Question

Hi Professor Puzzler, I was wondering if you could explain what an axiom is?

Katie M, Grade 11
South Dakota

Answer

Hi Katie,

Well, I'm guessing that you're taking a Geometry class, because that's when many students first see that term.

An axiom is something that you believe or accept to be true without having ever proven it.  It is something that you consider to be "obviously true." You might not realize it, but your life is filled with axioms - things that have never been proven to you, but you believe anyway.  I once asked a group of high school students to name some things they couldn't prove, but they were confident of anyway.  Here were some of their answers:

• My parents love me.
• The sun will rise tomorrow.
• Gravity keeps me from falling out into space.
• There is a God.
• 1 + 1 = 2.

Why are axioms important? Because when you are proving something, there will always be fundamental building blocks of ideas that your proof is based on, and it's important to remember that the most fundamental building blocks are actually things you haven't proved at all.

In a way, an axiom is sort of like what the Bible says about faith: faith is the substance of things unseen.

Euclid had some axioms (or postulates), and one of his very important axioms was that if you have a line, and a point that's not on the line, there's only one line that goes through the point, and is parallel to the line.  That might seem obvious, but some other mathemeticians like Lobachevsky, Riemman, and Gauss had some different ideas, and their notions of geometry turned out to be very different from Euclid's.

The assumptions you start with can drastically change your results!

In modern usage, the "obviously true" concept is not how axioms are always viewed; in another sense, we could view an axiom as simply a "rule of the game" in mathematics.  In other words, mathematicians might say, "Let's start from assumption X, and see what sort of mathematics we develop!"  The assumption, or axiom they begin with may not be something that's "obviously true," but often valuable results come from such game playing.

Thanks for writing,
Professor Puzzler

Question

Please explain the difference between the words "they're" and "their."

Andy K.
Grade 5

Answer

Hi Andy,

The answer isn't too complicated.  The word "their" is a possessive word.  That means that it shows that someone owns something.  In this case, it means that something belongs to a group of people (them). 

• They brought their car to the repair shop.

"They're" is a contraction of "they" and "are".  

• They're having car problems.

Here is a sentence that contains both words:

• They're hoping that their car will be fixed soon.

Thanks for asking!
Professor Puzzler

I get file attachments from both friends and strangers. Should I just open the ones from friends?

I would even think twice before opening file attachments from friends. What if your friend's computer has been infected by a virus, and the virus emails you a message with itself attached? You get the email, think it's from your friend, and open the attachment. *Poof!* Your computer is now infected!

The only time you should open an attachment even from a friend is if it is a file type that can't carry viruses (generally speaking you can open image files, but even with those, believe it or not, someone developed a virus to attach to an image (read below for a question and answer about that).

If you have any doubt about whether a file type can carry a virus, don't open the email. Call or email your friend and say "Did you send me this file?" If they say no, obviously you aren't going to open it. And if the message is from a stranger? Don't open it at all! I occasionally get resumes from people who want to work for me, and rather than mailing them, they send them as Microsoft Word Documents. I don't know them from Adam, and I won't open their attachments.

I get emails with picture files (stuff with .gif?x=5, .bmp, and .jpg?x=5 file extensions) attached. I know there are some kinds of email attachments I should never open; what about these? Can I get infected through these?

Well...yes, technically, it is possible, but only under the following scenario. Your computer has to already be infected with another virus whose purpose is to act as interpreter for the image virus. Seems kind of pointless to me. (The "Perrun Virus" was an example of this kind of virus, which attached to jpg files. A lot of hype, not much action)

However, you still need to be careful when opening images attached to emails. Be sure that the file extension really is an image extension (the ones you listed, plus a few others). I've seen emails come in with file names like "yourpicture.jpg?x=5.exe". Clever. The extension isn't really 'jpg', it's 'exe', and you already know you should never open those. And remember: if the attachment is from someone you don't know, why would you bother opening it anyway?

Is it okay to put my credit card number, expiration date, and other information in an email? I'd like to purchase a product online, and they want me to put my credit card info on their website; is it really any different to put it in an email?

Actually, this question is the one that finally convinced me it was time to create my Q&A website. I was absolutely horrified yesterday to receive an email from a potential customer who wanted to buy one of my products, and had put his credit card number, expiration date and name in his email to me! Never, never, never do this! Don't even think about it! People tend to think that email is a private correspondence between them and their intended recipient. That would be a nice theory, but it is not guaranteed!

Remember that emails do not send or receive over secure sockets, which means if someone was looking and analyzing in the right place at the right moment, they could intercept your data packets and snag your credit card number. Where your credit card number is concerned, it is better to be paranoid than sorry.

I'm kind of annoyed that after buying my AntiVirus software, the company is hitting me up for a "subscription renewal"? What in blue blazes is that, and do I really need to do it?

Yes, you need to keep renewing your subscription. It's one of the most painful expenses you'll face each year--not because it costs so much (all things considered, it really isn't so bad) but because it's a fee you have to pay for the malice and moral bankruptcy of the virus creators.

See, that yearly fee you pay helps to pay the costs of all the teams of computer geeks who are working to circumvent the viruses that are being cranked out on a daily basis. You may say "But it's not fair that I have to pay for someone else's deviant behavior." And you would be exactly right in saying that. It isn't fair.

But it also isn't fair to ask a software company to protect your computer from new viruses every day for free either. You see, every time a new virus is invented, some software developer has do design a way of capturing and removing that virus. And guess what! Software developers don't work for free, and we shouldn't expect them to! So, grin and bear it, and keep reminding yourself, not a penny of that money goes to the guy who invented the virus.