From: Anders Sandberg (asa@nada.kth.se)
Date: Wed Aug 06 2003 - 13:13:05 MDT
On Wed, Aug 06, 2003 at 11:01:17AM -0700, Robbie Lindauer wrote:
> What kind of medium
> would support the interference-less communication of spin-spin
> coupled-pairs over long distances will have to be left to better
> physicists than me. Perhaps someone who gets a free pass could jump in?
Spin interactions are electromagnetic, so you get the usual 1/r^2 drop
in strength. The problem is that you get a thermal noise level kT, so
the range scales as 1/sqrt(kT) - it needs to be extremely cold to get a
good range.
> Then on the client nodes you'd use something like pre-executed
> instructions (assuming that the computers you build would be faster
> than the communication medium) where you execute all the possible (or
> likely) scenarios "virtually" until you know which scenario is the
> actual one, commit once confirmation is received and move on. This
> would allow relatively efficient communication method - only send the
> confirmed instruction set's signature rather than sending the whole
> thing.
I wonder how it feels to be uploaded on such a system :-)
> I don't see this particular problem as technically less tractable than
> actually creating a replica of a personality in any computer AT ALL.
Not really, and you are essentially (ignoring the spin coupling part
which is likely tricky hardware) scaling up an ordinary cluster
architecture. Some problems with long latencies, but nothing unusual. I
would likely go with optic communications instead, although having
reversible communication (Robin has an old paper about it, very
creative!) would be neat.
> I do see that it's likely to be very expensive and organizationally
> getting enough people together to agree that it's a good enough idea
> that they could dedicate three or four generations worth of lives to
> building such a thing sounds like the a genuinely intractable problem.
Use it for porn first. Seriously. Maybe computer games too. While
optimal solutions melt the heart of engineers (and people like me with
an engineering mindset), to get something built soon and creatively it
better give people what they want. The www was a success thanks to
showing pictures rather than being a clever solution. Once people have
funded the start of the M-brain to process their porn, spam, games and
backup mindstates, then we can build the useful stuff on top of it.
> Storage would have to be standard, I'm only proposing a communication
> mechanism. The problem is how to keep the nodes in sync. If there
> is a moore's law of networking speed, then we can expect with Gigabit
> wireless over sattelite TODAY, we can expect multi-terrabyte wireless
> over stellar distances within the next 100 years or so.
Such laws only work up to physical limits (although they nicely enough
do sneak around them quite often). There are problems with long-range
communications. Here is the relevant part of my paper (in LaTeX
notation):
\subsection{Bandwidth}
\begin{quote}
There is an old network saying: Bandwidth problems can be cured with
money. Latency problems are harder because the speed of light is
fixed. You can't bribe God. -- David Clark
\end{quote}
Unfortunately, the amount of information that can be sent over an
information channel is limited. According to the Nyquist theorem, the
highest signal rate that can be carried over a channel with bandwidth
$W$ Hz is $C = 2W$ bits/second. By using multilevel signaling $C = 2W
\log_2 M$, where $M$ is the number of discrete signal levels, but the
more levels in the signal, the more noise-sensitive it
becomes. Furthermore, forcing a physical quantity into one of $2^k$
possible ranges seems to be $2^k$ as hard as forcing it into one of
two ranges, rather than just $k$ times as hard \cite{Bennett94}. In
the following we will assume binary signals through the channel.
Using higher and higher frequencies of the electromagnetic
spectrum extremely high signal rates can be sent in a directional
manner, for example using lasers. Unfortunately there are some
problems involved with extremely high frequencies due to pair
production: in the presence of another particle or a field, the
gamma-ray photon may split up into pairs of electrons and
positrons. This occurs at a frequency of
\begin{equation}\nu = {2 m_e c^2 \over h}\end{equation}
at a bandwidth of $2 \nu \approx 4.9\cdot 10^{20}$ bit/s. Although
this does not necessarily imply a limit on the bandwidth, it implies a
growing source of noise. And since the energies of individual quanta
become higher, the number of quanta per Watt signal-strength decreases,
leading to increasing noise (see below).
Also, there is an upper limit to the rate of information that can be
sent using electromagnetic radiation for a given average energy
\cite{Caves94, Lachmann99}:
\begin{equation}
C=\left(\frac{512\pi^4}{1215h^3c^2}\frac{A_tA_r}{d^2}E^3\right)^{1/4}
\end{equation}
where $A_t$ and $A_r$ are the areas of the the transmitter and
receiver respectively, $d$ their distance and $E$ the power of the
transmitter. For a transmitter and receiver one square meter each one
meter apart and with a 1 J/s energy budget the information rate is
$1.61\cdot 10^{21}$ bits per second. The rate scales as $E^{3/4}$. The
optimal spectrum turns out to correspond to blackbody radiation, but
if the receiver can only detect the energy and timing of arriving
photons the spectrum instead corresponds to the spectrum of black
bodies in a one-dimensional world and the information rate becomes
\begin{equation}
C=\left(\frac{4\pi^2}{3h}E\right)^{1/2}
\end{equation}
which is independent of transmitter and receiver area and
distance. For an 1 J/s energy budget the maximum information rate
becomes $2.03\cdot 10^{17}$.
One obvious way to circumvent this problem is to send information
encoded in small pieces of matter at high speed. The energy
requirements are much larger when lightspeed is approached, so the
energy efficiency
\begin{equation}
\eta = {C \over P} = \frac{km}{(\gamma -1) mc^2}
= \frac{k}{c^2} {\sqrt{1-v^2/c^2} \over {1-\sqrt{1-v^2/c^2}}}
\end{equation}
(where $P$ is the energy used to accelerate the matter, $k$ is the
number of bits per kilogram and $v$ is the final speed) decreases
towards zero. On the other hand, the efficiency for very low speeds is
high, but is balanced by the longer delays.
As always, Bekenstein's bound introduces a constraint on information
flow. The message channel can be viewed as a chain of regions of size
$R$ containing energy $E$, in which information flows from one to the
next in time $R/c$ (assuming light-speed transmission). This gives a
bandwidth limitation of
\begin{equation}
C \leq \left ({2 \pi c \over \hbar \ln 2} \right) {R E \over (R /c)} =
\left ({\
2 \pi \over \hbar \ln 2} \right) E
\end{equation}
or around $9\cdot10^{34}$ bit/(s J).
Regardless of the amount of energy used in transmitting information,
an additional limit is the Planck bandwidth
\begin{equation}W = 2 \sqrt{c^5/hG} = 2\cdot 10^{43} {\rm
bit/s}\end{equation}
At this bandwidth, quantum gravity becomes important and the
wavelength of individual quanta becomes less than their
Schwartzchild-radius.
It should be noted that the above limits apply to single channels; by
using several noninteracting channels the information transmission
can be increased further.
\subsection{Noise}
\label{sec:noise}
In reality, the channel capacity is somewhat lower due to noise.
Shannon demonstrated that the maximal channel capacity (also
called the error-free capacity) in the presence of noise is
\begin{equation}C= W \log_2 (1+ {S \over N})\end{equation}
where $S$ is the signal power and $N$ the noise power. Shannon also
proved that if the information rate is lower than the error-free
capacity, then it is possible to use a suitable coding to completely
avoid errors. If energy dissipation is no problem, then noise can be
ignored. Otherwise, the bandwidth will at least grow as the logarithm
of the power used.
Noise leads to the problem that energy has to be expended in
sending the information. In a noiseless channel information can be
sent without dissipation \cite{Landauer94}, but the minimum energy per
unit of information required to transmit information over a channel
with effective noise temperature $T$ satisfies the inequality
\begin{equation}\frac{E}{I}\geq kT \label{eq:levitin}\end{equation}
as shown by \cite{Levitin98}. The dissipation will be $E(T)$ J, where
$E(T)$ is the minimum possible energy for the system with a given
entropy; not all energy used in the information channel will be lost.
For extremely dense and high-bandwith systems energy dissipation from
communication will likely play an important role, a role that cannot
easily be circumvented with reversible computing. The exact amount of
communications used is however very architecture dependent, ranging
from nearly none in passive repositories of information to $R^6$ in
3D-structures where every node communicates with every other node.
-- ----------------------------------------------------------------------- Anders Sandberg Towards Ascension! asa@nada.kth.se http://www.nada.kth.se/~asa/ GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y
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