Category Archives: Articles

A universal way to solve problems, from a mathematical genius

By Zat Rana | August 25, 2018

It took Claude Shannon about a decade to fully formulate his seminal theory of information.

He first flirted with the idea of establishing a common foundation for the many information technologies of his day (like the telephone, the radio, and the television) in graduate school.

It wasn’t until 1948, however, that he published A Mathematical Theory of Communication.

This wasn’t his only big contribution, though. As a student at MIT, at the humble age of 21, he published a thesis that many consider possibly the most important master’s thesis of the century.

To the average person, this may not mean much. He’s not exactly a household name. But if it wasn’t for Shannon’s work, what we think of as the modern computer may not exist. His influence is enormous not just in computer science, but also in physics and engineering.

The word genius is thrown around casually, but there are very few people who actually deserve the moniker like Claude Shannon. He thought differently, and he thought playfully.

One of the subtle causes behind what manifested as such genius, however, was the way he attacked problems. He didn’t just formulate a question and then look for answers, but he was methodological in developing a process to help him see beyond what was in sight.

His problems were different from many of the problems we are likely to deal with, but the template and its reasoning can be generalized to some degree, and when it is, it may just help us think sharper, too.

All problems have a shape and a form. To solve them, we have to first understand them.

Build a core before filling the details

The importance of getting to an answer isn’t lost on any of us, but many of us do neglect how important it is to ask a question in such a way that an answer is actually available to us.

We are quick to jump around from one detail to another, hoping that they eventually connect, rather than focusing our energy on developing an intuition for what it is we are working with.

This is where Shannon did the opposite. In fact, as his biographers note in A Mind at Play, he did this to the point that some contemporary mathematicians thought that he wasn’t as rigorous as he could be in the steps he was taking to build a coherent picture. They, naturally, wanted the details.

Shannon’s reasoning, however, was that it isn’t until you eliminate the inessential from the problem you are working on that you can see the core that will guide you to an answer.

In fact, often, when you get to such a core, you may not even recognize the problem anymore, which illustrates how important it is to get the bigger picture right before you go chasing after the details. Otherwise, you start by pointing yourself in the wrong direction.

Details are important and useful. Many details are actually disproportionately important and useful relative to their representation. But there are equally as many details that are useless.

If you don’t find the core of a problem, you start off with all of the wrong details, which is then going to encourage you to add many more of the wrong kinds of details until you’re stuck.

Starting by pruning away at what is unimportant is how you discipline yourself to see behind the fog created by the inessential. That’s when you’ll find the foundation you are looking for.

Finding the true form of the problem is almost as important as the answer that comes after.

Continue reading at: https://qz.com/1365059/a-universal-way-to-solve-problems-from-a-mathematical-genius/

The Best Holiday Sites on the Internet by homeschool.com

Get the holiday season started with fun activities and some great opportunities to learn about familiar, and not-so-familiar, holiday traditions and history. Within many of the sites listed below are additional links with even more ideas to try.

In addition to learning about traditions join in the festivities with links to recipes, crafts, cards, and music that give added richness to the holidays!



Chanukah December 15

Chanukah commemorates the victory of the Maccabees over Syria that took place more than 2000 years ago. Called the “Festival of Lights,” Chanukah is an eight-day holiday celebrated by Jewish people around the world. This year Chanukah begins at sunset, December 15, and ends on December 23.

The Virtual Chanukah web site allows users to discover the customs of the holiday such as lighting the menorah, singing traditional songs, and making Chanukah recipes.

In addition to the traditional side, the Chanukah Time, Hanukkah Fun, and Torah Tots websites bring some fun to the holiday with screen savers, games, crafts, and puzzles designed for children. More fun sites include HanuKat and the Hanukkah for Children web sites with online stories, recipes and activities.

Hanukkah eCards, Hanukkah Recipes, and some Hanukkah music allow users to enjoy the holiday in additional ways.

Winter Solstice December 21

Winter solstice designates the time of the year when the Sun changes its direction and begins to move toward the opposite hemisphere. It occurs around December 21 when the Sun is directly above the Tropic of Capricorn and marks the shortest day of the year. In the Northern Hemisphere, the December solstice is the winter solstice to signal the beginning of winter.

The following sites are useful for learning about the solstice, the change of seasons, and the celebration of winter.

The Winter Solstice offers winter solstice quizzes, ancient myths about the winter solstice, and ideas for winter fun, while the Celebrate Winter!  website from Education World provides more than a dozen activities for celebrating the Solstice.

Frosty Activities is a website for kids developed by kids! This site has activities, puzzles, and games all centered on winter fun and the Curing Cabin Fever website offers some great ideas for keeping kids engaged and busy during the holiday breaks and bad weather moments.

The Season’s Greetings & eCards allow you to share the holiday fun with friends and relatives. Winter is also a great time to cook up some warming recipes and enjoy time with the family. The Recipezaar  site has more than 6,000 winter recipes to choose from, including soups, stews, gingerbread, and pies.

Christmas December 25

Christmas is the celebration of the birth of Jesus Christ and is a joyous and busy time for millions of Christians all over the world. Many of the holiday traditions and celebrations we observe today came from our European ancestors but over the years gift giving, feasting, and decorating have blended into the common customs associated with the holiday. However, not everyone celebrates Christmas on the same day or in the same way and this holiday season is a great time to learn about other cultures and traditions.

Both Around the World and Christmas Around the World provide an extensive list by country with links to information on how Christmas is celebrated in other parts of the world. On the other side the American Christmas page shares American holiday traditions sorted by decade from 1840 to 2000.

World Book’s Christmas website also has information on world Christmas customs plus has historical information on Santa Claus, the Christmas tree, and Christmas recipes and crafts. The Noel, Noel, Noel site offers a list of family-friendly activities such as crafts, stories, and games that the family can do together. The site also includes printable Christmas sheet music.

For a very traditional Christmas check out the Victorian Christmas website for holiday decorating and entertaining ideas with a Victorian twist.

More entertaining inspiration can be found from the Epicurious Food, Christmas Entertaining and the Christmas-Cookies.com.

Christmas Crafts has ideas and online instructions for homemade Christmas crafts and the Holiday Crafts Countdown offers 30 days of Christmas and holiday crafts.

The Christmas Songs website provides both song lyrics and MIDI files for holiday music and Blue Mountain Christmas eCards gives users a chance to send a free Christmas greeting to friends and family.

For some holiday fun, check out the True Cost of the 12 Days of Christmas website to see the Christmas Price Index calculation of the cost of goods and services bought by the True Love in the holiday classic, “The Twelve Days of Christmas” or get ready to watch Santa race around the world on Christmas Eve at NORAD Tracks Santa.

The North Pole.com, Christmas on the Net, and Santa’s Net websites have additional resources, links, and ideas for celebrating the Christmas season.

Kwanzaa December 26

Kwanzaa was developed to celebrate the African traditions of family, community and culture. Kwanzaa is based on the old African festival of the harvest of the first crops and begins on December 26 and ends on January 1.

The Official Kwanzaa Web Site comes from the founder of the celebration, Dr. Maulana Karenga and has extensive provides information about the history and festivities. From CNN comes the interactive Kwanzaa Page  with Information and links about the holiday and Kwanzaa Land provides general information about Kwanzaa, educational activities, recipes and music.

Several other sites including Kwanzaa Recipes and Food Network offer food ideas and recipes for celebrating Kwanzaa.

Kwanzaa Activities for Children gives children craft ideas and coloring pages and the Billy Bear Web site explains the seven principles of Kwanzaa and has craft ideas as well.

Kwanzaa eCards offers a choice of greetings to send for the Kwanzaa season.

Seasons Greetings!

December is a wonderful time to celebrate! The winter season arrives and brings with it the calmness of a new snow, the excitement of festival lights, and a collection of holidays that offer the opportunity to learn about different cultures and celebrations around the world.

Before things get too chaotic, take the time this holiday season to learn the history of family traditions and perhaps incorporate some new ones into festivities. Discover the history and traditions of other holidays as well, which will make your own celebrations much more meaningful.

Seasons Greetings!

A Pilgrim Letter from Plimoth Plantation for Your Classroom

Article from http://www.scholastic.com newsletter.

Dear Aunt Constance:

I was so grateful to arrive in the New World, but I am now beginning to wish that we had never left home. I know that father had a hard life in England because he was punished for following his conscience and worshiping in the Separatist Church, but I wonder if it could have been as hard as this.

We arrived here just as winter did. It is bitter cold and snow is almost always upon the ground, but God has blessed us with a place to start our new town. There is a fair brook running under a high hill that Father says will offer us protection from our enemies. The men have begun building houses on land, but we must remain on the ship until they are nearer to being finished. I never thought I would still be aboard the ship for so long after we arrived! I suppose it is safer on the ship. I know not what to think of the naturals of this place that are called Indians. The first time some of our men encountered them, there was a fight though by God’s blessing no one was injured. We are on our guard now.

Master Goodman—the one with the dogs—has become quite ill. He was out cutting thatch with Peter Brown when his dogs chased a great deer deep into the forest. They chased after them and were soon lost, and had to pass the night in the wilderness. When they found their way back the next afternoon, Master Goodman had to have his shoes cut off his feet as they were so swollen with the cold. Many of our party have already died, among them Mary’s mother and father. I cannot think how lost I would be in this strange and frightful place without mother and father. I pray that they will not succumb to scurvy and other diseases.

I mean not to be so grim, but I fear that things could get far worse. We are near to scraping the bottoms of the barrels of rice, peas, and biscuit, and the men have had little fortune in hunting. I am worried, though I know that with God’s help we will survive this dark winter.

Your loving niece,
Lizzy

Get out and vote

voteCalvin Coolidge, Thirtieth President of the United States said, “If the people fail to vote, a government will be developed which is not their government… The whole system of American Government rests on the ballot box. Unless citizens perform their duties there, such a system of government is doomed to failure.”

Of the 52 million voter-eligible Evangelical Christians in America, 10 million were not registered to vote for the 2006 Election, and over 20 million who were registered, did not vote. Quite simply, less than 40 percent of all eligible to vote Evangelical Christians in America… voted.

Millions of evangelical Christians, out of apathy, ignorance, or indifference, choose not to vote in election after election. Our absence from the voting booth has contributed greatly to the moral, spiritual, economic, and political disintegration of America.

Dwight D. Eisenhower, 34th President of the United States said, “The future of this republic is in the hands of the American voter.”

Franklin D. Roosevelt, 32nd President of the United States said, “Let us never forget that government is ourselves and not an alien power over us. The ultimate rulers of our democracy are not a President and senators and congressman and government officials, but the voters of this country.”

Too often, Christians are being misled about participation of their churches in the elective process. While pastors and church elders are prohibited from endorsing candidates or parties on behalf of their congregations because of the tax-exempt status of the church, the Internal Revenue Service has specifically stated that “activities intended to encourage people to participate in the election process, such as voter registration and get-out-the-vote drives, would not be prohibited political campaign activity if conducted in a nonpartisan manner.”

“We Christians are commanded by Christ Himself to be ‘salt and light’ to the culture in which we live, and Voting is an important aspect of that duty,” writes David Crowe, the Founder and President of Restore America.

Read more at: http://www.conservativecrusader.com/articles/restore-america-get-out-the-christian-vote

The 10,000 Hour Rule,” sometimes called “The Ten Year Rule.”

Thomas Edison was fond of saying that genius is 99% perspiration and 1% inspiration, but all of the recent research suggests that “genius” is 1 percent inspiration, 29 percent good instruction, mentoring, and encouragement, and 70 percent perspiration. In other words, geniuses (people who are highly successful at what they do)
are made, not born.

Studies of what makes some children more successful as grownups than others (and considered “geniuses” at what they do) have come up with this rule to predict future achievement.

You can find out what the rule is and how you can make it work for your children here:

http://www.homeschoolmarketplace.com/e-zines/ejournalaug1010.html