Rapid approximations of antilogs might be used with a trial and error method to make calculated guesses of a function that combines logs and original scalar (integration?) values. But the thing I am thinking about is that it might represent another class of compression methods that can be crudely associated with (crudely effective) compression operations. It would be very crude but it might illuminate a problem that is (if I am not mistaken) an essential issue in discrete computational mathematics. Jim Bromer
On Tue, Jun 25, 2019 at 2:09 PM Jim Bromer <jimbro...@gmail.com> wrote: > 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 <jimbro...@gmail.com> 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 <br...@adaptroninc.com> >> 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-M821862fb5d8b0db2ffbe9b31 Delivery options: https://agi.topicbox.com/groups/agi/subscription
