To be fair, the Banach-Tarski paradox you're referring to uses 3D Euclidean space instead of the curved Minkowski spacetime of General Relativity. I'm certain the Lebesque measure (the key ingredient to Banach-Tarski, along with the Axiom of Choice) can be extended to that spacetime, and I'm pretty sure it can be used to generate the same type of paradox. That might actually have interesting physical consequences for the theory, which, incidentally, would be entirely avoided by quantizing it. Considering how much most mathematicians like the Axiom of Choice, this could be a great (mathematician's) argument against GR and for Quantum.
Empathy and compassion are often taken too locally. You just spent a million dollars of your health insurance company's money to live a horrible extra year? That's almost 50 years of person-hours working for $10/hour, 40 hours/week. Where's the compassion for the working masses instead of the sick guy? It's callous *not* to be callous, sometimes. I'd say this is the same situation--we fight your fire against policy and we'll get burned, which will burn other people later on.
I agree, though, that people don't treat each other terribly well much of the time. Your ideas are interesting, but they lack rigor. They'd be much more interesting with more solid reasoning backing them up.
A quick Python script shows there are 81 primes (including this one) in the 2001 numbers a distance at most 1000 from the above. So, for this large a number, a random guess would give *around* a 4% chance of getting a prime. Adding in the constraint that the number's a palindrome (which makes the picture look nice) may or may not make it more rare. I just tried randomly generating 10,000 33-digit binary palindromes which resulted in 418 of them being prime, giving the same *around* 4% chance of getting a prime palindrome of this length randomly.
So, given the available space and the artistic desire to choose a binary palindrome, they only had a 4% chance of getting a prime--a coincidence? Probably:(.
"Integer" back in VB6 had a max value of ~32k, so it's even worse than just forgetting cents. Also, it had a lot of automatic type conversions. For instance,
Dim TotalSales As Integer
TotalSales = 15.45
is quite legal, and automatically rounds the cents off. How convenient!
(In MS's favor, they've done a better job with the.NET family, at least VC#.)
I disagree. A poor summary makes me go straight to the story's comments for a decent one. This story is a good example, and the comments included a particularly good summary (the above).
I'd imagine the majority of readers would prefer longer, better summaries than shorter, less informative ones. Of course, without a detailed survey and such I can't say for sure.... My point, though, is that I doubt there's much consensus on what a summary is "supposed" to do, and randomly saying one attribute is required without backup is silly.
I don't believe so, since you'd have to know precisely what "gravity" means, and that's a very involved (and currently unclear) definition. My point is, if you don't know what you're saying about something so apparently simple as "gravity", how can you be certain "no theist theory holds"? Fundamentally, you could even ask why your (or anyone's) reasoning is valid. You're basing your life on a series of fundamental principles (eg. if a and b then a) that seem just as fundamentally baseless to me as the less logical ones you probably dislike (eg. God loves me, so he might give me what I want if I pray hard).
I love logic and do fundamentally believe in it out of a requirement for practicality. It also really bothers me that even logic is quite baseless when you think about it. It sure makes one less sure about one's reasoning to think that the most rigorous, formal, algorithmic, and/or correct ideas humans have come up with might well be fundamentally flawed. For me, this observation just illustrates the importance of incredibly solid reasoning, all the time (since I do accept basic formal logic, for instance, and some vague set theory that mostly aligns with standard ZFC, as far as I'm aware). Grand statements should rightly be met with skepticism (including this one).
Yes, but would you know? That's often the point of social psych studies--you expect something and, if you're not a dimwit, you're right most of the time. But you wouldn't know you were right until you did the study. (I actually find the original result interesting in its own right, too. After thinking about it, it matches the expectations I think I would have had had I considered the elderly's views of the young. But I wouldn't have thought of that without the above story.)
It's certainly helpful to society for fundamental knowledge to be completely free: addition, multiplication, 0, binary, etc. Some advanced topics might fall into that category too (say... Riemannian geometry which backs General Relativity, or the linear algebra backing Quantum). But how is it helpful to society for, say, the Green-Tao Theorem to be unpatentable? I think most mathematicians would publish their results, effectively freeing them, regardless of patent laws. But I don't see why Terrence Tao and Ben Green shouldn't be allowed to patent their idea if they found a real-world use for it and were so inclined.
I'd bet almost no pure math is done for the money. People that smart should be able to play the stock market if they wanted to, for instance. Is it this convenient accident--that most mathematicians simply don't care much about money or royalties or what have you--that's really behind the idea that math *shouldn't* be patentable? What would we say if mathematicians fought tooth and nail for patent protection instead of quietly pretty much ignoring any such thing? I'd guess our idealism would vanish in the face of real humans really wanting money for their work.
It's more like saying pi=3.1415927, considering one year is about 32 million seconds. At some point accurate is accurate.
The only real issue in my mind is, will we still be using UTC when leap seconds seconds accumulate to effect a significant number of its applications? Since they've been added about once per year, I doubt it.
but I image leaving "pheromone traces" over network routes to indicate quality (latency, bandwidth, whatever) is something that will make sure security researchers have jobs for a long, long time.
Why? I don't see why you'd need uniquely identifiable information left behind in the "pheromone". Hopefully a decent spec would also be sensitive to privacy concerns and would simply have an "off" bit as well.
VB(6, the predecessor to.NET) needed to die, since it was designed for a different era that's passed.
It has no cross platform compatibility, no built-in class library to speak of, and no template support. It's object-oriented, but in a way that allows you to never make your own classes if you choose--an interesting idea to try that, IMO, fails in the long term. Its use of built-in objects is schizophrenic: strings have no methods, but UI objects do. Numeric data types are somewhat nonstandard (Integer max is 2^15-1...). Run time error logging is terrible and requires numbering your code lines manually, without offering a stack trace.
It also wasn't designed to support many tasks that became common: resolution independence, quality image resizing, taking the inverse cosine, scrolling, skinning, and data serialization all require you to implement it yourself or use third party libraries. Even Windows API calls require you to know the DLL name and method signature which, again, are found only with the help of third parties.
Some of these defects could have been addressed with future versions. However, that would have required extensions to a broken system instead of a clean design made to avoid previous faults. Some changes would have been breaking, particularly better OO support. All in all, I'm glad MS decided to let pure VB die in favor of the much better-thought-out.NET family. I know it's convenient to say they did it for the money, and they may well have, but that doesn't invalidate all the other benefits of that decision.
The article mostly ignores the text of the add, which is also manipulative (in the ways many ads are). For instance, "McAfee would like to ensure you continue to enjoy a fast and safe online experience" implies your internet will slow down or be scarily unsafe without their product. "We do care about your security" tries to demolish negative views of large companies by putting on a human face. The ad follows up with a friendly special deal (just for everyone): "we would like to offer... protection... at a very competitive price:... 50% off". They don't give price comparisons justifying their use of "competitive", either. They slip the assertion at the end of a sentence that has another idea as its focus in the hopes you'll just accept that their price is in fact competitive. That manipulation is probably the most clever device in the ad.
One thing that struck me as improbable was that the full price the ad quotes is 49.98 pounds, which happens to be neatly divisible by 2. It seems as if the full price was calibrated to be cut in half just so ads could say "50% off" instead of the messier "nearly 50% off", or similar. The ad finishes with a list including some scary words (anti... "virus", "spam", and "spyware") followed by the comforting thought that their product "preserves you and your computer from the most dangerous online threats." At the bottom, they add a sense of urgency to accepting their offer: "Offer expires 31 December 2009," so you don't put off renewing your subscription.
It's speculation, but I don't think a single part of that ad was written with the motivation of actually helping users. Every part of it is dripping with pretty transparent manipulation with the clear motivation of getting you to buy, buy, buy.
Disclaimer: I've formally studied special relativity, quantum, and differential geometry, but never GR. This isn't an expert opinion.
GR takes an arrangement of matter, energy, and momentum and figures out what this arrangement forces distances between points in spacetime to be. If you change the arrangement, distances change--LA and New York are one distance without Jupiter, and another with Jupiter, for instance. The "speed of gravity" says that distances change at the speed of light. More specifically, you can imagine that, hypothetically, moving objects radiate light. As the light reaches a point in spacetime, the distance between that point and those very near it is updated based on the new arrangement of matter.
The "warp drive" paper (which, incidentally, was helpful to me; the introduction is accessible) discusses a related effect. Through clever changes in distance, the ship travels from star A to star B and back in an arbitrarily short amount of time as measured by an observer at star A. Even light can piggy-back on this warp bubble, and so changes in the arrangement of matter near the starting point of the ship's journey can get propagated to star B more quickly than normal. That is, if the arrangement near star A changes at launch, distances at star B are updated arbitrarily quickly, since the hypothetical light emitted by the changing object took a ride on the warp ship.
A gravity wave detector at star B would "see" the hypothetical photons as usual. Part of the machine would have updated distances before another part, since the wave of photons would hit them at different times. However, I don't see anything wrong with that. In all of this, the definition of "the speed of light" has moved closer to "the time light takes to travel from A to B" instead of ~300,000 km/s.
Slashdot Mirror
To be fair, the Banach-Tarski paradox you're referring to uses 3D Euclidean space instead of the curved Minkowski spacetime of General Relativity. I'm certain the Lebesque measure (the key ingredient to Banach-Tarski, along with the Axiom of Choice) can be extended to that spacetime, and I'm pretty sure it can be used to generate the same type of paradox. That might actually have interesting physical consequences for the theory, which, incidentally, would be entirely avoided by quantizing it. Considering how much most mathematicians like the Axiom of Choice, this could be a great (mathematician's) argument against GR and for Quantum.
Empathy and compassion are often taken too locally. You just spent a million dollars of your health insurance company's money to live a horrible extra year? That's almost 50 years of person-hours working for $10/hour, 40 hours/week. Where's the compassion for the working masses instead of the sick guy? It's callous *not* to be callous, sometimes. I'd say this is the same situation--we fight your fire against policy and we'll get burned, which will burn other people later on.
I agree, though, that people don't treat each other terribly well much of the time. Your ideas are interesting, but they lack rigor. They'd be much more interesting with more solid reasoning backing them up.
A quick Python script shows there are 81 primes (including this one) in the 2001 numbers a distance at most 1000 from the above. So, for this large a number, a random guess would give *around* a 4% chance of getting a prime. Adding in the constraint that the number's a palindrome (which makes the picture look nice) may or may not make it more rare. I just tried randomly generating 10,000 33-digit binary palindromes which resulted in 418 of them being prime, giving the same *around* 4% chance of getting a prime palindrome of this length randomly.
So, given the available space and the artistic desire to choose a binary palindrome, they only had a 4% chance of getting a prime--a coincidence? Probably :(.
What? The number is...
110010111001001010100100111010011 (binary)
1972549D3 (hex)
6830770643 (decimal)
Dim TotalSales As Integer
TotalSales = 15.45
is quite legal, and automatically rounds the cents off. How convenient! (In MS's favor, they've done a better job with the .NET family, at least VC#.)
I disagree. A poor summary makes me go straight to the story's comments for a decent one. This story is a good example, and the comments included a particularly good summary (the above).
I'd imagine the majority of readers would prefer longer, better summaries than shorter, less informative ones. Of course, without a detailed survey and such I can't say for sure.... My point, though, is that I doubt there's much consensus on what a summary is "supposed" to do, and randomly saying one attribute is required without backup is silly.
"I have empirical proof that gravity exists"
I don't believe so, since you'd have to know precisely what "gravity" means, and that's a very involved (and currently unclear) definition. My point is, if you don't know what you're saying about something so apparently simple as "gravity", how can you be certain "no theist theory holds"? Fundamentally, you could even ask why your (or anyone's) reasoning is valid. You're basing your life on a series of fundamental principles (eg. if a and b then a) that seem just as fundamentally baseless to me as the less logical ones you probably dislike (eg. God loves me, so he might give me what I want if I pray hard).
I love logic and do fundamentally believe in it out of a requirement for practicality. It also really bothers me that even logic is quite baseless when you think about it. It sure makes one less sure about one's reasoning to think that the most rigorous, formal, algorithmic, and/or correct ideas humans have come up with might well be fundamentally flawed. For me, this observation just illustrates the importance of incredibly solid reasoning, all the time (since I do accept basic formal logic, for instance, and some vague set theory that mostly aligns with standard ZFC, as far as I'm aware). Grand statements should rightly be met with skepticism (including this one).
"I would bet"
Yes, but would you know? That's often the point of social psych studies--you expect something and, if you're not a dimwit, you're right most of the time. But you wouldn't know you were right until you did the study. (I actually find the original result interesting in its own right, too. After thinking about it, it matches the expectations I think I would have had had I considered the elderly's views of the young. But I wouldn't have thought of that without the above story.)
Why? I'm inclined to agree, but why?
It's certainly helpful to society for fundamental knowledge to be completely free: addition, multiplication, 0, binary, etc. Some advanced topics might fall into that category too (say... Riemannian geometry which backs General Relativity, or the linear algebra backing Quantum). But how is it helpful to society for, say, the Green-Tao Theorem to be unpatentable? I think most mathematicians would publish their results, effectively freeing them, regardless of patent laws. But I don't see why Terrence Tao and Ben Green shouldn't be allowed to patent their idea if they found a real-world use for it and were so inclined.
I'd bet almost no pure math is done for the money. People that smart should be able to play the stock market if they wanted to, for instance. Is it this convenient accident--that most mathematicians simply don't care much about money or royalties or what have you--that's really behind the idea that math *shouldn't* be patentable? What would we say if mathematicians fought tooth and nail for patent protection instead of quietly pretty much ignoring any such thing? I'd guess our idealism would vanish in the face of real humans really wanting money for their work.
It's more like saying pi=3.1415927, considering one year is about 32 million seconds. At some point accurate is accurate. The only real issue in my mind is, will we still be using UTC when leap seconds seconds accumulate to effect a significant number of its applications? Since they've been added about once per year, I doubt it.
Summary: the article is full of weasel words and is very non-technical. If that's not your cup of tea, read the paper linked above.
but I image leaving "pheromone traces" over network routes to indicate quality (latency, bandwidth, whatever) is something that will make sure security researchers have jobs for a long, long time.
Why? I don't see why you'd need uniquely identifiable information left behind in the "pheromone". Hopefully a decent spec would also be sensitive to privacy concerns and would simply have an "off" bit as well.
VB(6, the predecessor to .NET) needed to die, since it was designed for a different era that's passed.
.NET family. I know it's convenient to say they did it for the money, and they may well have, but that doesn't invalidate all the other benefits of that decision.
It has no cross platform compatibility, no built-in class library to speak of, and no template support. It's object-oriented, but in a way that allows you to never make your own classes if you choose--an interesting idea to try that, IMO, fails in the long term. Its use of built-in objects is schizophrenic: strings have no methods, but UI objects do. Numeric data types are somewhat nonstandard (Integer max is 2^15-1...). Run time error logging is terrible and requires numbering your code lines manually, without offering a stack trace.
It also wasn't designed to support many tasks that became common: resolution independence, quality image resizing, taking the inverse cosine, scrolling, skinning, and data serialization all require you to implement it yourself or use third party libraries. Even Windows API calls require you to know the DLL name and method signature which, again, are found only with the help of third parties.
Some of these defects could have been addressed with future versions. However, that would have required extensions to a broken system instead of a clean design made to avoid previous faults. Some changes would have been breaking, particularly better OO support. All in all, I'm glad MS decided to let pure VB die in favor of the much better-thought-out
The article mostly ignores the text of the add, which is also manipulative (in the ways many ads are). For instance, "McAfee would like to ensure you continue to enjoy a fast and safe online experience" implies your internet will slow down or be scarily unsafe without their product. "We do care about your security" tries to demolish negative views of large companies by putting on a human face. The ad follows up with a friendly special deal (just for everyone): "we would like to offer ... protection ... at a very competitive price: ... 50% off". They don't give price comparisons justifying their use of "competitive", either. They slip the assertion at the end of a sentence that has another idea as its focus in the hopes you'll just accept that their price is in fact competitive. That manipulation is probably the most clever device in the ad.
One thing that struck me as improbable was that the full price the ad quotes is 49.98 pounds, which happens to be neatly divisible by 2. It seems as if the full price was calibrated to be cut in half just so ads could say "50% off" instead of the messier "nearly 50% off", or similar. The ad finishes with a list including some scary words (anti... "virus", "spam", and "spyware") followed by the comforting thought that their product "preserves you and your computer from the most dangerous online threats." At the bottom, they add a sense of urgency to accepting their offer: "Offer expires 31 December 2009," so you don't put off renewing your subscription.
It's speculation, but I don't think a single part of that ad was written with the motivation of actually helping users. Every part of it is dripping with pretty transparent manipulation with the clear motivation of getting you to buy, buy, buy.
Disclaimer: I've formally studied special relativity, quantum, and differential geometry, but never GR. This isn't an expert opinion.
GR takes an arrangement of matter, energy, and momentum and figures out what this arrangement forces distances between points in spacetime to be. If you change the arrangement, distances change--LA and New York are one distance without Jupiter, and another with Jupiter, for instance. The "speed of gravity" says that distances change at the speed of light. More specifically, you can imagine that, hypothetically, moving objects radiate light. As the light reaches a point in spacetime, the distance between that point and those very near it is updated based on the new arrangement of matter.
The "warp drive" paper (which, incidentally, was helpful to me; the introduction is accessible) discusses a related effect. Through clever changes in distance, the ship travels from star A to star B and back in an arbitrarily short amount of time as measured by an observer at star A. Even light can piggy-back on this warp bubble, and so changes in the arrangement of matter near the starting point of the ship's journey can get propagated to star B more quickly than normal. That is, if the arrangement near star A changes at launch, distances at star B are updated arbitrarily quickly, since the hypothetical light emitted by the changing object took a ride on the warp ship.
A gravity wave detector at star B would "see" the hypothetical photons as usual. Part of the machine would have updated distances before another part, since the wave of photons would hit them at different times. However, I don't see anything wrong with that. In all of this, the definition of "the speed of light" has moved closer to "the time light takes to travel from A to B" instead of ~300,000 km/s.