Unless I would see it myself, I would never think that there is more interests in this two topics than coverage on the internet. But lets start from the beginning.
One of the first things I did when I started this blog was to add Google analytics code to it. To those who never heard about it - Google analytics is a hit tracker with a very nice GUI and simple installation. My traffic is very low now, so using hit tracker is more like getting use to see bad news - I even caught my self once worrying if my blog will get a negative number of visits tomorrow.... However even for a small blog like mine Analytics provides some useful information - what posts are more popular and from where my visitors come.
Unsurprisingly, most of my visitors are form the USA. What is interesting however is how they get to my blog. Analytics provides me with search terms which were clicked on - in my case this is too little to conclude anything, but it is also possible using Google webmaster tools to get the top 20 queries in which my blog showed up. This is still a small data pool, but it is possible to get two interesting results from it.
Almost all the search terms that return my blog in the first 10 results, are relatively long. But they can be easily divided into two groups:
1. Einstein connection to math or Einstein quotes.
2. The longest word in English.
I wrote about two of this subjects - a long time ago I wrote a short post about the longest word in english, which I expanded after noticing that it got visits from Google. I also wrote a post discussing some of Einstein quotes. Perhaps I will write also about Einstein connection to math some day. It is an interesting topic - but unfortunately it requires me to do a bit of research which I don't have time to do now.
I am of course very glad that what I wrote on Math Pages got to the first ten results in Google even for a long search term, but I am also surprised. Such result clearly suggests that while not many people are interested in this two subjects, those who are have problems finding what they want. If it would be easy to find what they were looking for they would not be using long search queris and my blog would in no way bee even near the top ten results. All of this clearly suggests that these topics are not well covered.
I don't think it is possible to add anything to my post about the longest word in English, but if you, my dear readers, want me to write something about Einstein, leave a comment on this post. If you want to write a post about Einstein yourself and submit it here you are also welcomed to contact me by leaving a comment.
Monday, March 31, 2008
Unless I would see it myself, I would never think that there is more interests in this two topics than coverage on the internet. But lets start from the beginning.
Friday, March 28, 2008
I didn't post any jokes for sometime so here goes:
Especially for those who are not mathematicians but have friends who are obsessed with math - A detailed guide for buying presents:
First of all what not to buy:
1. Epsilons. While they are more than zero and are very useful, they are not good presents. First of all they are so small that that they are very easy to lose - moreover it is even difficult to see them. Besides, true mathematicians use their own personally made epsilons.
2. Empty set. It is important, but there is nothing in it. Don't be greedy.
3. Calculators. It may sound surprising to you but we have no use for them. For simple calculations we have our mind, and for difficult a powerful computer is needed. Besides, calculators are almost useless when writing proofs.
Now, lets look on some good ideas for a gift:
1. Mersenne prime poster. The Mersenne project attempts to find primes of the form . The currently largest known prime is a Mersenne prime. It is about 9.8 million digits long.
You can find the poster here.
2. A cake with a mathematical theme. See the image below for example:
4. Moneyis a great present - perhaps not as personal as you would like, but still a good present. Especially if the person you want to give the present to is still a student. He will appreciate such a gift a lot...
Wednesday, March 26, 2008
Google is probably the most well known internet company in the world. They are the best search engine, but they are much more than just a search engine.
As of now there are 7 main pillars that make Google what it is now, and define its future:
4. Video - Google video and Youtube
6. iGoogle - combined with web history and bookmarks
7. Open source programs
There are more products by Google, but in my opinion these seven are the most important. It is easy to notice that they can can be further divided into 3 categories:
Both Adsense and search are excellent tools for generating money. Google.com has about 75 million unique visitors each day. Adsense is shown to these visitors and is also displayed on millions of other pages in the internet.
In my opinion, Google does a great job in making their ads unobtrusive, and sometimes they are even useful. It is possible however to completely block them as well as other ads - you can read more about how to do it in my post about AdBlock. Not all people use ad blocking software, but this number is growing. Soon ads will either disappear or change there form into something less obtrusive.
The main reason why sites like Blogger and Youtube exist is user generated content. They provide a simple and even free way to communicate your creativity to the world, and even make money from it. These both sites started as separate companies and were later acquired by Google. Why would a search company be interested in something like this?
Youtube is the most popular video site. I feel that Wordpress is better than Blogger, but it is also more complex. By owning these two sites Google owns a large share in the user generated content world.. And we shouldn't forget picasa. It is less popular than flickr, but it is better in some ways - mainly because it is firstly a program and not a web site.
Store 100% reality
You probably already know about this - Google apparently has a plan to store all your data on their servers effectively moving the whole world into the cloud computing. Presumably this new service will be called Gdrive. Even today, this is something we can only dream about. Probably it will happen in the next 10-15 years.
Even today, Google gives a 6.5 GB email account plus 1 GB for photos (with picasa web albums).
Google bookmarks and web history are another example of how our data (and information about us) is getting stored on Google servers.
The question is:
This is the weak link in Google plan - even if they will build a server capable to store 100% of all the data in the world, will people use it?
The answer is very simple - people will use it. I am not talking about some small percent of world population that don't mind posting personal photos on the internet. When Gdrive will appear, security experts will warn people about potential data/identity loss, but it will not stop the adoption of Gdrive.
The main strength of Google is in their motto - "Don't be evil." The motto is only words, but Google has actions to back it up. They give a lot of service for free, and people like free. They sponsor open source projects, and give grants for developing free software. They do a lot for the people.
All of this makes them a company people like and trust. Eventually this will be the true reason behind the success of Gdrive.
Sunday, March 23, 2008
I was very surprised to found out today that in fact Hitler didn't believe in evolution as presented by Darwin. It is well known that Hitler believed in the racial supremacy of German people, and it is often claimed that the basis for this idea was evolution. This claim is based on the definition of evolution as "the preservation of favored races in the struggle for life". It is very simple to get from this definition to racism and genocide. But this definition is not correct.
In fact, what Darwin said was the opposite of this definition. According to Darwin, it is not the best species that survive but the most adaptable. Moreover, there is no way to define what a "best" creature (or race) is from evolutionary point of view.
For example, scientists are pretty sure that dinosaurs ruled the earth for over 100 million years. It is logical to assume that they were the best product of evolution then. But they got extinct. Therefore, they were less adaptable than other creatures, and can no longer be considered "winners" in the race of evolution.
From this example it is clear that no specie can be defined as the best product of evolution - because it is fully possible that this particular specie will be extinct tomorrow.
As we now see, it is not correct that Hitler based his views on the theory of evolution proposed by Darwin. While he used the world evolution to justify his ideas, it was a different theory that was behind this word..
Surprisingly, it turns out that Hitler believed that the world was created by God and rejected Darwin theory of evolution. We can see this from the following quotes:
The fox remains always a fox, the goose remains a goose, and the tiger will retain the character of a tiger. - Adolf Hitler, Mein Kampf, vol. ii, ch. xi
For it was by the Will of God that men were made of a certain bodily shape, were given their natures and their faculties. - Adolf Hitler, Mein Kampf, vol. ii, ch. x
From where do we get the right to believe, that from the very beginning Man was not what he is today? Looking at Nature tells us, that in the realm of plants and animals changes and developments happen. But nowhere inside a kind shows such a development as the breadth of the jump , as Man must supposedly have made, if he has developed from an ape-like state to what he is today. - Adolf Hitler, Hitler's Tabletalk (Tischgesprache im Fuhrerhauptquartier)
It it very clear that this quotes deny evolution. Moreover, they seem to suggest that he believed in God. But then, what was the evolution he spoke about?
As it seems from what he did, the evolution was not an evolution, but rather a place in a list. He simply decided what nations was more superior than other nations and than used historical connections to make a list - with German people on top of the list, and Jews somewhere near the end.
When you have such a list it is very easy to talk about evolution. Evolution becomes simply a movement in the list...
Thursday, March 20, 2008
This is not a why "I hate windows" post - I see no reason for having such strong feelings to a software... This post is just a list of reasons that caused me to choose to use Linux and not windows, and a list of things that are missing in Linux.
This one should be obvious - windows is simply too expensive. Perhaps its price is normal in the USA market, but it is too high for people living outside of the USA. Linux is free.
It is of course possible to download an illegal copy of windows and install it. Microsoft fights piracy as hard as it can, but this is simply not enough. But why bother? When I bought my new computer, I wanted to install windows on it. But when I started to install it turned out that I don't have the serial number... I wanted to dual-boot, and I already had a Linux CD laying on my desk. So I installed it. I thought to partition the disk, but for some reason the installer failed to partition the disk. So I was forced to install it on all of the disk.
While it may seem strange, but it is obvious from this story that the reason that caused me to use Linux was price and nothing else.
On the same hardware, Linux works better. This is partially due to the fact that there is no need in an antivirus on Linux. It also seems that the code is more efficient. My current computer is capable of running Compiz with all of its visual effects easily, but it would be too weak to run Aero (according to the official specs - my video card is too weak).
There are much more applications for windows than for Linux. Moreover there are applications whose performance or functions are unmatched by anything that you can install on a Linux only machine. For example - Rosetta stone. This is a very effective language learning program, but there is no way to run it on Linux. I used it to learn German - I finished level one and soon after it I was forced to switch to Linux...
On the other hand, it is much more simple to install applications in Linux. All you need to do is to make a search in the database of available applicators (a rather large database, by the way). Installing is as simple as pressing a button. Plus all the applications are free.
I don't use computer to play games, so I don't care about it, but the choice of games for Linux is rather limited. So if you like to play games more advanced than tetris, this is not the right OS for you.
On a final note, Linux is a great OS, as long as you feel comfortable enough to use the command line from time to time... I am using Linux for over a year now, and I managed to break it only once - took one week to fully fix.
I will probably dual boot my computer at some point - mainly because of the Rosetta stone not working in Linux, and because some gadgets are also not working in Linux due to lack of drivers.
However, I am very happy with Linux - as of now the disto I am using is Ubuntu, and it is both very functional and has a nice GUI.
Saturday, March 15, 2008
I just found a rather interesting program, called phun. The main idea of the program is creating simple mechanical "creatures" cars, catapults and the like. I embedded a short video below:
I played with this little program a few hours yesterday.. There are also features not shown in the video - turning gravity off, water, chains and so on. I doubt it can be used to study physics - even for schoolchildren, but it is a good way to expose children to mechanics. Overall a very nice program - plus it is free.
You can see more about this program in the official video:
Friday, March 14, 2008
From Wikipedia: "Pi Day and Pi Approximation Day are two holidays held to celebrate the mathematical constant π (pi). Pi Day is observed on March 14 (3/14 in American date format), due to π being equal to roughly 3.14. Sometimes it is celebrated on March 14 at 1:59 p.m. (commonly known as Pi Minute). If π is truncated to seven decimal places, it becomes 3.1415926, making March 14 at 1:59:26 p.m., Pi Second (or sometimes March 14, 1592 at 6:53:58 a.m.). Pi Approximation Day may be observed on any of several dates, most often July 22 (22/7 (European date format) is a popular approximation of π). March 14 also happens to be Albert Einstein's birthday."
I totally miss the point of this holiday... It is always nice to have a reason for celebration, but this one seems a bit too odd even to me. Perhaps I will change my mind with time, but a celebration connected to the existence of math constant simply doesn't make sense to me. Although celebrating Einstein birthday does look like a good idea (by saying "good idea" I mean a good reason to eat a cake)...
Pi is a very fascinating number. It is also perhaps the most well known transcendental number, and it has a very long history. But there is no reason to regard it as anything more than a number, or make a celebration because of its existence.
Thursday, March 13, 2008
In the previous post I wrote about false logic that is often used in building claims about God. The example I used was a funny but totally false definition of Atheism. While I do believe in God I don't think that by using false logic it is possible to make other people believe in Him. In this post I intend to present proofs of God existence that are based on false logic, or are based on an incomplete logic.
First of all lets - a few words about the title. This post is about logic and proofs. Because of this I thought it would be a good idea to present an obvious example of a false proof. Also, the logic used in this proof is similar to the false logic in the proofs of God existence.
We are going to proof the following statement:
The logic used here is clearly false however.
With this example in mind lets turn to the main part of this post:
Every effect has a cause; there cannot be an infinite regress of finite causes; therefore, there must be an uncaused cause or necessary being; this being is God (The Cosmological Argument, proponents- Aquinas).
It should be obvious why this is wrong. First of all why "there cannot be an infinite regress of finite causes"? This should be proofed. Moreover, it is not impossible for the cause and effect line to form a circle. Think about a light wave for example. But this is just a side note. The main problem with this particular statement is that it is in fact a definition of God. It defines God as an uncaused cause - but this is not a full definition of God. If for example you believe that the Big Bang was this "uncaused cause" than according to this statement you should worship it. If we go with the second option - "necessary being", it is also not enough. The fact that there was a being doesn't mean that this being didn't "die" immediately after creating the world, for example.
There is observable order or design in the world that cannot be attributed to the object itself; this observable order argues for an intelligent being who established this order; this being is God (The Teleological Argument, proponents- Aquinas).
In this one we have the unicorn argument again. The whole proof is based on "cannot be attributed to the object itself" But this isn't proofed. So the argument falls.
Man has an idea of an infinite and perfect being. Existence is a necessary part of perfection. (Therefore) an infinite and perfect being exists, since the very concept of perfection requires existence (The Ontological Argument, proponents- Anselm).
Unicorn again. Using the same argument - America has a perfect president. (Not that I have anything against him and Maths pages is not about politics anyway).
All people believe that something is true. If God is the God of truth and the true God, then God is truth. This Truth (capital T) is the context for all other truth. Therefore the existence of truth implies the existence of Truth, which implies the existence of God (The Argument from Truth, proponents- Augustine, A. Strong).
It becomes a little boring.. The same logic again. As I said in the beginning the unicorn argument is very popular. In this particular one it is taken to the very limit - we first assume that "God is the true God" and than base our proof on this. But this assumption requires proof. Moreover. in this assumption we already say that He exists - but this is exactly what we are suppose to proof...
If you want you can read about other such false proofs here.
The last thing I want to discuss is an example of a proof that uses mostly correct logic, but is simply incomplete:
It is not very clear how this one is connected to God at all, but lets think a bit about it. For a moment, forget about what we want to proof and think what our world would look like without light - without all light. In reality it will cause all of us to die, but in this mind game we can ignore the rules of physics, and focus on the question - will there be a word for darkness in such world?
Without light we would not know what darkness is. So why should we have a word for it?
From this we come to the following conclusion - since it is clear that evil and injustice exists in our world and we have a word and a definition for them, God must also exists.
But this argument is simply not complete. All it shows in this form is that there are good people. Even the understanding of what is good and what is not is different from nation to nation and even from person to person.
On a final note, I don't know a proof of God existence that uses correct logic. If you know (or think you know) you are welcomed to leave a comment.
Friday, March 7, 2008
Sometimes I am very surprised by what people say when they want to prove that God exist (or don't exists).. Personally I believe in God. But I don't see how listening to poor arguments will cause anyone who doesn't believe in Him to change his mind. Unfortunately there is more than enough examples on the internet of poor logic practiced by Christians... I don't want to say anything bad about people who make these arguments, or those who believe in them. What I want is to discuss some examples of such poor logic, with the hope that it will help both sides in the debate. As always comments are welcomed.
In this post I want to focus on the following picture (I found it on the internet - author unknown):
This is a rather funny image... But what is written there is not correct. Lets examine this definition, word by word.
First of all, why dinosaurs? What they have to do with atheism? If we will look scientifically on dinosaurs they are simple, albeit large animals. No more and no less. They have importance, but they are totally irrelevant to the definition or discussion of atheism. The only connection between dinosaurs and atheism is dates - the problem to explain from a religious point of view when the dinosaurs "walked the earth". But nothing is said about dates in this image. If, for example, it would be written "humans" instead of "dinosaurs" it would be more logical - there is a very obvious difference between humans and animals.
"..nothing magically exploded.." How many atheists you know who use the word "magically" to expalin something? From its very definition magic is something supernatural. If you believe in magic but not in God, you have a very strange understanding of supernatural...
"The belief that.." This is not precise. As I see it people don't believe in what science says. They believe in what scientists say them. The difference is, perhaps, not very obvious but very important. Most of the people in the world never been in a lab. They also lack the required knowledge to understand the math behind the theories presented to them by scientists.
And for a good reason - it is not their business to deal with cosmological problems. Because of this they trust those who are dealing with these problems - scientists. People trust them, just as they trust doctors or engineers.
"..rearranged itself for no reason.." Stars are created from dust clouds by gravity. More generally, the matter in the universe tends to arrange itself, while maximizing size and stability. This is seen well in the creation of heavy elements from helium in stars, and in the decay of radioactive matter. The examples I mentioned happen for a well known reasons - gravity etc.
".. there was nothing.." This is what the Bible says also.
"..nothing happened to nothing.." Logically impossible... Science doesn't claim that "nothing happened" - as far as I know the claim is "we don't know what happened". The current theories fail when used to explain what happened in the plank time after the Big Bang...
"..creating everything.." This one is correct. But again there is nothing here that contradicts the Bible - it is merely a claim that our world had a beginning, that it is not eternal.
Monday, March 3, 2008
Mathematicians tend to be humans (exceptions unknown). Because of this they are forced to use the same languages as those around them. Some words, however, have different meaning when used in mathematics. A perfect example of this is the word "or".
The following stories (they are real) show this difference very well:
Sandwich Shop Worker: “Would you like mustard or mayonnaise on your sandwich?”
Customer: “Yes, please.”
(Sandwich shop worker stares)
Customer: “Oops! I mean. Um…mayonnaise.”
Sandwich Shop Worker: “How would you like to pay? Cash or credit?”
And a second one:
Customer: “Can I have the giant Yorkshire Pudding?”Source.
Worker: “Sure, would you like it served with Beef or Pork?”
Customer: “Yes, I’ll have beef or pork.”
Worker: “No, would you like Beef OR Pork?”
Customer: “YES, beef or pork!”
It may sound surprising but from a mathematical perceptive the workers are the one who behaved strangely. In mathematics, if you say "I want beef or pork" it can also mean that you want both. It sounds confusing, but it is perfectly logical.
Consider the following: Let P and Q be two statements. When the statement A="P or Q is true" is true?
If P is true and Q is false, A is true.
If P is false and Q is true, A is true.
If P is false and Q is false, A is false.
If P is true and Q is true, A is true.
The first three situations should be obvious. Concerning the forth lets see an example. In the example we will take P="x is positive" and Q="x>1". For x=2 both P and Q are true. Question:
Is 2 positive or greater than 1? The question sounds weird sounds weird, but is it possible to answer "no"? If you answered "no" than it follows that 2 is not positive and not greater than one. But this is not true. Therefore A is true.
We can use the same argument for the "beef or pork" situation. If you say you want beef or pork and are served both, can you say that you didn't get what you ordered?
We are all familiar with the "type the text shown in the picture to prove you are human" check, but is it enough? As of now, it is generally believed that a computer cannot decipher such image. But it may become possible with the advance in image recognition technology. Who knows perhaps it is even already possible.. Sometimes simple questions, like "What is 4+7" are used, but this is also something a computer can solve. It is more difficult, but possible.
A better solution is something like this:
For a niche blog such verification would be a very good idea - it will instantly assure that the people who comment know the subject well enough and are not spammers.
Despite the spam comments math pages is being hit with now, I am not going to use this way to fight with spam. I simply have no way to do it - Blogger doesn't allows me to put such checks. Unfortunately, perhaps.
Probably in the future it will become the norm, and in order to comment on a rocket science blog you well have to answer something like this:
What is the cosine of an ultraviolet wave traveling at a velocity of 27 kilojoules with a frequency of 3, as it extends perpendicular to the angle of inference, in an isotonic solution?I have no idea, I am not a rocket scientists after all, so don't ask me.