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Old 04-10-2007, 11:19 AM   #76
Choobus
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how is that complex?
Assuming you are referring to the Mandelbrot Set in the previous post, it is highly complex because the number of bits required to represent it completely is greater that the number needed to describe the matter/energy composition of the known universe.

Even the first iteration result is more complex than the original formula.
yeah, but the generating formula is very simple and contains all that information.

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Old 04-10-2007, 12:03 PM   #77
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As to Orr's argument, it's absurd for independent reasons. You can't just posit that God doesn't follow any rules.
But you can do the inverse? Claim that god must be complex (as Dawkins defines complex)? And therefore that it can't exist, because it must follow the same evolutionary processes as carbon-based life? I don't think Orr is positing anything; he's refuting, or at least calling into question Dawkins' thesis.

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Old 04-10-2007, 01:22 PM   #78
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how is that complex?
Assuming you are referring to the Mandelbrot Set in the previous post, it is highly complex because the number of bits required to represent it completely is greater that the number needed to describe the matter/energy composition of the known universe.

Even the first iteration result is more complex than the original formula.
yeah, but the generating formula is very simple and contains all that information.
I disagree. The information is an emergent property of the function, not a constituent of it.
The complexity of the function is simply that of fewer than twenty symbols selected from an alphabet of fewer than 100.

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Old 04-10-2007, 01:27 PM   #79
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As to Orr's argument, it's absurd for independent reasons. You can't just posit that God doesn't follow any rules.
But you can do the inverse? Claim that god must be complex (as Dawkins defines complex)? And therefore that it can't exist, because it must follow the same evolutionary processes as carbon-based life? I don't think Orr is positing anything; he's refuting, or at least calling into question Dawkins' thesis.
Dawkins merely repeats the theist claim that God must be ultra-complex to have designed and executed a plan for the universe including humanity. He does so in preparation for shooting it down.

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Old 04-10-2007, 01:36 PM   #80
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Assuming you are referring to the Mandelbrot Set in the previous post, it is highly complex because the number of bits required to represent it completely is greater that the number needed to describe the matter/energy composition of the known universe.

Even the first iteration result is more complex than the original formula.
yeah, but the generating formula is very simple and contains all that information.
I disagree. The information is an emergent property of the function, not a constituent of it.
The complexity of the function is simply that of fewer than twenty symbols selected from an alphabet of fewer than 100.
Sometimes when writing a computer program I might have an array of data (scattering cross sections say) or I might use a generating function to calculate a particular value as needed. In both cases the information I need is included in the code. You say it's emergent but I don't see the difference. You have to perform some operations to find the right value in an array, and you have to perform some slightly different operations to generate the value you want from a function. To me these are the same.

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Old 04-10-2007, 02:58 PM   #81
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Sometimes when writing a computer program I might have an array of data (scattering cross sections say) or I might use a generating function to calculate a particular value as needed. In both cases the information I need is included in the code. You say it's emergent but I don't see the difference. You have to perform some operations to find the right value in an array, and you have to perform some slightly different operations to generate the value you want from a function. To me these are the same.
In a very general sense, a function of some parameter is the same as an array indexed by the same set of parameter values. In fact, some functions use an array lookup for part of its operation to speed up computations.

The complexity of the output of a function is not, in principle, related to that of the function code or the code plus its execution.

Obviously, a long program whose output is only the value zero, is much more complex than its output. By the same reason, the program can be much less complex than its output.

A self-replicating program or molecule, after it has duplicated itself more than once, has output clearly more complex than itself. "ABC ABC" is at least one bit more complex than "ABC".

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Old 04-10-2007, 03:09 PM   #82
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As to Orr's argument, it's absurd for independent reasons. You can't just posit that God doesn't follow any rules.
But you can do the inverse? Claim that god must be complex (as Dawkins defines complex)? And therefore that it can't exist, because it must follow the same evolutionary processes as carbon-based life? I don't think Orr is positing anything; he's refuting, or at least calling into question Dawkins' thesis.
A creator deity that is not complex would not be active and theistic is all I'm saying; it would be deistic or some other poetic, worthless nonsense. Dawkins's argument isn't perfect, but as Sternwallow said, it is reactive and takes for granted the same assumptions as the apologetic one to show how it is flawed. The key is not that some unknown thing must be complex but that people usually argue that it is.

The fact that god is inadequately defined is a broad problem that plagues all discussions on religion. You can't get very far at all without considering some hypothetical definitions (although really it is all just mental masturbation if you ask me).
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Old 04-10-2007, 03:24 PM   #83
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The complexity of the output of a function is not, in principle, related to that of the function code or the code plus its execution.

Obviously, a long program whose output is only the value zero, is much more complex than its output. By the same reason, the program can be much less complex than its output.
If a function always outputs a constant, it reduces to a much simpler function. I would argue that the effective complexity should be considered from this reduced form, not from the needless computations that happen to be involved.
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Old 04-10-2007, 03:42 PM   #84
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But is the information truly contained within, or even an emergent property of, any given function?

Take a simple function, or better yet, a very simple operation: 1 + 1

Is all the information contained in that function? If I were to show that to someone who had never seen any of those symbols before, wouldn't they need some extra information in order to perform the operation? To take whoneeds's example from above, a function can only "always output a constant" if someone or something has enough additional information to now how to utilize the information contained in the function.

It seems to me that, while operations or functions such as 1 + 1, or fn = (2n) + (f(n - 1)), or whatever, contains information, they don't contain all the information neccessary to actually complete the operation or function.
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Old 04-10-2007, 04:02 PM   #85
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The complexity of the output of a function is not, in principle, related to that of the function code or the code plus its execution.

Obviously, a long program whose output is only the value zero, is much more complex than its output. By the same reason, the program can be much less complex than its output.
If a function always outputs a constant, it reduces to a much simpler function. I would argue that the effective complexity should be considered from this reduced form, not from the needless computations that happen to be involved.
Computability issues suggest that it is not always possible to identify, by inspection, what code is needless. A function that returns "1" if a given string of digits appears in a contiguous section of the decimal expansion of Pi is not necessarily possible to simplify to one that ignores its input and returns "1" always.

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Old 04-10-2007, 04:12 PM   #86
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But is the information truly contained within, or even an emergent property of, any given function?

Take a simple function, or better yet, a very simple operation: 1 + 1

Is all the information contained in that function? If I were to show that to someone who had never seen any of those symbols before, wouldn't they need some extra information in order to perform the operation? To take whoneeds's example from above, a function can only "always output a constant" if someone or something has enough additional information to now how to utilize the information contained in the function.

It seems to me that, while operations or functions such as 1 + 1, or fn = (2n) + (f(n - 1)), or whatever, contains information, they don't contain all the information neccessary to actually complete the operation or function.
A good point. It is not just the simplicity of the symbols although that is closely related to the process needed to "execute" it. The complexity of the output can still be greater than the combined complexity of the symbolic code and its execution as in the Mandelbrot Set.

The function "Zn = Zn-1^2 + C" can be translated into the simpler language as "1', meaning "execute the first and only subroutine available, which can be represented as 'Zn = Zn-1^2 + C'".

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Old 04-10-2007, 04:25 PM   #87
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The complexity of the output of a function is not, in principle, related to that of the function code or the code plus its execution.

Obviously, a long program whose output is only the value zero, is much more complex than its output. By the same reason, the program can be much less complex than its output.
If a function always outputs a constant, it reduces to a much simpler function. I would argue that the effective complexity should be considered from this reduced form, not from the needless computations that happen to be involved.
Computability issues suggest that it is not always possible to identify, by inspection, what code is needless. A function that returns "1" if a given string of digits appears in a contiguous section of the decimal expansion of Pi is not necessarily possible to simplify to one that ignores its input and returns "1" always.
I'm not sure where you're going there. I'm just talking about mathematically reducing a function.

If you had a function that performed a million multiply and the same number of divide operations to always output the exact same thing as the input, then its effective complexity is independent of those operations; it's just a unity gain, or effectively no operation at all.
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