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.

(video in title-link)

Hi-Yo, Silver! Away!

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

Edward Frenkel: Let’s Stop Hating Math

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Logarithm Identities & Properties | Pt. 1

Product / Addition Rule for Logarithms

Quotient / Subtraction Law for Logarithms

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

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

One way we could view this is as

   =  { – ∪  0 ∪  }  =  { . . .-3, -2, -1, 0, 1, 2, 3, . . .}

Adding every element in  in such a way that every   is added it’s additive inverse  such that   –: ( -3 )  is paired with : ( 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!

*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  .
*It’s indeterminate ! 

Music, Linguistics and Mathematics

May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life.

– James Sylvester

Music, Linguistics and Mathematics – these should be at the foundation of our learning.

 

Don’t let the force hit you on the way down!

If F = ma and we know that a = Δv/Δt, then it follows naturally that F = m*(Δv/Δt). Working towards solving for Δv, cross-multiplication by Δt gives us m*(Δv) = (F*(Δt)) , and dividing both sides throughout by m, we find that Δv = (F/m)*(Δt).

Notice that a quick manipulation of our first equation, F = ma, leads us to (F/m) is = a . This simplifies our equation for ‘change in velocity’ to Δv = a*(Δt)

We can now expand out the Δv and get (Vf – Vi) = a*(Δt)

Solving for ‘final velocity’ we find that Vf = Vi + a*(Δt)

Voila!

illusion + hallucination = hallucillusion

 

Relax your mind, follow the letters, and let your peripheral gaze do the walking.

enjoy!

oh! and make sure you’ve got it in HD!  😉

 

Intersection & Union via Science and Art

With use of a Venn Diagram, this picture serves to illustrate what is formally referred to as an ‘intersection of sets’. Intersecting two or more sets means you’re isolating the elements that can be seen as mutual in all of them; elements that they all share.

Using Set Builder Notation, if we were to denote Science and Art by S and T respectfully, then the intersection of set S and set T would be written as S ∩ T. This can be read as “S intersect T”, or “S and T” and even “S cap T” for simplicity. Notice that this operation is a way to go about collecting all of the elements that are shared in both S and T.

How about if you were to want to look at the elements that are in both S and T, and S or T, all at the same time? Or, more explicitly, what if we were to want to see the elements in S, the elements in T, and the elements in S and T all at the same time?

This is where the notion of a “union of sets’ comes in, denoted S ∪ T. This notation is read as “S union T”, “S or T”, or even “S cup T”. Notice though, the use of “or” in this context; here we’re using what is called the ‘ inclusive “or” ‘, which is an extension of the truth-functional logical operator for inclusive disjunction.

In everyday life, there are two ways we can go about using the word “or” in discussion. Allow me to illustrate; If you were to ask me whether I want to go to Cuba or Japan next weekend, it’s intuitively obvious that I can choose one or the other, while choosing both is implicitly out of the question. However, if I were to ask you whether you would like pie or ice cream for dessert, I shouldn’t be surprised if you reply telling me that you’d like a little bit of both.  In day-to-day conversation, our use of the disjunctive operator is highly dependent the content of the discussion.

Do you see how this could present a level of ambiguity in mathematics, where often context can be easily lost or difficult to translate due to abstraction? This is why we define our use of “or” in set theory (and the majority of mathematics and mathematical logic for that matter) as being that of the inclusive disjunctive operator.

Can you think of any other ‘operations’ that would be useful to define in a system such as the one we’re using?

What is it that makes something an ‘operation’ per se?

I look forward to hearing your thoughts!