Sunday, August 29, 2010
Mathematica Link for Excel
Excel Link for Mathematica , what a great product. All the time I have wasted in the past... I was actually using Mathematica without Excel. Unbelievable. Mathematica's Table and Excel's sheets are the perfect marriage. What a combination.  And it works. I am impressed.
Video minidemo Excel Mathematica link
The ExcelLink for Mathematica is a very nice product and works in a way as can be expected as the minidemo below shows. There are of course two potential groups of users of the link: 1) users interfacing with a Mathematica Notebook, 2) users interfacing with an Excel sheet.' The follow minidemo shows the ExcelLink from the perspective of the Mathematica Notebook user.
When done with prerecording this video on my pc I noticed a window with a percentage bar called 'interleaving video' so if I would do this with a mic attached to the PC I could add voice comments, I suppose. Next time, I'll try one.
When done with prerecording this video on my pc I noticed a window with a percentage bar called 'interleaving video' so if I would do this with a mic attached to the PC I could add voice comments, I suppose. Next time, I'll try one.
Saturday, August 28, 2010
Mathematica Link for Excel 3.2
I have a pet problem which I will probably never solve entirely but that's why it is such a pet, that problem, I mean. Through only a few lines of well thought out Mathematica code I can generate a matrix which needs to be further analyzed in, for example, Excel. With Excel 2010's huge dimensions this is finally possible. All I need now is a working interface between Mathematica and Excel. I experimented with it in the past, version 2.x, but that ended in a bunch off AddIn errors.  The installer says 'uninstall' previous versions. Why can't the installer do that for me? RED FLAGs! I better wait until tomorrow. I shouldn't be doing this on a Saturday evening anyway.
FORA.tv Mathematics Video
Just visited FORA.tv for the first time. I was watching a music clip on YouTube when I noticed in the right selection ladder the title: "Do scientists have a sense of humour?" That's basicly how I found FORA.tv. They use the tag "The world is thinking". A search on mathematics resulted in 87 videos. Videos of reasonable length, not the 10min YouTube type. For example:
And much more. Enjoy FORA.tv.
P.S.
Here is the YouTube teaser...
John Barrow: Not Just About the Numbers
An overview of different types of mathematics and its applications. What is mathematics and why does it 'work'? 53min
John Barrow on Codebreaking in Everyday Life
Everything we buy, from books to baked beans, has a product code printed on it. More sophisticated checkdigit codes exist on official documents, bank notes and air tickets. 60min
Wilfred Hodges: The Geometry of Music
Geometers study shapes and how they transform into one other. Musicians create shapes and transform them. 55min
And much more. Enjoy FORA.tv.
P.S.
Here is the YouTube teaser...
Friday, August 27, 2010
ToBlogList
Topics I will/might blog about when time permits.
ToBlogList:
3x+1 problem; past and current influence;
OU 2010; M208/MT365 what is wrong with these courses;
Can't wait to start on MST209;
60 or 90 in 2011;
Must narrow the field of what I will be able to study, i.e.: mandatory topics = B10 upto BSc; Complex analysis; Group Representation Theory; Combinatorics.
What deeply fascinate me: Number Theory, Group Theory  the deep connections between the two;
ToBlogList:
3x+1 problem; past and current influence;
OU 2010; M208/MT365 what is wrong with these courses;
Can't wait to start on MST209;
60 or 90 in 2011;
Must narrow the field of what I will be able to study, i.e.: mandatory topics = B10 upto BSc; Complex analysis; Group Representation Theory; Combinatorics.
What deeply fascinate me: Number Theory, Group Theory  the deep connections between the two;
9 divided by 11 = 3000.
An offtopic post. About building 7. If you know what I mean by building 7 then this post is not for you. Otherwise start by watching the short YTclip in this post. If you dare to confront it, that is. Beware, it might change your life considerably. Don't say I did not warn you! You do not have to watch.  One thing though, it is not your opinion they are after...
Is that all? Yes. And it is already working, I am sure.
Or go straight to the Truth.
Is that all? Yes. And it is already working, I am sure.
Or go straight to the Truth.
Sunday, August 22, 2010
My first 4Dexperiment
What you see are the 3D and 2D projections of the rotation of a tesseract in the Z,W plane in 4D.
Result M208  TMA05
I scored 75. 11/20 on question 6. I used a methoud using indirect symmetries. Works just as well. I had 18 bricks as an answer of course. It is an abstract combinatorial counting problem.
I very much doubt if the person who is tutoring me on M208 really 'owns' the materials or is merely pretending. I suspect the last so a discussion won't work. I haven't got a leg to stand on if I don't score high in the nineties at the exam. Which will be very difficult due to the time constraints anyway.
P.S.
Analysis. The difference between $\mathbf{R}$ and $\mathbf{Q}$ is where mathematics feels more like a creation than an invention. Did mathematics exist before humans populated the earth? Did we discover math or did we create it? This could lead to interesting thought or discussion. Riemann created a function which is continuous but nowhere differentiable. $$f(x)=\begin{cases}\frac{1}{q} \text{ if rational and }x=\frac{p}{q},(p,q)=1\\0 \text{ if irrational}\end{cases}$$
I very much doubt if the person who is tutoring me on M208 really 'owns' the materials or is merely pretending. I suspect the last so a discussion won't work. I haven't got a leg to stand on if I don't score high in the nineties at the exam. Which will be very difficult due to the time constraints anyway.
P.S.
Analysis. The difference between $\mathbf{R}$ and $\mathbf{Q}$ is where mathematics feels more like a creation than an invention. Did mathematics exist before humans populated the earth? Did we discover math or did we create it? This could lead to interesting thought or discussion. Riemann created a function which is continuous but nowhere differentiable. $$f(x)=\begin{cases}\frac{1}{q} \text{ if rational and }x=\frac{p}{q},(p,q)=1\\0 \text{ if irrational}\end{cases}$$
Thursday, August 19, 2010
Sophus Lie  Lie Groups
From the book Groups and Symmetries, From Finite Groups to Lie Groups By Yvette KosmannSchwarzbach ( and translated by Stephanie Frank Singer ).
Once you understand the concept of a 'group' you can hardly imagine that there were days that you didn't understand groups or worse: that you were completely ignorant about them. That's basically how important groups are, they are as fundamental to mathematics as numbers or graphs.  Although Lie Groups aren't part of M208 or courses I planned for next year I am studying them. I am making progress but it's slow. I am no longer in complete darkness but there is a lot of mist.
Tuesday, August 17, 2010
Programming 4D rotations, SO(4).
Just had a ( minor ) cognition. I was trying to figure out a formula for rotating around a 4dimensional line. As will become clear soon I did not make much progress. But let's start from the beginning.
If you follow my blog you might have seen videos of a Mathematica program I wrote. You can select a cube or tetrahedron, then from a list of all the rotationaxes of that polyhedron and rotate the object with a rotation slider control. The rotation is visible as well as a projection of it in 2D.  I wanted to extend this to 4D. So take a 4D polyhedron, i.e. a tesseract. Show the rotationaxes (...) rotate it and show projections in 3D and 2D.  In order to do so I would need 4D rotationformulas, I supposed that they would depend on an axis and an angle just like in 3D.
The 4D space is simply created by adding an ( imaginary ) axis. Points in 4D have four coordinates. Concepts like distance and angle are similar to the defintions for 2D and 3D. In 2D we rotate around a centre of rotation, a point. But extend 2D to 3D and you see that a 2D rotation is actually a 3D rotation around the zaxis. Thinking along these lines there is no such thing as rotating around a line in 4D. In 4D and above we rotate around planes and the six standard rotational planes in 4D are the XY, XZ, YZ, UX, UY and UZ planes.  This makes perfect sense because if you rotate a cube in 3D along one of the standard rotation axes X, Y and Z the equivalent 4D rotations are those in the YZ, XZ and XY planes. The remaining three rotations seem to distort the cube or make it disappear all together, while in 4Dreality the cube would remain fixed of course.
It turns out that the formula for rotation are simple. Setting up a hypercube is not too difficult either. Haven't added it to the program though.
What might prove difficult though is finding ( computable ) data of the symmetry groups of the 4Dpolyhedra.
This website 4D Euclidean Space was very helpful in learning and compiling this data.
If you follow my blog you might have seen videos of a Mathematica program I wrote. You can select a cube or tetrahedron, then from a list of all the rotationaxes of that polyhedron and rotate the object with a rotation slider control. The rotation is visible as well as a projection of it in 2D.  I wanted to extend this to 4D. So take a 4D polyhedron, i.e. a tesseract. Show the rotationaxes (...) rotate it and show projections in 3D and 2D.  In order to do so I would need 4D rotationformulas, I supposed that they would depend on an axis and an angle just like in 3D.
The 4D space is simply created by adding an ( imaginary ) axis. Points in 4D have four coordinates. Concepts like distance and angle are similar to the defintions for 2D and 3D. In 2D we rotate around a centre of rotation, a point. But extend 2D to 3D and you see that a 2D rotation is actually a 3D rotation around the zaxis. Thinking along these lines there is no such thing as rotating around a line in 4D. In 4D and above we rotate around planes and the six standard rotational planes in 4D are the XY, XZ, YZ, UX, UY and UZ planes.  This makes perfect sense because if you rotate a cube in 3D along one of the standard rotation axes X, Y and Z the equivalent 4D rotations are those in the YZ, XZ and XY planes. The remaining three rotations seem to distort the cube or make it disappear all together, while in 4Dreality the cube would remain fixed of course.
It turns out that the formula for rotation are simple. Setting up a hypercube is not too difficult either. Haven't added it to the program though.
What might prove difficult though is finding ( computable ) data of the symmetry groups of the 4Dpolyhedra.
This website 4D Euclidean Space was very helpful in learning and compiling this data.
Sunday, August 15, 2010
Usage of TabView in Mathematica
Creating a tabbed view userinterface is as simple as: TabView[{a>1,b>2}]. A more realistic example is shown in the video below.
Saturday, August 14, 2010
Bookmarks
I have been storing bookmarks for over four years now on Delicious but I have failed to organize them in a way I like. My interests have changed dramatically, I think that I could erase half of the bookmarks that I stored. Anyway, now that Google supports Pages I can tick away 'Developing Personal Website' from my ToDo list and use Blogger instead. For starters, I added a Links page to this site.
Tuesday, August 10, 2010
New Youtube Video
I made a tiny Mathematica program which demonstrates all the 23+1 rotations of the Cube. If you haven't done Group Theory yet: the Cube has four diagonals, which can be permuted in 4! = 24 = 23+1 ways. The 23+1 rotations create just these permutations.  I joined Facebook ( at last ), found an M208 study group but with disappointing little discussion. Here is the video:
Monday, August 9, 2010
Vinay Deolalikar
Vinay Deolalikar ( mathematician working for HP Computers ) claims to have solved one of the $1,000,000 open problems of the Clay Institute: P=NP? I think the P stands for Polynomial Time, which is used in the field of modelling of the computation process itself which goes back to Alan Turing.  My motto is: "Every Problem has a Solution".
Saturday, August 7, 2010
Monday, August 2, 2010
Group Theory  Exercise  Continued
I have been working on the problem that I published last week....
S3
Element  Order  Permutation Sign  Transpositions
()  1  +1  ()
(1,2,3)  3  +1  (1,2)(1,3)
(1,3,2)  3  +1  (1,3)(1,2)
(1,2)  2  1  (1,2)
(1.3)  2  1  (1,3)
(2,3)  2  1  (1,2)
Now take the following subgroup of A5:
()  1  +1  ()
(3,4,5)  3  +1  (3,4)(4,5)
(3,5,4)  3  +1  (3,5)(3,4)
(1,2)(4,5)  2  +1  (1,2)(4,5)
(1,2)(3,4)  2  +1  (1,2)(3,4)
(1,2)(3,5)  2  +1  (1,2)(3,5)
This is a group with S3 structure but conisting entirely of even permutations.
If any group of n elements is a subgroup of A(n+2) it must have an isomorphic copy consisting of all positive permutations.
S3
Element  Order  Permutation Sign  Transpositions
()  1  +1  ()
(1,2,3)  3  +1  (1,2)(1,3)
(1,3,2)  3  +1  (1,3)(1,2)
(1,2)  2  1  (1,2)
(1.3)  2  1  (1,3)
(2,3)  2  1  (1,2)
Now take the following subgroup of A5:
()  1  +1  ()
(3,4,5)  3  +1  (3,4)(4,5)
(3,5,4)  3  +1  (3,5)(3,4)
(1,2)(4,5)  2  +1  (1,2)(4,5)
(1,2)(3,4)  2  +1  (1,2)(3,4)
(1,2)(3,5)  2  +1  (1,2)(3,5)
This is a group with S3 structure but conisting entirely of even permutations.
If any group of n elements is a subgroup of A(n+2) it must have an isomorphic copy consisting of all positive permutations.
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Mathematics: is it the fabric of MEST?
This is my voyage
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To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before
(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)