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Comment by wnevets | Hacker News Reader

I know some of those words. Anyone have a ELI5?

Take a simple differential equation as an example, like dy/dx = x. To solve this we need to find a function y(x) whose derivative is equal to x. This particular differential equation is well-behaved, and the solution is simply 0.5*x^2, which you can verify using basic calculus.

Not all differential equations are nicely behaved. Many do not have analytic solutions at all, meaning that we can't even write down a function that satisfies the equation. However, such equations can still be solved approximately using computational techniques. This can be incredibly difficult and computationally expensive (note the huge resources required to achieve this breakthrough) but can produce very useful results.

How many 5 year olds do you know that understand "well behaved differential equations" and derivatives?

ELI5 is not for actual 5 year olds.

In this case it should be ELIHAHSPE.

Explain like I have a high school physics education.

They teach diffy-q in high school now?

I don't know. But I would imagine most high schoolers could at least understand what a differential equation is, if explained. Aside from if they could solve one.

I did derivatives and integrals in my highschool calc course, circa 2007

Which order were they taught in?

I had the same curriculum but was utterly bewildered by derivatives being the first topic. For the simple reason that until that point I had habitually looked at "wholes" in the external world, only then to wonder "what kinds of things progressively make it up?"

I feel like to derive something, you start with the assumption that you know what you're talking about fist. Yet the thing is actually the sum of its parts. Therefore integration seems more natural at first, and only then can things similar to it be derived with confidence.

So the teaching order seemed backwards. I wonder if anyone has felt the same way.

Yep! Archimedes was essentially doing integrals 2000 years ago. He got close to infinitesimals, and centuries later we had derivatives and limits. It's strange to teach them in the reverse order (i.e. Most sophisticated theory first, like teaching the reals before the integers).

I have an online series that starts with the historic order which you might like:

http://betterexplained.com/calculus/lesson-1

Thanks!

Every school I've ever been at in British Columbia (High School, College, University) - starts with derivatives, and then moves onto integral calculus.

They start with the calculating slope on a curve f(x) being lim h->0 f(x+h)-f(x)/h - spend a few weeks deriving various derivatives, show how you can find tops/bottoms of curves (derivate=0), talk about limit theory a bit, take a bunch more complicated equations derivatives.

Then, once that's figured out - take the inverse, and look at area's under curves, volumes, etc... My brain lost it at integration by parts (so many parts) - too much memorization, and so came an end to my mathematics education in that space.

I'm happy they were taught in that order, mostly on being exasperated with having to memorize all the integration by parts formulas.

Thankfully, you don't have to remember the integration by parts formula, just the usual derivative of a product and rearrange.

EDIT: Ordinary differential equations, yes - we do here in .au, at least in Maths C (advanced maths) in Queensland. Partial differential equations, the kind that are very useful in the kinds of physics simulations discussed - not so much.

And even with that background, our foreign lecturers were regularly disappointed at our lack of mathematics competency in University ("Now I have to waste the next 4 weeks teaching you things we learnt in highschool in my home country before I can move on to what this subject is actually about").

These were Asian/Indian and a Ukrainian lecturer, that I recall.

Ah Russian math lecturers in first year courses. Always making it perfectly clear that as far as they're concerned they might as well be lecturing to a bunch of 8 year olds.

I always wondered if they just said that, as part of bluster. Hard to believe entire classes of graduate math students are at a lower level than all 11th grade Russians. (It wasn't just the first year undergrads I heard of getting scolded by Russian lecturers)

I know Russia values math highly and does push their students, but there's a limit to believability.

Having worked with a few asian/eastern engineers, I do believe that a number of things conspire against western maths education: our culture doesn't value mathematics competency (in some circles people are even afraid to admit to an interest); the way we teach maths here in .au is bloody awful (standardized tests make teachers hate their jobs); and teaching generally is a much less respected/lower-paid profession relative to other occupations compared to better-performing countries (so our quality of teachers is much worse).

I had differential equations in high school. I must say it proved to be very helpful later at university.

> ELI5 is not for actual 5 year olds.

True in general, but it would be nice to meet the five-year-olds for whom it's the right forum.

Agreed, but I was implying that he didn't simplify it nearly enough. I actually understood the parent post more clearly than this ELI5 version.

The real math that describes the behavior of fusion reactors is too complicated to actually carry out, so physicists have to make some simplifying assumptions. They try to choose assumptions so that the results they get are still valid, kind of like when you say, "Keep the change" at the grocery store. You assume that giving up small amounts of money on occasion won't make you go bankrupt, even though you're not actually adding it up all the time to keep track of how much you've given up.

It turns out that one of the simplifying assumptions that physicists have been making over the years does change the result. Giving up the "spare change" does make you "go bankrupt." In this case, ignoring small-scale turbulence makes you lose a significant amount of heat. But figuring that out required some really hairy math and a butt-load of computing power.

Is that simple enough for you?

People don't say "keep the change" at a grocery store.

I do. I don't like small coins.

Yes! That was way better, thank you!

You bet.

I'm reminded of this clip of Feynman talking about magnets: https://www.youtube.com/watch?v=wMFPe-DwULM

Maybe it's 5 in dog years

As you might know, turbulence is when simple streams of laminar flow (in say, plasma) turn into chaotic filaments and vortices. As a filament or vortex separates/stretches from your laminar flow region, it steals away heat/energy.

Scientists often assume that you can accurately approximate stuff by neglecting irrelevant parts of the physics (basketballs vs ping pong balls; protons vs electrons). Turns out that ping pong balls greatly affect the outcome and amount of heat/energy dissipation in the basketballs.

This doesn't surprise me too much, since critical behavior often happens in regimes where two separate aggregate effects become relevant. But the details are all still just a big mystery :)

P.S. someone posted a much better description than the OP. I'll reiterate: http://news.mit.edu/2016/heat-loss-fusion-reactors-0121

A fusion reactor needs a lot of energy (heat & electricity) in order to make more. But a big problem is that the heat wants to escape. (Think of when you hold something warm -- the warmth you feel is the heat escaping into your hands! How would you stop it from doing that?) Different kind of reactors try to keep the heat in in different ways, but several of them do it with big magnets, which basically can keep the fuel floating so it doesn't touch anything.

Now there are two main parts to the stuff inside the reactor, ions & electrons. Think of them as mac & cheese. When the reactor gets really hot, these bits start jostling around. (It's in the nature of hot things to want to move more, and really "hot" means that the little atomic components of everything are wiggling and moving faster and more excitedly.) Think of boiling the mac and cheese. For a long time scientists thought that the wiggles of the ions would diminish the wiggles of the electrons, because 1) the ions & electrons want to be near each other so they form a clump (like how the noodles absorb the cheese but waaaay stronger) and 2) because each ion/noodle is way bigger than each piece of cheese powder/electron, so its wiggles should be way stronger.

Now to figure these things out, scientists have to use computers to predict how it all might work. But the formulas they use don't have a single answer they can just solve by hand. Instead the computer can take a guess and then spend a lot of time seeing how good the guess was, and trying to make it better. A computer can do things fast, but it's hard because when it does math, it's only figuring out how a single piece of cheese dust moves at a time! There are so many little pieces and knowing how a few cheese dusts move won't give us a good idea what a big pot of mac n' cheese is like. (Could you learn how sand feels by holding one grain?) So they have to keep the computer running until it can tell them what a lot of cheese moves like. Even harder is that they need to watch the cheese move for a long time to make sure it's "stable". (For example, if you put mac and cheese back on a hot stove it might be quiet for a bit before suddenly a big cheese bubble burst and splattered everywhere. We need to know if there are bursting bubbles or not, so just looking for a second won't be enough to tell us.) So the computer also has to do this guessing for many little tiny moments, until they add up to a longer amount of time. Then they can figure out how the sauce behaves when you leave it on the stove for a while.

Ultimately these scientists found that the ions & electrons don't act exactly like we thought. The heat actually causes the electrons/cheese to stretch out into long strands that pull away from the main blob! Also when the cheese starts swirling around, instead of bumping into the noodles and stopping, they can bump strong enough that the noodles and cheese all start swirling together crazily. These two things give us big clues on why our reactors won't stay as hot as we want them to, because they explain why the mac and cheese gets so wiggly and wild, and with the discovery we can now try to find new ways to build better reactors that work better.

All the guessing by the computers was so much work it would've taken a single computer 15 million hours (over 1700 years!), but they got 17000 computers to all work as a team and give them answers in about a month. Then the scientists could get a couple answers in a year, which made them feel more confident that they probably did things right.

NOTE: Totally not a physicist or anything, and I probably started with a bad analogy, but wanted to try this as a writing challenge. Also I know you probably didn't want it this simpified, but I tried to take "ELI5" at face value for once.

I don't know if an actual 5-year-old would be able to understand this, but kudos for the attempt!

Haha I agree. ELI9ish-and-already-quite-into-science?

Fusion is hard.

[meta] - I love the crosspolination between HN and reddit wrt many things. The thought that some random off reddit invented the idea of ELI5 And now its a valid comment request is fucking awesome. The internet evolved a bit when they invented that.

The "Explain it like I'm five" idiom was not invented by Reddit.

I didn't know this, thanks. Where was it invented?

I don't know, I've just heard it before Reddit existed.

You know that opening a Poke Ball releases a tremendous amount of energy, because on television they show a big flash of light. Imagine if you could open a thousand poke balls every second. We call that fusion.

What MIT did was make it easier to open all these poke balls in a sustained way. This is important because once fusion is sorted out, our political leaders like Ted Cruz could use all that energy to do really interesting things.

One side effect is that a lot of poke monsters will be released as well, which could cause problems...and so we as a society need to think about the long term ramifications.

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