📚 Instadeq Reading List: May 2021

The importance of nomenclature, notation, and language as tools of thought has long been recognized. In chemistry and in botany the establishment of systems of nomenclature did much to stimulate and to channel later investigation

Mathematical notation provides perhaps the best-known and best-developed example of language used consciously as a tool of thought

In addition to the executability and universality emphasized in the introduction, a good notation should embody characteristics familiar to any user of mathematical notation:

Ease of Expressing Constructs Arising in Problems:

If it is to be effective as a tool of thought, a notation must allow convenient expression not only of notions arising directly from a problem, but also of those arising in subsequent analysis, generalization, and specialization.

Suggestivity:

A notation will be said to be suggestive if the forms of the expressions arising in one set of problems suggest related expressions which find application in other problems.

Subordination of Detail:

As Babbage remarked in the passage cited by Cajori, brevity facilitates reasoning. Brevity is achieved by subordinating detail

Economy:

The utility of a language as a tool of thought increases with the range of topics it can treat, but decreases with the amount of vocabulary and the complexity of grammatical rules which the user must keep in mind. Economy of notation is therefore important.

Economy requires that a large number of ideas be expressible in terms of a relatively small vocabulary. A fundamental scheme for achieving this is the introduction of grammatical rules by which meaningful phrases and sentences can be constructed by combining elements of the vocabulary.

Retrospectively it’s difficult not to be disappointed, to feel that computers have not yet been nearly as transformative as far older tools for thought, such as language and writing. Today, it’s common in technology circles to pay lip service to the pioneering dreams of the past. But nostalgia aside there is little determined effort to pursue the vision of transformative new tools for thought

Why is it that the technology industry has made comparatively little effort developing this vision of transformative tools for thought?

Online there is much well-deserved veneration for these people. But such veneration can veer into an unhealthy reverence for the good old days, a belief that giants once roamed the earth, and today’s work is lesser

What creative steps would be needed to invent Hindu-Arabic numerals, starting from the Roman numerals? Is there a creative practice in which such steps would be likely to occur?

The most powerful tools for thought express deep insights into the underlying subject matter

Conventional tech industry product practice will not produce deep enough subject matter insights to create transformative tools for thought

The aspiration is for any team serious about making transformative tools for thought. It’s to create a culture that combines the best parts of modern product practice with the best parts of the (very different) modern research culture. Diagram: 'insight' and 'making', pointing to each other in a loop You need the insight-through-making loop to operate, whereby deep, original insights about the subject feed back to change and improve the system, and changes to the system result in deep, original insights about the subject.

People with expertise on one side of the loop often have trouble perceiving (much less understanding and participating in) the nature of the work that goes on on the other side of the loop. You have researchers, brilliant in their domain, who think of making as something essentially trivial, “just a matter of implementation”. And you have makers who don’t understand research at all, who see it as merely a rather slow and dysfunctional (and unprofitable) making process

Why isn’t there more work on tools for thought today?

It is, for instance, common to hear technologists allude to Steve Jobs’s metaphor of computers as “bicycles for the mind”. But in practice it’s rarely more than lip service. Many pioneers of computing have been deeply disappointed in the limited use of computers as tools to improve human cognition

Our experience is that many of today’s technology leaders genuinely venerate Engelbart, Kay, and their colleagues. Many even feel that computers have huge potential as tools for improving human thinking. But they don’t see how to build good businesses around developing new tools for thought. And without such business opportunities, work languishes.

What makes it difficult to build companies that develop tools for thought?

Many tools for thought are public goods. They often cost a lot to develop initially, but it’s easy for others to duplicate and improve on them, free riding on the initial investment. While such duplication and improvement is good for our society as a whole, it’s bad for the companies that make that initial investment

Pioneers such as Alan Turing and Alonzo Church were exploring extremely basic and fundamental (and seemingly esoteric) questions about logic, mathematics, and the nature of what is provable. Out of those explorations the idea of a computer emerged, after many years; it was a discovered concept, not a goal. Fundamental, open-ended questions seem to be at least as good a source of breakthroughs as goals, no matter how ambitious

There’s a lot of work on tools for thought that takes the form of toys, or “educational” environments. Tools for writing that aren’t used by actual writers. Tools for mathematics that aren’t used by actual mathematicians. Even though the creators of such tools have good intentions, it’s difficult not to be suspicious of this pattern. It’s very easy to slip into a cargo cult mode, doing work that seems (say) mathematical, but which actually avoids engagement with the heart of the subject

Good tools for thought arise mostly as a byproduct of doing original work on serious problems