Well done, you've produced a list of governments who support a war on Iraq. If by contries you actually mean the majority opinion of the citizens in those countries, your list reduces roughly to "Kuwait, Israel".
You're right, this isn't unilateral, it's trilateral. In world of 180+ countries that's just so much better.
I'm surprised nobody has mentioned Fred Hoyle yet.
In my very personal opinion, the best scifi book ever written his "The Black Cloud", which must have appeared in the 1950s.
There are no spaceships, no laser battles, no bug-eyed, man-eating aliens, and the story itself was set in the very near future (the 1960s, in fact).
One thing about this book is that it presents probably the most original alien I have ever read about. In fact, the extreme unoriginality of aliens in most scifi really pisses me off. Do you remember seeing some Star Trek film, in which other races make first contact with Earth? Here a Vulcan steps out of his spaceship (basically a human with pointy ears), and some onlooker says "It's like nothing we've ever seen before". Like, wow. Pointy ears. How amazingly exotic. The point is, any alien will be FAR LESS related to us than any of those truly weird creatures you can see in any rock pool at the beach, yet almost all scifi still treats aliens as basically human with some simple modifications (four arms, green skin, etc).
I could go on about this. There are some other original creatures in the books out there: The Moties ("The Mote in God's eye", Larry Niven) are anatomically uninspired, but at least have a very interesting sociology; the Scrode-riders ("A Fire Upon The Deep", Vernor Vinge) are actually pretty cool, and I LOVE the role they play in the book. There may be some other examples, but most aliens suck in my opinion. Read the Black Cloud for the most interesting alien there is.
Besides that, the book is very nicely written, has interesting characters (one of them is very obviously Fred Hoyle himself), bashes politicians (which I always apreciate), and gives, in my opinion, a very realistic account of how things develop on Earth (administratively and sociologically) in a very special kind of crisis.
Lastly, this book can serve as the very definition of "hard" science fiction - which is to be expected, as Hoyle was in fact one of the world's leading astronomers (he coined the term "big bang, afik), and narrowly missed a Nobel Prize in physics for explaning the creation of heavy elements in stars.
What I'm about to emphasise has already been pointed out by another poster, but I'll elaborate a bit. What you have written about the butterfly effect etc is correct. And irrelevant. Nobody is trying to predict the weather for the next 50 years, but rather the climate.
Here's the difference. To predict the weather would mean to give the exact distribution of temperature, rainfall, wind etc at a certain date. This is what the weather report after the news is all about. This cannot be done reliably more than about 3 days into the future, because the system is so chaotic.
The climate is a different matter. It's basically an average of the weather. What they want to predict is things like the average temperature for period 2000-2010 in North America, for example. Over long periods (centuries or more), climate seems to be chaotic, too. It is certainly at least partially chaotic on smaller timescales, but there should be trends that are more or less predictable on medium timescales (decades?).
For example, if there are more greenhouse gases in the atmosphere, then this has an effect on the average weather, so one might expect average temperatures to rise. But even this is not yet completely understood. For example, increased levels of CO2 might increase cloud formation, which might increase albedo, and hence decrease the temperature. This is not yet completely understood, not because the subject matter is inherintly chaotic and thus impossible to understand, but rather because the science of climatology is not yet sufficiently advanced. This is precisely the point behind this project - to advance our understanding in climatology, so that we can better understand the effects of greenhouse gases, for example. By no means does this justify the American energy policy of sitting back and happily burning fossil fuels with gusto, until the scientists are 99.8% sure that it was a bad thing and now it's too late. That's a bit like Russian roulette: "The scientists can't yet prove that this chamber is loaded, so we might as well pull the trigger".
To sum up what is known so far: increased levels of CO2 (and other "greenhouse" gases) has a very real effect on the climate. Exactly what this effect is, is not yet 100% sure, but it seems most likely to raise the temperature. On the other hand, the world average temperature has increased dramatically over the last few decades, correlating strongly with rising CO2 levels. Of course, there are natural climate fluctuations, so this could still be a coincidence. We haven't proved with 100% certainty that our increased emissions are responsible for global warming, but it seems very likely. That is why we should try to do something about it.
In summary: Global warming is a very real threat, and not just to some unheard-of third world countries. It affects you, Americans, too. Yes, you! Hence this project is very important and potentially very useful. I hope they get a lot of support.
In many European cities the town centres are declared pedestrian zones, so there're no cars (and no congestion). One could do something similar for the segway: declare the city centre a pedestrian/segway zone, and the sidewalks themselves a purely pedestrian zone. Elsewhere, as has been amply pointed out, one could limit segways to bicycle paths.
Basically, there are three categories of traffic:
(1) cars and motorbikes, (2) bicycles and segways,
(3) pedestrians or skaters. To some extent, zoning already exists for these three categories, with some overlap (bicylces are allowed on roads, for example). Segways only require a slight elaboration of this.
Olympia also demonstrated a mobile phone
version of Soundbug, that will be aimed at
business workers. The device can be stuck to a
car windscreen, meaning that drivers can have a
hands-free conversation without having to wear
a headset.
Oh. And I first thought the idea was to attach this thing to your skull...
What most people don't seem to know is that Heisenberg didn't visit Bohr alone. Carl Friedrich von Weizsäcker was also there, and he is still alive today.
He gave an interview with the Süddeutsche Zeitung one or two days ago. His recollection of the meeting is rather interesting (the interview is in German, sorry).
Firstly, he says that Heisenberg started an A-bomb project in 1939, in which Weizsäcker took part, but by 1941 they came to the conclusion that they would not be able to succeed before the war was over. The problem was the tremendous effort needed to separate the isotopes. So from 1941 on they were only interested in building a reactor. Once that worked (it never did, as the heavy water production was sabotaged) there might have been the possibility to create Plutonium and build a bomb with that. But they didn't expect this to happen before the war was over by conventional means.
The reason Heisenberg went to see Bohr, according to Weizsäcker, was that they didn't want the Americans or the British to build a bomb either. If they stated publically that they're not working on a bomb, then of course nobody would have believed them. But Heisenberg thought that they might believe Bohr. So he hoped that Bohr could convince the Allies not to build the bomb either.
This was not motivated by pure pacifism - he didn't want Germany to get nuked.
In 1941 the war looked pretty good for Germany, they were winning on all fronts. So basically Heisenberg believed that a German victory was inevitable, but with conventional weapons. He tried to explain this to Bohr, who was shocked. Bohr may have understood Heisenberg's "inevitable" to mean that he WAS working on a bomb, and planning to use it. But Weizsäcker suggests that Bohr may well have understood correctly, and didn't want the Germans to win (conventionally), and therefor figured that the Allies would have to build a bomb, to avoid a Nazi victory.
What we can accept as quite reliable, is the following: (a) Heisenberg did lead an A-bomb project from 1939 to 1941. (b) He came to the conclusion that he couldn't build a bomb before the war was over. (c) He continued working on a reactor from 1941 onwards (possibly with the option of producing Plutonium for later weapons use).
And what also seem quite plausible: (d) that he tried to convince Bohr that he was only working on a reactor, not a bomb. This is what he claimed afterwards, and is backed up by Weizsäcker. Many people might not believe these two, so here is another interesting piece of the puzzle:
I read some time ago, either in Physics Today or in Scientific American that when Bohr came to Los Alamos, he brought with him a sketch which Heisenberg had made during his 1941 visit. Bohr claimed it depicted a bomb which Heisenberg was building, but the people at Los Alamos recognised it as a heavy water reactor. As far as I remember, the sketch depicted a large bottle, filled with water (presumably heavy water, but only labelled "H2O"), and some stuff inside. Can anybody dig up this sketch on the net? At any rate, this strongly suggests that Bohr had misunderstood Heisenberg, and mistook Heisenberg's reactor for a bomb.
First, here's a link to the
original article in Nature, where you can download the paper in PDF format.
Secondly, the electrical analogy is an excellent one. Basically, quantum theory started in 1900 with Planck postulating that atoms radiate energy (light, heat) only in discrete quantities. He used this as a "mathematical trick" to derive the spectrum of black-body radiation. (However, he didn't believe his "trick" was true in any literal sense until much later, about 1913). Then in 1905 Einstein postulated the existence of photons, and used them to explain the photoelectrical effect. I'll briefly explain what that is:
When you shine light on a metal plate, it can free electrons from the metal, which can then fly a short distance to a second plate and produce an electric current. What happens is that the electrons in the metal absorb some light and use this energy to break free from the metal (they need a certain threshold energy for this). Any additional energy they have left is then invested in their movement. According to the wave theory of light, the brighter the light you shine on the plate, the more energy the electrons absorb, and the more of them should be able to break free. But, that's not what happens. If you shine a very bright red light at the plate, you don't get any electrons, but a faint blue light, even if it contains much less energy in total, will liberate plenty of electrons. Einstein's explanation was that the photons of red light, having a longer wavelength, each contain less energy. If the light is very bright then you might have LOTS of photons, but each photon only has a relatively low energy. Now, typically, the probability that a given electron is hit by a photon is quite small. This means that those (lucky few) electrons that do aborb a photon will generally only absorb one, not more. If this is a red light photon, then this energy is simply not enough to break free of the metal, so there's no photo effect. But if you shine blue light at the plate, then each photon carries enough energy to liberate an electron, which is why you expect the effect to work with blue light. If you make the light brighter, then there are more photons, hence more electrons are released. But they each still have the same amount of energy. Incidentally, this is what Einstein got his Nobel prize for, not relativity.
Now for the analogy. What has been done in the Grenoble experiment is to confirm the analogue of Planck's result. So we now know (as we had guessed for a long time) that gravitational energy, at least in bound states, comes in discrete quantities. This does not yet imply the existence of gravitons, which would be analogous to photons. So the next experiment we would need is a gravitational version of the photo effect:
Imagine a system in which neutrons are bound in some state and need a little tug to be freed (I have no idea how to bind a neutron in a state such that such a weak tug could pull it free - remember that all other forces are SO much stronger than gravity). Then maybe we could see them pulled free by gravity, and notice the strange effect, that if we increase the gravitational field (by moving a large object near to it - with the experiment done in zero gee) we can pull free MORE neutrons, but each liberated neutron still starts off with the same energy (i.e. speed).
Anybody have any ideas for such a setup? Maybe we should study neutrons orbiting a small lead ball in a zero gee?
Ever read Fred Hoyle's
"The Black Cloud"? Besides being the best science fiction I've ever read, it contains a highly interesting life-form, which, despite it's MASSIVE intelligence, had never thought of the possibility that there might life on planets...
Factoring has not yet been shown to be NP-complete, but it certainly is in NP. NP is the set of all problems for which a guessed solution can be tested in polynomial time. This is obviously the case in factoring: if you guess a factorisation of some number, just multiply out your guess and see if it really gives the orginal number. If so, your guess was right, if not, it was wrong. If one can show P=NP, then ALL problems in NP, not just the NP-complete ones, would have polynomial time solutions.
Every (useful) trapdoor function is in NP, by definition. In fact, every PK scheme is in NP, again by definition: if you guess the key, you can check in polynomial time whether your guess is correct.
A polynomial time solution to an NP complete problem would translate to polynomial time solutions to ALL NP problems (that's the definition of NP-hard). This would be a disaster for PK.
With the advent of quantum computers, all non-quantum cryptography will probably become crackable, anyway. Quantum cryptography is the only way to go in the future.
This SPED (single photon emmiting diode - we may expect this name to become nearly as commonplace as LED one day) also provides a cool way to implement a true random number generator.
The basic idea is that, as far as we know, the only TRUE source of randomness in nature is the collapse of a quantum wavefunction. Basically, the state of a quantum system is really the superpostion of several "pure" states. When the system is measured (I won't go into what constitutes a "measurement", that's a never-ending debate), this superposition collapses into one of these pure states. Which state this will be is, as far as we can tell, entirely random. Only the probability of each outcome is known in advance. Besides this, all other physical processes seem to be deterministic. So any true randomness in nature must have its origin in the collapse of some wavefunction.
How do we exploit this? Fire a single photon at a beamsplitter, then measure whether the photon has been transmitted or reflected. The outcome will be random in a true sense, the probability of each outcome will depend on the beamsplitter. But, importantly, there will be no correlation between successive outcomes if the transmission : reflection ratio of the beamsplitter is 1:1. If our two detectors (one for transmission, one for refection) aren't perfect and lose a photon, we can always fire another photon, so this should even work with imperfect detectors, like a CCD.
This can now be implemented, all we need is a SPED, a beamsplitter and two CCDs. These can all be made pretty small, so might even fit on a chip, and hey presto! You got yourself a little hardware random bit generator. The only problem left is that the thing must be cooled to some pretty low temperaure.
I've always been of the opinion that a random number generator should be hardware, not software.
Even if we do send the digits of pi to the base 10, any reasonably intelligent alien should figure out what it is, even they don't use base 10 themselves. Even if they have a totally different way of representing numbers that we haven't thought of yet.
Our system of mathematics and our discipline of deductive logic is a product of the
organization of the human nervous system.
This is true, but that doesn't make our logic arbitrary. In fact our logic is based on a type of "natural logic", according to which the whole universe is organised. That the why our mathematics (which is derived from "our" logic) is so damn good at describing the universe. The reason our logic coincides (or at least closely approximates) this universal logic is just evolution: those of our potential ancestors who had a better grasp of logic had a survival advantage. So there was (still is, see the Darwin awards) a selection pressure in favour of those who understood this natural logic.
OK, if they are viewing the star's light through the atmosphere, and using the differrence to detect the composition of
the atmosphere, then it's absorption. And anything that would "block" wavelengths, means the absorption would
increase, and provide a reading showing that it would have more sodium, not less. Am I wrong? Maybe I am wrong, but
the more I think about it, the more I feel the statement above just doesn't add up.
Yes, you are wrong. The point is that you detect sodium by noticing that certain wavelengths are abosorbed more than others, and these happen to be the same wavelengths absorbed by sodium. If there are clouds blocking all but the highest reaches of the atmosphere, then none of the light that reaches us has gone through the lower atmosphere, in which there might be more sodium than above the clouds. So yes, more light is being absorbed, but that holds for ALL wavelengths, not just those absorbed by sodium.
Seems this reporter may be the
typical reporter reporting on a subject she may not actually comprehend - and she's the one that's supposed to be
informing us!
I didn't notice any obvious mistakes in this particular story. And that actually surprises me, because this particular reporter (Deborah Zabarenko) usually makes lots of them, I've noticed.
Certainly the New Scientist's claim that Chaitin's works blows huge holes into mathematics is nonsense. As pointed out elsewhere this has interesting philosophical consequences, but in practice one doesn't really notice it. Just about all mathematical statements one normally comes across are in fact provable. Often enough it takes ages to prove something, and then people always come along and suggest that this thing is obviously one of Godel's uprovable statements. Remember the Four Colour Theorem, or Fermat's Last Theorem? They used to be quoted as classical candidates of unprovable results, but have since been proved.
In the New Scientist article Chaitin now mentions the problem of odd perfect numbers or the Riemann Hypothesis, and (according to the article) suggests that we should start getting used to the idea that these are unprovable. I disagree (though one can claim I'm biased - as some of my own work relies on the Riemann Hypothesis). I'll try to explain the reason (which is based on my intuition, so may very well be wrong) below.
Some mathematical statements seem to be true simply because it would be a great coincidence for them to be false. The classical example is the Godbach Conjecture, which claims that every even number greater than 2 is the sum of two primes. For small even numbers this is easily checked, and as one starts checking larger even numbers one notices that there are LOTS of ways to write it as the sum of a pair of numbers, more than enough to make it highly unprobable that none of these pairs would be prime pairs. So basically, one can see the Goldbach Conjecture as being true for heuristic reasons. Now I think that it has already been proved for sufficiently large even numbers, so that there remain only finitely many cases to check (though still far more than today's computers can handle), so this example is a bit outdated. Perhaps a better example is the twin prime conjecture, which states that there are infinitely many primes p such that p+2 is also prime. Again a heuristic argument shows that this should be true. One must of course be careful with heuristic arguments: one might also expect to find infinitely many prime triples (p,p+2,p+4), but there is acually only one (3,5,7), as any such triple must contain a multiple of 3.
But one can conceive of statements that should be true for heuristic reasons, and for which there is no "reason" for the heuristic argument to be false. Such statements would then be true, but if there also exists no "reason" for it to be true, it would be impossible to prove. These "reasons" are essentially what Chaitin calls "connections" between different pieces of mathematics, and they are what enable us to prove things. So basically I claim that there are many statements in mathematics (almost all so obscure that we'll never come across them) for which there exist no "reasons" to be true or false, but which are nevertheless true for heuristic reasons. In other words these statements are true by accident (though, of course, very likely accidents).
These, I believe, are the statements who's existence is proved by Godel's theorem.
(Note that a heuristic reason doesn't suffice as a proof, and that the word "reason" (in quotes above) means a deeper connection, which can lead to a proof. Of course, heuristic reasons can also lead to proofs, but then additional "reasons" are the required extra ingredients. Off the point, can we conceive of a time when a proof that there exists no "reason" for a statement to be false, together with a heuristic argument in favour of the statement, will be considered a proof that the statement is true??)
This particular configuration chain, which is impossible (note the impossible - I didn't say nearly impossible, nor did I say almost impossible - just impossible) outside of organic or artificially constructed containment, is the first really solid evidence of life off the Earth.
We don't know for sure that such a structure cannot have formed some non-biological way. The fact that you (or whoever) can't think of a mechanism to form such chains doesn't mean that such a mechanism doesn't exist. At most, it says something about your (or our) lack of imagination. And as we're not too clued up on all the geological processes on Mars yet, this is hardly surpising.
Rather, the whole point behind the meteorite is that it contains a whole bunch of independent clues, each of which might also have a non-biological explanation. But the fact that there're so many clues makes the biological explanation more likely. That is wonderful, but we might still be wrong.
One should always keep some healthy scepticism. Think of how often we've been wrong before.
The whole thing will only work when there's enough daylight, anyway. I guess they'll just have to switch them off at night:) (during which time, of course, the bacteria will happily be burning off their sugars and releasing the CO2 back into the atmosphere).
Way to go.
Look, mass extinctions are nothing new.
The earth has been going through phases of
extinction for the past couple billion years. It's part of the natural order of things. It's more than natural. It's necessary.
Without these periods of extinction, we'd have none of the genetic and biological diversity you see among organisms. The world would atrophy -- there'd be little intense selective pressure, and the next time a an asteroid collides with the earth, we'd be unprepared. We'd have forgotten how to select.
It's time to stop pretending that humans are the saviors of the planet. We're not. We're just one
species among millions. We're not even the most populous or prevalent. Heck, there are countless species we haven't even discovered yet. Why are we so arrogant?
If the planet wants to die, if nature has decreed that another mass extinction shall occur, then who are we to stop it? Sure, we might suffer if
we die too, but why should we change the direction of an entire biosphere just because of our own preference? As if our own preference were the
deciding factor. That's human arrogance.
There are better things to spend our time and effort on. Human catastrophes caused by human
agencies surround us everyday. Let's work on those before we start trying to play Deity.
-----
Satire aside, the point I'm trying to make is that not everything that's natural is good. But it's true that we still shouldn't try to mess with nature, because we don't understand it, and risk screwing things up even more.
As to global warming, the problem is that the current warming trend does NOT appear to be one of the natural warming cycles (or at least not completely), but that it is at least partially, possibly largely, caused by humans. Caused by our burning of fossil fuels, which releases carbon into the atmosphere that, prior to the industrial revolution remained locked undergound and out of the ecosystem. We have done damage. We certainly should try to control the damage as much as we can.
Slashdot Mirror
Well done, you've produced a list of governments who support a war on Iraq. If by contries you actually mean the majority opinion of the citizens in those countries, your list reduces roughly to "Kuwait, Israel".
You're right, this isn't unilateral, it's trilateral. In world of 180+ countries that's just so much better.
There are more than two parties in the USA.
Really? I always thought American politics were so easy to explain: There are two parties: The right wing, and the extreme right wing.
I'm surprised nobody has mentioned Fred Hoyle yet. In my very personal opinion, the best scifi book ever written his "The Black Cloud", which must have appeared in the 1950s.
There are no spaceships, no laser battles, no bug-eyed, man-eating aliens, and the story itself was set in the very near future (the 1960s, in fact).
One thing about this book is that it presents probably the most original alien I have ever read about. In fact, the extreme unoriginality of aliens in most scifi really pisses me off. Do you remember seeing some Star Trek film, in which other races make first contact with Earth? Here a Vulcan steps out of his spaceship (basically a human with pointy ears), and some onlooker says "It's like nothing we've ever seen before". Like, wow. Pointy ears. How amazingly exotic. The point is, any alien will be FAR LESS related to us than any of those truly weird creatures you can see in any rock pool at the beach, yet almost all scifi still treats aliens as basically human with some simple modifications (four arms, green skin, etc). I could go on about this. There are some other original creatures in the books out there: The Moties ("The Mote in God's eye", Larry Niven) are anatomically uninspired, but at least have a very interesting sociology; the Scrode-riders ("A Fire Upon The Deep", Vernor Vinge) are actually pretty cool, and I LOVE the role they play in the book. There may be some other examples, but most aliens suck in my opinion. Read the Black Cloud for the most interesting alien there is.
Besides that, the book is very nicely written, has interesting characters (one of them is very obviously Fred Hoyle himself), bashes politicians (which I always apreciate), and gives, in my opinion, a very realistic account of how things develop on Earth (administratively and sociologically) in a very special kind of crisis.
Lastly, this book can serve as the very definition of "hard" science fiction - which is to be expected, as Hoyle was in fact one of the world's leading astronomers (he coined the term "big bang, afik), and narrowly missed a Nobel Prize in physics for explaning the creation of heavy elements in stars.
So that's why so many girls play with Eliza...
Mammon, actually. Capitalism, not Christianity, is the primary religion in the USA.
When Micro$oft and $cientology finally merge, they'll sue you for posting their copyrighted TOS in the net :)
What I'm about to emphasise has already been pointed out by another poster, but I'll elaborate a bit. What you have written about the butterfly effect etc is correct. And irrelevant. Nobody is trying to predict the weather for the next 50 years, but rather the climate.
Here's the difference. To predict the weather would mean to give the exact distribution of temperature, rainfall, wind etc at a certain date. This is what the weather report after the news is all about. This cannot be done reliably more than about 3 days into the future, because the system is so chaotic.
The climate is a different matter. It's basically an average of the weather. What they want to predict is things like the average temperature for period 2000-2010 in North America, for example. Over long periods (centuries or more), climate seems to be chaotic, too. It is certainly at least partially chaotic on smaller timescales, but there should be trends that are more or less predictable on medium timescales (decades?).
For example, if there are more greenhouse gases in the atmosphere, then this has an effect on the average weather, so one might expect average temperatures to rise. But even this is not yet completely understood. For example, increased levels of CO2 might increase cloud formation, which might increase albedo, and hence decrease the temperature. This is not yet completely understood, not because the subject matter is inherintly chaotic and thus impossible to understand, but rather because the science of climatology is not yet sufficiently advanced. This is precisely the point behind this project - to advance our understanding in climatology, so that we can better understand the effects of greenhouse gases, for example. By no means does this justify the American energy policy of sitting back and happily burning fossil fuels with gusto, until the scientists are 99.8% sure that it was a bad thing and now it's too late. That's a bit like Russian roulette: "The scientists can't yet prove that this chamber is loaded, so we might as well pull the trigger".
To sum up what is known so far: increased levels of CO2 (and other "greenhouse" gases) has a very real effect on the climate. Exactly what this effect is, is not yet 100% sure, but it seems most likely to raise the temperature. On the other hand, the world average temperature has increased dramatically over the last few decades, correlating strongly with rising CO2 levels. Of course, there are natural climate fluctuations, so this could still be a coincidence. We haven't proved with 100% certainty that our increased emissions are responsible for global warming, but it seems very likely. That is why we should try to do something about it.
In summary: Global warming is a very real threat, and not just to some unheard-of third world countries. It affects you, Americans, too. Yes, you! Hence this project is very important and potentially very useful. I hope they get a lot of support.
In many European cities the town centres are declared pedestrian zones, so there're no cars (and no congestion). One could do something similar for the segway: declare the city centre a pedestrian/segway zone, and the sidewalks themselves a purely pedestrian zone. Elsewhere, as has been amply pointed out, one could limit segways to bicycle paths.
Basically, there are three categories of traffic: (1) cars and motorbikes, (2) bicycles and segways, (3) pedestrians or skaters. To some extent, zoning already exists for these three categories, with some overlap (bicylces are allowed on roads, for example). Segways only require a slight elaboration of this.
What most people don't seem to know is that Heisenberg didn't visit Bohr alone. Carl Friedrich von Weizsäcker was also there, and he is still alive today.
He gave an interview with the Süddeutsche Zeitung one or two days ago. His recollection of the meeting is rather interesting (the interview is in German, sorry).
Firstly, he says that Heisenberg started an A-bomb project in 1939, in which Weizsäcker took part, but by 1941 they came to the conclusion that they would not be able to succeed before the war was over. The problem was the tremendous effort needed to separate the isotopes. So from 1941 on they were only interested in building a reactor. Once that worked (it never did, as the heavy water production was sabotaged) there might have been the possibility to create Plutonium and build a bomb with that. But they didn't expect this to happen before the war was over by conventional means.
The reason Heisenberg went to see Bohr, according to Weizsäcker, was that they didn't want the Americans or the British to build a bomb either. If they stated publically that they're not working on a bomb, then of course nobody would have believed them. But Heisenberg thought that they might believe Bohr. So he hoped that Bohr could convince the Allies not to build the bomb either. This was not motivated by pure pacifism - he didn't want Germany to get nuked.
In 1941 the war looked pretty good for Germany, they were winning on all fronts. So basically Heisenberg believed that a German victory was inevitable, but with conventional weapons. He tried to explain this to Bohr, who was shocked. Bohr may have understood Heisenberg's "inevitable" to mean that he WAS working on a bomb, and planning to use it. But Weizsäcker suggests that Bohr may well have understood correctly, and didn't want the Germans to win (conventionally), and therefor figured that the Allies would have to build a bomb, to avoid a Nazi victory.
What we can accept as quite reliable, is the following: (a) Heisenberg did lead an A-bomb project from 1939 to 1941. (b) He came to the conclusion that he couldn't build a bomb before the war was over. (c) He continued working on a reactor from 1941 onwards (possibly with the option of producing Plutonium for later weapons use).
And what also seem quite plausible: (d) that he tried to convince Bohr that he was only working on a reactor, not a bomb. This is what he claimed afterwards, and is backed up by Weizsäcker. Many people might not believe these two, so here is another interesting piece of the puzzle:
I read some time ago, either in Physics Today or in Scientific American that when Bohr came to Los Alamos, he brought with him a sketch which Heisenberg had made during his 1941 visit. Bohr claimed it depicted a bomb which Heisenberg was building, but the people at Los Alamos recognised it as a heavy water reactor. As far as I remember, the sketch depicted a large bottle, filled with water (presumably heavy water, but only labelled "H2O"), and some stuff inside. Can anybody dig up this sketch on the net? At any rate, this strongly suggests that Bohr had misunderstood Heisenberg, and mistook Heisenberg's reactor for a bomb.
Oh wait...
First, here's a link to the original article in Nature, where you can download the paper in PDF format.
Secondly, the electrical analogy is an excellent one. Basically, quantum theory started in 1900 with Planck postulating that atoms radiate energy (light, heat) only in discrete quantities. He used this as a "mathematical trick" to derive the spectrum of black-body radiation. (However, he didn't believe his "trick" was true in any literal sense until much later, about 1913). Then in 1905 Einstein postulated the existence of photons, and used them to explain the photoelectrical effect. I'll briefly explain what that is:
When you shine light on a metal plate, it can free electrons from the metal, which can then fly a short distance to a second plate and produce an electric current. What happens is that the electrons in the metal absorb some light and use this energy to break free from the metal (they need a certain threshold energy for this). Any additional energy they have left is then invested in their movement. According to the wave theory of light, the brighter the light you shine on the plate, the more energy the electrons absorb, and the more of them should be able to break free. But, that's not what happens. If you shine a very bright red light at the plate, you don't get any electrons, but a faint blue light, even if it contains much less energy in total, will liberate plenty of electrons. Einstein's explanation was that the photons of red light, having a longer wavelength, each contain less energy. If the light is very bright then you might have LOTS of photons, but each photon only has a relatively low energy. Now, typically, the probability that a given electron is hit by a photon is quite small. This means that those (lucky few) electrons that do aborb a photon will generally only absorb one, not more. If this is a red light photon, then this energy is simply not enough to break free of the metal, so there's no photo effect. But if you shine blue light at the plate, then each photon carries enough energy to liberate an electron, which is why you expect the effect to work with blue light. If you make the light brighter, then there are more photons, hence more electrons are released. But they each still have the same amount of energy. Incidentally, this is what Einstein got his Nobel prize for, not relativity.
Now for the analogy. What has been done in the Grenoble experiment is to confirm the analogue of Planck's result. So we now know (as we had guessed for a long time) that gravitational energy, at least in bound states, comes in discrete quantities. This does not yet imply the existence of gravitons, which would be analogous to photons. So the next experiment we would need is a gravitational version of the photo effect:
Imagine a system in which neutrons are bound in some state and need a little tug to be freed (I have no idea how to bind a neutron in a state such that such a weak tug could pull it free - remember that all other forces are SO much stronger than gravity). Then maybe we could see them pulled free by gravity, and notice the strange effect, that if we increase the gravitational field (by moving a large object near to it - with the experiment done in zero gee) we can pull free MORE neutrons, but each liberated neutron still starts off with the same energy (i.e. speed).
Anybody have any ideas for such a setup? Maybe we should study neutrons orbiting a small lead ball in a zero gee?
Good point.
Ever read Fred Hoyle's "The Black Cloud"? Besides being the best science fiction I've ever read, it contains a highly interesting life-form, which, despite it's MASSIVE intelligence, had never thought of the possibility that there might life on planets...
Every (useful) trapdoor function is in NP, by definition. In fact, every PK scheme is in NP, again by definition: if you guess the key, you can check in polynomial time whether your guess is correct.
A polynomial time solution to an NP complete problem would translate to polynomial time solutions to ALL NP problems (that's the definition of NP-hard). This would be a disaster for PK.
With the advent of quantum computers, all non-quantum cryptography will probably become crackable, anyway. Quantum cryptography is the only way to go in the future.
This SPED (single photon emmiting diode - we may expect this name to become nearly as commonplace as LED one day) also provides a cool way to implement a true random number generator.
The basic idea is that, as far as we know, the only TRUE source of randomness in nature is the collapse of a quantum wavefunction. Basically, the state of a quantum system is really the superpostion of several "pure" states. When the system is measured (I won't go into what constitutes a "measurement", that's a never-ending debate), this superposition collapses into one of these pure states. Which state this will be is, as far as we can tell, entirely random. Only the probability of each outcome is known in advance. Besides this, all other physical processes seem to be deterministic. So any true randomness in nature must have its origin in the collapse of some wavefunction.
How do we exploit this? Fire a single photon at a beamsplitter, then measure whether the photon has been transmitted or reflected. The outcome will be random in a true sense, the probability of each outcome will depend on the beamsplitter. But, importantly, there will be no correlation between successive outcomes if the transmission : reflection ratio of the beamsplitter is 1:1. If our two detectors (one for transmission, one for refection) aren't perfect and lose a photon, we can always fire another photon, so this should even work with imperfect detectors, like a CCD.
This can now be implemented, all we need is a SPED, a beamsplitter and two CCDs. These can all be made pretty small, so might even fit on a chip, and hey presto! You got yourself a little hardware random bit generator. The only problem left is that the thing must be cooled to some pretty low temperaure.
I've always been of the opinion that a random number generator should be hardware, not software.
South Africans are always quick to point out that not everything revolves around the Aussies.
See for example this 1998 article.
This is true, but that doesn't make our logic arbitrary. In fact our logic is based on a type of "natural logic", according to which the whole universe is organised. That the why our mathematics (which is derived from "our" logic) is so damn good at describing the universe. The reason our logic coincides (or at least closely approximates) this universal logic is just evolution: those of our potential ancestors who had a better grasp of logic had a survival advantage. So there was (still is, see the Darwin awards) a selection pressure in favour of those who understood this natural logic.
Certainly the New Scientist's claim that Chaitin's works blows huge holes into mathematics is nonsense. As pointed out elsewhere this has interesting philosophical consequences, but in practice one doesn't really notice it. Just about all mathematical statements one normally comes across are in fact provable. Often enough it takes ages to prove something, and then people always come along and suggest that this thing is obviously one of Godel's uprovable statements. Remember the Four Colour Theorem, or Fermat's Last Theorem? They used to be quoted as classical candidates of unprovable results, but have since been proved.
In the New Scientist article Chaitin now mentions the problem of odd perfect numbers or the Riemann Hypothesis, and (according to the article) suggests that we should start getting used to the idea that these are unprovable. I disagree (though one can claim I'm biased - as some of my own work relies on the Riemann Hypothesis). I'll try to explain the reason (which is based on my intuition, so may very well be wrong) below.
Some mathematical statements seem to be true simply because it would be a great coincidence for them to be false. The classical example is the Godbach Conjecture, which claims that every even number greater than 2 is the sum of two primes. For small even numbers this is easily checked, and as one starts checking larger even numbers one notices that there are LOTS of ways to write it as the sum of a pair of numbers, more than enough to make it highly unprobable that none of these pairs would be prime pairs. So basically, one can see the Goldbach Conjecture as being true for heuristic reasons. Now I think that it has already been proved for sufficiently large even numbers, so that there remain only finitely many cases to check (though still far more than today's computers can handle), so this example is a bit outdated. Perhaps a better example is the twin prime conjecture, which states that there are infinitely many primes p such that p+2 is also prime. Again a heuristic argument shows that this should be true. One must of course be careful with heuristic arguments: one might also expect to find infinitely many prime triples (p,p+2,p+4), but there is acually only one (3,5,7), as any such triple must contain a multiple of 3.
But one can conceive of statements that should be true for heuristic reasons, and for which there is no "reason" for the heuristic argument to be false. Such statements would then be true, but if there also exists no "reason" for it to be true, it would be impossible to prove. These "reasons" are essentially what Chaitin calls "connections" between different pieces of mathematics, and they are what enable us to prove things. So basically I claim that there are many statements in mathematics (almost all so obscure that we'll never come across them) for which there exist no "reasons" to be true or false, but which are nevertheless true for heuristic reasons. In other words these statements are true by accident (though, of course, very likely accidents).
These, I believe, are the statements who's existence is proved by Godel's theorem. (Note that a heuristic reason doesn't suffice as a proof, and that the word "reason" (in quotes above) means a deeper connection, which can lead to a proof. Of course, heuristic reasons can also lead to proofs, but then additional "reasons" are the required extra ingredients. Off the point, can we conceive of a time when a proof that there exists no "reason" for a statement to be false, together with a heuristic argument in favour of the statement, will be considered a proof that the statement is true??)
This particular configuration chain, which is impossible (note the impossible - I didn't say nearly impossible, nor did I say almost impossible - just impossible) outside of organic or artificially constructed containment, is the first really solid evidence of life off the Earth.
We don't know for sure that such a structure cannot have formed some non-biological way. The fact that you (or whoever) can't think of a mechanism to form such chains doesn't mean that such a mechanism doesn't exist. At most, it says something about your (or our) lack of imagination. And as we're not too clued up on all the geological processes on Mars yet, this is hardly surpising.
Rather, the whole point behind the meteorite is that it contains a whole bunch of independent clues, each of which might also have a non-biological explanation. But the fact that there're so many clues makes the biological explanation more likely. That is wonderful, but we might still be wrong.
One should always keep some healthy scepticism. Think of how often we've been wrong before.
The whole thing will only work when there's enough daylight, anyway. I guess they'll just have to switch them off at night :) (during which time, of course, the bacteria will happily be burning off their sugars and releasing the CO2 back into the atmosphere).
Way to go.
Look, mass extinctions are nothing new. The earth has been going through phases of extinction for the past couple billion years. It's part of the natural order of things. It's more than natural. It's necessary.
Without these periods of extinction, we'd have none of the genetic and biological diversity you see among organisms. The world would atrophy -- there'd be little intense selective pressure, and the next time a an asteroid collides with the earth, we'd be unprepared. We'd have forgotten how to select.
It's time to stop pretending that humans are the saviors of the planet. We're not. We're just one species among millions. We're not even the most populous or prevalent. Heck, there are countless species we haven't even discovered yet. Why are we so arrogant?
If the planet wants to die, if nature has decreed that another mass extinction shall occur, then who are we to stop it? Sure, we might suffer if we die too, but why should we change the direction of an entire biosphere just because of our own preference? As if our own preference were the deciding factor. That's human arrogance.
There are better things to spend our time and effort on. Human catastrophes caused by human agencies surround us everyday. Let's work on those before we start trying to play Deity.
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Satire aside, the point I'm trying to make is that not everything that's natural is good. But it's true that we still shouldn't try to mess with nature, because we don't understand it, and risk screwing things up even more.
As to global warming, the problem is that the current warming trend does NOT appear to be one of the natural warming cycles (or at least not completely), but that it is at least partially, possibly largely, caused by humans. Caused by our burning of fossil fuels, which releases carbon into the atmosphere that, prior to the industrial revolution remained locked undergound and out of the ecosystem. We have done damage. We certainly should try to control the damage as much as we can.