Ok, how about this: What is the axiom of choice and why is it such a controversial axiom?
Are you genuinely interested in having me supply lay interpretations of various math concepts? Almost anything you could ask about is already explained in places like mathworld or wikipedia, but if you truly find their articles too detailed or jargony, I am willing to explicate and simplify as best as I am able.
There are over six times as many people in California than there are in Finland. That might explain it a little.
There are almost 250 times more people in China than there are in Finland, yet there is only one Chinese IKEA location. I don't think population has anything to do with it.
Don't be a smartass, implicit in Kyrsimys' explanation was that California and Finland have comparable standards of living.
One cannot believe two completely contradictory things at the same time.
I think Richard Dawkins would accuse you of doing just that. Also, the vast majority psychologists and psychological researchers would disagree with you, especially as concerns the tendency of humans to selectively fail to apply their own beliefs when it would have a negative impact on their self-image. It is also hard to say categorically that humans cannot believe contradictory things in cases where it is inobvious (but true nonetheless) that a contradiction exists.
[23:20:03] <jimsfriend> Fabian, it might also be good to let warp know that failure doesn't mean he should give up, just that he should try again
[23:20:12] <jimsfriend> if he is socially awkward he might take rejection a bit hard
This is actually true. I have actually dated a whopping 2 women during my life. Ending the relationship was in both cases really painful. The post-effects lasted for quite long time. I'm not very eager to repeat the experience for a third time.
I'm just gonna toss this out there ... if you find yourself too caught up in remembering all the times you've been hurt, there are a few non-toxic, non-addictive psychedelic drugs that can help you work through those emotions. Such an approach is perhaps not appropriate for everyone, but many people find such "psychic exploration" invaluable.
Dextromethorphan is fairly ideal for a beginner, as it is not a controlled substance, and while it positively alters your emotional and perceptual state, it doesn't impair cognitive function. Some describe the DXM high as giving you the ability to be peacefully detached from your intrinsic emotional responses, allowing you to think deeply about profoundly disturbing and painful experiences without experiencing any of the negativity that overwhelms you otherwise.
Anyway, it might be worth a shot. Disclaimer: it is still possible to use non-toxic, non-addictive substances for the wrong reasons and become psychologically dependent on them. E.g., using DXM regularly because you want to feel detached, as opposed to using it occasionally because you have an issue you want to explore. Also, very important, taking DXM on an MAOI or SSRI (i.e. virtually all modern antidepressants) will kill you. Together they will prevent the reuptake of serotonin enough for your serotonin levels to become fatal.
Can you explain, in simple terms, the ramifications of the Poincaré conjecture?
I'll help you out again, Warp. Suppose you have a flexible sheet of rubber or some such. The edges of the sheet are tacky and will stick to each other if pressed together. What sort of things can we do with this sheet? We could join two edges into a cylinder and then join the edges of the cylinder into a torus:
We can make a sphere by folding the four corners together in the center and joining the edges wherever they touch:
Of course we would have to inflate that to make it seem like a sphere, but that's why we are using a flexible rubber sheet! In both of those examples we got rid of the edges by gluing them to each other. There are lots of different shapes without edges we can make, but since our rubber is so flexible, it turns out some shapes that may initially look different are actually the same. Inflate a little here, deflate a little there ... voila!
Of course, the sphere and the torus can never be made to look the same no matter how much you might push and pull on the rubber. The torus has a hole in it, while the sphere does not, and that makes them fundamentally different in ways that can be described rigorously using mathematical concepts. It turns out, though, that any shape you make that 1) has no edges, 2) has no holes, 3) doesn't pass the sheet through itself (which would be impossible if you were manipulating a sheet of rubber in the real world) is actually equivalent to the sphere. That is, there is no edgeless, holeless, 2-dimensional surface embedded in 3-dimensional space that is not deformable into the sphere.
The Poincare conjecture asks if this is true for a 3-dimensional sheet in 4-dimensional space. As far as I know, there aren't any practical applications of this knowledge, and there may well never be. As I mentioned before, intellectual exploration of this nature is an end unto itself. Perhaps this book will help you to understand the significance, beauty, and artistry of "useless" mathematical exploration.
Chess is a game of skill without elements of chance and with perfect information. Hm hm. You certainly don't see random guys at home in front of the TV with a beer watching a good chess game after a long day's work. So I'm going to say it's not a sport.
I feel compelled to point out that chess is broadcast on TV in Iceland. (As Go is in Japan and China.)
I wonder if Warp was actually thinking of the riemann-zeta function which has been practically applied as a "random number generator" for cryptographic and other purposes since world war 2 (at least according to Neal Stephenson)
Well, the Riemann hypothesis is a claim that the Riemann-zeta function behaves in a particular manner, so yes, that's what we were both talking about. I am not familiar with Neal Stephenson's fiction, but I think he was fast and loose with his portrayal of the Riemann-zeta function. To my knowledge, it has never been used for cryptographic purposes or as a random number generator. Cryptography in WWII was limited to electromechanical devices that performed transpositions and substitutions. I don't think modern cryptographic methods came about until the 70's.
In 1997 there was a paper in the Duke Mathematical Journal entitled Zeta Functions, One-Way Functions, and Pseudorandom Number Generators, but I'm not clear how much it really has to do with the Riemann hypothesis. A brief description I found mentions that the pseudorandom number generator in the paper is based on the theory of elliptic curves, but about the one-way function only mentions it was "based on the theory of zeta functions." The Riemann-zeta function is a zeta function, obviously, but that short description doesn't lead me to believe the Riemann hypothesis actually had anything to do with it. (There are lots of different zeta functions.)
Dear Fabian,
Could you explain me in simple terms the Riemann hypothesis and why it has such a great importance in the field of mathematics?
No.
I'll tackle this one. The Riemann hypothesis states that a particular mathematical function has a particular property. I don't think it will add anything to the discussion to get any more detailed than that.
The Riemann hypothesis is important to mathematicians because it is unusually interesting. For one, its formulation is simple and easy to understand, yet it has remained impervious to proof for a century and a half. It also links together seemingly unrelated areas of mathematics, namely number theory and complex analysis. Discoveries that link previously unrelated fields together are always exciting because then you can use ideas from one to discover new insights in the other. A recent discovery along these lines was the addition of homotopy theory to algebra, which allows one to use techniques from algebraic topology to solve problems in algebraic geometry.
If you are looking for any practical importance, it really doesn't have any that I know of. Because of what it says about prime numbers and their distribution, the correctness of certain algorithms for determining primality depend on the correctness of the hypothesis, but proving it won't break RSA or anything like that. Nowadays, mathematics is sufficiently advanced that very little of the new theoretical work has any practical importance. Really, deep exploration in mathematics is just an end unto itself, like sports, chess, music, or art.
2001: A Space Odyssey is off the hook now because Transformers is officially the worst movie I've ever seen.
I think Peter Sobczynski's review closely mirrors many of my own views on the film:
1 Star, "Might As Well Be 'Uwe Boll's Go-Bots'"
The Transformers came along several years after I had already outgrown both toys and syndicated television cartoons that were barely-disguised commercials for said toys, so I was unable to experience them first-hand during their heyday. (I do recall slinking into a movie theater to catch the cheapo 1986 animated film “Transformers: The Movie,” mostly because at that time, one didn’t easily pass up on the opportunity to see a film that utilized the vocal talents of both Orson Welles, in the last film before his death, and Judd Nelson, in one of the last films before his career death.) As a result, I went into the screening of “Transformers,” an epic-sized screen adaptation of the property from the collective minds of director Michael Bay and co-producer Steven Spielberg, without any real kind of pre-conceived notions of what should and shouldn’t be on display in such a production. However, even if I had gone into the film expecting the worst, I doubt that even I could have contemplated something as grotesquely awful as this monstrosity. Produced with an abundance of money and technological knowhow and a complete absence of wit, style or excitement, this is less a film than it is a full-out assault on the senses that confuses bludgeoning a viewer with noisy spectacle without actually entertaining them.
Although the storyline for “Transformers” is so bizarrely convoluted that it seems to have been designed solely to defy any attempt at a coherent synopsis, I will nevertheless attempt to provide one. In a prologue, we learn of a faraway planet called Cybertron that was populated entirely by robots under the thrall of a mysterious, all-powerful cube known as the All Spark. Alas, this mechanical utopia was not to last and the robots separated into two factions–the heroic Autobots, led by Optimus Prime, and the villainous Decepticons, led by the monstrous Megatron–that went to war when Megatron attempted to seize the All Spark for his own ends. In the ensuing battle, Cybertron was destroyed and the All Spark was lost in space. For centuries, the Autobots and Decepticons have combed the galaxy looking for the All Spark and as the film opens, it turns out it has finally turned up on some distant and insignificant planet known to its denizens as Earth.
Reps from both sides of the conflict quickly arrive on the planet and, while waiting for their brethren to arrive, go about seeking the whereabouts of the All Spark in their own inimitable manners. A Decepticon disguised as an Army helicopter turns up in Qatar and proceeds to blow the hell out of an American military base, with the exception of a single rag-tag platoon led by manly men Lennox (Josh Duhamel) and Epps (Tyrese Gibson), while attempting to download information from the various military computers. When this gets interrupted, another Decepticon, this one in the form of a boombox, somehow finds its way onto Air Force One and only the complete shutdown of the entire military computer system is able to prevent yet another hack. In Washington, the Secretary of Defense (Jon Voight) brings in the top computer geeks from throughout the country (at least the ones who weren’t all blown to hell in “Live Free or Die Hard”) to figure out what this unknown force is looking for. Luckily, superhot computer babe Maggie (Rachael Taylor) quickly discovers that the hacks are focusing on a mysterious government faction known as Sector 7 and their top-secret “Project Iceman.” The military is convinced that the attacks are coming from Russia or North Korea (though al Qaeda is strangely never mentioned) but Maggie is convinced that the threat may not be human after all.
Meanwhile, in California, obnoxiously gawky teener Sam Witwicky (Shia LaBeouf) is off to purchase his first car, mostly in an effort to win the heart of teen queen Mikaela (Megan Fox). He winds up picking a beat-up Camaro that sometimes seems to have a mind of its own–when Sam actually manages to get Mikaela into his car, it breaks down at the local makeout place and the radio starts blasting “Let’s Get It On.” This doesn’t seem to faze Sam that much but when his car takes off in the middle of the night, he follows it to a junkyard and witnesses it transform into an Autobot and send out a signal. Before long, one of the Decepticons arrives and nearly destroys Sam and Mikaela before Sam’s car arrives in the nick of time, transforms back into a robot and smacks the attacker down. Soon, the other Autobots, led by Optimus Prime (voice of Peter Cullen), arrive and fill Sam in on the details. It seems that Sam’s grandfather, an Arctic explorer, accidentally stumbled upon the long-buried Megatron and inadvertently semi-activated him in a way that imprinted the coordinates showing the location of the All Spark on the lenses of his eyeglasses. Now the two factions are once again ready to do battle for the All Spark–the Autobots want to return it to Cybertron and attempt to revive their home while the Decepticons want to use its powers to turn all the machines on Earth against mankind and destroy the world as we know it–and the fate of the world hinges in the balance.
Since this is pretty much the point in “Transformers” where the storyline pretty much devolves into a series of loud and ungainly sequences in which giant robots beat the crap out of each other while laying waste to Los Angeles, the Hoover Dam and other sundry locations mixed in with conspiracy theories, heartfelt speeches and a highly unexpected explanation for the existence of the Hoover Dam, let us now take a moment to leave this bizarrely convoluted storyline and wonder what the hell screenwriters Roberto Orci & Alex Kurtzman could have been thinking when they slapped it together. Let’s face it, anyone attending “Transformers” is going to do so for one reason and one reason only–to see as many robot smackdowns as humanly possible. Therefore, you would assume that anyone charged with putting this on paper would want to figure out the simplest and most direct narrative line to get to the CGI carnage. Here, Orci & Kurtzman have given us a storyline so unwieldy that it often seems at times as though they are going out of their way to frustrate viewers.
For starters, while the opening military base attack does have a certain oomph to it, virtually all the subsequent material involving the military team could have been excised without losing anything but about 40 minutes of the absurdly overlong 145 minute running time. Then there are the strangely juvenile and utterly nonsensical sequences that have been shoved in for reasons that completely elude me. For example, there is a protracted sequence where the Autobots, in their various car and truck forms, follow Sam back to his house so that he can look for those damned eyeglasses. Now if you or I were an Autobot trying to keep a low profile, we might retain our auto forms so as not to arouse suspicion from anyone in the area. Of course, such logic might not appeal much to the ADD-afflicted 12-year-olds that this film is clearly being aimed at because these Autobots instead choose to assume their full-on robot forms and clomp around in Sam’s backyard so that we can all revel in the hilarity of a) Sam’s clueless parents somehow not noticing the GIANT ROBOTS IN THEIR BACK YARD and b) said giant robots trying to hide under porches and alongside walls in order to avoid detection. (I will spare you the various urination and crotch-smashing gags that have also been included, even though you would think that such concerns would be meaningless to giant robots.) The screenplay is so incompetent, in fact, that when the writers do stumble upon a potentially decent idea, such as having the grandfather discover the frozen Megatron in the Arctic, they don’t have any idea of what to do with it–what might have made for a great prologue in an ordinary blockbuster is instead tossed away in a flurry of mid-film exposition at a point when most sentient beings will have already mentally checked out.
Granted, one does not go to a film like “Transformers” for the complex narrative–one goes to allow our inner children to revel in the sight of enormous robots wreaking elaborate and expensive havoc on everything they see. And yet, if anything, the film is actually a bigger failure at this than it is at storytelling. For starters, the film is visually ugly–maybe it was the inevitable degradation of the image that comes from adding in the countless CGI effects or maybe cinematographer Mitchell Amundsen figured he could clean things up in post-production but whichever it was, there were points in the print that I saw where the image was so grainy that it almost looked like a bootleg video. This is especially odd when you consider that Michael Bay, whatever his faults as a filmmaker may be, can usually be relied upon to create a good-looking movie.
Then again, it soon becomes apparent that he isn’t exactly on his A-game either. Over the years, many have dumped on Bay for being nothing more than a purveyor of soulless cinematic junk food–and you can hardly blame people for thinking that of the auteur of such craptaculars as “Pearl Harbor,” “The Island” and “Bad Boys 2" (my personal choice for the third-worst movie ever made)–but to be fair, the man can usually put together a decent action sequence and I will even cheerfully admit to more or less liking both “The Rock” and “Armageddon” for the way that they provided their fenderheaded thrills with style and humor. With “Transformers,” however, he seems to have forgotten everything that he once knew about shooting an action scene and instead presents us with one of the most graceless action extravaganzas I’ve ever seen. As usual, his whiplash editing style–if there is a shot on display lasting more than ten seconds, it has escaped my mind–means that it is impossible to get any real sense of what the hell is going on or where any of the characters are in relation to each other. This time, however, he couples that flaw with the bizarre decision to shoot most of his scenes of robots duking it out in close-ups instead of pulling the camera back to let us get a better look at them and their sheer size in relation to everything else. Because of this, the scale aspect is lost and since the various robots rolling around on the ground or shooting at each other are more or less interchangeable, it becomes almost impossible to determine which one is which at any given point. (One of the Autobots apparently dies in battle but it is handled so badly that I didn’t even realize it until Optimus Prime eventually offered an elegy to his fallen comrade.) The results are such a mess, in fact, that I would be willing to bet that a little kid armed with nothing more than a couple of action figures and Dad’s DV camera could come up with better and more coherent action scenes than the ones seen here.
“Transformers” is a gargantuan mess from start to finish and even the fan-heavy and highly enthusiastic crowd that I saw it with seemed to begin growing restless as it lumbered along to the sequel-set-up that it calls an ending. To be fair, there were two elements on display that helped serve as minor respites from the rest of the noisy non-spectacle. The first is the presence of Megan Fox as the central hottie–there is no real purpose for her character and there is certainly no evidence that she can indeed act but she is such a gorgeous presence on the screen (even though she is theoretically supposed to be playing a high-school junior) that she will inspire the kind of reactions in most male viewers not usually seen outside of the collected works of Tex Avery. The other is the completely screw-loose supporting performance from John Turturro as a shadowy government agent who crosses paths with our young hero. By any sane critical standard, his performance would be considered an embarrassment of scenery-chewing on a level not seen since Marlon Brando put on the prairie dress and sauntered through “The Missouri Breaks”–perhaps this was his manner of rebelling against the substandard material. However, his barking-mad turn gives the film the only real juice it has (and its only genuine laugh when he interrupts a jargon-heavy briefing to admonish an underling with “Try to keep up with the acronyms!”) and when “Transformers” comes to its blessed end and you flee to the parking lot with a throbbing headache and an emptied soul, it is the only aspect that doesn’t hurt too much to think about a second time.
Here's a score that's a little better than before, but I screwed up in level 32, so this can be improved by several percent, maybe?
Using the same placement guidelines as before, here's the best start so far, incorporating anubis' suggestions:
1. Red.
2,3,4,5. -1 life.
6. Upgrade red (2).
7,8,9,10. Upgrade red (3), -1 life.
11,12. Blue, -1 life.
13,14. Upgrade red (6).
15,16,17,18,19. Upgrade red (7).
20. 2x blue, -1 life.
21. Sell red.
22. Purple, -1 life.
23. -3 lives.
24,25. Purple.
26,27. 2x blue.
28,29. 2x blue.
30. Blue.
You could theoretically have 12 lives at the end of that, though it's not very likely. You have to target well and get lucky. I think that can be improved with some purple upgrades as well, but I haven't worked it all out yet.
Upgrading Red1 to level 2 on wave 6 instead of 4 is good for a 0.76% improvement, you're right. I forgot I'd been buying early there only for an outdated strategy I needed the life on. If you don't have concrete examples of further improvements in the first 19 waves I'd tend to doubt they exist. I did a pretty detailed analysis of waves 9-19, and I do have the highest legitimate score on the scoreboards. (One possibility is to buy a level 2 Red1 instead of upgrading the level 3 one to 7, but I think that leaves you with too few lives.) Anyway, feel free to try to beat my score, we now know it can be beaten by at least 1.3%.
Here's the first 28 waves of a strategy that is definitively superior to the one I used to achieve my high score. (At wave 29 you can transform it into my high score game, only with 0.65% more money.) Finishing a game is so boring, though, I doubt I'll finish this off any time soon.
1: Red1.
4: Upgrade Red1 to level 2.
10: Upgrade Red1 to level 3, -1 life minimum.
12: Blue1, -4 lives minimum.
14: Upgrade Red1 to level 7.
19: 2x Blue1, sell the Red1 at the end of the level.
20: Purple2.
21: Blue1.
22: Blue1.
23: Blue1.
25: Purple2 where the Red1 used to be.
27: -2 lives minimum.
29-50: On your own! Just keep adding Blue1 towers in strategic spots and slowly upgrade your firepower where it is cost effective.
- Turn target locking off for all towers, and initially, set targeting to hard.
- Change tower targeting as needed so that you don't target a creep that requires only one hit with two towers.
- Towards the end of a wave, use close tower targeting to focus firepower on creeps that are about to escape.
- It's not cost effective to get Red3 towers until wave 42, at the very earliest. You might be able to wait until wave 44, I'm not sure.
- Always buy towers after hitting the "send next" button!
This score isn't perfect, but it's as close as I care to get. I'm getting a little sick of this game and my mistakes this time around were really minor. I'll post a tutorial in a bit.
I'll write down what I'm doing the next time I play, but a video would be quite long. I don't usually play through all of the levels all at once, and even if I did I think the video would be over an hour long! (I also "multitable" when I play so I can correct mistakes without starting over. My mistake at level 45 last time was so catastrophic because it was my last remaining board.)
Argh! This would have been the world record if I hadn't died on the last level. (You can see I have more money than in my previous picture.) Oh well. I screwed up big time in level 45 and was only barely able to save it by putting in that ridiculous junk near the exit. If I try again I think I might be able to end the game with $7.15 - $7.2 million.
Phil and Baxter, can you finish your abandoned movie so we can have a movie with no glitches? Now it seems sensible to have two versions of this movie.
This is the 1155th time I’ll speak to you from this forum, and the last. Know that it is with a heavy heart I type these, the last words I will ever record. I need not be reminded of the oath forsworn, short days ago, that the unsuccessful conclusion of my run would perforce coincide with the ineluctable conclusion of my life.
I know more than some see me as a naught but a nuisance, a bother, and I am pleased to think that I shall be able to free those from any further effects of my presence, though I fear it is at a cost which will give pain to my friends. I have already explained to you, however, that my career here has in any case reached its crisis, and that no possible conclusion could be more congenial to me than this. Indeed, if I may make a full confession to you, I was quite convinced that my effort would be rejected, and I allowed its submission under the persuasion that some development of this sort would follow.
My friends, no one, not in my situation, can appreciate my feeling of sadness at this parting. To this site, and the kindness of its members, I owe everything. Here I have lived a quarter of a decade, and have passed from a boy to a man. Here my dreams have been born, and one is buried. But I never forgot, how oft we tremble in the frost to catch snowflakes, on nose, or lash, or lips, knowing they must melt.
I take my leave of you with these simple words: remember me, and pray believe me to be, my dear friends,
......Very sincerely yours,
............xebra
----
hypocrisy
I uploaded a couple of alternate avatars:
Those are normal, angry, playful, punish, comfort, guru, hyperactive, and bleh. I don't have anything for tired, hope, or sadness yet.
We can make a sphere by folding the four corners together in the center and joining the edges wherever they touch:
Of course we would have to inflate that to make it seem like a sphere, but that's why we are using a flexible rubber sheet! In both of those examples we got rid of the edges by gluing them to each other. There are lots of different shapes without edges we can make, but since our rubber is so flexible, it turns out some shapes that may initially look different are actually the same. Inflate a little here, deflate a little there ... voila!
Of course, the sphere and the torus can never be made to look the same no matter how much you might push and pull on the rubber. The torus has a hole in it, while the sphere does not, and that makes them fundamentally different in ways that can be described rigorously using mathematical concepts. It turns out, though, that any shape you make that 1) has no edges, 2) has no holes, 3) doesn't pass the sheet through itself (which would be impossible if you were manipulating a sheet of rubber in the real world) is actually equivalent to the sphere. That is, there is no edgeless, holeless, 2-dimensional surface embedded in 3-dimensional space that is not deformable into the sphere.
The Poincare conjecture asks if this is true for a 3-dimensional sheet in 4-dimensional space. As far as I know, there aren't any practical applications of this knowledge, and there may well never be. As I mentioned before, intellectual exploration of this nature is an end unto itself. Perhaps this book will help you to understand the significance, beauty, and artistry of "useless" mathematical exploration.
Using the same placement guidelines as before, here's the best start so far, incorporating anubis' suggestions:
1. Red.
2,3,4,5. -1 life.
6. Upgrade red (2).
7,8,9,10. Upgrade red (3), -1 life.
11,12. Blue, -1 life.
13,14. Upgrade red (6).
15,16,17,18,19. Upgrade red (7).
20. 2x blue, -1 life.
21. Sell red.
22. Purple, -1 life.
23. -3 lives.
24,25. Purple.
26,27. 2x blue.
28,29. 2x blue.
30. Blue.
You could theoretically have 12 lives at the end of that, though it's not very likely. You have to target well and get lucky. I think that can be improved with some purple upgrades as well, but I haven't worked it all out yet.
1: Red1.
4: Upgrade Red1 to level 2.
10: Upgrade Red1 to level 3, -1 life minimum.
12: Blue1, -4 lives minimum.
14: Upgrade Red1 to level 7.
19: 2x Blue1, sell the Red1 at the end of the level.
20: Purple2.
21: Blue1.
22: Blue1.
23: Blue1.
25: Purple2 where the Red1 used to be.
27: -2 lives minimum.
29-50: On your own! Just keep adding Blue1 towers in strategic spots and slowly upgrade your firepower where it is cost effective.
- Turn target locking off for all towers, and initially, set targeting to hard.
- Change tower targeting as needed so that you don't target a creep that requires only one hit with two towers.
- Towards the end of a wave, use close tower targeting to focus firepower on creeps that are about to escape.
- It's not cost effective to get Red3 towers until wave 42, at the very earliest. You might be able to wait until wave 44, I'm not sure.
- Always buy towers after hitting the "send next" button!
I'm not sure yet where I can trade those extra lives for more money early on.
Those are normal, angry, playful, punish, comfort, guru, hyperactive, and bleh. I don't have anything for tired, hope, or sadness yet.