In the (is this shape fillable by 1x2 dominoes?) example given by EWD to demonstrate the power of formal reasoning methods, a slight change to the problem statement:
For the shape Q, instead of clipping opposite corners of the 8x8 square board, one (what would lay under a) white square and one black square, which are non-adjacent, are randomly removed.
makes the elegant proof argument fail.
Real world programming is usually like this, it is hard to cast the problem in the framework of a formal language, like first order predicate logic, and manipulation of uninterpreted formulae (i.e. the problem now mapped into the domain of first order logic) using the rules of first order logic might not lead to anything useful.
It seems to me that EWD is showcasing some example programming problems that are elegantly handled by his formal proof techniques, while ignoring the vast swathes of programming problems that might not be well handled by these techniques.
There is an extremely elegant solution to this modified question as well. In fact, it is always possible to fill a chessboard with dominoes with two squares of opposite color removed, by a very straightforward method (Gomory's Theorem). See Problem 2 at https://www.cut-the-knot.org/do_you_know/chessboard.shtml and note that the result generalizes to any bipartite Hamiltonian graph, such as any rectangular grid with an even number of cells.
(Much more generally, Hall's marriage theorem characterizes which finite bipartite graphs have a perfect matching, and there are polynomial-time algorithms to compute maximum cardinality matchings in arbitrary finite graphs.)
Essentially what you're arguing for is the desirability of untrustworthy software.
Typically people have insisted that it's too expensive to prove software correct, but as the machines and techniques improve proven-correct software becomes cheaper and cheaper.
The last argument standing is that it's unpopular.
On my current project the way totals and taxes are applied different on two different screens leading to slightly different totals. No one knows which one is actually correct or used by the customers in practice. Thus, you could say there is no correct answer.
Most software development is wrestling with malleable requirements.
As the old joke goes: writing software from requirements is like walking on water, both are easy when frozen
> No one knows which one is actually correct or used by the customers in practice.
Automating BS is bad.
> Thus, you could say there is no correct answer.
I object to such fatalism.
Kind of the whole point of computers is to find and eliminate such ambiguities.
I don't mind playing irrational games for entertainment, but they are "no basis for a system of government", eh?
> Most software development is wrestling with malleable requirements.
Sure but that's no excuse for automating irrational systems. There's no written requirement that the math to compute totals and taxes shall be mysterious?
Write down a Hamiltonian cycle for the (undirected) graph where the nodes are given by the squares of the chessboard and are connected by edges if they are (orthogonally) adjacent. Notice that because the squares are different colors, deleting them from the Hamiltonian cycle partitions it into two even length paths. Cover each even length path with dominoes.
The part where you notice the two paths are even length feels a bit like dark magic the first time you see it. Notice that if you have two different coloured squares which are consecutive on the cycle the paths you get are length 64-2 and 0, then if as you move one of them further and further along the path you have to move in steps of 2 to keep them opposite colours.
You can draw a big "C" shape that goes around 3 edges of the board and then fill in the middle with wiggles. This works for any rectangular board where one of the edge lengths is even. You already need one of the side lengths to be even to solve the problem because if both sides are odd then the number of squares is odd, and good luck covering an odd number of squares with dominoes.
Could it be possible that the coffee lobby is behind this 'counter'-study?, since a relatively simple inference from the OP has catastrophic consequences for the coffee business:
Deep sleep is necessary for the slow electrical waves that clear the brain of waste including amyloid proteins. (Excessive) coffee intake reduces the quality and quantity of deep sleep, thus leading to a build up of waste products including amyloid, resulting in cognitive declines such as Alzheimer's etc. Therefore, coffee intake (indirectly) causes Alzheimer's.
Admitting that last part is suicidal for the coffee business.
@dukeyukey, from these '_lot_ of studies', if we remove those that are directly or indirectly funded by the coffee lobby, are we left with the empty set ∅ ?
We have a _lot_ of studies and evidence that says coffee reduces overall mortality by quite a bit, and it holds for both caffeinated and decaf coffee. It seems like coffee specifically reduces the risk of Alzheimer's as well.
That result is almost certainly bullshit, at least for Alzheimer's. Or the effect is so minimal that it doesn't practically matter.
Why? Because Finland is the country that consumes the most coffee per capita in the world. Finland also has the highest amount of Alzheimer patients per capita. Correlation is not causation, but based on this, it should rather be suspected that coffee causes Alzheimer's rather than helps with it.
a kilogram of gasoline gives you about 13 kWatt-hrs,
a kilogram of coal a little less, about 8 kWatt-hrs,
a kilogram of lithium ion battery can store only 0.2 kWatt-hrs, and,
a kilogram of water at 1 km altitude is just 0.0027 kWatt-hrs.
On the other hand,
a kilogram of Uranium 235 gives you 24000 kWatt-hrs!! There’s a lot of energy in Uranium 235!
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So, barring antimatter, U235 is the ULTIMATE BATTERY.
Most fusion research seems to be focused on fusing the lightest elements, usually isotopes of hydrogen: deuterium and tritium and occasionally lithium to produce energy.
I wonder how much research has been done on the fusion of heavy elements such as lead (Pb)? If it were possible to reverse the fission of U235, i.e., fuse the fission end products such as Pb back into U235 in an energy efficient manner, and with a very low carbon footprint [1], that would solve the energy storage problem.
[1] Also from the article: "CO2 emissions resulting from current storage technologies range from 104 to 407 kg per Mega Watt-hour of delivered energy. Compare this with coal, which releases almost a 1000 kg of CO2 per Mega Watt-hour produced. " This is the CO2 emissions created in the construction and maintenance of the energy storage facility averaged over the total energy stored and delivered during its lifetime.
Yudkin [1] must be chortling ;)
Warren Buffett, have your boys been slacking off? Somebody is gonna get really hurt...bad!
[1] https://en.wikipedia.org/wiki/Pure,_White_and_Deadly