I’m a self learned wiz kid turned Architect. Stared with an Apple IIe, using AppleSoft Basic, ProDos and Begal Basic at age 10. Picked up LPC in college before the Dot Com Explosion. Wrote some Object C in the USAF for one of my instructors. Got a break from a booming computer manufacture testing server software. Left the Boom and went to work for a Dot Com built from the ashes of Sun Micro in CS. Mentoring in Java solidified me as a professional developer. Danced in the light of the sun for 13 years, before turning to the dark side. An evil MVP mentored me in the ways of C# .NET. I have not looked back since.Interests include:~ Windows Presentation Foundation and Silverlight~ Parallel Programming~ Instruction Set Simulation and Visualization~ CPU to GPU code conversion~ Performance Optimizations~ Mathematics and Number Theory~ Domain Specific Languages~ Virtual Machine Design and Optimization~ Graphics Development~ Compiler Theory and Assembler Conversion Methodology~ CUDA, OpenCL, Direct Compute, Quantum MechanicsIEEE Associate Member 2001 - 2010

Look on YouTube. Category theory is used in Linear Algebra and most importantly quantum mechanics. You I suggest the Stanford University Open Course ware on Quantum Mechanics, there is also probability some good Linear Algebra open course wear at Stanford
as well. Quantum Mechanics II Lecture series starts with a good opener on linear algebra, as it pertains to QED. All linear algebra operations are function operations of observable events. It does get much into category theory and complex math, but it is
the 'real' stuff that is observable and that is what the course shows how to design mathematical proofs of. Here is the link to the courses:

Lecture 1 | Modern Physics: Quantum Mechanics (Stanford)

Is this anything like creating a transform on a set [(Location Vector) * (Fule Burn Function)] on a manifold to give you a set of vectors that map to the manifold for any given Vector Location? I made another post on Session 3 of 3, where I am trying to corelate
this to Complex manifold mappings using the vector color intensity map of Complex numbers for a given function: sin(z). Here are com complex mapped visuals to give an example:

Complex Color Map of: z^3 (example)

If I create a specialized pixel shader for your mapped function in 'z' manifold space that transforms your function asserted as a complex color map to a new set of locations for the function, would this be the same as creating a moniod or manoid that has
the correct compisition? After the pixelshader is applied to the manifold, the result set of vecotrs are given as a function transformed into a new vector locaction set. Any point in in the complex map can be reverse trnsformed back to a Real/Imaginary pair
by computing the function of RGBx => RGBy. Am I totally off the compisition beaten path with this?

Wow! This is all great stuff! I have been thinking of this in terms of complex maps, where you take the function of something like sin(z) and map it out using the color map explorer. The interesting thing I have been thinking of is that the map is like
your corridnate system, each point has an RGB value from 0 to 255. Values on the map can be transformed back to a Real and Imaginary pair for a pixel on the map. Well, if you take the map, and use a pixel shader to transform the RGB values you could then
create a pixle shader that transforms the corridanes of your manifold to what ever mapping you like just by supplying the map from RGBx => RGBy. Totally covariant. Nifty thing is you can creat pixel shaders that do all kinds of analysis on the manifold,
like a pixelshader that just modifies all the R values in the map, when you do the on a complex z map it produces some very interesting results. I did this with the sin(z) and then just used a pixelshader in photoshop and watch the map change in real time,
I could instantly see when the value of R being modified caused the polar shift in the map to be inverse sin(z). I will work on a prototype demo in silverlight to show how this actaully works. The code for the complex mapper I found on The Codeproject:
http://www.codeproject.com/KB/recipes/ComplexExplorer.aspx I'm going to integrate this project with an exsisting Silverlight Caculator with graphing:
http://blogs.zibmak.net/ If I can wrap my head around the concept of compisition, I will attempt to create an interface where you can dynamically create a covariant pixelshader for math functions and add them to a moniod?!?!
Just don't know if I have totally wrapped my head around the concept of moniods and the other one?!?! "maniods?" ~err the one that takes the compisition and applies a functor to it, in this case the funcrot would be a pixelshader that does mapping from RGBx
=> RRGBy on a manifold expresed as a complex color map.... Am I totally in another ball park? Or is this in line with what this series is attempting to accomplish?

Today7 the spacks jumped circuits and crosss polinated. See my opst at: http://tinyurl.com/34eqrjv relateds to my unifide thery ofquantium tansidential fluid space mathematics.,

## Comments

## Brian Beckman: The Zen of Stateless State - The State Monad - Part 2

Look on YouTube. Category theory is used in Linear Algebra and most importantly quantum mechanics. You I suggest the Stanford University Open Course ware on Quantum Mechanics, there is also probability some good Linear Algebra open course wear at Stanford as well. Quantum Mechanics II Lecture series starts with a good opener on linear algebra, as it pertains to QED. All linear algebra operations are function operations of observable events. It does get much into category theory and complex math, but it is the 'real' stuff that is observable and that is what the course shows how to design mathematical proofs of. Here is the link to the courses:

Lecture 1 | Modern Physics: Quantum Mechanics (Stanford)

General Link:

http://www.youtube.com/user/StanfordUniversity

Linerar Algerbra:

Lecture 1 | Introduction to Linear Dynamical Systems

~Proto-Bytes

## E2E: Whiteboard Jam Session with Brian Beckman and Greg Meredith - Monads and Coordinate Systems

Is this anything like creating a transform on a set [(Location Vector) * (Fule Burn Function)] on a manifold to give you a set of vectors that map to the manifold for any given Vector Location? I made another post on Session 3 of 3, where I am trying to corelate this to Complex manifold mappings using the vector color intensity map of Complex numbers for a given function: sin(z). Here are com complex mapped visuals to give an example:

Complex Color Map of: z^3 (example)

If I create a specialized pixel shader for your mapped function in 'z' manifold space that transforms your function asserted as a complex color map to a new set of locations for the function, would this be the same as creating a moniod or manoid that has the correct compisition? After the pixelshader is applied to the manifold, the result set of vecotrs are given as a function transformed into a new vector locaction set. Any point in in the complex map can be reverse trnsformed back to a Real/Imaginary pair by computing the function of RGBx => RGBy. Am I totally off the compisition beaten path with this?

## E2E: Brian Beckman and Erik Meijer - Co/Contravariance in Physics and Programming, 3 of n

Wow! This is all great stuff! I have been thinking of this in terms of complex maps, where you take the function of something like sin(z) and map it out using the color map explorer. The interesting thing I have been thinking of is that the map is like your corridnate system, each point has an RGB value from 0 to 255. Values on the map can be transformed back to a Real and Imaginary pair for a pixel on the map. Well, if you take the map, and use a pixel shader to transform the RGB values you could then create a pixle shader that transforms the corridanes of your manifold to what ever mapping you like just by supplying the map from RGBx => RGBy. Totally covariant. Nifty thing is you can creat pixel shaders that do all kinds of analysis on the manifold, like a pixelshader that just modifies all the R values in the map, when you do the on a complex z map it produces some very interesting results. I did this with the sin(z) and then just used a pixelshader in photoshop and watch the map change in real time, I could instantly see when the value of R being modified caused the polar shift in the map to be inverse sin(z). I will work on a prototype demo in silverlight to show how this actaully works. The code for the complex mapper I found on The Codeproject: http://www.codeproject.com/KB/recipes/ComplexExplorer.aspx I'm going to integrate this project with an exsisting Silverlight Caculator with graphing: http://blogs.zibmak.net/ If I can wrap my head around the concept of compisition, I will attempt to create an interface where you can dynamically create a covariant pixelshader for math functions and add them to a moniod?!?! Just don't know if I have totally wrapped my head around the concept of moniods and the other one?!?! "maniods?" ~err the one that takes the compisition and applies a functor to it, in this case the funcrot would be a pixelshader that does mapping from RGBx => RRGBy on a manifold expresed as a complex color map.... Am I totally in another ball park? Or is this in line with what this series is attempting to accomplish?

## C9 Lectures: Dr. Brian Beckman - Covariance and Contravariance in Physics 1 of 1

Today7 the spacks jumped circuits and crosss polinated. See my opst at:

http://tinyurl.com/34eqrjv relateds to my unifide thery ofquantium tansidential fluid space mathematics.,Ptoto-Bytes## Silverlight WritableBitmap Performance Test from Rene Schulte

Nice demo!