Archive

Archive for October, 2010

Mike Cohn on Leading a Self-Organizing Team

October 31st, 2010 No comments

Wednesday 8 December I will be attending a “go home meeting” featuring the Scrum expert Mike Cohn. Really looking forward to it, as Mr. Cohn is one of the big names in this racket.

From his own description:

One of the challenges of agile is coming to grips with the role of leaders and managers of self-organizing teams. Many go to the extreme of refusing to exert any influence on their teams at all. Others retain too much of a command-and-control style. Leading a self-organizing team can be a fine line.

In this session you will learn the proper ways to influence the path taken by a team to solving the problems given to it. You will learn how to become comfortable in this role. You’ll understand why influencing a self-organizing team is neither sneaky nor inappropriate but is necessary.

Categories: Conference Tags: ,

Pythagorean proof

October 26th, 2010 No comments

I recently wrote a blog post on beautiful mathematics. Mathematics can be beautiful or pleasing in many ways, one of them being if the proof is elegant.

Apparently one of the theorems for which the greatest number of proofs exists is the Pythagorean theorem.

The theorem states that

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

or

\displaystyle{a^2 + b^2 = c^2}

One of the more beautiful or elegant proofs is the one below.

File:Pythagorean proof (1).svg

Categories: Writing Tags: ,

Personal Backup Solution

October 24th, 2010 No comments

Just read a nice blog post by @4nd3rs (in Danish) about his considerations about online backups; what to use and local vs. remote backup.

In the following I will try to describe my own setup. It has been a work in progress, but right now I feel it meets the requirements of myself and the family.

As any other modern family we have a number of computers running both Windows and OSX. When we moved into our house, I decided I did not want to run any cables anywhere or rather my wife decided we did not want to do this, so all devices are connected using wireless to the internet and the NAS.

The main storage and backup devices is a Drobo FS with 3 TB of storage. Data Robotics has their own concept of RAID, called BeyondRaid, and having three disks in the NAS enables it to exercise protection for single disk failure. The Mac is using the Drobo for backup via TimeMachine. Apart from shared documents the main content of the Drobo is pictures and music as the device also serves as storage for our Sonos music system. Whatever requirements the Windows machines have for backup, it is handled remotely.

For remote backup we recently moved from using JungleDisk and Amazon S3 to iDrive. For iDrive I have a Pro-account where the Drobo is back up to and each other family member has their own Basic account. The professional account is $5/month for one PC and 150GB. They have a family pack for 5 PCs and 500GB, which is $15/month; I guess we will move here when the need raises.

The main reason from moving away from Amazon was cost. It is dead cheap if you only have a small amount of data, but can get quite expensive if you have a lot, especially to extract the data if required.

We also use DropBox and each of us has an account. Personally I can’t remember when I used an USB stick last. It is just great for “moving” files back and forth, e.g. between work and home, and also for file sharing.

Categories: Miscellaneous Tags:

Playing with LaTeX

October 21st, 2010 No comments

Just learned that the plug-in I use to format \LaTeX has an option that lets you control the size of the formula when using displaystyle. Have to try it.

\displaystyle{f = \frac{1}{2}a_0 + \sum_{n=1}^{\infty}\left\{a_n\cos nt + b_n \sin nt \right\}}

with the coefficients

\displaystyle{a_n = \frac{1}{\pi}\int_{-\pi}^\pi f(t) \cos nt \mbox{dt}, b_n = \frac{1}{\pi}\int_{-\pi}^\pi f(t) \sin nt \mbox{dt}}

Beautiful.

Categories: Writing Tags:

Laying on those kilometers

October 21st, 2010 3 comments

I finally did it. It has been too long, and right now, I am sore as hell.

I am talking about the distance of my run today.

Ever since “loosing” the front ligament in my left knee last December I have had a hard time running more than 10 km (the exception was the 3 x 5 km I did at the DFH relay back in August). Today I did 17.

I am tired and sore, but in the muscles and not the knee(s) which is really, really good. The time was horrible (around 4:45/km on average), but it was good to be out more than an hour.

I hope I can keep this up, with one long stretch, a shorter one and one or two days with intervals each week. 3 times very week would be nice, 4 times great, but going into the dark season I do not have much hope. Will try though :)

Categories: Exercise, Private, Running Tags: ,

Beautiful Mathematics

October 8th, 2010 2 comments

While reading an article on the General Unified Theory, I came across a reference to what the author considered beautiful mathematical equations. It got me thinking: what would I consider beautiful math? I must confess right away, that it has been many years since I have done anything remotely advanced in the area of mathematics and not since my master thesis on the mathematical properties of artificial neural networks – drop me a line if you are unable to fall asleep, and I will send you a copy – have I really done any heavy math.

However, the seed was laid in my mind and during my run early this morning I began to consider if I could actually remember any mathematical equations, beautiful or not.

The first one that came to mind was Archimedes’ Recurrence Formula. Being a diver, I have always had a soft spot for old Archi :)

Let a_n and b_n be the perimeters of the circumscribed and inscribed n-gon and a_{2n} and b_{2n} the perimeters of the circumscribed and inscribed 2n-gon. Then

\displaystyle{a_{2n} = \frac{2a_nb_n}{a_nb_n}, b_{2n} = \sqrt{a_{2n}b_n}, a_\infty = b_\infty}

Of course the cool thing is that the successive application gives the Archimedes algorithm, which can be used to provide successive approximations to \pi.

The next equation that came to my mind was Eulers Formula or Eulers Identity, which states that

\displaystyle{e^{ix} = \cos x + i \sin x}

where i is the imaginary unit. The beautiful equation arises when setting x = \pi,

\displaystyle{e^{i\pi} + 1 = 0}

The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of points in the complex plane such that the corresponding Julia set is connected and not computable.

“The” Mandelbrot set is the set obtained from the quadratic recurrence equation

\displaystyle{z_{n+1} + z_n^2 + C, z_0 = C}

where points C in the complex plane for which the orbit of z_n does not tend to infinity are in the set.

The image below displays the famous and well known Valley of the Sea Horses.

MandelbrotSet

The next one that came to my mind was the Riemann Hypothesis.

The Riemann hypothesis is a deep mathematical conjecture which states that the non-trivial Riemann zeta function zeros, i.e., the values of s other than -2, -4, -6, \ldots such that \zeta(s) = 0 (where \zeta(s) is the Riemann zeta function) all lie on the “critical line” \sigma = \mathbb R [s] = 1/2  (where \mathbb R[s] denotes the real part of s).

The Riemann zeta-function \zeta(s) is the function of a complex variable s initially defined by the following infinite series:

\displaystyle{\zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s}}

The Riemann hypothesis can be stated as:

\displaystyle{\zeta(\alpha + i\beta) = 0, \beta \not= 0 \Rightarrow \alpha = \frac{1}{2}}

One could go on and on, but I will finish off with another of my favorites, namely the Gaussian Integral.

The Gaussian integral, also called the probability integral is the integral of the one-dimensional Gaussian function over (-\infty, \infty)

\displaystyle{\int_{-\infty}^\infty e^{-x^2}dx = \sqrt{\pi}}

Categories: Writing Tags: ,