I think Newton's method of finding a root could provide another class of compression systems. With a variance of the function itself, I think the range of possible systems could be expanded in interesting ways. I don't know if that could be useful. I am really looking for something that can be used to simplify complicated (and complex) ordering functions.
On Tue, Jun 25, 2019 at 8:20 AM Jim Bromer <[email protected]> wrote: > Brett, > Steve has been talking about something similar. I understand the value of > being able to add and subtract rates or ratios as a substitute for > multiplication and division but I am wondering if this might be used to > alleviate fundamental problems in comparing discrete states. I also might > be able to use something like that in my idea of a mathematical index. When > using log values to represent ratios you are losing information (like the > actual numbers of activations and inhibitions) so it is a major compression > technique which compresses both the data and the mathematical function that > uses the data. So I might use various ratios (of probability for example) > to derive an evaluation of a 'conceptual index'. There are certain > mathematical series which can be expressed as relatively simple functions. > But the functions combine addition and multiplication so the division > between the two methods becomes an obstacle to the employment of them to > resolve important computational problems. There are mathematical work > arounds but they become so complicated that it does not look like ti would > be effective from an amateur's point of view. I just had an interesting > thought. You can use functions of varying ratios as a compression method. > Or, since I envision my (conjectured) mathematical conceptual index as > needing to use different 'recipes' of ratios between different kinds of > conceptual evaluations, it might be very useful. Thanks for mentioning this > idea. > Jim Bromer > > > On Mon, Jun 24, 2019 at 8:45 AM Brett N Martensen <[email protected]> > wrote: > >> What you are discussing is neural coding mechanisms. As you are aware >> spiking approaches use spike timing and spiking rates as one idea. I have >> another idea. A neuron fires as a result of the sum of the number of >> exciting synaptic connections minus the number of inhibitor connections >> exceeding a threshold. If the number of synaptic connections from a single >> source neuron is the log of a value then the neuron fires when a given >> ratio of values is recognized. So just the synaptic connections from two >> source neurons is sufficient for a target neuron to fire. One source uses >> excitation connections and the other uses inhibition connections. This is >> based on Log(A/B) = Log(A) - Log(B). It converts ratios into subtraction >> which is what you get when you sum the number of exciting and inhibiting >> synapses. I think one of the reasons few people use this idea is that >> spikes are easily measured but counting the number of synaptic connections >> is practically impossible without microscopic observation. >> *Artificial General Intelligence List <https://agi.topicbox.com/latest>* >> / AGI / see discussions <https://agi.topicbox.com/groups/agi> + >> participants <https://agi.topicbox.com/groups/agi/members> + delivery >> options <https://agi.topicbox.com/groups/agi/subscription> Permalink >> <https://agi.topicbox.com/groups/agi/T395236743964cb4b-M81b3979cf01d86a924588f90> >> ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T395236743964cb4b-M4a237c91ac005a642126d8c3 Delivery options: https://agi.topicbox.com/groups/agi/subscription
