this Chinese New Year is the Year of the Goat, Sheep, or Ram.

There is some cultural variation which might contribute to the confusion:

In Vietnamese, the sign is mui, which is unambiguously goat.[7] In Japan, on the other hand, the sign is hitsuji, sheep;[7] while in Korea[8] and Mongolia the sign is also sheep or ram. Within China, there may be a regional distinction with the zodiacal yáng more likely to be thought of as a goat in the south, while tending to be thought of as a sheep in the north.[9]

According to a scholar cited on, Goat is likely more accurate for Chinese New Year:

The Chinese word yang in oracle-bone script – the ancient characters found on bones used for divination in the Bronze Age – looked like an animal with two horns and a pointy face, said Professor Ho Che-wah, head of the department of Chinese literature at Chinese University.

But the character could be translated to goat, sheep or ram in English.

Ho said that while sheep had a long history in Chinese society, the country's culinary past suggested the goat as the most likely animal to have been included in the zodiac.

In modern Chinese, the two-horned word in question is 羊 (yáng), which Wiktionary translates as "caprid, eg. sheep, goat, antelope". (My scientifically-minded friend Roger calls this year the Year of the Caprid.) As of this writing, an image search for "羊年" (yáng nián, "year of the 羊") returns mostly goat- and antelope-like depictions of the animal. Here are the first two search results:

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Based on all the above, I would go with "Year of the Goat", but I don't feel strongly enough to get religious about it.

The SCMP article mentions that the Hong Kong Tourism Board is thinking "outside the box" and going with Sheep-of-non-specific-gender:

[O]ne character appears to be male with blue wool and the other is female with pink wool, a dress and heels, meaning it could also be the Year of the Ram or Year of the Ewe.

We could think even further out of the box and leave this planet altogether. How about Year of the Tauntaun?

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Eddie Murphy

I didn't pay much attention to SNL's 40th year celebration until I saw a discussion on Facebook about Eddie Murphy's brief appearance. I learned that to many observers he had seemed nervous, awkward, downright afraid. Some people thought the cameras had been cut off early to spare him from further embarrassing himself.

After watching both edited and unedited versions of the video, I say: bullshit.

Chris Rock's introduction was 100% excellent. It was heartfelt, it was funny, it was beautifully written, it was delivered with perfect energy and timing, and it honored Eddie without getting sentimental.

When Eddie came out and spoke he didn't seem afraid to me at all. He seemed mature, dignified, and respectful. Did he have it in him to electrify us like he used to? Did he have the desire? Maybe, maybe not. It doesn't matter. He wasn't there to perform for us but to speak to us as himself, which in a way I value even more. Anyone who thought Chris Rock was the intro to The Eddie Murphy Show had it wrong. Chris Rock was the show. He presented Eddie with a verbal lifetime achievement award, and Eddie accepted it graciously.

As for being cut off early — it seems to me that in the unedited version Eddie was cut off late. He says "Let's have some more show," gets the audience applauding by clapping his own hands, and turns to direct our attention to the stage as if to bring on the next thing. It seems clear to me the camera was supposed to cut away during the applause. Of course I don't know for sure, but it looks a lot like the editing covered up the director's failure to cut away on cue rather than any fault of Eddie's.

I don't get why so many people are treating Eddie like a sick, broken man. If he is, I don't see it. And I reject the notion that Eddie Murphy needs to get on some road to artistic salvation that happens to consist of making us all happy like he used to. He doesn't owe us his old laugh, he doesn't owe us a few gags and impressions, he doesn't owe us thrills of any kind.

Eddie Murphy was huge to me growing up. I'm glad stratospheric fame didn't do to him what it did to Michael Jackson and Elvis. I attribute that to discipline and impulse control, maybe combined with a lack of certain self-destructive impulses in the first place. Eddie Murphy has taken care of his body, his mind, his finances, and as far as I know his family. (I consider it a good sign that I don't know.) If he chooses to give us more of himself I'll be delighted. Until then, I respect him for living life on his own terms, and I refuse to join the pity party.

The Arrest of Sureshbhai Patel

NBC News:

An Alabama police officer was arrested on an assault charge Thursday and could be fired for slamming a 57-year-old Indian man to the ground last week, leaving the grandfather partially paralyzed.

I try not to rush to judgment about cops' use of force, but in this case it seems clear that what Officer Parker did was excessive. Watch the video and see how fast Patel's feet flew out from under him. One foot was almost at shoulder level at the moment when his face hit the ground. Although one grainy, silent video is no substitute for having been there, it's hard to imagine that Officer Parker perceived a degree of threat that warranted that amount of force.

Frame 1Frame 2Frame 3

As far as I know the Madison police department is handling this properly so far. Of course it's terrible that this happened in the first place, but I'd like to believe this police department is setting a positive example by showing it has standards that it takes very seriously.

This all started with a civilian calling 911 while following Patel in his car — a grimly familiar scenario. I suppose it's also a positive that this time no one got shot.