A common misunderstanding

A few days ago, one of the lectures in the university told us about a funny (but real) news report he once heard on TV. It was shortly after the discovery that 2^(42,643,801)-1 is a prime. (For more information about this go to Mersenne prime search website). On this TV program a reporter was interviewing a math professor. The conversation went like this: (R= reporter, P=professor)

R: So what do you have to say about the discovery of the largest prime number 2^(42,643,801)?
P: The number 2^(42,643,801) is not prime since it is an even number. You must have ment to say 2^(42,643,801)-1.
R: Well, they are close enough. The important thing is that this is the largest prime number.
P: It is not the largest. Euclid proved that there is an infinite number of prime numbers so there is no such thing as the largest prime.
R: Is it still correct today that there are infinity many prime numbers?

I really find it hilarious how some people think that a mathematical proof is something that is subject to changes. Sure, sometimes we have errors or we find better proof, but the there is no change in the fact itself. I suppose it is somewhat understandable why people act like this - they are too used to seeing things change. But it is still hilarious to watch, as long as you not part of the discussion.

Unique captchas

Apparently some sites use captchas to assure the intelligence level of their users:

The reliability of wikipedia

As you all know there are many articles on wikipedia, and their quality varies greatly. However the main problem is that in many cases it is impossible to tell if a particular article is accurate or not. For example, I just found the following article on wikipedia:

Beard-second
The beard-second is a unit of length inspired by the light year, but used for extremely short distances such as those in nuclear physics. The beard-second is defined as the length an average physicist's beard grows in a second, or about 5 nanometers[1].

One beard-second equals 50 Ångströms (10^-10 m). 20000 Beard seconds equal 1 RCH. 2000 Beard seconds = 1 RBC.

Google search supports the beard-second for unit conversions.[2]

Unsurprisingly, this article is being considered for deletion in accordance with Wikipedia's deletion policy. Suprisingly, the part about Google supporting beard second in unit conversion is actually true. After a quick search on the internet, it seems that the beard second was invented as a teaching exercise a few years ago.

In this case, the article seems to be a joke, but in reality it is about a funny teaching exercise....

The future

Found on the web - Pizza 2015:

Operator: "Thank you for calling Pizza Hut. May I have your..."

Customer: "Hi, I'd like to order."

Operator: "May I have your NIDN first, sir?"

Customer: "My National ID Number, yeah, hold on, eh, it's 6102049998-45-54610."

Operator: "Thank you, Mr. Sheehan. I see you live at 1752 Meadowland Drive, and the phone number's 494-2399. Your office number over at Lincoln Insurance is 745-2302 and your cell number's 266-2566. Which number are you calling from, sir?"

Customer: "Huh? I'm at home. Where d'ya get all this information?"

Operator: "We're wired into the system, sir."

Customer: (Sighs) "Oh, well, I'd like to order a couple of your All-Meat Special pizzas..."

Operator: "I don't think that's a good idea, sir."

Customer: "Whaddya mean?"

Operator: "Sir, your medical records indicate that you've got very high blood pressure and extremely high cholesterol. Your National Health Care provider won't allow such an unhealthy choice."

Customer: "Dang. What do you recommend, then?"

Operator: "You might try our low-fat Soybean Yoghurt Pizza. I'm sure you'll like it."

Customer: "What makes you think I'd like something like that?"

Operator: "Well, you checked out 'Gourmet Soybean Recipes' from your local library last week, sir. That's why I made the suggestion."

Customer: "All right, all right. Give me two family-sized ones, then. What's the damage?"

Operator: "That should be plenty for you, your wife and your four kids, sir. The 'damage,' as you put it, heh, heh, comes to $49.99."

Customer: "Lemme give you my credit card number."

Operator: "I'm sorry sir, but I'm afraid you'll have to pay in cash. Your credit card balance is over its limit."

Customer: "I'll run over to the ATM and get some cash before your driver gets here."

Operator: "That won't work either, sir. Your checking account's overdrawn."

Customer: "Never mind. Just send the pizzas. I'll have the cash ready. How long will it take?

Operator: "We're running a little behind, sir. It'll be about 45 minutes, sir. If you're in a hurry you might want to pick 'em up while you're out getting the cash, but carrying pizzas on a motorcycle can be a little awkward."

Customer: "How the heck do you know I'm riding a bike?"

Operator: "It says here you're in arrears on your car payments, so your car got repo'ed. But your Harley's paid up, so I just assumed that you'd be using it."

Customer: "@#%/$@&?#!"

Operator: "I'd advise watching your language, sir. You've already got a July 2006 conviction for cussing out a cop."

Customer: (Speechless)

Operator: "Will there be anything else, sir?"

Customer: "No, nothing. Oh, yeah, don't forget the two free liters of Coke your ad says I get with the pizzas."

Operator: "I'm sorry sir, but our ad's exclusionary clause prevents us from offering free soda to diabetics."

Politics

The only good thing in politics, in my opinion, is that most of the time it doesn't influence you directly. Unfortunately, this is not the case for me now. The rest of the post is my complains, so feel free not to read it.
First of all, there are elections to the mayor office at Jerusalem at the middle of next month. As of now, I don't even intend to vote because I don't have the time nor the desire to check the information available on the candidates. Also, I will probably be too busy studying anyways. What annoys my most is that for some reason I got a call asking me to help with the election process - to take attendance notes. I have no idea why they called me with this..

Secondly, next week I suppose to start a new semester. However the university already sent letters telling all the students that the semester will not open because the government doesn't give them the money they need. They even included a long list of emails in the letter to where we can send complains. I really doubt that anything will happen to the semester, but who knows...

Thirdly, due to government policies and economical crisis the apartments in Jerusalem are rather expensive now, and my family and I are currently looking for a new apartment. Horrible timing... I certainly hope that we will find something soon.

On a somewhat brighter note, here are link to some political jokes I found:

Two political candidates were having a hot debate. Finally one of
them jumped up and yelled at the other: "What about the powerful
interests that control you?"

The other guy screamed back, "You leave my wife out of this."

Found this one here, follow the link for more.
Also check the Circle vs. Square webcomic, its author did an excellent job making fun of politics without insulting anybody.

What is persistence?

The following story is from Clientopia. I do not know if it is real or not, but after reading it you will surely understand what does it means to completely concentrate on your goal leaving behind any doubts...
---------------------------------------------------------------


I have had my company mobile for nearly 2 years, out of the 50 odd calls I've had, only 3 were legitimate, the rest were wrong numbers. This is a transcript of the one man who has called me more than 35 times.

Me: Hello, XXX IT, XXXX speaking, how can I help?

Random: Is that Brian?

Me: No, this is XXXX

Random: Are you sure?

Me: I should think I am. I've never been called Brian, and there isn't a Brian involved with this mobile

Random: Oh, can you put me through to him?

Me: No, as there isn't a Brian here, or in XXX IT

Random: Now I know you're lying, this is the number he gave me, now put him on the phone!

Me: I'm sorry, you've got the wrong number

Random: NO I HAVE NOT! BRIAN GAVE ME THIS NUMBER

Me: Then Brian got the wrong number

Random: I THINK HE KNOWS HIS OWN MOBILE NUMBER

Me: On the current evidence, I would say he doesn't, I cannot help, goodbye. *click*

----

He rings back, I don't answer.

----

12 (!) calls later he gives up. Then calls back the next day:

Me: I'm sorry you've got the wrong number, you rang yesterday several times.

Random: THIS NUMBER WAS GIVEN TO ME SO PUT ME THROUGH

Me: *click*

He has since called back several more times.

How old!?

I didn't post anything humorous for a lot of time, so here goes. As far as I know this one is a real story.
---------------------------

Customer: “I’d like two tickets for [movie], please.”

Coworker: “That movie is rated R. Can I see your ID?”

Customer: *shows an ID that states she is 18*

Coworker: “You need to be 21 in order to purchase an R-rated ticket for someone else.”

Customer: “But it’s for my son!”

Coworker: “How old is your son?”

Customer: “16…”

Coworker: “So you’re 18… and you have a 16 year old son?”

Customer: “That’s right!”

Coworker: “Let me get my manager…”

Manager: “Ma’am, you need to be 21 to purchase a ticket for a minor.”

Customer: “But he’s my son!”

Manager: “You’re telling me you gave birth when you were two years old?”

Customer: “YES! It happens, I promise you!”

--------------------
I found this story here.

Amazingly funny

I just read a post on Astroengine about a recent development concerning LHC. I rare write about post written on other blogs, but this time I felt is was just unfair not to share this. The main idea is that some person named Tia Aumiller decieded to open a group called: "People for the Ethical Treatment of Hadrons" (PETH).

It is not 1 July today, but I really hope that this is not a prank... Anyway, this organization has already protested in front of CERN. Their claims are:

“You’ve got these subatomic particles accelerated at great speeds for the sole purpose of being destroyed. No one thinks of the ethical implications of this. There’s a limited supply of hadrons in the universe. Do we just want to go around destroying them? What if we run out? What if the hadrons can feel pain? Will we look back at this hundreds of years from now and regret it? Kinda like we do with the killing of bacteria with antibiotics now.”

It is just unbelievable and extremely hilarious. I really have no idea how crazy somebody has to be to really believe in this.

Update: After checking this a bit, this story turned out to be fake. However it is still very funny so I am not removing this post from my blog. I guess I should learn a lesson from this - no posting of things that look fake, even if they are funny...

Lets do math!

I just found the best cat photo for a long time:

Original unknown

You are not going to say no to him, right?
Unfortunately, this is not a question that is likely to be solved soon. It already stood for a long time, and only a few weeks ago there was another unsuccessful attempt to prove it. Well, to be precise there are such "attempt" every week, but most of them are just attempt to get attention (and to win the one million dollar prize) by people who simply don't know math well enough to prove this theorem. The attempt I mentioned was a paper submitted by a professor who already had some previous work done about the RH. While this proof was met without much optimism, it looked serious. But even in his paper an error was found in 24 hours.

By the way, while there is a prize for proving RH, there is no prize for showing that it is wrong. In my opinion the reason for this is that showing it wrong doesn't necessary require mathematical advance. All you need to show that it is wrong is to find a zero of the Riemann zeta function which is not on the critical line. This can be done using a computer, without bringing any new ideas to math.

Math kitty

Photo by Dave Hogg

Apparently cats love studying math, only they are rarely caught doing so...

The weirdest "Hello" ever

Today in the morning I was just entering the Einstein Institute Building in the Hebrew University when another student was going outside. I talked with him a few time before, he is also studying mathematics, and is a really nice person. We both were in a hurry, because it was almost the time for our lectures to begin, so we just said "Hello" and went on. Well, almost. I just said "hello". He said" Oh! Hello professor, how are you doing?". I am not a professor, and nobody was standing behind me. Since it was totally unexpected, and I was in a hurry I even didn't react in any way to this. That was a weird morning... While I want to do an advanced degree in math, I am sure I never told him about it, so I really fail to see why he would joke like this.. Well, it might be prophetic. :)

On a more serious note, the semester ends on 4/9. Oh should I say, the exam month begins on 4/9. Anyway you put it, it is good news actually. I feel that I really want to start learning new courses, that is I want to start the next semester. I need to study a lot for two of the exams, I don't feel that I know these courses material well enough. But I am sure I will manage.

The genius of Newton

This is just a short joke I found today:

Archimedes, Pascal, and Newton are playing hide-and-seek.
Archimedes covers his eyes and starts counting.
Pascal looks around and hides behind a bush.
Newton grabs a stick and scrapes a one meter by one meter square in the dirt and stands in it. Otherwise he does not hide at all.
Archimedes opens his eyes and looks around. Of course, he immediately sees Newton and calls "I see Newton" Newton calmly says "But hang on, one Newton in a square meter is a Pascal!"

It is handy when you have physical units named after you......

Cats are the best....

I usually don't see dreams, and I see dreams about mathematics only very rarely. However, this night I had a dream about mathematics, and my cat managed to turn it into the most bizarre dream I ever had... The first part of this post is the story itself, hope you will find it funny, and the second part is about power series.

In my dream I had a conversation about sums of infinite power series. I have no idea why I would see a dream about them, it is not like I was thinking much about this. Just when the conversation turned to a specific simple problem, my cat decieded that he wants my pillow. In other words he came and sat down on it (I guess I should be thankful that he didn't sit on my head...). Naturally, this waked my up and I attempted to remove him, while still half emerged in the dream. This effectively turned the conversation I had in my dream in a conversation with my cat. Eventually I manged to convince him to get off (not before he tried to bite me for this).
I have always claimed that while dogs are "mens best friend", cats are "mathematician best friend". Now I am sure in this. Somewhere deep inside them hides a mathematical mind... :)

Photo by Per Ola Wiberg..(PO...or Powi)

Now, to the problem I mentioned. It shall be named the dreaming cat problem (for no reason whatsoever). The problem is as follows: Suppose you have an infinite sum:

Suppose also that the sum converges for all x such that |x|<>R. R is a fixed positive number. If you will write instead of x, M-x (M is a fixed number) what will happen, if anything? The answer - absolutely nothing interesting. The only thing that will change is that now the sum will converge for all x such that |M-x| to ? This is more interesting, we will now get that the series converges for |x|<=<.

This is result is not obvious, so it is time to proof all what I written. Firstly, lets proof that there is indeed such R. To do this we will use the root exam for infinite sums. This exam says that any given infinite sum converges if (The limit is when n approaches infinity) and it doesn't converge if the limit is greater than one. If we will take this upper limit from the series we have we will get .

If we will suppose that the right side is equal to we will get that the sum converges for all |x|R.

To proof the second part, we will first need to proof a different statement. Given two different infinite sums and which converge for and , for what x the sum ) converges? Lets use the above method:

So we get that .
We can now use this formula to solve the problem. Lets suppose that for all n. Then . From this we will get that R in the above formula is 1. Now if we will divide by we will get that But is exactly R from the statement I wanted to proof, so we get that indeed this new series will converge for all |x|<=<.

Circle Versus Square

Surprisingly, I found myself without ideas for what to write today. This is the first time it happens to me.. This is not to say that I have nothing to write about, I have a post about solving third and fourth degree polynomials that I am slowly writing (it is hard to write in Latex), but it is not finish yet, and it is clear that I will not be able to finish it today.

However, lack of ideas never stopped me before so it is not going to stop me now. In other words, it is clearly the time to write about a webcomic I found some time ago. The comic is about a Circle and a Square. It is very simple, black and white. However, it is very funny to read.
The two main characters (circle and square) are in a constant fight with each other. The reason for fighting is that the square hates all circles without any reason. If they were human, the square would have killed the poor circle a lot of comic stripes ago, but since they both are geometrical figures this is impossible - in the comic number 5 you can watch them discover their immortality. My general impression from the comic is that the square is the one who attacks, while the circle "puts him in his place", however it is not clear from the first strips.

Posted with permission

By the way, the comic author, Wakcher, has recieverd threats for legeal action because of this webcomic. Suprisingly, there are people who find a fight between two geometrical figures "offending to all the mathematicians" and "consider aking for formal appology". I would not be suprised to find out that these threats, which he published on his website, are not real. The last one is just to razy to believe that anyone would write such a letter. However, the letters he published are hilarious, so if you want to have a good laugh go read them. It is not pirate bay legal page, but it is close (and without profanity).

Who knows perhaps that comic will cause people to think a bit more about geometry (and mathemaics as a whole)... Take for example the question of circle and square being immortal as concepts. If they are inded immortal, we can conclude that they were from the beginning of the world, if not before. But if they existed before and exist now, where are they? Does the concept of "Math Universe" have some basis? Is math invented or discovered?

Theses two question have no clear answer. It is more a matter of faith. There are mathmaticians who think that math is discovered, and there are those who desagree. I personally see a lot of reasons to think that math is discoverd, but this is not something that I can prove.

Mathematical jokes

It have been some time since I posted anything funny so here goes:

Q. Why do mathematicians like national parks?
A. Because of the natural logs.

Person 1: What's the integral of 1/cabin?
Person 2: A natural log cabin.
Person 1: No, a houseboat – you forgot to add the c!

The indefinite integral of 1/cabin is "ln(cabin) + c", or "A natural log cabin plus the sea", ie. "A houseboat".

A mathematician and his best friend, an engineer, attend a public lecture on geometry in thirteen-dimensional space. "How did you like it?" the mathematician wants to know after the talk. "My head's spinning," the engineer confesses. "How can you develop any intuition for thirteen-dimensional space?" "Well, it's not even difficult. All I do is visualize the situation in n-dimensional space and then set n = 13."

Found at Wikipedia

Really bad logic

I found a site about logical paradoxes. I love such paradoxes, so I was really happy to stumble on such a site. However, while some of the paradoxes mentioned on that site are classical examples, the explanations were of extremely low quality. The reason I am writing this is that one of the paradoxes I read there has an interesting connection with set theory. I am not going to link to this site, but I will write the "paradox" here:

The paradox arises from considering the following two statements:
1. All ravens are black.
2. Anything that isn't black isn't a raven.
Obviously, both of the statements are true. Also, they clearly say the exact some thing. Therefore if I can find somethings that shows that the second one is true, it must follow that so is the first one. Lets suppose that I found a green parrot. It is green and it is not a raven, so it supports the second statement. So, because I found a green parrot I conclude that all the ravens are black.

The problem is that the line of thought shown in this "paradox" is not correct. I never heard before about this paradox, so it might be an invention of the owner of the site I find it on. Or, it is not explained properly there (who ever wrote it managed to make the barber paradox look weird..).

If we will look on this paradox from set theory point of view, we will see that statements say:
1. If a is in A, then a is in B.
2. If a is not in B, then a is not in A.
The paradox tries then to sell us the idea that: If c is in C and not in B then all a are in B. In this form the fact that this paradox is just a game of words becomes clear. While there are paradoxes, the only paradox in this is that some people (at least the owner of the site I found it on) actually see this as a paradox...

A bit of humor

Due to the sudden need to buy a new refrigerator, I don't have as much time as usual to blog. If all goes well I will get the refrigerator tomorrow, and will continue to write about polynomials. But meanwhile - a bit of humor. I found the following picture on the net:

For some reason it reminds me about the fact that a proof of a theorem can be wrong, but if proven it is correct forever... Yes, I think too much about math.

I also found two excellent posts today. One of them is a very detailed answer to questions from "Some myths and analyses on learning and teaching mathematics" by George Brown. The answer was written by Beans at Me Or My Maths. My own experience is not the same as his - so I feel that I would answer differently to some of the questions, but it was an interesting post to read. In this post, he also linked to a collection of 36 methods of proofs. In this list are such excellent proofs as proof by imagination....

Have you ever saw the photo of Pythagoras?

This was a question asked on a lecture today - by the professor. After not getting an answer, he concluded that we didn't see the photo, so he told us he will draw it. I thought about photographing it, but my cell phone camera is not very good. The drawing you see below is my recreation of his drawing:



I am starting to think that this particular professor has a special love to Pythagoras theorem.. Not so long ago he told the class a story about a graduate student, who was asked on a final test for M.S. what do you know about Pythagoras theorem (in Hebrew theorem and trial is the same word), and he answered I think the jury decided he is not guilty...

Buying a refrigerator

Unfortunately, I have to buy a new refrigerator. The old one has been working for a long time, but it appears that it is time for him to go to the great electronics beyond. Because of this and some other things, I spent most of the afternoon in shops today. Not a good way to spend half a day...

Now to the reason I am writing this post. I was asking people for recommendations, what company has good quality, and where to look for good deals for some time already. So I figured it would be a good idea to post this question to my blog. Currently I am looking at LG, Sharp, Amcor and Siemens. The Siemens are all too tall, and Sharp is expensive. LG looks like it will break any minute. Amcor is nice, but I heard that they all have a little defect, because of which they require constant maintenance. If you have any experience with these please share it with me..

Since this is a math blog - a bonus question. If the following integral (the borders are 1 and plus infinity) is finite, and f(x) is continues everywhere:

Does it means that the limit of f(x) when x approaches infinity is zero? I will publish the answer after a few days, meanwhile feel free to say what you think in the comments.

Quantum cat

A quantum cat. I am sure Schroedinger didn't think that his little experiments will become the reason for so many jokes..

Science is fun sometimes, isn't it?

Since in this case we see the cat, we are sure that he is in the box (and we know he is alive). And therefore this is not a paradox. However, it is always good to think about puzzles of quantum mechanics...