The Simplest Path
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Off With Their Heads
Member # 4045
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written Thursday, May 31 2007 13:48
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The math for imaginary numbers wouldn't have been invented if it didn't have some use. (Wikipedia lists some of the uses.) Moreover, I dare you to explain to me why the square root of negative one does not exist in a way that does not also apply to the square root of two or to negative one itself. (This can be done, but it's harder than it at first appears.) [ Thursday, May 31, 2007 13:54: Message edited by: Kelandon ] -------------------- Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens. Smoo: Get ready to face the walls! Ephesos: In conclusion, yarr. Kelandon's Pink and Pretty Page!!: the authorized location for all things by me The Archive of all released BoE scenarios ever Posts: 7968 | Registered: Saturday, February 28 2004 08:00 |
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Guardian
Member # 2080
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written Thursday, May 31 2007 15:02
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quote:1. Those aren't uses aren't in useful in any relevant sense. 2. Huh? That last bit doesn't make any sense... Oh well, I'll still take a stab at it... Any number times itself regardless of whether it's positive or negative will yield a positive number in the answer. To get a negative answer in multiplication, one must multiply a negative number by a positive number. 'ie, -1 * -1 = 1, not -1. whereas, 1 * -1 = -1' Thus the square root of -1 can't exist, since a negative number can't have a number that can be multiplied by itself to make a negative number(since all numbers multiplied by themselves makes a positive number). Now, 2, like 1(square root of which is 1), has a square root. It approximately 1.4142135... there are more numbers beyond the 5, but my dollar store calculator only goes out to 8 digits. Anyway, the point is that any positive number has a square root, even if it isn't a whole number, but a negative number can't have a square root because of how multiplication works. Period. [ Thursday, May 31, 2007 15:05: Message edited by: Bandit Keith ] -------------------- Did you know: When asked about his voicing of Unicron, Orson Welles is quoted as saying, "Unicron was the perfect character for me to play. I find it easy to relate to him. We're both the size of a planet and we both can eat said planet." Did you know: After the Holocaust, Germany decided that it takes at least 57 murders before they'll even consider prosecution and guys like Ted Bundy would known as 'Weekend Warriors' Did you know: Most facts on the internet are made up with little or no thought to decency or good sense. And that most of the people who make them die a lonely pathetic death. Posts: 1918 | Registered: Sunday, October 13 2002 07:00 |
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Law Bringer
Member # 335
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written Thursday, May 31 2007 16:42
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quote:What list are you looking at? Quantum mechanics and electric circuits are rather important. So's signal processing, O user of the internet. I've never thought about control theory and I have no idea how imaginary numbers can be useful in cartography, but those are all useful. quote:That's a property of real numbers, not all numbers. You've just defined numbers as the set of real numbers and begged the question. quote:And -2 has a square root. It's approximately 1.4142135i. That's only less legitimate than the square root of 2 if you define imaginary numbers as non-numbers, which again provides only circular justification. Anyway, the point is that any positive number has a square root, even if it isn't a whole number, but a negative number can't have a square root because of how multiplication works. Period.[/QB][/QUOTE] That's how real numbers work, not how multiplication works. I can multiply i by i and get -1 with no trouble at all. —Alorael, who doesn't really see how the nonexistence of imaginary numbers relegates them to pure evil. They're useful even if they're only theoretical. Posts: 14579 | Registered: Saturday, December 1 2001 08:00 |
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Guardian
Member # 2080
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written Thursday, May 31 2007 17:03
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Um, I hate to break it ya, A, but your arguments don't make any sense. You're saying basically that 'imaginary numbers work because they don't have to follow math rules'. Your statement is that by multiplying i by itself you get -1. Of course, that's the premise behind i, but that goes back into the self-reinforcing loop thing I talked about earlier. To get -1, you have to multiply something that was just made up and can't mathematically exist. [ Thursday, May 31, 2007 17:04: Message edited by: Bandit Keith ] -------------------- Did you know: When asked about his voicing of Unicron, Orson Welles is quoted as saying, "Unicron was the perfect character for me to play. I find it easy to relate to him. We're both the size of a planet and we both can eat said planet." Did you know: After the Holocaust, Germany decided that it takes at least 57 murders before they'll even consider prosecution and guys like Ted Bundy would known as 'Weekend Warriors' Did you know: Most facts on the internet are made up with little or no thought to decency or good sense. And that most of the people who make them die a lonely pathetic death. Posts: 1918 | Registered: Sunday, October 13 2002 07:00 |
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Off With Their Heads
Member # 4045
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written Thursday, May 31 2007 18:04
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quote:You said that imaginary numbers don't exist. I asked you to give a reason why imaginary numbers don't exist, a reason that doesn't apply equally well to negative numbers or irrational numbers. quote:That's true of the set of so-called "real" numbers. That doesn't have anything to do with whether a number "exists" or not. I could just as easily say that any number that exists, when multiplied by itself, will yield an integer as an answer. Then I could claim that one-half does not exist. Why is your statement any more valid than this? [ Thursday, May 31, 2007 18:07: Message edited by: Kelandon ] -------------------- Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens. Smoo: Get ready to face the walls! Ephesos: In conclusion, yarr. Kelandon's Pink and Pretty Page!!: the authorized location for all things by me The Archive of all released BoE scenarios ever Posts: 7968 | Registered: Saturday, February 28 2004 08:00 |
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Guardian
Member # 2080
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written Thursday, May 31 2007 18:22
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Because my statement wasn't created make a point that doesn't hold up. I never said that negative numbers or partial numbers(fractions/decimals) don't exist. They do. They can be used in sound math formulas and have a value. Not being a whole number doesn't make something not exist. I'm saying the square root of a negative number doesn't exist. You're somehow not getting the entire part where I explained how you can't get a negative by multiplying the same number by itself. That is a proven mathematical impossibility, so the square root of a negative can't exist. Now, the flaw in your statement(other the obvious lack of valid reasoning behind it) is in that fractions, like negative numbers have a value and can be used in non-theoretical math. Again, it doesn't have to be a whole number to be a number. Since they are based on trying to make something that the name itself admits doesn't exist work, imaginary numbers don't actually exist and all the self-reinforcing equations in the world can't really change that fact. -------------------- Did you know: When asked about his voicing of Unicron, Orson Welles is quoted as saying, "Unicron was the perfect character for me to play. I find it easy to relate to him. We're both the size of a planet and we both can eat said planet." Did you know: After the Holocaust, Germany decided that it takes at least 57 murders before they'll even consider prosecution and guys like Ted Bundy would known as 'Weekend Warriors' Did you know: Most facts on the internet are made up with little or no thought to decency or good sense. And that most of the people who make them die a lonely pathetic death. Posts: 1918 | Registered: Sunday, October 13 2002 07:00 |
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Law Bringer
Member # 335
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written Thursday, May 31 2007 18:53
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quote:It's not a proven mathematical impossibility. It is, in fact, a proven possibility, and numbers that have this property are called imaginary numbers. Mathematically there is nothing wrong with imaginary numbers. Your objection can't be mathematical unless you declare the laws of mathematics by fiat, which you appear to be doing. You object to imaginary numbers because they describe nothing that exists in the real world. You reject Kel's arguments because they're made to prove a point. Fair enough, but how are your arguments not set up to prove a point, namely that imaginary numbers don't exist? I've never seen -3, but I admit it is a useful concept. —Alorael, who thinks your basic objection is two-pronged: firstly, imaginary numbers do not describe anything real; secondly, they are really weird. The latter is true but has been considered true of negative numbers and fractions in certain times and places. Weirdness has nothing to do with validity. Imaginary numbers do describe real things as well: you've been given examples. You don't have to like non-real math, but you have to admit that it exists, that it has real-world applications, and that it therefore has a valid, non-self-referential reason for existing. Posts: 14579 | Registered: Saturday, December 1 2001 08:00 |
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Lifecrafter
Member # 7723
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written Thursday, May 31 2007 18:59
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*counts to i on his third hand* Posts: 701 | Registered: Thursday, November 30 2006 08:00 |
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Guardian
Member # 2080
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written Thursday, May 31 2007 19:26
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This argument is clearly going nowhere. I should've stopped a long time ago. Using y'all's version of logic, there's no way for me to win it anyway. Pure and simple. It doesn't make one of us right or wrong, it just ensures that one of us(in this case me) has no chance at winning. I could give an example of what I'm talking about, but I've stopped caring now. -------------------- Did you know: When asked about his voicing of Unicron, Orson Welles is quoted as saying, "Unicron was the perfect character for me to play. I find it easy to relate to him. We're both the size of a planet and we both can eat said planet." Did you know: After the Holocaust, Germany decided that it takes at least 57 murders before they'll even consider prosecution and guys like Ted Bundy would known as 'Weekend Warriors' Did you know: Most facts on the internet are made up with little or no thought to decency or good sense. And that most of the people who make them die a lonely pathetic death. Posts: 1918 | Registered: Sunday, October 13 2002 07:00 |
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Law Bringer
Member # 2984
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written Thursday, May 31 2007 19:39
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quote:Let's call it a draw?  :P -------------------- Encyclopaedia • Archives • Members • RSS [Topic / Forum] • Blog • Polaris • NaNoWriMo Look on my works, ye mighty, and despair. I have a love of woodwind instruments. Posts: 8752 | Registered: Wednesday, May 14 2003 07:00 |
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Shaper
Member # 73
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written Thursday, May 31 2007 19:55
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 -------------------- My Myspace, with some of my audial and visual art The Lyceum - The Headquarters of the Blades designing community The Louvre - The Blades of Avernum graphics database Alexandria - The Blades of Exile Scenario database BoE Webring - Self explanatory Polaris - Free porn here Odd Todd - Fun for the unemployed (and everyone else too) They Might Be Giants - Four websites for one of the greatest bands in existance -------------------- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Posts: 2957 | Registered: Thursday, October 4 2001 07:00 |
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? Man, ? Amazing
Member # 5755
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written Thursday, May 31 2007 21:34
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We have sunk so low as to argue about mathematics? What happened to the good topics?? Oh, wait. nm. -------------------- WWtNSD? Posts: 4114 | Registered: Monday, April 25 2005 07:00 |
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...b10010b...
Member # 869
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written Thursday, May 31 2007 22:02
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quote:I'm, uh, hoping they use a different definition of "meme" than the standard one, because in Dawkins' formulation every idea is a meme, and I don't really want to rid myself of all ideas. Lone Flame: All mathematics is created by defining it into existence according to a set of axioms (rules). In this regard imaginary numbers are not different from any other kind of number. Mathematics with complex (real and imaginary) numbers just plays by a different set of rules than mathematics with only real numbers. Mathematics is a human construct: if humans aren't allowed to change the rules when it's useful to do so, then who is? [ Thursday, May 31, 2007 22:09: Message edited by: Thuryl ] -------------------- The Empire Always Loses: This Time For Sure! Posts: 9973 | Registered: Saturday, March 30 2002 08:00 |
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Electric Sheep One
Member # 3431
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written Thursday, May 31 2007 22:31
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Consider the 2-by-2 matrix 0 1 -1 0. I will name this matrix "i", to avoid having to write it all out again. Consider as well the two-by-two matrix 1 0 0 1. I will call this matrix '1' (one), because like the ordinary number 1, multiplying anything (that is, any 2-by-2 matrix) by the matrix 1 produces no change. Now notice that i*i, using matrix multiplication, equals -1. This pair of 2-by-2 matrices is actually very useful, because practical mathematics (such as physics) is full of two-component things. In particular it is very common to need 2-by-2 matrices that are arbitrary linear combinations of the matrices defined above: z = x + i*y, where z is a 2-by-2 matrix and x and y are ordinary real numbers. Complex arithmetic is nothing but using those two-by-two matrices, in a condensed notation where we don't have to keep writing out all the components all the time. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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Lifecrafter
Member # 7723
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written Friday, June 1 2007 02:48
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He's specifying "viral memes," which "insist" on being spread, not because they are good ideas, but because they invoke fear or some other emotion. I'm curious as to his take on this because it seems like the point, as someone else mentioned, is just not to have bad ideas. Does the book give some novel way to identify these memes? If not it would seem uninspired. And yes, Jesus did exist. The Bible is not the only historical reference to him. Whether you believe he is what it claims is another subject. Posts: 701 | Registered: Thursday, November 30 2006 08:00 |
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Warrior
Member # 4638
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written Friday, June 1 2007 04:49
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Meme: 1. Arguably, there is some difference between a meme and an idea. Meme of course comes from the word gene. A meme like a gene exerts some level of control over its host. A meme like a gene is primarily concerned with self replication. Viral memes are those memes that lead to the destruction of the host when they are expressed. e.g. According to this above analysis, the "obsession with celebrity" could be considered a viral meme. This meme through its influence has created a whole real word infrastructure to promote itself, tabloids, E! network, etc. It exerts control over those who are infected with it (they become obsessed with the lives of celebrities). Ultimately, it effects the lives of those infected negatively (this one we could argue about forever, however, it does not provide food, shelter, real human interaction, or contribute to progress). On balance, it appears that it would be beneficial to free the world from such viral memes. 2. When I used the word eliminate it was in error. A more accurate description is to “free” yourself from such memes. When a meme, like a gene, is expressed, it is not obvious to the individual that the meme is being expressed. Its influence is subtle. Memes infect individuals with rigid ways of thinking, subtly changing their perception of reality from what is there, to a meme influenced illusion. 3. You asked if the book gives novel ways to identify viral memes. Yes, although identifying memes is primarily done through the process of freeing oneself from memes. It is not primarily concerned with identifying memes because that is not the goal. The goal is freedom and awakening. 4. Are you sure Jesus existed? I have read the Bible very thoroughly and just from the material in the Bible, I think it is possible to make a case that "Jesus" did not in fact exist. Further, there are numerous investigations of his existence / non-existence, e.g.: http://home.ca.inter.net/~oblio/home.htm 5. quote:This is a very interesting question. It is addressed in The Simplest Path. [ Friday, June 01, 2007 06:13: Message edited by: Ceylon ] -------------------- You are asleep. Be careful what you pretend to be because you are what you pretend to be. So it goes. Posts: 93 | Registered: Tuesday, June 29 2004 07:00 |
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Electric Sheep One
Member # 3431
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written Friday, June 1 2007 04:53
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I don't think this is so clear. Any ancient texts that mention Jesus are available now only in much later copies, made by Christians. There is considerable reason to suspect, for example, that the famous description by Josephus has been significantly altered from the original. (Wikipedia gives a pretty good discussion here, I think. The strongest point seems to be that early Christian writers did not mention this passage by Josephus, even though they knew of his writings, and the Jesus reference as we now have it would have been very relevant to their discussions.) That having been said, it is a very far-fetched idea to suggest that Jesus never existed. Ancient critics of Christianity may not have offered any clear evidence for Jesus's existence, but they did all take it for granted. Several lone geniuses have founded durable religious movements, so there is nothing implausible about one more. A world religion launched in historical times around a fictitious founder is considerably less plausible. -------------------- We're not doing cool. We're doing pretty. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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Off With Their Heads
Member # 4045
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written Friday, June 1 2007 06:23
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There are too many and too varied references for them all to have been doctored. Yes, Josephus's was almost certainly modified in the form that we have it, but Suetonius and Tacitus also mention Jesus (Life of Claudius, 25.5, and Annals, 15.33, respectively). Tacitus's mention is by no means complimentary, so if it was altered by Christians, it was altered very poorly and incompletely. Tacitus was only a few decades after Jesus's death, so while the exact details of Jesus's life might not have been available to him, he probably would've been able to know whether or not Jesus really lived, and he expresses no doubt. It's hard to know any details for certain from two thousand years ago, but to the extent that we know anything, we can be pretty sure that Jesus existed in some form or other. Four independent sources (the Gospels, Josephus, Suetonius, and Tacitus) is more than we get for most people. -------------------- Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens. Smoo: Get ready to face the walls! Ephesos: In conclusion, yarr. Kelandon's Pink and Pretty Page!!: the authorized location for all things by me The Archive of all released BoE scenarios ever Posts: 7968 | Registered: Saturday, February 28 2004 08:00 |
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Lifecrafter
Member # 7723
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written Friday, June 1 2007 08:53
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This is awkward to say, but Kelandon and SoT made my points for me? One might as well doubt Alexander, Augustus or Aristotle. Posts: 701 | Registered: Thursday, November 30 2006 08:00 |
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Lifecrafter
Member # 7723
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written Friday, June 1 2007 09:08
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How do you free yourself from memes if you don't identify them? What is the difference between a meme and an idea? You know what I hate, when people say, "X is ok as long as I don't hurt anyone." That's gotta be a viral idea. I reckon that's a clash of relativistic v absolute ideaologies, though. The funny thing is that X often does infringe on other people's freedom. (Like when my neighbor smokes hurting himself and me when his fumes waft in through my window). Posts: 701 | Registered: Thursday, November 30 2006 08:00 |
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Warrior
Member # 4638
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written Friday, June 1 2007 09:55
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You do identify them. You are taught how to identify them through practice. The practice begins with a set of memes that are core memes that many people are limited by. Even if you as an individual are not so limited, the exercises help you learn how to free yourself. I am not sure why you think it is core to identify the meme before you can begin the process of freeing yourself. Precise identification of memes can be difficult, since memes may be amorphous and their influence may be subtle. If you are in a dark room and are trying to find a way out, do you need to precisely identify the room before you find the door. No, you just do what is needed to find the door. Once you let light into the room it is easier to define the room. As I said before: quote:Memes are cultural units that subtlety influence our behavior. Their primary purpose is self proliferation. All memes are ideas. But they are ideas with special properties of propagation and a propensity to skew one's perception of reality. Gaining freedom from such memes does not lead to the elimination of ideas. Freedom in this case is the ability to perceive reality as it really is, without the influence of the lenses of our own memeplexes. e.g. Since we are talking about Jesus also in this thread, why not take the Christian idea of "original sin." “Original sin” is an idea. Many people with a Christian upbringing are “infected” with this meme. If “original sin” is part of your memeplex, you will not necessarily think about it everyday (and in fact probably won’t). But this meme may subtly influence your actions. It may make you feel unworthy of your achievements because you are ultimately unworthy because of original sin. It may change your perception of people’s actions and make you suspicious. Etc. [ Friday, June 01, 2007 10:02: Message edited by: Ceylon ] -------------------- You are asleep. Be careful what you pretend to be because you are what you pretend to be. So it goes. Posts: 93 | Registered: Tuesday, June 29 2004 07:00 |
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Lifecrafter
Member # 7723
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written Friday, June 1 2007 10:32
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I'm reading you loud and clear, but I'm still missing the novelty. The idea of the original sin should make one tolerant and forgiving and give a realistic view of ones shortcomings. We all have them. If you know can acknowledge that then you're better for it. It shouldn't make you suspicious. As far as self-worth that's also off. What we're unworthy of is everlasting life, as death is the penalty for sin. It's a gift. But the Bible is very clear that God appreciates good activity, even saying he would be unrighteous to overlook it. It also encourages people to recognize goodness in others. I find it to be extraordinarily rare that anybody but a Christian can understand the Bible. This illustrates that fact. I love the terminology though ... "memeplex." Posts: 701 | Registered: Thursday, November 30 2006 08:00 |
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Councilor
Member # 6600
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written Friday, June 1 2007 11:26
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Originally by Ceylon: quote:So, would "Do not murder" be a meme, since it is prolific, influences behavior, and alters people's perceptions? If it isn't, then why isn't it? And if it is, then do you really advocate its destruction? Dikiyoba. Posts: 4346 | Registered: Friday, December 23 2005 08:00 |
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Raven v. Writing Desk
Member # 261
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written Friday, June 1 2007 11:31
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Wouldn't it be a bit simpler, and more useful, to just say "avoid herd mentality" than attempt to decry a poorly demarcated subclass of ideas? -------------------- Slarty vs. Desk • Desk vs. Slarty • Timeline of Ermarian • G4 Strategy Central Posts: 3560 | Registered: Wednesday, November 7 2001 08:00 |
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Lifecrafter
Member # 7723
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written Friday, June 1 2007 11:51
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"Do not murder" is clearly constructive. I don't quite see how interest in celebrities is quite as clearly destructiive. I'd like to hear that. This is curious to me because it seems to be an attempt to establish some sort of absolute morality absent the traditional means of establishing such absoluteness (e.g. religion) while at the same time attacking religion. Who's to say which "memes" are constructive and which are destructive? You say "original sin" is destructive I say the opposite. Is there a test? Posts: 701 | Registered: Thursday, November 30 2006 08:00 |