Defective Fuzzy Operators, Fuzzy Defective Operators

So what are defective fuzzy operators? They are the typical fuzzy operators, such as union/or intersection/and and complement/not but they don't return crisp fuzzy sets. Instead they return fuzzy fuzzy sets. So the boundaries of your resultant fuzzy set don't match the input fuzzy sets.

This appears to be a new technology. One may say that my model is wrong if the operators return the wrong results. I say that fuzzy operators as they typical are thought of are defective, and need to be replaced with more realistic, real world operators.

Perhaps there are fractal fuzzy operators or fuzzy fractal operators. And don't forget faulty fuzzy operators and fuzzy faulty operators

Something to think about.

Fractional and Transcendental Derivatives

So, if you have a fractal hierarchy that bends, its motion can be described with fractional derivatives. But what is a transcendental derivative? That seems very interesting, and I am pursuing information on it.

Continuous Hierarchy from a geographical perspective

We have artificial political boundaries that form from bivalent thinking. But the world is geographical. There aren't really lines where my property, city, county, state, or country begins or ends. Of course, you shouldn't trespass or steal--but that's a social idea, not a geographical idea. You would let your neighbor stand on your driveway to talk to you, but if he was just standing there all day long, you might be concerned for him.

As a youngster, I thought about what it meant to have a house that was on a state or country line. Would that mean you would have to pay taxes in both states? Neither state? The state of your choice? Whatever side of the house you spent the most time in?

Continuous Hierarchy, a new definition

So I don't think that set membership should be a quality of continuous hierarchy. Instead continuous hierarchy should be more like exploration. You wander around a "space" and find elements, without any set boundaries. There is no membership in sets. Sets are abstractions which don't belong in continuous hierarchy. What there is is relativity. You place elements relative to each other, not on coordinates like in a set or not in a set. The location of each element is uncertain, as well as the velocity.

Now how does this relate to speech? A sentence is a landscape of information.

Multidimensional Electricity

I know that direct current electricity runs from positive to negative. But what if there were more poles to electricity? There are 4 forces. Can we leverage the forces in these to generate other types of electricity? Maybe we can remotely control electricity? Alternating current can be thought of as a 2 dimensional wave. What about an ocean of electricity, a 3 dimensional wave? Or even more untapped dimensions. Light might be thought of as an ocean of electricity. How many dimensions are there to light? Complex numbers were perhaps invented to get rid of discontinuities between surfaces in space. What about the discontinuities between stars in space? Could some complex number system allow us to travel between stars?

Editor's Note: After viewing a lecture on Physics, I realize that there is a field of electricity.

Subjective Computer Science

Well, computer science is really a subjective science...here's why. The people who write the requirements have their own view of what the product will be. The people who design the product have their own view of what the product will be. The people who implement the design have their own view of what the product will be. The people who test the implementation have their own view of what the product will be. The people who put the product into production have their own view of what the product will be. The technical writers have their own view of what the product will be. The technical and sales support team has their own view of what the product will be. And the customer has their own view of what the software should do. Ideally, the software should do what the customer wants. But each customer has different wants, thus there are conflicting requirements, conflicting designs, conflicting implementations, conflicting testing, conflicting deployments, conflicting documentation, and conflicting technical support.

All these views and conflicts are what are so interesting in computer science. So instead of trying to stomp out different views, or conquer the world, we should embrace conflicting ideas. Here are some examples. Everyone has a different set of search terms they want to look for. Everyone has a different set of applications they use for work and entertainment. Diversity is good. Choice is good.

Now, how do we make diversity and choice possible? One approach would be to set some standards for people to adhere to. This stifles creativity, and sets the stage for software that doesn't please the customer. One way to make diversity and choice possible is to implement a pluggable interface. This is form of a standard. But there can be different pluggable interfaces for different products. Wouldn't it be nice if you could use the same plugin in different products? Say you had a plugin that worked in ImageJ. Wouldn't it be nice to be able to use the same plugin in Adobe Photoshop and the GIMP? Wouldn't it be nice to use the same interface builder format for Xcode, Eclipse, Visual Studio and NetBeans? What if I could write XML applications that would work in Safari, Firefox, and IE? It's the same fucking problem all the time. Everyone wants to reinvent the wheel. Do I use CLI or Babel?

So what is the solution to all this? At a fundamental level, we have to accept that there is diversity. There is uncertainty in all numbers. There is uncertainty in the elements in a set. There is uncertainty in the order of elements in a set.

Uncertainty and Continuous Hierarchy

Uncertainty may be thought of as a form of continuous hierarchy. You aren't certain of the levels within the hierarchy, the nodes within the hierarchy, and where the arcs are connected within the hierarchy.

For elements, you aren't certain exactly what the element's value is.
For sets, you aren't exactly certain what the elements are.
For both, you aren't sure whether it's an element or a set, or both.
For order, you aren't certain of the order of the elements.

Thus uncertainty is a form of continuous hierarchy.