A .PDF has been sent to Bruno and Russel.
APP A and B without diagrams is shown below.
cheers,
colin
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Appendix A – Introduction to notation
In this nomenclature to X(.) is simply a notation which labels a literal
chunk of the universe (the natural world) as a process by using a
mathematical function as a designation. The symbol X(.) is merely a sign
or a pointer to a real natural process, not a mathematical model or other
idealisation of it. It is best thought of as a ‘surgical excision’ of a
chunk of the universe subsequently labeled X(.). The boundary of a subset
is notional, or ontological in that it is chosen merely because we wish to
characterise X(.) explicitly. Please note that the nomenclature does not
demand a clean boundary between X(.) and its container/parent, U(.).
Consider the depiction shown in figure 1. Universe U(.) contains scientist
C(.) and the studied objects C1(.) and C2(.). Within scientist C(.) is
brain B(.) which has an unspecified subset P(.) responsible for phenomenal
consciousness.
<<<< FIGURE 1 DELETED >>>>
The act of ‘being’ B(.) delivers phenomenal consciousness [P(.)]. The
square brackets are a ‘first person’ operator and [P(.)] can be read as
‘the contents of P(.)’. This is the mandated first-person source of
scientific evidence. Scientist C(.) formulates a hypothesised statement hN
of regularity relating the two objects. This hypothesis is shown as a
belief configured in the brain of the scientist and is an abducted
formulation in respect of the actual target generalisation tN that
correlates the appearance of C1(.) and C2(.). This statement hN, if
predictively successful, will become tN. Note that the subset of the
universe that impinges on the senses of scientist C(.) is called T(.). The
combined effect of all experimental apparatus and measurement transduction
impinges on the senses of the scientist. The easiest way to imagine this
is to consider vision where the final transit of photons from the observed
phenomena (say a meter or C1(.) itself if directly observed) is through
the intervening space and onto the retina of the scientist. From that
point the sensory measurements in the eyes through to the brain of the
scientist is labelled S(.). This sensory data S(.) is then used to
construct the phenomenal consciousness P(.) which scientist C(.)
experiences as the visual scene portion of the totality of [P(.)]. As a
result C(.) experiences objects C1(.) and C2(.) as [P(S(T(C1(.))))] and
[P(S(T(C2(.))))] respectively. This nomenclature designates the ‘surgical
resection’ of the previously excised chunks of the universe U(.), allowing
them to operate as a single whole.
Appendix B – Proof: zombies can’t do science
Figure 2 shows human and zombie scientists doing identical science. Their
bodies are identical with the exception of their brain material. The
studied objects cause identical impinging sensory interactions via T(.).
Their identical sensory measurements S(.) transmit the sensory data to the
brain material. Remember objects C1(.) and C2(.), each embedded in T(.),
are literally labels applied to real-world phenomena outside the
scientist. Consider that the visible evidence of a generalisation tN can
be found in the correlated behaviour of C1(.) and C2(.). Let us depict
that correlated behaviour as related to tN as follows:
tN = REGI(fN( C1(.), C2(.) )) (a)
This equation depicts the access that an ‘ideal brain’ has to a belief
that accurately portrays the law of nature tN. The brain involved
naturally observes C1(.) and C2(.), which is captured by the process
fN(.). This ideal brain then habituates a regularity (an ‘ínvariant’) from
the observation using REGI(.) which is reported as tN. Equation (a) tells
us that chunk on matter that would equivalently and naturally access the
law tN is REGI(fN(.)). What we can now do is contrast the human and zombie
scientist’s access to ‘being’ the chunk of ideal matter represented by
equation (a).
<<<< FIGURE 2 DELETED >>>>
Firstly we look at the human scientist shown in figure 2. Let us depict
the correlated behaviour of the objects mapped into the brain of the human
scientist as follows:
hN = REGH( P( S( T(C1(.), C2(.)) ) ) (b)
Hypothesis hN is the human scientist’s formulation in lieu of tN. This
has been done by the innate process REGH(.) which extracts regularities
from the operation of the brain subsystem P(.), the phenomenality
generator. This has been fed by sensory measurements S(.) which resulted
from impinging environmental impact T(.) which originated from the objects
C1(.) and C2(.). Now we look at what brain subprocess P(.) human scientist
C(.) must have to have in order that:
tN = hN (c)
or, substituting (a) and (b) in (c):
REGI(fN( C1(.), C2(.) )) = REGH( P( S( T(C1(.), C2(.)) ) ) (d)
What this is telling us is that regardless of the regularity extractor
REG, the net result is that ‘observation’ fN(.) is being performed by
P(S(T(.))). This means that within P(.), in order that the same regularity
be accessible:
fN( C1(.), C2(.) ) = P( S( T(C1(.), C2(.))) (e)
To see what this means first consider that we know for sure that human
scientists can access laws of nature. We have done it for centuries. Human
regularity extractor REGH(.) works. Our goal is not to contest this
capability and we can assume that the benchmark regularity extractor
REGI(.) is at least as capable and therefore we can assume they are equal:
REGI(.) = REGH(.) (f)
Next note we also no that human scientist C(.) has phenomenality [P(.)].
The phenomenal representation provided by [P(.)] does not have to be
accurate. It merely has to be repeatable. This means that if the
measurement is of temperature, there is no need for the brain material
B(.) to get hot or cold. It merely means that whatever phenomenal
representation is constructed that varies with temperature, it has to
consistently, systematically vary with the real temperature as delivered
by S(.) in depiction of C1(.) and C2(.). Let us assume that brain B(.)
creates proxy phenomena C’1(.) and C’2(.). to represent C1(.) and C2(.)
respectively. If our human scientist is to function to enable access to
our law of nature then equation (e) must have the form such that REG(.)
will extract tN:
P( S( T(C1(.), C2(.))) = fN( C’1(.), C’2(.) ) (g)
Only when equation (g) is satisfied is regularity tN available to the
brain involved. If the form of the left hand side does anything else, the
regularity in it will not be tN. As a result [P(S(T(C1(.))))] and
[P(S(T(C2(.))))] correlate exactly like objects C1(.) and C2(.) do.
Impinging S(T(.)) is used to construct P(.) within B(.), which is (via
mysterious mechanism of the ‘hard problem’) behaving systematically as
C1(.) and C2(.) are behaving. This phenomenal representation [P(.)] is
experienced by C(.). The mysterious mechanism is used to ensure that the
brain process P(.) is constrained to that end. Without that mechanism and
constraint P(.) could not be constructed by B(.). The difference between
the external phenomena C1(.) and C2(.) and the phenomenal representation
C’1(.) and C’2(.) is merely a systematic error which is correlated out of
the equations by the act of contrasting phenomenon with phenomenon
(equivalent to test and control).
The fact that we don’t know what the exact physics is does not matter. It
does tell us, however, that somehow P(.) performs an inverse mapping from
S(T(.)) back to something sufficiently similar to C1(.) and C2(.) to
betray tN to the human scientist. The net effect is that the scientist has
a depiction of C1(.) and C2(.) that is independent of that provided by
S(.). This is achieved through the use of a-priori knowledge of the
external world acquired genetically and used to create a literal
phenomenal depiction of the external world within which can be expressed
the correlative behaviours of the phenomena external to the human
scientist.
Things are very different for the zombie scientist. Zombie scientist Z(.)
has a different brain BZ(.) with no capacity to create P(.). Zombie
scientist Z(.) has some form of regularity extractor REGZ(.) which it
applies solely to S(.). The zombie has identical T(.) is impinging on
identical sensory systems S(.). The zombie equivalent to equation (b) is:
hN = REGZ( S( T(C1(.), C2(.)) ) ) (h)
This is all that the zombie has. This places an entirely different demand
on equation (e) as follows:
fN( C1(.), C2(.) ) = S( T(C1(.), C2(.)) (i)
In order that the zombie brain BZ(.) ends up configured with access to tN
through the zombie’s REGZ(.) regularity extractor, S(T(.)) has to behave
like fN(.). There are an infinite number of hN that present the same S(.)
sensory feeds and an infinite number of different configurations of the
external world that generate the same T(.). In order that hN be somewhere
near tN it has to be known already. No unambiguous mental phenomena that
repeatably and directly reflects the correlative behaviour of C1(.) and
C2(.) is available. All zombie Z(.) has is S(.) to work with.
Zombie S(.) is thus fundamentally prevented from any awareness of C1(.)
and C2(.). The zombie can make an infinite number of hypotheses hN and
could only ever accidentally be able to get any of them to converge on the
actual generalisation predictive of C1(.) and C2(.) in any systematic way.
Even if that happened the zombie could never know it. Indeed the very
presence of C1(.) and C2(.) is completely absent from Z(.). No science at
all is possible except for perhaps noting that certain parts of the data
stream S(.) correlate with certain other parts of the data stream S(.).
Indeed the regularity extractor REGZ(.) can only extract such regularities
from S(.). The originating causality is completely hidden from the zombie.
This correlation’s relationship with C1(.) and C2(.), and therefore
generalisation tN, is completely out of reach of the zombie. There is no
way for the zombie to contextualise any sensory data with respect to the
external world without an a-priori model which mapped all sensory feeds
into something that presented REGZ(.) something sufficient to find the
natural law being sought. That model is not available and even if it was
it would have to be pre-programmed with all potential novelty and how to
adapt current beliefs to new beliefs. This too means knowing everything
a-priori and leaves the zombie in the same position.
Having reached this point we can now generalise the argument to the
behaviour in respect of novelty. Let us say that completely different
behaviour in the external world occurs and that it is as a result of
objects C3(.) and C4(.) never before encountered. Because the humans
scientist has a phenomenal representation of the external world, the
novelty is available for the regularity extractor REGH(.) to use. The
zombie only has S(.) to apply to REGZ(.). The extent to which the novelty
is visible is dependent on the difference C3(.) and C4(.) present to S(.),
which is far removed from C3(.) and C4(.). Hence zombies can’t do science
and conversely phenomenal consciousness is necessary for science.
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Received on Tue Nov 21 2006 - 01:12:05 PST