One thing I find impresive about the evolution of storage: 20TB was the total hard drive space manufactured in 1995, just 14 years ago.
I believe you meant 20 petabytes. You could already get gigabyte drives back then, and it's hard to imagine that fewer than 20,000 of them were manufactured during the course of the year.
Well, sort of. The tesla is a measure of field intensity, and if you've got a 1.5T magnet, every cubic millimeter inside the bore experiences that same field intensity, and the same "energy density". (It's not like a small-bore 1.5T system has a "more concentrated" field than a wide-bore 1.5T system.) But it's a static field, and (to a first but very accurate approximation) static fields don't do much to living systems.
(As long as you hold still, that is. If you're in a very high-field magnet, you need to move carefully -- moving through a static field is equivalent to sitting still in a dynamic field, and moving your head too quickly in a 7T or 9T field can do some pretty weird things.)
The gradients in an MRI scanner do generate dynamic fields, and in fact there are software restrictions to keep you from changing those fields quickly enough to cause neurological problems. In normal operation, though, they don't produce any perceptible effects in the patient.
TMS imposes much higher deltas over a small area -- it's a fairly strong field that changes very quickly.
Good catch. "We" (well, our actual researchers, not me) built a small-animal CT system that captures 2D images, rotating the animal instead of the gantry between views. That's very different from a clinical CT system.
However, those clinical scanners are getting wider. You can now get scanners that acquire 64 slices at a time -- instead of an N-pixel linear sensor, they use an N x 64-pixel sensor, and scan in a helical pattern. It's all about speed in the clinical arena.
That's exactly what you have to do, and assume (usually safely) that every heart cycle is pretty much identical. We call it "cardiac gating". You can either do it "prospectively", which means triggering acquisition at a particular point in the cardiac cycle, or "retrospectively", where you acquire freely and then go back and pick out the acquisitions that happened at the cardiac phase you want.
It's still tricky, though, particularly for MRI, where you're generating a lot of electrical noise -- electrical monitoring (conventional ECG) just won't work. We use optical sensors. Of course, we're imaging mice with 600bpm pulse rates, which makes it trickier still.
For CT, I think each "exposure" we do is typically 10ms or less, which lets us get multiple phases even in a mouse. For MR, well, remember when I said the physics is over my head? Yeah, that. But I know we can routinely split the mouse cardiac cycle into 8 phases, and sometimes more. You're imaging for a pretty long time to do that, though -- collect views through many cardiac cycles at 0ms offset, then at 10ms offset, then 20, then...
My problem with the assessment however, becomes even more glaringly obvious when you look at the micro SD proposal in the grandparent. If you are going to have a single SD card reader and plug these cards in as needed, the weight estimate is ok. If however all 1 PB of data must be immediately available to your software, the weight gos up dramatically.
If I were really going to try something like this, I'd probably come up with a way to put lots of bare chips on a single substrate, eliminating even the meager additional weight of the MicroSD packaging. (I'm guessing that the chips in a 16GB MicroSD card are a significant part of the total mass.) At the very least, I'd come up with an efficient gang-socketing scheme.
Mozilla's Benjamin Smedberg says they're currently "[sprinting] as fast as possible to get basic code working, running simple testcase plugins and content tabs in a separate process," after which they'll fix everything that breaks in the process.
This sentence was a little hard to process.
(I note that the "process" of Slashdot incremental improvement has now reached a point where clicking anywhere in the text-entry box causes the box to LOSE focus. If you don't want us using Safari, there are more efficient ways to get us to move.)
A fundamental difference between MRI and CT is that computing the MRI image involves (at least in some cases) a 2-D FFT. While signal to noise ratio is an issue, the processing is not an ill-posed problem.
Hmm. My group definitely calls the process of moving from k-space to image space "reconstruction". There are good reasons for doing more than a simple 2D FFT (most of which, I'll admit, are over my head).
I've been lucky enough to work with MR and CT imaging researchers for a while now. One of the benefits of this job is that I've gotten to learn a lot about how these images are acquired and reconstructed. It's not quite as bad as making sausage, but it's a lot more involved than a "snapshot".
For CT, we acquire a bunch of 2D images through you from different angles, then do a lot of number crunching to generate a 3D volume. The problem is that you don't hold still while we're doing it. You can try; you can even hold your breath, but you can't "hold your heart". As your organs move between views, we get motion artifacts -- shape distortion, bright or dark areas, even "things" that aren't really there.
For MR, it's even worse. I can barely tread water in the physics of it, but we're effectively capturing a line at a time in 3D space. (We're actually acquiring data in "k-space", then running it through a Fourier transform to make it spatial.) Not only is it subject to motion artifacts, it's also subject to susceptibility artifacts (distortions because of the magnetic properties of certain materials), flow artifacts (blood moves through vessels between the time that we apply a magnetic pulse and the time that we read back emitted signals), and lots of other things.
fMRI is just adding yet another layer of aggregation and interpretation on top of all this. Sure, it's a "visualization of data generated by repeated scans", but so is every CT or MRI image.
3D imaging, especially MRI, is hideously complicated and indirect. It's almost inconceivable that it could yield results with any physical significance.
...and yet, it does. It's become so routine, so reliable, so well-understood and well-controlled, that doctors and researchers know they can rely on it as a matter of course. They still have to be aware of the errors and distortions that can arise, but that's true of every imaging or monitoring system, all the way down to the stethoscope and the fever thermometer.
Luminous efficiency is the ratio of light emitted to power consumed. Luminous efficacy also incorporates the eye's response to the emitted spectrum.
Luminous efficacy isn't the appropriate measure here, unless you're completely unconcerned about color. If you want "white" light, you've got to emit red and blue wavelengths, which give lousy luminous efficacy, along with green, which gives great efficacy. The eye isn't nearly as sensitive to red or blue as it is to green light, but without them, you can't get to white.
The maximum possible luminous efficacy for a "white" light, something approximating sunlight, is around 15 percent. That assumes 100% wall-plug efficiency -- every watt of electric energy that comes in gets converted to a watt of visible light. So, if you've got 11% luminous efficacy in a white light, that translates to 75% efficiency.
If you want to get the maximum possible luminous efficacy -- the "brightest" light for a given amount of power -- get a fluorescent bulb with a pure-green or blue-green phosphor. Then you can get 50-75% true luminous efficacy, but your dinner won't look very appetizing, and neither will your date.
Heh. At Virginia Tech in the early '80's, they used SSN's as student ID's, too. Test results and grades would be posted on the doors of classrooms, identified by SSN with names omitted, for "privacy". Of course, the lists were still sorted alphabetically by name.
Biking for an hour at 25MPH costs 1181 kcal, according to this calendar (others suggest it costs even more calories), which translates to 1373 watt-hours. (Your body isn't that efficient at converting fuel to energy.) So let's assume your 250W figure is correct, and your body is about 18% efficient in converting calories to power.
Biking for an hour at 65MPH (if you could) would burn 18669 calories -- remember, wind resistance goes up as the cube of speed. That works out to -- let's see -- 21712 watt-hours. Assuming the same 18% efficiency (and some active cooling for your legs, not to mention the rest of your body), you'd be putting out 3.95KW to sustain that speed.
When you look at it that way, spending five times the energy to move a car, with probably five or ten times the frontal surface area and more than ten times the passenger and cargo capacity, starts to sound like not such a bad deal.
The picture we get from such a technique is no picture at all. To create a picture, we would need a dense array of ears of great sensitivity not unlike a retina.
As I understand it, the picture we get from such a technique is exactly a picture -- it's formulated in the same areas of our brain, and subject to the same mental operations. As others have pointed out, we get a lot more information from our ears than we would get from two single-pixel image sensors. (Think about how you can tell, from a pair of receptors at opposite sides of your head, whether a sound is coming from ahead or behind, above or below.)
I don't know how blackbody radiation is generated, if not from electrons dropping into lower energy states, but isn't it possible to get blackbody radiation from materials completely lacking electrons? Even for normal materials hot enough to glow, how do you get the essentially-continuous spectrum of blackbody radiation?
I was telling people twenty or more years ago that I wanted a handheld device that I could take on the trail, hold up, look through like a little window, and see an overlay showing trail distances, climbs/descents, geographic feature names, and so forth. In 1990, you could do it as a slow, clumsy demo on a "handheld device" tethered to a room full of equipment. Now, with GPS, built-in cameras and good inertial tracking, we're really just a good eye-tracking layer away from a true implementation.
"Prescience" entails a great deal of paying attention.
I tried to buy Vinge lunch at CHI '99, but he declined, saying that he had to meet with the folks from the MIT wearables group. A Deepness in the Sky was freshly out, but he was already soaking up info to pour into Rainbows End (no apostrophe). I wonder who he's hanging out with now.
Alas, it doesn't look like his retirement from teaching is having much effect on his cicada-like rate of new releases...
The maximum resolution of a telescope is proportional to the diameter of its objective (main lens or mirror), and inversely proportional to the wavelength at which it's observing. This is observing at wavelengths 100 times longer than the visible and near-IR instruments like Hubble observe, so it's at a 100x disadvantage coming out of the starting gate.
We've never had images anywhere near this good in this part of the spectrum. I'm very sorry that they offend you.
But you're right. We definitely shouldn't field any instruments until we're ready to deliver, power and support an array at Neptune's distance. After all, it's not like we learn anything from intermediate steps. Just look at all the money we wasted, wasted, on Hubble. Or Palomar. Or Galileo's first telescope. (After all, who needed to know that Jupiter had moons, or Saturn had rings?)
..as I recall, the campus newspaper charged by the line for classified ads
The good news for his bank account was that all of his projects were written in perl!
The bad news was that the first Perl interpreter was still five years or so in the future, so all those lines of $_\{} and whatnot were correctly interpreted as line noise.
In your calculations you forgot the small factoid that it may be another thousand years before it goes supernova. It has brightened considerably in the past only to dim back down. It was Fox news (fair and balanced) that mentions it going supernova, not the paper presented at the meeting that merely states a 15% shrinkage and nothing else.
Well, yes. It's been known as a variable for a very long time, and while I don't know how long its diameter has been monitored, it seems likely that its changes in brightness would be accompanied by changes in size. A 15% change in diameter isn't quite so impressive against a history of twofold changes in brightness.
In fact, here's an article claiming that its diameter varies from 550 to 920 times that of the Sun (alas, the link the article cites is dead). They might mean, though, that measurements using different techniques yield results in this range, not that the actual size varies within that range. From the Berkeley press release:
"Since the 1921 measurement, its size has been re-measured by many different interferometer systems over a range of wavelengths where the diameter measured varies by about 30 percent," Wishnow said. "At a given wavelength, however, the star has not varied in size much beyond the measurement uncertainties."
So, looking for stars in a light-polluted sky is easier with a telescope, because it makes the stars appear brighter relative to their background.
Is this a joke? Light pollution turns the sky an awful pink-ish gray from what would otherwise be black, zodiacal light notwithstanding. That being the case, how exactly would it be easier to see a point source of light against a lighter background versus a darker background?
Looking for stars in a light-polluted sky is easier with a telescope than it is without a telescope, because the telescope increases the apparent brightness of the stars relative to the brightness of their background. I'm sorry that I wasn't repetitive enough to head off your rant. Looking for stars is easier in a non-light-polluted sky, of course, whether you're using a telescope or not.
With nebulae, comets, or other extended objects, especially where the object's apparent brightness doesn't exceed the sky's apparent brightness, the telescope doesn't help much at all.
Ludicrous! This is clearly being spoken by a person who has never looked through a telescope in their entire life.
Heh. There's quite a bit more to telescopes than just "looking through" one. But even if that's all you're doing, you're overlooking a few very important points.
The apparently brightness of *any* astronomical object, be it a galaxy such as M31, or a globular cluster like M13, is entirely a function of aperture when magnification is held constant. The views of the Orion Nebula through a 4 inch reflector at 100x will be eviscerated by the same 100x view through a 20 inch reflector. (And yes, I have looked through instruments of both size, though I own a 12 inch reflector personally.)
Congratulations. You're obviously quite proud. Now, let's compare notes for these scopes against a polluted sky.
Under a typically nasty suburban sky, light pollution might be something like 18 magnitudes per square arc-second. In other words, each square arc-second of sky sheds as much light on your eye as an 18th-magnitude star.
The four-inch scope will collect something like 200 times as much light as a fully-dilated eye (100mm objective vs. 7mm pupil). At 100x, it will then spread that light across an angular area 100^2 times as large. An extended object -- a nebula, a distant galaxy, the sky itself -- will appear "100 times as large", but 50 times (just under four magnitudes) dimmer than what the naked eye sees. But stars will still be pinpoints (assuming good optics), and they will appear 200 times (almost six magnitudes) brighter. Thus, the telescope makes it easier to see dim stars against a light-polluted sky.
With the 20-inch scope, you're collecting 25 times as much light as the 4-inch, 5000 times as much as the naked eye. Spread that over 10,000 times the area, and extended objects still appear slightly (less than one magnitude) dimmer than they do to the unaided eye, but stars are 5000 times (over 9 magnitudes) brighter.
No matter what size telescope you use, 100x magnification "stretches the contrast" between extended and pointlike objects by 10,000 times, or ten magnitudes. (Within limits -- for a scope smaller than two inches you'd be exceeding the resolution limit of the optics, and for a scope larger than about 24", the exit pupil would be too big to get all the light into your eye.)
Now, suppose you're looking for a faint nebula, comet, or other extended object. No matter how large your telescope, no matter the magnification, it's not going to change the contrast between that object and the background brightness of the sky. If the sky itself has a higher surface brightness than the object you're looking for, it's going to be really hard to spot that object, unless you can find filters that knock back the skyglow more than they darken your target.
Slashdot Mirror
One thing I find impresive about the evolution of storage: 20TB was the total hard drive space manufactured in 1995, just 14 years ago.
I believe you meant 20 petabytes. You could already get gigabyte drives back then, and it's hard to imagine that fewer than 20,000 of them were manufactured during the course of the year.
But, yes, exponential growth is impressive.
...it must be pretty abstract, since an "automated teller machine machine" is apparently running in emulation anyhow.
Well, sort of. The tesla is a measure of field intensity, and if you've got a 1.5T magnet, every cubic millimeter inside the bore experiences that same field intensity, and the same "energy density". (It's not like a small-bore 1.5T system has a "more concentrated" field than a wide-bore 1.5T system.) But it's a static field, and (to a first but very accurate approximation) static fields don't do much to living systems.
(As long as you hold still, that is. If you're in a very high-field magnet, you need to move carefully -- moving through a static field is equivalent to sitting still in a dynamic field, and moving your head too quickly in a 7T or 9T field can do some pretty weird things.)
The gradients in an MRI scanner do generate dynamic fields, and in fact there are software restrictions to keep you from changing those fields quickly enough to cause neurological problems. In normal operation, though, they don't produce any perceptible effects in the patient.
TMS imposes much higher deltas over a small area -- it's a fairly strong field that changes very quickly.
Good catch. "We" (well, our actual researchers, not me) built a small-animal CT system that captures 2D images, rotating the animal instead of the gantry between views. That's very different from a clinical CT system.
However, those clinical scanners are getting wider. You can now get scanners that acquire 64 slices at a time -- instead of an N-pixel linear sensor, they use an N x 64-pixel sensor, and scan in a helical pattern. It's all about speed in the clinical arena.
That's exactly what you have to do, and assume (usually safely) that every heart cycle is pretty much identical. We call it "cardiac gating". You can either do it "prospectively", which means triggering acquisition at a particular point in the cardiac cycle, or "retrospectively", where you acquire freely and then go back and pick out the acquisitions that happened at the cardiac phase you want.
It's still tricky, though, particularly for MRI, where you're generating a lot of electrical noise -- electrical monitoring (conventional ECG) just won't work. We use optical sensors. Of course, we're imaging mice with 600bpm pulse rates, which makes it trickier still.
For CT, I think each "exposure" we do is typically 10ms or less, which lets us get multiple phases even in a mouse. For MR, well, remember when I said the physics is over my head? Yeah, that. But I know we can routinely split the mouse cardiac cycle into 8 phases, and sometimes more. You're imaging for a pretty long time to do that, though -- collect views through many cardiac cycles at 0ms offset, then at 10ms offset, then 20, then...
My problem with the assessment however, becomes even more glaringly obvious when you look at the micro SD proposal in the grandparent. If you are going to have a single SD card reader and plug these cards in as needed, the weight estimate is ok. If however all 1 PB of data must be immediately available to your software, the weight gos up dramatically.
If I were really going to try something like this, I'd probably come up with a way to put lots of bare chips on a single substrate, eliminating even the meager additional weight of the MicroSD packaging. (I'm guessing that the chips in a 16GB MicroSD card are a significant part of the total mass.) At the very least, I'd come up with an efficient gang-socketing scheme.
Not if you do it reversibly.
And five or six inches tall. ProFiles came in 5 meg (what you had) and 10 meg (what I got with my Lisa, er, "Mac L").
...weighs something like 300mg/card. That's 48GB/gram, or a bit over 20g/TB, or 20Kg/PB.
Mozilla's Benjamin Smedberg says they're currently "[sprinting] as fast as possible to get basic code working, running simple testcase plugins and content tabs in a separate process," after which they'll fix everything that breaks in the process.
This sentence was a little hard to process.
(I note that the "process" of Slashdot incremental improvement has now reached a point where clicking anywhere in the text-entry box causes the box to LOSE focus. If you don't want us using Safari, there are more efficient ways to get us to move.)
A fundamental difference between MRI and CT is that computing the MRI image involves (at least in some cases) a 2-D FFT. While signal to noise ratio is an issue, the processing is not an ill-posed problem.
Hmm. My group definitely calls the process of moving from k-space to image space "reconstruction". There are good reasons for doing more than a simple 2D FFT (most of which, I'll admit, are over my head).
I've been lucky enough to work with MR and CT imaging researchers for a while now. One of the benefits of this job is that I've gotten to learn a lot about how these images are acquired and reconstructed. It's not quite as bad as making sausage, but it's a lot more involved than a "snapshot".
For CT, we acquire a bunch of 2D images through you from different angles, then do a lot of number crunching to generate a 3D volume. The problem is that you don't hold still while we're doing it. You can try; you can even hold your breath, but you can't "hold your heart". As your organs move between views, we get motion artifacts -- shape distortion, bright or dark areas, even "things" that aren't really there.
For MR, it's even worse. I can barely tread water in the physics of it, but we're effectively capturing a line at a time in 3D space. (We're actually acquiring data in "k-space", then running it through a Fourier transform to make it spatial.) Not only is it subject to motion artifacts, it's also subject to susceptibility artifacts (distortions because of the magnetic properties of certain materials), flow artifacts (blood moves through vessels between the time that we apply a magnetic pulse and the time that we read back emitted signals), and lots of other things.
fMRI is just adding yet another layer of aggregation and interpretation on top of all this. Sure, it's a "visualization of data generated by repeated scans", but so is every CT or MRI image.
3D imaging, especially MRI, is hideously complicated and indirect. It's almost inconceivable that it could yield results with any physical significance.
...and yet, it does. It's become so routine, so reliable, so well-understood and well-controlled, that doctors and researchers know they can rely on it as a matter of course. They still have to be aware of the errors and distortions that can arise, but that's true of every imaging or monitoring system, all the way down to the stethoscope and the fever thermometer.
Luminous efficiency is the ratio of light emitted to power consumed. Luminous efficacy also incorporates the eye's response to the emitted spectrum.
Luminous efficacy isn't the appropriate measure here, unless you're completely unconcerned about color. If you want "white" light, you've got to emit red and blue wavelengths, which give lousy luminous efficacy, along with green, which gives great efficacy. The eye isn't nearly as sensitive to red or blue as it is to green light, but without them, you can't get to white.
The maximum possible luminous efficacy for a "white" light, something approximating sunlight, is around 15 percent. That assumes 100% wall-plug efficiency -- every watt of electric energy that comes in gets converted to a watt of visible light. So, if you've got 11% luminous efficacy in a white light, that translates to 75% efficiency.
If you want to get the maximum possible luminous efficacy -- the "brightest" light for a given amount of power -- get a fluorescent bulb with a pure-green or blue-green phosphor. Then you can get 50-75% true luminous efficacy, but your dinner won't look very appetizing, and neither will your date.
Heh. At Virginia Tech in the early '80's, they used SSN's as student ID's, too. Test results and grades would be posted on the doors of classrooms, identified by SSN with names omitted, for "privacy". Of course, the lists were still sorted alphabetically by name.
Biking for an hour at 25MPH costs 1181 kcal, according to this calendar (others suggest it costs even more calories), which translates to 1373 watt-hours. (Your body isn't that efficient at converting fuel to energy.) So let's assume your 250W figure is correct, and your body is about 18% efficient in converting calories to power.
Biking for an hour at 65MPH (if you could) would burn 18669 calories -- remember, wind resistance goes up as the cube of speed. That works out to -- let's see -- 21712 watt-hours. Assuming the same 18% efficiency (and some active cooling for your legs, not to mention the rest of your body), you'd be putting out 3.95KW to sustain that speed.
When you look at it that way, spending five times the energy to move a car, with probably five or ten times the frontal surface area and more than ten times the passenger and cargo capacity, starts to sound like not such a bad deal.
The picture we get from such a technique is no picture at all. To create a picture, we would need a dense array of ears of great sensitivity not unlike a retina.
As I understand it, the picture we get from such a technique is exactly a picture -- it's formulated in the same areas of our brain, and subject to the same mental operations. As others have pointed out, we get a lot more information from our ears than we would get from two single-pixel image sensors. (Think about how you can tell, from a pair of receptors at opposite sides of your head, whether a sound is coming from ahead or behind, above or below.)
I don't know how blackbody radiation is generated, if not from electrons dropping into lower energy states, but isn't it possible to get blackbody radiation from materials completely lacking electrons? Even for normal materials hot enough to glow, how do you get the essentially-continuous spectrum of blackbody radiation?
I was telling people twenty or more years ago that I wanted a handheld device that I could take on the trail, hold up, look through like a little window, and see an overlay showing trail distances, climbs/descents, geographic feature names, and so forth. In 1990, you could do it as a slow, clumsy demo on a "handheld device" tethered to a room full of equipment. Now, with GPS, built-in cameras and good inertial tracking, we're really just a good eye-tracking layer away from a true implementation.
"Prescience" entails a great deal of paying attention.
I tried to buy Vinge lunch at CHI '99, but he declined, saying that he had to meet with the folks from the MIT wearables group. A Deepness in the Sky was freshly out, but he was already soaking up info to pour into Rainbows End (no apostrophe). I wonder who he's hanging out with now.
Alas, it doesn't look like his retirement from teaching is having much effect on his cicada-like rate of new releases...
The maximum resolution of a telescope is proportional to the diameter of its objective (main lens or mirror), and inversely proportional to the wavelength at which it's observing. This is observing at wavelengths 100 times longer than the visible and near-IR instruments like Hubble observe, so it's at a 100x disadvantage coming out of the starting gate.
We've never had images anywhere near this good in this part of the spectrum. I'm very sorry that they offend you.
But you're right. We definitely shouldn't field any instruments until we're ready to deliver, power and support an array at Neptune's distance. After all, it's not like we learn anything from intermediate steps. Just look at all the money we wasted, wasted, on Hubble. Or Palomar. Or Galileo's first telescope. (After all, who needed to know that Jupiter had moons, or Saturn had rings?)
..as I recall, the campus newspaper charged by the line for classified ads
The good news for his bank account was that all of his projects were written in perl!
The bad news was that the first Perl interpreter was still five years or so in the future, so all those lines of $_\{} and whatnot were correctly interpreted as line noise.
...as I recall, the campus newspaper charged by the line for classified ads.
I should have said "If it happened around this time of the year".
No, I'm not counting my supernovae before they hatch.
In your calculations you forgot the small factoid that it may be another thousand years before it goes supernova. It has brightened considerably in the past only to dim back down. It was Fox news (fair and balanced) that mentions it going supernova, not the paper presented at the meeting that merely states a 15% shrinkage and nothing else.
Well, yes. It's been known as a variable for a very long time, and while I don't know how long its diameter has been monitored, it seems likely that its changes in brightness would be accompanied by changes in size. A 15% change in diameter isn't quite so impressive against a history of twofold changes in brightness.
In fact, here's an article claiming that its diameter varies from 550 to 920 times that of the Sun (alas, the link the article cites is dead). They might mean, though, that measurements using different techniques yield results in this range, not that the actual size varies within that range. From the Berkeley press release:
"Since the 1921 measurement, its size has been re-measured by many different interferometer systems over a range of wavelengths where the diameter measured varies by about 30 percent," Wishnow said. "At a given wavelength, however, the star has not varied in size much beyond the measurement uncertainties."
So, looking for stars in a light-polluted sky is easier with a telescope, because it makes the stars appear brighter relative to their background.
Is this a joke? Light pollution turns the sky an awful pink-ish gray from what would otherwise be black, zodiacal light notwithstanding. That being the case, how exactly would it be easier to see a point source of light against a lighter background versus a darker background?
Looking for stars in a light-polluted sky is easier with a telescope than it is without a telescope, because the telescope increases the apparent brightness of the stars relative to the brightness of their background. I'm sorry that I wasn't repetitive enough to head off your rant. Looking for stars is easier in a non-light-polluted sky, of course, whether you're using a telescope or not.
With nebulae, comets, or other extended objects, especially where the object's apparent brightness doesn't exceed the sky's apparent brightness, the telescope doesn't help much at all.
Ludicrous! This is clearly being spoken by a person who has never looked through a telescope in their entire life.
Heh. There's quite a bit more to telescopes than just "looking through" one. But even if that's all you're doing, you're overlooking a few very important points.
The apparently brightness of *any* astronomical object, be it a galaxy such as M31, or a globular cluster like M13, is entirely a function of aperture when magnification is held constant. The views of the Orion Nebula through a 4 inch reflector at 100x will be eviscerated by the same 100x view through a 20 inch reflector. (And yes, I have looked through instruments of both size, though I own a 12 inch reflector personally.)
Congratulations. You're obviously quite proud. Now, let's compare notes for these scopes against a polluted sky.
Under a typically nasty suburban sky, light pollution might be something like 18 magnitudes per square arc-second. In other words, each square arc-second of sky sheds as much light on your eye as an 18th-magnitude star.
The four-inch scope will collect something like 200 times as much light as a fully-dilated eye (100mm objective vs. 7mm pupil). At 100x, it will then spread that light across an angular area 100^2 times as large. An extended object -- a nebula, a distant galaxy, the sky itself -- will appear "100 times as large", but 50 times (just under four magnitudes) dimmer than what the naked eye sees. But stars will still be pinpoints (assuming good optics), and they will appear 200 times (almost six magnitudes) brighter. Thus, the telescope makes it easier to see dim stars against a light-polluted sky.
With the 20-inch scope, you're collecting 25 times as much light as the 4-inch, 5000 times as much as the naked eye. Spread that over 10,000 times the area, and extended objects still appear slightly (less than one magnitude) dimmer than they do to the unaided eye, but stars are 5000 times (over 9 magnitudes) brighter.
No matter what size telescope you use, 100x magnification "stretches the contrast" between extended and pointlike objects by 10,000 times, or ten magnitudes. (Within limits -- for a scope smaller than two inches you'd be exceeding the resolution limit of the optics, and for a scope larger than about 24", the exit pupil would be too big to get all the light into your eye.)
Now, suppose you're looking for a faint nebula, comet, or other extended object. No matter how large your telescope, no matter the magnification, it's not going to change the contrast between that object and the background brightness of the sky. If the sky itself has a higher surface brightness than the object you're looking for, it's going to be really hard to spot that object, unless you can find filters that knock back the skyglow more than they darken your target.