Monday, December 31, 2007

Happy new year!

Happy new Year!

In Israel the New year and Christmas are not celebrated. At least not officially. Officially we have Rosh Hashana (It is the biblical new year) which is celebrated about two month earlier.
So unfortunately there is no vacation for me ...

I intended to write here a bit about calendars but .. I don't have enough time now so I will do it in the next post.

Saturday, December 29, 2007

Albert Einstein quotes

Just a short selection:

“Anyone who has never made a mistake has never tried anything new.”

“Everyone should be respected as an individual, but no one idolized.”

“Try not to become a man of success but rather to become a man of value.”

“Life is like riding a bicycle. To keep your balance you must keep moving”

"A happy man is too satisfied with the present to dwell too much on the future."

"To punish me for my contempt of authority, Fate has made me an authority myself."

It is very interesting that he was also offered to become a president of Israel. He refused.
You are probably wondering why I posted this quotes. Well everyone knows who Albert Einstein is. Even my spell check application knows his name... But there are things about him that should be also well known but are usually not talked about.
As far as I know he was divorced, married his cousin soon after the divorce and then cheated on her. At my opinion at least he should not be looked on as an example to family life.. Why am I bringing this? Simply. As he said himself - “Everyone should be respected as an individual, but no one idolized.” We should learn from him but should not idolize him. However the attitude that at least I usually see is closer to idolization than to respect.
This is not the main point of this post however. It is a well known "fact" that he did very poorly at school. However this is a lie. There is a permanent exhibition about him at the Hebrew University. His Diploma is also there. He did very well in school.
When I was in school I was often told that all of the famous scientists did well only in a specific field but were horrible in all the rest. I of course believed it. But this is a dangerous thing to believe in because if you do, you will always have an excuse no to do something that is difficult for you. You will say to yourself that it is OK to fail in something, because even those scientists failed in something, and they still became famous. But this is a very wrong mind set.
While it is fine if you fail in something, it is unacceptable if you don't try to be good in it because it is hard for you.

This is entirely unrelated to math. But this is a blog about math and science, so it would be unfair to post something that doesn't have connection to math.
Einstein ones said: "If you have difficulties with math, I assure you that mine are greater."
Well what can I say - lets not make him an idol and lets not think that if math was difficult for him it will be difficult for us.
As a fun fact - at Hebrew university, in the information for new math students it is said that you don't need to be Einstein to graduate...

Wednesday, December 26, 2007

Behind the name

Many of the well known companies have a very unique story behind their names. This is a short list:

Adobe - came from name of the river Adobe Creek that ran behind the house of founder John Warnock.

Apache - It got its name because its founders got started by applying patches to code written for NCSA's httpd daemon. The result was 'A PAtCHy'server -- thus, the name Apache

Apple Computers - favorite fruit of founder Steve Jobs. He was three months late in filing a name for the business, and he threatened to call his company Apple Computers if the other colleagues didn't suggest a better name by 5 o'clock.
(Either this was the best name or the others just didn't care - what you think is more probable?)

CISCO - its not an acronym but the short for San Francisco.

Google - the name started as a jokey boast about the amount of information the search-engine
would be able to search. It was originally named 'Googol', a word for the number represented by 1 followed by 100 zeros. After founders, Stanford grad students Sergey Brin and Larry Page presented their project to an angel investor, they received a cheque made out to 'Google'

Hotmail - Founder Jack Smith got the idea of accessing e-mail via the web from a computer anywhere in the world. When Sabeer Bhatia came up with the business plan for the mail service, he tried all kinds of names ending in 'mail' and finally settled for hotmail as it included the letters "html" - the programming language used to write web pages. It was initially referred to
as HoTMaiL with selective upper casing.

HP - Bill Hewlett and Dave Packard tossed a coin to decide whether the company they founded would be called Hewlett-Packard or Packard-Hewlett.

Intel - Bob Noyce and Gordon Moore wanted to name their new company 'Moore Noyce' but that was already trademarked by a hotel chain, so they had to settle for an acronym of INTegrated ELectronics.

Microsoft - coined by Bill Gates to represent the company that was devoted to MICROcomputer SOFTware. Originally christened Micro-Soft, the '-' was removed later on.

Motorola - Founder Paul Galvin came up with this name when his company started manufacturing radios for cars. The popular radio company at the time was called Victrola.

Red Hat - Company founder Marc Ewing was given the Cornell lacrosse team cap (with red and white stripes) while at college by his grandfather. He lost it and had to search for it desperately. The manual of the beta version of Red Hat Linux actually had an appeal to readers to return his Red Hat if found by anyone !

SAP - "Systems, Applications, Products in Data Processing", formed by 4 ex-IBM employees who used to work in the 'Systems/Applications/Projects"

SUN - founded by 4 Stanford University buddies, SUN is the acronym for Stanford University Network.

Xerox - The inventor, Chestor Carlson, named his product trying to say 'dry' (as it was dry copying, markedly different from the then prevailing wet copying). The Greek root 'xer' means dry.

Yahoo! - the word was invented by Jonathan Swift and used in his book 'Gulliver's Travels'. It represents a person who is repulsive in appearance and action and is barely human. Yahoo! founders Jerry Yang and David Filo selected the name because they considered themselves yahoos.
(And why they think that I will use their servers exactly?)

Tuesday, December 25, 2007

You know that you are a mathematician when:

.. when you see an advertisement that reads "... in partnership with H&O", and the first thought that comes to your mind is: I know what it means H - stands for quaternions, O - stands for octonions and ... What?!?.

I hope it doesn't sound like math is the only thing I think about...

Anyway, it is a good thing that when mathematicians think too much about math they are at least not very dangerous. You just need to remember that if the person you are talking to doesn't know math well enough - it is not a good idea to talk with him about cantor sets, cardinalities, vector spaces, etc... Even if you feel that it is simple and you are sure that you can explain it, hold you self.

Monday, December 24, 2007

Invented or discovered?

Is math invented or discovered? It is a very ancient question. It dates back to the ancient Greek mathematicians. They believed that everything is a number - and they took this philosophy very serious. In fact, according to a legend the man who discovered that is irrational payed for this with his life. He proved that while sailing in the sea with his friends, and when he told them, they threw him out of the boat. For them such a proof was totally unacceptable.

In our days this sound weird. Killing for money and power is more or less common. But killing because of a mathematical question? This is not something you hear all the time.
But anyway, back to the question. If math is invented what does it mean? Does it mean that it is a mere game of thought? But if so why there are wrong answers? And if it is only a game of thought, then why it actually describes something real? Take E8 for example. Some people believe that it describes the shape of our universe and also all the particles are described in this symmetry.
The math is build on a logical basis. In fact, it is an old joke that math professors are the only one who can say that what they teach is always true and correct and it will stay so. But it does not explain why so often pure mathematics is found to either be useful in natural sciences or to describe something that exists in the real world.

If math is discovered, what is this strange "universe" that we are discovering then? The term Mathiverse is sometimes used for this. Also in some mathematical jokes we are told about things like "function city", "fractal forest" and so on. But are they real? Well the functions are real, but I really doubt that they have a city to live in. I cannot prove this of course, so all I can do is to say what I think about it, and it is fine if you think differently.

Personally, I believe that math is discovered. But I don't believe that we can talk about mathematical "entities" as if they were humans - they don't have cities, and they don't drink tea. So for me the term Mathiverse is just a reference to a very real set of objects. They are real because we can use them, and they are important because a lot of what we have depends on how well we understand them. Even the fact that you are reading it now is only possible because someone understood math well enough to build this monitor.

By the way the in the first paragraph is brought to you by a script that integrates latex to blogger (unfortunately there is no official way to type formulas here). You can get it here, and you can find its author here.

Thursday, December 20, 2007

Strike in the University

You probably don't know about this but all the universities in Israel (there are seven) are partially close for about two month now. The professors are on strike so they just don't show up.
They have a serious disagreement with the treasury. In Israel the professors salary is payed by the universities, but all the agreements about it are done with the government. Or more precisely are not done at all. The last contract they had ended a few years ago and the government simply refused to do a new contract. It lasted in this way for a few years and all went well - except for the inflation. Because of inflation the professors lost about 35% of their salary. At the end of last year they tried to begin talks with government officials about this but without any success.
This year they decided not to show up to classes until their demands are met. It didn't help. As far as I know the government refused to acknowledge the problem and they even said they don't care if the semester will be canceled because of this.
The students are the main victims in all of this, but for different reasons they prefer to wait and see what happens. Officially they support the professors, but many of them a very angry.
Personally I support the professors. I didn't go to any of the demonstrations and I don't plan to go. Partially it is because half of my courses are taught despite the strike but mainly because I simply don't see any point in such demonstrations. The government already showed clearly what they want. Their plan is to modify the universities so that they will bring immediate profit. It was already stated in a public enough way. As a side note there is even a poster near the entrance to the Hebrew University - "We want education not education ltd." So what is needed is a change of policy. And for this to happen ... only God knows what can cause this.
I hope the strike will end soon and that the professors will get what they want.

Saturday, December 15, 2007

Readability level

I recently did a check of this blog readability level on website grader. The site checks different specs including readability, google rank and so on. Strangely I got a Phd level. Since I tried to write it as simple as I could I was very surprised and amused by this result.

Anyway, I recently stumbled upon a site about octomatic number system. It is a system of base 8.
As of itself it is not very interesting - as I already wrote in a previous post, Evolution of numbers, all number systems that can be used for geometry are isomorphic to each other. However on this site they also offer to use different signs for the numbers:

What is interesting is the second row from below. The signs here are directly connected to binary. You can see it for your self if we will line to be 1 and empty space zero we will get:
000 001 010 011 100 101 110 111
And from the image you can tell immediately that 111=7. The same rule works for large numbers: 100111001 is for example 4*8*8+7*8+1=313.

The bottom row is a handwritten form. Personally I doubt that it is a good form, but it is their choice...

Friday, November 30, 2007

Should you go shopping?

This is a simple proof that you shouldn't. You cannot find anything useful in shops. And I am going to prove you this right now. The proof is by induction. I am going to prove that in any group of shops no matter how large, there is nothing interesting or useful.
Lets start with n=0 this is with the empty set. There are no shops in it so there is nothing interesting in them. Now lets suppose that we proved this for n=k. We just need to prove it now for n=k+1.
Lets therefore look at a random group of k+1 shops - {a1, a2, a3, a4 ....a(K+1)}. It can be viewed as a union of two groups - {a1,...,ak} and {a2,...,a(K+1)}. Since they both have the some number of shops in them - k, we know from our assumption that there is nothing interesting or useful in any shop in both of them. And since we don't get anything new when we unite the groups there is nothing interesting in the union also. And this completes the proof.

Now lets see another example. Lets suppose you have a random group of people. Is it true that all of them male or all of them female? In other words is it possible by choosing people randomly to get a group where there are both men and women? By now you probably think that I am crazy since I actually asked such a question, right?
Well lets see what math says about this. For n=1 we have a group with one human in it - either a a man or a woman obviously. Now lets suppose that we proved for n=k that any random group of size k has only men or only women. As in the previous example we can now look on a K+1 group as a union of two groups. And since we know that any group of the size k contains only men or only women they both contain only men or only women. Because a2 belongs to both groups and naturally has only one gender :) all the rest have to be the same gender - that is either male of female. And this completes the proof.

So now, after you saw this what do you think about mathematics?

Update: I guess I should have written this part in the first place but anyway: These proofs are wrong. It can be seen easily - just by simple example. In fact all the idea behind those proofs is that induction must be used with great care - or you might proof something that is plain wrong. A good way to check yourself is to try and prove your statement for n=3 and n=4. In the examples here there was no proof whatsoever. Induction is a very valuable and powerful tool but it is meant to be used for proving that some statement is correct for all n, when you know that it is correct for at least some n, and not for proving something you know that is not correct.

Wednesday, November 28, 2007

Evolution of numbers

We all know how numbers look. And sometimes it is even hard to imagine that they can have a different form that what is familiar to us. But while math is a rather ancient science our number system and our numbers are not very old. This photo shows their development in time:

As you can see even numbers in the middle ages were different from modern numbers. And I am sure that you would not even think that there is any connection between our numbers and Hindu.

It is a surprising fact however that there is just one number system. You will probably say it is not correct. But it is. Yes, there were a lot of different number system in history. Even in the present we have more then one. Take the binary system for example.
But if we want a number system that is good enough for both algebra and geometry, that is a system that lets us measure distance we discovery that there is only one such system - they are all isomorphic to each other. It means that you can give different names to numbers, you can have it in base 17 (for example) and not in base 10 but it will still be the same thing. In mathematical language - we have only one mathematical structure that is a complete ordered field.

Saturday, November 24, 2007

A bit of humor

Theorem: Every positive integer is interesting.
Proof: By contradiction, assume that there exists an uninteresting positive integer. Then there must be a smallest uninteresting positive integer. But that's pretty interesting! Therefore a contradiction!

(I really doubt that you will manage to proof this one in school..)

Top ten excuses for not doing homework:

1. I accidentally divided by zero and my paper burst into flames.
2. It was Isaac Newton's birthday.
3. I could only get arbitrarily close to my textbook. I couldn't actually reach it.
4. I have the proof, but there isn't room to write it in this margin.
5. I was watching the World Series and got tied up trying to prove that it converged.
6. I have a solar powered calculator and it was cloudy.
7. I locked the paper in my trunk but a four-dimensional dog got in and ate it.
8. I couldn't figure out whether I am the square root of negative one or i is the square root of negative one.
9. I took time out to snack on a doughnut and a cup of coffee. I spent the rest of the night trying to figure which one to drink.
10. I could have sworn I put the homework inside a Klein bottle, but this morning I couldn't find it

Q: What is the world's longest song?
A: "Aleph-nought Bottles of Beer on the Wall."

(Aleght-nought is infinity. It is from Group theory)

A story:
Some famous mathematician was to give a keynote speech at a conference. When he was asked for an advance summary, he said he would present a proof of Fermat's Last Theorem -- but they shouldn't announce it. Although when he arrived, he spoke on a much more prosaic topic. Afterwards the conference organizers asked why he said he'd talk about the theorem and then didn't. He replied that this was his standard practice, just in case he was killed on the way to the conference.

Another story:
I don't know if the previous story was real but this one is:
WHEN G. H. Hardy faced a stormy sea passage from Scandinavia to England, he took out an unusual insurance policy. Hardy scribbled a postcard to a friend with the words: "Have proved the Riemann hypothesis". God, Hardy reasoned, would not let him die in a shipwreck, because he would then be feted for solving the most famous problem in mathematics. He survived the trip.

A mathematician organizes a lottery in which the prize is an infinite amount of money. When the winning ticket is drawn, and the jubilant winner comes to claim his prize, the mathematician explains the mode of payment:
"1 dollar now, 1/2 dollar next week, 1/3 dollar the week after that..."

(This is a reason for not playing with mathematician in math games. Also as a interesting fact, you chance of winning in a real world lottery is less then the possibility that you will die this week.)

Tuesday, October 9, 2007

The longest word in English

This post turned out to be surprisingly popular, so I rewrote it to include not only the longest word but also a few other linguistic anomalies - a hill name 85 letters long for example. Happy reading...


The longest word turned out to be a scientific one, a full name of a protein - Titin, also known as connectin. It is 189,819 letters long. Professional dictionary writers regard generic names of chemical compounds as verbal formula rather than as English words, so it is a bit disputable if this can be viewed as a true word. it is too long to post here, so I am posting a shorter one instead - this one is only 1185 letters long:
I didn't even tried to read it or to pronounce it. This is however a perfectly real word and an example to the problems scientists have when they are out of words.

The longest word coined by a major author is a name of a fictional dish (183 letters):


For a long time it was the longest word known.

The longest officially recognized place name is a name of a hill in New Zealand (85 letters):


The name is often shortened to Taumata by the locals for ease of conversation. It translates roughly as "The summit where Tamatea, the man with the big knees, the climber of mountains, the land-swallower who traveled about, played his nose flute to his loved one".

Also the longest nontechnical word is (29 letters):


It is "the act or habit of estimating or describing something as worthless, or making something to be worthless by deprecation". This word is frequently used in maths and maths related subjects.
The is some disute about this word status - as of now wikipedia claims that the longest non coined and not technical word is (28 letters):


It is a political position that originated in nineteenth-century Britain, where antidisestablishmentarians were opposed to proposals to remove the Church of England's status as the state church of England forwarded principally by both Payne and Tuffin.)

Source - wikipedia.

Tuesday, October 2, 2007

Funny quotes

“Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.” -- Bertrand Russell

“Mathematics is the art of giving the same name to different things.” -- J. H. Poincare

"Mathematics consists in proving the most obvious thing in the least obvious way." -- George Polya

"A tragedy of mathematics is a beautiful conjecture ruined by an ugly fact.”

"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."

“Mathematics is like love; a simple idea, but it can get complicated.”

"Obvious is the most dangerous word in mathematics." -- E.T. Bell

"Mathematics is not a deductive science – that's a clichĂ©. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork." -- Paul Halmos

"Small minds discuss persons. Average minds discuss events. Great minds discuss ideas. Really great minds discuss mathematics."

An expert is a man who has made all the mistakes, which can be made, in a very narrow field.
Quoted in A L Mackay, Dictionary of Scientific Quotations (London 1994)

I consider that I understand an equation when I can predict the properties of its solutions, without actually solving it.
Quoted in F Wilczek, B Devine, Longing for the Harmonies

This result is too beautiful to be false; it is more important to have beauty in one's equations than to have them fit experiment.
The evolution of the Physicist's Picture of Nature Scientific American 208 (5) (1963)

What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school... It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it... That is because I don't understand it. Nobody does.
QED, The Strange Theory of Light and Matter, (London, 1990) 9.

And the most important one:
God used beautiful mathematics in creating the world. Paul Dirac

Wednesday, September 26, 2007

Article about primes

It is just a short article about basic properties of prime numbers. It's main purpose is to be a short introduction to what primes are.
Also this is the first article I have ever published on my site so I hope it is good enough.

Tuesday, September 25, 2007

New computer

My faithful but rather old computer suddenly died. It wasn't a surprise - I owned it for 7 years. I bought a new computer now a Core 2 duo 6550. It should last for a long time.
Because i was without my comp I coudn't post to the blog or to the site. Now I am in the prosses of installing all the programs I need into the new computer. I hope I will find time for this project.

Saturday, September 15, 2007


There are already plenty of links on Math Pages so in order to give to new links some spotlight it is time to do a short overview of recent addition.
Recent additions to computer section:
1. LiveCD - if you want to make custom live CD for your self or for other people this is the place to go. They will build you a live CD while letting you choose what it will include. It is based on Debian.
2. Linux network reference guide - it is pretty self explanatory. If you are running linux and want to learn how to use the terminal, it worth a look at.
If you don't know what linux/LiveCD is go here.

Recent additions to Student staff:
1. SpeQMathematics - a simple yet powerful and advanced program. For windows.
2. Equation Sheet - create personal equation sheets.

Recent additions to math section:
The shortest shortcut - how to multiply large numbers in your head.

Recent addition to physics section:
13 things that don't make sense - strange but true facts. There are no logical explanation for them to this day.

Thursday, September 13, 2007

I like AdBlock plus

If I would ever make a list of the best Firefox extensions, Ad Block would be on the top of this list.. It is simply the best an extension can be - it does its gob very well, and it doesn't distracts (unlike stumbleupon...). Moreover it removes the visual assault ads tend to be sometimes...

I installed it along time ago and since then I rarely see ads. It is very good in removing them, especially when used together with the Customize Google extension, which allows to also remove all the ads you normally see in your search results and in Gmail (and other Google products). Without the customize Google extension, Ad-block blocks Google ads only when you visit a website not own by Google.
If you want to be even more ad free, you can also install Element Hiding Helper for Ad Block and Filterset.G Updater. Together this four extension provide an excellent defense from all ads there are.. Also, if even this is not enough, it is very easy to create your own filters in Ad Block - just a few mouse clicks. I had to do this maybe 2-3 times in the last year.

I was never felt disturbed by Google ads, so I even didn't notice that this extension blocks them also. Actually I was sure it doesn't block them at all because it didn't block them in search results. However when I added Google ads to this blog and to my site I couldn't see them, they were completely blocked.

When inserting the code on my site I did a mistake so the adds appeared on top of content, blocking it from view. But because of Ad Block I didn't see this until today. I checked the site today with Ad Block turned off and fixed this. Now the ads are displayed at the bottom of the page and I will probably leave them there.
So... if you don't want to see ads get Firefox with Ad Block plus and with the customize Google extension. You will not see even those ads you actually wanted to see :).

The only problem with this setup is that is considered to be unmoral by some. If you are surprised by this, think why about why we have so much free services/sites on the internet? The reason for this is that they are paying their bills using adverting. Ads are not the only way to make money on the internet, but it is the most common one. By installing ad blocking software, you are killing this revenue model.

In the end this is a good thing. It is possible to make money online without ads, and probably this is where the internet is heading now. So, feel free to install ad block... This what I did anyway ;).

Wednesday, September 12, 2007

Template decisions

I am quite dissatisfied with my web site template. I tried to pick the best one, but they all are horrible enough to my taste. The main template issue is categories. I need to think about some nice way to organize them, so that they will be easily viewable.
What I thought about is something like that:
1. Make subtopics in every category. This is, Calculus, Linear Algebra, Number Theory, Topology and so on in math and Mechanics, Cosmology, Electricity, Quantum Physics etc in physics.
2. Organize the links in two columns instead of just one.

I hope I will manage to finish this by the end of the week.

Update round

Besides opening this blog today I also added a lot of links to the site. There is a lot more to add, but it will take some time. I think I have only added by now about half of my bookmarks. Perhaps I will finish adding them this week. Also I have a half written article that I want to finish writing and publish it on the site.
I plan to ad ads to my site and to the blog today. This is not something I want to do but I need money so I don't want to miss this opportunity. Also I added this blog to my wink account, claimID and to stumble upon. Hope it will bring some traffic.
Meanwhile you are all invited to check my site. It is not completely finished yet but it should be useful already. And make sure you checked the links in the fun category also.
Update: I added ads to the blog, they should start working soon. The blog is not indexed yet by google so it takes some time.

First post

I just created this blog to be used together with my site - Math Pages.
I intend to use it to post updates about my site. Perhaps I will also find other uses for it in the future. I hope that I will be able to write two or three posts per week. It depends on how much free time I will have.