When I first saw the article it sounded like the post-processing that is done to improve the focus of images that were originally taken out-of-focus. You can extract a lot of features by convolving an image with the inverse of the defocussing transfer function.
But doing this has a downside: It also brings to a point focus, or nearly so, the light from patches of a certain range of shapes. They weren't originally points - but photographing them defocussed made the same shape blur as a point light source would have, so the post-processing turned them into points. You extract features that would have been unreadable (like a license plate number), but also "sprinkle glitter and pepper" over the image.
Not only are the original images taken out-of-focus, but they have also been optically distorted by a specially shaped glass plate (this is the actually wavefront coding part). This optical distortion affects in-focus and out-of-focus objects equally, and I think that is what allows them to deconvolve the image without introducing a lot of noise. Even if it does introduce some noise, they can probably filter that out with a weak blurring filter.
Since the corporate site is still down, the best place to read about this is probably the website of the Imaging Systems Laboratory at the University of Colorado at Boulder, which I think is where all this technology was originally developed. Someone else posted that link elsewhere in the comments, but I will post it again here, properly hyperlinked for convenient Slashdotting.;-)
I'm not sure depth of field is relevant for afocal systems operating at infinite conjugates. And as a practical matter, at those distances the clarity of an image is primarily limited by diffraction for a telescope that's reasonable well-corrected for aberration (which the original Hubble was not).
As a practical point, spherical aberration can be corrected pretty well by defocusing the system. They considered doing this with Hubble, but when they calculated the amount of spherical aberration in the mirror, they discovered that they didn't have enough translation range for their sensor to defocus the system enough to make up for it.
Incidentally, there's no way that you can stop down an f/10 system to f/6.4 . f/6.4 corresponds to a larger aperture for the same focal length, so I'm guessing that you're actually stopping the telescope down to f/12.8 .
Those artifacts look like ringing from the Gibbs phenomenon (you see it a lot in poor quality JPEG or MPEG images) due to filtering out too many of the harmonics in the image spectrum. They can probably be eliminated by apodizing the filter. Even with the artifacts, though, I think you'll agree that for severe out-of-focus images, filtered focus-invariant images look a lot better than traditional images.
Woot! Another OpSci person reads Slashdot!:-) (Okay, well, technically I'm an alumnus [B.S. optical engineering 2002], but I'll probably come back;-) )
From some of their "interactive" pages, (namingly this page [colorado.edu]), it seems as if they are using the "waviness" (I am still unclear about this) to do some amount of tomography.
From skimming the website of the Imaging Systems Laboratory at the University of Colorado at Boulder (directed by W.T. Cathey, who wrote one of the standard texts on optical information processing and holography), the way they achieve this depth of focus trick is half optical and half digital signal processing. They use a cubic phase filter (which literally could be a specially warped piece of glass immediately after the lens) to distort the wavefront, so the image captured by a CCD or CMOS array is uniformly blurred by this cubic phase. I think the cubic phase that's applied makes the phase errors due to defocus more evident (probably akin to recording the phase by interference in off-axis holography (invented by Emmett Leith [my advisor:-)] and Juris Upatneiks), or measuring wavefront distortion using a Shack-Hartmann wavefront sensor). Since the cubic phase error that was applied is known, it's easy to deconvolve the image to remove its effect, and the phase errors due to defocus probably interact with the cubic phase in a way that's visible in the image spectrum, so a filter can be applied to remove the effect of defocus as well.
I'd rather have a device tell me in words, or maybe in pictures, how my money, family, friends, and work are doing--it's simpler and less ambiguous.
This device is really meant to be a toy, and as a commercial product it is marketed as such. And even as such, I think it would be difficult to distinguish between this device and a glass sphere with some embedded LEDs being driven by a pseudorandom number generator (which would be a lot simpler and cheaper to build).
I think laser action is strictly due to the light-matter interaction, but the fact that the incident photon and the emitted photon are coherent with each other probably is a consequence of the Bose-Einstein statistics governing photon behavior. Nonetheless, I'm impressed by your understanding of physics as an interested layman and by the fact that you have some understanding of bosons and fermions--all that stuff confused me until quite recently.;-)
If you modulate a non-time-varying signal onto your sine wave, you're not adding any information to it, so only the fundamental frequency of the sine wave is present. When you modulate a time-varying waveform onto your sine wave, you add additional information to it, so additional frequencies are required to support that information. For example, if you put a slow sine wave on a fast sine wave, say sin(t/10) on sin(t), then the sin(t) wave is now carrying the information about the sin(t/10) wave. If you calculate the spectrum of the wave (by Fourier transformation, for example), you will find that the sum and difference frequencies of the two waves are present in addition to the fundamental frequency of the fast wave. I think it is probably also possible to manipulate the trigonometic functions to show that [sin(t/10)][(sin(t)] has the sum and difference frequencies in it, but I'm too tired to do it so I will leave it as an exercise for the reader.:-p
Yay, someone who actually understands the subject!:-)
His use of the word "interference" is confusing to say the least. RF engineers talk about interference as the superposition of singnals as you receive them. He talks about interference as the interaction of signals in space.
I think Reed could have made the whole story clearer, at least to a EE/Optics guy like myself, by using the word "crosstalk", which has a much more precise meaning than "interference".
Wow, I provoked a lot more responses than I expected! I will try to organize my responses to the most common comments or objections.
The number one objection seems to be to the soap bubble example. The soap bubble probably isn't the clearest example of interference phenomenon to explain, but it is an example from everyday experience, which is why I chose it.
The colors from a soap bubble are due to light interfering with light. Light is partially reflected from each surface of the soap film, and the reflected beams do interfere with each other and result in the colors that you see. That's about all the detail I want to go into describing it, but if I still don't believe me, it's probably described better and in more detail in either Hecht Optics, Born & Wolf Principles of Optics, or Lipson, Lipson & Tannhauser Optical Physics (in any of those books, look for the section on "multiple-beam interference").
It is true that when two beams of light cross paths in vacuum, if you were to observe them after they cross, you could not tell that they crossed. However, in the region in which they cross, they can interfere with each other. Again, any of the references I mentioned above will probably explain this much better than I can.
The second most common objection was to my description of diffraction in a pinhole camera. On this count, I will admit that I was playing it very fast and loose when I said that diffraction was due to photons interfering with each other, but OTOH Reed used the phrase "photons interfering" to describe a phenomenon that in optics and electromagnetics is normally described as diffraction. Reed explicitly denies the existence of diffraction in the pinhole camera. On this count, he is dead wrong because you can conduct an experiment, observing the images of pinhole cameras with smaller and smaller pinholes, and eventually making the pinhole smaller makes the picture worse! (not just dimmer, but blurrier as well) This is because of diffraction, but again, you'd be much better off reading about it from a book than listening to me try to explain it.
The other interesting objection introduced the notions of Laplace (or Fourier) transforms, and the spectra that arise from these mathematical operations. This is a different spectrum than the physical spectrum associated with light or radio waves. However, even the abstract world of signals and systems or communications theory, you can arrange for two signals to interfere with each other, and even to interfere in such a way that it is impossible to recover the original signals without a prioriknowledge. For example, if you multiply sin x with cos x, you get out a sine wave at twice the signal frequency of either of the original waves. If you received this signal without a priori knowledge, there would be no way to tell if if was meant to be one signal or two signals. Admittedly, this is a very simple and contrived example, but this can still occur with more complicated signals.
Even worse, once you physically manifest this signal by modulating it onto an electromagnetic carrier wave (like radio does), this communications spectrum is now superimposed on the physical spectrum of the electromagnetic wave. Now the signal is subject to the physical phenomenon of interference, which can further corrupt the signal if you don't allocate communications channels in the electromagnetic spectrum properly. And I think it's the allocation of commmunications channels which is what the article is trying to be about. However, that doesn't change the fact that Reed is dead wrong in the way he describes or interprets many of his physical examples, probably because he has a lot of background in computer science but not as much in physics.
Furthermore, Reed is wrong if he thinks that ultrawideband (UWB) or frequency hopping will increase the Shannon limit within a given range of the electromagnetic spectrum. Ultrawideband will interfere with other electromagnetic signals. It requires a lot of electromagnetic bandwidth, hence the name.:-p This increases the likelihood that it will overlap with other channels, which means that it probably would be a less efficient way to allocate spectrum than FM radio, for example. This may not be an issue for the other channels if the signal-to-noise ratio is high enough to compensate, but it does not mean that the interference phenomenon does not exist or does not take place. The advantage of ultrawideband is that it has a wide bandwidth, which enables faster data transfer rates, but it wouldn't be any faster than multiplexing the same data across enough FM channels to have an equivalent bandwidth (coding and SNR ratios and all other things being equal). The problem is that allocating a ton of bandwidth to a single UWB channel means that instead of several somewhat underutilized channels occupying some range of the spectrum, you might end up with one highly underutilized channel filling that entire range of the spectrum.
Frequency hopping can improve the efficiency of the spectrum allocation by moving communications channels to unused regions of the spectrum, but it does not create communication capacity where there is none. Furthermore, those channels have to be allocated in advance to prevent them from with other signals.
Reed is probably right that the electromagnetic spectrum is inefficiently utilized. But the many of the physical examples or explanations of physical phenomena that he presents are dead wrong, which was the point that I was trying to make in my original post.
Ok, so I drastically overgeneralized, and even worse, I'm wrong, and I just realized why. The reason why pretty much all ground-to-ground transmitters have their antennae oriented vertically is because the antenna is basically a dipole radiator, and a dipole radiates no power in the direction of its dipole axis. Therefore, if you want to transmit in any arbitrary direction in the horizontal plane, you must orient the antenna vertically.
I believe there are certain applications where it is preferrable to orient the antenna horizontally, even at the cost of omnidirectionality, and I think one of the reasons for doing this is that a horizontally-polarized radio wave will reflect off the ionosphere better than a vertically polarized wave--I was mixing the two cases up.
It would have been much better if Reed had used the term 'interact' rather than 'interfere'.
If I make the subsitution s/interfere/interact/, then Reed's statements become correct, because then he means that photons obey Bose-Einstein statistics instead of Fermi-Dirac statistics, which is true. However, he should use the word "interact", because "interference" refers to a different physical phenomenon in optics and electromagnetic waves, which in turn is different from the communications-theoretic interpretation of interference, or "crosstalk", which I think is what Reed really wants to talk about. Of course, if that's what he meant, it would have been much less ambiguous if he just said "crosstalk", but I suppose that "crosstalk" counts as technical jargon that would be too confusing to use in popular press. However, he uses the word "interfere" in his physical examples, and in way that is incorrect, or at least subject to misinterpretation, in that context.
You are being no less sloppy with your statement that diffraction effects are "due to photons interfering with each other". You can do the same experiment with a single photon, and still get difraction. You probably already knew this, but I'm just making the point that its hard to explain quantum mechanics without being sloppy!
I knew I was playing it very fast and loose with that statement, hence the phrase "loosely speaking".;-) I was really considering the statement from a classical electrodynamic viewpoint instead of a quantum viewpoint just because it is a lot more intuitive and descriptive of the macroscopic phenomena that Reed was trying to explain (very badly, I might add) with quantum mechanics. I admit that I was very sloppy to use quantum-mechanical terminology, but AFAIK I am not incorrect to say that photons interfere, because you can observe the interference by detecting the photons.
I think I agree that diffraction still occurs when you run many trials of single-photon experiments, but I have no intuition for why that occurs. (I guess, by considering particle diffraction, that the diffraction phenomenon is implicitly described by the wavefunction of a particle, but it's hardly intuitive:-p) The multi-photon or classical electrodynamic case is much more intuitive (I can mentally picture the photons or EM waves interfering), and gives essentially the same result (IIRC, it's the statistical average of the single-particle case).
I'm just making the point that its hard to explain quantum mechanics without being sloppy!
Now that's a statement with which I cannot disagree!:-)
Actually, the phenomenon of stimulated emission, which gives rise to lasers, is a consequence of light-matter interaction, not light-light interaction. The incident photon stimulates an excited atom into emitting a photon, so it is the atom that interacts with the incident photon, not the emitted photon.
If you switch to a different type of sensor or encoding scheme - for example, utilize frequency hopping (aka spread spectrum) then you could easily broadcast the two signals over the same range of frequencies (colors).
But if you're broadcasting two signals on exactly the same frequency, you can only distinguish between the two signals if you use some multiplexing scheme like time-division or code-division, in which case each signal can only use the bandwidth that the other signal does not. If each signal is broadcast under the assumption that it is the only one at that frequency, they will interfere, and it will be impossible to recover either signal exactly. (One possible exception is polarization multiplexing, except that all ground-to-ground radio transmitters are polarized in the same direction in order to reflect off the ionosphere, so this is not an option in radio. Furthermore, Reed's theories do not allow for polarization multiplexing because, by denying the existence of interference, he denies the vectoral nature of EM waves and therefore denies the existence of polarization)
Overall the article has a lot of merit in providing a different and, in my mind, compelling metaphor of bandwidth as colors as opposed to the classical bandwidth as land. As to his ideas of limitless bandwidth being true, the idea is beyond my ability to see how this is feasible, but that does not detract from his idea that we could actually be communicating a LOT more over the current spectrum than we are today.
The only way to get more bang for the buck for a fixed amount of bandwidth is to come up with more efficient coding schemes. Nothing which Reed presents allows him to circumvent the Shannon limit, which is the upper bound on how much information can be transmitted over a communication channel with a fixed amount of bandwidth.
I can't even begin to discuss all the things that are wrong with Reed's theories as described in the article, but I'll address some howlers.
"Photons, whether they are light photons, radio photons, or gamma-ray photons, simply do not interfere with one another," he explains. "They pass through one another."
There are some very commonplace phenomena, such as the colors on a soap bubble or oil slick, which are the manifestation of interference of light. There are more fundamental experiments that can be done with lasers or radio waves to demonstrate interference.
Reed uses the example of a pinhole camera, or camera obscura: If a room is sealed against light except for one pinhole, an image of the outside will be projected against the opposite wall. "If photons interfered with one another as they squeezed through that tiny hole, we wouldn't get a clear image on that back wall," Reed says.
Actually, if you do the experiment, there is a specific pinhole size at which you get the best image. Make the pinhole any smaller and the image starts getting blurrier because of diffraction effects which, loosely speaking, are due to the photons interfering with each other.
If you whine that it's completely counterintuitive that a wave could squeeze through a pinhole and "reorganize" itself on the other side, Reed nods happily and then piles on: "If photons can pass through one another, then they aren't actually occupying space at all, since the definition of 'occupying' is 'displacing.' So, yes, it's counterintuitive. It's quantum mechanics."
From his misunderstandings of the nature of light so far, it's impossible for him to have any real understanding of the quantum nature of light. He wouldn't know Schrodinger's equation if it walked up to him and smacked him upside the head, seeing as how Schrodinger's equation is a wave equation and predicts all sorts of interference phenomena.
The most fundamental problem is that he admits the notion of frequency, which is intrinsicly tied to the wave nature of light and radio. If he admits the wave nature of light, then he also has to admit interference of light as a natural phenomenon and not as a detection artifact, at which point all of his theories crumble.
Yeah, that was the one. I think there was also a command-line version called toc, or maybe that's one of the two protocols that AOL uses for instant messaging, but I'm feeling too lazy today to look up the details.:-p
Most companies have set marketting budgets how they use that money is a different question. You presume to have better predictionary abilities than their marketting department, and are probably right, but never the less that is marketting's decission and the money doesn't belong to development, hence if marketting wants to spend it for dancing girls in bikinis they can do it.
I agree that balancing good technology with good marketing and business acumen is the key to financial success, but overallocation of resources to marketing and gratuitous spending of marketing money will ultimately undermine a technology company's financial health. Again, I fail to understand why a semiconductor manufacturer like On that does not sell product to the general public feels compelled to spend money advertising to the general public. Likewise, I fear for the economy if CEOs or IT departments decide to use Oracle databases based on an Super Bowl ad.
Microsoft is hiring because they are making huge profits. They are hiring in line with their growth. If they were suffering significant losses like semiconductor companies I have NO DOUBT they would revise their hiring plans. They have some borg'ish intelligence thing going on there because of the braintrust they've created.
Probably true, but having a vibrant internship program and a continual stream of fresh blood and new ideas seems like it would help keep the rainy days away.
20$ internships is pretty darn high. I hope this was for a graduate student or regardless of your abilities they are likely overpaying you as an intern. Or perhaps the cost of living is higher there.
Actually, for a junior or senior engineering undegraduate, $20/hour is fairly typical. By that stage, an engineering undergraduate has at least been exposed to most of the basic technical skills used daily by full-time engineers. I would argue that an engineering student who takes an internship of less than $15/hour is being dramatically underpaid.
Lose the boycot stance. Companies are in business for the shareholders, to grow their investments as their appointed representatives see fit. Next time write your complaint to the board and go out and make your own stake in life.
I will concede that maybe my boycott stance is immature, but I am fully within my rights to boycott whatever company I want for whatever reasons I want. I've been boycotting Amazon.com ever since I heard about the one-click patent and will continue to do so until they adopt a more reasonable position on intellectual property. To be honest, I will probably never have to interact with On Semiconductor again, so boycotting them will probably just end up being political posturing. I will concede that both companies are just behaving the way most publicly-traded companies do, but that doesn't mean I have to like them or that I have to do business with them.
There also used to be a neat AOL Instant Messenger client (actually linked to by AOL) written in Tcl/Tk which was more featureful than AOL's Windows client. Unfortunately, the name escapes me at the moment...
Not every cost-cutting decision is a good one. To have had me as an intern would have cost them about $10,000 (at most) for the summer, and raised the possibility that, when the industry recovered, I would have wanted to work for them after I graduated. That's probably less than a day's worth of the CEO's salary, or less than it cost from them to display their logo during one televised Arizona Diamondbacks game. (Why companies like On or Oracle advertise on TV is an even greater mystery to me...do CEOs actually make major business decisions based on a television ad? If so, I really fear for our economic future...) My point is that executive perks and gratuitious advertising should probably go before you start laying off engineers and engineering interns, who may be difficult to woo back when the industry recovers. However, it's my understanding that this would be counter to Motorola corporate culture, which I guess was one of the things which trickled down to On.
Admittedly, I don't know exactly what the financial situation was at On. But when I saw that they were running ads during Diamondback games in the months after my internship program was cut, I have to wonder about their financial priorities. Even if this was only because they were contractually obligated to continue running these ads, they probably shouldn't have signed that contract in the first place if their financial situation was as tenuous as it proved to be.
The worst part of the experience for me was that On could not figure out in advance that they could not afford to hire me as an intern. I would not have been nearly so bitter if they had rejected me outright. Instead, they gave me an offer, and I went through all the paperwork to accept that offer, and one week before my internship was supposed to start, they told me that they had cut the program. Some advance warning that this might happen would have been nice, so that I would have a chance to apply for internships elsewhere, but at that point, it was too late. Overall, it may have been a good reality check for me, but the net effect is that I'm still bitter at On.:-p
Another slightly better counterexample would be my friend who worked at Nortel Networks that same summer. Nortel was also in bad financial straits that summer (probably still are), but instead of cutting their internship program, they restricted their layoffs to specific expendable positions in specific programs. Thus my friend still had his internship that summer, and might very well work for them after he receives his graduate degree. Furthermore, he can come back to school and share his positive internship experience with his friends, and the net result is that quite a few budding engineers know that Nortel is a good place to work. That one internship was probably a better investment for Nortel than any television ad has been for On.
They don't owe me anything. My point is cutting the entire internship program will probably prove to be bad business decision for them in the long-run. At least in engineering, internship programs are a powerful recruiting tool, and companies tend to offer internships to students whom they would like to hire once that student graduates. When On offered a position and suddenly reneged on that offer, that left a bad taste in my mouth, so even if they wanted to hire me in the future, I probably wouldn't accept their offer. Furthermore, when my friends ask me about employment at On, the only experience I have to share is how little they care about their employees.
Contrast this to what Microsoft is doing. Even though the industry is in a slump, they are continuing to pursue the best and brightest students and lure them through their internship program. Those students come back from their internship and tell their friends about how cool the experience was. Even though I'm not interested in doing business with Microsoft either (for different reasons), their internship program is a good investment for them and their internship practices are a model for other less-visionary companies to emulate.
The general rule is that techie internships (computer science, engineering, etc.) are paid, and fuzzy internships (business, politics, journalism, arts) are unpaid. There are some exceptions to the latter where fuzzies get paid, but there are very rarely to the former where techies are not paid. The reason is simple economics: there is more demand for and less supply of techies, so techies can always blow off unpaid internships and go somewhere else where they get paid, whereas that's not always true for fuzzies.
OTOH, that doesn't mean that short-sighted tech companies won't slash their internship programs or otherwise leave techies out in the cold. I was supposed to have an engineering internship at On Semiconductor (a Motorola spin-off) paying about $20/hour during the summer of 2001. Unfortunately, the semiconductor industry collapsed that spring, and On cut their entire internship program in addition to cutting lots of permanent positions. Guess who won't ever work for On, or buy any of their parts unless I absolutely have to...:-p
Slashdot Mirror
Since the corporate site is still down, the best place to read about this is probably the website of the Imaging Systems Laboratory at the University of Colorado at Boulder, which I think is where all this technology was originally developed. Someone else posted that link elsewhere in the comments, but I will post it again here, properly hyperlinked for convenient Slashdotting.
I'm not sure depth of field is relevant for afocal systems operating at infinite conjugates. And as a practical matter, at those distances the clarity of an image is primarily limited by diffraction for a telescope that's reasonable well-corrected for aberration (which the original Hubble was not).
As a practical point, spherical aberration can be corrected pretty well by defocusing the system. They considered doing this with Hubble, but when they calculated the amount of spherical aberration in the mirror, they discovered that they didn't have enough translation range for their sensor to defocus the system enough to make up for it.
Incidentally, there's no way that you can stop down an f/10 system to f/6.4 . f/6.4 corresponds to a larger aperture for the same focal length, so I'm guessing that you're actually stopping the telescope down to f/12.8 .
I dare you to move your cursor with your 108-button mouse... ;-)
I'd rather have a device tell me in words, or maybe in pictures, how my money, family, friends, and work are doing--it's simpler and less ambiguous.
This device is really meant to be a toy, and as a commercial product it is marketed as such. And even as such, I think it would be difficult to distinguish between this device and a glass sphere with some embedded LEDs being driven by a pseudorandom number generator (which would be a lot simpler and cheaper to build).
I think laser action is strictly due to the light-matter interaction, but the fact that the incident photon and the emitted photon are coherent with each other probably is a consequence of the Bose-Einstein statistics governing photon behavior. Nonetheless, I'm impressed by your understanding of physics as an interested layman and by the fact that you have some understanding of bosons and fermions--all that stuff confused me until quite recently. ;-)
If you modulate a non-time-varying signal onto your sine wave, you're not adding any information to it, so only the fundamental frequency of the sine wave is present. When you modulate a time-varying waveform onto your sine wave, you add additional information to it, so additional frequencies are required to support that information. For example, if you put a slow sine wave on a fast sine wave, say sin(t/10) on sin(t), then the sin(t) wave is now carrying the information about the sin(t/10) wave. If you calculate the spectrum of the wave (by Fourier transformation, for example), you will find that the sum and difference frequencies of the two waves are present in addition to the fundamental frequency of the fast wave. I think it is probably also possible to manipulate the trigonometic functions to show that [sin(t/10)][(sin(t)] has the sum and difference frequencies in it, but I'm too tired to do it so I will leave it as an exercise for the reader. :-p
The colors from a soap bubble are due to light interfering with light. Light is partially reflected from each surface of the soap film, and the reflected beams do interfere with each other and result in the colors that you see. That's about all the detail I want to go into describing it, but if I still don't believe me, it's probably described better and in more detail in either Hecht Optics, Born & Wolf Principles of Optics, or Lipson, Lipson & Tannhauser Optical Physics (in any of those books, look for the section on "multiple-beam interference").
It is true that when two beams of light cross paths in vacuum, if you were to observe them after they cross, you could not tell that they crossed. However, in the region in which they cross, they can interfere with each other. Again, any of the references I mentioned above will probably explain this much better than I can.
Even worse, once you physically manifest this signal by modulating it onto an electromagnetic carrier wave (like radio does), this communications spectrum is now superimposed on the physical spectrum of the electromagnetic wave. Now the signal is subject to the physical phenomenon of interference, which can further corrupt the signal if you don't allocate communications channels in the electromagnetic spectrum properly. And I think it's the allocation of commmunications channels which is what the article is trying to be about. However, that doesn't change the fact that Reed is dead wrong in the way he describes or interprets many of his physical examples, probably because he has a lot of background in computer science but not as much in physics.
Furthermore, Reed is wrong if he thinks that ultrawideband (UWB) or frequency hopping will increase the Shannon limit within a given range of the electromagnetic spectrum. Ultrawideband will interfere with other electromagnetic signals. It requires a lot of electromagnetic bandwidth, hence the name.
Frequency hopping can improve the efficiency of the spectrum allocation by moving communications channels to unused regions of the spectrum, but it does not create communication capacity where there is none. Furthermore, those channels have to be allocated in advance to prevent them from with other signals.
Reed is probably right that the electromagnetic spectrum is inefficiently utilized. But the many of the physical examples or explanations of physical phenomena that he presents are dead wrong, which was the point that I was trying to make in my original post.
Ok, so I drastically overgeneralized, and even worse, I'm wrong, and I just realized why. The reason why pretty much all ground-to-ground transmitters have their antennae oriented vertically is because the antenna is basically a dipole radiator, and a dipole radiates no power in the direction of its dipole axis. Therefore, if you want to transmit in any arbitrary direction in the horizontal plane, you must orient the antenna vertically.
I believe there are certain applications where it is preferrable to orient the antenna horizontally, even at the cost of omnidirectionality, and I think one of the reasons for doing this is that a horizontally-polarized radio wave will reflect off the ionosphere better than a vertically polarized wave--I was mixing the two cases up.
I think I agree that diffraction still occurs when you run many trials of single-photon experiments, but I have no intuition for why that occurs. (I guess, by considering particle diffraction, that the diffraction phenomenon is implicitly described by the wavefunction of a particle, but it's hardly intuitive
Now that's a statement with which I cannot disagree!
Actually, the phenomenon of stimulated emission, which gives rise to lasers, is a consequence of light-matter interaction, not light-light interaction. The incident photon stimulates an excited atom into emitting a photon, so it is the atom that interacts with the incident photon, not the emitted photon.
The only way to get more bang for the buck for a fixed amount of bandwidth is to come up with more efficient coding schemes. Nothing which Reed presents allows him to circumvent the Shannon limit, which is the upper bound on how much information can be transmitted over a communication channel with a fixed amount of bandwidth.
There are some very commonplace phenomena, such as the colors on a soap bubble or oil slick, which are the manifestation of interference of light. There are more fundamental experiments that can be done with lasers or radio waves to demonstrate interference.
Actually, if you do the experiment, there is a specific pinhole size at which you get the best image. Make the pinhole any smaller and the image starts getting blurrier because of diffraction effects which, loosely speaking, are due to the photons interfering with each other.
From his misunderstandings of the nature of light so far, it's impossible for him to have any real understanding of the quantum nature of light. He wouldn't know Schrodinger's equation if it walked up to him and smacked him upside the head, seeing as how Schrodinger's equation is a wave equation and predicts all sorts of interference phenomena.
The most fundamental problem is that he admits the notion of frequency, which is intrinsicly tied to the wave nature of light and radio. If he admits the wave nature of light, then he also has to admit interference of light as a natural phenomenon and not as a detection artifact, at which point all of his theories crumble.
Yeah, but how does it compare with areal underwater basket weaving program, one that actually has a scheduled class and location? (although at this point in the semester, you'd have to wait until they offer it again next semester...)
:-)
Go Cats! Bear Down!
Yeah, that was the one. I think there was also a command-line version called toc, or maybe that's one of the two protocols that AOL uses for instant messaging, but I'm feeling too lazy today to look up the details. :-p
Probably true, but having a vibrant internship program and a continual stream of fresh blood and new ideas seems like it would help keep the rainy days away.
Actually, for a junior or senior engineering undegraduate, $20/hour is fairly typical. By that stage, an engineering undergraduate has at least been exposed to most of the basic technical skills used daily by full-time engineers. I would argue that an engineering student who takes an internship of less than $15/hour is being dramatically underpaid.
I will concede that maybe my boycott stance is immature, but I am fully within my rights to boycott whatever company I want for whatever reasons I want. I've been boycotting Amazon.com ever since I heard about the one-click patent and will continue to do so until they adopt a more reasonable position on intellectual property. To be honest, I will probably never have to interact with On Semiconductor again, so boycotting them will probably just end up being political posturing. I will concede that both companies are just behaving the way most publicly-traded companies do, but that doesn't mean I have to like them or that I have to do business with them.
There also used to be a neat AOL Instant Messenger client (actually linked to by AOL) written in Tcl/Tk which was more featureful than AOL's Windows client. Unfortunately, the name escapes me at the moment...
Not every cost-cutting decision is a good one. To have had me as an intern would have cost them about $10,000 (at most) for the summer, and raised the possibility that, when the industry recovered, I would have wanted to work for them after I graduated. That's probably less than a day's worth of the CEO's salary, or less than it cost from them to display their logo during one televised Arizona Diamondbacks game. (Why companies like On or Oracle advertise on TV is an even greater mystery to me...do CEOs actually make major business decisions based on a television ad? If so, I really fear for our economic future...) My point is that executive perks and gratuitious advertising should probably go before you start laying off engineers and engineering interns, who may be difficult to woo back when the industry recovers. However, it's my understanding that this would be counter to Motorola corporate culture, which I guess was one of the things which trickled down to On.
:-p
Admittedly, I don't know exactly what the financial situation was at On. But when I saw that they were running ads during Diamondback games in the months after my internship program was cut, I have to wonder about their financial priorities. Even if this was only because they were contractually obligated to continue running these ads, they probably shouldn't have signed that contract in the first place if their financial situation was as tenuous as it proved to be.
The worst part of the experience for me was that On could not figure out in advance that they could not afford to hire me as an intern. I would not have been nearly so bitter if they had rejected me outright. Instead, they gave me an offer, and I went through all the paperwork to accept that offer, and one week before my internship was supposed to start, they told me that they had cut the program. Some advance warning that this might happen would have been nice, so that I would have a chance to apply for internships elsewhere, but at that point, it was too late. Overall, it may have been a good reality check for me, but the net effect is that I'm still bitter at On.
Another slightly better counterexample would be my friend who worked at Nortel Networks that same summer. Nortel was also in bad financial straits that summer (probably still are), but instead of cutting their internship program, they restricted their layoffs to specific expendable positions in specific programs. Thus my friend still had his internship that summer, and might very well work for them after he receives his graduate degree. Furthermore, he can come back to school and share his positive internship experience with his friends, and the net result is that quite a few budding engineers know that Nortel is a good place to work. That one internship was probably a better investment for Nortel than any television ad has been for On.
Right, but if you're trying to get work done, it's just stupid. Even the best-written software can't compensate for excessive user stupidity. :-p
Well, techies still tend to be more useful than politicians, lawyers or MBAs... :-p
They don't owe me anything. My point is cutting the entire internship program will probably prove to be bad business decision for them in the long-run. At least in engineering, internship programs are a powerful recruiting tool, and companies tend to offer internships to students whom they would like to hire once that student graduates. When On offered a position and suddenly reneged on that offer, that left a bad taste in my mouth, so even if they wanted to hire me in the future, I probably wouldn't accept their offer. Furthermore, when my friends ask me about employment at On, the only experience I have to share is how little they care about their employees.
Contrast this to what Microsoft is doing. Even though the industry is in a slump, they are continuing to pursue the best and brightest students and lure them through their internship program. Those students come back from their internship and tell their friends about how cool the experience was. Even though I'm not interested in doing business with Microsoft either (for different reasons), their internship program is a good investment for them and their internship practices are a model for other less-visionary companies to emulate.
The general rule is that techie internships (computer science, engineering, etc.) are paid, and fuzzy internships (business, politics, journalism, arts) are unpaid. There are some exceptions to the latter where fuzzies get paid, but there are very rarely to the former where techies are not paid. The reason is simple economics: there is more demand for and less supply of techies, so techies can always blow off unpaid internships and go somewhere else where they get paid, whereas that's not always true for fuzzies.
:-p
OTOH, that doesn't mean that short-sighted tech companies won't slash their internship programs or otherwise leave techies out in the cold. I was supposed to have an engineering internship at On Semiconductor (a Motorola spin-off) paying about $20/hour during the summer of 2001. Unfortunately, the semiconductor industry collapsed that spring, and On cut their entire internship program in addition to cutting lots of permanent positions. Guess who won't ever work for On, or buy any of their parts unless I absolutely have to...