On Jun 4, 2011, at 1:03 PM, Rex Allen <[email protected]> wrote:
On Sat, Jun 4, 2011 at 1:51 PM, Jason Resch <[email protected]>
wrote:
On Sat, Jun 4, 2011 at 12:06 PM, Rex Allen
<[email protected]> wrote:
On Sat, Jun 4, 2011 at 12:21 PM, Jason Resch
<[email protected]> wrote:
One thing I thought of recently which is a good way of showing how
computation occurs due to the objective truth or falsehood of
mathematical
propositions is as follows:
Most would agree that a statement such as "8 is composite" has an
eternal
objective truth.
Assuming certain of axioms and rules of inference, sure.
Godel showed no single axiomatic system captures all mathematical
truth, any
fixed set of axioms can at best approximate mathematical truth. If
mathematical truth cannot be fully captured by a set of axioms, it
must
exist outside sets of axioms altogether.
Then perhaps the correct conclusion to draw is that there is no such
thing as "mathematical truth"?
Perhaps there is just human belief.
Perhaps so, perhaps there is only Rex's beliefs. Perhaps only rex's
beliefs at this exact moment. But what explanatory power does that
offer? What model for decision making can there be with such a world
view?
The fractal is just an example of a simple formula leading to very
complex
output. The same is true for the UDA:
for i = 0 to inf:
for each j in set of programs:
execute single instruction of program j
add i to set of programs
That simple formula executes all programs.
Following those instructions will let someone "execute" all
"programs".
What is the engine providing the computations which drive the universe?
Or, alternatively, configuring a physical system in a way that
represents those instructions will allow someone to interpret the
system's subsequent states as being analogous to the "execution" of
all "programs".
Do you think pi has an objective (not human invented or approximated)
value, whether or not any person computed it?
Is there an answer to the question what is the googleplexth decimal
digit of pi given no one in this universe could ever computed it?
If there is, then there are also objective values to the omega
constant, or the state of the uda after X steps. These values exist
without the need for someone to execute them, anymore than we need to
compute the billionth digit of pi for it to have it's value.
Is extraordinary complexity required for the manifestation of
"mind"?
If so, why?
I don't know what lower bound of information or complexity is
required for
minds.
Then why do you believe that information of complexity is required
for minds?
I think information is a critical component of consciousness. The
very definition of consciousness: "having awareness of ones own
thoughts and sensations.". Awareness is defined as having knowledge
or information. Therefore consciousness is the possession of
information (about ones thoughts ir sensations).
There are also reasons to believe in the informational basis if
consciousness due to multiple realizeability. Minds can take
different physical forms because information cab take many physical
forms.
Lastly there is an argument realted to zombies. A zombie cannot feel
any different or be less conscious than a conscious person who is
physically identical. This is because the informational content of
both the person and the zombie is necessarily the same (given the
identical physical states). Therefore the conscious person does not
and cannot know anything more about what they are feeling or
experiencing than the zombie does. Both must be equally conscious.
Is it that these recursive relations cause our experience, or are
just
a way of thinking about our experience?
Is it:
Recursive relations cause thought.
OR:
Recursion is just a label that we apply to some of our implicational
beliefs.
The latter seems more plausible to me.
Through recursion one can implement any form of computation.
But, ultimately, what is computation?
A process. More specifically one that connects a succession of states
via some well-defined relation(s).
Recursion is
common and easy to show in different mathematical formulas, while
showing a
Turing machine is more difficult. Many programs which can be
easily defined
through recursion can also be implemented without recursion, so I
was not
implying recursion is necessary for minds.
Then what do you believe is necessary for minds?
An informational process.
Jason
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