XKCD: It's more than a comic

I get the idea, though I hadn't actually heard of tau. And I guess I don't get it well enough to find it funny. Except maybe in the meta sense that it sparked an argument about which is better.

I've never heard of tau until now, but it makes sense to me. it's not so much better that it would be worth redoing math education from scratch, but it's one of those little "the world would be slightly simpler if we had done it like this in the first place" things.

Regarding the confusion, this is all pretty basic high school math, isn't it? Mostly geometry, a bit of trig and integrals were mentioned once.

Trig doesn't really go away when you get into higher level math or physics though. It just gets compounded into more trig, and if you can't remember it intuitively you're going to be double checking yourself a lot. Trig is only "just" trig if it's the highest level of math you take before you graduate.

Every couple of weeks or so, anyone who doesnt possess and engineering degree just has to say "meh" and pass on to another comic.

Among other mathematical quirks, I still expect that, any day now, the math textbooks will say that functions for sine and cosine need to have parentheses to indicate grouping. You know, so there's a clear difference between "sin x + y" and "sin x + y" that comes across even when the italics get lost.

Just treat sin and cos and similar functions as having precedence equal to a unary operator like "-" or "not". It's not really confusing if you have consistent rules. That said, a computer programmer would automatically use sin(x) or sin(x + y) because you have to enclose function arguments in parens... unless you're working with a language in which those functions are or can be constructed as unary operators.

Fun times.

edited 19th Nov '13 6:55:42 AM by Fighteer

Parenthesis make more sense, since I don't know what an unary operator is. I'd imagine most students won't either. People already have a difficult enough time learning math without ambiguities. Also that italics format doesn't work if you're doing the stuff by hand, since it's kinda hard to italicize with pencil and paper.

You have studied order of operations, aka precedence, in your math courses, right? It's part of basic algebra.

1. Parentheses
2. Negation
3. Exponentiation
4. Multiplication/division
5. Addition/subtraction

• -1 * 5 + 3 is calculated as [0] - 1 = -1, -1 * 5 = -5, -5 + 3 = -2.
• 24 - 2³ * 3 is calculated as 2³ = 8, 8 * 3 = 24, 24 - 24 = 0.
• (24 - 2)³ * 3 is calculated as 24 - 2 = 22, 22³ = 10648, 10648 * 3 = 31944.

Negation is a unary operator; it has only one operand. Most other operators are binary - they accept two operands. Operations at the same level of precedence occur left-to-right. You only need parentheses when you want to change the order of operations. Otherwise they are superfluous and should not be used.

Edit: I did some reading just now and it would appear that the precedence of unary - and exponentiation is ambiguous, with different textbooks and formula interpreters handling it differently. For example -3² is 9 in some applications and -9 in others. For that reason, it would make sense to use parentheses to guarantee the result that's intended.

edited 19th Nov '13 7:38:02 AM by Fighteer

The negative sign was never mentioned as part of the order of operations in any of my classes. It was always PEMDAS. Still don't see how making sin like that would reduce confusion as to if sin x + y is sin(x)+y or sin(x+y).

Also haven't taken a math class since 2007.

Yeah, I edited that in — unary operators are somewhat ambiguous in terms of precedence, coming before or after exponentiation depending on who you ask. http://en.wikipedia.org/wiki/Order_of_operations

They always occur before the MDAS part, though.

But the textbook approach to situations like sin x + y is to make it unambiguous with use of parentheses.

edited 19th Nov '13 7:43:09 AM by Fighteer

Also, if I'm not mistaken, the multiplication/division and addition/subtraction levels are to be done from left-to-right - that is, if you have 6/3*2, you evaluate it as (6/3)*2 (which equals 4) and not 6/(3*2) (which equals 1).

Anyway this week's What If? is about stirring tea, and if you can heat up the tea just by doi- wait that was last week's where's the new one

Snzzzzzzzz....

I said that: within a given level of precedence, operations occur left-to-right. It becomes easier to understand why this is if you treat division as inverse multiplication and subtraction as inverse addition, so 6 / 3 * 2 becomes 6 * 1/3 * 2. Then the order of operations doesn't matter.

You're right, I just missed it. Sorry.

Okay, for real this time: Loneliest Human

edited 19th Nov '13 8:49:51 AM by ShadowHog

I was just about to post it. Surprisingly few jokes here, except of course for the obligatory dig at Moon landing conspiracy theorists and the "To Earth" sign.

I will quibble not with his methodology but with the idea behind it. While the physical distance of the Apollo command module astronauts was the greatest in history, they were hardly isolated — except for the short period when they were in the Moon's shadow, they had radio communication with their fellow astronauts and everyone on Earth.

True psychological isolation comes not just from physical distance but from the inability to communicate with your fellow humans, and those Antarctic explorers, marooned sailors, and such were vastly more out of touch than any astronaut could ever be.

edited 19th Nov '13 11:40:56 AM by Fighteer

Sure.

So then the question is probably along the lines of "which individual was out of communication with any others for the longest time", which is a hard thing to answer rigorously. Probably someone who just goes out into the wilderness somewhere and stays there.

You'd also have to decide what constitutes "communication."

For instance, let's imagine a tribe in Papua New guinea. The tribe believes that they must have a guru who prays and meditates all day every day for the tribe, and everyone else can go about their daily business without thinking about religion. The guru is chosen by some arbitrary and almost entirely random sign, as a child, and the child grows up with a vaguely religious education and knowledge that they'll be the guru. When the child's grown up they're put in a locked room, with just a hole in the door for food and water, and until they die of old age they spend their life without any connection to the world outside the room except the daily tray of food and water, which is passed through the hole in the door without a word.

Does the food constitute communication? If it doesn't this guru will almost certainly be the most isolated person on the planet; but if you do count this supply of necessities as communication the guru enjoys human contact every day, and is clearly not isolated.

...Did that ever actually happen somewhere? Because I cannot imagine that ending well.

Is it me or does the last image have no alt-text? I was expecting a joke about him breaking his reading glasses in reference to the classic X Files / Outer Limits episodes.

It's not just you.

No, I invented it as a thought experiment to illustrate a possible boundary where we'd have to define what constitutes "communication."

I placed it in Papua New Guinea because it's a fascinating place that contains a great number of tribes that are not well known, so it's a relatively plausible place to find a new tribe with a bizarre (to us) tradition.

That said I don't think my scenario was really all that plausible - I agree that it would not end well, as the isolated person would probably "break" somehow - either literally, out of the "cage," or figuratively, by losing his mind. Also, the process by which a child is "selected" would have to always produce a child whenever the old (probably not all that old) guru happens to die, and even then you'd have a transition during the child's "education." Either that, or you'd have a supply of "selected" children available at all times, including at least one whose "education" is complete.

I'm sure there are dozens of other holes that you could poke at my scenario, and it's almost entirely impossible that it'd really happen.

Then again, I know that there are people in the Philippines who have themselves crucified (but usually not mortally) every year because they want to commit to their devotion to Jesus, and I can say with a pretty high confidence that I wouldn't have believed that if I didn't read about it in a reliable source, and I wouldn't have been able to conceive of it myself, at least without trying to think of a tradition that almost no-one would believe. I would argue that a scenario where someone asks to be crucified as a display of devotion to a belief is only slightly less incredible than the scenario I invented. If the cause of the request for crucifixion wasn't religious I'd say it's less likely than the isolation of the guru I invented, though this of course is just my opinion.

edited 19th Nov '13 4:36:18 PM by BestOf

Hmm, I dont have the link right now, but wernt there several ex-Japanese soldiers who continued at their post for decades after Imperial Japan lost the war? That's the most extreme real life examples I can think of...

There were, but I think they were usually in (small) groups, so they weren't isolated from each other - until all but one had died, obviously.

That said there might very well have also been individual soldiers who went through that alone, as well.

EDIT: Of course I had to find out.

Some soldiers were discovered as late as 1974, but none of them lived in isolation from the end of the war to that point. I looked at each case that had a Wikipedia article, and it seems they either were in groups for most of the time or had some contact (mostly hostile) with the people in the islands they hid in.

Teruo Nakamura was, of the ones I found, the one that spent the longest on his own: from 1956 to 1974. Before 1956 he had been part of a group (that later surrendered,) but he left the group because he thought they had tried to kill him. After that he was, as far as I can tell, on his own until he was discovered in 1974.

edited 19th Nov '13 5:07:47 PM by BestOf

White Beret Guy's being cheerfully goofy again.

That… that's a soup outlet.

…

Imma gonna go lie down while I try to figure out the logistics of that.