>Actually seeing that effort through to the finish line can be a vivid demonstration for students of this predictive power of what might otherwise be viewed as “merely abstract” and not concretely useful mathematics.

This is how I feel about engineering.

If you design something, prove it out with logic and math. It will work.

Or you will learn where you were wrong.

>If you design something, prove it out with logic and math. It will work. >Or you will learn where you were wrong.

In other words, if you design something and prove it out with logic and math, sometimes it will work and sometimes it won't...

Honestly, pretty much. It has a better chance of working then just trying stuff though. For advanced stuff a thought out model can bring up success rate from 0.0001% to 50%. And when it fails, you will learn more from the failure.

Except that if you build something on a model that it is based on sound logic and math, it will have a much higher probability of working than otherwise.

Also, specific to Engineering, there are countless tools that help making sure your product will have a high probability of working as intended, anything from CAD tools, simulation tools (which it could be argued are a more automated way of applying logic and math), QA processes, etc.

Just on the point of simulations and not specifically being down on your suggestion of using them but thought people would be interested. I listened to a great podcast from Sean Brady, a forensic structural engineer, who said that if you can’t verify your simulation by doing the maths on paper then you shouldn’t be using it because you don’t understand how it is getting the results. He said that simulation tools allow engineers to make more mistakes faster than ever before because the simulations are complicated to set up and engineers tend to get distracted from what they are trying to simulate by tweaking the parameters until the simulation ‘compiles’ and feel they have achieved the correct result once that happens...

Doing the math by hand might work for some structural problems but isn't feasible for many domains

Yes and no...when learning about the LRFD (Load Resistance Factor Design) for structural engineering, we'd design a component (a portion of a floor, for example) and we'd size it for live loads (dancers), Dead Loads (piano), environmental loads, and NVH issues (the floor moving when people walked on it)

The last one there was more a comfort level thing...people like to not fall down to the next floor, but they also like to not feel AS IF they'd fall down to the next floor...to you overdesign to remove the vibration.

9 times out of 10, it was that NVH aspect that drove the design.

More that your model was wrong and your math needs to get better.

Yes.

And for 'discovered' things, there is no reason to make a mistake.

However, most of the time you are working on something that is New.

>However, most of the time you are working on something that is New.

So I was just thinking about that today. I just bought one of those ridiculous 'incline' rowing machines; as you 'row' it lifts your body off the ground to provide resistance (in addition to the normal rowing motions) - I'd bet money this design lasts rather longer than the type of cheap rowing machine that uses gas pistons to provide the resistance.

There's all sorts of ordinary, everyday stuff that must be engineered to not come apart while using the absolute minimum of material (or the absolute cheapest and lightest of material; I imagine shipping was a significant portion of the cost to me)

I mean, that's the thing about engineering stuff. If you are willing to spend money on lots of high quality raw materials, even someone like me without much engineering background at all can design something that lasts just by massively over-speccing everything. The engineering skill comes in when you have to build a rowing machine that can stand up to vigorous use by a fifteen stone american, but they only give you a buck fifty worth of aluminum to work with.

I mean, I guess what I'm saying is that I look around my world and I see a bunch of stuff that must have taken a huge amount of engineering skill to make (I mean, to make at the price point that I got it at... to be functional in spite of the absolute minimum of raw materials) - would all that stuff be 'new' to an engineer?

I tell my students that the purpose of Engineering is not to build something stronger. It is to build something as weak as possible without breaking. Any baron can conscript a bunch of peasants and build a castle with walls 10 meters thick. But some will go bankrupt trying. Or, get an engineer to figure out how to build a wall 50 cm thick that can withstand trebuchet attacks.

If you're not minimizing something, you're not engineering.

"Among the hundreds of quotes that [Alice] Calaprice notes are misattributed to Einstein are many that are subtly debatable. Some are edited or paraphrased to sharpen or neaten the original. 'Everything should be made as simple as possible, but no simpler' might, says Calaprice, be a compressed version of lines from a 1933 lecture by Einstein: 'It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.'" From: https://www.nature.com/articles/d41586-018-05004-4

You forget "...to last 5 days longer than the warranty."

Really the blame for that lies with the public for not demanding a longer warranty.

If enough people were prepared to pay double to buy something with a 25 year warranty, I'm sure companies would step up and make those products. People don't want to pay enough for it though.

No warranty necessary. Reputation alone would be enough. At least in those cases where people care about a reputation for longevity.

Paying more now for a longer lasting product depends on how much you discount the future (ie effectively your internal interest rate), and on how likely you'll think that you'll even want to use that gadged in the future. Eg the NES was probably ridiculously over-engineered for most people, since realistically they'd only need to not fall apart until you buy a SNES or Playstation.

People do, though; There is a thriving market for (heavy and expensive) stuff built to last a really long time. Obviously, if you want your product to be light and/or cheap, especially if (as in my case) your light product is supporting something very heavy, some sacrifices will have to be made.

Thank you, honestly I've been struggling with a decision I made at work around array design ... But honestly based on this concept I can only defend the way I fell

How much was it? A Concept 2 rower will last 'forever' and they are only about $900.

Like 180 or so? Where I live, the major cost of owning stuff is storage, so something light and compact is worth a premium, which I am paying here in terms of reduced longevity compared to a better machine. I bought with the expectation that if it fell into disuse for any period of time, I would give it away rather than store it, and the expectation of a 12 month service life.

If I enjoyed selling things more, I probably would have gone for something more expensive anyhow, but I think the light weight is worth a lot in my situation.

But if it doesn't, you'll be able to trace the failure back to the flaw in the logic (or mistake in the math), which will give you a path forward to correct the failure. If you just try things and they don't work, it can be much less obvious where to go from there.

It's a good exercise for discovering that how right you think you are is mostly irrelevant.

Sometimes the model that you did the logic and math on really did describe the real world enough to predict success - sometimes it is wrong enough to matter.

As opposed to say, faith, where your explanation always works.

In theory, theory and practice are the same. In practice…

The stronger point is that if you design it without logic and math, it very likely won't work.

alternatively, it will work, but you won't know why it worked.

And so you might not know how to replicate it, yet alone adapt it.

With enough experience you might be able to build an informal, tacit model in your brain, though.

And sometimes it works, but users hate it.

> Beware of bugs in the above code; I have only proved it correct, not tried it.

– Donald E. Knuth (1977)

Why climb Everest? Because it was there!

Pursue your passions, whether it is climbing a huge mountain or finding identical packs of skittles. It is what makes the world great and interesting.

Can I ask the point of quoting a snippet of the article without comment?

I admit; I don't read most articles. I prefer the HNer snippets like this. I generally find HN comments to be more cogent and provocative than most editorial nonsense. So, thank you parent, for choosing and posting a snippet which you considered worthy.

I also don't read most articles posted on HN, although I voraciously read the comments. And that's because the comments are better and more interesting than the articles in most cases.

How would you know, the article is worse then? ;)

I used to read the articles more often. And sometimes I do click through.

Yes, it's pretty obvious that lots of HN readers don't actually read the article.

At this point, it should be an official HN rule: "do not read the article, go directly to the comments and speculate what the article is about based on the character-limited title"

For many of us, submitted articles are just social objects for provoking a discussion on particular topics. Also, sometimes the articles are really worth a read, other times they're garbage; usually they're something in-between. Going straight to comments is the fastest way to discover which is which.

Commenting without reading the article is fine. Speculating about what's in the article without having read it is a problem.

so we're reddit, just without the memes?

that does seem a bit disappointing. I think anyone simply quoting the article needs to explicitly show that that is the case because it was very misleading.

still this article was fascinating to me, from the idea that someone would go to the effort to the results of such effort. then top off my fascination with the idea of trying elsewhere in the country should there be more than one manufacturing point or trying to buy up a production lot as seeing the results of that as well.

Now how many packs of M&Ms? There are six colors there. If you go with the peanut version it probably is worse because they you have the variability of the peanuts which would make the chances of encountering packs with more variation in just the number of candies.

> so we're reddit, just without the memes?

Kind of? And with slightly higher average standards of discourse? And I believe this is actually a compliment.

In my experience, HN comments under article are almost always more useful and more informative than the original article. The same is the case with various subreddits. When I read, say, /r/SpaceX, I also immediately jump into comments, as there is better quality info there.

This applies to mainstream news stories in particular. On HN, there's a good chance you'll find someone who was - or knows someone who was - involved in the topic first-hand, and who then proceeds to debunk various nonsense a typical news story contains. That's a huge value-added.

> I think anyone simply quoting the article needs to explicitly show that that is the case because it was very misleading.

Sure, I think making it clear what text is quoted (and from where) should be an obvious rule. And it doesn't have anything to do with whether or not others read the article; it simply saves brain cycles trying to understand the comment.

It's weird to me how often people try to shoehorn aspects of the site into reddit/not-reddit. It has always been common to talk about some piece of tech that's related to the article, in a way that's not touched by the article itself and doesn't need it to be read first. That doesn't make those comments shallow, and I wouldn't put it in a list of distinguishing factors of reddit either. I agree with the idea that it's not a problem until you're speculating on the article, or raising a point that the article already addressed.

>so we're reddit, just without the memes?

There are memes here too, just not in the form of image macros, so the faux-intelligentsia here pretends they're better than those boorish rubes that frequent reddit

>> so we're reddit, just without the memes?

HN has memes. Turning unlikely things into SaaS, Rust/Crystal strike force and bikeshedding are all too real here.

And now apparently not reading source material has that potential as well. Which is kind of hilarious.

Well, TBF, thats the generally normal forum behaviour when you 'know your audience'

For example, know that most HNers are fairly informed individuals in tech. Thus, I trust that I am going to find a good deal of content and insightful comments without reading the article - because I can typically glean the gist of the article and the tidbits that would have interested me anyway, from the HN community.

> For example, know that most HNers are fairly informed individuals in tech

Ha. If that were true, why are there hourly front-page articles about "facebook is leaking your info!!!" and "google is evil!!", or my favorite "bitcoin {is,isn't} a great thing!!" ?

At the risk of angering folks and being downvoted/flagged, I think either there is a major disconnect between the types of people on HN that upvote articles and the people on HN who comment on articles, OR folks here are, on average, not as informed as you think they are.

Because if youre also well informed you should be able to filter those super easily!

Plenty of other sites exist that link to content. I don’t come to HN for that, I come to HN for the forum and their take on the content. Which in my opinion just isn’t matched by any other place these days. (Though if anyone wants to share a contrary oppinion I’d love to hear about those!)

I will go out on a limb and speculate that even more don't read the directions.

I thought it was the standout quote that would get people interested in this article.

Provides us (hn users) a place to discuss that thought.

In my experience, without this, there would have been a ton of "yeah, why bother?" comments on HN.

Sometimes it's an invitation to discuss an interesting part of the article.

This sounds like a version of the birthday paradox. The chance that two Skittles packs are identical is very small, and the chance that a Skittles pack is identical to at least one pack in a large group is still small. However, the chance that an identical pair exists in a large group is not small.

It's really hard for the human brain to comprehend what these type of long odds mean practically speaking. This is a great project that illustrates it rather well.

This is a big part why I like to play games of chance like poker and football simulators. It's a way of testing out your math-predictive skills.

Simulation proves only the theory - sampling and experimentation proves the implementation. Otherwise it might be entirely possible for the packaging process to fill an exact match at a far higher rate - and for the mix to NOT be random.

But the experiment also does not prove much beyond that it was 488 in this particular one case or does it?

He also has 488 samples of skittle distributions which can be used to validate the model assumptions on their own.

Or to make a lot of kids happy.

It would not have been practical to design a simulation of a Skittles packaging machine, as the design of those machines is not public information.

How would he know what distribution to use for the simulation without a sufficiently large dataset to use as an example? A simulation of a made-up system is pretty worthless.

But a simulation would not be able to prove your assumptions correct and would do nothing but validate your math.

All your math can be correct but if your assumptions are incorrect, your results may not be accurate.

But "fill bags with random colors" is already basing your simulation on the assumption that the colors are uniformly distributed. And in fact, that seems to be one of the things he found incorrect in his actual experiment.