Humble opinion about God and science

For some reason many physicists in the past and present such as Einstein and Hawking used the term God when they wanted to describe something essential and fundamental such as the laws of physics or the Big Bang theory. For most people this was an indication of their religiosity. However, anybody who knows the context of those words can tell that truth is different. Here is an article explaining this issue.

My personal point of view is that science does not require God by definition and not because science can prove that God does not exist. Defining science as the rational understanding of nature based on fundamental laws (and axioms), the acknowledgement of the existence of God would contradict this premise. Using God to explain something in science would be equivalent to admit an irrational element in the theory. In other words, admitting something that is not based on fundamental laws or axioms.

However, I think there is still the inconsistent possibility to put God outside science as the something beyond the laws of physics and axioms. Some would place God as the creator of the laws of physics and axioms. I do not see any consistent and rational way to put God as the explanation of absolutely anything. Having said that, I do not consider myself as completely consistent and rational being and I do not think anybody was, is or will ever be, so, here it lies a window for the endless debate for the existence of God.

Will we ever find a rational and consistent explanation for our consciousness and existence? Something tells me that the most likely answer is NOT.

Inverse Tomography

A few years ago I had the pleasure to attend Pedro Goldman's presentation (Argentinian scientist) about his research in inverse tomography and applications to the calculation of the optimal dosage of radiation for radiotherapy.

Fast Optimization or the Radiation Therapy of Tumors -the Impossible Possible


Sitting down on my chair I would not expect that this was going to be one of the most shocking and interesting presentations I ever attended.

This research field is mathematically interesting and extremely important for medical physics.

Computational Law

I did not know about this this research field until my last trip to Beijing China where I met Set Chandler, who develops his programs in Mathematica

http://www.wolfram.com/products/mathematica/portraits/sethchandler/

The general idea is to develop models as response of the implementation of the laws. The idea is to minimize the subjectivity in today's approach.

A much more ambitious project is to analyse the self consistency of the laws and their level of complexity. The complexity does not only depend on the document's length but also in how intricate is the relation with itself and other laws.

Videos created in Mathematica

I just learned about a video channel for videos created in Mathematica.

http://vimeo.com/channels/mathematica

Medical Imaging

Medical Imaging is today a very active multidisciplinary research field where differential geometry, high performance computing  and diverse mathematics meet together.

In my trip to China I had the opportunity to see some of the latests developments at professor Bart M. ter Haar Romeny's group at the University of Eindhoven in Holland.

Some of the lastest thesis in his group that can be donwloaded are

• E.M. Franken, Enhancement of Crossing Elongated Structures in Images, PhD. Thesis, 2008, Technische Universiteit Eindhoven. Advisors: B.M. ter Haar Romenij, R. Duits

• M.A.van Almsick, Context Models of Lines and Contours, PhD. Thesis, 2007, Technische Universiteit Eindhoven. Advisors: B.M. ter Haar Romeny, L.M.J. Florack

• E. Balmashnova, Scale-Euclidean Invariant Object Retrieval, PhD. Thesis, 2007, Technische Universiteit Eindhoven.Advisors: B.M. ter Haar Romenij,co-advisor: L.M.J. Florack

• F.M.W. Kanters, Towards Object Based Image Editing, PhD. Thesis, 2007, TU/e. Advisors: B.M. ter Haar Romenij, L.M.J. Florack

• B. Platel, Exploring the Deep Structure of Images, PhD. Thesis, 2007, Technische Universiteit Eindhoven. Advisors: B.M. ter Haar Romenij, Co-advisor: L.M.J. Florack

Additionally, professor Romeny has a book entitled


Front-End Vision and Multi-Scale Image Analysis: Multi-scale Computer Vision Theory and Applications, written in Mathematica

Online version

The complete package can be found at
http://extras.springer.com/2003/978-1-4020-1507-6

If you are not afraid of modestly advanced mathematics and want something really applied, try this.

The canonical coset decomposition of unitary matrices through Householder transformations

My paper describing the connection between the Householder decomposition of and the canonical coset parametrization of unitary operators was published today in the Journal of Mathematical Physics

J. Math. Phys. 51, 082101 (2010)

http://arxiv.org/abs/1008.2477

This parametrization is very useful for calculating the parameters that uniquely characterises a given unitary operator U(N). I show that instead of solving a complicated systems of non-linear equations one can perform very stable and efficient Householder transformations.  Right now I am working on some practical applications based on that result.

Independent Component Analysis

I was already familiar with the Principal component analysis, which is a method for finding a linear combination of variables such that the possible correlation between them disappears i.e. elimination of the diagonal elements of the covariance matrix. Statistical independence implies the elimination of correlation but the opposite is not necessarily true because there is possible association between the variables on higher orders.  The Independent Component Analysis seems to be the generalization needed to go beyond the simple correlation.

• Bartlett, M.S. and Movellan, J.R. and Sejnowski, T.J., Face recognition by independent component analysis, IEEE Transactions on neural networks,13, pp 1450--1464, 2002

• Hyvarinen, A. and Oja, E. Independent component analysis: a tutorial, Neural Networks, 13, pp 411--430 2000