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When most people speak of Math, what they have in mind is more its mechanism than its essence. This "Math" consists of assigning meaning to a set of symbols, blindly shuffling around these symbols according to arcane rules, and then interpreting a meaning from the shuffled result.
The process is not unlike casting lots. This mechanism of math evolved for a reason: Unfortunately, most people are not comfortable with bundling up meaning into abstract symbols and making them dance.
Thus, the power of math beyond arithmetic is generally reserved for a clergy of scientists and engineers many of whom struggle with symbolic abstractions more than they'll actually admit.
We are no longer constrained by pencil and paper. The symbolic shuffle should no longer be taken for granted as the fundamental mechanism for understanding quantity and change. Math needs a new interface. Project Kill Math is my umbrella project for techniques that enable Essay on meaningful symbols to model and solve meaningful problems of quantity using concrete representations and intuition-guided exploration.
In the long term, I hope to develop a widely-usable, insight-generating alternative to symbolic math. Someday there will be an introductory essay on this page, and it will move you to tears.
That essay is not yet written -- it will take a lot more thinking, and a lot of examples, before I understand what I'm trying to do well enough. Here's what I have for you so far: Media for Thinking the Unthinkable presents a collection of interactive representations for designing and understanding systems, and consolidates a lot of the work listed below.
Scrubbing Calculator demonstrates a tool for exploring practical algebraic problems without symbolic variables. Instead of x's and y's, you connect concrete numbers and adjust them interactively.
Interactive Exploration of a Dynamical System demonstrates a tool for manipulating differential equations where every variable is shown as a plot, and every parameter has a knob that can be adjusted in realtime.
This helps the user develop a sense for how the parameters of the system influence its behavior. Up And Down the Ladder of Abstraction is an interactive essay about using visualization in a systematic way to design and understand systems.
Simulation As A Practical Tool is its early precursor, where I started working out the ideas behind this effort. Below is a collection of blog-quality ramblings on the topic, which I suppose are intended more to attract like-minded people than to convince the skeptical.
The skeptical should refuse to be convinced until they see more examples. My plan is to collect a number of meaningful problems across different application areas and areas of mathematics, and for each one, design a means of solving it that is line with the philosophy here, and compare the benefits of this solution to the benefits of a conventional solution.
The techniques and design patterns that emerge during this process will, hopefully, inform a more general framework in the long term. As always, if you're playing with ideas along similar lines, I'd love to see what you've come up with.
Some additional thoughts were published in this Fast Company article. Currently, that power is restricted to the tiny subset of people comfortable with manipulating abstract symbols.
By comparison, consider literacy. The ability to receive thoughts from a person who is not at the same place or time is a similarly great power.
The dramatic social consequences of the rise of literacy are well known. Linguistic literacy has enjoyed much more popular success than mathematical literacy.Photography and sociology have approximately the same birth date, if you count sociology’s birth as the publication of Comte’s work which gave it its name, and photography’s birth as the date in when Daguerre made public his method for fixing an image on a metal plate.
2 From the beginning, both worked on a variety of projects. Among these, for both, was the exploration of society.
A VERY, VERY SHORT HISTORY. To understand fully any country's political system, one needs to understand something of its history. This is especially true of the United Kingdom because its history has been very different from most other nations and, as a result, its political system is very different from most other nations too.
This forgery, Christ and the Disciples at Emmaus, was completed in To produce it, van Meegeren studied seventeenth-century pigment formulas, incorporated volatile flower oils in his pigments to create hardness, and used badger-hair brushes (a single modern bristle embedded in the paint would give him away) on canvas recycled from an unimportant seventeenth-century painting.
Discourse is a term becoming increasingly common in a wide range of academic and non-academic contexts. Discourse can be defined variously. Cook ( ) views discourse as “a stretch of language perceived to be meaningful unified and purposive”, whereas Nunan () asserts that discourse.
This commentary on Ludwig Wittgenstein's concept of a "language game" is based on his important book, the Philosophical Investigations, in which he introduced that concept. EVOLUTION TRENDS The "INFORMATION AGE" & its Evolution into the "Holographic Age" Challenges & Realistic Goals For Survival & Creating A Desirable Future.