Well, two weeks later I've finally taken my first dual photograph using a scanning laser instead of a projector and a photocell. As I said, it was (conceptually) trivial. But you're probably not reading this...
x=0.9999...
So 10x = 9.9999....
So 10x-x=9
So x = 1
The sequence 0.9, 0.99, 0.999 never reaches 1. You're quite right to say that. But the definition of 'recurring' says that 0.999... recurring isn't any of the numbers in the sequence but the limit. And the limit is 1, even though the sequence never gets there.
The idea with limits is that the limit is the number that your sequence gets arbitrarily close to. Not reaches, but gets arbitrarily close to. That sequence gets as close as you like to 1. Choose a closeness and I'll find a number of the form 0.999...999 (finite # of 9's) that is closer. So by definition 1 is the limit. I'm glossing over some details here of course. Margins not being big enough 'n' all that...
...a sarcasm sensor. Just in case you think I'm making some kind of racist stereotyping comment here is my evidence:
Edgar Escultura is a well known crackpot on sci.math. He claimed to have proved Fermat's Last Theorem years ago. (He also believes 0.999... recurring is less than 1.) He contacted Andrew Wiles about it. Wiles's response is in this article. As a result of this reply the article I linked to was published in the Manila Times. Can there be any doubt that, at least in Manila, there's a serious lack of appreciation of sarcasm?
Or maybe I'm wrong. Perhaps the editor of the Manila Times is in fact an incredibly sarcastic bastard!
Tell me an interesting prediction that Kurzweil made where he's not been "far of"?
The guy is a charlatan and I'm amazed that anyone intelligent enough to write entire sentences in English could be taken in by him.
Re:Subjective / Objective Viewpoints of Consciousn
on
Download Your Brain
·
· Score: 2, Interesting
We're all copies. Of the hundred trillion cells in our body a large proportion are replaced, or have a large proportion of their atoms replaced, over time. Even if this weren't the case, I can't see what harm would be done by replacing all of the atoms in someone's body with identical ones. Because of this I find it hard to put value on the specific atoms that make up my body but instead I value their functionality. If that functionality can be (destructively) reproduced by a machine I'm happy to walk into that machine. If other people aren't, then they can choose not to use it. But someome claiming to be me will thumb my nose at them from its shiny new robot body at their funerals.
It's interesting when someone makes a statement...
on
Download Your Brain
·
· Score: 2, Insightful
...like this. It of course doesn't say anything about when brain downloads are likely to become available. But it does say a lot about how out of touch with reality so-called experts are. Of course when your job is such that closing the quality control loop takes longer than your lifetime it's only to be expected that your work might not have the same quality expected from people working in other fields.
Art is one of the most important experiences we can have and in our society the premier art form is probably film. Why shouldn't a few hours of film be the emotional highlight of your childhood? What should be? The first time mama wiped your ass?
...make arrays start at zero or allow ^C to interrupt a running program? No? Then wake me up when someone finally figures out how to make Matlab tolerable to use.
...Lucas also released some shitty low res version recorded from a shaky non-orthogonal camera with truly awful sound for a low-cost he might be able to recoup some of his 'losses'.
Many people would rather see such a version than spend $10 on a version shown on a big screen with THX authorized sound and the correct colors. Given that this market is so large it's ridiculous to complain of piracy because these people don't care about the quality and trying to force them to pay for a fancy version is doomed to failure. Give them what they want and let the people who want something more expensive pay for it. Many of these complaints of so-called piracy are really about suppliers failing to get off their fat asses and look at what is actually being demanded.
What do CS people know about algorithms? Now they might be able to write down a proposition that expresses the fact that an array is sorted, and prove using the Curry-Howard isomorphism that there certainly exists a function that has the right type signature for sorting, but as for actually coming up with an algorithm, I think that would be beneath them.
Copyright is a form of bargain between "The People" and creators. We allow creators to curb other people's rights because has been in our interest to do so - we get interesting creations out of it. The flip side is that data is trivial to copy - and more importantly, two people in the privacy of their own home can exchange data easily. If you are able to detect such a private exchange then it is inevitable that you can detect other things also. So copyright on the one hand, and privacy and freedom on the other, though both enshrined in law, are mutually contradictory.
So at any moment in time we must keep asking: "Is it worth sacrificing this much freedom and privacy for the kind of creativity we receive in return?" When my DVD player asks me for my fingerprint before I can watch Monster-in-Law my personal opinion is that maybe we have sacrificed too much for the sake of 'creativity'.
I don't know about you but I read that as a grand "fuck you" to the rest of the world. "We own the entire rest of the universe and we'll blast you to subatomic particles if you try to have a piece..."
I found that if I drink as many pints of beer as I can before I go out drinking I tend to drink less when I'm out. This might not work for everyone but it works for me. It has the advantage that it doesn't require you to find some obscure leaf and the kind of intoxication it causes is remarkably similar to that caused by drinking lots of beer while you're out.
With new LifeDrive(TM) technology, you can quickly drag and drop thousands of files from your PC onto your LifeDrive mobile manager with the folder structure intact.
It's called LifeDrive(TM) technology? I call that "having a file system". Have I accidentally fallen through a time warp. I mean we are half a decade into the 21st century aren't we?
Of course what that paragraph reveals is that file support on the Palm has always been dreadful. The Palm has always had a flat file system in RAM making it a terrible place to store files. So the marketing folks at Palm are deluded into thinking that a directory structure is actually a significant advance.
When are PDA manufacturers going to stop making gimmicks for playing games and videos and start making PDAs that you can actually use for work again? I must be really weird. Am I the only person in the world who misses the old clamshell design? I'd still be using my Psion 3 if it hadn't been stolen. Hell, I'm thinking of getting my Psion II back out in protest against he toys that PDA manufacturers are currently releasing. In fact, I would if I could get hold of a serial cable for it at a reasonable price. Or maybe I'll try to get hold of one of those pocket size PC compatible HPs.
Yes, I've seen Treos. That's not a keyboard unless you're from Lilliput. Yes, I know you can buy an external keyboard, but just try using one anywhere other than at a desk where you might as well be using a laptop anyway. The Clie wasn't bad but Sony have stopped producing those. That leaves the clamshell Zaurus which is horribly expensive.
What preprocessor? The C/C++ preprocessor? What does that have to do with anything? It's certainly not part of the C++ type mechanism, though it certainly is part of C++.
I correctly answered the question "what can C++ do that Object Pascal can't?". But you imagined that I answered the question "what are the advantages of C++?" Of course that was very convenient for you as it gave you an opportunity to blindly evangelize about your favourite language without even the slightest regard for the computational tasks that I might actually have on my TODO list (or even whether or not I might be using languages other than C++ for those tasks). That's the problem with religious zealots - they misread everything around them as an excuse to launch into proselytization. Oh well, I guess it's more interesting than "do you realize that the recent increase in the number of earthquakes is a sign of the iminence of the second coming...?"
Is the type system in Pascal Turing complete in the sense that you can use it to perform arbitrarily complex computations at compile time? If not, then I have a very long list of things you can do with a C++ compiler that you can't do with a Pascal compiler.
Slashdot Mirror
Well, two weeks later I've finally taken my first dual photograph using a scanning laser instead of a projector and a photocell. As I said, it was (conceptually) trivial. But you're probably not reading this...
So 10x = 9.9999....
So 10x-x=9
So x = 1
The sequence 0.9, 0.99, 0.999 never reaches 1. You're quite right to say that. But the definition of 'recurring' says that 0.999... recurring isn't any of the numbers in the sequence but the limit. And the limit is 1, even though the sequence never gets there.
The idea with limits is that the limit is the number that your sequence gets arbitrarily close to. Not reaches, but gets arbitrarily close to. That sequence gets as close as you like to 1. Choose a closeness and I'll find a number of the form 0.999...999 (finite # of 9's) that is closer. So by definition 1 is the limit. I'm glossing over some details here of course. Margins not being big enough 'n' all that...
Edgar Escultura is a well known crackpot on sci.math. He claimed to have proved Fermat's Last Theorem years ago. (He also believes 0.999... recurring is less than 1.) He contacted Andrew Wiles about it. Wiles's response is in this article. As a result of this reply the article I linked to was published in the Manila Times. Can there be any doubt that, at least in Manila, there's a serious lack of appreciation of sarcasm?
Or maybe I'm wrong. Perhaps the editor of the Manila Times is in fact an incredibly sarcastic bastard!
The guy is a charlatan and I'm amazed that anyone intelligent enough to write entire sentences in English could be taken in by him.
We're all copies. Of the hundred trillion cells in our body a large proportion are replaced, or have a large proportion of their atoms replaced, over time. Even if this weren't the case, I can't see what harm would be done by replacing all of the atoms in someone's body with identical ones. Because of this I find it hard to put value on the specific atoms that make up my body but instead I value their functionality. If that functionality can be (destructively) reproduced by a machine I'm happy to walk into that machine. If other people aren't, then they can choose not to use it. But someome claiming to be me will thumb my nose at them from its shiny new robot body at their funerals.
I think the copy might disagree with you.
...like this. It of course doesn't say anything about when brain downloads are likely to become available. But it does say a lot about how out of touch with reality so-called experts are. Of course when your job is such that closing the quality control loop takes longer than your lifetime it's only to be expected that your work might not have the same quality expected from people working in other fields.
Art is one of the most important experiences we can have and in our society the premier art form is probably film. Why shouldn't a few hours of film be the emotional highlight of your childhood? What should be? The first time mama wiped your ass?
...make arrays start at zero or allow ^C to interrupt a running program? No? Then wake me up when someone finally figures out how to make Matlab tolerable to use.
Many people would rather see such a version than spend $10 on a version shown on a big screen with THX authorized sound and the correct colors. Given that this market is so large it's ridiculous to complain of piracy because these people don't care about the quality and trying to force them to pay for a fancy version is doomed to failure. Give them what they want and let the people who want something more expensive pay for it. Many of these complaints of so-called piracy are really about suppliers failing to get off their fat asses and look at what is actually being demanded.
All your base are belong to us.
Export Plasma TVs and DVD players? Are you under the misguided impression that these things are made in and exported from the US?
What do CS people know about algorithms? Now they might be able to write down a proposition that expresses the fact that an array is sorted, and prove using the Curry-Howard isomorphism that there certainly exists a function that has the right type signature for sorting, but as for actually coming up with an algorithm, I think that would be beneath them.
So at any moment in time we must keep asking: "Is it worth sacrificing this much freedom and privacy for the kind of creativity we receive in return?" When my DVD player asks me for my fingerprint before I can watch Monster-in-Law my personal opinion is that maybe we have sacrificed too much for the sake of 'creativity'.
I don't know about you but I read that as a grand "fuck you" to the rest of the world. "We own the entire rest of the universe and we'll blast you to subatomic particles if you try to have a piece..."
Georgia? Not only is it an obscure leaf, I have to travel to an obscure place to get it :-)
I found that if I drink as many pints of beer as I can before I go out drinking I tend to drink less when I'm out. This might not work for everyone but it works for me. It has the advantage that it doesn't require you to find some obscure leaf and the kind of intoxication it causes is remarkably similar to that caused by drinking lots of beer while you're out.
Of course what that paragraph reveals is that file support on the Palm has always been dreadful. The Palm has always had a flat file system in RAM making it a terrible place to store files. So the marketing folks at Palm are deluded into thinking that a directory structure is actually a significant advance.
Yes, I've seen Treos. That's not a keyboard unless you're from Lilliput. Yes, I know you can buy an external keyboard, but just try using one anywhere other than at a desk where you might as well be using a laptop anyway. The Clie wasn't bad but Sony have stopped producing those. That leaves the clamshell Zaurus which is horribly expensive.
I dunno. I've seen Silent Running and gardening seemed to make the evil hippy guy go pretty loopy.
...for those people whose "Software Update" doesn't work. I'm lucky I'm not one of them.
What preprocessor? The C/C++ preprocessor? What does that have to do with anything? It's certainly not part of the C++ type mechanism, though it certainly is part of C++.
I correctly answered the question "what can C++ do that Object Pascal can't?". But you imagined that I answered the question "what are the advantages of C++?" Of course that was very convenient for you as it gave you an opportunity to blindly evangelize about your favourite language without even the slightest regard for the computational tasks that I might actually have on my TODO list (or even whether or not I might be using languages other than C++ for those tasks). That's the problem with religious zealots - they misread everything around them as an excuse to launch into proselytization. Oh well, I guess it's more interesting than "do you realize that the recent increase in the number of earthquakes is a sign of the iminence of the second coming...?"
Is the type system in Pascal Turing complete in the sense that you can use it to perform arbitrarily complex computations at compile time? If not, then I have a very long list of things you can do with a C++ compiler that you can't do with a Pascal compiler.