If you do that, the oil, gas, and desalination infrastructure of the Gulf states will go down together with Iran. And besides that, why do you want to fight Iran to begin with?
[...] you can always reverse (a process) to determine [...]
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.
The bet does not really matter, the central question is whether they have a fair coin or if they are trying to me in some way. Even without the magic store, I would be very suspicious of anyone approaching random people with an offer like that.
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.
One could look at the likelihood of spontaneous coal fires and their effects, gather evidence about the activities surrounding the event, essentially trying to narrow down the set of possible states that would lead to the incident and then see what proportion of those states cause the sinking by fire, military action, or something else. But then attaching a number to that seems a dauting task.
Let us start with coin flips. You repeatedly flip a coin and the number of heads will come out to be about half the number of trials.
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.
Something Bayesian. Despite my best effort I just do not get Bayesian probability, it more or less just does not make sense to me. Can you convince me otherwise? What is your best example of something with a probability that can not be analyzed in terms of frequencies or other proportions? And your Bayesian account of it must make sense, I am 90 % certain that P != NP and that is why I would take bets based on those odds does not cut it.
He will get the same as the others if he works the same number of hours to run the company. The dept would ideally be company debt and not personal dept, after all one reason to found a company is to separate personal and business risks. But if you invest personal money in the company, you get that money back plus some risk and opportunity premium just as you would pay back any other loan. What fraction that is will of course depend on the amount, premium, and payback period. Just investing some money will not provide you a perpetual income.
Envy is the completely wrong framing, it is about fairness. If you design widgets and 99 people build them and everyone works the same number of hours, then the fair share is 1 % for everyone. One percent of the work, one percent of the profit. If you take 2 % [1] while everyone else only gets 0.99 %, that is unfair. And look, the difference for each individual is tiny, 0.99 % or 1 %, that makes it easy to dismiss despite being the source of the unfair inequality.
Because the gap indicates unfairness and people care about that. If you are poor, raising the floor will be good enough, you primary worry will be sufficient income. Once you reach a comfortable life, your priority will - or at least may - shift, now you are in a position that allows you to worry if the situation is fair.
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.
I personally would not look for the way they reason in the weights, at least not directly. In principle I could replace a large language model with a map from all possible input strings to output token or output token distribution without any weights. I have a hard time imagining how you would even tell, at the level of weights and activations, if the next token being the is the result of some proper reasoning or a hallucination. But those weights do not exist for the sake of it, they encode a lot of text the model has seen during training, and I would imagine this is what drives the reasoning. Can you evaluate the following polynomial ... will be related to To evaluate a polynomial ... seen in the training data. This is the level at which I would look for the reasoning, memorized patterns how to do specific things, maybe with some kind of placeholder variables for generalization. Ultimately such a structure would of course also be represented in the weights but I could imagine that this makes it unnecessary hard to understand. Or maybe not, maybe the learned patterns are so complex that they do not have a simple representation.
Why would a RTX 5090 with 32 GB not be able to deal with a 40 GB model? Is there anything preventing me from swapping the weights that do not fit into VRAM in and out of RAM? PCIe 5.0 x16 should max out around 64 GB/s, so slower than the unified memory machine, but at least it should be possible.
Vaguely related, there is also the unfinished Cathedral of Justo [1] near Madrid built by a solo developer since 1961 and essentially by hand and more or less from scrap and whatever people donated. Justo Gallego Martínez died in 2021 at age 96 and donated the building to some foundation for completion.
What do you prefer, a plane crash or a nuclear war? But that does not matter, I did not say a airplane crashing is preferable over something, I said it is not a bad event for everyone. It is bad for the people on board and their friends and families but there are also people that benefit from a crash. That still does not mean that people benefiting from the event are in favor of more airplanes crashing. And for the majority of people it will essentially be neutral, half the planet might never even hear about this particular crash and for many more it will be a thirty second news segment they once saw.
The point of the example is that something that would generally be judged as obviously bad often turns out to not be bad from all perspectives. The same obviously also holds for good things. But I did not intend to imply any economics. The crash investigation might uncover an issue that gets fixed and prevents future crashes, also in this sense the crash had a positive effect. The better outcome in some overall sense would probably still have been for the airplane not to crash and the families spending the money on something better than funerals.
[...] 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?
1. An airplane crashes, everyone dies. Clearly a bad thing. Not so quick. For the funeral industry this means additional business, a good thing. And this is true for a LOT [1] of things, they are not good or bad, right or wrong, their judgment depends on perspective and personal preferences.
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.