obviously the difference between a 36mp camera and a 21mp camera is 15mp. duh.
you don't need differential calculus and a Ouija board to figure that out.
It's really very simple
Correct! It's really very simple that the raw numbers alone don't matter.
Consider two automobiles with equal, stated horsepower. Will one be "faster" than the other? That would depend upon other factors in each vehicle. Gear ratios, tire diameter, vehicle weight, etc. Will one be "quicker" than the other? The same factors come into play as with "faster", however, now the amount of horsepower is largely irrelevant since it is torque which moves the car off the line and horsepower which keeps it at a set speed. What is the torque curve of each vehicle? What are the gear ratios which will be affected by that torque curve? If you are driving with the right torque curve and the right gear ratios to maintain the motor's RPM at or near the torque peak, the car will feel perceptibly quicker than another car with less well balanced specs.
If you have one 60 watt lamp, will adding another create twice as much "light"? No, even if both lamps are identical, doubling the number of lumens does not double the actual perceived light level. Certainly not in an enclosed room where bounced light values contribute to the perceived light levels. Therefore, the two lamps would first need to have equal lumen values. Then, the lamps would need to exist within the same space. Change the space or move away from one light source or move both lamps apart and the perceived light levels at any location will also change. Still, doubling the number of lumens does not double the perceived light level. Will a 100 watt amplifier play twice as loud as a 50 watt amp? No, you need to add approximately ten times the "watts" to double the perceived SPL. Everything else equal that is. Is the input Voltage to both amps equal? Is the input sensitivity equal in both amps? How about input impedance? The amp cannot produce output until it has an input signal. If the input signal is lower on one amp, possibly that amp will not even reach full output. (Compare this to light sensitivity of a sensor through a lens of a variable "speed".) The amp alone makes no sound, no watts until it is connected to a load. Watts are a function of Voltage plus Amperage over Impedance. Depending on the very complex load values of most multi-way consumer level speaker systems, two equal "wattage" amps may easily not be equal in perceived or measured output levels. Adding 3dB of electrical sensitivity in the speaker system is generally considered to be the equal of doubling the wattage output of the amplifier. Though, this is a very crude concept of how "power" is actually delivered to a "load". Since the speaker also must operate within a space, electrical power output is not equivalent to acoustic power output unless the speaker systems are identical (not likely to happen in the real world) and the location of the speaker's individual drivers are equally distributed within a constant cubic total space and have equal dispersion into the space. Again, not very likely in the real world. Load a driver into a horn and you've altered the dispersion pattern but not the electrical sensitivity of the driver itself. Add a window or a doorway and the acoustic power output will drop since the reflected energy within the space has now been altered. Move the (largely omni-directional) low frequency driver closer to a reflecting surface and its output will be equal to the direct and reflected energy arriving at the listener's position. Move it close to one reflecting surface (the floor) and it will have "X" power. Move it against two reflecting surfaces (the floor and a wall) and the output will increase by a predictable amount based on frequency and wavelength travel plus distance travelled. Again, against three surfaces (the floor and a corner) and the bass level again increases in a predictable manner. However, due to the difference in wavelength size and the increasingly directional manner in which high frequencies travel in space, the same cannot easily be said of upper frequency content. Place a low frequency sinewave in a too small space and the reflected wave will interfere with the direct wave which will cause a null point (no sound) or a room "node" which will increase the acoustic output in one area of the room but not another. Move your head side to side or up and down by a few inches and, with most consumer speaker systems in most domestic listening rooms, you will have a different perceived sound quality and likely a different "image" of the performers. Move the speakers to a short wall and they will perform differently than when they are on the long wall.
Therefore, looking only at a static spec of "X" megapixels most importantly ignores the rest of the systems within the camera, the monitor and the printing devices. The resolution of the system is considered the output of the system which can only occur when there is a "load" into which the image can be placed. Like the amp without a load, the resolution of the system is largely dependent upon what device is being used to view or print the image. On a two inch smart phone screen, a 2 Mp image will be sufficient. On a 20" diagonal monitor, it will not be adequate. Print to a piece of photo paper and the same issues apply though now the paper becomes yet another determining factor in the final resolution of the image. Certainly, the resolution (pixel count) of the printer will affect the image quality. How is the color mixed. By additive or subtractive means? How many colors can be mixed in the printer? What is the noise/distortion value of the system? Unless you can define the sensitivity of the system to energy from input to output as a raw electrical signal, you cannot define the amount of noise added to the final resolution of the system.
So far in this discussion, I would say no one has paid much attention to how images are actually stored on a pixel. A single pixel accounts for a single color and intensity created by combining the three primary values of RGB and converting them into one electrical signal. It is only when those pixel values are assembled and then reassembled by a processing system that all the pixels together create what we would call an " image" rather than the on-off or 0-1 numerical values of the digital system itself. Therefore, just as with a digital audio recording, say, a 24/196 processor vs a low bit rate MP3, a higher resolution processor will create a higher resolution image by looking at a higher number of samples and doing so more times. None the less, does aliasing occur within the system? Inevitably, it does in a digital system and to the extent it does and is not adequately filtered from the system output, then final image resolution will be reduced. That alone assumes an otherwise perfect transfer from a digital state to and analog output. Not going to happen in the real world. Does the filter affect the electrical phase and time value of the signal output? Again, inevitably any filter will affect output quality in some way. Do reading and processing errors account for a large portion of the final signal processing? If so - and, yes, they will in the real world, then image quality will be affected at the final output according to the amount of error correction and signal buffering which occurs within the system.
If the image were a single overall color and intensity at the plane of the sensor, there would be no difference between pixel counts at the sensor or system capacities overall. (An audio amplifier is tested with a single sinewave frequency yet is tasked with producing multiple frequencies of varying and dynamic intensitiy. How the system is tested and spec'd has little to nothing to do with how it is used.) Once the image contains more than one color and varying degrees of intensity, the ability of the pixel to record each color as a single, uniform color and intensity and then for the system to reconstruct the image is dependent upon the entire system's total accurracy/fideilty. (To the discerning eye or ear, accuracy and fidelity are not complementary values and one can actually interfere with the other. For example, an image can be color correct [accuracy] but dimensionally flat [fidelity]. Virtually any audio component will be flat [accurate] in its frequency output yet systems vary considerably in their musical fidelity.) As with an audio system, the photographic chain is only as strong as its weakest link. A larger pixel amounts to a higher light sensitivity which, in turn, accounts for more variations in the captured image. If all else is equal - and it will not be in real world conditions. Assuming the processing system and the rest of the image processing devices are up the the task, a raw pixel count is reduced to a small - but marketable - part of what makes for a higher resolution final image. It becomes similar to two automobiles with equal stated horsepower. Nice for marketing purposes on paper but not very useful in the real world.
