can my monitor represent information about every possible object or can it not. — Zelebg
That is not the answer, just refusal to accept the premise of the question, and is beside the point since the bottom resolution can be fixed to arbitrary size and precision. Say, human faces. My monitor can show every possible human face at least down to a scale and precision of an electron microscope. Therefore, there is only a finite number of unique human faces. Yes? — Zelebg
That is not the answer, just refusal to accept the premise of the question — Zelebg
and is beside the point since the bottom resolution can be fixed to arbitrary size and precision. Say, human faces. My monitor can show every possible human face at least down to a scale and precision of an electron microscope. Therefore, there is only a finite number of unique human faces. Yes?
Your may want to rephrase your qestion?
Faces can differ in details that are smaller than the resolution that can be captured with an electron microscope. Also, different faces, even if they look the same in a particular pair of photographs, can move very differently from each other, which can completely alter our perceptions of what those faces look like.
My monitor can indeed represent any and every possible information. — Zelebg
Can any information be digitally encoded? The answer is yes, and to arbitrary given precision. — Zelebg
Can any information be digitally encoded? The answer is yes, and to arbitrary given precision. — Zelebg
So, for some arbitrary given resolution and some arbitrary given size of an object, such that it maximally occupies the whole screen, say 800x600 resolution and passport style photographs of human faces - there exist a finite number of possible human faces for that particular specified size and resolution. Yes? — Zelebg
In triary computers, yes, 1/3 could be digitized, but 1/2 could not. You can't escape this problem with any digital system. — god must be atheist
Sure, but so what? Nothing interesting results from this.
Of you want to get to the interesting question, let's take Max Tegmark's argument that in our Hubble Sphere, there are only a finite number of possible states.
I hear what you are saying. But the emphasis is on, what you described as, AT TIMES. That is, not always.I certainly don't agree that with Zelebg, but this assertion of yours is wrong. Computers can and do represent rational numbersat times with perfect accuracy. This is done by representing them as a pair of integers, rather than in a "floating point" format. — Douglas Alan
Now this is funny. Don't you see that is exactly what I'm saying? All I have to do is set my arbitrary resolution to planck scale and define the arbitrary given size as that of the universe to match Tegmark. — Zelebg
Once you enter into a variable the value of 1/7, and you use that variable's value in calculations, you will immediately lose the perfect accuracy, as the calculations storage go on binary code representation. — god must be atheist
This is not true. A programming language that supports doing mathematical calculations with rational numbers will typically not force you to ever convert the rational number to a floating point number. The program can run from beginning to end using only rational numbers, and can consequently produce results with perfect precision and accuracy. (Assuming that the numbers being represented are accurately represented as rationals.) — Douglas Alan
Perfectly true. But the numbers will be thus represented as long as a program is run written in that particular programming language. If you run a different program, written in a more conventional programming language, that does not have that feature programmed into its structure, then you lose accuracy of rationals with infinite repetitions. — god must be atheist
Douglas, Where did ZelebG go? You see what you've done? We quibbled, and ZG took the opportunity of the moment that we weren't watching, and he ran away. — god must be atheist
So, |>, do they have a table in C++ , in Java, and in all other languages, for ALL imaginable non-reducible fractions of integers? — god must be atheist
Yes, I have agreed as much. The problem is that Tegmark is making a contentious premise in his argument, and therefore, we cannot be sure of his conclusion.
Well, no, the number of distinct digital photos of a given resolution is finite. — SophistiCat
I think he means numbers don't exist and all objects up to and including the universe are forever finite — Gregory
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