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<nettime> The New Computer Science
Alan Shapiro on Tue, 4 Aug 2009 15:19:06 +0200 (CEST)


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<nettime> The New Computer Science


Dear nettime,

Choreograph.net just published the essay "A Proposal for Developing Quantum
Computing in Software", by Alan N. Shapiro and Alexis Clancy (see link 
below).
This is an essay on the new computer science, which is based on new 
mathematics.

I am sending you one-fourth of the text to publish on nettime.
If you decide to publish it (i hope so), please include the link to the
full text at Choreograph.net.

Best regards,
Alan N. Shapiro

"A Proposal for Developing Quantum Computing in Software" published here:
http://www.choreograph.net/




A Proposal for Developing Quantum Computing in Software

by Alan N. Shapiro and Alexis Clancy

[We] believe that the invention of a new computer science, one more powerful 
than that which presently exists, is possible; a more powerful computer 
science that often goes by the name of Artificial Intelligence. Shapiro 
Technologies will go beyond the digital or binary computing paradigm that 
has persisted since the seminal work of the Second World War generation of 
information theorists such as Alan Turing, John von Neumann, Norbert Wiener, 
and Claude Shannon, so as to achieve quantum computing.

A measurement of superpositions yields only one value, and at the same time 
destroys all the others. Computer scientists working on quantum computers 
therefore rely heavily on the Fourier transform, a mathematical operation 
that transforms one function of a real variable into another, called the 
frequency domain representation of the first function, as the hypothesized 
way to solve the problem. The quantum Fourier transform is primarily thought 
of as being implemented in hardware. A hypothetical quantum computing device 
would have so-called 'reversible logic gates' which continuously allow 
sequences of reversible decompositions into mathematical unitary matrices.

The goal of quantum computing has been clearly and explicitly defined by 
computer scientists, but the mathematics of how to implement qubits and 
superposition states does not yet exist. It should be noted right away that 
most efforts to realize quantum computing are, in my view, too one-sidedly 
hardware-centric.

A crucial characteristic of quantum mechanics known as entanglement occurs 
under certain experimental conditions. Subatomic particles become 
'inextricably linked' in such a way that a change to one of them is 
instantly 'reflected in its counterpart', no matter how physically separated 
they are. Quantum theory postulates a superposition of states that 
destabilizes the intuitive sensorial notion of spatial separation. Entangled 
particles transcend space and remoteness. They belong to a 'shared' system 
that acts as a single entity. The distance that divides the particles no 
longer plays any influencing role that would lead them to be regarded as 
having distinct identities. Once the entanglement state is established, the 
subatomic duo stays forever bonded. The two particles will always have 
either precisely opposing or 'elegantly complementing' relative values of 
key quantum properties such as polarization direction, regardless of how far 
apart they travel from one another.

Quantum mechanical phenomena, such as superposition and entanglement, are 
made use of to perform operations on what are called quantum bits, or 
qubits. Instead of the classical binary or digital bit, which has the 
discrete value of 0 or 1, there is a qubit, which may have a third state, an 
in-between-state, the momentary value of which is determined by the 
superposition of the state of many other bits in the system.

Entanglement and superpositioning enable this third state, which can be 
cultivated to correspond with the anticipated choice space of the 'user'.

Third Space mechanics: I consider a model to be a dynamic series of frames. 
In modeling a universe, I consider two sets. First, the set F of everything 
that I know. Second, the set D of everything that I do not know. Something 
can either be known to me or unknown to me. It cannot be both. ["_F_eicte" 
is the Irish word for "seen." _D_ofhiecte is the Irish word for "unseen."]

The set F of everything that I know is characterised by collapsed wave form 
Kroneker Delta functions which are finite, bounded and measured. [A Kroneker 
Delta function is a function whose value is one at a unique instance, zero 
everywhere else. It best describes the collapse of a waveform on 
measurement, the wave collapsing to an absolute negation of probability at a 
certain point on this measurement.]

The set D of everything that I do not know is characterised by Schrödinger 
type equations, spacewise infinite and unbounded. However, the perimeter of 
the set F of everything that I know presents a problem, as a point on this 
perimeter exists in both spaces F and D [Imagine someone standing on the 
border of Belgium and The Netherlands - essentially, they are standing in 
both countries at the same time]. This contradicts the first Rule. I correct 
this model by introducing a small cleft about the perimeter, small yet big 
enough to exist. Epsilon small. I call this cleft the Epsilon Cleft. This is 
the Third Space.

Locally and superficially, the dimensionality of F strictly does not go 
beyond 2D, and it is Euclidean. The dimensionality of D is a function of 
time; as time progresses, symmetry breaks [i.e the character of an absolute 
law dictating the character of D is no longer a given. See here] and as many 
dimensions as are needed to patch the model are used. Ignoring the first 
term, the sequence (as stated previously) is 4, 11, 26, 57. The Epsilon 
Cleft is the source of these dimensions. My assertion that symmetry will 
always break (as long as there is time) dictates that the Epsilon Cleft will 
have an inexhaustible supply of dimensions. [This assertion is taken as a 
direct inference of Gödel's Incompleteness Theorems.] It is therefore 
countably infinite. Adopting this attitude towards a model renders the 
'problem' of innumerable infinites not a problem, but rather an actual 
contributor to an overall dynamic and evolving model.

I like to view spaces like the Epsilon Cleft as a "novelty" space. I find 
them to be analogous to the "No Mind" structure referred to in the Samurai 
Creed ("I have no sword. I make No Mind my sword.") and the characteristic 
consciousness produced by Samadhi practices of Buddhist and Hindu Yogic 
meditation; I place my faith in the Epsilon Cleft to provide a space for 
novelty to emerge. In this case, we design the solution space such that the 
novelty that emerges is Artificial Life.

In a Riemann type geometry, a conic represents a pinch of some sort. An 
unmolested bounded space can be taken to be a sphere but some stress on the 
system will render it not so - the most basic morphing will be 
hyperbolically conical. I state gravity to be a constraint simply due to its 
universality with respect to binding a system. With respect to separating 
the time and space factors, I feel that, as we are dealing with a spacetime 
metric, the mutation function is a coupled bivariable function. It is almost 
a rule of thumb that nature will not use a simple linear function to do 
anything - a simple non-linear function is generally the case. The geometry 
can be taken to be a quantum geometry, but I believe that most of what we 
experience has its origin in these kinds of spaces. I feel that the solution 
space metric we will design should embody these qualities and also be 
breathable (my term) and elastic - a mathematical weave as opposed to a 
mathematical covering (1). I am inspired by Goethe's quote: Search nothing 
beyond the phenomena, they themselves are the theory.

Where the challenge lies is in accessing a Schrödinger waveform to "play" 
with. It may be of use to draw on a conjecture that I developed regarding 
Schrödinger's Equations and Parametric Normal Distributions. The question I 
pose is this: Do statistics imitate life, or does life imitate statistics? 
The conjecture is based on the meditation that, because Gauss' rigorous 
definition of the Normal Distribution [the ubiquitous "Bell Curve" (because 
it looks like a bell) seen in most statistical models, particularly in 
models whose elements have the possibility to chose their state] predated 
the development of Quantum Theory, the results of experimentation and 
thought experiments were mathematically retrofitted into Gauss' model and 
taken to be a system of "statistical aggregates." However, it is my view 
that Gauss' Normal Distribution is a trans-dimensional fractal, mimicking in 
form and behaviour its quantum origins on a macro scale.

We want incompleteness. Some methodologies exist in electronic engineering 
where a least element is applied to create a mesh for the mathematical space 
used for examining given problems. But this has little to do with Gödel's 
incompleteness - it is just a method that works. Where the novelty in our 
proposed methodology lies is in the assertion that the "gaps" left in a 
given frame due to a Möbius inflection are the physical manifestation of 
incompleteness. This is a significant breakthrough, and it is the real way 
forward for Artificial Intelligence.

What we will practice is the strategy of reversibility - overturn the 
negatively connoted perception of limit into a positive opportunity. 
Incompleteness will be a positive program for growing embodiment and 
vitality. For the first time, computer programming (Java) will be extended 
from classical combinatorial logic to the programming of the real conditions 
for emergence.

Quantum physics was never philosophically understood by its practitioners, 
who opted to just use it, and subsequently developed practical statistical 
methods for doing so. No trans-disciplinary knowledge there. So far, all 
that the physicists and mathematicians have done are "clever tricks." Even 
the quantum teleportation experiment has to use the "clever trick" of the 
joint Bell-state analysis or measurement of a third particle that is 
independent of the entangled pair.

The way to take measurements on both sides of a created universe, of the 
model and its phantom, to access all of the quantum information that is 
going on in the system, is to have a safe, protected space in between where 
one is allowed to be, prior to 'becoming (measurable).' First, we will have 
a portion that conforms to the definition of a universal computing device 
made by Turing in "On Computable Numbers," the q-state, the third possible 
state of the qubit, as a statistical aggregate of all the other states that 
we are interested in (for a particular systems design). That is no problem. 
Second, we will have a portion that goes beyond Turing's definition. Along 
these lines, we want to perceive quantum states of musical resonance which 
are going on in the system in real-time, not just Normal Distribution stuff 
that existing computer science and mathematics have been able to handle.

Here is the answer to the riddle of quantum physics: not measure, but 
perceive. And an expansion of consciousness supports an expanded perception. 
Quantum behaviour is a reality. Physicists thought that they could not 
observe or measure this reality without destroying the information therein. 
But they conceptualized the methodology of observation conventionally. The 
space from which one can observe the reality of quantum behaviour without 
destroying the information therein is also a reality, a fact of nature. We 
do not have to invent this space, we only have to perceive it. This space of 
non-destructive observation really exists, just as quantum behaviour really 
exists, and we will get it working in software. To perceive this space, we 
have to change our consciousness. That's all that we have to do! We have to 
recognize as being scientific some ways of perceiving that belong to other 
traditions that Western science has so far small-mindedly regarded as 
non-scientific. This expanded perceiving includes creative mathematics, the 
deconstruction of classical spacetime mechanics, Buddhist and Hinduist 
meditation/ontologies, Aboriginal-sacred-mystical-expanded consciousness 
thinking, and Continental semiotics/grammatology.




NOTES

1 - In mathematics, a Metric Space is a set where a specific concept of 
distance between elements of the set is defined and implemented. 
Three-dimensional Euclidean space - a way of thinking about space that 
belongs to the Western metaphysical 'construction of reality' as it was 
originated by the Ancient Greek thinkers - corresponds to our 'intuitive 
understanding' of space. Another example of Western metaphysics is the 
Aristotelian classifiying logic of "A is true or B is true," the limits of 
which as an intelligent system of logic are nowadays showing more and more. 
The geometric properties of the Metric Space depend on the Metric chosen. By 
conceptualizing a different Metric, interesting Non-Euclidean Geometries can 
be constructed, for example, those used in the Einsteinian theory of general 
relativity. Metric Spaces are Topological Spaces, and there is a continuous 
function between Metric Spaces (small changes in input result in small 
changes in output). 


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