It's not independent, and, yes, you are making that assumption even though you don't understand it yet.
Have you seriously read nothing in this discussion? Pixel density is not an abstract, mathematical fiction.
It is a restatement of pixel
size. It has absolutely nothing to do with what you do to other variables in an equation that allows you to solve for other display attributes.
You and spungoflex are the ones making an assumption to hold values constant because you're trying to solve an equation rather than look at what's right in front of you.
One can make an explicit decision to hold PPI constant while varying the screen dimensions, which is what you are referring to. That is not the same thing as independence.
No. In order for your argument to work that display size changes ppi, you have to hold a third value constant (resolution). I am saying that you cannot hold
any of those values constant against each other.
Resolution and pixel density are independent of display size. You can pick any two values and solve for the third, but that does not create a
causal relationship in the real, physical world that we live in.
The equation is simply pixels / inches = PPI. How much more obvious can it be that they are related?
And the fuel economy measure is miles / gallons. But neither the number of miles driven nor the number of gallons in the tank
causes fuel economy to change.
Pixels per INCH. If one varies inches in this equation, PPI changes. Therefore, a dependent variable.
No. Display size is the dependent variable in the equation, because it cannot be adjusted in the real world by itself. You can't magically resize a display to any arbitrary size you want outside of theory land.
Here's how you build an LCD: you take pixels, which have a measurable physical size, which you can state in ppi, dot pitch, or outright inches or millimeters. Then you put a number of them together in a grid. Those two values,
pixel size and
resolution, both of which you can independently select, determine the third, display size. You can't do it the other way around. You can't say that you need a screen of exactly 6.632" in diagonal size and exactly 1000x1000 resolution and therefore the pixels are automatically .00632", because the
size of the pixels is not dependent on the size of the display. They are the size that they are, no matter what you do to them.
It MUST have screen dimensions and it MUST have a resolution. Only then does PPI exist.
No. The value of 'ppi' exists wholly independently of the display. All you need to calculate ppi is
one pixel.
Say a pixel falls off the production line and you want to find out the density of the display it was going into. Take that one pixel and put it under a microscope. Measure it. Let's say it 0.05" across.
You're done! You know it's for a 20ppi display. You don't need to know what the final size or resolution is. It's irrelevant. You don't even need 20 pixels. You don't need an inch of pixels. You just need that one, solitary pixel to calculate ppi.
What you continue to harp on is the equivalent of claiming that V * A = W and that Watts aren't related to Volts.
No. What I'm saying is that a change in voltage is not a change in wattage unless you are specifically stacking the deck by holding amperage constant.
If I give you the two figures of 100W and 1000W in isolation, with no other information, you cannot tell me that the higher wattage
necessarily is associated with a higher voltage. They're independent properties. One has no bearing on the other in isolation. That they're related
in an equation does not make them
caused by each other in the real world.
The same is true of miles per gallon. If I tell you that one vehicle has a 1 gallon fuel tank, and another vehicle has a five gallon fuel tank, you can't tell me that the 1-gallon vehicle
necessarily gets higher mpg. You can't tell me from the fuel capacity either the consumption rate or the range.
Causation is also irrelevant.
Causation is the entire point of this discussion. Causation is what makes an independent variable
independent (although your lack of understanding this does explain why you misused "dependent variable" above). The comment was that smaller screens
necessarily have higher pixel density.
This is not true. There is no causal link between the size of a display and the size of its pixels.
Units have no "causation", but they can be related. They are measurements.
Measurements must have causation or they cannot be defined. They are frequently related in mathematical equations that allow you to
calculate variable C by knowing parameters A and B. That most definitely
does not mean that changing A causes C to change as well. You need to know what all three are doing, and when you move from math to reality, you also need to know which two of the three you can actually physically manipulate.