Showing posts with label logic. Show all posts
Showing posts with label logic. Show all posts

November 2 - From Boole...to Google?

Posted on November 2, 2021


This is an update of my post published on November 2, 2010:


Happy Birthday, George Boole!

Born in England on this day in 1815, Boole grew up to become a mathematician. He came up with a kind of algebra we now call Boolean Algebra. The three most common operations of this kind of algebra are still used today in computer science, logic systems, and even in Google searches:

AND
OR and
NOT.

Boole did not create the first computer. However, in hindsight he has been called the founder of computer science. Here's why:

In the 1930s an American named Claude Shannon and a Russian named Victor Shestakov both (separately) realized that Boolean Algebra could be used with electrical switches. Each switch has only two states: On and Off, or True and False, 1 and 0. The AND, OR, and NOT functions can be made into logic gates that serve as the foundation for the digital revolution.



If you search for puppy AND kitten, you will only get pages that include both words.
If you search for puppy OR kitten, you will get pages that either one or both words.
If you search for puppy NOT kitten, you will get pages that include the
word "puppy," but do not include the word "kitten."

So AND and NOT limit and focus your search.
OR widens your search.





Let's see how Boolean logic works. Say there are a lot of foods on a table: a ham sandwich, a green apple, a brownie, a banana, an orange, an Oreo cookie, a yellow cookie decorated with yellow frosting, and a white container full of plain yogurt. Which foods would you get with the following “searches”?

  1. fruit AND yellow
  2. fruit OR yellow
  3. NOT fruit
  4. NOT yellow
  5. fruit NOT yellow
  6. yellow NOT fruit
ANSWERS: 
1. banana 
2. apple, banana, orange, yellow cookie 
3. sandwich, brownie, both cookies, yogurt 
4. sandwich, apple, brownie, orange, Oreo, yogurt 
5. apple and orange 
6. yellow cookie

Learn more

  • Here is a quickie guide to how Boolean terms can focus or widen a search using a search engine. 
  • I tried using the Boolean terms with Google and immediately realized that NOT does not work. Instead, I found out, you type a minus sign immediately before the term you want to exclude. Also, to be recognized as the OR operator, you have to type capital letters OR
  • Here is an explanation of how to Boolify your web search - and a search engine meant for kids.




September 10 – Happy Birthday, Charles Sanders Peirce

Posted on September 10, 2018

So, today's famous birthday pointed out that certain kinds of logic could be carried out by something as simple as an electrical switching circuit. 


And eventually people did just that as they created digital computers.

He began the formal branch of semiotics, which is the study of meaning-making. And he founded pragmatism, which is the philosophy of considering practical effects of ideas in a changing universe.


Born on this date in 1839, in Massachusetts in the U.S., Charles Sanders Peirce has a LOT of fields listed in his Wikipedia bio: logic, mathematics, statistics, philosophy, metrology (the study of measurement), chemistry, experimental psychology, economics, linguistics (the study of languages), and the history of science.

W.O.W.!

Peirce's dad was a professor at Harvard University - a math and astronomy professor - and Peirce graduated with honors from Harvard himself. However, he had a painful physical disorder that probably were the causes of his outbursts of temper and his difficulties with others, and because of these problems, Peirce had a lot of difficulty maintaining jobs and earning enough money for a happy and comfortable life.

So, despite the fact he is considered a really important and original thinker, many of Peirce's writings remain unpublished even now.



Let's celebrate Peirce with some logic fun! Here is a simple lesson on logic - and you can see why logic and mathematics are linked. Here are some printable logic puzzles, and here are a few videos about logical fallacies and critical thinking. 


My Answer to Viral Math Puzzle:
I got 2 + 3 + 3 + 11 = 19.  The 2 is from the clock, which shows the time to be 2:00. The 3 and 3 are from the two bunches of bananas, with three bananas in each bunch. The 11 was from the six-sided hexagon with the five-sided pentagon inside.

Are there any other valid answers? (I think I could justify an answer of 22.) Remember, another "correct" answer must be able to fit with all of the parts of the puzzle.



July 9 – Happy Birthday, Nicolaas Govert de Bruijn

Posted on July 9, 2016
Mathematical analysis.

Number theory.

Combinatorics.

Logic.

These are the fields in which mathematician Nicolaas Govert de Bruijn (born in the Netherlands on this date in 1918) worked and made important contributions.

Do you know how these various fields are used? 

Analysis is the branch of math that studies continuous change. It can be used in physics and engineering; for example, it can be used to process signals such as radio waves or images.

Here is a Pinterest board with links to tons of analysis activities for kids.  

Number theory is a branch of pure mathematics. It studies integers – positive and negative numbers that are not fractional – numbers like 55, -13, and 1,892,282. Things like prime numbers are included in number theory.

Here are some number theory games for kids.







Combinatorics is, as you might imagine, the study of combinations of objects that belong to a certain set. It's basically all about counting, but it also can involve mathematical “structures” such as graphs or necklace problems.

Check out this unit on combinatorics...for kids!

Logic is the study of the form of arguments. It discovers which arguments are valid and which are “fallacies” (false) or paradoxes (self-contradictory).

How about logic in six kid-friendly animations? Here you go!








Also on this date:

































Independence Day in Argentina
















Plan ahead:

Check out my Pinterest boards for:
And here are my Pinterest boards for: