Digital Trivia

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Writing text messages (SMS) with your computer is a reasonable thing to do (of course this is only true when you have a computer at hand)! The typing is faster when you have a full keyboard and usually the costs are lower when you send text messages over the Internet. Sometimes its even free!

However, I do not know many people doing it. One reason might be, that usually the number of allowed characters is lower and that some advertisement is automatically attached to the message… and who wants to spam his friends? Another reason that stops people from sending text messages with their computer could be the procedure of logging on to a website before writing the message. With this it might even take longer to send the message in the end.

A couple of months ago, I wrote a little widget which helps to make writing text messages easier.

1. Since it is in Dashboard, you will always have fast access to it!
2. It uses your Mac’s AddressBook with auto completion. So you only need to type the first letters of the receivers name!
3. The provider is limited to TerraSIP. They charge 4.9 euro cents per message (worldwide) and have no advertisement

Here are some screenshots:

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Sorry, this entry is only available in Deutsch.

A couple of months ago, I posted a review of Peter Schorer’s proof on my blog. To my delight, I received some competent feedback on this topic by other researchers including Schorer himself. He kindly gave me some in-depth hints and comments on my paper which led to some changes. Thus, a reviewed version is now available and can be downloaded here:

State of the Collatz Problem (englisch) (PDF 188KB)

Please note that this report is written on a paper which is now outdated! A couple of days ago, Peter Schorer told me that a newer (and supposedly simpler) version of his proof is now available which I would like to announce here as well. The latest version of his paper can be downloaded here:
http://www.occampress.com/solutionsubmit2.pdf

Altough a newer version of his proof is available, my report can still be used to get an understanding of the structures and ideas used in Schorers work.

Are you kiddin’? To open a new Safari window just hit CMD+N!

Well, obviously this article is not about how to open a new Safari window from within Safari! Have you ever tried to open a new Safari window when there is already one open? Clicking the Dock icon will only bring the actual window to front. The only other option I know is right-clicking on the Dock icon and choose New Window. This takes some time and soon becomes annoying!

This becomes even more annoying when you use Spaces. Have you ever tried to open a new Safari window in an other space? The intuitive thing is to click the dock icon but this just brings you back to the space where a Safari window is already open. I practically stopped using spaces because of this shortcoming!

Now, finally with Snow Leopard (Mac OS X 10.6) there is a solution! Now it’s possible to define a system wide keyboard shortcut that opens a new Safari window! Here is how, in two simple steps: Read more…

The heart of many kryptosystems lies in the difficulty to find a discrete logarithm. That is, a number x such that w^x is congruent to y mod p, given w, y and p. However, if such factorization of the numerus p is known, the Haskell program presented here solves the discrete logarithm in a reasonable time. (Note that no efficient algorithm  for solving the integer factorization is known (this problem lies in NP)).

Given the factorization, it splits the discrete logarithm problem into smaller sub-problems and solves them using the baby-step giant-step algorithm. Finally, the solutions of the sub-problems are put back together with an implementation of the chinese remainder theorem.

During our practicals, we were given a 512 bit long discrete value of potentiantion and the according factorization into 69 integers. Furthermore, all but two factors were quite small. The program found the missing exponent in a little less than 20 secs on my laptop. Almost all of the time is spent on the baby-step giant-step for the two large factors. Surprisingly, solving the set of simulateous congruences using the chinese remainder theorem is done in no time.

Download:

Haskell file for the discrete logarithm with sample data

Needed modules:

Haskell module for modulus arithmetic

Haskell module for integer arithmetic

UPDATE: A newer version of the paper is available! For more information, see the corresponding post. The link below has also been updated to match the new version.

The Collatz problem, sometimes also referred to as the 3x+1 problem is an unsolved conjecture in mathematics. Lothar Collatz proposed it more than 70 years ago in his student days.

(Wikipedia: http://en.wikipedia.org/wiki/Collatz_conjecture)

Then last year, Peter Schorer published first versions of his paper proposing a proof. As part of my Number Theory studies I wrote a paper that discusses Schorer’s claim.
I posted the paper on my Blog for all those who might be interested in this topic.

You can download it here:

State of the Collatz Problem (PDF 188KB)

Abstract  - We discuss a claimed proof to the Collatz-Conjecture that has been published by Peter Schorer. This is, we explain the basic concepts, terminology and lemmas he uses, as well as the proof itself. After reading this paper the reader should be able to quickly orient herself in Schorer’s original paper. Secondly we discuss and name several points in his work that give reason to critisism and skepticism. A short Haskell-program has been developed along with this paper and can be found in the appendix.

Also a tiny Haskell program printing out a (possibly infinite) so called tuple-set can be found here: collatz.zip (ZIP 4KB)

As you might know, the timestamp option of the date command under Unix prints out the number of seconds since the start of the Unix epoch (1/1/1970).

On friday the 13th 11:31:30 pm, my coevals and myself were contemporary witnesses of a singular event in history. That is when the timestamp turned to 1234567890.

A similar significant event will take place in approximately 273 years.