agreed. even tarkovsky himself thinks it's his artistic failure. but yet, the message seems so clear to me - discovering something inherently humane, in an inhumane, alien place far away from the familiar world.
i guess this worked better in stalker but the trouble is there may be some other thing going on there which makes the story more complicated than the story in solyaris
@BalarkaSen I just mean there's like, five different fundamental conflicts going on. mankind's engagement with God, the discovery of the inhumane, grief, and many other things I've already forgotten
@MikeMiller I just think the final message in stalker is rather confusing; a mixture of hope and hopelessness. It's as if it's reflecting the director's own confusion about his emotional ties to Russia and estrangement with the USSR.
I was considering doing that, and since I shared my last name anyway when sharing my email... Also one only finds an architect or a chess player when googling my name
I was very not happy when I found some of my students posting their homework questions on MSE. ... Well, if someone says it's not correct and tells you how to do it, you're effectively cheating.
Evening everyone, quick question, I'm trying to find a bijection between $\mathbb{Z_+}$ and $\mathbb{Z_+}^n$, but I'm not particularly sure how to construct a function that's surjective to $\mathbb{Z_+}^n$
Well... hmm... If it's not good practice to ask the question on SO, but it's also impossible to contact my professors, but it's also probably not advised to do the rest of the problem set going in blind
We shall explain the group operation geometrically, then we will use the geometry to proof get a explicit algebraic formula which adds two points on the elliptic curve.
@Alessandro, I could also define $f\left((x_i)_{i \in \mathbb{Z_+}}\right) = ((x_i)_{i \in \mathbb{Z_+}})_k $, where $k \in [1, ..., n]$, but I'm sure that it wouldn't be surjective either
And if I assume my answer was correct for this one question, it's almost certain that if I stretch my assumption to later questions I will get something wrong
The thing to be careful with in probability (I taught the course 2 years ago and had my own issues) is not to cavalierly assume events are equally likely when they're not, @OneRayny. And use conditional probability carefully.
Can someone explain why the number of ways you can add up numbers between 1 and 49 to add up to fifty is not a sum of combinations of $\sum_j=1^50\binom{49}{j-1}$?
@TedShifrin, There is an explicit injection for the $n = 2$ case, if you define $f(n, m) =2^n3^m$, and it follows from another theorem that if there is an injective map from $f : B \to \mathbb{Z_+}$ then $B$ (in this case $\mathbb{Z_+} \times \mathbb{Z_+}$) is countable
@Fargle There is a natural way to define a binary operation on E that makes E into a group.We shall explain the group operation geometrically, then use the geometry to get an explicit algebraic formula which adds two points on the elliptic curve.
Yeah, a sum of stars and bars for every number of bars, with the added mess of dividing every combination by two because of repetitions (1,49) (49,1) (Which makes a mess because it will give 24.5 but I guess just round off to the higher integer)
Here's an idea: Map $\Bbb Z_+^n\to\{x_0+x_1\pi+\dotsb+x_n\pi^n\mid x_i\in\Bbb Z_+\}$ and then map that to $\Bbb Z_+$ in the unique bijective increasing function @Perturbative
@TedShifrin: That set he just described is a discrete subset of $[0,\infty)$. The bijection is given by "Take the first element, then the second, then the thrid, then ..."
lol so you could in principle get a formula for the number of partitions by finding a formula for the number of partitions into k parts, where the k parts are equal or not depending on a partition of k
thus giving a formula for the partitions of n in terms of... all the smaller partitions
@TedShifrin, I'm not sure if this is correct, but if we define $f : \mathbb{Z_+} \to \mathbb{Z_+} \times \mathbb{Z_+}$ such that $f(x) = ((x, i))_{i \in \mathbb{Z_+}}$, would that be a surjection? The only issue, I think I'm having here is with notation
@TedShifrin, my idea was pick a single value of $x$ and then have the tuple $(x, i)$, range over all possible values of $i\in \mathbb{Z_+}$, but I was having trouble on how to properly define a function that would do that
@TedShifrin, Hmm, well intuitively I would draw the $y = x$ line and fill in everything above the $x$-axis and below the line and do the same for the $y$-axis. Translating that into this problem $f(x) = (x, x)$ would be said $y = x$ line, but I can't seem to define a function to do "fill in" everything in that $x$ by $x$ square
actually I think aliens won't even talk to us. We as adults think that the size of genitals is irrelevant. Now think what aliens think of being irrelevant. There are very few human thoughts that might be interesting for an alien. But the first contact will be probably with some stoned Teenies.
