NoSuchPlace

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Stupid Questions December 2016

Thank you I fixed it. I think the same argument shows that that question is also undefined. I think the real takeaway is that physics doesn't deal well with some infinities.

Stupid Questions December 2016

As you point out later in the thread the light can never touch any given sphere, since no matter which one you pick there will always be another sphere in front of it to block the light. At the same time the light beam must eventually hit something because the centre sphere is in its way. So your light beam must both eventually hit a sphere and never hit a sphere so your system is contradictory and thus ill defined.

You could make the question answerable by instead asking for the limit of the light beam as number of steps of packing done goes to infinity in which case the light reflects back at 180°, since it does that in every step of the packing. Alternately you could ask what happens to the light beam if it is reflected of a shape which is the limit of the packing you described, in which case it will split in three since the shape produced is a cube (since it will have no empty spaces). (Edit:no it doesn't the answer to this question is again undefined via the argument in the first paragraph, since the matter it bounced of of had to belong to some sphere)

Open thread, Aug. 10 - Aug. 16, 2015

Since I don't spend all my time inside avoiding every risk hoping for someone to find the cure to aging, I probably value a infinite life a large but finite amount times more than a year of life. This means that I must discount in such a way that after a finite number of button press Omega would need to grant me an infinite life span.

So I preform some Fermi calculations to obtain an upper bound on the number of button presses I need to obtain Immortality, press the button that often, then leave.

Prior probabilities and statistical significance

They are different concepts, either you use statistical significance or you do Bayesian updating (ie. using priors):

If you are using a 5% threshold roughly speaking this means that you will accept a hypothesis if the chance of getting equally strong data if your hypothesis is false is 5% or less.

If you are doing Bayesian updating you start with a probability for how likely a statement is (this is your prior) and update based on how likely your data would be if your statement was true or false.

here is an xkcd which highlights the difference: https://xkcd.com/1132/

Consistent extrapolated beliefs about math?

In particular, I intuitively believe that "my beliefs about the integers are consistent, because the integers exist". That's an uncomfortable situation to be in, because we know that a consistent theory can't assert its own consistency.

That is true, however you don't appear to be asserting the consistency of your beliefs, you are asserting the consistency of a particular subset of your beliefs which does not contain the assertion of its consistency. This is not in conflict with Gödel's incompleteness theorem which implies that no theory may consistently assert its own consistency. Gödel's incompleteness theorem does not forbid proofs of consistency by more powerful theories: for example there are proofs of the consistency of Peano arithmetic

Harry Potter and the Methods of Rationality discussion thread, July 2014, chapter 102

Quirrell doesn't have a very large window in which to drink the blood.

According to this he should have plenty of time:

"Is it possible to Transfigure a living subject into a target that is static, such as a coin - no, excuse me, I'm terribly sorry, let's just say a steel ball."

Professor McGonagall shook her head. "Mr. Potter, even inanimate objects undergo small internal changes over time. There would be no visible changes to your body afterwards, and for the first minute, you would notice nothing wrong. But in an hour you would be sick, and in a day you would be dead."

I could see the drinker getting sick

From the transfiguration rules:

"I will never Transfigure anything that looks like food or anything else that goes inside a human body."

This presumably means don't transfigure anything into food. However it could also be interpreted to mean, don't transfigure food into anything. I am somewhat disappointed in McGonagall for not catching that ambiguity.

Also Quirrell is not a recognized transfiguration authority:

"If I am not sure whether a Transfiguration is safe, I will not try it until I have asked Professor McGonagall or Professor Flitwick or Professor Snape or the Headmaster, who are the only recognised authorities on Transfiguration at Hogwarts. Asking another student is not acceptable, even if they say that they remember asking the same question."

"Even if the current Defence Professor at Hogwarts tells me that a Transfiguration is safe, and even if I see the Defence Professor do it and nothing bad seems to happen, I will not try it myself."

However since Quirrells past is unknown (as far as Hogwarts is concerned) he could be one of the best transfigures in the world and he wouldn't be recognized as an authority. Also I don't see Quirrell neglecting something as useful and versatile as transfiguration, so I would expect him to know how dangerous eating formerly transfigured food is.

Harry Potter and the Methods of Rationality discussion thread, July 2014, chapter 102

Also, won't Quirrell die of transfiguration sickness if he drinks the blood of transfigured Rarity?

No, the unicorn will, but by the time Quirrell drinks it blood it won't be transfigured any more, so he will be fine.

Harry Potter and the Methods of Rationality discussion thread, July 2014, chapter 102

These seem to be the relevant quotes:

"For some reason or other," said the amused voice of Professor Quirrell, "it seems that the scion of Malfoy is able to cast surprisingly strong magic for a first-year student. Due to the purity of his blood, of course. Certainly the good Lord Malfoy would not have openly flouted the underage magic laws by arranging for his son to receive a wand before his acceptance into Hogwarts."

and

Only there was a reason why they usually didn't bother giving wands to nine-year-olds. Age counted too, it wasn't just how long you'd held a wand. Granger's birthday had been only a few days into the year, when Harry had bought her that pouch. That meant she was twelve now, that she'd been twelve almost since the start of Hogwarts. And the truth was, Draco hadn't been practicing much outside of class, probably not nearly as much as Hermione Granger of Ravenclaw. Draco hadn't thought he needed any more practice to stay ahead...

-both hpmor ch.78

So from this it seems magic power increases with age, spells cast and time since first getting your wand (though the third could simply be due to the second)

So the reason Harry can only just now cast second year spells, is that he has only recently become sufficiently powerful. His partial transfiguration and patronous v2.0 don't actually require a lot of spell power they only require you to do clever things.

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