We already use symbols for infinity, but infinity in mathematics doesn't mean what you mean. Infinity is the size of any set for which the size of the set is bigger than any number you can name.
The set of all counting numbers is infinite. There are things (like the color blue, the number 3/4, and your mother) which are not in that set, but still the set is clearly larger than any numeric size you could give, no matter how large.
There are also multiple orders of infinities.
I'm not sure how valid your notion of infinity is in mathematics at all, since (for example), we can't even determine whether there is such a thing in arithmetic as an infinity bigger than the reals. In fact, we've proven that the question can't be answered based only in what's in the reals - you have to make up a new axiom to define whether all infinities map to either the countable infinity or the reals, or whether there are bigger ones.
Presumably that falsity in our confirmed postulates would come up in the same way it always does - the model would suggest some extreme physical conditions under which we would test the postulate, and a prediction of how the measured value would vary from what we expect.
After all, time being constant had quite a bit of experimental evidence backing it up before special relativity came along, but today we accept that if you move fast enough, it's not.
There is an alternate explanation to "you are transmitting something". The "transmitting something" explanation is the Copenhagen Interpretation.
The alternative is that every time you measure a quantum property (as is done on each end in quantum entanglement experiments) the miniscule slice of reality that we see as the universe splits. Each slice, to remain consistent, has to give compatible answers on both ends of the entanglement experiment, so it looks as if you transmitted something telling the other end what the answer was.
This is the Multiple Worlds Interpretation of quantum mechanics, and afaik it is the one to which most quantum physicists subscribe. The mathematics for this interpretation are simpler (in that the math we use for quantum mechanics right now supports this interpretation, with no extra stuff needed).
Some people are hung up on what we experience as the universe being the real reality, and MW Interpretation sounds like it generates a bunch of extra realities continually.
IMO, those people are what's known in science as "wrong".
You can't do tricks like oo - oo = 0 because, for example, there are infinite counting numbers (1, 2, 3,...). There are also infinite counting numbers > 1 (2, 3,...). If you subtract the second infinity from the first, clearly one number is left over.
I can map the numbers (1, 2, 3,...) one-to-one onto the numbers (2, 3, 4,...) without skipping any on either side, so the two infinities are clearly equal, even though subtracting one from the other leaves 1.
Similar reasoning (infinite even counting numbers vs. the infinite total of all counting numbers) applies to dividing infinities.
And we haven't even started discussing higher orders of infinities. The number of real numbers is... hmm, saying infinitely bigger is really an infinite understatement, but anyway, it's infinitely bigger than the number of counting numbers. Read up on Cantor's Diagonalization Proof if you'd like to learn more.
You can discuss infinities in math, but only by making up new math to manipulate them.
And the limit of the graph 1/x as x->0 is undefined. It grows without bound to larger numbers as you approach 0 from the positive numbers, and without bound to smaller numbers (or bigger negative numbers, if you like) as you approach 0 from the negative.
We just elected to define some of those previously undefined limits (e.g. 1/x^2 as x->0) as some order of infinity. Others remain undefined, and there is argument about how valid various infinities are.
I can't think of anywhere that infinities are allowed, or at least liked, in physics. There appears to be such a thing as a smallest distance (at least inasmuch as there is such a thing as distance at all, see quantum mechanics). There are ways of deriving the physical constants that involve infinities canceling out, but for the most part that bit is despised. Physicists would love to see another way of formulating it that gives the right answers.
That's a bad analogy. Einstein's relativity equations break down to the newtonian equations for any problem in everyday experience. They must because Newton's equations give the right answers for everyday experience (or else they would have been trashed or consigned to use in some very limited problem domain long ago). So must Einstein's, or else they'd be clearly wrong.
Quantum mechanics equates to classical mechanics when you aggregate enough interactions together (the WKB expansion is one example of doing the math to demonstrate that). (Anything on an everyday scale involves > 10^18 atoms interacting, after all.) If QM didn't do that, it would clearly be wrong.
Well, clearly either QM or general relativity are wrong anyway, since they're incompatible, but finding an experiment where both have measurable effects is a bitch. Otherwise we would already be well on our way to finding a theory that covers both domains.
I think we want a system that we can ask to do a complex task in natural language, and which will perform the task, only asking for further instruction when what we've told it is sufficiently ambiguous.
I suspect consciousness will be a byproduct in such a system (as it is in us), but to me, consciousness is not the goal. In fact, if we could achieve it without consciousness, that would be better, since a whole swath of ethical issues in AI go away.
Which reminds me of something else I thought yesterday regarding this: is anyone considering the ethical issues?
I don't think this simulation approaches the trouble spot yet, but at some point we have a good enough simulation of a brain that we're essentially maintaining a sentient creature in an environment with very limited stimuli (a torture in itself) with a half-functioning brain. I'm sure we'd decide that what we learn is worth it, but we should at least acknowledge the issue.
Eventually, it's going to be a simulation of a human we're torturing for science.
I believe you are mistaken. I don't know which herbal remedies are good and which aren't, but the reason pharmaceutical companies spend all that money on R&D (a significant fraction of what they spend on marketing!) is so they can patent the drug and have a monopoly.
If the drug is more effective than natural remedies; great! If not, well, how could they afford to market a drug to be competitive with patented drugs without getting a monopoly on it? After all, anybody could then come along and undercut them on price, since the first company already paid for much of the marketing.
It is quite frequent that a newly patented drug that is shilled off on us is less effective than the old one that fell out of patent, but unless you do the legwork yourself (your doctor is biased by the pharmacy reps pushing their wares), you will be using the new, expensive drug.
You're obviously a troll rather than interested in honest conversation, but someone worthwhile might be interested in the response, so I'll give one.
You're dead wrong. I have been extremely fortunate, not in my financial start (I once couldn't go to school for a week because we couldn't afford a new pair of shoes), but in my intellectual start. I was lucky enough to get a full scholarship, and I make a healthy six figures in middle America, so I'm doing fine financially.
I have takenoffwork multiple times and completed the work I went after (with the exception of the first time). I am no marketer, and I find the things most marketers do to be disgustingly self-serving. I have failed in business, at least so far.
Remember that the first two of those were done 7-9 years ago, so any argument that I was copying existing projects mindlessly is BS.
I am no stranger to risk. My point stands: people who can rely on their parents to bail them out if a risk fails have a huge advantage in business (and in life in general, of course). Regardless of any "fairness" issue, it is to our advantage as a society to do our best to see that people who could improve our lives get a chance to do so, with as much chance of success as makes sense when the risks & rewards are weighed.
Honestly, I probably never could have taken the risks I did if I hadn't had the genetic & environmental luck I've had - I can't see how someone living on $50k can afford to take enough time out to get anything at all done when they have a family to feed.
Of course, being 17, you probably have never thought of what taking a financial risk means when you have real responsibility.
Right; because there's no difference between someone who supports a family on $50k per year with no inheritance and someone who: a) is supported their whole life and gets $millions in inheritance/giveaways or b) gets a job that pays $hundreds of thousands per year (or millions) because of who they/their parents know
All of those people have equal opportunity to invest, by which I mean be owners of the expensive things necessary to get work done rather than the people actually doing work.
I'm not saying people who start with no money can't succeed, or people who start with money are guaranteed to succeed. I'm saying people with a healthy start (or ludicrously easy start) discount just how many times they can fail without consequences, and how much easier it is to succeed, in comparison to people with a middling or disadvantaged start.
I should point out that I'm not a libertarian; I'm just questioning the consistency of his beliefs.
I'm on the fence about copyright & patent. What we're doing now obviously is broken. I don't believe it should go away altogether without some mechanism for supporting people who create great works, though, even if that mechanism had to be big gov.
As a libertarian, how can you defend the notion of intellectual property? I didn't sign a contract agreeing not to copy books/music/movies or duplicate patented designs.
Vote *for* things that do nearly the most net good you think you can get approved. Vote *against* things that do no net good or are far from the maximum practically attainable good.
Make that your precedent. Voting against something that you believe is for the good because it sets a precedent of regulating something is just foolish. Let the precedent be voting for things that are clearly good for the country, and against everything else.
The easiest, most foolproof way for someone determined to scam your password is to put a keylogger physically inline with your keyboard. I suspect one could be made small enough to fit inside the connector.
If the device you use to access your encrypted drive is accessible for 10 minutes, you are vulnerable. It doesn't matter what the software is or how you use *that device* to validate anything.
Congress & the prez are talking about bad incentives in the health care system. IMO this is one of the most obvious wrong incentives: the fact that there is no research into and marketing for cheap, widely available remedies, because you can't get a government-sponsored monopoly on them.
I agree with your original point. I was just arguing with your apparent disputation that the classical KE equation was correct rather than the relativistic one.
I don't necessarily agree that we'll never see it in our lifetimes, but the minimum energy needed is the KE of the moving ship (or whatever), and I agree that people don't generally have any comprehension of just how much that is. (On the order of 100x the energy released from fission of an amount of plutonium massing the same as your ship, assuming perfect efficiency in capturing the energy and turning it to KE.)
I thought we were talking about whether the KE equation is correct or not. Was I wrong that your assertion is that the relativistic mass equation is wrong?
(BTW, I personally think it's wrong, just because as we learn more there will be refinements. But I also believe it's a much better approximation than KE=1/2mv^2.)
Now you seem to be arguing that it will be very expensive to move a macroscopic amount of mass to relativistic speeds. I agree.
We push subatomic particles at relativistic speeds all the time and observe the mass change. Or maybe you think it works differently when it's lots of particles moving together?
Then there's the fact that the classical KE formula *just happens* to be the first order approximation of the relativistic formula for KE:
E = mc^2/(1 - v^2/c^2)^.5
which expands to: E = mc^2 (1 +.5*v^2/c^2 + 3/8*v^4/c^4...) E ~= mc^2 +.5*mv^2
Rest energy (RE) = mc^2
KE = E - RE ~= (mc^2 +.5*mv^2) - mc^2 = 1/2mv^2
But that's just luck. Those hundreds of physicists spending years of their lives double checking all of this obviously have it wrong.
According to special relativity, mass is nothing more or less than a measure of the energy in a system. (If you don't believe me, look up mass-energy equivalence.)
Mass increases with velocity by a factor of (1-v^2/c^2)^-.5.
The mass of a million ton spacecraft moving at.5 c is therefore a million tons times (1-(.5)^2)^-.5 = million tons * 1.1547.
So, at 100% efficiency both in the concentration of energy in the fuel (i.e. total mass conversion) and in propulsion, the fuel must weigh 1.1547 * million tons - million tons = ~155,000 tons.
Slashdot Mirror
We already use symbols for infinity, but infinity in mathematics doesn't mean what you mean. Infinity is the size of any set for which the size of the set is bigger than any number you can name.
The set of all counting numbers is infinite. There are things (like the color blue, the number 3/4, and your mother) which are not in that set, but still the set is clearly larger than any numeric size you could give, no matter how large.
There are also multiple orders of infinities.
I'm not sure how valid your notion of infinity is in mathematics at all, since (for example), we can't even determine whether there is such a thing in arithmetic as an infinity bigger than the reals. In fact, we've proven that the question can't be answered based only in what's in the reals - you have to make up a new axiom to define whether all infinities map to either the countable infinity or the reals, or whether there are bigger ones.
Presumably that falsity in our confirmed postulates would come up in the same way it always does - the model would suggest some extreme physical conditions under which we would test the postulate, and a prediction of how the measured value would vary from what we expect.
After all, time being constant had quite a bit of experimental evidence backing it up before special relativity came along, but today we accept that if you move fast enough, it's not.
There is an alternate explanation to "you are transmitting something". The "transmitting something" explanation is the Copenhagen Interpretation.
The alternative is that every time you measure a quantum property (as is done on each end in quantum entanglement experiments) the miniscule slice of reality that we see as the universe splits. Each slice, to remain consistent, has to give compatible answers on both ends of the entanglement experiment, so it looks as if you transmitted something telling the other end what the answer was.
This is the Multiple Worlds Interpretation of quantum mechanics, and afaik it is the one to which most quantum physicists subscribe. The mathematics for this interpretation are simpler (in that the math we use for quantum mechanics right now supports this interpretation, with no extra stuff needed).
Some people are hung up on what we experience as the universe being the real reality, and MW Interpretation sounds like it generates a bunch of extra realities continually.
IMO, those people are what's known in science as "wrong".
You can't do tricks like oo - oo = 0 because, for example, there are infinite counting numbers (1, 2, 3, ...). There are also infinite counting numbers > 1 (2, 3, ...). If you subtract the second infinity from the first, clearly one number is left over.
I can map the numbers (1, 2, 3, ...) one-to-one onto the numbers (2, 3, 4, ...) without skipping any on either side, so the two infinities are clearly equal, even though subtracting one from the other leaves 1.
Similar reasoning (infinite even counting numbers vs. the infinite total of all counting numbers) applies to dividing infinities.
And we haven't even started discussing higher orders of infinities. The number of real numbers is ... hmm, saying infinitely bigger is really an infinite understatement, but anyway, it's infinitely bigger than the number of counting numbers. Read up on Cantor's Diagonalization Proof if you'd like to learn more.
You can discuss infinities in math, but only by making up new math to manipulate them.
And the limit of the graph 1/x as x->0 is undefined. It grows without bound to larger numbers as you approach 0 from the positive numbers, and without bound to smaller numbers (or bigger negative numbers, if you like) as you approach 0 from the negative.
We just elected to define some of those previously undefined limits (e.g. 1/x^2 as x->0) as some order of infinity. Others remain undefined, and there is argument about how valid various infinities are.
I can't think of anywhere that infinities are allowed, or at least liked, in physics. There appears to be such a thing as a smallest distance (at least inasmuch as there is such a thing as distance at all, see quantum mechanics). There are ways of deriving the physical constants that involve infinities canceling out, but for the most part that bit is despised. Physicists would love to see another way of formulating it that gives the right answers.
That's a bad analogy. Einstein's relativity equations break down to the newtonian equations for any problem in everyday experience. They must because Newton's equations give the right answers for everyday experience (or else they would have been trashed or consigned to use in some very limited problem domain long ago). So must Einstein's, or else they'd be clearly wrong.
Quantum mechanics equates to classical mechanics when you aggregate enough interactions together (the WKB expansion is one example of doing the math to demonstrate that). (Anything on an everyday scale involves > 10^18 atoms interacting, after all.) If QM didn't do that, it would clearly be wrong.
Well, clearly either QM or general relativity are wrong anyway, since they're incompatible, but finding an experiment where both have measurable effects is a bitch. Otherwise we would already be well on our way to finding a theory that covers both domains.
I think we want a system that we can ask to do a complex task in natural language, and which will perform the task, only asking for further instruction when what we've told it is sufficiently ambiguous.
I suspect consciousness will be a byproduct in such a system (as it is in us), but to me, consciousness is not the goal. In fact, if we could achieve it without consciousness, that would be better, since a whole swath of ethical issues in AI go away.
Which reminds me of something else I thought yesterday regarding this: is anyone considering the ethical issues?
I don't think this simulation approaches the trouble spot yet, but at some point we have a good enough simulation of a brain that we're essentially maintaining a sentient creature in an environment with very limited stimuli (a torture in itself) with a half-functioning brain. I'm sure we'd decide that what we learn is worth it, but we should at least acknowledge the issue.
Eventually, it's going to be a simulation of a human we're torturing for science.
Bravo!
Well done, sir.
I believe you are mistaken. I don't know which herbal remedies are good and which aren't, but the reason pharmaceutical companies spend all that money on R&D (a significant fraction of what they spend on marketing!) is so they can patent the drug and have a monopoly.
If the drug is more effective than natural remedies; great! If not, well, how could they afford to market a drug to be competitive with patented drugs without getting a monopoly on it? After all, anybody could then come along and undercut them on price, since the first company already paid for much of the marketing.
It is quite frequent that a newly patented drug that is shilled off on us is less effective than the old one that fell out of patent, but unless you do the legwork yourself (your doctor is biased by the pharmacy reps pushing their wares), you will be using the new, expensive drug.
You're obviously a troll rather than interested in honest conversation, but someone worthwhile might be interested in the response, so I'll give one.
You're dead wrong. I have been extremely fortunate, not in my financial start (I once couldn't go to school for a week because we couldn't afford a new pair of shoes), but in my intellectual start. I was lucky enough to get a full scholarship, and I make a healthy six figures in middle America, so I'm doing fine financially.
I have taken off work multiple times and completed the work I went after (with the exception of the first time). I am no marketer, and I find the things most marketers do to be disgustingly self-serving. I have failed in business, at least so far.
Remember that the first two of those were done 7-9 years ago, so any argument that I was copying existing projects mindlessly is BS.
I am no stranger to risk. My point stands: people who can rely on their parents to bail them out if a risk fails have a huge advantage in business (and in life in general, of course). Regardless of any "fairness" issue, it is to our advantage as a society to do our best to see that people who could improve our lives get a chance to do so, with as much chance of success as makes sense when the risks & rewards are weighed.
Honestly, I probably never could have taken the risks I did if I hadn't had the genetic & environmental luck I've had - I can't see how someone living on $50k can afford to take enough time out to get anything at all done when they have a family to feed.
Of course, being 17, you probably have never thought of what taking a financial risk means when you have real responsibility.
Right; because there's no difference between someone who supports a family on $50k per year with no inheritance and someone who:
a) is supported their whole life and gets $millions in inheritance/giveaways
or
b) gets a job that pays $hundreds of thousands per year (or millions) because of who they/their parents know
All of those people have equal opportunity to invest, by which I mean be owners of the expensive things necessary to get work done rather than the people actually doing work.
I'm not saying people who start with no money can't succeed, or people who start with money are guaranteed to succeed. I'm saying people with a healthy start (or ludicrously easy start) discount just how many times they can fail without consequences, and how much easier it is to succeed, in comparison to people with a middling or disadvantaged start.
Have you read Vernor Vinge's "Rainbows End"?
I've felt the same way about all of Crichton's stuff :-(
I should point out that I'm not a libertarian; I'm just questioning the consistency of his beliefs.
I'm on the fence about copyright & patent. What we're doing now obviously is broken. I don't believe it should go away altogether without some mechanism for supporting people who create great works, though, even if that mechanism had to be big gov.
As a libertarian, how can you defend the notion of intellectual property? I didn't sign a contract agreeing not to copy books/music/movies or duplicate patented designs.
Trademark law is just fraud law, IMO.
The slippery slope argument is fallacious.
Vote *for* things that do nearly the most net good you think you can get approved. Vote *against* things that do no net good or are far from the maximum practically attainable good.
Make that your precedent. Voting against something that you believe is for the good because it sets a precedent of regulating something is just foolish. Let the precedent be voting for things that are clearly good for the country, and against everything else.
The easiest, most foolproof way for someone determined to scam your password is to put a keylogger physically inline with your keyboard. I suspect one could be made small enough to fit inside the connector.
If the device you use to access your encrypted drive is accessible for 10 minutes, you are vulnerable. It doesn't matter what the software is or how you use *that device* to validate anything.
Parent: win.
Congress & the prez are talking about bad incentives in the health care system. IMO this is one of the most obvious wrong incentives: the fact that there is no research into and marketing for cheap, widely available remedies, because you can't get a government-sponsored monopoly on them.
I agree with your original point. I was just arguing with your apparent disputation that the classical KE equation was correct rather than the relativistic one.
I don't necessarily agree that we'll never see it in our lifetimes, but the minimum energy needed is the KE of the moving ship (or whatever), and I agree that people don't generally have any comprehension of just how much that is. (On the order of 100x the energy released from fission of an amount of plutonium massing the same as your ship, assuming perfect efficiency in capturing the energy and turning it to KE.)
As opposed to when they gave the prize to Yasser Arafat?
I thought we were talking about whether the KE equation is correct or not. Was I wrong that your assertion is that the relativistic mass equation is wrong?
(BTW, I personally think it's wrong, just because as we learn more there will be refinements. But I also believe it's a much better approximation than KE=1/2mv^2.)
Now you seem to be arguing that it will be very expensive to move a macroscopic amount of mass to relativistic speeds. I agree.
We push subatomic particles at relativistic speeds all the time and observe the mass change. Or maybe you think it works differently when it's lots of particles moving together?
Then there's the fact that the classical KE formula *just happens* to be the first order approximation of the relativistic formula for KE:
E = mc^2/(1 - v^2/c^2)^.5
which expands to: .5*v^2/c^2 + 3/8*v^4/c^4 ...) .5*mv^2
E = mc^2 (1 +
E ~= mc^2 +
Rest energy (RE) = mc^2
KE = E - RE ~= (mc^2 + .5*mv^2) - mc^2 = 1/2mv^2
But that's just luck. Those hundreds of physicists spending years of their lives double checking all of this obviously have it wrong.
Er, typo. 115,000 tons.
According to special relativity, mass is nothing more or less than a measure of the energy in a system. (If you don't believe me, look up mass-energy equivalence.)
Mass increases with velocity by a factor of (1-v^2/c^2)^-.5.
The mass of a million ton spacecraft moving at .5 c is therefore a million tons times (1-(.5)^2)^-.5 = million tons * 1.1547.
So, at 100% efficiency both in the concentration of energy in the fuel (i.e. total mass conversion) and in propulsion, the fuel must weigh 1.1547 * million tons - million tons = ~155,000 tons.