Why does a carpenter cut the end off a 10-foot board to get a required 9ft-2in, thereby wasting 8% of the input and incurring dumpster charges? Suppose the architect's design specified the cutlist, to be transmitted to the board "factory", which would cut boards to the required lengths, tagging them with RFID serial numbers indexed to the design, stacking them so the first ones to be used are on the top, and truck to the site without passing through Home Depot?
The vast majority of the boards and carpenters gets come pre-cut to 92 and 5'8". That is exactly the size you need for an 8' wall. It is only a tiny minority of borders that the carpenter is actually cutting on site. The majority are already pre-cut to the exact size needed.
It would be possible to cut boards to the exact site in a factory. However, you would lose more in the logistics cost of managing all the different possible sizes that you need. Thus two by fours come size multiple of two feet except for the 92 and 5/8's and 104 and 5/8's. Those later too are the extremely common sizes that are used in most commonly.
The truck has to pass through something like Home Depot anyway because all those boards come not on a truck they come on a railroad car and then they'd have to be transferred to trucks to get them to wherever. That Home Depot-like place is also a good place to stage things if you actually are building you'll discover that the dedicated lumber yards are very good at breaking apart all the different pallets of lumber and they figure out exactly what you need and they put those all into one group and bring it to you. Yes, you do sometimes have to cut a 10 foot 2 by 4 and 9 foot 2 inches. However, you are never in the situation where you have a 12 foot 2 by 4, you have to cut to that size because Lumberyard has already figured that out and gotten you the closest to the right size for you. Having been in construction, I can inform you that there are very few boards that actually return to the lumber yard at the end of the build. They are generally right on and getting you the exact amount of lumber you need from the blueprint
Going from 8 ft to 9 ft ceilings adds 12.5% more volume. For an 1,800 square foot house, in a 30x60 ft form factor, that increases the surface area exposed to outside air by 5.55%. This would create a small increase in the heating and cooling price per square foot, but a similar decrease in the cost per cubic foot.
You missed something important: many people are moving from a much older house with poor insulation. They can double their surface area and yet see their HVAC bills go down by a lot because modern houses are so much better.
construction cost maybe, heating/cool expenses difference won't be so tiny, quite the opposite and it's not only about expenses, lower ceiling is also faster to cool/heat, so you have to wait shorter time
I can really understand high ceiling (in new residential buildings) only for people who use fake built-in second floor (dunno the word in English, maybe mezzanine by my quick research) for like bed or something, but what's the point then and why not build proper separated 2nd floor if you are building new house
The larger use of energy in HVAC is recovery from losses from convection, conduction, radiation, and air leaks. The one time heating or cooling is small.
You can buy kit houses that basically do what you're describing, up to and including entire log cabins that go together like Lincoln logs of yore (which end up being MORE expensive because they literally build the house at the "factory" and then disassemble it, put it on a truck and reassemble it onsite).
The big problem with kit homes ends up being what happens when (not if) you @#$@ something up.
And the big builders are already bypassing Home Depot, they buy from suppliers that you've never even heard of (the smaller ones buy from suppliers you've heard of, but when you went in everything was 5x the price of Home Depot, because they don't want you as a customer - they want the builders who buy on account and get 80-90% discounts on "list price").
Lumber is transported from sawmills via rail cars to some depot where it will then get trucked to places like Home Depot.
There are some large-scale lumberyards that still have a railroad siding and will get lumber by the carload.
A delivery of lumber for a typical house is a full load (or more than one) via truck, and obviously a train isn't going to come to a construction jobsite. So the llumber at the construction site is already hand picked...
It's no big deal at all to cut off ends to make it fit exactly, but when framing most of the 2x4s, etc. are already the exact size you need. You just trim off the top and bottom plates at the edges of the rooms.
Check out this 156-page tome: https://arxiv.org/abs/2104.13478:
"Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges"
The intro says that it "...serves a dual purpose: on one hand, it provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers. On the other hand, it gives a constructive procedure to incorporate prior physical knowledge into neural architectures and provide principled way to build future architectures yet to be invented."
Working all the way through that, besides relearning a lot of my undergrad EE math (some time in the previous century), I learned a whole new bunch of differential geometry that will help next time I open a General Relativity book for fun.
I have very little formal education in advanced maths, but I’m highly motivated to learn the math needed to understand AI. Should i take a stab at parsing through and trying to understand this paper (maybe even using AI to help, heh) or would that be counter-productive from the get-go and I'm better off spending my time following some structured courses in pre-requisite maths before trying to understand these research papers?
And any prereqs you need. I also find the math-is-fun site to be excellent when I need to brush up on something from long ago and want a concise explanation. i.e. A 10 minute review, more than a few pithy sentences, yet less than a dozen-hour diatribe.
I once worked with a company that provided IM services to hyper competitive, testosterone poisoned options traders. On the first fine trading day of a January new year, our IM provider rolled out an incompatible "upgrade" to some DLL that we (our software, hence our customers) relied on, that broke our service. Our customers, ahem, let their displeasure be known.
Another developer and I were tasked with fixing it. The Customer Service manager (although one of the most conniving political-destructive assholes I have ever not-quite worked with), actually carried a crap umbrella. Instead of constantly flaming us with how many millions of dollars our outage was costing every minute, he held up that umbrella and diverted the crap. His forbearance let us focus. He discretely approached every 20 minutes, toes not quite into entering office, calmly inquiring how it was going. In just over an hour (between his visits 3 and 4), Nate and I had the diagnosis, the fix, and had rolled it out to production, to the relief of pension funds worldwide.
As much as I dislike the memory of that manager to this day, I praise his wisdom every chance I get.
A little stoichometry suggests that, ignoring oxygen, hydrogen, and energy input, the cited worldwide market for C2H4 would be satisfied by just about 1 gigaton of CO2. So if "we need to process gigatons of CO2 annually", that ethylene's gonna pile up.
Earth escape velocity is 11.1 km/s, which is Mach 32 at sea level. They have some more engineering to do, maybe even invent something better than carbon fibers.
