• the right interface can have an incredible power
  • making something that was previously extremely hard, available to everyone (switching from Roman to Arabic numerals as an interface to mathematics)
  • making invention possible (Feynman Diagrams)
  • making Solving Things Visually possible (Cartesian Coordinates)
    • Data Visualization can be thought of as an alternative, sometimes more powerful, interface to data
  • working with the amounts of data for which we don't have enough Pixel Space (Collection-Browsing Interfaces)
• most powerful interfaces so far were static - how much more can we do in the Dynamic Medium?
  • generic Simulator is one idea
  • what would be a Second-Order Tool Building tool for inventing "interfaces" (in the broad sense described above)?
• references:
  • Bret Victor's Thesis
  • Gottfried Wilhelm Leibniz attributed his discoveries in mathematics to inventing new notation

These representations weren't mere scientific "discoveries". Each of them essentially enabled all subsequent scientific breakthroughs thereafter. A powerful new form of representation affects everything, forever.

— CDG Research Agenda - Bret Victor

• new powerful notations "stick around" and infect human thinking for generations

Back in the days of Roman numerals, basic multiplication was considered this incredibly technical concept that only official mathematicians could handle, but then once Arabic numerals came around, you could actually do arithmetic on paper, and we found that 7-year-olds can understand multiplication.

It's not that multiplication itself was difficult. It was just that the representation of numbers — the interface — was wrong

— The Utopian UI Architect

it's a question meant to stimulate thought: what design process could take you from Roman numerals to Hindu-Arabic numerals? (...) it seems fair to say that any person who could invent Hindu-Arabic numerals, starting from the Roman numerals, would be both one of the great mathematical geniuses who ever lived, and one of the great design geniuses who ever lived. They'd have to be extraordinarily capable in both domains, capable of an insight-through-making loop which used the evolving system of numerals to improve not just their own mathematical ideas, but to have original, world-class insights into mathematics; and also to use those mathematical insights to improve their evolving system of numerals

— How can we develop transformative tools for thought? - Andy Matuschak, Michale Nielsen

The representation of a task can radically affect our reasoning abilities and performance. For example, the game of tic-tac-toe (opposing players mark X's and O's in a 3x3 grid) can be equivalently represented as a game of drawing numbered cards with the goal of selecting three that sum to 15. From a computational perspective, these two problems are isomorphic. However, the tic-tac-toe representation is significantly easier to work with because the representational form of the problem makes visible the most relevant constraints implicit in the problem. As Simon writes, in mathematics, "solving a problem simply means representing a problem so as to make the solution transparent"

— How Bodies Matter: Five Themes for Interaction Design - Scott Klemmer, et al.