# Understanding Mathematics

People wrote differently in those days, obviously the vulgar mechanick may be a man and he that is able to reason nimbly and judiciously may be a woman, (and either or both may be children).

for complicated mathematics building on simpler mathematics.

The following examples illustrate the difference between the two approaches to understanding mathematics described above.

You won’t be able to learn how to understand mathematics from abstract principles and a few examples. Instead you need to study the substance of mathematics. I’m hoping that the answers to the following

will illustrate how mathematics is meant to make sense and is built on a logical procession rather than a bunch of arbitrarily conceived rules.

One of the main things that turned me on to mathematics were certain concepts and arguments that I found particularly beautiful and intriguing. I’m listing some of these below even though they may not be frequently asked about. But I’ll hope you’ll enjoy them, and perhaps get more interested in mathematics for its own sake.

## Solving Mathematical Problems

The most important thing to realize when solving difficult mathematical problems is that one never solves such a problem on the first attempt. Rather one needs to build a sequence of problems that lead up to the problem of interest, and solve each of them. At each step experience is gained that’s necessary or useful for the solution of the next problem. Other only loosely related problems may have to be solved, to generate experience and insight.

Students (and scholars too) often neglect to check their answers. I suspect a major reason is that traditional and widely used teaching methods require the solution of many similar problems, each of which becomes a chore to be gotten over with rather than an exciting learning opportunity. In my opinion, each problem should be different and add a new insight and experience. However, it is amazing just how easy it is to make mistakes. So it is imperative that all answers be checked for plausibility. Just how to do that depends of course on the problem.

There is a famous book: G. Polya, How to Solve It , 2nd ed., Princeton University Press, 1957, ISBN 0-691-08097-6. It was first published in 1945. This is a serious attempt by a master at transferring problem solving techniques. Click here to see an html version of Polya’s summary.

The main thing that keeps mathematics alive and interesting of course are unsolved problems. Many open problems that are important in the contemporary view are hard just to understand. But here are

for which you can form your own conjectures. The word simple in this context means that the problem is easy to state and the question is easy to understand. It does not mean that the problem is easy to solve. In fact all of these open problems are difficult. (That’s why they are unsolved, it’s not that nobody tried!)

## Acquiring Mathematical Understanding

Since this is directed to undergraduate students a more specific question is how does one acquire mathematical understanding by taking classes? But that does not mean that classes are the only way to learn something. In fact, they often are a bad way! You learn by doing. For example, it’s questionable that we should have programming classes at all, most people learn programming much more quickly and enjoyably by picking a programming problem they are interested in and care about, and solving it. In particular, when you are no longer a student you will have acquired the skills necessary to learn anything you like by reading and communicating with peers and experts. That’s a much more exciting way to learn than taking classes!

Here are some suggestions regarding class work:

# Ask Jud – The world’s finest virtual tarot

Do you need to ask a question? Are you looking for answers? Jud offers you a space to ask anything you want. However, before each question you must write a petition. If the answer is not what you expected, at least you make catharsis and ask again.

## The world’s best virtual tarot

Jud is a virtual tarot that that can answer all kinds of questions. Questions about the present, the past, and your future. He can be a bit tempermental, requiring that each question be presented with a petition of “Jud, please answer the following question” or “Jud, please answer” before each question is asked. Failure to correctly petition will not bring results.

Jud was born in 2007. As he began to age, he realized he had an ability to read the fortunes of others, and quickly became a star in his small hometown. To expand his operaion, he knew he had to join the digital age. Through the use of modern technology, he is able to answer thousands of questions every day from people all over the world.

In early 2016, the demand for Jud’s services became so high, he brougt on 10 additional team members from around the country to increase answer throughput. With a large team, and his mind in overdrive, he is now able to answer upwards of 13,240 questions per day (Average over the past 30 days), with pinpoint accuracy. Though the team members are new, they are just as tempermental. Requiring a correct petition each and every time.

## Has Jud ever been seen?

A dark and blury photograph of Jud was captured in early 2010. The developed image is shown below:

## The Twitter migration of 2015

In early 2015, Jud moved part of his online presence to Twitter, under the handle @TheAskJud. It wasn’t before long before the crowds of people following his presence online made the jump to Twitter. His ability to answer many different types of questions, both online and on Twitter attracted many.

His Twitter has been inactive for two years due to an oversubscription of requests. Twitter hadn’t created the tooling for him to keep up with demand. Though there may come a time for him to return, there are no plans at this time.

## Questions?

I am Ask Jud, the world’s best virtual tarot

# Understanding Mathematics

People wrote differently in those days, obviously the vulgar mechanick may be a man and he that is able to reason nimbly and judiciously may be a woman, (and either or both may be children).

for complicated mathematics building on simpler mathematics.

The following examples illustrate the difference between the two approaches to understanding mathematics described above.

You won’t be able to learn how to understand mathematics from abstract principles and a few examples. Instead you need to study the substance of mathematics. I’m hoping that the answers to the following

will illustrate how mathematics is meant to make sense and is built on a logical procession rather than a bunch of arbitrarily conceived rules.

One of the main things that turned me on to mathematics were certain concepts and arguments that I found particularly beautiful and intriguing. I’m listing some of these below even though they may not be frequently asked about. But I’ll hope you’ll enjoy them, and perhaps get more interested in mathematics for its own sake.

## Solving Mathematical Problems

The most important thing to realize when solving difficult mathematical problems is that one never solves such a problem on the first attempt. Rather one needs to build a sequence of problems that lead up to the problem of interest, and solve each of them. At each step experience is gained that’s necessary or useful for the solution of the next problem. Other only loosely related problems may have to be solved, to generate experience and insight.

Students (and scholars too) often neglect to check their answers. I suspect a major reason is that traditional and widely used teaching methods require the solution of many similar problems, each of which becomes a chore to be gotten over with rather than an exciting learning opportunity. In my opinion, each problem should be different and add a new insight and experience. However, it is amazing just how easy it is to make mistakes. So it is imperative that all answers be checked for plausibility. Just how to do that depends of course on the problem.

There is a famous book: G. Polya, How to Solve It , 2nd ed., Princeton University Press, 1957, ISBN 0-691-08097-6. It was first published in 1945. This is a serious attempt by a master at transferring problem solving techniques. Click here to see an html version of Polya’s summary.

The main thing that keeps mathematics alive and interesting of course are unsolved problems. Many open problems that are important in the contemporary view are hard just to understand. But here are

for which you can form your own conjectures. The word simple in this context means that the problem is easy to state and the question is easy to understand. It does not mean that the problem is easy to solve. In fact all of these open problems are difficult. (That’s why they are unsolved, it’s not that nobody tried!)

## Acquiring Mathematical Understanding

Since this is directed to undergraduate students a more specific question is how does one acquire mathematical understanding by taking classes? But that does not mean that classes are the only way to learn something. In fact, they often are a bad way! You learn by doing. For example, it’s questionable that we should have programming classes at all, most people learn programming much more quickly and enjoyably by picking a programming problem they are interested in and care about, and solving it. In particular, when you are no longer a student you will have acquired the skills necessary to learn anything you like by reading and communicating with peers and experts. That’s a much more exciting way to learn than taking classes!

Here are some suggestions regarding class work:

# how to use peter answers

## Peter s Answers to Fan s Questions

Thank you to all of Peter s amazing fans who participated in our Question Answer fan activity and sent in questions for him! With his busy schedule, Peter has just now sent us some of his answers for your enjoyment. He had fun reading the large amount of questions from his fans and responding to a chosen few with his usual witty humor and charm. Thanks Peter for being such a good sport! We look forward to doing more fan based activities with you on your website.

What s the funniest thing that happened to you on a set?

Not the funniest, but I had the most fun playing Backgammon with Glenn Close. She’s very competitive.

I have noticed that in your career you have not made films from the time of the kings. Would you like to?

Yes. I recently did a period piece in the 1920’ where I played Bugs Moran. Head of the Chicago Mobs Irish territory. Had so much fun playing that period. I’d like to do more period pieces. Scorpion King was the closest I got to playing that “ln time of kings”, different time then Middle Ages but I still got to wear some chaimail shirts, carry a sword, and ride a horse. I’d like to do more of that. It’s so fun traveling back to different time periods.

What is the first thing you notice in someone?

Their eyes. It’s the window to the soul

How many Ethan’s naughty magic chocolates do you think you ate during the filming of the movie?

Any plans on writing any more YA novels or sequels to After The Red Rain?

Not at this time. I’m focusing my writing on some screenplays and TV shows I’ve been working on.

Do u speak some Italian ? Or would you like to learn it?

I speak some. I can understand more then I speak. When I go back to Italy I pick it up fairly quickly. But I’d like study it more and be more affluent.

What s your favorite song at the moment ?

The Weight by The Band. Been learning to play it in my guitar so it’s stuck in my head all the time.

If you could meet any person dead or alive, who would it be?

If you could be anyone for one day who and why?

Hmmm. I kinda like being me.

What s one place you haven t traveled to but would like to someday?

A few. India. Bali. And Africa.

## The Passport Peter Project Has Launched!

Get ready, the Passport Peter project has officially launched! Here is your chance to get involved in a project that lets you use your creativity while having fun at the same time. You will get to share your adventure with others on Twitter and the final project will be sent to Peter himself so that he can enjoy the travels, photos and journaling.

There are a few rules that have to be maintained during your visit with Peter . Please make sure that you read through this list and follow it. The bottom line is to have fun and give Peter a great gift to enjoy when the project is over.

• Send Passport Peter on his next journey within 3 days after receiving him.

• Post ONE photo of you and Passport Peter on Twitter making sure to tag @OfficialPFWeb with photo with your location and city, state (Heinz Stadium, Pittsburgh, PA)

• All photos must be PG-rated. Use your creativity with them but please keep it classy.

• Make a ONE page journal entry about your time and adventures with Passport Peter . The real Peter will get to read all these amazing entries at the end of Passport Peter s trip around the world so have fun when you chronicle his adventures with you.

Peter will be choosing one lucky photo from all those that are submitted to win a special prize. So make sure that you use your creativity, have fun and enjoy your 3 days with Passport Peter on this chance to show Peter your town, friends and life.

## New Trailer For Gangster Land, Opening Dec. 1st

Watch the new action packed trailer with Peter as Bugs Moran in the new movie Gangster Land . Mark your calendars for the December 1st release date of Gangster Land . Catch Peter s new movie in theaters, on Demand Digital. View the new article in the Hollywood Reporter here.

# How Does Ask Peter Work? The Code Behind the Prank

For a number of years, one of my hobbies has been researching paranormal scams. These are situations where an individual claims they can predict the future, that they ve discovered the secret to antigravity, or that they work for the government and know the truth about aliens. A common thread in all of that surreal research is that generally, an unnerving number of people are very, very gullible.

That gullibility multiplies significantly when the event being portrayed includes something that appears supernatural or magical in nature. Deep down, many people still want to believe in magic and when they are presented with the opportunity to believe again, they jump all over it.

A case in point is a website that is very popular among the prankster community called Ask Peter (or Peter Answers). The footer text lists the page as a Virtual Tarot, as though the page truly has the ability to predict your future or answer any of your questions. In this article, I answer the question: how does Ask Peter work?

### How Does Ask Peter Work? The Believer Perspective

First, I m going to show you how the website works for the person off of the street who knows nothing about the inner workings of Ask Peter. When you first arrive at the website, you ll see a very simple web form.

The point of the website is that it s a sort of electronic tarot which will peek into your future and answer your questions accordingly. However, Peter is a fickle psychic, and he must be treated with respect or he won t answer your question. Therefore, before you ask a question, you must petition Peter with the sentence, Peter, please answer the following question: If you re using the Peter Answers site alone and you don t know the secret behind the site, you ll typically get an answer like this:

What s up with that? Ah, but it s all part of the show, folks. The magic really happens when you bring in a second person who knows Peter s terrible secret (after reading this article, that will be you!) The second person needs to type in the petition and question for you, and then you ll get the answer which is usually remarkably accurate.

If the person typing the question knows the secret, you ll get such an answer. In the second half of this article, I m going to share Peter s terrible secret, and welcome you into the secret society of Ask Peter insiders. If you enjoy the childlike, magical perspective offered by your blissful ignorance, then stop reading this article now. Otherwise, if you would like to be immune to this particular scam How to Protect Yourself From 3 of the Biggest Online Scams Right Now How to Protect Yourself From 3 of the Biggest Online Scams Right Now People will always fall foul of the scammers. Three of the most devastating scams at the moment have yielded hundreds of millions of dollars for cybercriminals. What can you do to protect yourself? Read More , then read on.

### Welcome to the Secret Society of Ask Peter

If you ve read this far, then you feel prepared for the secret knowledge of how Ask Peter works. Let s take a closer look.

The ultimate secret to Ask Peter is actually a bit of creative JavaScripting What Is JavaScript and How Does It Work? What Is JavaScript and How Does It Work? What is Javascript? It’s a programming language used to enhance web pages. It includes dynamically updating web pages, user interfaces and more. Let’s dive into what Javascript is all about. Read More . Getting Peter to answer a question doesn t take reverence and politeness, it takes a very plain period. That s right in the Petition field, just type a . and start typing the answer to the question that you re going to ask in the next field.

At the end of the answer, type another . and then continue typing the rest of Peter, please answer the following question: To the person sitting next to you, it only appears as though you ve typed that one question especially if you re a fast typist.

So, now you know the secret. Submitting the question that you ve already entered the answer for and clicking OK will result in Peter providing your answer. The person next to you who s watching will be astounded and flabbergasted by the amazing accuracy of this virtual tarot. Just don t be too accurate, as you ll raise suspicion. Once you re through, you can proudly claim another Ask Peter believer under your belt. In doing so, you ve perfectly portrayed the terrible gullibility that runs rampant throughout the world.

Let s take a closer look at how the background scripting for Ask Peter actually works.

Now, the creators of this website were clever enough to suspect that discerning tech geeks would try peeking under the hood, so they ve incorporated a few safeguards. The first, of course, is processing all entries through CSS using class inp to handle each input field. You simply can t see how these fields are processed without access to the CSS files 10 Simple CSS Code Examples You Can Learn in 10 Minutes 10 Simple CSS Code Examples You Can Learn in 10 Minutes We’ll go over how to create an inline stylesheet so you can practice your CSS skills. Then we’ll move onto 10 basic CSS examples. From there, your imagination is the limit! Read More . However, if you look closely at the form code, you ll discover an interesting anomaly.

At the footer of the page script, you can see various variables used to return different text to the text field:

Each variable is given a coded name that looks similar, but it isn t with zero and the letter O in various places in the name. The technique is clearly intended to cover up the true purpose of the script, but it s obvious that if you aren t aware of the secret use of . behind the entry of the answer, then the page is coded to provide lots of different error messages back to you.

What does this mean to those of you who aren t JavaScript programmers? It means that instead of one, single function and variable handling the input text that gets entered into each field and returning a text value to the answer field, there are multiple things that happen with every individual keypress. This means that there s a whole lot of TomFoolery going on with the text that you enter into each text field.

## Now You Know the Real Answer

The answer, of course, is that if you re in the Petition field, the script returns what you type into the field, but watches for the moment you type the . character. At that point, it starts typing the rest of the statement Peter, please answer as it saves each character you re actually typing into a variable until you type . again. Finally, once you click OK your saved text that was stored in a string variable is displayed below in the form of Peter s Answer.

Now that you know the inner workings of this online Prank 7 Pranks to Play on iPhone Users 7 Pranks to Play on iPhone Users Pranking your friends is lots of fun, and there some great ways to do it if you get a few minutes alone with their iPhone. Read More , are you more likely to try it out on a friend?

Share your opinion about this online virtual tarot in the comment section below, and if you do try it out on a friend, let us know how it went!

# Understanding Mathematics

People wrote differently in those days, obviously the vulgar mechanick may be a man and he that is able to reason nimbly and judiciously may be a woman, (and either or both may be children).

for complicated mathematics building on simpler mathematics.

The following examples illustrate the difference between the two approaches to understanding mathematics described above.

You won’t be able to learn how to understand mathematics from abstract principles and a few examples. Instead you need to study the substance of mathematics. I’m hoping that the answers to the following

will illustrate how mathematics is meant to make sense and is built on a logical procession rather than a bunch of arbitrarily conceived rules.

One of the main things that turned me on to mathematics were certain concepts and arguments that I found particularly beautiful and intriguing. I’m listing some of these below even though they may not be frequently asked about. But I’ll hope you’ll enjoy them, and perhaps get more interested in mathematics for its own sake.

## Solving Mathematical Problems

The most important thing to realize when solving difficult mathematical problems is that one never solves such a problem on the first attempt. Rather one needs to build a sequence of problems that lead up to the problem of interest, and solve each of them. At each step experience is gained that’s necessary or useful for the solution of the next problem. Other only loosely related problems may have to be solved, to generate experience and insight.

Students (and scholars too) often neglect to check their answers. I suspect a major reason is that traditional and widely used teaching methods require the solution of many similar problems, each of which becomes a chore to be gotten over with rather than an exciting learning opportunity. In my opinion, each problem should be different and add a new insight and experience. However, it is amazing just how easy it is to make mistakes. So it is imperative that all answers be checked for plausibility. Just how to do that depends of course on the problem.

There is a famous book: G. Polya, How to Solve It , 2nd ed., Princeton University Press, 1957, ISBN 0-691-08097-6. It was first published in 1945. This is a serious attempt by a master at transferring problem solving techniques. Click here to see an html version of Polya’s summary.

The main thing that keeps mathematics alive and interesting of course are unsolved problems. Many open problems that are important in the contemporary view are hard just to understand. But here are

for which you can form your own conjectures. The word simple in this context means that the problem is easy to state and the question is easy to understand. It does not mean that the problem is easy to solve. In fact all of these open problems are difficult. (That’s why they are unsolved, it’s not that nobody tried!)

## Acquiring Mathematical Understanding

Since this is directed to undergraduate students a more specific question is how does one acquire mathematical understanding by taking classes? But that does not mean that classes are the only way to learn something. In fact, they often are a bad way! You learn by doing. For example, it’s questionable that we should have programming classes at all, most people learn programming much more quickly and enjoyably by picking a programming problem they are interested in and care about, and solving it. In particular, when you are no longer a student you will have acquired the skills necessary to learn anything you like by reading and communicating with peers and experts. That’s a much more exciting way to learn than taking classes!

Here are some suggestions regarding class work:

# Understanding Mathematics

People wrote differently in those days, obviously the vulgar mechanick may be a man and he that is able to reason nimbly and judiciously may be a woman, (and either or both may be children).

for complicated mathematics building on simpler mathematics.

The following examples illustrate the difference between the two approaches to understanding mathematics described above.

You won’t be able to learn how to understand mathematics from abstract principles and a few examples. Instead you need to study the substance of mathematics. I’m hoping that the answers to the following

will illustrate how mathematics is meant to make sense and is built on a logical procession rather than a bunch of arbitrarily conceived rules.

One of the main things that turned me on to mathematics were certain concepts and arguments that I found particularly beautiful and intriguing. I’m listing some of these below even though they may not be frequently asked about. But I’ll hope you’ll enjoy them, and perhaps get more interested in mathematics for its own sake.

## Solving Mathematical Problems

The most important thing to realize when solving difficult mathematical problems is that one never solves such a problem on the first attempt. Rather one needs to build a sequence of problems that lead up to the problem of interest, and solve each of them. At each step experience is gained that’s necessary or useful for the solution of the next problem. Other only loosely related problems may have to be solved, to generate experience and insight.

Students (and scholars too) often neglect to check their answers. I suspect a major reason is that traditional and widely used teaching methods require the solution of many similar problems, each of which becomes a chore to be gotten over with rather than an exciting learning opportunity. In my opinion, each problem should be different and add a new insight and experience. However, it is amazing just how easy it is to make mistakes. So it is imperative that all answers be checked for plausibility. Just how to do that depends of course on the problem.

There is a famous book: G. Polya, How to Solve It , 2nd ed., Princeton University Press, 1957, ISBN 0-691-08097-6. It was first published in 1945. This is a serious attempt by a master at transferring problem solving techniques. Click here to see an html version of Polya’s summary.

The main thing that keeps mathematics alive and interesting of course are unsolved problems. Many open problems that are important in the contemporary view are hard just to understand. But here are

for which you can form your own conjectures. The word simple in this context means that the problem is easy to state and the question is easy to understand. It does not mean that the problem is easy to solve. In fact all of these open problems are difficult. (That’s why they are unsolved, it’s not that nobody tried!)

## Acquiring Mathematical Understanding

Since this is directed to undergraduate students a more specific question is how does one acquire mathematical understanding by taking classes? But that does not mean that classes are the only way to learn something. In fact, they often are a bad way! You learn by doing. For example, it’s questionable that we should have programming classes at all, most people learn programming much more quickly and enjoyably by picking a programming problem they are interested in and care about, and solving it. In particular, when you are no longer a student you will have acquired the skills necessary to learn anything you like by reading and communicating with peers and experts. That’s a much more exciting way to learn than taking classes!

Here are some suggestions regarding class work:

# Ask Jud – The world’s finest virtual tarot

Do you need to ask a question? Are you looking for answers? Jud offers you a space to ask anything you want. However, before each question you must write a petition. If the answer is not what you expected, at least you make catharsis and ask again.

## The world’s best virtual tarot

Jud is a virtual tarot that that can answer all kinds of questions. Questions about the present, the past, and your future. He can be a bit tempermental, requiring that each question be presented with a petition of “Jud, please answer the following question” or “Jud, please answer” before each question is asked. Failure to correctly petition will not bring results.

Jud was born in 2007. As he began to age, he realized he had an ability to read the fortunes of others, and quickly became a star in his small hometown. To expand his operaion, he knew he had to join the digital age. Through the use of modern technology, he is able to answer thousands of questions every day from people all over the world.

In early 2016, the demand for Jud’s services became so high, he brougt on 10 additional team members from around the country to increase answer throughput. With a large team, and his mind in overdrive, he is now able to answer upwards of 13,240 questions per day (Average over the past 30 days), with pinpoint accuracy. Though the team members are new, they are just as tempermental. Requiring a correct petition each and every time.

## Has Jud ever been seen?

A dark and blury photograph of Jud was captured in early 2010. The developed image is shown below:

## The Twitter migration of 2015

In early 2015, Jud moved part of his online presence to Twitter, under the handle @TheAskJud. It wasn’t before long before the crowds of people following his presence online made the jump to Twitter. His ability to answer many different types of questions, both online and on Twitter attracted many.

His Twitter has been inactive for two years due to an oversubscription of requests. Twitter hadn’t created the tooling for him to keep up with demand. Though there may come a time for him to return, there are no plans at this time.

## Questions?

I am Ask Jud, the world’s best virtual tarot

# How Does Ask Peter Work? The Code Behind the Prank

For a number of years, one of my hobbies has been researching paranormal scams. These are situations where an individual claims they can predict the future, that they ve discovered the secret to antigravity, or that they work for the government and know the truth about aliens. A common thread in all of that surreal research is that generally, an unnerving number of people are very, very gullible.

That gullibility multiplies significantly when the event being portrayed includes something that appears supernatural or magical in nature. Deep down, many people still want to believe in magic and when they are presented with the opportunity to believe again, they jump all over it.

A case in point is a website that is very popular among the prankster community called Ask Peter (or Peter Answers). The footer text lists the page as a Virtual Tarot, as though the page truly has the ability to predict your future or answer any of your questions. In this article, I answer the question: how does Ask Peter work?

### How Does Ask Peter Work? The Believer Perspective

First, I m going to show you how the website works for the person off of the street who knows nothing about the inner workings of Ask Peter. When you first arrive at the website, you ll see a very simple web form.

The point of the website is that it s a sort of electronic tarot which will peek into your future and answer your questions accordingly. However, Peter is a fickle psychic, and he must be treated with respect or he won t answer your question. Therefore, before you ask a question, you must petition Peter with the sentence, Peter, please answer the following question: If you re using the Peter Answers site alone and you don t know the secret behind the site, you ll typically get an answer like this:

What s up with that? Ah, but it s all part of the show, folks. The magic really happens when you bring in a second person who knows Peter s terrible secret (after reading this article, that will be you!) The second person needs to type in the petition and question for you, and then you ll get the answer which is usually remarkably accurate.

If the person typing the question knows the secret, you ll get such an answer. In the second half of this article, I m going to share Peter s terrible secret, and welcome you into the secret society of Ask Peter insiders. If you enjoy the childlike, magical perspective offered by your blissful ignorance, then stop reading this article now. Otherwise, if you would like to be immune to this particular scam How to Protect Yourself From 3 of the Biggest Online Scams Right Now How to Protect Yourself From 3 of the Biggest Online Scams Right Now People will always fall foul of the scammers. Three of the most devastating scams at the moment have yielded hundreds of millions of dollars for cybercriminals. What can you do to protect yourself? Read More , then read on.

### Welcome to the Secret Society of Ask Peter

If you ve read this far, then you feel prepared for the secret knowledge of how Ask Peter works. Let s take a closer look.

The ultimate secret to Ask Peter is actually a bit of creative JavaScripting What Is JavaScript and How Does It Work? What Is JavaScript and How Does It Work? What is Javascript? It’s a programming language used to enhance web pages. It includes dynamically updating web pages, user interfaces and more. Let’s dive into what Javascript is all about. Read More . Getting Peter to answer a question doesn t take reverence and politeness, it takes a very plain period. That s right in the Petition field, just type a . and start typing the answer to the question that you re going to ask in the next field.

At the end of the answer, type another . and then continue typing the rest of Peter, please answer the following question: To the person sitting next to you, it only appears as though you ve typed that one question especially if you re a fast typist.

So, now you know the secret. Submitting the question that you ve already entered the answer for and clicking OK will result in Peter providing your answer. The person next to you who s watching will be astounded and flabbergasted by the amazing accuracy of this virtual tarot. Just don t be too accurate, as you ll raise suspicion. Once you re through, you can proudly claim another Ask Peter believer under your belt. In doing so, you ve perfectly portrayed the terrible gullibility that runs rampant throughout the world.

Let s take a closer look at how the background scripting for Ask Peter actually works.

Now, the creators of this website were clever enough to suspect that discerning tech geeks would try peeking under the hood, so they ve incorporated a few safeguards. The first, of course, is processing all entries through CSS using class inp to handle each input field. You simply can t see how these fields are processed without access to the CSS files 10 Simple CSS Code Examples You Can Learn in 10 Minutes 10 Simple CSS Code Examples You Can Learn in 10 Minutes We’ll go over how to create an inline stylesheet so you can practice your CSS skills. Then we’ll move onto 10 basic CSS examples. From there, your imagination is the limit! Read More . However, if you look closely at the form code, you ll discover an interesting anomaly.

At the footer of the page script, you can see various variables used to return different text to the text field:

Each variable is given a coded name that looks similar, but it isn t with zero and the letter O in various places in the name. The technique is clearly intended to cover up the true purpose of the script, but it s obvious that if you aren t aware of the secret use of . behind the entry of the answer, then the page is coded to provide lots of different error messages back to you.

What does this mean to those of you who aren t JavaScript programmers? It means that instead of one, single function and variable handling the input text that gets entered into each field and returning a text value to the answer field, there are multiple things that happen with every individual keypress. This means that there s a whole lot of TomFoolery going on with the text that you enter into each text field.

## Now You Know the Real Answer

The answer, of course, is that if you re in the Petition field, the script returns what you type into the field, but watches for the moment you type the . character. At that point, it starts typing the rest of the statement Peter, please answer as it saves each character you re actually typing into a variable until you type . again. Finally, once you click OK your saved text that was stored in a string variable is displayed below in the form of Peter s Answer.

Now that you know the inner workings of this online Prank 7 Pranks to Play on iPhone Users 7 Pranks to Play on iPhone Users Pranking your friends is lots of fun, and there some great ways to do it if you get a few minutes alone with their iPhone. Read More , are you more likely to try it out on a friend?

Share your opinion about this online virtual tarot in the comment section below, and if you do try it out on a friend, let us know how it went!

# Understanding Mathematics

People wrote differently in those days, obviously the vulgar mechanick may be a man and he that is able to reason nimbly and judiciously may be a woman, (and either or both may be children).

for complicated mathematics building on simpler mathematics.

The following examples illustrate the difference between the two approaches to understanding mathematics described above.

You won’t be able to learn how to understand mathematics from abstract principles and a few examples. Instead you need to study the substance of mathematics. I’m hoping that the answers to the following

will illustrate how mathematics is meant to make sense and is built on a logical procession rather than a bunch of arbitrarily conceived rules.

One of the main things that turned me on to mathematics were certain concepts and arguments that I found particularly beautiful and intriguing. I’m listing some of these below even though they may not be frequently asked about. But I’ll hope you’ll enjoy them, and perhaps get more interested in mathematics for its own sake.

## Solving Mathematical Problems

The most important thing to realize when solving difficult mathematical problems is that one never solves such a problem on the first attempt. Rather one needs to build a sequence of problems that lead up to the problem of interest, and solve each of them. At each step experience is gained that’s necessary or useful for the solution of the next problem. Other only loosely related problems may have to be solved, to generate experience and insight.

Students (and scholars too) often neglect to check their answers. I suspect a major reason is that traditional and widely used teaching methods require the solution of many similar problems, each of which becomes a chore to be gotten over with rather than an exciting learning opportunity. In my opinion, each problem should be different and add a new insight and experience. However, it is amazing just how easy it is to make mistakes. So it is imperative that all answers be checked for plausibility. Just how to do that depends of course on the problem.

There is a famous book: G. Polya, How to Solve It , 2nd ed., Princeton University Press, 1957, ISBN 0-691-08097-6. It was first published in 1945. This is a serious attempt by a master at transferring problem solving techniques. Click here to see an html version of Polya’s summary.

The main thing that keeps mathematics alive and interesting of course are unsolved problems. Many open problems that are important in the contemporary view are hard just to understand. But here are

for which you can form your own conjectures. The word simple in this context means that the problem is easy to state and the question is easy to understand. It does not mean that the problem is easy to solve. In fact all of these open problems are difficult. (That’s why they are unsolved, it’s not that nobody tried!)

## Acquiring Mathematical Understanding

Since this is directed to undergraduate students a more specific question is how does one acquire mathematical understanding by taking classes? But that does not mean that classes are the only way to learn something. In fact, they often are a bad way! You learn by doing. For example, it’s questionable that we should have programming classes at all, most people learn programming much more quickly and enjoyably by picking a programming problem they are interested in and care about, and solving it. In particular, when you are no longer a student you will have acquired the skills necessary to learn anything you like by reading and communicating with peers and experts. That’s a much more exciting way to learn than taking classes!

Here are some suggestions regarding class work: