Since our physics don't apply anywhere near the big bang, there are no calculations that can tell you what goes on if such an event were to occur; likewise, while projecting backwards until you get to something ridiculous (cosmologists call the ridiculous point a singularity, but what they mean is that nothing we know applies there, which is ridiculous from the standpoint of continuing with any attempt at explanation (no framework).) Once you've reached the ridiculous, traipsing onward and trying to imagine what led to this undefinable, non-rule-following thing you're talking about, not jsut multiple times, but even once, is absurd. Without a working physics model, it's all hand waving.
Cosmology at this level is about as sensible as religion. That is to say, not at all.
This is slashdot. These people are pretty smart. I don't think it's expecting to much for this audience to actually understand the issues. If you want to argue that people in general don't understand cameras and that's ok, I disagree - understanding means smarter purchasing, which has all manner of positive consequences. If you want to argue that people don't understand cameras and you give up, that's fine. I don't.
Me too. I have fully working SWTPC systems, GIMIX, a COSMAC ELF, an SC/MP, and some others from the days before Apple. [rubs hands together, grins.]
I sold an Altair 8800 and an Altair 680 some years back -- made what I thought at the time was an obscene amount of money on both sales -- but methinks I still should have waited longer. Never did get my hands on an IMSAI chassis.
Best part is, I have written full-machine emulations like this one to replace the real things, so when they go... they're not really gone. It's still fun to do 6809 assembly programming. Not so much fun to do 6800, 6502, 1802, 8080 or z80 assembly, but still.... fun anyway.:)
ok, granted... now, how does that change anything I said?
Assuming a prime lens (or a zoom at any one fixed zoom setting):
First: The lens focal length sets what the lens presents at the focal plane. The ultimate sharpness of the lens and the focus determines the detail prior to diffraction. The f-stop of the lens sets the absolute diffraction by affecting the Airy disc radius. The linearity of the presented light will vary with the lens design (and settings in the case of a zoom) from highly linear to highly non-linear (fisheyes, etc.)
Second: The sensor takes some portion of the light from 0 to 100% in some handy aspect ratio at the focal plane; this results in the hardware-limited FOV for the camera+lens combo.
Third: The sensel density sets the (always linear) sample rate across the (often nonlinear) light the lens presents at the focal plane; this sets the hardware-limited resolution, and, in combination with the f-stop of the lens, also determines if the samples will be diffraction limited (basically, if one sensel impinges significantly upon an Airy disc centered upon a neighboring sensel.)
Bayer or other (Foveon, et al) weirdness ensues, the camera applies various curves, sharpening, etc., etc., and we get RGB samples of some useful bit depth in some useful image format, which we may or may not post-process further.
The lens focal length remains constant in all of this, providing same lens-based FOV and magnification.
My point was, and remains, that suggesting a lens focal length change in mm due to a change in crop is misleading and inappropriate. So is suggesting a linear lens FOV change based on a change in crop. That's not what is going on, and that's not even what *looks* like is going on.
As soon as I hear (or see the result of) "multiply by 1.x" I know the speaker doesn't understand what is going on (or can't be bothered to explain it) and consequently is making even more of a mess out of a subject that isn't all that simple in the first place.
Yeah, some of them recognize themselves in an obvious and repeatable way; others either can't, or just don't have a combination of interests that demonstrate it in a way that I could swear to it. We've got one cat that uses the mirror to groom himself; ducks his head, rolls his eyes up to see, and goes right to any dust bunnies or etc. stuck to him and wipes them off, twists to the sides, etc. You can set him up to do this by sticking something to him, and it's 100% repeatable. It's very clear he knows both that the reflection is not another cat, but an image of him, and that the view is reversed. He gets annoyed if whatever it is doesn't come off - lipstick marks and things like that result in meows and obviously intensified attempts to remove same.
Frankly, this doesn't surprise me at all; in the wild, they hunt fish in the water, and reflections are part and parcel of that experience. Seems to me it would be a lot more difficult to do effectively that if you didn't understand what you were looking at, especially if the water surface was in motion.
I agree; degrees of consciousness is closer than "yes" or "no", but I also reserve some questions for nature of consciousness -- I'm not at all willing to concede that our variety is the only worthwhile type. Cats and dogs both clearly enjoy vastly enhanced sense of smell, and for all I know, they exist "in" that space the way most humans do visually. We just don't have the tools to figure it out at this point. I think we're inherently misled by our own experience (and a lot of hubris, as is made obvious by human treatment of other animals in general.)
I wrote micrometer - italicized u, followed by m, but the broken Perl engine stripped the micro out. Sorry. Slashdot: broken for technical typography by design. Perfect for a tech site, eh?
You're suffering from a number of misconceptions. First of all, focal length is not a shorthand for FOV. FOV is a function of the lens FOV (which may be, and often is, nonlinear) and the intercept made by the sensor or exposed film region. It can vary in both aspect and area, given the relatively constant circle of light delivered by the lens to the focal plane. In other words, it varies enormously, and it does so independent of the focal length, so it is *silly* to use focal length as a shorthand for FOV.
Second, nothing about what a specific lens presents to the sensor - FOV or Magnification - varies from camera to camera. You get a varied intercept with the crop formed by the sensor (or film) boundaries, and you get varied magnification by sensel density of the sensor (and this is not without consequence, as the various lens artifacts - chromatic aberration, diffraction, coma and so on - all are magnified as well by a tighter sensel pitch.)
Neither one, however, "changes" the lens.
The entire concept underneath a statement like "I put the 400mm lens on my crop camera, so now it is like a 640mm lens" is invalid. It isn't like one as you would instantly find out if you simply put a 640 lens on the FF camera, shot an image, and the compared the results. They won't even be remotely the same result -- every pixel will be different, the sample rates will be different, the image won't even compress in a similar fashion, and the only way you can *make* them even remotely similar is to scale one of the images, thereby no longer working with anything even close to the actual camera result -- and that's why this misconception should be educated out of the photographic community. It's a false equivalence, and for that matter, one that gets further and further from any kind of sensible description as lenses get wider. For example, a 1.6 crop of a fisheye won't even *slightly* resemble what the fisheye delivers in FOV on a FF. What it will do, however, is deliver a constant magnification that is simply cropped off.
People look at lenses like this: If I buy a 100mm lens, I'll be pretty close. If I buy a 200mm lens, I'll be twice as close (1D thinking.) This is true. When they start talking about crop factors, and they say, "I'll put this 400mm lens on my crop camera and I'll be 1.6x as close (640mm)", they're flat-out wrong. They'll be exactly as close as they were with the FF camera, with the caveat that there will be a perceptible difference due to the sensel pitch, but this difference can even go the other way.
For instance, Canon's FF 5DmkII camera has a sensel pitch of 6.4m, but its 10D 1.6 crop camera has a sensel pitch of 7.4m, so the image will actually be less magnified on the crop camera given the same 400mm prime, rather than the 1.6x magnification that the erroneous thinking leads one to anticipate.
That's what I'm telling you. It doesn't. The focal length of the lens has one constant result: Image scaling at the focal plane. The sensor intercept with the focal plane has one constant result: crop as a function of the lens FOV. The latter changes (both in aspect and area) from medium format to 35mm/ff, to 1.6 and 1.3 crops, to the various tiny also-ran sensors in the point and shoots. Image scaling doesn't change -- and when someone calls a 400mm lens a 640mm lens, they're not generally talking about FOV, they're talking about scaling - how "close" they can get to the subject. In fact, speaking as a pro photographer of several decades, I'd go so far to say that lenses over 100mm are almost never selected with FOV in mind at all (other than as an irritation), but rather as a means to get closer to the subject. When you call that 400mm lens a 640mm lens, you're just fooling yourself. You're no closer than you would have been on a FF camera - unless your cropped camera is sporting a higher sensel density. If we're talking about wide-angle lenses, it's even less appropriate, because they tend to be distorted and even the FOV isn't as linear a derivative of the intercept as we'd like to think with our constant crop factors. The extreme example is the fisheye; you can "1.6x" one of those and you sure as heck won't get 1.6 the FF/35mm FOV, and you will *still* get exactly the same magnification.
The idea of making the focal length some kind of magical constant that tracks the sensor size is incorrect and misleading. A 400mm lens is a 400mm lens, period. FOV is something else entirely. And as I said, I think you'll find most thinking is about magnification anyway.
Bottom line, you move a lens from a FF camera to a crop camera, the only difference in actual magnification is from the sensel density.
I know what he was talking about. There's no lag in my live viewfinder. It runs at video rates (30 hz), which is about as fast as my eye runs. No lag. It'll shoot without further ado from there, no particular shutter delay, either. I shoot live action this way (martial arts); no problems - I get the right moment using the live viewfinder. And I'm *not* shooting ahead at all.
The source of "shutter lag" is an old or crummy camera. Buy a decent DSLR - for example Canon 550, 60D, 7D, 5DmkII - no lag. Buy one of these point-and-shoot wonders... well, you get what you pay for.
No problem. My next car -- and every car after that -- will be electric. Kuwait - really the entire region - had better get after some diversification, because that whole buckets of oil thing is going to come to a screeching halt in the next decade or three. Thorium reactors, PV, wind, etc... I see the Kuwaiti palace garage being fitted out for camels again eventually. One hump or two?
On my full frame sensor is 400 on my crop sensor SLR its about 600mm.
No. It's 400mm in both cases, You've conflated field of view with magnification. The lens puts the same image at the focal plane; the crop sensor doesn't capture the edges (because the sensor is smaller) and this gives you the same field of view as a 640mm lens, but the information in the crop isn't any larger.
There are only two factors that affect captured magnification: One is the lens; the other is the sensel density on the sensor. For instance, if there are twice as many sensels across a specific linear measure of a sensor as compared to another, it will give you twice the detail, exactly the same effect as doubling the mm of the attached lens.
If, however, you have a crop sensor and a FF sensor of the same sensel density, moving a 400mm lens between the cameras will give the same magnification, but not capture the edges on the crop sensor.
Practical example: Canon 20D, a crop sensor camera, and a Canon 5DmkII, a FF camera, both have sensel densities of 6.4m. Consequently, if you put your 400mm lens on one, then the other, given that the scene hasn't changed and the cameras are placed on the same tripod, they'll capture exactly the same image in terms of magnification. But the 20D will not capture the image at the edges, because the sensor is smaller, which effectively "crops" off the edges.
The dog needs your approval, and will do most anything to get it. It's a pack animal and its success is based in co-operation; it's not that effective on its own. The cat isn't concerned about your approval. That's because it's not a pack animal, it's a highly effective solitary predator - it doesn't need you, and it has no built-in bias to please you. On the other hand if *you* please *it*, you will find they are just as friendly as dogs, and can be rewarded into doing pretty much the same things - fetch, roll over, sit, lay down, get down, shake, high five, etc.
So clearly they have the capacity to interact - they're just not giving it up in the hope you'll like them; they're simply already ok, by their very nature.
Cats have convinced us to keep them around and feed them without them having to do anything for us,
On the contrary, cats have earned a place beside us for centuries by keeping down mouse and rat populations, particularly with regard to granaries, farms, etc. In fact, when people get confused about this, we get things like the black death - they were killing cats with the idea that they were responsible for the disease, when in fact the cats were keeping the rodent population down. Once they started killing the cats, they were basically doomed. Same thing happens in modern small towns, especially out west, where I live; little old ladies get all flustered because cats are crapping on their roses, the town starts trapping strays, and within a year or so, there's a huge rodent population explosion.
I live with cats in an old, very large building, and one thing I don't have is a rodent problem. I absolutely credit the cats for this. In terms of sanitation and keeping food safe for consumption, the cats are a far better deal than rodents. And if birds were stealing my seeds from the fields, presuming I had fields, the first thing I'd do is make friends with some cats, reward them for any birds they caught, and that'd be the end of the bird problem. You teach one cat to catch mice or birds, and by that, I mean reward them when they do it, and the rest of the cats will figure out it in no time flat.
So do cats, especially the slower, more powerful cats that are comparable in speed to wolves. Most species of cats are considerably more deadly on a per-animal basis than any wolf - faster, more athletic, sharper claws, ability to climb, night vision - and don't require pack strategies to succeed. Wolves use those strategies because one wolf isn't all that effective, as compared to a cat of equal size.
Compare a lion to a cheetah and you'll see exactly what I mean. If the cheetah decides you're dinner, you're dinner, that's the end of it -- even if you're a gazelle. It's not so much a hunt as it is a murder. Lions will do very wolf-like surround and overwhelm, even to the point of co-operative pinning by limb and neck. Domestic cats - the little guys we're familiar with - are more like cheetahs than lions; they're incredibly fast and agile compared to their prey, and generally don't need pack behavior to be successful.
As an owner of many, many cats (currently eleven of them, 9 have their own 6000 cubic foot habitat, 2 others enjoy about 15000 cubic feet with the humans here) and many dogs, I would definitely say that there is a social difference, but that it is a difference we see on average -- there are exceptions for dogs, and exceptions for cats. I won't drop any anecdotes other than to say I've shared space with both gregarious cats and retiring dogs, though that is atypical.
I *will* say that the social difference generally inherent to the species affects the behavior a great deal, but isn't a direct reflection on intelligence. These animals naturally approach the world differently; they have different tool sets. Cats are stealthy, predators that kill from ambush using great precision and skill and this is evident in how they comport themselves in play, social settings and so forth. Dogs are pack animals, very comfortable in groups under almost any circumstance, and this is also evident in how they behave. Cats do what they please and this is a very successful strategy for them; dogs work well with others.
If you want to go by brain mass, well, lions and tigers, end of story. But I think that's pretty silly. It has to be about brain sophistication (ever try to teach a cow? But then look what a horse can learn...), and we don't really know how to measure that. There are numerous soft science tests/benchmarks, like an animal recognizing itself in a mirror (both dogs and cats can do this, to my certain knowledge) to demonstrate what psycho-babblers like to call a "sense of self", but again, they make certain assumptions that may very well not be valid - one thing I will also say with great certainty is that cats and dogs are not human-like; while both species may evidence every emotion we are familiar with (and again, I can vouch for this quite confidently), the balance of those emotions is different, the things that stimulate them are different, the durations are different, and the tendency to hold a "chip" is different, though absolutely present.
Honestly, I don't think this question can be settled - or even successfully approached - with the technology and knowledge we currently possess. Personally, I suspect both species are a lot smarter than we think they are; we just don't care about the same things, and we're probably not measuring even close to the right things. That's strictly one fellow's opinion based on a lot of co-habitation.
...and I was simply attempting to continue in your humorous vein by alluding to something with veins, but alas, the moderators recognized neither of our efforts, rendering us symbolically redundantly redundant, regardless of our intended thrust. We've been given the shaft, symbolically speaking. Those dicks.
Slashdot Mirror
In this context, "near" doesn't mean what you think it means. You might want to look into some of the niggling details here.
Since our physics don't apply anywhere near the big bang, there are no calculations that can tell you what goes on if such an event were to occur; likewise, while projecting backwards until you get to something ridiculous (cosmologists call the ridiculous point a singularity, but what they mean is that nothing we know applies there, which is ridiculous from the standpoint of continuing with any attempt at explanation (no framework).) Once you've reached the ridiculous, traipsing onward and trying to imagine what led to this undefinable, non-rule-following thing you're talking about, not jsut multiple times, but even once, is absurd. Without a working physics model, it's all hand waving.
Cosmology at this level is about as sensible as religion. That is to say, not at all.
OOOPS!
Yes, but this turtle, you see, has concentric rings. And a very large black hole. Which, if you ask me, it should probably get looked at.
"too" much. FFS.
This is slashdot. These people are pretty smart. I don't think it's expecting to much for this audience to actually understand the issues. If you want to argue that people in general don't understand cameras and that's ok, I disagree - understanding means smarter purchasing, which has all manner of positive consequences. If you want to argue that people don't understand cameras and you give up, that's fine. I don't.
Me too. I have fully working SWTPC systems, GIMIX, a COSMAC ELF, an SC/MP, and some others from the days before Apple. [rubs hands together, grins.]
I sold an Altair 8800 and an Altair 680 some years back -- made what I thought at the time was an obscene amount of money on both sales -- but methinks I still should have waited longer. Never did get my hands on an IMSAI chassis.
Best part is, I have written full-machine emulations like this one to replace the real things, so when they go... they're not really gone. It's still fun to do 6809 assembly programming. Not so much fun to do 6800, 6502, 1802, 8080 or z80 assembly, but still.... fun anyway. :)
ok, granted... now, how does that change anything I said?
Assuming a prime lens (or a zoom at any one fixed zoom setting):
First: The lens focal length sets what the lens presents at the focal plane. The ultimate sharpness of the lens and the focus determines the detail prior to diffraction. The f-stop of the lens sets the absolute diffraction by affecting the Airy disc radius. The linearity of the presented light will vary with the lens design (and settings in the case of a zoom) from highly linear to highly non-linear (fisheyes, etc.)
Second: The sensor takes some portion of the light from 0 to 100% in some handy aspect ratio at the focal plane; this results in the hardware-limited FOV for the camera+lens combo.
Third: The sensel density sets the (always linear) sample rate across the (often nonlinear) light the lens presents at the focal plane; this sets the hardware-limited resolution, and, in combination with the f-stop of the lens, also determines if the samples will be diffraction limited (basically, if one sensel impinges significantly upon an Airy disc centered upon a neighboring sensel.)
Bayer or other (Foveon, et al) weirdness ensues, the camera applies various curves, sharpening, etc., etc., and we get RGB samples of some useful bit depth in some useful image format, which we may or may not post-process further.
The lens focal length remains constant in all of this, providing same lens-based FOV and magnification.
My point was, and remains, that suggesting a lens focal length change in mm due to a change in crop is misleading and inappropriate. So is suggesting a linear lens FOV change based on a change in crop. That's not what is going on, and that's not even what *looks* like is going on.
As soon as I hear (or see the result of) "multiply by 1.x" I know the speaker doesn't understand what is going on (or can't be bothered to explain it) and consequently is making even more of a mess out of a subject that isn't all that simple in the first place.
Yeah, some of them recognize themselves in an obvious and repeatable way; others either can't, or just don't have a combination of interests that demonstrate it in a way that I could swear to it. We've got one cat that uses the mirror to groom himself; ducks his head, rolls his eyes up to see, and goes right to any dust bunnies or etc. stuck to him and wipes them off, twists to the sides, etc. You can set him up to do this by sticking something to him, and it's 100% repeatable. It's very clear he knows both that the reflection is not another cat, but an image of him, and that the view is reversed. He gets annoyed if whatever it is doesn't come off - lipstick marks and things like that result in meows and obviously intensified attempts to remove same.
Frankly, this doesn't surprise me at all; in the wild, they hunt fish in the water, and reflections are part and parcel of that experience. Seems to me it would be a lot more difficult to do effectively that if you didn't understand what you were looking at, especially if the water surface was in motion.
I agree; degrees of consciousness is closer than "yes" or "no", but I also reserve some questions for nature of consciousness -- I'm not at all willing to concede that our variety is the only worthwhile type. Cats and dogs both clearly enjoy vastly enhanced sense of smell, and for all I know, they exist "in" that space the way most humans do visually. We just don't have the tools to figure it out at this point. I think we're inherently misled by our own experience (and a lot of hubris, as is made obvious by human treatment of other animals in general.)
I wrote micrometer - italicized u, followed by m, but the broken Perl engine stripped the micro out. Sorry. Slashdot: broken for technical typography by design. Perfect for a tech site, eh?
You're suffering from a number of misconceptions. First of all, focal length is not a shorthand for FOV. FOV is a function of the lens FOV (which may be, and often is, nonlinear) and the intercept made by the sensor or exposed film region. It can vary in both aspect and area, given the relatively constant circle of light delivered by the lens to the focal plane. In other words, it varies enormously, and it does so independent of the focal length, so it is *silly* to use focal length as a shorthand for FOV.
Second, nothing about what a specific lens presents to the sensor - FOV or Magnification - varies from camera to camera. You get a varied intercept with the crop formed by the sensor (or film) boundaries, and you get varied magnification by sensel density of the sensor (and this is not without consequence, as the various lens artifacts - chromatic aberration, diffraction, coma and so on - all are magnified as well by a tighter sensel pitch.)
Neither one, however, "changes" the lens.
The entire concept underneath a statement like "I put the 400mm lens on my crop camera, so now it is like a 640mm lens" is invalid. It isn't like one as you would instantly find out if you simply put a 640 lens on the FF camera, shot an image, and the compared the results. They won't even be remotely the same result -- every pixel will be different, the sample rates will be different, the image won't even compress in a similar fashion, and the only way you can *make* them even remotely similar is to scale one of the images, thereby no longer working with anything even close to the actual camera result -- and that's why this misconception should be educated out of the photographic community. It's a false equivalence, and for that matter, one that gets further and further from any kind of sensible description as lenses get wider. For example, a 1.6 crop of a fisheye won't even *slightly* resemble what the fisheye delivers in FOV on a FF. What it will do, however, is deliver a constant magnification that is simply cropped off.
People look at lenses like this: If I buy a 100mm lens, I'll be pretty close. If I buy a 200mm lens, I'll be twice as close (1D thinking.) This is true. When they start talking about crop factors, and they say, "I'll put this 400mm lens on my crop camera and I'll be 1.6x as close (640mm)", they're flat-out wrong. They'll be exactly as close as they were with the FF camera, with the caveat that there will be a perceptible difference due to the sensel pitch, but this difference can even go the other way.
For instance, Canon's FF 5DmkII camera has a sensel pitch of 6.4m, but its 10D 1.6 crop camera has a sensel pitch of 7.4m, so the image will actually be less magnified on the crop camera given the same 400mm prime, rather than the 1.6x magnification that the erroneous thinking leads one to anticipate.
That's what I'm telling you. It doesn't. The focal length of the lens has one constant result: Image scaling at the focal plane. The sensor intercept with the focal plane has one constant result: crop as a function of the lens FOV. The latter changes (both in aspect and area) from medium format to 35mm/ff, to 1.6 and 1.3 crops, to the various tiny also-ran sensors in the point and shoots. Image scaling doesn't change -- and when someone calls a 400mm lens a 640mm lens, they're not generally talking about FOV, they're talking about scaling - how "close" they can get to the subject. In fact, speaking as a pro photographer of several decades, I'd go so far to say that lenses over 100mm are almost never selected with FOV in mind at all (other than as an irritation), but rather as a means to get closer to the subject. When you call that 400mm lens a 640mm lens, you're just fooling yourself. You're no closer than you would have been on a FF camera - unless your cropped camera is sporting a higher sensel density. If we're talking about wide-angle lenses, it's even less appropriate, because they tend to be distorted and even the FOV isn't as linear a derivative of the intercept as we'd like to think with our constant crop factors. The extreme example is the fisheye; you can "1.6x" one of those and you sure as heck won't get 1.6 the FF/35mm FOV, and you will *still* get exactly the same magnification.
The idea of making the focal length some kind of magical constant that tracks the sensor size is incorrect and misleading. A 400mm lens is a 400mm lens, period. FOV is something else entirely. And as I said, I think you'll find most thinking is about magnification anyway.
Bottom line, you move a lens from a FF camera to a crop camera, the only difference in actual magnification is from the sensel density.
I know what he was talking about. There's no lag in my live viewfinder. It runs at video rates (30 hz), which is about as fast as my eye runs. No lag. It'll shoot without further ado from there, no particular shutter delay, either. I shoot live action this way (martial arts); no problems - I get the right moment using the live viewfinder. And I'm *not* shooting ahead at all.
The source of "shutter lag" is an old or crummy camera. Buy a decent DSLR - for example Canon 550, 60D, 7D, 5DmkII - no lag. Buy one of these point-and-shoot wonders... well, you get what you pay for.
The officer was wrong. You could have fought that one, and won.
Lag? What lag? My LVF is... live. There's no lag.
No problem. My next car -- and every car after that -- will be electric. Kuwait - really the entire region - had better get after some diversification, because that whole buckets of oil thing is going to come to a screeching halt in the next decade or three. Thorium reactors, PV, wind, etc... I see the Kuwaiti palace garage being fitted out for camels again eventually. One hump or two?
No, it doesn't. It gives you 400mm, period. On your crop camera, it just loses the edges. FOV is not the same as zoom.
No. It's 400mm in both cases, You've conflated field of view with magnification. The lens puts the same image at the focal plane; the crop sensor doesn't capture the edges (because the sensor is smaller) and this gives you the same field of view as a 640mm lens, but the information in the crop isn't any larger.
There are only two factors that affect captured magnification: One is the lens; the other is the sensel density on the sensor. For instance, if there are twice as many sensels across a specific linear measure of a sensor as compared to another, it will give you twice the detail, exactly the same effect as doubling the mm of the attached lens.
If, however, you have a crop sensor and a FF sensor of the same sensel density, moving a 400mm lens between the cameras will give the same magnification, but not capture the edges on the crop sensor.
Practical example: Canon 20D, a crop sensor camera, and a Canon 5DmkII, a FF camera, both have sensel densities of 6.4m. Consequently, if you put your 400mm lens on one, then the other, given that the scene hasn't changed and the cameras are placed on the same tripod, they'll capture exactly the same image in terms of magnification. But the 20D will not capture the image at the edges, because the sensor is smaller, which effectively "crops" off the edges.
The dog needs your approval, and will do most anything to get it. It's a pack animal and its success is based in co-operation; it's not that effective on its own. The cat isn't concerned about your approval. That's because it's not a pack animal, it's a highly effective solitary predator - it doesn't need you, and it has no built-in bias to please you. On the other hand if *you* please *it*, you will find they are just as friendly as dogs, and can be rewarded into doing pretty much the same things - fetch, roll over, sit, lay down, get down, shake, high five, etc. So clearly they have the capacity to interact - they're just not giving it up in the hope you'll like them; they're simply already ok, by their very nature.
On the contrary, cats have earned a place beside us for centuries by keeping down mouse and rat populations, particularly with regard to granaries, farms, etc. In fact, when people get confused about this, we get things like the black death - they were killing cats with the idea that they were responsible for the disease, when in fact the cats were keeping the rodent population down. Once they started killing the cats, they were basically doomed. Same thing happens in modern small towns, especially out west, where I live; little old ladies get all flustered because cats are crapping on their roses, the town starts trapping strays, and within a year or so, there's a huge rodent population explosion.
I live with cats in an old, very large building, and one thing I don't have is a rodent problem. I absolutely credit the cats for this. In terms of sanitation and keeping food safe for consumption, the cats are a far better deal than rodents. And if birds were stealing my seeds from the fields, presuming I had fields, the first thing I'd do is make friends with some cats, reward them for any birds they caught, and that'd be the end of the bird problem. You teach one cat to catch mice or birds, and by that, I mean reward them when they do it, and the rest of the cats will figure out it in no time flat.
So do cats, especially the slower, more powerful cats that are comparable in speed to wolves. Most species of cats are considerably more deadly on a per-animal basis than any wolf - faster, more athletic, sharper claws, ability to climb, night vision - and don't require pack strategies to succeed. Wolves use those strategies because one wolf isn't all that effective, as compared to a cat of equal size.
Compare a lion to a cheetah and you'll see exactly what I mean. If the cheetah decides you're dinner, you're dinner, that's the end of it -- even if you're a gazelle. It's not so much a hunt as it is a murder. Lions will do very wolf-like surround and overwhelm, even to the point of co-operative pinning by limb and neck. Domestic cats - the little guys we're familiar with - are more like cheetahs than lions; they're incredibly fast and agile compared to their prey, and generally don't need pack behavior to be successful.
Wrong.
Cats can be trained to do the same tricks dogs do; plus others - witness their employment in many a show.
As an owner of many, many cats (currently eleven of them, 9 have their own 6000 cubic foot habitat, 2 others enjoy about 15000 cubic feet with the humans here) and many dogs, I would definitely say that there is a social difference, but that it is a difference we see on average -- there are exceptions for dogs, and exceptions for cats. I won't drop any anecdotes other than to say I've shared space with both gregarious cats and retiring dogs, though that is atypical.
I *will* say that the social difference generally inherent to the species affects the behavior a great deal, but isn't a direct reflection on intelligence. These animals naturally approach the world differently; they have different tool sets. Cats are stealthy, predators that kill from ambush using great precision and skill and this is evident in how they comport themselves in play, social settings and so forth. Dogs are pack animals, very comfortable in groups under almost any circumstance, and this is also evident in how they behave. Cats do what they please and this is a very successful strategy for them; dogs work well with others.
If you want to go by brain mass, well, lions and tigers, end of story. But I think that's pretty silly. It has to be about brain sophistication (ever try to teach a cow? But then look what a horse can learn...), and we don't really know how to measure that. There are numerous soft science tests/benchmarks, like an animal recognizing itself in a mirror (both dogs and cats can do this, to my certain knowledge) to demonstrate what psycho-babblers like to call a "sense of self", but again, they make certain assumptions that may very well not be valid - one thing I will also say with great certainty is that cats and dogs are not human-like; while both species may evidence every emotion we are familiar with (and again, I can vouch for this quite confidently), the balance of those emotions is different, the things that stimulate them are different, the durations are different, and the tendency to hold a "chip" is different, though absolutely present.
Honestly, I don't think this question can be settled - or even successfully approached - with the technology and knowledge we currently possess. Personally, I suspect both species are a lot smarter than we think they are; we just don't care about the same things, and we're probably not measuring even close to the right things. That's strictly one fellow's opinion based on a lot of co-habitation.
No, baby, it's not about the length - it's about how you plug it in.