Artist Statement
Teeth Series
9/23/08
Teeth are sets. They adhere to certain basic qualities that define them as teeth. They work
together with a common purpose. No tooth is independent. In working with teeth visually, I am
looking at the basic qualities that define them: white, hard and square. This is a relevant idea for
many areas of mathematics. It is breaking down the object to its fundamental elements and evaluating them; saying that if the fundamentals come down to just white, square and hard, then can we get the same results by replacing those things with other white, square and hard things. Experimentation must occur to discover the breaking point or discovery of the true basic elements: i.e. how far you can break down components with out loosing the original meaning.
There is a human tendency to want to categorize. In order to do this we must consciously or
subconsciously consider what the basic elements are in order to make accurate categories. There is an effect from things being visually ordered; we can suddenly see at a glance what would have taken hours of study to see. For example in a pile of clothes once organized you can see if you are out of socks or not, where as in a pile you would have had to dig for a while before coming to that conclusion. In areas of complication this is a commonly used tool to gain more understanding about what is going on. This is actually the foundation of mathematics. We need to have tools to be able to order things in a way such that we can understand what would
otherwise be too vast to tackle. This is a beautiful concept and can be a difficult thing, which is why we have so many areas of high level mathematics.
In abstract math you learn about sets of numbers and how if sets are created such that the
numbers interact in a certain desired way then they can be understood. These sets with this high level of functionality get a special name called groups. In a group the elements (i.e. numbers) in the group must all have the same fundamental properties. In fact if there are two groups with the same fundamental qualities, then you can relate the two groups and consider them equal. This is called an isomorphism (iso from ‘same’ and morph from ‘shape’). This is a very powerful concept in making headway into understanding more complicated schemes. This concept does not stop at mathematics. If we are trying to work through any kind of problem we have to first understand the basic things that create the problem in order to arrive at a solution. We can then relate certain problems to each other and apply our solution from the original problem to the other problems with out having to work through the whole problem again. So you can see how this is such a powerful tool for problem solving!
So we ask: What are the basic elements? Can we change all the other properties without changing the
original meaning? Given the basic elements can we derive all other properties? This series is an
exploration of the derivations of the basic qualities.
Teeth Series
9/23/08
Teeth are sets. They adhere to certain basic qualities that define them as teeth. They work
together with a common purpose. No tooth is independent. In working with teeth visually, I am
looking at the basic qualities that define them: white, hard and square. This is a relevant idea for
many areas of mathematics. It is breaking down the object to its fundamental elements and evaluating them; saying that if the fundamentals come down to just white, square and hard, then can we get the same results by replacing those things with other white, square and hard things. Experimentation must occur to discover the breaking point or discovery of the true basic elements: i.e. how far you can break down components with out loosing the original meaning.
There is a human tendency to want to categorize. In order to do this we must consciously or
subconsciously consider what the basic elements are in order to make accurate categories. There is an effect from things being visually ordered; we can suddenly see at a glance what would have taken hours of study to see. For example in a pile of clothes once organized you can see if you are out of socks or not, where as in a pile you would have had to dig for a while before coming to that conclusion. In areas of complication this is a commonly used tool to gain more understanding about what is going on. This is actually the foundation of mathematics. We need to have tools to be able to order things in a way such that we can understand what would
otherwise be too vast to tackle. This is a beautiful concept and can be a difficult thing, which is why we have so many areas of high level mathematics.
In abstract math you learn about sets of numbers and how if sets are created such that the
numbers interact in a certain desired way then they can be understood. These sets with this high level of functionality get a special name called groups. In a group the elements (i.e. numbers) in the group must all have the same fundamental properties. In fact if there are two groups with the same fundamental qualities, then you can relate the two groups and consider them equal. This is called an isomorphism (iso from ‘same’ and morph from ‘shape’). This is a very powerful concept in making headway into understanding more complicated schemes. This concept does not stop at mathematics. If we are trying to work through any kind of problem we have to first understand the basic things that create the problem in order to arrive at a solution. We can then relate certain problems to each other and apply our solution from the original problem to the other problems with out having to work through the whole problem again. So you can see how this is such a powerful tool for problem solving!
So we ask: What are the basic elements? Can we change all the other properties without changing the
original meaning? Given the basic elements can we derive all other properties? This series is an
exploration of the derivations of the basic qualities.
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