The first online site I signed up to was Lord of the Rings related. Other variations of Mormegil, Beleg and Turin were already taken and to a 14(ish, not sure) year old it sounded pretty cool. By now I'm quite attached to it.
(September 21st, 2017, 23:23)TheHumanHydra Wrote: suboptimal, I never thought to meet a food or beverage flavorist. What an unusual and interesting occupation. Have soft drinks lost their fizz for you yet?
No, not yet. You'd be surprised at how many different tasting orange and grape sodas are out there, though.
So is the World of Coke "Taste It" section in Atlanta your mecca ? That bitter one from Italy is pretty nasty...
Darrell
Actually, I've never been to Atlanta except in passing through Hartsfield-Jackson. What I can say about Coke is that I prefer it over Pepsi (the latter is too sweet & fruity for my liking) and that Americans haven't had "good" Coke unless they've had it in a foreign country or buy the stuff that's kosher for passover (white or yellow caps in March/April) as it's made with sugar instead of high fructose corn syrup.
(September 22nd, 2017, 11:40)thestick Wrote: 1. Pursuing a bachelor's in economics.
So what's next? When robotics, AI and automation make labor unnecessary, what happens?
Darrell
Assuming that we don't want to think that labor will survive, three things pop into mind. One, we become cyborgs. Two, we revolt. Three, big business and government either give us free shiny doodads or create pointless busywork to keep us in a trance-like state while they slowly cull us. You'd probably want to ask a historian, political scientist, or futurist for that, though; labor is so fundamental to economics that it's a bit hard to imagine society without it.
(March 12th, 2024, 07:40)naufragar Wrote:"But naufragar, I want to be an emperor, not a product manager." Soon, my bloodthirsty friend, soon.
Classical mechanics (plus a bit of quantum mechanics)
Programmer
I'm working on Elite : Dangerous at the moment.
And given my answer to the first question, I feel I should weigh in on the infinity question.
The trouble is that there are two concepts of infinity that are useful: the limit of a sequence that becomes indefinitely large, and the size of an infinite set. The latter (aka cardinality) has been covered extensively by other answers.
The sequence limit concept could be expressed as "an arbitrarily large number", which is what most people think the concept of infinity means. The use of this concept is for when you want to inspect what happens as you move very far to the right on the number line.
For example, what is the value of 2x / (1+x) as x gets very large?
In this case, you can just plug in infinity in place of x, cancel things out, and you end up with the answer 2. Here's a graphical demonstration.
This is dangerous maths though. You need to have an idea of what you're allowed to do and what you aren't. And the explanations of what you can do are all a bit hand-wavey (why can't you say 2 infinity = infinity, for instance?) because it's not been treated here in a rigorous way. It's possible to prove that you're allowed to do that substitution and cancellation and the like, but it's not a simple or short proof at all.
Back to the initial question, the real problem is in its formulation. It's taking a useful shorthand that people use to solve equations like the one above quickly, and trying to apply it to a situation it's not appropriate for: you can't just start with infinity, you need to have an equation which you are taking a limit for. If you try to formulate the initial question properly, you end up asking something like what the value of (1+x) - x is as x gets very large. This isn't a very difficult problem to answer, as it's always 1 everywhere.
What I'm really saying is that "1 + infinity = infinity" is a useful concept in the context of considering a limit, but it's not valid algebra by itself.
(September 21st, 2017, 11:53)TheHumanHydra Wrote: 1) What degrees and diplomas do you have?
2) Is there anything of note you specialized in during your education?
3) What is your current job and/or your career?
4) Is there anything of note you specialize in at your job?
5) Are there any past jobs you've done that are of interest?
6) What is your name, address, and credit card PIN?
1) Degree: Business Studies, majoring in accounting. Post Grad Cert Corporate Treasury (part statistics, part economics, part accounting)
2) Not really, no.
3) Civil Servant. I flunked out of accountancy exams first time round (frankly, I couldn't handle work and study at the same time), and that happened at the height of the crash, so getting back into finance was very hard indeed (looking at around 2012, when I got the post grad, I was seeing jobs I'd have walked into eight years earlier, "trainee" positions, now requiring five years prior experience. Total catch 22 situation right there).
3) My job has four main functions currently, read over investigation files (just to enusre they're complete, I'm not a copper) before submitting them to the Super for direction, write correspondence for the Super, keep on top of reminders down to the Sergeants in Charge and manage the TUSLA liaisons (TUSLA being the child welfare agency). None of it really notable, because it's mainly pushing other people's paperwork around.
5) Not really no. I've been a trainee accountant, a call centre dood, a factory floor stiff for Dell* and a male check out girl.
6) Uostwiss R Diwoh, Greek Town, Springfield. 1234.
*I was working for Dell at the time the "Arbeit macht frei" sign was stolen from Auschwitz. The joke doing the rounds on the floor was that the company had it stolen to put up over the front entrance to the factory.
Travelling on a mote of dust, suspended in a sunbeam.
(September 22nd, 2017, 10:47)AdrienIer Wrote: Unfortunately I can't see what's after the "2*" and after "was"...
The pointless answer is that modulo 1 all numbers are equal, therefore 0=1 in this particular circumstance. But taking numbers modulo 1 is entirely pointless, so they're only equal in very limited circumstances.
The actual answer, of course, is that inifinity is not a number, and (N+1) - N = 1 is only true for N a number. *insert gif about infinity saying "I am not a number"*
There definitely are different degrees of infinity. What's funny is that twice an infinity is still the same infinity. n times an infinity as well. But there are different degrees of infinity because while the number of Integers is the same infinity as the number of Rationals (the numbers written a/b with a and b integers), it's not the same as the number of Real numbers. There are infinitely more Real numbers than there are Rational numbers, while there are the same number of Rational numbers as there are Integers.
The two invisiblish bits are "Sigma 'n' where 'n' goes from 1 to infinity". Yeah, I still remember some of my mathematics.
Travelling on a mote of dust, suspended in a sunbeam.
(September 22nd, 2017, 10:47)AdrienIer Wrote: There definitely are different degrees of infinity. What's funny is that twice an infinity is still the same infinity. n times an infinity as well. But there are different degrees of infinity because while the number of Integers is the same infinity as the number of Rationals (the numbers written a/b with a and b integers), it's not the same as the number of Real numbers. There are infinitely more Real numbers than there are Rational numbers, while there are the same number of Rational numbers as there are Integers.
If anyone cares besides those who obviously already know it -- here's the proof of that as "classically" taught since Cantor, and whose amusing paraphrase was first devised by Hilbert in his excellent headwear. First off, the definitions we need:
We define two sets A and B as having the same cardinality ("size") when there exists a bijective function f : A -> B.
"Bijective" means both injective and surjective. "Injective" means that f(x) = f(y) => x = y -- that is to say, no two members of A are mapped to the same element of B, i.e. no element of B is mapped to more than once. "Surjective" means that every element of B is mapped to at least once. Bijective, therefore, means that every element of B is mapped to exactly once. That's all we need.
To use a practical example, if all the students of Linear Algebra 101 enter the auditorium and sit down, and everyone finds exactly one seat and not one remains vacant, then we map every student to a unique chair and thus the sets of chairs and students have the same cardinality. With finite sets, this is an intuitive definition; it becomes more amusing if we hold infinite sets to the same standards.
Let's define the cardinality of N, the set of all natural numbers, of which there are infinitely many (precisely because every natural number, by definition, has a successor), as ℵ_0 ("aleph-null") or, for this post and because we lack inline LaTeX, just ℵ -- since the Greek alphabet did not suffice to suggest this craft as magical, or perhaps due to Kabbalistic influence. The name isn't too important.
Let's assume, in boundless optimism, that we have as many attendent students in Linear Algebra 101 as there are natural numbers, and an auditorium that holds just as many seats, i.e. ℵ students on ℵ seats, so that student No. x is mapped to the seat No. f(x) := x. The students enter the auditorium and sit down, and obviously, everyone finds their place.
One student, however, is always late. Let's call him Zero. This guy barges in and demands a seat. But isn't the auditorium full already? -- No issue, as it turns out: we simply shift everyone one place to the right. More formally, we define a map
f(0) := 1,
f(x) := x + 1 for all x > 0.
This is a bijective mapping from N_0 (the set of natural numbers including zero) to N (the set of natural numbers not including zero). These sets, therefore, have the same cardinality.
What's also always late is public transportation. The tramway arrives fifteen minutes later, which coincidentally holds just as many students wanting to attend Linear Algebra 101 as are already in the auditorium. Let's call them -1, -2, -3, etc. ("Obviously", there are as many negative as positive numbers; formally, you'd look at the bijective function f : N -> -N; f(x) := -x.)
Can they all find a seat?
Yes.
f(x) := 2x + 1 for all x >= 0
f(x) := -2x for all x < 0
Conclusion: There are as many positive integers as there are integers total (including zero or not).
Because public transportation is so notoriously unreliable, fifteen minutes after that, there arrive ℵ tramways each holding ℵ students. (When constructing the rational numbers from the integers, you can choose any integer for the numerator and just as many for the denominator.) Can they all find a seat?
This is a considerably more surprising answer: Yes! To help visualize the solution, arrange them in a grid like this:
(Start in the top-left corner, and go along the diagonals while counting the numbers -- skipping all fractions that could be simplified further, like 6/2 or 3/6.)
Now for why it doesn't work with real numbers.
Assume we could have a countable (this word designates any set of cardinality ℵ 0) list of all real numbers (in any order) between 0 and 1 (non-inclusive), specifically including non-periodical fractions, like this:
Define a number z := 0.z_1 z_2 z_3 z_4 z_5...., where the z_n are the digits of said number. Now define
z_n := anything you want! -- except the n-th digit of f(n).
Is z on the list? It cannot be. Consider if z were equal to f(n). But z is -- by definition! -- distinct from f(n) in at least one digit past the decimal point, namely, at z_n. However, z is a real number between 0 and 1, so it should be on the list if these were countable. Conclusion: They are not.
The real interval (0, 1) "is larger" (has a larger cardinality) than the set of rational numbers. (Because (0,1) is a mere subset of the real numbers, obviously the same applies to all the real numbers.) We could call this cardinality ℵ 1, and one could naturally ask "how much bigger" this is than ℵ 0 -- or rather, we could pose the question like this: are there any cardinal numbers between ℵ 0 and ℵ 1? This is left as an exercise to the reader.
Hush, Adrien
A discription of Hilbert's Hotel without using the Hotel, nice.
Edit: removed Coeurva's spoilers from within my spoilers as they were spoiling them.
Travelling on a mote of dust, suspended in a sunbeam.
(September 25th, 2017, 10:17)thestick Wrote: Assuming that we don't want to think that labor will survive, three things pop into mind. One, we become cyborgs. Two, we revolt. Three, big business and government either give us free shiny doodads or create pointless busywork to keep us in a trance-like state while they slowly cull us. You'd probably want to ask a historian, political scientist, or futurist for that, though; labor is so fundamental to economics that it's a bit hard to imagine society without it.
I feel like I'm jacking a Math thread . No labor seems inevitable, other than a technical elite. No labor means no labor force means no market for goods & services means no capitalism. No labor means no workers means no communism. Need to find something else .
(September 25th, 2017, 10:17)thestick Wrote: Assuming that we don't want to think that labor will survive, three things pop into mind. One, we become cyborgs. Two, we revolt. Three, big business and government either give us free shiny doodads or create pointless busywork to keep us in a trance-like state while they slowly cull us. You'd probably want to ask a historian, political scientist, or futurist for that, though; labor is so fundamental to economics that it's a bit hard to imagine society without it.
I feel like I'm jacking a Math thread . No labor seems inevitable, other than a technical elite. No labor means no labor force means no market for goods & services means no capitalism. No labor means no workers means no communism. Need to find something else .
(September 21st, 2017, 11:53)TheHumanHydra Wrote: 1) What degrees and diplomas do you have?
2) Is there anything of note you specialized in during your education?
3) What is your current job and/or your career?
4) Is there anything of note you specialize in at your job?
5) Are there any past jobs you've done that are of interest?
6) What is your name, address, and credit card PIN?
1) MPP
2) Not really. Was always too much of a generalist for my own good.
3) Data Analyst for a school system.
4) I move spreadsheets and I know things.
5) Worked on a presidential campaign.
6) Cyneheard, 101 Marten, Wiltshire, 0786
. No labor seems inevitable, other than a technical elite. No labor means no labor force means no market for goods & services means no capitalism. No labor means no workers means no communism. Need to find something else 
.
? That bitter one from Italy is pretty nasty...
-- here's the proof of that as "classically" taught since Cantor, and whose amusing paraphrase was first devised by Hilbert in his excellent headwear. First off, the definitions we need:
