Mathematica Training Online by O'Reilly

Opening the eyes of young minds to be receptive to nature's patterns is a challenging task. In the realm of Mathematics and Science, where it can sometimes get boring when one can't initially perceive inner beauty, it is even harder to cultivate interest. In our age of technology and connectivity, it is great that the O'Reilly Publishing company recently announced a wonderful endeavor:
Their school of technology will soon be providing a browser-based version of Wolfram's Mathematica, a powerful technical computing and education software which will be used to teach math and science topics online.
Honing skills to detect patterns in nature is best done with actual hands-on and brains-on tinkering. Via ajax-based web technologies, O'Reilly will deliver the power of Mathematica to let students to do real interactive work in math and science, giving a genuine educational experience for students around the world.

Source: http://www.oreilly.com/emails/press/ost-newcert.html

The Simplelarity Principle

Here is an Article from Scientific American so full of beautiful concepts to tackle for the Archetyper. I will first list down the phrases from that article which ring a bell, and then tell you what I think:

• core tool of skepticism: how to see through information obfuscation


• what Tufte teaches about analytical design: Good displays of data help to reveal knowledge relevant to understanding mechanism, process and dynamics, cause and effect. We see the unthinkable and think the unseeable


• Clear and precise seeing becomes as one with clear and precise thinking.
  - the Feynman-Tufte Principle: a visual display of data should be simple enough to fit on the side of a van


• Simple design, intense content

What stands out for me is our tendency to simplify complexity in order to understand. Using Diagrams, Web Interfaces, Lists, Theories (Grand Unified Theory or TOE, String Theory), Math and Symbolisms, Metaphors, Analogies and Parables - it is proven time and time again that the most effective method to understand our universe is simplification. Why is this so?

Why is it that we dont "complexify" things in order to make them more understandable? To me, this is a pattern worth noticing, so relevant to our era that I must give it a name: The Simplelarity Principle.

The word - Simplelarity (simple-larity) stems from my observation that the tendency of Intelligence towards "Simplification" runs counter to the Singularity. In Vinge's and Kurzweil's terms, the Singularity is defined as the point where machines surpasses human intelligence and everything becomes unpredictable (think post-event horizon). Well, unpredictability means chaos and complexity. On the other hand, Simplelarity simply means that when machines, and/or humans become super-smart, everything about the universe would have been simplified via Mental Models or Tools to make everything understandable and predictable. Higher Intelligences must be able to simplify things better, not make a mess, right?

Brains and Minds use tools and mental models to simplify and make sense of the world. If we all become more intelligent and better at simplifying things, just as the Feynman-Tufte Principle example shows, then the world will 'become' a much simpler and better place, more understandable and easier to manage.
Hence we would never cross the 'Event Horizon', rather, we will just stay on the 'Prevent Horizon'. Simplelarity is Bliss.

Escher, the Droste Effect, and Video Feedback

A few weeks ago, I mentioned I was reading Am I A Strange Loop? by Hofstadter. I was contemplating on writing about Video Feedback loops and my own childhood experience with two mirrors facing each other when I came across this fascinating website that I cant help but share it.
These are attempts to answer some questions about Escher's picture, such as: "what's in the blurry white hole in the middle? Using a bit of math, and some computer algorithm, Escher's methods are unraveled in fascinating detail. Its a feast for those inclined in Arts and Mathematics.

Symmetry and Archetypes: Its a Small Universe !

Carl Sagan said that "there's something terribly beautiful, austere, glorious, majestic about the fact that the same laws apply everywhere". This is called Symmetry - a property of our universe where the laws of nature are the same in all parts of the cosmos (except inside the singularity, perhaps).
This post mainly shows the connection between the laws of nature and universal concepts. The Laws of Nature include the laws of physics, atomic laws, chemical laws, and so on. And the universal concepts are the archetypes.
Cosmic Laws and Universal Concepts are linked via Emergence. Let us follow the chain of emergence: The laws that govern the most basic elementary 'particles' give way to the behavior of atoms which follow atomic laws, producing molecules that follow chemical laws, which made possible the emergence of biological life, animals and ecosystems, which supported the evolution of conscious beings - able to perceive and ponder itself via concepts and paradigms. These concepts and archetypes are very similar to Plato's Forms, and they will be perceived by any intelligent and sentient being in another part of the universe, by way of symmetry.
There will be a difference in language, of course, but nevertheless, these Archetypes or Platonic "Forms" will be understood, in one way or another. Like Mathematics, there will be a common ground between us and sentient beings that live thousands of light-years away in another galaxy. If its just distance that separates us from extra-terrestrials, but they are only a "thought" away, then it means that Symmetry makes the universe seem smaller. Its a small world universe after all. :)

Computation: A Tool to Decipher Nature's Patterns

If you've ever wondered about the shape of seashells and how the patterns on their outer shell came to be, then its worth to revisit "A New Kind of Science" (NKS) from Stephen Wolfram. Using the sheer power of computation to model the inner details behind nature's shape-making processes, Wolfram has provided a breakthrough insight to learn how shapes and patterns arise in nature. NKS, together with its software Mathematica gives a toyful learning environment to play with the inner workings of nature. With Cellular Automata, we discover that nature follows some pretty simple basic rules to come up with interesting patterns, such as those of the seashell.
Complex as our world may seem, it runs on basic discreet laws that can be deciphered. This idea is in unison with the focus of Archetyper.com - to recognize patterns, basic laws and simple rules within different emergent levels of the natural world. This task ignites the sense of wonder and awe that comes with living in a universe as mysterious as ours, and provides a continuous stream of insight to understand our world better.

Prime Numbers and Quantum Physics

Here's a great story that illustrates why it is good to look into patterns from other fields of study and apply it to another field to gain novel new insights. The pattern discovered from one discipline can then be used to solve problems in another field that may have been unsolvable (or would have taken decades to solve) from within that field alone. In this case, the connection is between Prime Numbers and Physics. This is what I call Archetyping.
The gist is that when prime numbers were plotted as points in some sort of graph (zeta landscape) using Riemann's equation, a pattern emerged that the zeros seemed to be "running in a straight line through the landscape". Hence, Riemann He proposed that all the zeros, infinitely many of them, would be sitting on this critical line — a conjecture that has become known as the Riemann Hypothesis. The connection to Quantum Physics is that "if you compare a strip of zeros from Riemann's critical line to the experimentally recorded energy levels in the nucleus of a large atom like erbium, the 68th atom in the periodic table of elements, the two are uncannily similar". And so, "If one could understand the mathematics describing the structure of the atomic nucleus in quantum physics, maybe the same math could solve the Riemann Hypothesis".
And so, insights from Quantum Physics resulted in great new many discoveries in Mathematics. A formula to predict all the numbers in the sequence, as well as solutions to other math-specific puzzles were gleaned from Quantum Physics largely inspired by the connection and the pattern.
I believe that a great many new things can solved in other fields using this "extra-disciplinary cooperation". Great questions in Science, Spirituality, Theology and Philosophy can be given a new light, specially in questions about the meaning of life and maybe even the afterlife, if we all learned a bit more to correlate and cooperate.