[CG] Re: Pragmatic Semiotic Information

Pragmatic Semiotic Information • 9 • https://inquiryintoinquiry.com/2024/03/16/pragmatic-semiotic-information-9/ Information Recapped — Reflection on the inverse relation between uncertainty and information led us to define the “information capacity” of a communication channel as the “average uncertainty reduction on receiving a sign”, taking the acronym “AURORAS” as a reminder of the definition. To see how channel capacity is computed in a concrete case let's return to the scene of uncertainty shown in Figure 5. Pragmatic Semiotic Information • Figure 5 • https://inquiryintoinquiry.files.wordpress.com/2024/03/pragmatic-semiotic-i… For the sake of the illustration let's assume we are dealing with the observational type of uncertainty and operating under the descriptive reading of signs, where the reception of a sign says something about what's true of our situation. Then we have the following cases. • On receiving the message “A” the additive measure of uncertainty is reduced from log 5 to log 3, so the net reduction is (log 5 - log 3). • On receiving the message “B” the additive measure of uncertainty is reduced from log 5 to log 2, so the net reduction is (log 5 - log 2). The average uncertainty reduction per sign of the language is computed by taking a “weighted average” of the reductions occurring in the channel, where the weight of each reduction is the number of options or outcomes falling under the associated sign. • The uncertainty reduction (log 5 - log 3) is assigned a weight of 3. • The uncertainty reduction (log 5 - log 2) is assigned a weight of 2. Finally, the weighted average of the two reductions is computed as follows. • (1/5) ∙ [ 3 ∙ (log 5 - log 3) + 2 ∙ (log 5 - log 2) ] Extracting the pattern of calculation yields the following worksheet for computing the capacity of a two‑symbol channel with frequencies partitioned as n = k₁ + k₂. Capacity of a channel {“A”, “B”} bearing the odds of 60 “A” to 40 “B” • https://inquiryintoinquiry.files.wordpress.com/2024/03/channel-capacity-60-… In other words, the capacity of the channel is slightly under 1 bit. That makes intuitive sense in as much as 3 against 2 is a near‑even split of 5 and the measure of the channel capacity, otherwise known as the “entropy”, is especially designed to attain its maximum of 1 bit when a two‑way partition is split 50‑50, that is, when the distribution is “uniform”. Regards, Jon cc: https://www.academia.edu/community/L6Pd9M cc: https://mathstodon.xyz/@Inquiry/112032763420333668