# Estimates of the range of a brain computer system

2001-04-15

The calculations below have not been checked with anyone or any source. Therefore I can't guarantee that the estimates are reasonable. It is likely that the analysis overestimates the performance. In other words do take the estimates with a grain of salt and view this document as some kind of starting point.

SI units are assumed below unless otherwise stated
N receiver noise power per unit bandwith
Kb=1.38·10-23
Sn signal to noise ratio
Ps power scattered from the source per unit bandwith
B bandwith
R bit transfer rate per unit bandwith (=roughly the power needed to transfer 1 Bit of information per unit time
see more details below)

I intensity of controlling rf field
f frequency or rf field
r distance to the satellite
pi=3.14
D size of receiver antenna (diameter)
A effective scattering crossection of the transponder
u micron=length unit=0.001 mm
Kr fraction of the scattered power reaching the receiver antenna
Sn signal to noise ratio

Relations:
N=KbT, neglecting external noise sources
Ps·Kr=Sn·N
A=Ps/I
Kr=(D/4r)2 assuming isotropic scattering
(When I calculated the numbers below I had a slightly different numerical factor in this expression for Kr. Therefore there will be a slight discrepancy if you check my numbers below.)
R = log2(1 + Sn)

Example [T=3K, Sn=3, r=600 km, D=0.8m]
=>
Kr=1.4·10-13,
R=2 (bits/sec per unit bandwith)
Ps =9·10-10 (W/unit bandwidth)
The effective crossection of the transponder needs some discussion. In order to improve the performance, it's conceivable that the tiny object, once anchored up on the right spot, might extend or flip open a few extensions, improving both the scattering efficiency as well as the directional properties. It seems likely that an isotropic radiator is to be preferred, ie no dead angles in the scattered radiation pattern.

The effective crossection A of the transponder is obtained from the ratio of the scattered power Ps to the incoming intensity I. Under ideal conditions, A may be very large, the upper limit being the size of the wavelength, ie even when the scattering system is much smaller. In the case under discussion the crossection is probably never larger than the physical size. Since the information extracted from the brain will be represented by some kind of modulation the real crossection will be smaller than the simple scattering crossection. Here however it is assumed that the crossection is roughly equal to the physical size, meaning that we overestimate the performance (by at least a factor of 2).
Example: A=10u2=1·10-11 => I=9·10-3(W/cm2unit bandwidth)
9 mW/cm2 to transfer 2 Bits/s ~5(mW/cm2per bit/s)
For the entire skull the power would be 1 W/bit/s
That latter information may be missunderstood. It means that an rf power of 1W directed unto the skull would allow each transponder to transfer 1 bit/s ie the total transfer from the brain would be multiplied by the number of transponders These numbers show that satellites are not the likely place where the receivers are located. However by changing Kr to 0.05 corresponding to the immediate vicinity of the person we get (assuming that the detector noise level is unchanged) 3·10-12 W/bit/s for the entire skull, and we're in business.
(Like I said before that number is the power directed unto the skull that enables each transponder to transfer 1 bit/s and the total bitrate grows with the number of transponders. )
In order to get a reliable communication channel it seems probable that the radiowaves used would be some kind of pulsed broadband spectrum where several different frequencies carry information. (Here we will not consider how such a spectrum would modify the analysis) This means the transponder would be a highly nontrivial component although not necessarily in the form of complex electronic circuitry (there isn't much room for that). In principle biomolecules are a kind of multichannel oscillators. I won't speculate on how its done but with huge research budgets one might expect some small wonders.
I beleive nerve signals contain information in such a form that it is suited for datacompression before it is turned over to the transponder.
Lets say we are monitoring a nerve signal carrying information from sense impressions. Typical reaction times are slower than 0.1 s. And lets assume we want to resolve 10 different situations. Then the needed bitrate for the information would be less than 7 bits/s per nerve fibre monitored. In addition it is necessary to send unique identification codes for the transponder as well as for the particular nerve signal. However under favorable conditions that part wouldn't have to be sent every time and therefore the added bandwidth from the 'identification tags' might not decrease the performance unduly.
This crude analysis totally neglects the possibility of using information from higher levels of brain function. Such information might make it possible to communicate important information like thoughts with a much smaller bitrate. 17 bits of information suffices to resolve 100000 different thoughts (including one for 'unidentifed') As more and more information is stored in the external databases more and more intelligent information may be communicated even in a very small bandwith.
Perhaps certain simple codes are being stored by the brain computer system in the redundant parts of the brain and every time a certain thought occurs there are correllating signals in the parts of the brain where the codes are stored and those correllating signals then give rise to a corresponding digital message handled by the transponder.
I mean that those codes would be something more conveniently handled and transferred by the brain computer system than the natural correllations associated with the thought in question.
Initially one should expect that the person is being very closely monitored and a lot of effort is exerted to maintain a high capacity communication. This seems to match the reports from some victims. If something goes wrong during this initial phase, those in charge of the experiment probably fear that they might cause very serious harm to the person. Something worse than the unworthy types of harassments often described. For instance if nothing turns out as expected there might be all sorts of catastrophic consequences like stroke or epilepsy or even other phenomena that could never happen naturally. In this initial phase the experimentors need to have information from external observers to compare with the brain computerdata for gradually improving the fit between model and reality. The totally absurd types of round the clock surveillance experiences of some victims seem to make more sense in this context. And due to the secrecy, those who make up the surveillance team need to be told some false story, that the person is very dangerous or very bad and needs that kind of treatment. Even the very absurd types of paranoia scenarios when somebody walks along with the subject on a different floor seems to have some kind of rationale. On the same time as it is deniable and therefore cannot be easily proven, it also provides brain patterns corresponding to the subjects 3 dimensional orientation. It's very unethical but on the same time those who perform the experiment know whats going on relative to the person and due to the deliberately arranged absurdity of the situation, the experimentor can be pretty sure about what the person is thinking, something that facilitates the fit of the experimental data to the model. Likewise the deceptive activities, creating false sounds making the person beleive the neighbours are after him also seem to make some sense, since the experimentor will know that his model is working if he can fool the subject. Hence despite appearances, some of the absurdity in such operations make sense scientifically, and not only because they want to study a person under conditions of psychological terror but also because they want to be sure about what the subject is thinking and thats a lot easier when they force the subject to experience unpleasant things. In no way am I denying that there are also many cases of totally meaningless psychological or physical torture and cruelty. The technology is boundless in application.
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Anyway we have argued that, at least in principle, one can handle a very large number of independent brain signals with a moderate rf power. As the distance r to the receiver is increased the performance goes down by 1/r2 As stated earlier the rf power is assumed to be distributed over a broad bandwith. Further I will make the added assumption that the external rf field contains complementary parts which together with the rest forms a seemingly random spectrum for anyone who doesn't know what part of the spectrum actually contains information. This is already a lot of detail and since I am only making guesses I won't go any further. The general idea is to make it hard to find out whether there is any communication going on, and also difficult to jam the communication without jamming other ordinary rf-communications.
Still editing.
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