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Teleporting an object 1 meter up gives it more energy the closer it is to the planet, because gravity gets weaker the further away it is. If you're at infinity, it adds 0 energy to move further away.
I think your error is in not putting real axes on your phase space diagram. If going to the right increases your potential energy, and the center has 0 potential energy, then being to the left of the origin means you have negative potential energy? This is not how orbits work; a real orbit would never leave the top right quadrant of the phase space since neither quantity can be negative.
You also simply assume that arrows of the same length are imparting the same amount of energy, but don't check; in reality, if you want the constant-energy contours to be a circle, the axes can't be linear. (Since if they were linear, an object that has half its energy as potential and half as kinetic would be at [0.5, 0.5], which is inside the unit circle.)
(I'm assuming that when you say "momentum" you mean kinetic energy, but those are different things. You claim that any point on the Y axis has equal momentum and energy, but setting aside the fact that these quantities use different units, momentum is proportional to speed, while kinetic energy scales quadratically.)
Why is it a sickness of soul to abuse an animal that's been legally defined as a "pet", but not to define an identical animal that has not been given this arbitrary label?
Eliezer's argument is the primary one I'm thinking of as an obvious rationalization.
https://benthams.substack.com/p/against-yudkowskys-implausible-position
I'm not confident about fetuses either, hence why I generally oppose abortion after the fetus has started developing a brain.
Different meanings of "bad". The former is making a moral claim, the second presumably a practical one about the person's health goals. "Bad as in evil" vs. "bad as in ineffective".
Hitler was an evil leader, but not an ineffective one. He was a bad person, but he was not bad at gaining political power.
It seems unlikely to me that the amount of animal-suffering-per-area goes down when a factory farm replaces a natural habitat; natural selection is a much worse optimizer than human intelligence.
And that's a false dichotomy anyway; even if factory farms did reduce suffering per area, you could instead pay for something else to be there that has even less suffering.
I agree with the first bullet point in theory, but see the Corrupted Hardware sequence of posts. It's hard to know the true impact of most interventions, and easy for people to come up with reasons why whatever they want to do happens to have large positive externalities. "Don't directly inflict pain" is something we can be very confident is actually a good thing, without worrying about second-order effects.
Additionally, there's no reason why doing bad things should be acceptable just due to also doing unrelated good things. Sure it's net positive from a consequentialist frame, but ceasing the bad things while continuing to do the good things is even more positive! Giving up meat is not some ultimate hardship like martyrdom, nor is there any strong argument that meat-eating is necessary in order to keep doing the other good things. It's more akin to quitting a minor drug addition; hard and requires a lot of self-control at first, but after the craving goes away your life is pretty much the same as it was before.
As for the rest of your comment, any line of reasoning that would equally excuse slavery and the holocaust is, I think, pretty suspect.
Do you also find it acceptable to torture humans you don't personally know, or a pet that someone purchased only for the joy of torturing it and not for any other service? If not, the companionship explanation is invalid and likely a rationalization.
I agree that this is technically a sound philosophy; the is-ought problem makes it impossible to say as a factual matter that any set of values is wrong. That said, I think you should ask yourself why you oppose the mistreatment of pets and not other animals. If you truly do not care about animal suffering, shouldn't the mistreatment of a pet be morally equivalent to someone damaging their own furniture? It may not have been a conscious decision on your part, but I expect that your oddly specific value system is at least partially downstream of the fact that you grew up eating meat and enjoy it.
Meat-eating (without offsetting) seems to me like an obvious rationality failure. Extremely few people actually take the position that torturing animals is fine; that it would be acceptable to do to a pet or even a stray. Yet people are happy to pay others to do it for them, as long as it occurs where they can't see it happening.
Attempts to point this out to them are usually met with deflection or anger, or among more level-headed people, with elaborate rationalizations that collapse under minimal scrutiny. ("Farming creates more animals, so as long as their lives are net positive, farming is net positive" relies on the extremely questionable assumption that their lives are net positive, and these people would never accept the same argument in favor of forcible breeding of humans. "Animals aren't sentient" relies on untested and very speculative ideas about consciousness, akin to the just-so stories that have plagued psychology. There's no way someone could justifiably be >95% confident of such a thing, and I highly doubt these people would accept a 5% chance of torturing a human in return for tastier food.)
So with the exception of hardcore moral relativists who reject any need to care about any other beings at all, I find it hard to take seriously any "rationalist" who continues to eat meat. It seems to me that they've adopted "rationalism" in the "beliefs as attire" sense, as they fail to follow through on even the most straightforward implications of their purported belief system as soon as those implications do not personally benefit them.
Change my mind?
Well that explains why you got the wrong answer! Springs, as you now point out, work opposite the way gravity does, in that the longer a spring is, the more energy it take to continue to deform it. (Assuming we mean an ideal spring, not one that's going to switch to plastic deformation at some point.) So if we were talking about springs, you would be correct that the most efficient time to teleport the spring longer would be when it's already as long as possible.
But we are not talking about springs, we are talking about gravity, which works differently. (Not only is the function going in a different direction, but also at a different rate. Gravity decreases as the inverse square of the distance, whereas spring force increases linearly with distance.) So your "simplification" is just wrong. You stated:
This is false. It takes more energy to move an object up by 1 meter on the surface of Earth than it does a million km away, because gravity gets weaker as you go further away. So if you want to maximize the gain in potential energy you get from your teleportation machine, you want to use it as close to the planet as possible.
(An easy way to see why this must be true is that an object's potential energy at infinity is finite, so each additional interval of distance must decrease in energy in order for the sum of all of them to stay finite.)