RE: Seely's Views 2

From: Glenn Morton <glennmorton@entouch.net>
Date: Sat Sep 04 2004 - 14:44:34 EDT

I want to add something to my reply to George. This is from Shannon:

        “Suppose there are two possible symbols 0 and 1, and we are
transmitting at a rate of 1000 symbols per second with probabiltiies
p0=p1=1/2. Thus our source is producing information at the rate of 1000
bits per second. During transmission the noise introduces errors so
that, on the average, 1 in 100 is received incorrectly (a 0 as a 1 or 1
as a 0). What is the rate of transmission of information? Certainly
less than 1000 bits per second since about 1% of the received symbols
are incorrect. Our first impulse might be to say the rate is 990 bits
per second, merely subtracting the expected number of errors. This is
not satisfactory since it fails to take into account hte recipient’s
lack of knowledge of where the errors occur. We may carry it to an
extreme case and suppose the noise so great that the received symbols
are entirely independent of the transmitted symbols. The probability of
recieving 1 is whatever was transmittd and similarly for 0. Then aobut
half of the received symbols are correct due to chance alone, and we
would be giving the system credit for transmitting 500 bits per second
while actually no information is being transmitted at all.” C. E.
Shannon, " A Mathematical theory of Communication" The Bell System
Technical Journal, 27(1948):3:379-423, p. 20 at
http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf

Shannon goes on to calculate that there is only 919 bits per second
transmission.

Now, consider that what the person receiving the message is trying to
do. He is trying to determine the truth of the transmission. He is
trying to determine that when he gets a 1, a 1 was really transmitted.
Similarly he is trying to determine if, when he gets a 0, a 0 was really
transmitted. This is exactly the place that we are placed when God
decides to send 1's and 0's to us in the
God-to-human-communication-system. We are trying to determine if the
statement we received (and understood, interpreted etc) was really what
God true or really false. Depending upon what probability we apply to
our ability to interpret the message properly is the amount of
transmission actually taking place. If we can only get it right 50% of
the time, we would actually have zero transmission from God because we
can't give credit to the transmission which is in reality due to getting
it right by pure chance. Now lets paraphrase Shannon:

        Suppose there are two possible cases for a Biblical passage,
true or false, and we are transmitting at a rate of 1000 passages per
second with probabiltiies p0=p1=1/2. Thus our source is producing
information at the rate of 1000 bits per second. During transmission the
interpretation, exegesis etc, all introduce errors so that, on the
average, 1 in 100 passages is perceived incorrectly (a false statement
as a true statement or a true statement as a false statement). What is
the rate of transmission of information? Certainly less than 1000 bits
per second since about 1% of the received passages are perceived
incorrectly. Our first impulse might be to say the rate is 990 passages
per second, merely subtracting the expected number of errors. This is
not satisfactory since it fails to take into account the recipient’s
lack of knowledge of where the errors occur. We may carry it to an
extreme case and suppose the problems of interpretation and exegesis is
so great that the perceived truth of the passages are entirely
independent of the transmitted truth values. The probability of
perceiving a passage to be true is whatever was the original truth
value and similarly for false statements. Then abut half of the received
passages are interpreted correctly due to chance alone, and we would be
giving the system credit for transmitting 500 passages per second while
actually no information is being transmitted at all.

This theorem is HIGHLY applicable to the question at hand. It represents
exactly what is happening when we let God send us false statements as he
accommodates himself to falsehood.
Received on Sat Sep 4 14:56:42 2004

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