actually, someone who knows the subject can tell when a particular line of though will lead you where there be dragons. and they're usually right. also: "how can I be impressed if what you're saying has no obvious connection to what I understand as reality?"
A Hilbert space is a complete vector space with a scalar (dot) product. The "complete" just means that any infinite sequence of items such that the distance between two successive ones goes to zero has a limit (the set of rational numbers is NOT complete). A trivial example is normal Euclidian 3D space. You don't need to explain anything about functions in order to explain Hilbert space, because any Euclidian space is a Hilbert space. When you do know about functions, you just show that any linear differential equation generates a Hilbert space with functions as it's points, and you can show that it is infinite dimensional if you need to. You just have to realize that there is a difference between configuration space ('where', commonly denoted as x, y, z) and wave-function space ('state', commonly denoted as psi or phi in quantum mechanics). The integration is performed in configuration space, and that's always finite-dimensional; the solutions to Schrodinger's equation are vectors in wave-function space, and you can write them as infinite sums.
There will always be problems when you actually have to go through the quantitative stuff. Each generation learns things in a certain order, using certain conventions. And, the fields being so vast, it's very easy to make it hard for the students in some areas, while making it easy in other areas.
I see your point. the age old problem of deciding what various words mean. As a sidenote, I went to the page and tried to go through the first PDF. I don't really like it, and i doubt the effort is of any use (anyone unfamiliar with the concepts will not be able to understand them from these lectures --- I think). But the guy trying to do it has to start somewhere.
My personal opinion is that you CAN discuss the principles without going into more details. I think it's pretty easy to explain the concept of a Hilbert space with absolutely no knowledge of calculus, because it's just geometry and common sense. It is problematic to teach physics without math, because you can get it horribly wrong. But you can explain graduate level concepts without math, and you can certainly describe the experiments that prove a formula works, even if you don't go through the complicated math involved in connecting the theory, formula and experiment. It took some time to get from quantum physics to the specific heat of metals in the statistical physics course. But I can tell anyone on the street "look, if we measure the way metals conduct heat, we find that they behave in a certain way. we are only able to explain that if we use quantum physics to describe part of the electrons as a gas moving around inside the metal. classical physics fails.", and that should be enough for a basic idea.
I really don't want to be an asshole about anything. but you should clearly see that this particular 2198xsmth image from wmap is actually not that detailed. It has more pixels, but the information contained is less than the one in the Planck picture. at least, that's the way I see them, and the human eye is usually good to tell this kind of things.
actually, that is the real justification. top scientists dream of things normal people call lame and stupid. However, society found that these dreamers are useful, because they stumble onto stuff that engineers can use.
what is the justification of becoming a champion tennis/football player (since it's the season)? sports was, is and always will be a dick measuring contest (even for women). so is science, for each individual scientist. you can't change that, it's in the genes.
I saw a presentation a few months ago by someone who was involved in this research. basically, they see fluctuations in this picture, and these fluctuations are in fact quantum fluctuations (or traces of) that have been blown up by the sheer speed of expansion at that particular time. this is one interesting thing they can see. on the basis of various correlations they can also impose limits on string theories. the various models have some parameters, and these measurements put bounds on those parameters.
any FTL traveling was actually relative motion between pieces that were far away from each other; since quantum fluctuations can be seen, it's obvious something like this happened. You are right in assuming this can't probably be used for tricks. but, since this research will lead to a better model of the universe, (think of it as the mother of all experiments, because they are actually measuring the big bang), it is more than likely that any possible FTL tricks we'll ever find will be related in some way to these studies.
for anyone spotting mistakes: please feel free to reveal them. I aim to understand, so I need to be told when I'm being an idiot.
"Dubbed 'Robofish', the device is a plaster cast of a three-spined stickleback fish that is mounted on a rare-earth magnet. It is controlled by an electromagnet that is located beneath the tank and controlled, in turn, by TestPoint and Microsoft Excel software packages on a PC"
I don't really understand why they call it a robot, since it's just a magnet being pulled and pushed from the exterior. Anyway, with this kind of setup, this can not be used in the open ocean.
I'm actually disappointed, as after the japanese made robots that can dance, making a robotic fish doesn't seem that complicated.
This is not a crazy idea. It's exactly what I'd want them to do. another poster says that speculation provides for liquidity. I've never tried to figure out a better system, except one where you're not allowed to buy and sell based on the evolution of prices; however I don't know exactly what the importance of liquidity and other stuff might be, so I might be wrong.
From the government's point of view, I can't see a better option than to enforce a minimum time interval. This would effectively slow down the markets, and allow for them to make decisions with a safer estimate of their evolution.
Sometime in the future they will most likely be forced to do it. when enough people will ask them.
I do not disagree with using statistics in the stock market, in the sense that the evolution of companies is subject to chance.
However, I disagree with those who take it to the next level, and use directly the premise that share prices are subject to chance. these are the guys who write programs to buy and sell stuff in a matter of seconds, with absolutely no importance given to what the various companies actually do. this model is inherently defective (snake eating its own tail).
I thought the point of the stock market was that people with money can buy shares into companies they think will be profitable. i pitty these idiots who try all their best to get as rich as possible as fast as possible.
and I pitty the rest of the world, who see clearly that these guys treat everything like a lottery, and still trust them.
I think it's the best idea, because we are humanoid, and we can help another humanoid deal with various problems. The simplest case would be for instance, in the event of some unusual problem, a direct interface robot-human. you put on your gloves, your headset, and you start moving naturally, while your moves are replicated by the robot. keep things as familiar as possible when going into the unknown. and remember: the department of redundancy department is your friend when in outer space.
what do you mean conspiracy theorists? In all seriousness, people are trying to learn about the universe, and they are being stopped there was all the CERN stuff last year... I mean, come on! a bird dropped a piece of bread and stopped it. and a few days ago we all learned that birds are very smart. now this.
regarding special relativity: "now that you've played with magnets... did you know that scientists are only able to explain their existence with special relativity? Special relativity is a more complicated way of looking at the things happening around us. Before special relativity, people figured that if you make an experiment in your room or in a moving train, you should see the same thing. Special relativity says that's true, but it's also true that nothing can move faster than light. And only by adding this requirement, were scientists able to explain magnets and the sun shining. I'll tell you more after you learn about arithmetic..." I think I could also do unsupervised machine learning ("it's like when I give you a picture of a house and tell you to make one yourself out of lego's" or smth). But I don't really know how SVD-decompositions work:)
I think Einstein was not talking about explaining how to use a theory; rather, he was saying that you should be able to explain to a six year old what you're trying to do, why you're doing it, and what differences there are to what they know.
The catch is that a six year old actually has the patience to listen, unlike a grown up who thinks having the right to an opinion means he's as smart as you.
"TeX is a small market" doesn't make sense. TeX, LaTeX and other derivatives are free, people use them as they see fit. Engineers do not need to write a lot of equations; heck, I have physics teachers who use word because they are too old to learn latex, and they haven't really had something complicated to write (experimental physics).
See this link for a good presentation of what TeX can actually do http://nitens.org/taraborelli/latex . For arts and stuff. Furthermore, consider that there are scientists who have to write equations as fast as normal text, because their normal text IS equations --- see this article for instance http://arxiv.org/abs/1007.0044 .
TeX is also a systematic system of writing. That means stuff like sympy (http://code.google.com/p/sympy/), maxima (http://maxima.sourceforge.net/), GiNaC (http://www.ginac.de/) and others can be used to make complicated symbolic computations and then output them automatically in a TeX file. Do you realize what this means in terms of productivity?
Anyway, my point is not to turn you into a TeX enthuziast. But, if you hear someone say that TeX is getting used more and more, don't act like we're just a couple of old farts talking about our half forgotten youth, because it really makes you look bad.
It's very rewarding to see someone say the same things you're thinking. Thank you for that.
Food for thought: doesn't this mean that we would have a lot to gain by trying to teach a few animals to talk? There are already hundreds of videos on youtube with cats and dogs making sounds very similar to human speach, and their enthusiastic owners will probably turn that into an evolutionary advantage ("hey, let's mate our dog with the one down the street, he can talk"). Beyond the cuteness factor, there is however the fact that we would have the possibility to converse with nonhuman intelligences. This in itself might lead to a much better understanding of humanity.
In the Star Trek universe, they thought of the prime directive. In Orson Scott Card's "Speaker for the Dead", they killed any notion of nonintervention.
As I understand it, there's someone saying there are so many patents / laws that no one can be sure not to break them; you're saying that everyone is free to read those patents / laws, so this is not an issue.
I remember that some time ago there was a story about some contracts (some company and their customers) that were written so that normal people couldn't really read them, and a judge decided the contract was void because of this.
And I don't see a reason why someone should own an idea, just because he had it first. so what? subsequent discoveries of the same idea are still because someone worked for it. Today you can't claim patents help because someone steals ideas to claim as their own; there's arxiv for proving that you did what you did.
My personal belief is that we are passed the point in human history where the concept of "intellectual property" is of any use. The thing is that today, if someone proves their worth as an inventor / programmer / artist / whatever, they will most likely be able to find at least a decently paid job, if not grants or something similar.
It might take time, it might be problematic, but the only stable solution to the fact that information is so cheap will be to give up the idea of ownership of information.
well, the difference between octopus (is this the correct plural form?) and a species we might find in another solar system is that we will be searching for species that have some technology. I think it's much easier to communicate with another species if they have some form of technology, because we already have something in common.
I do however want to thank you for reminding me about the octupus. My problem is that I live far away from places where I could play with apes, dolphins or octupus... By the way: what are the methods of communication that have been tried?
as a PhD student in physics, the interstellar travel mechanism closest to being theoretically possible that I've seen so far is the Infinite Improbability Drive.
everybody has a right to their opinion. the ASCAP believes that the invisible pink unicorn are real, even though nobody is seeing or hearing them. or are you one of those who thinks if a tree falls in the woods it makes no sound unless there's someone there to hear it?
you, sir, are the perfect example of a radical extreme terrorist! the way you say "invisible pink unicorn" makes me think that you don't even like unicorns, so you are obviously a very bad man.
the dollar bill says "In God we trust". and everybody pays for dollar bills. why shouldn't you pay for the invisible unicorn copies?
In fact, I will propose that they start asking for royalties from people who think about songs. I mean... the church says you are not allowed to think about adultery, so it's obvious that thinking matters, and you should pay for it.
mod parent up. i'm not sure wether it's funny, insightful or plain stupid, but it needs to be seen by others. as a sidenote, our brain is perfectly capable of performing complex numerical computations. the problem is that we don't have a way of consciously accessing those functions. similar problems will arise for any system designed on "levels".
the best we came up with (as far as I know) is to have an algorithm that mimicks the human brain:) so it would only be useful for robots going in places where humans can't follow. because, at least for now, we lack the technology of efficiently simulating the human brain. These guys are trying to do just that (I think): rethink the hardware to simulate brains more efficiently.
Slashdot Mirror
actually, someone who knows the subject can tell when a particular line of though will lead you where there be dragons. and they're usually right.
also: "how can I be impressed if what you're saying has no obvious connection to what I understand as reality?"
A Hilbert space is a complete vector space with a scalar (dot) product. The "complete" just means that any infinite sequence of items such that the distance between two successive ones goes to zero has a limit (the set of rational numbers is NOT complete). A trivial example is normal Euclidian 3D space.
You don't need to explain anything about functions in order to explain Hilbert space, because any Euclidian space is a Hilbert space. When you do know about functions, you just show that any linear differential equation generates a Hilbert space with functions as it's points, and you can show that it is infinite dimensional if you need to. You just have to realize that there is a difference between configuration space ('where', commonly denoted as x, y, z) and wave-function space ('state', commonly denoted as psi or phi in quantum mechanics). The integration is performed in configuration space, and that's always finite-dimensional; the solutions to Schrodinger's equation are vectors in wave-function space, and you can write them as infinite sums.
There will always be problems when you actually have to go through the quantitative stuff. Each generation learns things in a certain order, using certain conventions. And, the fields being so vast, it's very easy to make it hard for the students in some areas, while making it easy in other areas.
I see your point. the age old problem of deciding what various words mean.
As a sidenote, I went to the page and tried to go through the first PDF. I don't really like it, and i doubt the effort is of any use (anyone unfamiliar with the concepts will not be able to understand them from these lectures --- I think). But the guy trying to do it has to start somewhere.
My personal opinion is that you CAN discuss the principles without going into more details. I think it's pretty easy to explain the concept of a Hilbert space with absolutely no knowledge of calculus, because it's just geometry and common sense.
It is problematic to teach physics without math, because you can get it horribly wrong. But you can explain graduate level concepts without math, and you can certainly describe the experiments that prove a formula works, even if you don't go through the complicated math involved in connecting the theory, formula and experiment.
It took some time to get from quantum physics to the specific heat of metals in the statistical physics course. But I can tell anyone on the street "look, if we measure the way metals conduct heat, we find that they behave in a certain way. we are only able to explain that if we use quantum physics to describe part of the electrons as a gas moving around inside the metal. classical physics fails.", and that should be enough for a basic idea.
this one http://www.astro.sunysb.edu/fwalter/TALKS/Australis/wmap.jpg ?
I really don't want to be an asshole about anything. but you should clearly see that this particular 2198xsmth image from wmap is actually not that detailed. It has more pixels, but the information contained is less than the one in the Planck picture. at least, that's the way I see them, and the human eye is usually good to tell this kind of things.
actually, that is the real justification. top scientists dream of things normal people call lame and stupid.
However, society found that these dreamers are useful, because they stumble onto stuff that engineers can use.
what is the justification of becoming a champion tennis/football player (since it's the season)? sports was, is and always will be a dick measuring contest (even for women). so is science, for each individual scientist. you can't change that, it's in the genes.
you have no idea what you're talking about.
the Planck image is made with microwaves.
what you showed is with visible light.
there's a difference.
I saw a presentation a few months ago by someone who was involved in this research.
basically, they see fluctuations in this picture, and these fluctuations are in fact quantum fluctuations (or traces of) that have been blown up by the sheer speed of expansion at that particular time. this is one interesting thing they can see.
on the basis of various correlations they can also impose limits on string theories. the various models have some parameters, and these measurements put bounds on those parameters.
any FTL traveling was actually relative motion between pieces that were far away from each other; since quantum fluctuations can be seen, it's obvious something like this happened. You are right in assuming this can't probably be used for tricks.
but, since this research will lead to a better model of the universe, (think of it as the mother of all experiments, because they are actually measuring the big bang), it is more than likely that any possible FTL tricks we'll ever find will be related in some way to these studies.
for anyone spotting mistakes: please feel free to reveal them. I aim to understand, so I need to be told when I'm being an idiot.
from the article:
"Dubbed 'Robofish', the device is a plaster cast of a three-spined stickleback fish that is mounted on a rare-earth magnet.
It is controlled by an electromagnet that is located beneath the tank and controlled, in turn, by TestPoint and Microsoft Excel software packages on a PC"
I don't really understand why they call it a robot, since it's just a magnet being pulled and pushed from the exterior. Anyway, with this kind of setup, this can not be used in the open ocean.
I'm actually disappointed, as after the japanese made robots that can dance, making a robotic fish doesn't seem that complicated.
This is not a crazy idea. It's exactly what I'd want them to do.
another poster says that speculation provides for liquidity. I've never tried to figure out a better system, except one where you're not allowed to buy and sell based on the evolution of prices; however I don't know exactly what the importance of liquidity and other stuff might be, so I might be wrong.
From the government's point of view, I can't see a better option than to enforce a minimum time interval. This would effectively slow down the markets, and allow for them to make decisions with a safer estimate of their evolution.
Sometime in the future they will most likely be forced to do it. when enough people will ask them.
I do not disagree with using statistics in the stock market, in the sense that the evolution of companies is subject to chance.
However, I disagree with those who take it to the next level, and use directly the premise that share prices are subject to chance. these are the guys who write programs to buy and sell stuff in a matter of seconds, with absolutely no importance given to what the various companies actually do. this model is inherently defective (snake eating its own tail).
I thought the point of the stock market was that people with money can buy shares into companies they think will be profitable. i pitty these idiots who try all their best to get as rich as possible as fast as possible. and I pitty the rest of the world, who see clearly that these guys treat everything like a lottery, and still trust them.
you're forgetting what kind of people you're talking to.
I think it's the best idea, because we are humanoid, and we can help another humanoid deal with various problems. The simplest case would be for instance, in the event of some unusual problem, a direct interface robot-human. you put on your gloves, your headset, and you start moving naturally, while your moves are replicated by the robot.
keep things as familiar as possible when going into the unknown. and remember: the department of redundancy department is your friend when in outer space.
what do you mean conspiracy theorists?
In all seriousness, people are trying to learn about the universe, and they are being stopped
there was all the CERN stuff last year... I mean, come on! a bird dropped a piece of bread and stopped it. and a few days ago we all learned that birds are very smart.
now this.
If there is a God, he might die laughing one day.
regarding special relativity: "now that you've played with magnets... did you know that scientists are only able to explain their existence with special relativity? Special relativity is a more complicated way of looking at the things happening around us. Before special relativity, people figured that if you make an experiment in your room or in a moving train, you should see the same thing. Special relativity says that's true, but it's also true that nothing can move faster than light. And only by adding this requirement, were scientists able to explain magnets and the sun shining. I'll tell you more after you learn about arithmetic..." :)
I think I could also do unsupervised machine learning ("it's like when I give you a picture of a house and tell you to make one yourself out of lego's" or smth).
But I don't really know how SVD-decompositions work
I think Einstein was not talking about explaining how to use a theory; rather, he was saying that you should be able to explain to a six year old what you're trying to do, why you're doing it, and what differences there are to what they know.
The catch is that a six year old actually has the patience to listen, unlike a grown up who thinks having the right to an opinion means he's as smart as you.
nope
"TeX is a small market" doesn't make sense. TeX, LaTeX and other derivatives are free, people use them as they see fit. Engineers do not need to write a lot of equations; heck, I have physics teachers who use word because they are too old to learn latex, and they haven't really had something complicated to write (experimental physics).
See this link for a good presentation of what TeX can actually do http://nitens.org/taraborelli/latex . For arts and stuff.
Furthermore, consider that there are scientists who have to write equations as fast as normal text, because their normal text IS equations --- see this article for instance http://arxiv.org/abs/1007.0044 .
TeX is also a systematic system of writing. That means stuff like sympy (http://code.google.com/p/sympy/), maxima (http://maxima.sourceforge.net/), GiNaC (http://www.ginac.de/) and others can be used to make complicated symbolic computations and then output them automatically in a TeX file. Do you realize what this means in terms of productivity?
Anyway, my point is not to turn you into a TeX enthuziast. But, if you hear someone say that TeX is getting used more and more, don't act like we're just a couple of old farts talking about our half forgotten youth, because it really makes you look bad.
It's very rewarding to see someone say the same things you're thinking. Thank you for that.
Food for thought: doesn't this mean that we would have a lot to gain by trying to teach a few animals to talk? There are already hundreds of videos on youtube with cats and dogs making sounds very similar to human speach, and their enthusiastic owners will probably turn that into an evolutionary advantage ("hey, let's mate our dog with the one down the street, he can talk"). Beyond the cuteness factor, there is however the fact that we would have the possibility to converse with nonhuman intelligences.
This in itself might lead to a much better understanding of humanity.
In the Star Trek universe, they thought of the prime directive. In Orson Scott Card's "Speaker for the Dead", they killed any notion of nonintervention.
As I understand it, there's someone saying there are so many patents / laws that no one can be sure not to break them; you're saying that everyone is free to read those patents / laws, so this is not an issue. I remember that some time ago there was a story about some contracts (some company and their customers) that were written so that normal people couldn't really read them, and a judge decided the contract was void because of this. And I don't see a reason why someone should own an idea, just because he had it first. so what? subsequent discoveries of the same idea are still because someone worked for it. Today you can't claim patents help because someone steals ideas to claim as their own; there's arxiv for proving that you did what you did. My personal belief is that we are passed the point in human history where the concept of "intellectual property" is of any use. The thing is that today, if someone proves their worth as an inventor / programmer / artist / whatever, they will most likely be able to find at least a decently paid job, if not grants or something similar. It might take time, it might be problematic, but the only stable solution to the fact that information is so cheap will be to give up the idea of ownership of information.
well, the difference between octopus (is this the correct plural form?) and a species we might find in another solar system is that we will be searching for species that have some technology. I think it's much easier to communicate with another species if they have some form of technology, because we already have something in common. I do however want to thank you for reminding me about the octupus. My problem is that I live far away from places where I could play with apes, dolphins or octupus... By the way: what are the methods of communication that have been tried?
as a PhD student in physics, the interstellar travel mechanism closest to being theoretically possible that I've seen so far is the Infinite Improbability Drive.
everybody has a right to their opinion. the ASCAP believes that the invisible pink unicorn are real, even though nobody is seeing or hearing them. or are you one of those who thinks if a tree falls in the woods it makes no sound unless there's someone there to hear it?
you, sir, are the perfect example of a radical extreme terrorist! the way you say "invisible pink unicorn" makes me think that you don't even like unicorns, so you are obviously a very bad man.
the dollar bill says "In God we trust". and everybody pays for dollar bills. why shouldn't you pay for the invisible unicorn copies?
In fact, I will propose that they start asking for royalties from people who think about songs. I mean... the church says you are not allowed to think about adultery, so it's obvious that thinking matters, and you should pay for it.
mod parent up. i'm not sure wether it's funny, insightful or plain stupid, but it needs to be seen by others.
as a sidenote, our brain is perfectly capable of performing complex numerical computations. the problem is that we don't have a way of consciously accessing those functions. similar problems will arise for any system designed on "levels".
the best we came up with (as far as I know) is to have an algorithm that mimicks the human brain :)
so it would only be useful for robots going in places where humans can't follow. because, at least for now, we lack the technology of efficiently simulating the human brain. These guys are trying to do just that (I think): rethink the hardware to simulate brains more efficiently.