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22 Mar Common Sense and Thresholds

Finding Thresholds

Threshold Conditions Threshold conditions are boundaries between states, and they exist everywhere, affecting everything. From a computational perspective, thresholds are a valuable tool for limiting the problem space to within manageable limits. In other words, knowing where the edges are can help us computationally color inside the lines.

How could we determine a threshold? Observing, experimenting, bracketing and generalizing! That is, enlist the services of an infinitely powerful computer for one week to see what randomly happens. After one week of exercising infinite power randomly, compare the string generated with all the available literature and find the longest string that has been matched. Then assume that probability limits the matching string length to specified percentage greater serendipity with more time. Extend the assumption to state that the threshold of what is not possible in a week, is some specified percentage of the threshold for a year. Extend the year into decades and centuries, decreasing the fraction by some reasonable percentage with each order of magnitude consistent with the problem space. Then do the experiment for a month, then a year, and bracket or refine the results.

These empirical results do nothing to dispel the random Hamlet theory because randomness may strike at unknown times. The results will, however, give us a good idea of the limits of “law abiding” processes, which are infinitely useful for computational domains.

Understanding Context Cross-Reference
Click on these Links to other posts and glossary/bibliography references

  

Section 5 #23

Fuzzy Logic Icon

 

Table of Context

 

Time Constraints Using this empirical methodology, we might assume that, in the random Hamlet, capricious randomness will be overcome by actual probability before the first scene is half over. Throughout modern science, many theories are built on assumptions that fail to account for some of the critical limiting constraints. Many of the constraints are not known in advance, so this is understandable. One of the most universal constraints is time. Time constrains almost every physical phenomenon, and time constrains people from achieving what they attempt. Methodological failure occurs when the results of the theories are treated as facts before there is adequate experimental evidence to support the equation. Improbability theories are very weak because the math of improbability becomes incalculable quickly for multi-dimensional problems, especially when insufficient attempts to discover hidden constraints and thresholds disable us from differentiating improbability from impossibility.

As we learn, we generalize. One of the important category of things that children learn is lines not to cross: thresholds. This understanding of the difference between good and bad, possible and impossible is fundamental to successful causal reasoning. If we could not use the process of elimination to exclude impossible causes, we would never be able to infer probable causes. Our ability to reason would collapse without thresholds.

Learning Common Sense

Babies learn the difference between flat and sloping when they encounter edges. As perceptions of altitude depth and gravity begin to develop, they are reinforced by the sensation of impact at the end of a fall. The illustration below shows how the characteristics of objects and results of actions correlate to help us build common sense expectations (correct or incorrect) about the real world. As I brought up in the introduction to this blog: “Modern computers lack the ability to innovate when presented with a new situation; more, they lack even the knowledge that we, or they, exist at all. We believe the next epoch in computing systems will arise when we can give machines the capacity for more self-awareness and ‘commonsense’ — the ability to think, learn, and act in the world with the resourcefulness and flexibility exhibited by people” (Singh 2004).

Common sense is one of the most difficult types of knowledge to characterize. We use common sense all day every day. It keeps us from walking down the middle of busy streets. It lets us choose to use a spoon instead of a fork to eat soup. We learn it through perception since it consists of knowledge of observable facts and interrelations between physical objects, including our bodies. Experience is also an essential element of learning common sense: we acquire it by observing results of actions and interactions between objects. We might say that a program has commonsense “if it automatically deduces for itself a sufficiently wide class of immediate consequences of anything that it is told and what it already knows” (McCarthy 1959).

Bald Rodent Safe CrackerPart of common sense is the simple knowledge of how things look and feel. For example, kids learn that…

RODENTS ARE FURRY.

This is common sense. The same kind of knowledge can be much more subjective. It can even be incorrect. For example…

CRIMINALS ARE DANGEROUS.

By classifying criminals carefully, we can find whole classes of criminals who are not dangerous.

Common Sense Domains

When we search for meaningfulness and expressiveness, we are likely to find salience. The furry-rodent example above may seem simplistic because common sense is all that is required, but common sense has consistently been one of the most difficult things to model on computers. In many closed domains of classification, simple logical formulae are wholly adequate for classifying the entire set of data elements and solutions within the domain. Toaster repair, for example, can be reduced to a set of comprehensive rules that will enable a machine-based reasoning system to solve any problem that may arise. Automated manufacture is an important application domain that has been automated through the use of formulae such as the one above.

No Common SenseUnfortunately, when the domain is not closed, there is a major shortcoming in the stoplight model illustrated on the previous post. Each of the constraints are applied directly to the end solution of the problem. Even in closed domains, several layers of intermediate solutions often precede the end solution. Accounting for intermediate solutions incrementally increases the complexity of problem solving. In the medical domain there can be complex interactions, especially those involving causal relations, that increase the complexity of the problem factorially. Furthermore, common sense can be misleading unless you apply more constraints to avoid possible unintended consequences, as they found at Air Force Academy.

My analysis is that communication can be at least as complex as diagnosing and healing, especially when seasoned by subtext, subterfuge and metaphor. Our model for understanding language will rely heavily on fuzzy logic, with threshold constraints, across multiple dimensions.

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