Weird I’m being downvoted. I thought I was asking a legit question. Oof

You can, and some devices do, use Newton's algorithm. For square roots, it consists of taking an initial guess z ; it can be pretty bad, say you guess sqrt(a) to just be a.

Then you calculate (z + a/z) / 2 *. This is a much better estimate. Now set that result to be z and plug it in again; and again; and again. It becomes a very good approximation to the square root pretty fast.

Example: calculating sqrt(5), starting with the estimate z=2 to get nice simple fractions instead of ugly decimals (a calculator obviously would not care, but I do).

• Step 0: z=2 ; z² = 4.
• Step 1: z = (2 + 5/2)/2 = 9/4 ; z² = 5.0625
• Step 2: z = (9/4 + 5·4/9)/2 = 161/72 ; z² ~ 5.00019
• Step 3: z = (161/72 + 5·72/161)/2 = 51841/23184 ; z² ~ 5.00000000186

It took us only 3 iterations to get 8 digits down. It can actually be shown that the number of correct digits roughly doubles each step. So with one more, we easily get the 10 or 12 digits most calculators use.

*: Note how (z + a/z) / 2 is in the middle between our previous guess z and a/z, which is another plausible guess (indeed, if z²=a, then a/z is just z; and if z is too small, then a/z is too large, and vice versa). The true reason behind the algorithm is based in calculus, one approximates using tangents at a curve to find places that should be closer to solutions.

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There is a mathematical concept called a taylor series that can be used to compute things like irrational roots. It is way beyond the scope of eli5. The basic concept is that you can repeatedly call this function and each iteration gets you closer to the real value.

True, but when the exponent is 76000 and you start multiplying numbers with tens of thousands of digits, it starts to rack up.

Yes, obviously. That's why I said series/ parallel.

It depends on the application. 2838393^1024 has 6600 digits, which is no problem for modern computers to calculate exactly in well under a second.

I haven't heard the one about mattress stores. The one about laundromats is plausible, but you aren't going to be able to launder much money through a laundromat. They may be an almost exclusively cash business, but it's not as much as you think.

I work at a bank, and the laundromats we work with bring in less than 1000 a week. The guy who owns the laundromat also has vending machines and a car wash that is included in the deposit. If they suddenly started bringing more than that, us bank tellers would immediately be suspicious. A mildly successful restaurant will easily bring in 1000+ a day in cash, it would be less suspicious if a restaurant was bringing in larger quantities of cash than usual, especially if they said something like their card reader is broken or they have some special that is really taking off.

In the case of buffalo, the storm is constantly being fuled by nearby Great Lakes https://en.m.wikipedia.org/wiki/Lake-effect_snow Basically cold air over warm water dumps whole lots of snow directly downwind

I literally work with a solar company that does EXACTLY what I described in repurposing EV batteries into home solar installs. You are the only brainwashed person here and you have zero idea how batteries work. All batteries have a life cycle, every last one. Batteries are also among the most reused, repurposed and recycled manufactured products in existence today.

The batteries in an EV will only outlast the vehicle if parts stop being made for that vehicle or the EV has so many issues that it costs more to repair than replace. The single most expensive part of an EV is the batteries, as long as the battery is safe and the repairs are not more expensive than replacing the vehicle, they will make the vehicle into an EV of Theseus because it's cheaper than replacing the battery. It's not uncommon to reclaim these batteries from EVs that were totaled in accidents.

Not a word of that changes the fact that ALL batteries have a limited amount of charge cycles before they need to be replaced, rebuilt or recycled. ALL BATTERIES. Every single last one. In fact every single time a battery goes through a charge cycle it holds slightly less of a charge. This is true for your Amazon rechargeable AA batteries just as much as it's true for EVs. It's simply the nature of the technology.

Yes but not all in series. For 25000 AA batteries that would give you about 37kV, you probably don't want/need so much.

It's a combination of tables with a few entries and clever algorithms.

What calculators do is a bit more complicated, but here is an approach that can be done with pen and paper and some time. Let's say we want to find the square root of 40. We know (look up) that 36 is a square, namely 6^(2), so the square root of 40 will be somewhere close to that.

40/6 = 6.666...

6 is too small for the square root, but 6.666... must be too large, so let's take the average of the two, 6.3333:

40/6.3333 = 6.3161 - pretty close!

Let's take the average of 6.3333 and 6.3161, which is 6.3247:

40/6.3247 = 6.32441 - even closer. Doing that two more steps:

6.324555321991

6.324555320336758664214273

Digits in bold are correct, so we got 18 correct digits in just four steps (or 19 if we round).

More digits of the square root of 40 for comparison: 6.324555320336758663997787

I don't buy it. Car companies don't want it to be modular because it doesn't benefit them. In Asia they have grab and go batteries in motorbikes all the time.

Why would Tesla or Toyota want to cooperate and build a modular battery so that a competitor could sell a battery for your car. They don't want duracell in the game.

Government could fix this, but won't because captured capitalism.

Down cycle into grid attached storage isn't really outlasting the car.

Buffalo is a little bit of a unique situation because it gets "Lake Effect" snow. It's located on the east shore of Lake Erie, which allows arctic wind to blow unobstructed. When you get a bad cold snap like we had last week, and the lake hasn't frozen, you end up with super-chilled air blowing over the surface of the much warmer lake water. The wind picks up moisture from the lake, freezes it, and then dumps it on shore.

smaller batteries? Do you mean cells?

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Go watch a how it's made on Tesla or Rivian batteries. Connecting them in series/parallel is exactly what they do.

Warm is relative term. If it's 10° below zero and -30 with the wind chill, you will automatically feel 20° warmer in an igloo since it blocks the wind. Then it will also trap body heat which could get it up to 25 or 30°. At that point the feels like temperature could be 60° warmer than outside, but still be below freezing. Also, the blocks of an igloo are quite thick, so even if the air inside is a bit above freezing, it won't completely melt the igloo. The inside layer of snow and ice might start to warm up a bit, but it will also constantly be cooled by the rest of the ice block.

This is a bit complicated... it has to do with thermal transfer rates as well as state change energy costs...so here goes.

Imagine the temperature outside the igloo is 0F. When the ice is warmer than 0F, it will want to radiate its heat out into the colder 0F air. For sake of this argument lets say that 0F Ice has Zero thermal energy. 10F ice has 10 thermal and so forth. I'm making the thermal numbers up for simplicity here...

You sit inside the igloo, warming the air up to 50F - but the air inside the igloo is far less dense than the ice. While ice at 10F has 10 Thermals (T) air at 10F only has 0.1T because there's so much less mass to the air.

That warm air wants to transfer the thermal energy to the ice - and it does - which absorbs it. Not the 0F ice has 0.1T (so its temp changes to 0.1F). It's not even - the ice inside the dome is warmer than the ice on the outside - but the internal temp of the ice is also trying to equalize

Over time the ice on the inside of the dome warms up to, oh, lets say its 10F so its got 10T but the outside ice is only at 2F. That 2F ice is radiating heat out to the cold 0F air.

Heat comes into the ice on the inside of the igloo and leaves the ice on the outside. It's slow but it only has to be fast enough that the rate of change never lets the ice get higher than 32F.

If the air inside got hot enough, it could overwhelm the interior, melting it - but one other factor is at play here. It only takes 1T to take ice from 30F to 31F, and 1T to go from 31F to 32F - but to MELT requires a state change. State changes in water take a lot more energy. Call it 5T. IF the surface of the ice reaches 32F, then more heat will start triggering a very very slow melt but at the same time the heat is still being sucked into the middle of the ice.

AND the warmer the ice on the inside is? The faster the heat moves to the middle. A bigger temp difference means a faster rate of change. Thus the heat that would melt the ice is moving away from the warmer ice faster than the ice can absorb it for the state change.

Of course the same is true for the temp diff between the warm air and the ice - so like I said - if the air is hot ENOUGH the ice will melt - how hot exactly? I have no idea - but warm enough to be able to survive apparently isn't warm enough to overwhelm the ice when it's super cold outside.

If the air outside is warmer, well then of course that works against the ice too. Igloos would work better at sub freezing temps, otherwise that heat wouldn't leave the ice - it'd stick around for the state change but on both sides of the ice.

That still doesn't quite add up in my head - when I bend a pencil, I'm over-flexing a single, rigid structure. The spine is lots of smaller rigid structures, held together by soft, bendy stuff.

Maybe watch some agriculture documentaries or something

That's nice and all but irrelevant if the subject isn't very country-specific. The other person even clarifies as much.

Anecdotal but I had a friend who smoked back in Junior High School. We asked why? He said it was cultural and his father encouraged him to do so. There was a belief smoking was masculine and if you didn't you may be perceived as homosexual.