9,770 karma · joined October 13, 2012
There is a precondition - constant non-zero Jacobian - to the inverse existing and the inverse is claimed to be of a specific kind - polynomial. The counter example satisfies the precondition and by mapping two different inputs to the same output makes any inverse impossible, including polynomial ones. But maybe that is already ELI7.
So I would certainly consider it likely, that they are trying to trick me. But the probability I would assign to this, would still be rooted in some frequency, somewhere under the hood I would try to estimate the possible situations leading to such an offer and in which fraction of them I will be tricked.
If I am doing a good job with that, then repeatedly being in this situation should result in me getting tricked with the probability I cooked up. If I am bad at figuring out the possible states and their probabilities, then I they will not match.
Where does that come from? It is not some intrinsic property of the coin, it comes from varying initial conditions. If you had enough precision when controlling your hand movements, you could in principle force an outcome with high probability.
But assuming you can not or at least do not do that, there is a certain set of initial states, some will lead to heads, some to tails, and each toss will start from a randomly selected initial state. So given my ignorance of the exact initial state, the coin will land heads with a probability equal to the number of initial states leading to heads divided by the number of initial states compatible with my observations of the initial state. [1]
Repeatedly tossing a coin will sample the set of initial states and the result will match the proportion of the number of states. At least as long as I am not wrong about the set of initial states.
The same applies to something like an election. I have imperfect knowledge about the state of the world but there is a set of states compatible with my knowledge about the world and certain subsets of them will lead to certain candidates to win.
[1] Maybe adjusted by some probability distribution over the initial states if they are not equally likely to be picked.
[1] 1.99 % if we want to be precise.
Also narrowing the gap is a way to raise the floor including in absence of growth while raising the floor without narrowing the gap depends on growth. But I think this is not too relevant in practice because taking a lot of money from a few wealthy people will often result in rather small changes as the money has to be spread among a lot of people.
ChatGPT was announced three and a half years ago, 30-11-2022.
[1] https://en.wikipedia.org/wiki/Planetary_Defense_Coordination...
[...] some detractions are more worthy of consideration than others.
This is probably quite hard to justify in general.
I want zero cents of my money to be wasted on climate change, I live now and I want to enjoy my life as much as possible. I do not care if the planet gets burned to a crisp in a hundred years when I am dead.
One can certainly have a different perspective and vehemently disagree, especially if you have children that will have to live through that future, but otherwise? How would you argue that this position is somehow less valid than any other?
2. Which means that there is generally no policy that makes everyone happy. So you need a party with a program that aims at finding compromises that are acceptable for everyone.
3. But nobody will vote for such a party. Why would you vote for a party that gives you 50 % of what you want if there is a different party that is more aligned with your views and preferences and promises to give you 90 % of what you want?
4. In consequence the political direction tends to hop between extremes instead of settling on compromises. One group gets really unhappy with the current situation, shows up for elections, votes their party into power, moves the situation into the direction of a different extreme, until others get unhappy enough to start the process all over again.
5. Even in political systems where [sometimes] a coalition of parties exercises the power and they are forced to compromise, the outcome is all but ideal. Things move slowly because finding compromises is hard if you do not really want to compromise. Voters look down on the party they voted for because they are not delivering what they promised but only compromises.
I guess the moral of the story is that the voters have to realize that their view is not the only valid one and that voting for compromises would probably yield better outcomes than voting for extremes and either going in that direction for some time until turning around or maybe arriving at a forced compromise that no one voted for.
[1] Exercise for the reader, find something politically relevant that does not depend on perspective and personal preferences.
[1] https://en.wikipedia.org/wiki/Coal-fired_power_station#/medi...
EDIT: To elaborate a bit, if you are burning oil or gas in a turbine, you do not need a cooling tower, the waste heat goes into the atmosphere with the exhaust. If you use fossil or nuclear fuels to produce steam for a steam turbine, you either need a river with enough flow to not boil all the fish if you reject the waste heat into it or you need a cooling tower to reject the heat into the atmosphere.
[1] https://www.aachen-gedenkt.de/traueranzeige/profdr-ingwalter...
[1] The bounds are important because they guarantee that there is at most one prime factor from that range and this ensures that we are not double counting anything. If the upper bound was larger than the square of the lower bound, then we would have to worry about double counting numbers with more than one large prime factor.