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wonderings
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a52
 RE: wonderings
Post: #26
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were the actions of the simulators in the talos principle ethical?

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02-03-2017 03:16 AM
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a52
 RE: wonderings
Post: #27
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most people do believe that animals should be afforded at least some of the ethical considerations we apply to humans, generally more the more intelligent the animal is. dolphins, elephants, high primates and certain parrots have rudimentary cultures and civilizations, as well as being capable of logically solving problems, feeling empathy towards members of their own species, their caretakers, and others, and feeling emotion and pain.
if this is the case, isn't what we're doing to these species through hunting and habitat loss comparable to how europeans abused african tribes in the late 19th century?

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02-03-2017 03:38 AM
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Wheat
 RE: wonderings
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that is not a good comparison and there's a lot to unpack with it.

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02-03-2017 03:50 AM
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a52
 RE: wonderings
Post: #29
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okay.

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02-03-2017 04:01 AM
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☆ C.H.W.O.K.A ☆
 RE: wonderings
Post: #30
i'm rad as hell, and i'm not gonna take it anymore

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(02-03-2017 03:15 AM)a52 Wrote:  if you perfectly simulated, atom by atom, a human being in a room, would they be conscious? sure, they could calculate and have internal thoughts. they could feel emotion and have opinions. they would THINK they were just as conscious as everybody else. but would they really have a sort of "point of view" the same way we do? or would their existence be like that of a calculation machine, grinding gears and sending signals but not actually, you know, seeing out of their own eyes?

your own self and brain is just atoms making meat and chemicals and blood and shit, just a meat computer calculating and sending signals. so the theoretical 1:1 simulation or replica is just as "alive" as any human, unless you have some notion of a soul
02-06-2017 09:10 PM
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Wheat
 RE: wonderings
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soul .exe

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02-06-2017 09:54 PM
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a52
 RE: wonderings
Post: #32
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consider some function that is zero at every point. now set the output of some input x0 as f(x0), where f is some differentiable function (say, f(x) = x2), so that the function is zero everywhere except at that point. now set some other point x1 to equal f(x1). repeat this process uncountably infinitely many times, until this new function equals f at every point.

is this function continuous and differentiable?

it seems like it's not, because at every point in its creation, it's just a string of points. then again, it seems like it is, because it equals f at every point, and f is both continuous and differentiable. then again, maybe making a function like this is impossible, because you have to do uncountably many definitions in order to cover the reals, and the whole point of uncountable numbers is that even with infinite time, you can't do uncountably many things.

but if you can't construct a function like this, how can you construct any function? what does continuity even mean, anyway? now that i think about it, the ideas of limits and continuity seem even more shaky than the infinitesimals they were meant to replace. they make sense, but they don't seem like they could ever be rigorously justified.

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(This post was last modified: 03-16-2017 01:45 AM by a52.)
03-16-2017 01:44 AM
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a52
 RE: wonderings
Post: #33
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even harder question: why am i pondering the nature of continuity and the real line when i should be doing my overdue history homework? it's a mystery.

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03-16-2017 01:47 AM
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a52
 RE: wonderings
Post: #34
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dear god, there's nothing scarier than the interval (0, 1).

(with the exception, perhaps, of 5-page essays on the civil war)

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03-16-2017 01:53 AM
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Kíeros
 RE: wonderings
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I think that provided there is some open interval (xn-δ,xn+δ) in which every point had been mapped to the continuous and differentiable function after uncountably many steps, then the function at xn would be continuous and differentiable.
The problem is that any function fn(x) does not fit this criterion, because you are going one point at a time, so it's a countably infinite number, so we can do a diagonal proof to find a point however close to xn that is still 0, and so at no time would it be continuous.

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03-16-2017 03:16 AM
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a52
 RE: wonderings
Post: #36
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(03-16-2017 01:44 AM)a52 Wrote:  continuity????????

related: https://www.youtube.com/#/watch?v=D2xYjiL8yyE

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03-16-2017 04:40 AM
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a52
 RE: wonderings
Post: #37
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If asked to find a random integer on (0, ∞), the only sensible answers are 0 and ∞.

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(This post was last modified: 04-06-2017 04:52 PM by a52.)
04-06-2017 04:52 PM
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a52
 RE: wonderings
Post: #38
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suppose n, a, and b are integers, a and b > 0, a != b, and n = a^2 + b^2

sqrt(n) = sqrt(a^2 + b^2)
sqrt(n) = ||a + bi|| by the definition of the complex modulus
n = ||(a + bi)^2|| by the fact that the square of a complex number has a modulus equal to the square of the modulus of the original number
n = ||a^2 - b^2 + 2abi||
n = sqrt((a^2 - b^2)^2 + (2ab)^2) definition of complex modulus
n^2 = (a^2 - b^2)^2 + (2ab)^2

conclusion: any number that can be written as the sum of two squares has a square that can also be written as the sum of two squares. by induction, this holds for all higher n^2^k, so long as the corresponding a's and b's are never equal and never equal zero.

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05-27-2017 02:18 AM
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qwerx3
 RE: wonderings
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and in fact, you can multiply a+bi with c+di to show that the product of any two numbers that can be written as a sum of two squares can also be written as a sum of two squares
05-27-2017 08:26 AM
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qwerx3
 RE: wonderings
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moreover we may exactly classify all numbers that can be written as a sum of two squares

lemma: Let p = 3 mod 4 and prime

if a^2+b^2 = 0 mod p then either a,b = 0 mod p (this is one solution) or we can divide by b (b is coprime to p so we can do this):

(a/b)^2=-1 mod p. So (a/b)^4=1 mod p, and thus the order of a/b in Z/pZ is 4. but wait, the cardinality of Z/pZ is p-1. and this is 2 mod 4. but by Lagrange's Theorem all element's order divide |Z/pZ| = p-1 so this is impossible!

therefore a,b = 0 mod p is the only solution.

(yeah ok we didn't really need group theory there, quadratic reciprocity does the trick too.)

anyway the punchline is that numbers with an odd number of any 3 mod 4 prime factor cannot be written as the sum of two squares. some minor details left out but you get the idea

(this is a necessary, and as it turns out, sufficient condition - what remains is to be able to show that all primes 1 mod 4 can be expressed as the sum of two squares, and you can use quadratic reciprocity)
05-27-2017 08:38 AM
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a52
 RE: wonderings
Post: #41
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things i hate:
string theory
the cosmological constant
quantum entanglement
the fact that all attempts to get around quantum entanglement still end up with some kind of superluminal communication (looking at you, de broglie bohm theory)

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06-04-2017 05:48 AM
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ICan'tGiveCredit
 RE: wonderings
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why do you hate superluminal communication?

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06-04-2017 02:23 PM
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a52
 RE: wonderings
Post: #43
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(06-04-2017 02:23 PM)ICantGiveCredit Wrote:  why do you hate superluminal communication?

it breaks relatively. even if you manage to somehow mush it into behaving, it still just seems wrong.

why is upwards infinity so much easier to swallow than downwards infinity? if you told somebody that the universe will exist forever and that it has already existed for an infinite amount of time, they would almost surely find the first statement much easier to accept. why?

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06-09-2017 01:48 AM
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