Friday, May 30, 2008

Will we face a global crisis as a race?

I must admit - I am an optimist. Despite all what is going on in the world lately, and the rather negative forecasts for the future, I believe that "all will be fine". To be precise, I believe that to all the problems we currently face as a race, solutions will be found in time. The reason for this believe is the following line of thought.
As a race, we always had members who tried to solve complex problems - even those problems that are far from the everyday reality. The Ancient Greeks, for example, tried to square the circle. The mathematicians of the present try to prove or disprove the existence of an odd perfect number.
It is hard to say what is the driving force behind those attempt to solve problems, but our present society is build on them. All the technology we use is a result of research - which was often done without any practical reason. While we don't have a solution for a constantly growing number of problems (a lot of which are self caused) , we are finding them one by one. A few days ago microbes that eat plastic were discovered, for example.

The most current problem is an economical one. The price of oil is going up, and the USA dollar is going down. There are many reasons for this - but there are also many solutions. An invention of an alternative fuel source would be an excellent way out of this situation. This may sound a bit too optimistic, but why not? Not so long ago someone discovered a way to make fuel from water. All what was required is to add some (cheap) chemicals to the water and you could use it as you would use ordinary fuel. This person was killed and his discovery died with him.

Another problem that we face is overpopulation. Personally I don't believe that we are in any serious danger because of it. According to the information I have, we already have the necessary technology to produce enough food for about 50 billion people. Waste is still an unsolved problem, but if we already found microbes that eat plastic, we will do fine.
There is also a not so elegant but interesting way to provide us with a large food base - we can eat insects. They breed very fast, and are a good source of protein. See the following video for an example:

Found at: Student Loan Consolidation

As a final note, I think that crisis come and go. The political landscape of the world will likely change greatly in the following decades, but it will be just more of the same...

Tuesday, May 27, 2008

Small scale and slow motion

A lot of research is done with the purpose to make computers faster and to generally improve them. One of the goals is to develop a fast optical computer. The advantages such a computer would have are clear - electricity heats the circuit it moves in, but not light. The problems needed to be solved in order for such a computer to be built are enormous, but surprisingly Nature managed to overcome at least some of them a long time ago - photonic crystals needed for such a computer were recently found in the shimmering, iridescent green scales of a beetle from Brazil. Read this article for the full story.

The reason I am writing about this is that it is an excellent example of an important principle at work. This principle is that all the inventions we made are already present in Nature in some form. It probably sounds a bit strange. But if we will look, we will see that the problems we use technology and science to solve, have a "more" natural solution already. For a simple example, lets look on nuclear fusion. We don't yet have control over it (probably it will happen soon, but not yet) but the problem we are trying to solve with it is a need of heat energy. The heat will be used to produce electricity, but we need to produce heat firstly.The nature has the some problem - in order for the universe to develop somehow, heat is needed. Heat is also needed for production of new, heavier elements. How did nature solve it? Nuclear fusion is exactly what heats stars. This example is cosmological, and it speaks more about properties of matter. Yet there are many more examples. The computer can be viewed as our attempt to recreate the human brain using technology, for example.

It can be argued that seeing such connection is a bit too much, and yet the problems we (as a race) face are in no way unique. And if so, there is good chance to see solutions of them already present in the Nature. But to find such solutions, we will need to look on the small scales.

The reason for this is that when viewed from another angle our world doesn't look the same. In the video below you will see a series of simple actions first in normal speed and then in slow motion. The actions stay the same, but there is a difference. It is well visible in the experiment with balloon and fire. In normal speed it looks like it was burn by the fire, but it looks differently in slow motion.

Friday, May 23, 2008

Burning Bibles

One of my friends sent me a very surprising BBC article today. While it is not surprising to hear about "crimes" committed by the "occupational regime", this article is different. Firstly, unlike other articles about Israel, what is said in it actually took place. Secondly, I have never heard about Jews burning bibles. While the New Testament is a rather unpopular book in the eyes of Orthodox Jews, such act is a strange thing to do.
After reading this article I checked an Israeli news site. It turned out that the BBC article was correct but not especially accurate. The following is a list of details that were either not mentioned or distorted:
1. Missioner activity is forbidden by law in Israel.
2. Burning of religious literature is also a criminal act.
3. Upon discovering this, a journalist filled a complain in the police department against the mayor deputy.
4. The BBC article says that "Messianic Jews complain of institutionalized discrimination and are demanding all those involved be put on trial". There is no mention of this in the Israeli articles I found. I hope it is not true. Such behavior reminds Hamas - first fire a rocket than blame Israel for firing back.
5. The deputy major is an Orthodox Jew. In the photo below he is standing near a pile of burned bibles. 6. It appears that not whole bibles were burned but only The New Testament.
7. The deputy major was acting according to a religious law that called Jews to destroy Christian property if they can do so without bringing harm on themselves. It was not a conflict between missionaries and authorities, but between two religions groups.

Overall, this is a very pitiful incident. It is very clear what that the reasons behind it were. The both sides wanted to please God. And they both committed crimes in the process.

I don't want to talk about the people involved in this incident, but I want to highlight a very worrying trend that surfaces in it. We all know the saying "Where books are burned, people will be burned next". This happened in Nazi Germany. Why did it happen then and why it happened again in a town called Or Ihuda (Light of Judea)?
To answer this question we will have to look on Nazi Germany. Recently I was told that I am wrong in saying that most ordinary Germans didn't want the war to begin. The argument I was presented with, is that if indeed an average German was a peaceful soul than more Jews would be saved. However, this argument ignores one important trait of our society. People prefer to be leaded by other - a large part of our society prefer others to think for them. I have recently read about a study that clearly showed that to direct a random crowd of people all you need is that a five percent of the crowd would know were to go. The same goes for politics. One person is not enough, but there is no need for the supporters of a particular idea to have a majority. They need only a small percent that will support them, and the rest will follow.

Why this happens, and how is this connected to bible burning? The answer is simple - people like to feel good about what they do. We want to feel that our deeds are right. Why do you think the phrase "Got mit uns" (God with us) was used by Nazis? Hitler, just as other before him, gave people confidence. People believed that what he says to do is right and didn't question him. Those who behave this way are similar to sheep. They just follow the herd, all you need to guide them is a few well trained dogs. In this case the dogs are the fear of responsibility for your actions - if instead of following you are going by yourself, all the responsibility is yours and yours only.
For religious leaders it is even simpler. They just say: "Do what I say and you will go to heaven. Disobey me an you will go to Hell." In many occasions it works surprisingly well.

I feel that by burning books people only show their weakness. Instead of showing what is wrong in what they burn or giving other people an option to choose, they prefer to destroy. However, it is a worrying trend.

Wednesday, May 21, 2008

A bit of news

After experiencing a rather unpleasant plan crash, I resolved to study more and to procrastinate less. Gladly I didn't stop on this. I decided to sit in University from 8:00 to 4:00 everyday. The extra hours should be enough for me to do a significant part of my homework during the week. No more doing-it-at-the-weekend mentality.
Overall it went well, although not without surprises. On Monday I came to the library at about 8:20 only to be told, with a rather surprised face, that the library opens at 9:00. That was a pity.. I went to an empty classroom and studied there instead, so not too much time was lost.

In other news, I am getting a lot of traffic to my posts about Linux. I am happy to get any visitors at this point, but it is a bit disappointing to see that while people come to this blog there is no reason for them to return. I will blog about Linux in the future, but it will never be the central theme of this blog.

I have also installed Firefox RC1 today. Almost all of my extensions are incompatible with it, but after using Nightly tester tools they all agreed to work. I failed to notice anything different, so there is not much to talk about now.

Saturday, May 17, 2008

Firefox Extensions

Firefox is not the most popular browser (yet) but it is the most customizable. The number of available extension for it is so great that there even some difficulty in finding an extension you need. This post is a list of extensions I found helpful. It also includes some tips about using the Mozilla add-ons site.

Lets start with how to search for extensions. If you already know the extension name you can search for it on the Mozilla site or if you have Firefox 3b5 you can use the built-in add-on search. It is not always simple however.
Firstly, especially if you use a beta version of Firefox, you may have compatibility issues. Unfortunately, if the add-on you want to install is not compatible with your browser version, the install button on the Mozilla site will simply not work. This is very easy to fix - you just need to open an account. When you are logged in, the site will still show that the add-on is incompatible but it will also offer to ignore this. Registering an account will also allow you to install experimental add-ons.
Secondly, despite the new look of the add-ons directory it is still hard to find good add-ons. The fact that an add-on is popular or even recommended doesn't always mean it will be of any use for you. For example - the AllInOne Sidebar is very popular - but I tried it and I saw no reason for me to use it.

And now to the extension list. The following list is the list of extensions I use. It is divided into extensions types.

1.Fighting with ads and other internet junk:
Adblock Plus - a very simply and highly customizable ad blocking solution.
Adblock Filterset.G Updater - Extra rules for ad-block. Update: It is no longer supported. For extra filters install EasyList+EasyElement filters.
Adblock Plus: Element Hiding Helper - Element Hiding Helper is a companion extension for Adblock Plus meant to make creating element hiding rules easier.
CustomizeGoogle - Allows to remove Google ads from search and other Google products.
Nuke Anything Enhanced - Remove any image or text from a page. The effect is temporal.
SafeCache, SafeHistory - Protect Firefox from some simple exploits.
CS Lite - A simple yet powerful cookie manager.

2. Customizing Firefox behavior and GUI:
Configuration Mania - Allows to change some normally hidden settings.
Download Statusbar - Firefox has a built in download manager, but it opens in its own window. This extension works in the status bar.
Forecastfox - Get weather forecast in your status bar.
Stop-or-Reload Button - This add-on merges the stop and reload button into one. It doesn't adds any extra functionality, but it saves space.
Fission - Moves the page load progress bar to the address bar. Both saves space and makes the progress more visible.
Personas for Firefox - Allows to change the Firefox theme without reloading. This add-on is in alpha version now.
Tab Mix Plus - Modifies and extends Firefox tab options. Very useful extension. You can get the latest beta version here.

3. Site specific extensions:
Better Gmail 2, Better GReader, Better YouTube - These three are collections of greasemonkey script built in an extension.
Firefox Universal Uploader - Allows to upload files from Firefox to 8 different photo/file sharing sites. Great for managing large collections of online files.
Smart Digg Button - See if a page you are visiting was dugg and if yes how many diggs it got.
Google Notebook - Integrates Google notebook into Firefox.
Google Reader Notifier - See how many unread items you have in the status bar.
StumbleUpon - A patent destroyer of any productivity and sanity. Install on your own risk. (It is also good for finding good sites and networking). The latest beta is here.
Googlepedia - Shows a relevant wikipedia article next to Google search results. You will need to block Google ads for it to work.
GButts - Shows links to Google services in a toolbar.
GMarks - a bookmark manager for Google bookmarks. GMarks includes a sidebar, a toolbar, a quick search with Home+Home similar to Google Desktop's Ctrl+Ctrl search, and full content search of your bookmarked pages.

4. Uncategorized (for now) extensions:
Copy Plain Text - copy text without formating. Especially useful for site owners.
Google Toolbar for Firefox - For me the main two things it offers are Google bookmarks and highlighting search terms on a page. It also allows yo to store your browsing history on Google servers.
Greasemonkey - A user script manager. You can read more about it in my post Modifying the net.
Nightly Tester Tools - If you use beta versions of Firefox, it is a good idea to install this extension. Besides other things it can override compatibly prompts.
MR Tech's Local Install - The primary goal of this extension is to provide the tools needed to install and manage extensions and themes locally. To do this the extension provides multi-extension installation support, hacking capabilities to the Extension/Theme manager windows, features to find and troubleshoot Extensions/Themes Build, GUID and Profile information.
Platypus - Create simple greasemonkey scripts. Knowledge of HTML is recommended but not required to use. You will need greasemonkey installed for it to work.
Prism for Firefox - Turn websites into applications.
Stylish - A user script manager similar to greasemonkey - read more.

Some popular but not recommended add-ons:
1. NoScript - it is a great extension, but it is too much trouble. If you are visiting a lot of dangerous sites you should use it, otherwise it is better to avoid.
2. Clipmarks and similar - I really fail to see the point in using them. Depending on your needs a personal site (for sharing what your found) or a blog for taking notes will work better.
3. AllInOne Sidebar - I installed it twice. Have no idea why it is consider useful.

Feel free to recommend your favorite extensions in the comments.

Friday, May 16, 2008

Plan crash

I intended to do a lot today - do my homework, write a post about Firefox extensions on this blog, and a lot of other things. Unfortunately, I didn't do a single thing from this list. Instead, I spent almost all the day in Hadassa Hospital emergency room with a family member. Thanks God he is better now, but he is still hospitalized.
I hope that I will be able to do all what I have to do tomorrow. The post about FF extensions is nearly finished - I will post it tomorrow.

Monday, May 12, 2008

Back to University

Finally, the winter break is over... Thats good news for me. I really missed studying. I can study at home, but it is just not the same. Besides, it is usually more funny at the lectures. I don't have a lot of courses this semester, but as it looks now I will have a lot of homework to do. On a less brighter side, one of my new professors has a "weak connection to reality" - I don't know how to describe it... During the second hour of the first lecture, he just set down for a few minutes in a corner and read his notes for 3-4 minutes. After this he stood up, turn to the board and asked: "What I did here?". Overall he managed to make a rather strange impression. Despite this, he explains well.

Since I will be busier now, I will post less to this blog. I will try my best to post as much as possible, but I simply have less time now.
During the last week I did one post per day - from now on I will try to do one post per two days. I did this during the previous semester, so it shouldn't be too difficult to continue.
If you want a specific topic to be covered you can use the Skribit widget in the sidebar to suggest it (or to vote for suggestion already there).

Saturday, May 10, 2008

Ant colony in 3D

Have you ever wondered how an ant colony is build under ground? We all have seen a simple 2D version - all you need to get one is to place ants in a thin glass container. But how will it look in 3D?
Unfortunately the only way to construct a 3D model involves a total destruction of the colony. It s done by pouring concrete inside the colony, and then when it becomes solid it is possible to digg the resulting structure out of the ground.

In this video 10 ton of concrete were poured in to a colony to create a rather amazing sculpture:

Friday, May 9, 2008

Victory over Nazi Germany

It is an important day today... 63 years ago Nazi Germany was defeated, and with this defeat the current state of word affairs was born. I am not going to write about politics on Math Pages, but I will note two facts about this date.
First of all, the victory over Nazi Germany is celebrated on the 9/5 in Russia and some other countries. In the west 8/5 is the official date of the war end. This is simply because different time zones. The end of war was announced at 8/5 11:30 PM at Germany - for Moscow that was 9/5 2:30 AM.
Secondly, this day is not celebrated or mentioned in Israel. It is a sad fact, but because of political issues with Russia this date is totally forgotten. People who were born in Israel don't know a thing about this date and don't celebrate it in anyway.

The following videos are here to remind us about what happened 63 years ago.

Soviet Victory Parade of 1945 [Part I]

Soviet Victory Parade of 1945 [Part II]

Russian Military Parade May 2007

Update: LatterDays wrote an excellent post about the reasons behind WW2 and how this part of world history relates to our present. You can read this post here.

Thursday, May 8, 2008

Inside LHC - Atlas detector

LHC is a particall colider. But to get data we also need a detector which will corectly detect what happened in the collusion. This detector is named ATLAS. In the video below you can see a simple animation that shows how it looks and how it is constructed.

Episode 1 - A new Hope

Episode 2 - The Particles Strike Back (Part 1)

Episode 3 - The Particles Strike Back (Part 2)

The next video is very short - but is shows very well the scale of LHC. Usually when we hear about such large constructions we cannot visualize them well. This video should make it easier.

From Space to Atlas

Wednesday, May 7, 2008

A bit of random staff

This post is a collection of links/reviews of some random (but interesting) staff I found on the web. I never did such a post on Math Pages before so we will see how it goes.

Firstly, a bit of humor. This ad was apparently seen and photographed somewhere in the USA:

It is hard to say what was the reason behind this ad - perhaps they simply didn't want anyone to come? I wonder if to actually get the help you need to past a reading test (being able to read 200 words per minute for example).

Also apparently somebody recently did an upgrade to Mathematics - we are now on version 2.12. I never heard about version 2, but from the release notes (if link doesn't work - download .txt here) it seems a good joke (written in bold because some people failed to understand it).
Examples of the fixes in the new version:
1. Pi now equals exactly 3.
2. The term "negative number" has been deemed offensive. The term "non-positive non-zero number" is now in use.
3. Fixed problem where 1 = .999...
4. Removed the Proof By Contradiction exploit.
5. Users may now enter the paradise Cantor created for us for a nominal monthly fee.

Now to some serious staff. For some reason I stumbled on a lot of surprisingly interesting articles this week - mostly about physics. What is also good about them is that they are very well written and explained. Enjoy:

Maxwell: Thermodynamics meets the demon - a very detailed explanation of what the Maxwell demon is. Also includes a short overview of the development of Thermodynamics.

Fusion 2.0 - "Fusion could one day generate limitless cheap energy from little more than water, while emitting no greenhouse gases. We look at its promise as the ultimate power panacea for a warming world." There are currently plans to build a large fusion reactor in France. It is expected to generate 500MW and the construction cost is 10 billion euros. It is easy to see from these numbers that this is a scientific experiment and not an economically feasible solution to the energy crisis - but it may prove to be a very important step.

The Mechanical Battery - the main idea is very simple. Instead of storing energy in a regular battery in chemical form why not store energy in a rotating wheel? This may sound very strange, but the idea is based on the fact that rotating objects store energy in direct proportion to their mass and RPM. The end result is more much more friendlier to the environment that batteries, and such a wheel can be both charged and recharged in a very short time without damaging itself. Perhaps, this technology will finally provide the necessary power for creating electrical cars...

Firefox God
- over 300 excellent extensions in different categories. If you are using Firefox, it is a good idea to visit this page.

Million dollar problems
- A list of the million dollar problems in math. They are all explained is a simple enough way.

Unsolved problems in physics - a very large and interesting list.

It would be a good idea to finish this post with something serious, but I didn't post anything funny for a long time so instead I will write about this page - 101 More Great Computer Quotes. Examples:

"I do not fear computers. I fear lack of them."
– Isaac Asimov

"A computer once beat me at chess, but it was no match for me at kick boxing."
– Emo Philips

"Getting information off the Internet is like taking a drink from a fire hydrant."
– Mitchell Kapor

"Programming can be fun, so can cryptography; however they should not be combined."
– Kreitzberg and Shneiderman

"Don't document the problem, fix it."
– Atli Björgvin Oddsson

Tuesday, May 6, 2008

How to uninstall Kiba-dock in Hardy

If you followed the instructions in my post about Installing kiba-dock in Hardy, it should be installed and working but it is not possible to uninstall it using apt-get or synaptic.
The only way to uninstall programs that were installed by using the make install command is to manually delete all the files created.
In the case of kiba-dock there are a lot of files created, but gladly only in two places.

Firstly, the uninstall process depends on why you want to uninstall Kiba-dock. There are two main reasons - either you want to reinstall it or to remove it. If you want to remove it completely and never to use again than you should also remove its configuration files from your home directory. To do this type in terminal (skip this step if you want to reinstall Kiba lately):

sudo rm -r $HOME/.kiba-dock

The other files created by the make install command are located in /usr/local. Don't remove the directory itself - you just need to delete all those that have kiba or akamaru in their names. Since there are a lot of those, and it takes time to find them all, I created a simple script that should remove all of them for you - download it here. This script will also remove the directory kiba in your home folder.

To use this script you will need to download it, then right click on it and go to Properties ->Permissions ->Allow executing file as program. This is all - just open it and select Run or Run in Terminal (you will be asked to enter your password).

Lastly, if you want to remove kiba-dock completely, you should also remove it from your application list. Type:

sudo rm '/usr/local/share/applications/Kiba-Dock.desktop'
sudo rm '/usr/local/share/applications/Kiba-Settings.desktop'

After this you system should be completely free from Kiba-dock.

Monday, May 5, 2008

An algorithm for solving Sudoku puzzles

In the previous post, Impossible Sudoku, I said that there exists a general algorithm that allows to solve any Sudoku puzzle. In this post I will present this algorithm and the solutions to the Sudoku puzzles I posted in the previous post.

First of all, in order to talk about solving Sudoku we need to define what a proper Sudoku is - A proper Sudoku puzzle is a puzzle that has unique solution. It is important to notice that in this definition there is no requirement that a proper Sudoku can be solved - the only thing we require is that there exists a way, and its is only one, to put the missing numbers in the puzzle without breaking the nine in row/column and nine in square rules.

In this post I will talk only about proper Sudoku puzzles. There are 6,670,903,752,021,072,936,960 such Sudoku by the way...

Now that we have this definition we can talk about solutions. Lets prove that all proper Sudoku puzzles can be solved:
A Sudoku puzzle it considered to be solvable if there exists a finite series of step that will produce a filled grid. T o prove that for all proper Sudoku puzzles such a series exists we will need to use linear algebra. If you are not familiar with it please, skip this paragraph. Lets define the following vector space:

This is a 81 dimensional vector space. is the field of natural numbers mod9. Now we can talk about a function from the group of all Sudoku puzzles to V. This function is not a nice one - it moves all the 1 in the puzzle to 0 and 9 to 8, so it loses information. However this is not important. What is important is that for proper Sudoku its solution is moved by the function to a unique vector in V. Because V is a vector space with finite dimension it must have a basis. The standard basis of V is clearly (1,0,0,...,0),.....(0,0,0,...,1). Lets selected one proper Sudoku. The solution of our Sudoku can be expressed therefore as a finite linear combination of these vectors. The problem is that each of them can appear more then one in the combination - we don't want this to happen. Therefore we will sum all the appearance of the same vector - for example if (1,0,0,...,0) appears 5 times in the combination we will write (5,0,0,...,0) instead of it. It is very easy to see that the puzzle we chose can also be written as a sum of part of the linear combination we got in the previous step - so lets sum a part of it to get the puzzle. What we now have is the following equation:

in this equation U is our original puzzle and w is the solution. are the remaining vectors in the linear combination. Each of them represents a number and a cell, so adding one of them is filling a cell. We already saw that k is a finite number, so indeed there exists a finite series of steps that solvs a certain proper Sudoku puzzle.

You are probably wondering why I wrote this prove - isn't it obvious that Sudoku puzzle can be solved? Well, yes. But if it is obvious, why not prove it? After the prove it is no longer obvious - it is just a plain fact.

Now that we have shown that there is a solution lets talk about how to find it. The algorithm consists of three main steps that are repeated until a solution is reached:

Step one - Scanning:
Cross-hatching: The scanning of rows to identify which line in a region may contain a certain numeral by a process of elimination. The process is repeated with the columns. It is important to perform this process systematically, checking all of the digits 1–9. It is usually faster to check for a digit in all of the grid at once than to check square by square.
Column check: After cross-hatching it is usually a good idea to use elimination on columns. It is done in the same manner as with squares.

Step two - Logic:
This step consists of attempts to make logical conclusions. For example in the puzzle above you don't know were 4 is in the center square. But you now that it must be in the right column of this square. You can use this information to conclude that it cannot be in the right column of the top-middle square. In this case this is enough to find 4 in that square.
Step three - Guess:
If you don't know you can always guess. In this step it is important not to make mistakes - otherwise it will not work.
If you want to make a guess you will need to find a good digit to guess. The best option is to find a cell (or row/column) with two candidate numbers. After finding such cell make a guess and then repeat steps one and two.
If you will get an impossibility at some point than your guess was wrong - and because there were only two candidate numbers it is the second number that should be in that cell.
If after repeating steps one and two you need to make another guess repeat step three - if your second guess is incorrect it means that your previous guess requires the second candidate in the cell you choose for the second guess.

1. Easy and medium puzzles can be solved using first step only. Hard puzzles require step two, and very hard step three.
2. Don't overuse step three - it makes the game much less fun.
3. For step three you will need to keep track of the numbers you wrote after the guess. The Gnome-Sudoku I mentioned in the previous post gas an inbuilt tracker function for cases like this.
4. It is possible to add another step to the algorithm - marks. It basically consist of recording all the candidates for a certain cell on the puzzle itself. I don't think that it is needed, and it is time consuming.

And now as promised - solution to the puzzles from the previous post:

Saturday, May 3, 2008

Impossible Sudoku

Sudoku is a very popular Japanese puzzle. You can read more about it here. I usually don't play games of any sort, including puzzles. But sometimes I find them useful as a distraction or as a good way to train the mind.
There is a very good Sudoku game available for Ubuntu (I don't know about any good one for Windows, sorry). It has puzzles at four difficulty levels and is also able to generate new puzzles.
If you are using Hardy you should already have it, otherwise simply type:

sudo aptitude install gnome-sudoku

The reason I am writing about it is that I have recently successfully solved the hardest Sudoku puzzle I have ever seen. Gnome Sudoku also calculates the difficulty score for each puzzle, the difficulty score for this one was 92%. I lately found one with even higher difficulty score (95%), but for some reason it was much easier to solve.
Overall, all Sudoku puzzles are solvable - if you know how to solve them. It is actually rather simple to solve even the most difficult Sudoku once you learn the general algorithm, but it takes a lot of time and require concentration. In the next post, An algorithm for solving Sudoku puzzles, I will write in more details about this general algorithm. Meanwhile you can try to solve the two puzzles I mentioned by yourself:

In the next post I will also post the solutions of these two puzzles.

Friday, May 2, 2008

Skribit - post topic suggestions

Skribit is exactly what it claims to be - a widget that allows blog readers to suggest topics they want to be written about. After reading a post at ProBlogger about this new widget, I decided to try it myself. This means that you can now use the Skribit widget in the right column to send me your suggestions about future post at Math Pages.

The widget comes with a default question (ie post topic suggestion):

Why are you using Skribit?

The answer to this is very simple. While it is advertised as a tool for finding topics to post about, I am not going to use it for this. I usually find myself with too much ideas. However, after blogging on Math Pages for a few months I feel that the topics that seem interesting to me are not of much interest to most of world population. This is not surprising - I never thought a blog about math and science can be popular outside of a close circle.
On the other hand, my three posts Upgrading to Hardy, Installing Kiba-dock in Hardy and Hardy Repositories list were an unexpected success. I wrote them just when people needed such posts.
After this I think it would be only natural to ask my readers and visitors to suggest topics they want to be written about on this blog. I hope that this new widget will help in this.

Also, I plan to write in it the titles/topics of the posts I plan to write in the next week or two. The widget allows visitors to vote on suggestions, so you are welcomed to express your opinion.

P.S. While you can suggests topics (and I really hope you will do that), I don't promise that I will write about the topic you suggested - but I will definitely consider your suggestions.

DIY multi-touch screen

Apparently it is possible to make a multi-touch screen at home, using only cheap components and software. The result is not elegant but it works, and works well - see the video:

Amazed? So was I... I am not going to try to build one myself. Well, maybe I will... I am using Linux so I am not sure that I will be able to find the right software, but it surely looks like an interesting thing to do.

Thursday, May 1, 2008

Ubuntu Hardy and Compiz

Ubuntu Hardy was released only a few days ago, but there are already videos on YouTube showing of how a Linux desktop can look now:

The best part is that it is very simple to get exactly the same setup on your computer - even if it is old.
To get the exactly same result you will need to customize the default installation slightly. Firstly you will need to add some repositories. The easies way to do this is described in the post Ubuntu Hardy Repositories list.
After adding all the extra repositories you will need to run the following command in terminal:
sudo aptitude install simple-ccsm compizconfig-settings-manager compiz-fusion-plugins-main
sudo aptitude install compiz-fusion-plugins-extra compiz-gnome compiz-plugins emerald
sudo aptitude install fusion-icon

This will install all the required programs. You can find themes for compiz at
To start emerald use the fusion icon: Aplications -> System Tools -> Fusion Icon.
Optionally, you can also install kiba-dock - but it is not available from any repository I know about. If you want to get it follow instructions in the post Installing Kiba-dock in Hardy.
You can also install a lot of themes for compiz using the package emerald-themes. To install it you will need to add the following repository (it is a feisty repository, so I don't recommend using it - do it on your own risk):

deb feisty eyecandy

You will then need to add the GPG key:

wget -O- | sudo apt-key add -

Unfortunately this repository is only for feisty - I don't recommend using it.