This is just subdivision of Bernstein polynomials. The unifying way of looking at this is via the blossom of the Bezier curve (Bernstein polynomial). You can derive all manner of shifts, change of basis transformations, and so on using the blossom. Subdivision is just a shift of the domain of definition of the original polynomial.
What do you find confusing about the idea of a diaper service? It seems too unsanitary for you? The idea that it might cost slightly more than disposable diapers is intolerable to you?
Do you have any reason to believe washing diapers actually is unsanitary?
The price tag and environmental impact of constant diaper delivery seems off the cuff like it would negate the original benefit of cloth diapers. Admittedly I have not done math on this one.
With the service we used, they picked up and dropped off diapers once per week using a big truck. They also drove around to do the same for many other people at the same time. You can't call this diaper delivery "constant". And if the emissions from this are significant, you could always use an electric van.
How are you feeling: do you still think this is something only for performative environmentalists or "trad wives"? Neither of these descriptions apply in even the remotest sense to my wife or I.
Cloth diapers are good. We used them for our last kid with a diaper service and are going to do it again washing them ourselves with our next who is due at the end of the month. Regular diapers are useful to have either way. But cloth diapers are obviously much better for the environment and if they're an option for you, you should consider them. Not a hard concept, not worth a big discussion.
> But cloth diapers are obviously much better for the environment
It's obvious only if you save and reuse the same set of cloth diapers for 2 or more babies. (Which places some constrains on brand, durability etc.) If you have only one kid, I am not sure which side is environmentally more friendly; growing and processing all that cotton (not to mention the plastic for all the waterproof covers) uses a lot of water and energy...
I assumed the environmental angle was the reduction in waste going to landfill with all the extra plastic generated, by the diaper and the small bags that are usually used to reduce smell and keep things clean during changing.
The energy saving would not be as clear to me, but i wouldn't be surprised if reusable were a better choice there as well, just not as clear cut.
The amount of waste generated by disposable diapers was a concern, and we tried reusable ones. But they leaked often, the absorption material in disposable ones is way better than the cotton pads you get with reusable ones.
I would be happy with a middle ground. Reusable outer "pants" and a disposable insert designed well to work with the reusable part, as plastic free as possible.
The energy saving is clear and gets better year after year as the grid continues to green. You can also line dry cloth diapers which saves a lot of energy.
I never had any trouble with cloth diapers. You can always have a blow out with any diaper, but I didn't have any issues beyond that. Of course, there's some technique, but it's easy enough to find a YouTube tutorial if you need it. Snappies and decent covers help.
We kept the diapers from our diaper service and the covers. The washing machines used by the service are much beefier and can handle these kind of loads easily, and will generally be more water efficient.
We also got a good number of used diapers on Offer Up.
When we're done with our diapers, we will rehome them instead of throwing them out.
Oops, talked to my wife and realized I got a detail wrong: we did not keep the diapers from the service, we gave them back. And the diapers we got from the service were almost surely used by plenty of other people before.
Someone else on here seemed confused about the logistics off the service. We lived in Brooklyn at the time. A big truck would drive around our neighborhood and pick up and drop off diapers from many people throughout the neighborhood at once. More amortization at work.
Also, one more thing: we're big on line drying. We will primarily line dry these diapers instead of drying them in a machine.
Oh, and one MORE thing: we got our current washer and dryer free from a friend who was about to throw them out when replacing them.
There are so many ways to mitigate and reduce environmental impact beyond the simple-minded apples-to-apples comparison many in this thread seem to be doing.
The truck would come by once a week to pick up all of our dirty diapers and drop off a new set of clean diapers. The service provided a bucket with a cloth bag inside of it that had enough capacity for one kid for a week. Packaging up = closing the lid of the bucket and leaving it outside the door of our apartment. They would drop off a new one of these buckets full of clean diapers each week (visiting many other people at the same time). Beyond all the environmental benefits, living in the city this was actually super convenient.
Do you wear clothes from the store without washing them? Imagine a product straight from a plastics factory constantly on your baby's skin, designed with chemicals to make them as convenient/effective/cheap as possible versus safe/minimal chemical exposure, covered in plastics dust from the process/other products being made in the factory from worse chemicals.
We used glass bottles and a diaper service (we're from Santa Cruz) and people made fun. Then right after there were questions about chemicals from plastic bottles and our friends understood.
A service is super easy. You can still use disposable for edge cases if needed. Why risk wrapping your child in highest profit possible+maximum convenience chemical creations 24/7 for years? Convience+chemicals+corporate profit greed have proven to be the worst combination for healthy/safe products in our capitalist system.
plastic is not free, there will never be more of it. I think that resolves the equation.
(this is an oversimplification obviously but I wanted to reframe it from "how much of our current resources does this action use" to "how much of our TOTAL resources does this action use")
Plastic is just hydrocarbos basically - hydrogen and carbon. You can totally synthetise it. Might just not be as cheap an convenient like making it from mined oil, at least initially.
water is not entirely free. it has to be cleaned, which costs energy. energy is free, but access is still limited. likewise cotton also requires effort to produce.
exactly, i mean water after use. using water to create or clean diapers pollutes it, and because overall we use and pollute water faster than nature recycles it through rain we have to add our own cleaning mechanisms to keep up. that's fine, but it makes the water not totally free.
> But cloth diapers are obviously much better for the environment
What about this is obvious? Water usage, transportation, fabrication factors, different usage patterns; seems like there are many things to tease apart here.
I think as a general rule: a reusable thing is more environmentally friendly than a single-use thing (especially when the reuse cycles are high). Yes, there are exceptions. But you’ve got the bizarre case to make here, if you want to suggest single-use diapers (that also use water, require transportation, are fabricated, packaged, etc.) are a more efficient use of resources.
My primary point is that it's not a slam dunk for either side. Nothing's obvious about the "impact" here. I you're interested in picking a product based on its environmental impact, there are going to be many factors to consider. Just peruse this 200 page report from the UK government on the subject:
This study has serious methodological issues. I would encourage you to carefully peruse it yourself before citing. This is far from the only issue, but the fact that someone who works at Procter and Gamble is on the study's advisory board is... fun.
I don't think it's that crazy. It's fairly well documented that a reusable cloth shopping bag has a break even with plastic shopping bags at around a 100-200 reuses, something most people won't reach.
With diapers, you have wash water, electricity, and a gas dryer in the mix.
Then you have people in this thread talking about services to pickup and wash them for you. How many trips car trips is that- 2 a week?
1. Id guess an average cloth diaper gets reused more than 100x
2. Think about the mass differences you’re comparing here. A standard plastic grocery bag is about 5 grams of material. A standard cloth bag is around 250. Cloth vs disposable diapers are approximately the same amount of material. This is the “gotcha, vegan! Iceberg lettuce is less efficient on a CO2 per calorie basis than beef! Eat more steak to be greener” type of argument.
3. You’re doing the thing contrarians often do of only counting one side of the ledger, while hand waving away the other. Disposable diapers require water, tree growing, tree cutting, tree transport, tree processing, bleaching, transport, packaging, product transport, disposal transport, disposal processing, etc etc. for each time a diaper is used. Really think about the full cradle-to-grave cycle of these things. Reusables must be washed, yes. But they, importantly, don’t require any of the other steps, which is, y’know, extremely significant. It’s not even remotely plausible single-use diapers are more resourceful than cloth ones.
I think it's plausible that cloth diapers are worse per use than disposable ones due to the mass industrialization of manufacture and resource intensity of cleaning.
You are right that we have to look at the full breakdown of the cradle to grave resource cost.
A washer and dry cycle is about 5 kilowatt hours, which is about the average household energy consumption in China or twice that in India.
Financially, in California it's about $3 per wash for power before accounting for water, soap, ect.
Let's say you got 10 diapers per day and washing every 2 days.
That's 15 cents and 250 watt hours per diaper use.
American use a lot of electricity, so washing diapers would be about a 10% household increase
Cloth shopping bags are a really bad comparison here.
Some things working in favor of cloth diapers here are general greening of the grid, mitigating issues with electricity consumption.
Beyond that, line drying diapers works very well and even preserves the life of the diapers.
Cloth diapers hold their value extremely well and can easily be bought/sold/given away on sites like OfferUp or groups like Buy Nothing.
ALso, "2 car trips per week": do you have no idea how this works? No diaper service in their right mind would send out cars to make bespoke trips to individuals. They're done using a big truck on a schedule to amortize the cost of pick up and drop off as much as possible.
But there are lots of exceptions, right? Like a huge bunch of medical equipment where cleaning the thing to make it safe for reuse would be both more expensive and worse for the environment than single-use versions.
In many parts of the world they throw them in a basin of water and laundry detergent, let them soak for a bit, then hand wash them. No medical equipment necessary.
Of course if you have a washing machine you just launder them like any other item of clothing.
I had planned to do cloth diapers if we had a diaper service available, for environmental reasons, but there's none where I live now and I definitely am not up for washing diapers by hand/pooping up my nice washing machine. Props to you for sticking with it.
I would be extremely surprised if that’s better for the environment than disposable diapers. The key for most of this stuff is economies of scale. It’s why the produce from the supermarket that was carried thousands of miles on a cargo ship is better for the environment than the produce from the farmer’s market that was carried 50 miles in a diesel truck.
Did you read the rest of his series? He addresses this in part 3:
> You’ve probably noticed this theory is hard to falsify: You think you’re not playing taste games? You think you “actually like” things because of the properties of those things? That’s because you’re playing higher-level games!
And it’s rather convenient that this is all supposed to be unconscious.
There’s also this weird sense of guilt. If you consciously change your tastes so you can fit in, that’s bad. If you unconsciously do that, that’s worse. If you unconsciously don’t try to fit in, you’re scum.
What? Arbitrary precision arithmetic implemented in a compiled language will be faster than the alternative. This is no great mystery. The same is true of essentially all low-level symbolic or numerical math algorithms. You need to get to a fairly high level before this stops being true.
The reason it's preferred to use "=" instead of "\in" is because the way that Landau notation is generally used in practice is as a kind of ellipsis or placeholder. For example, the Taylor expansion e^x = 1 + x + O(x^2). I could just as well write e^x = 1 + x + ..., but the former conveys more meaning about what is hidden behind the ellipsis. It's an abuse of notation, but in the contexts that it's used, it's not clear what additional clarity using "\in" would bring over "=". Maybe also that big O is mainly used as a notation to facilitate doing calculations, less describing what family a function belongs to. Here are Knuth's thoughts, which I agree with: https://micromath.wordpress.com/2008/04/14/donald-knuth-calc...
> The symbol ∈ only is a viable solution in a portion of the use cases. For instance, an assertion such as O(n)⋅O(n) = O(n²) would not be correctly describable as O(n)⋅O(n) ∈ O(n²). Perhaps O(n)⋅O(n) ⊂ O(n²) would be defensible, but now one has to devote a non-trivial amount of thought into deciding which of the connectives =, ∈, ∋, ⊂, ⊃ to use in a given context. For instance the assertion “Since sin(y) = sin(x) + O(|y−x|), we have sin(x+O(1/n)) = sin(x) + O(1/n)” would now become “Since sin(y) ∈ sin(x) + O(|y−x|), we have sin(x+O(1/n)) ⊂ \sin(x) + O(1/n)”. Using the equality sign for all of these use cases instead is more intuitive and corresponds more closely to how the verb “is” (“to be”) is actually used in mathematical English.
and
> … Nevertheless most of us still often think in mereological terms rather than set-theoretic or first-order terms […] without requiring translation to set theory or first order logic; indeed, such a translation would only serve to slow that mathematician down as he or she would usually have translate it back into mereological form in order to wield it effectively. Because of this, I think it is worth adjusting our notational conventions to more closely align with our actual thought processes… I don’t see much advantage in interpreting each instance of the O() notation in the exponential type bound f(n) = O(\exp(O(nᴼ⁽¹⁾))) or the calculation (1 + O(1/n))ᴼ⁽ⁿ⁾ = \exp(O(1/n)⋅O(n)) = \exp(O(1)) = O(1) (for n sufficiently large), in terms of ideals.
But it's not completely different and a "≃" would not mean the same thing, in fact it would weaken the statement.
e^x ≃ 1 + x + O(x^2) would only assert that lim (x->0) (e^x)/(1+x) = 1.
However "e^x = 1 + x + O(x^2)" means that for some function r(x) belonging to the set O(x^2), e^x is exactly equal to 1 + x + r(x). Another way to rewrite that equation that eliminates the "abuse of notation" would be:
e^x − (1 + x) ∈ O(x^2)
The particular r(x) in O(x^2) which makes it strictly equal is being left out, that's true, and usually it's left out for brevity or practical reasons or even because it's not even be known what r(x) is... but nevertheless it is not an asymptotic equation or an approximation, it is exactly equal to the value on the right hand side for some particular r(x) the exact details of which are being omitted for one reason or another.
Why are you asking HN? Do you have anyone you know in your personal life you can talk to? Family or friends? Hopefully someone you know well can give you some honest feedback and help you figure out what would be a better fit for you. I don't see how a bunch of strangers on HN could possibly help seeing as they know nothing about you and totally lack context.
Maybe they are looking for people who've experienced transitioning from tech to something else. Even if they know lots of supportive people in real life, it's possible none of those people may have gone through this process.
It’s 2026, why bother asking people when AI exists. /s
On a more serious note, there’s nothing wrong in asking strangers something like this. Plus asking here doesn’t preclude the possibility of also asking to friends and family.
Well, it's certainly not parametric CAD -- it's a drawing program that happens to be in 3D, with limited (and, I'm very glad to see, growing) ability to use history for some more structured creation. But the biggest limitation is that it's numerics are mediocre, and subtle -- everything is in float space, and it's very easy to get into a space where things just don't make sense, especially far from the origin. In a CAD tool I'd expect to be able to enforce constraints to resolve this ("these two points must match"); I've been able to do that somewhat with my plug-in when the precision is there but the error stack-up has been too high, but there's also cases where the precision just doesn't exist.
You're in luck! As of a year ago, I work at McNeel on the math team on Rhino's in-house CAD kernel. Luckily, we own the entirety of the kernel, so we are free to improve it. I've been in the field of numerical methods for most of my career in academia and industry, so you are preaching to the converted when you say that Rhino's numerics are mediocre. At McNeel, I'm actively pursuing strategies to improve this situation, although it will be a massive long term project.
Hopefully you know that you can reach out to the McNeel developers directly and on the Discourse forums. But I would also love to chat directly if you're interested. It sounds like you're working on a project that is both sophisticated and interesting, which directly stresses many of the known pain points in the kernel. If you're interested, I can shoot an email to the address you've got listed in your profile from my McNeel email.
I think this definition is a bit too strict. CAD just means computer aided design. Architects use Rhino to design buildings. You use it to design airplanes. CAD doesn't even have to be 3D.
You could design entirely in notepad.exe, and that would be computer aided design by your definition.
Rather than that definition being too strict, this one is too litteral.
It was perfectly reasonable to characterize the tool as not really CAD, even though a 3d drawing/modelling/rendering/visualizing program is on a computer and is part of a design process.
I made a conscious choice to work at a small company rather than a large company because of this. The politics are smaller, but that doesn't mean the stakes are.
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