Yep, sqrt(-1) = i. Powers of i are actually really neat imo since they form a loop: i^0 = 1
i^1 = i
i^2 = -1
i^3 (or i^2 x i or -1 x i) = -i
Now the loop starts:
i^4 = i^2 x i^2 = 1 x 1 = 1
i^5 = i^4 x i^1 = 1 x i = i
etc
Any evaluation of i to the power k boils down to i^(k%4). For example, i^726 = i^2 = -1. I know this was super useful in calc 1 or 2 and not used for any of my other math classes, it’s just a fun concept to me
From a purely utilitarianism perspective, assuming all utility is linear and unscaled:
5/6 chance I’m on the side track * 1 person saved = 5/6
1/6 chance on the main track * 1/10 chance my switch is real * 10 people saved = 1/6
Seems pretty clear that you should not flip the switch. However, if I am on the main track, this thinking will lead to no-one flipping the switch and no lives saved whereas everyone thinking it will lead to a guaranteed save -> utility of 10/6.
If I can assume more than half the people can be rational and will think like me then I should flip the switch.
Except that if people are chosen randomly there is 2/3 chance that you are on the main track according to Bayes. Let’s assume there are 10 people.
The probability to be chosen is 1/6 (all are chosen if 6 is rolled) + (5/6) × (1/10) (only one is chosen to go to the side track if 1-5 is rolled) = 15/60 = 1/4.
The probability that you are on the side track knowing that you have been chosen is the probability that you have been chosen knowing that the side track is selected (1/10) × the probability that the side track is selected (5/6) divided by the probability for you to be selected at all (1/4), so (1/10)×(5/6)/(1/4) = 20/60 = 1/3. So there is a 2/3 chance that you are on the main track.
If you do not flip the switch, (2/3)×10 = 20/3 people die.
If you flip the switch, 1/3 (you if on side track) + 10 × 2/3 × 9 / 10 (switch misfires 9 out of 10 times if on the main track) = 190/30 = 19/3 die. This is slightly better than not flipping the switch, you save 1/3 people more. That’s an arm and a leg.
I don’t get it. Do we know that the trolley is heading for the people or not? Do we know if flipping the switch moves it away from whatever track that the people are on? Or is it going in the main track in all instances unless you hit the switch?
I assume a villain would aim the trolley at the people, regardless of what track they’re on. That’s why they’re villains. So I would always flip it.
It’s a standard runaway trolley problem. The trolley is traveling down the main track unless the switch is flipped to send it down the side track. The lever is labeled such that there is no ambiguity which way it is set, the blindfolds notwithstanding. The villain is pernicious and will be equally (though not exceedingly so) delighted to see you die by your own action where inaction would have had saved you. You can somehow trust that the announcement in the headphones is true and not a lie. Such as, for example, you have seen this exact situation happen many times before on TV and survivors/witnesses have described the villain to be truthful every time.
There’s a five in six chance you are picked 1 out of X, and a one in six chance you are 10 out of X.
If you’ve been picked, there are three possible outcomes.
Flipping the lever kills you. 5/6 x 1/X
Flilling the lever saves you and 9 other people. 1/6 x 1/X
Flipping the lever does nothing at all. 1/6 x 9/X
From a purely statistical standpoint, you’re five times more likely to die flipping the lever, but the expected value, measured in lives saved, for flipping the lever is twice as high as not.
From a purely altruistic measure, you should always flip the lever, because at worst you kill yourself, at best you save 10 people, and you can do it with significant confidence that it doesn’t actually matter.
But back to my original question, 5/6X vs 1/6X vs 9/6X where as X approaches infinity, the difference becomes negligible.
Good question to ask, since specifics of selection process may affect the decision outcome! Other variants include growing humans in a vat from scratch on demand, using Star Trek transporter clones, or abducting the necessary number of people from a pre-selected list where your name happens to be the first one. For now, imagine the potential population as the 5 billion living cognizant adults.
as X approaches infinity, the difference becomes negligible
It may be negligible to the 4.999… billion adults sleeping comfortably and securely in their beds tonight, but the problem presupposed that you have already been abducted. It remains underdefined whether you refers to you the specific person reading this meme, or a more general you-the-unfortunate who has been chosen and is now listening to this on the headphones.
I wouldn't agree with your paraphrased characterization but I think the reason that the experiment results are widely misunderstood is for the same reason any retraction or updated information can't reach the entire same audience as the original information.
The experiment was popularised by Feynman in the 60's and widely discussed as the basis for quantum mechanic. Feynman generally was a fucking rad dude, but he did have a penchant for the poetic, which is probably why he was so popular. Einstein weighed in on the concept too, so big names with big topics in a lunar-landing sci-fi loving era. And quantum mechanics was a fun new mindfuck development in its own right.
So, when a few decades later, the tech catches up to the theory, in experiments by smaller-fame scientists, and the theory further refined; then you've got a legion of adults who grew up with the 60's romantic understanding published in mainstream media, teaching that to the next generation... and you get this.
I can personally blame Brian Greene's 2005 https://www.penguin.co.uk/books/54483/the-fabric-of-the-cosmos-by-brian-greene/9780141011110. His section on the experiment didn't feel right at the time, but feels aren't reals, so I just went with my very limited understanding of an expert's overview. The refined explanation now feels a lot more sensible, for what it's worth.
Okay so what would a more accurate summary be, because what I got from that is that the Dual slit was debunked by us not having the proper tools to actually measure things this small. If that’s not it then I sincerely do not get it.
“The experiment is bullshit, we just can’t measure shit.”
The experiment is limited by our existing tools and evidence, and this will impact both its accuracy and our interpretation of the results, but it's the best we have for now and still worthwhile as a way of producing additional evidence for other researchers.
Also, researchers typically don't condense information into soundbites well, which prevents people from easily understanding and remembering the accurate information. Which allows bad interpretations by other people of the researchers interpretations of rough results to gain traction.
In other words, normal science problems.
An experiment isn't bullshit just because we can't achieve perfection in methodology or human analysis. And we can't refine our theories and tools without multiple inaccurate answers being compared to find congruence.
The bullshit starts with the people whose theories which rely on the inaccurate parts refuse to modify the theory when the evidence disagrees.
Basically my understanding as gathered from the original post, is that the Dual slit experiment does not actually make any meaningful statements because the thing that it intends to measure cannot be accurately measured. However the measurements we got from the imprecise are weird, but that’s to be expected because that’s basically the same as looking at the moon with a magnifying glass and trying to make as accurate astronomical predictions
I want to clarify that the “cannot” here refers not to the inadequacy of our tools (which hypothetically could have been fixed in the future by building better tools), but by a fundamental prohibition of the quantum mechanics theory. Practically, the single-photon lasers and detectors used here are like 90%+ efficient - plenty good enough to distinguish between the two monkey scenarios. But some observables in quantum mechanics are “orthogonal” - you can measure one or the other, but not both at the same time - the math will not allow it. The typical example of that is “position” and “momentum” of a particle.
The math is quite beautiful actually, the analogy I’d use is something like asking “Which way is east at the North Pole?” In your head you can either know “This direction is east.” or “I am standing at the North Pole.” but you cannot hold both pieces of knowledge in your head at the same time.
The orthogonal observables in this experiment are the “which-way top/bottom slit” information and the “which-interference-category Pattern 4/Pattern 5” information. It’s even more beautiful in the delayed choice quantum eraser experiment that I was ranting about here. There, both pieces of information are stored orthogonally in a single photon. You can choose at a later time to either measure it one way, which will tell you the which-way info, or in a different way, which will tell you the interference category info, but there is no hypothetical way to measure it in both. The only way you can get the category info out to allow your computer to draw the interference pattern is if you guarantee that the which-way information has been irrecoverably erased. It is as if the whole universe conspires to censor this information from you! But it’s just the consequence of the math rules in use.
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