Hilbert Spaces and Nietzsche's genealogy
January 4th 2007 03:02
Hi,
Here we go, after a presentation, a little bit about (meta)physics. In this post i present the core that will guide all ideas that will follow, so take your time to understand it clearly. Before reading it, i strongly advise you to read about these ideas, if you're not familiarized to:
- linear transforms, Hilbert spaces, Fourier transform, Dirac's delta
- Nietzsche's "genealogy" philosophic concept
first of all, as everybody do, i have to explain why the term "physics". I won't spend time explaining physical laws, that's not the point here, but this is the best term to be used in the place that philosophers used to write metaphysics. Since Nietzsche most of the philosophers agree that studying the "meta" part of the physics (i mean soul, spirit, god, and all these things) became completely out of scope, since none of these is what we call "real". So, by "physics" i mean the study of the "real" part of the world, and how do we "beings" interact with it.
I'll start with maths, and how they can be used to describe the "real".
In some engineering fields people have been using the concepts of modeling the interpretation of the world as being a linear transform in a non-orthogonal basis (that means a irreversible transform). It means that the facts that happen in reality are as vectors, that latter are projected into other bases, and "interpretation" is the process of projecting the facts from the "real" base to the "interpreted" base (the "being" base). This processes have normally pretty names like artificial intelligence and neural networks.
Explaining it better: artificial intelligences, when interacting with the "real", collect some information, by using sensors or other data. To get to conclusion of how to react, they take this vector of data and projects this into other base (what means apply a linear transform). This base though is not orthogonal, which means that the information, after being transformed, cannot be untransformed back again. These transformations succeed une après l'autre, reducing the components of the vector. The resulting vector can so be used by the "being" to take conclusions, and thus react.
This is the base of some successful theories, which have their ways of working with it. But mathematically speaking, it's nothing harder than linear transforms. We just have to add some things like the "interpreted" base is always changing, adapting to the environment, etc. The problem is that the vectors in the real world have infinite dimension. This conclusion i get from philosophy.
In Nietzsche's work we have the concept of his "genealogy", that has being exploited by people like Sartre, Camus, Heidegger, etc.. It's tuff to tell you a place in Nietzche's work where he explains it clearly because he is never clear, even though it seems...I think the best reference on this idea would be "Beyond Good and Evil" (ref.289, has a good explanation...). What this idea state is that there's always something deeper inside something we discover, and that the real truth is not reachable by beings. In his work Nietzsche attacks the concepts of what is truth (and why do we search it), and the "facts" that prove something or not.
Another important thing that Nietzsche's philosophy attacks is the existence of "good" and "evil", what he says that are not "real". This is another important point we'll get to later.
So where do these 2 ideas meet?
The intersection is this: the world, or what i'll call from now on the "real", is a space of vectors (which are actually the facts that happen), which have an infinite dimension, like in an Hilbert's space (sorry for the term..). The "beings" though do not have an infinite base inside their "minds", so they are not able to get all the information they have access to and store it. And worse, the base where the "beings" are projecting the vectors of the "real" is not orthogonal, which makes the transform irreversible, and the information untrue.
In the part of the "good" and "evil" thing: these concepts are like the Dirac's delta: they are vectors that are non zero only in one component of them. This is why Nietzsche attacks them, stating that these are things that are not real, just like an engineer will never see a real Dirac's delta in a non-mathematical system.
The main goal of this post is to show the interface of these 2 ideas: they are all about the same thing, but separated in 2 domains that we hardly see touching each other. With the conclusion of the analogy between Hilbert spaces and the "real", we can get to conclusions in many aspects of physics, which we will later apply to ethics (how we should behave in society), and then to "wisdom" (how we should behave to ourselves), following an organisation proposed by french philosopher Luc Ferry.
That's pretty much information for a first post, and i'll get more explanations about it in the next one, before starting the conclusions we can take after it.
Thanks.
Rgs,Uula
Here we go, after a presentation, a little bit about (meta)physics. In this post i present the core that will guide all ideas that will follow, so take your time to understand it clearly. Before reading it, i strongly advise you to read about these ideas, if you're not familiarized to:
- linear transforms, Hilbert spaces, Fourier transform, Dirac's delta
- Nietzsche's "genealogy" philosophic concept
first of all, as everybody do, i have to explain why the term "physics". I won't spend time explaining physical laws, that's not the point here, but this is the best term to be used in the place that philosophers used to write metaphysics. Since Nietzsche most of the philosophers agree that studying the "meta" part of the physics (i mean soul, spirit, god, and all these things) became completely out of scope, since none of these is what we call "real". So, by "physics" i mean the study of the "real" part of the world, and how do we "beings" interact with it.
I'll start with maths, and how they can be used to describe the "real".
In some engineering fields people have been using the concepts of modeling the interpretation of the world as being a linear transform in a non-orthogonal basis (that means a irreversible transform). It means that the facts that happen in reality are as vectors, that latter are projected into other bases, and "interpretation" is the process of projecting the facts from the "real" base to the "interpreted" base (the "being" base). This processes have normally pretty names like artificial intelligence and neural networks.
Explaining it better: artificial intelligences, when interacting with the "real", collect some information, by using sensors or other data. To get to conclusion of how to react, they take this vector of data and projects this into other base (what means apply a linear transform). This base though is not orthogonal, which means that the information, after being transformed, cannot be untransformed back again. These transformations succeed une après l'autre, reducing the components of the vector. The resulting vector can so be used by the "being" to take conclusions, and thus react.
This is the base of some successful theories, which have their ways of working with it. But mathematically speaking, it's nothing harder than linear transforms. We just have to add some things like the "interpreted" base is always changing, adapting to the environment, etc. The problem is that the vectors in the real world have infinite dimension. This conclusion i get from philosophy.
In Nietzsche's work we have the concept of his "genealogy", that has being exploited by people like Sartre, Camus, Heidegger, etc.. It's tuff to tell you a place in Nietzche's work where he explains it clearly because he is never clear, even though it seems...I think the best reference on this idea would be "Beyond Good and Evil" (ref.289, has a good explanation...). What this idea state is that there's always something deeper inside something we discover, and that the real truth is not reachable by beings. In his work Nietzsche attacks the concepts of what is truth (and why do we search it), and the "facts" that prove something or not.
Another important thing that Nietzsche's philosophy attacks is the existence of "good" and "evil", what he says that are not "real". This is another important point we'll get to later.
So where do these 2 ideas meet?
The intersection is this: the world, or what i'll call from now on the "real", is a space of vectors (which are actually the facts that happen), which have an infinite dimension, like in an Hilbert's space (sorry for the term..). The "beings" though do not have an infinite base inside their "minds", so they are not able to get all the information they have access to and store it. And worse, the base where the "beings" are projecting the vectors of the "real" is not orthogonal, which makes the transform irreversible, and the information untrue.
In the part of the "good" and "evil" thing: these concepts are like the Dirac's delta: they are vectors that are non zero only in one component of them. This is why Nietzsche attacks them, stating that these are things that are not real, just like an engineer will never see a real Dirac's delta in a non-mathematical system.
The main goal of this post is to show the interface of these 2 ideas: they are all about the same thing, but separated in 2 domains that we hardly see touching each other. With the conclusion of the analogy between Hilbert spaces and the "real", we can get to conclusions in many aspects of physics, which we will later apply to ethics (how we should behave in society), and then to "wisdom" (how we should behave to ourselves), following an organisation proposed by french philosopher Luc Ferry.
That's pretty much information for a first post, and i'll get more explanations about it in the next one, before starting the conclusions we can take after it.
Thanks.
Rgs,Uula
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