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"THE NOW SYMBOL"
Andrey Makushkin
toAndrey(at)yahoo.com
July 22, 2017
Abstract
In the context of Artificial Intelligence, there exists a question of how symbols get their meaning called "Symbol Grounding".[1] The problem of symbol grounding can be solved by the NOW symbol. The meaning of the NOW symbol is defined for all objects and observers. It is the only symbol needed to describe observation of the environment. The NOW symbol brings concept of time into the learning system. It can be used to reason about the nature of time. It can also be used to reason about symbolic and connectionist systems. Thinking about learning systems in terms of the NOW symbol gets rid of all measurement units.
The Problem
Reasoning about observing the real world requires concepts such as time, event, state, object and observer used in physics to describe the information transfer in the real world. Assume, an observer is any object that changes its state or generates events as a result of detecting an event. An observer could be a sensor, an actuator, a neuron or a rock. After all a CCD sensor is made of silica. Rock's state changes when it absorbs light.
Values are measures of an object's state from an absolute reference point such as zero. The reference point and scale usually have nothing to do with the object whos properties are measured. They are qualities of an observer. Values can also measure a change in an object's state or the rate of change. In reality an observer cannot directly measure the state of an object such as its color or temperature. It can only observe events. [REFERENCES?] A photon arriving at the retina, hair deflecting in a cochlea, tactile input, molecule locking into a receptor in the nose, they are all events occuring in the sensor's environment. When we are looking at observations expressed in terms of values we are frequently looking at the number of events per unit of time. Ironically Quantification, a concept that has to give meaning to observation is the reason observations lose their grounding.[2] Belief that one can model observation as a stochastic process comes from Digital Signal Processing (DSP). In DSP random variables such as amplitude, frequency, phase which define the observed stochastic process are defined apriori. In learning finding random variables, sometimes called features, is one of the goals. What is the difference between 20 and 68? None because 20 degrees Celsius is 68 degrees Fahrenheit. Values are meaningless without units.
Desire to get rid of all units and blend all sensory domains might lead to realization that time is the only unit needed to express all inputs. This is easily achieved in artificial systems. Some analog to digital converters (ADCs) measure how much time it takes for an electric charge to decay measuring voltage from a sensor in terms of time. If all your sensors produce analog electric signals and this type of ADC is used, all your sensory perceptions are represented in terms of time at some point in the system. However, a more general primitive than time is needed. If we model an observer as a function, one can argue that even if it is a function of time, an observer without state (memory) does not have a concept of time.
Symbols are different than values since they are not associated with units. Observers accepting multiple types of symbols make determination of the event source or its type or its magnitude. When these symbols are fed to a learning system they expose the symbol grounding problem.
The reverse, when output is meaningless is also possible. In "The Hitchhikers Guide to Galaxy" a giant computer gives an answer to "the ultimate question of life, the universe and everything" as forty two warning that it lacks meaning because it is not a question.
The Solution
The NOW symbol is an abstract symbol that can help us describe interactions with the environment and communications among parts of a learning system. The NOW symbol is defined as the instance in time at which an external event is detected by an observer. A sensor detecting a change in the environment or an actuator detecting a command to move. Any signal change that meets an observer's criteria can cause the NOW symbol reception. The transfer of the symbol takes place at the exact time when an observer detects an event. The NOW symbol can be expressed in terms of an observer's local time. It could be implemented as a construct "if a than f(t)" where f() implements the observer's process, t is the time of the function call and a is the condition of detecting a change in the environment. Which can be looked at as a binary classifier. In this example t is the smallest quanta of information yet since time is continuous its resolution is limited only by an observer's precision. Formally, the NOW symbol can be defined as the time of an event in a point process on the real time line.[4] The advantage of using a point process is that a single random variable describing the frequency of the events is defined apriori.
Introduction of the NOW symbol changes a classic model of sampling the world where each observer always receives a value that varies in time. In the new model the number of observers detecting an event (receiving the NOW symbol) varies in time but the symbol they receive is always the NOW symbol. An observer generates its own events to communicate with other observers. It does not pass the received NOW symbol to another observer directly. This NOW symbol is meaningless to other observers.
The NOW symbol does not carry the information about the type of the event or its magnitude. Detecting an event does not generate any values. Multiple events are not perceived by an individual observer as related to one another or related to objects in the environment. Events occur as a result of observing a change in the environment (state of the world) or caused by sensor recalibration. For example shifting attention while sensing a joint position without moving.[REFERENCES?]
An adavantage of expressing information in terms of events is since there are no quantities and no units stimula from different domains is processed as stimula from one domain. Using the NOW symbol allows looking at processing from a single neuron's perspective as opposed to concentrating on neural coding as a global mechanism.
Whereas sensors translate events into the NOW symbols, actuators translate the NOW symbols into actions. Every voluntary answer your brain gives to any question is expressed in terms of the NOW symbol because it involves muscle movement.[3] A muscle fiber only needs to know if it has to contract right NOW. Biology dictates that the only correct question is "when should I twitch that muscle fiber?" and the answer is always now. Now is also the best answer because all information available before now is taken into account.
Taking embodyment into account, it can be assumed the number of observers and actuators in a learning system changes slowly over time. Individual observers change the way they detect the changes. Observers can detect events generated by other observers. Biological NNs have evolved to sense the environment in terms of the NOW symbol. To understand how the NOW symbol transfer takes place in biological neural networks (NNs) each neuron has to be viewed as an observer. In addition, each synapse becomes an individual observer. Each synapse might or might not observe an event depending on the stimuli. The strength of artificial neural networks lies in the fact that they force the designer to present inputs to the learning system in terms of the grounded NOW symbols. If a point process is used as an underlying model, each neuron can perform frequency analysis as a learning mechanism.
Ability to share information using a predefined set of symbols vs learning from the real world have been treated as two separate domains because an agreed upon symbol seemed to be impossible. Having an agreed upon symbol allows us to treat sensing and acting in the environment as communicating with the environment. The NOW grounded symbol has meaning for every observer since the existence of the observer implies it exists now. Any process affecting that observer exists only right now. Now is a point in time which defines which events have affected the current state of an observer.
References:
[1] https://en.wikipedia.org/wiki/Symbol_grounding_problem
[2] https://en.wikipedia.org/wiki/Quantification_(science)
[3] https://www.ted.com/talks/daniel_wolpert_the_real_reason_for_brains
[4] https://en.wikipedia.org/wiki/Point_process