What the Internet of 2025 Might Look Like

What the Internet of 2025 Might Look Like

In case you weren’t already aware, today’s the 25th birthday of the Internet!

That’s right, a quarter of a century ago, the World Wide Web first hit cyberspace, and shortly thereafter we began to connect (or dial in) to this new wave of communication and information technology.

Here’s a quick timeline of the history of the World Wide Web so that you can get yourself better acquainted ; http://bit.ly/Pu06iQ

Now… take a look at what the experts are predicting for the 10 years.

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Hi-Yo, Silver! Away!

About that ‘Common Core’ photo going around…

About that 'Common Core' photo going around...

Most people have their times tables memorized, know a few algorithms for adding, subtracting and dividing, and may even be aware of how to manipulate decimals, fractions, and percentages. However, ask these very same people ‘why’ it works’ or ‘how’ it works that way, and you’ll often get blank stares or rules from the rote.

The Core Common Standards don’t aim to rid us of the useful algorithms that we know, they’re here to change the way we understand them, use them and think about them. If everyone has a properly developed sense for numbers and their interactions, it would make the step from Arithmetic to Geometry and Algebra so intuitive that we’ll have students writing their own algorithms for these sorts of operations – never mind needing to teach them the procedure.

Michio Kaku: The Origin of Intelligence

“I have a new theory of consciousness based on evolution. And that is consciousness is the number of feedback loops required to create a model of your position in space with relationship to other organisms and finally in relationship to time.”

~ Dr. Michio Kaku

Brought to you by Big Think !

http://bigthink.com/big-think-tv/the-origin-of-intelligence

Zero and Infinity

To see the world in a grain of sand, and to see heaven in a wild flower, hold infinity in the palm of your hands, and eternity in an hour.

~ William Blake

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Take the set of all Integers \mathbb{Z} where \mathbb{Z} = the set of all positive and negative Natural Numbers  \mathbb{N} = {1, 2, 3, 4, 5, . . . } and zero = { 0 }  (not to be confused with the empty set) . 

One way we could view this is as

 \mathbb{Z}  =  { \mathbb{N} ∪  0 ∪ \mathbb{N} }  =  { . . .-3, -2, -1, 0, 1, 2, 3, . . .}

Adding every element in \mathbb{Z} in such a way that every  \mathbb{N} is added it’s additive inverse  such that   –\mathbb{N}: ( -3 )  is paired with \mathbb{N}: ( 3 ), similarly  ( -a ) with  ( a )

.  .   .  + ( -3 )  + ( -2 )  +  ( -1 )  +  0  +  1  +  2  +  3  +  .   .   .

becomes

0  +  ( -1 + 1 )  +  ( -2 + 2 )  +  ( -3 + 3 )  +  .  .  .

This results in

0  +  0  +  0  +  0  +  .  .  .

=  0

Now we see that, at least intuitively, a possible value for the sum of all integers (negative infinity + positive infinity over the natural numbers)  could be equal to 0.

How many other ordered pairs can we construct? *

Give it a try!

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*Not to be confused with the empty set
*Note that this would have worked even if we hadn’t included zero in the definition of \mathbb{Z} .
*It’s indeterminate ! 

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