Intuitively I do not think this would work. Well, I mean it depends on what you are doing. For graduate oral exams it might be a good way to prepare.
But if you want to get dexterity in some field, i.e. being able to actual solve problems, I think it would not work so well. I think there is a difference in how the brain stores and recalls information in this case. If you learn a definition by heart or learn a proof technique by heart, you would be able to recall it perfectly when asked directly for it. However, I suspect that when you would be actually solving a problem and you would need to recall this information your brain would not be able to make the connection.
That is why in mathematics one is usually required to solve a lot of problems and why studying the theory by heart does not help much. When you do a lot of textbook problems you brain starts making connections between the chucks of proof techniques and the chunks of definitions and the chunks of whatever features your textbook problems have. Those connections are the most important part of learning mathematics and you would not get them by simply learning facts.
Basically, to say it in another way, you would learn the theory, but you would not learn the problem solving associated with this theory.
Source: I studied mathematics, the wrong way for many years.
EDIT: The most bitter experience I had studying mathematics. It was the first year of my graduate studies and I took an undergrad class in Graph Theory as my introduction to discrete mathematics. Since I was now a graduate student I decided to approach the class in the graduate student way. That means I focused really hard on learning the theory and learned all the proofs and all the proof techniques that we went through. And that was very fun because the proofs in Graph Theory tend to be very elegant. And I fell in love with the field. And then came the exam and I was feeling really good about all of this, because for maybe the first time in my life I had learned 105% of the theory required for the exam. That was the worst grade I got in my whole mathematics studying career. The problems on the exam were much simpler than any example or theorem encountered during class, but I just could not make the connections between the proof techniques that I had memorized and what I was looking at on my exam paper.
I retook the exam three years later (it had no influence on my grade at this point), with very little preparation, but the preparation was 100% in solving exam type problems. I could maybe recall 60% of the theory and proof techniques. I got top grade.
Any bits of knowledge that have solidified such that they can be retrieved effortlessly, can be used as building blocks to construct or understand higher order knowledge.
Memorization may not (initially) help with understanding the particular thing you're trying to memorise per se, but dismissing it altogether as not being generally relevant for creating understanding is wrong.
Also, knowledge is bidirectional. A higher order concept you learned because you were able to use a more basic building block to reach that understanding, may later provide the insight that then allows you to get a better, revised understanding of the lower building block too, without compromising any of its dependents.
I agree with the claim that problem solving is essential to learning mathematics. And I have had the exact same experience where I did well on math exams by ignoring most of the theory and proofs of main results, and focusing solely on examples and problem solving.
However, I think straight-up memorizing definitions and theorem statements is really useful for problem-solving/exam prep, just so they're at your fingertips. There's no way you're passing a real analysis exam if you can't regurgitate the epsilon-delta definition of a limit in your sleep.
What seems to occur (at least for me) is that you naturally memorize all of these things in a somewhat inefficient fashion by doing problems. If the concept gets used in enough problems, it slowly burrows its way into your memory - and this is a very durable kind of memory, as you point out. But I do think for things like graduate school qualifying exams you can "juice" the process by explicitly memorizing core material.
Probably it's not as useful for doing research, though.
I never remember explicitly learning the epsilon-delta definition. By the time I had worked through enough problems, read enough books etc I just knew it.
I saw other students learning definitions etc off by heart and to me it seemed liked they were doing it because they hadn't really understood the material and it would get some them marks. It was probably the right exam strategy if you didn't deeply understand the material to optimise your marks and get a reasonable pass mark but I don't think it was the right way to really learn mathematics or get one of the top marks.
I did learn and test myself on the structure of some of the more complicated proofs in my finals I mostly revised by doing old papers though.
(Feel I should offer some credentials but also don't want to brag, but feel I am about as qualified as one can be to talk about doing extremely well in maths exams :-))
I think it's a good tool for quick access to many useful tools in a toolkit. Yes, you need to know how to apply the tools, but quickly being able to manipulate a problem into several other forms makes lots of problems much easier.
See, this is a case where they went for the bombastic headline and in the process hid away a really cool achievement.
So basically they created some sort of general purpose math library, that can automatically detect the type of problem, find the correct library to solve it, and input the right inputs to get the right output. That is all very impressive and would be a great product actually, if refined.
The fact that it's been done is no reason not to do it again. Even if two implementations were somehow a bad thing, Wolfram Alpha is the closedest of closed source, and replacing it with something auditable is a win for science.
I'm certain that, if someone came up with a workable replacement for Excel, then it would have a market in academia. (Would it earn the creator promotions? I think clickbait-y titles are more likely, not less, to get promotions.) I base this largely on the success of TeX in the hard sciences, which, by and large, won't touch Word unless absolutely forced to do so. (At least, that's how it is in math.) This is rather ahistorical, since TeX actually predates Word, but I still believe it.
Something about this cannot be right, surely?
You are saying one can invest in a solar setup and have 7+ years of free electricity, and all that starting after 3.5 years?
I would be very suspicious around claims from people trying to sell you solar panels. There are a lot of incentives in the US such as tax credits. This is good but a lot of people in green energy industry include that into calculations, which is fine except its under the assumption that the incentive will persist. Even Tesla shows you "net effective" price of their car by calculating the gas savings (e.g. Model 3 purchase price is 47k but they "potential savings" price is 38k which include potential incentives and gas savings of $8,600)
There are other gotchas like PACE loans being senior to your mortgage. So if you get a PACE loan, the loan is transferred to the person buying the home and is senior to your mortgage.
I'm also suspicious around the maintenance and longevity claims. For instance, from my experience, the energy efficient light bulbs do not live up to to their claims. I changed about half of my lightbulbs within three years and they supposedly have a 20+ year lifespan. It's fine that they don't have a crazy lifespan, but it just shows the industry is okay with outright false claims.
Overall I think the industry is so juiced by incentives and manipulated by regulations that it attracts shady players.
LED bulbs can last 20 years if they're designed to. Most of what is sold is generally very low quality, with poor heat management, low quality power
circuitry and excessive load on the LEDs, which all result in shortened life. It's a shame. Some of the first bulbs I got were good quality and I still have them in frequent use 10+ years later. Many others have been quickly failing junk.
I have been living fully off solar (and some wind here and there) for 10 years. Its amazing. Never do I stress powerlines going down, brownouts, etc.
You can run a fridge, lights and a laptop 24.7 on about $300 of solar. You can add panels as your needs and budget increases. The biggest cost is the battery.
Do you have a writeup of your setup? Do you use lead acid for your batteries?
Besides the money issue, the biggest concern I have are balancing the batteries, getting the right inverters, keeping the panels clear and figuring out what inefficiencies are during the non-summer seasons.
I'd check out Lithium Solar on youtube - he's got a fairly comprehensive set of videos on almost every topic regarding batteries, inverters and general setup.
I'd love to learn more about your setup. I'm very interested in investing in a solar + battery self-sufficient setup for myself, but without electrical engineering experience it's quite intimidating.
Likewise, I have been living off-grid with solar for well over 20 years.
My batteries have always been lead-acid, simply because L.A. is still much cheaper than Lithium and alternatives.
I've recently taken my first set of Lead-Acid batteries out of service. They powered a small fridge, etc, via 200W of solar panels for over 20 years with essentially zero maintenance, except for occasional top-up of distilled water.
Inverters were a problem at first. I had a series of Inverters die over the years, until I started buying Victron products. Have had zero problems since. Rule one, is "don't buy cheap inverters".
The best part is that secondhand solar panels are now very cheap. The reason is that Gov regulations for grid-tie prohibits the use of second-hand panels, so people doing upgrades will basically throw away their old panels.
My setup runs a conventional fridge/freezer, and a large computer which is on-line for most of the day, as well as my workshop full of electrical tools. I do have a large generator, but the only time it gets run is when I have some welding to do. I don't even gave a battery charger hooked to it.
There are so many myths about solar: Lead-Acid batteries don't last as they are destroyed by deep-cycles. Yes, but when you size the system, you should aim for a deep discharge maybe once a month. This still should result in twenty years life or so. I live in a wet and cloudy part of Australia, and this winter my batteries have never been as low as 80% capacity, and it is rare if the batteries haven't returned to 100% charge by 10:00am each day.
Probably the main problem with solar is that people are stupid. One of my neighbours installed a modest solar system, only to have it regularly fail due to low battery voltage. Long story short: The supplier fitted a Watt meter which tracked the consumption at each outlet. It showed that that the problem was in his daughter's bedroom. A quick search revealed a huge radiator under her bed that she was running each night. Problem solved.
I'd be curious what your wind setup looks like. I have some land off grid which gets good wind, and I'm trying to decide whether that could be a reasonable alternative to solar. I don't see nearly as much information about residential wind turbines as I do solar.
Sorry, but no. If anything solar gear has got cheaper in recent times. Secondhand Solar Panels are almost free at present. And the price of batteries is dropping fast.
It's not wildly far off but I think his battery costs are a stretch. In fact double that would be a challenge to have a quality and reliable system. But it is definitely lass than 3x. Right now the best value for batteries I'm getting is 0.18 per w/h. To get 0.08 you would have to doing something like recycling small cell or ev batteries which isn't necessarily scalable and comes with some risks.
Panel costs are accurate and the additional electronic expense is not super high. $1000 should be enough for most setups.
For most people the issue is space. This is going to be another thing where the poor are taxed. A significant amount of single family residences dropping off the grid will cause prices to go up for the people that don't have the luxury of 4000 sq ft to fill with solar panels.
The $0.08wh is something that you have to hunt around for.
Just a cursory look on Aliexpress gives $0.12wh for LiFePo4 batteries [0] [1].
Looking on Alibaba, I see some potential sellers that might get below that $0.12 but it takes looking around and potentially talking with sellers. I do think it's possible but it requires some hunting, especially in the 'consumer' quantities we're talking about (sub qty 100).
One reason is that this will make it a matter of survival for energy companies and governments to mandate connection to the grid and buying of electricity, for fear of having these critical companies fail.
Because this is not going to make all energy cheaper. It's going to massively increase the cost of "legacy" energy while making some types of energy free.
Perhaps they will use a "social" cost-sharing, or ... well I don't know, but essentially the time will come when living in the countryside will come with "free" energy (not unlimited though), and cities will come with punitively expensive energy.
PV can scale down pretty far, yeah, but it can also scale up. Having guys crawl around on rooftops trying not to damage your shingles is a lot more expensive than just setting up some panels in a field. The majority of PV getting installed is utility-scale, not household-scale, so you can buy cheap PV energy and live half a block from a supermarket and half a block from a chichi cafe.
As for costs, there's been concern for more than a decade about the "utility death spiral" scenario: some users disconnecting from a grid would spread the fixed costs of things like transmission and black start over a smaller number of remaining users, leading more of them to disconnect, and so on. So far it hasn't materialized anywhere, but as far as I know it could. I don't think the same scenario is likely with "legacy energy" like gasoline and natural gas, because the fixed costs are so low.
Taxation of energy is a big revenue stream for the governments. What happens when people start putting independent energy sources to power themselves and it causes significant revenue drop ? Would the government tax them for putting up solar on their property ? Couple this with electrification of transportation and you have another taxation source (fossil fuels) losing revenue. This would lead to a disruption in the social power dynamics in a country.
Yes, energy companies can invest in these too, but why would I buy from them if I have my own generation ?
Fuel tax will definitely be replaced with some other form of car tax, at least in most of Europe. I don't see any way around that.
But I don't quite see how free countryside electricity would mean expensive electricity in cities? Large scale wind and solar will decrease grid prices too, and most people live in cities anyway so the people dropping off grid doesn't seem like an issue for electricity transfer costs. Plus off-grid won't happen anywhere with a real winter, so most of Europe is excluded already.
Of course they will, but energy companies have a larger minimum capital expenditure than a household looking to invest in generation. And the energy company will likely still carry the full cost of transporting energy, which becomes more expensive with more energy sources connecting to the grid.
It would be a change in the dynamics of economies of scale vs small and nimble, greater lobbying power is one thing economies of scale still have a big advantage in so GP's comment seems plausible.
Exactly. There will be no need for "legacy" energy. Companies that are too invested in fossil energy can die and be replaced with companies that invested in solar.
I'm not sure about the US as installation costs there are very expensive, but in my part of Europe I had 10kW of roof mount solar installed for €10,800 at the end of last year.
The calculations I did for it in 2020 were that the payback period would be 7 years, or 6 with government incentives. That was when electricity was 15c/kWh though... if energy prices stay at the current level I will break even in less than 4 years. I generate around 8000kWh a year, which at current prices is €3200.
The panels should last forever (assuming no physical damage from hail storms etc), they just decrease in efficiency. The inverter should last at least 10 years, but that's easy to replace as it's not on the roof.
I very recently solved my sleep problems which had been bothering me for a couple of years.
1. I cut my caffeine intake to zero.
2. I forced myself to sleep at about the same time each night. (most important)
3. I stopped using alarms. I wake up when I need to.
4. I wear a sleeping mask which helps me get an hour more of sleep. Otherwise I'd be awake at the first lights of dawn.
Once your circadian rhythm is retuned, points 1 and 2 stop being so important. I no longer have trouble sleeping if I drink a cup of coffee. And if I go to sleep late once or twice, it does not ruin my sleeping for the rest of the week.
For any vehicle that goes in the wilderness or even just off road, an ICE drivetrain works better, because (apart from being lighter), if something goes wrong, you might run out of fuel (example, you get lost and you eventually run out of fuel). Then it is much easier to source some fuel, than it would be to recharge or tow a vehicle with an EV drivetrain. And as a preventative measure, it is also easier to increase your vehicle's range by carrying more fuel on board with you.
Sure, if there was a will, a lot of vehicles and journeys could be accomplished with a EV drivetrain, however, not without compromises.
So really, I do not think there is demand at this point.
But in this particular case I bet it is the actual state of being alone that is the cause of mental decline, the mechanism being that one is literally not using all the parts of the brain that one developed to socialize with others.
But if you want to get dexterity in some field, i.e. being able to actual solve problems, I think it would not work so well. I think there is a difference in how the brain stores and recalls information in this case. If you learn a definition by heart or learn a proof technique by heart, you would be able to recall it perfectly when asked directly for it. However, I suspect that when you would be actually solving a problem and you would need to recall this information your brain would not be able to make the connection.
That is why in mathematics one is usually required to solve a lot of problems and why studying the theory by heart does not help much. When you do a lot of textbook problems you brain starts making connections between the chucks of proof techniques and the chunks of definitions and the chunks of whatever features your textbook problems have. Those connections are the most important part of learning mathematics and you would not get them by simply learning facts.
Basically, to say it in another way, you would learn the theory, but you would not learn the problem solving associated with this theory.
Source: I studied mathematics, the wrong way for many years.
EDIT: The most bitter experience I had studying mathematics. It was the first year of my graduate studies and I took an undergrad class in Graph Theory as my introduction to discrete mathematics. Since I was now a graduate student I decided to approach the class in the graduate student way. That means I focused really hard on learning the theory and learned all the proofs and all the proof techniques that we went through. And that was very fun because the proofs in Graph Theory tend to be very elegant. And I fell in love with the field. And then came the exam and I was feeling really good about all of this, because for maybe the first time in my life I had learned 105% of the theory required for the exam. That was the worst grade I got in my whole mathematics studying career. The problems on the exam were much simpler than any example or theorem encountered during class, but I just could not make the connections between the proof techniques that I had memorized and what I was looking at on my exam paper. I retook the exam three years later (it had no influence on my grade at this point), with very little preparation, but the preparation was 100% in solving exam type problems. I could maybe recall 60% of the theory and proof techniques. I got top grade.