On Notation

last updated: January 4, 2021



A series or system of written symbols that represent information

In the unstoppable force of 'human progress,' I've so far focused on the dimensions of human emotion (see

). However, there is tremendous value being created along another vector: notation. For the knowledge worker, superior notation is one of the greatest deltas of productivity. And only recently have creators of new notation been able to profit from it and by capture the value they've created.

Better notation works by presenting information (or meta-information) and facilitating our engagement with it, by abstracting away or highlighting connections and future connections.

Some History

Before Arabic numerals, it was almost impossible to do basic arithmetic with large numbers. You needed excellent mental math or some physical analog, like an abacus. Leibniz notation allowed mathematicians to apply calculus to the rest of science. Mendelev organized the elements of the world into a table, which kicked off a chemical revolution. Or take William Playfair, who single-handedly invented most of the graphs still in use today (except the scatter plot), in order to explain economics to the populace and policy-makers of his time. Imagine a world before a time-series plot. Seriously, imagine having to look at a table of figures in order to try and figure out if a value was increasing or decreasing over time. And then take the time (no pun intended) to be grateful for Mr. Playfair, who also had the good taste to make his graphs beautiful.


One person who understood this dynamic especially well was Steve Jobs. VisiCalc was clearly a part of his early success, and he would say that "VisiCalc propelled the success of Apple more than any other single event." But he understood what could be made possible with technology. He would often relate the anecdote of the bicycle making humans more efficient than the most efficient animal (the condor). Jobs' vision was to make the Apple like a 'bicycle for the mind.'

Graphic from March 1973, Scientific American article on origin and impact of the bicycle by Wilson. Found
Graphic from March 1973, Scientific American article on origin and impact of the bicycle by Wilson. Found here.

Better notation means you can go deeper and faster with certain information than ever before. And sometimes notation is so good it can remain constant for a thousand years.

For example, musical notation was invented around 1000 AD. It a composer to write down a series of notes in such a way that the relation between notes is always clear, so that a musician can play it on their instrument. What are essentially black squiggles on a page allow for easy identification of the length of a note, the pitch, and accidentals (a flat or sharp note). It is excellent notation that has survived the test of time, and will continue to survive until a better version is proposed.

Imagine if the inventor of musical notation, the Italian monk Guido d'Arezzo, could have captured a tiny fraction of the massive human value he opened for the world. During his lifetime, from 991 to 1033, that would have been impossible. However, the advent of software and patent laws means that there is now a way where there used to be none.

The Electronic Spreadsheet

Some revolutions are immediately explosive. First publicly sold as 'VisiCalc' (the visible calculator), the electronic spreadsheet was then spearheaded by Lotus 1-2-3 and then Excel (who has dominated since, and is now finally being threatened by newcomer Google Sheets). In its first year of business, Lotus had revenue of $56M (yes, that's million) and went public. The following year, revenue tripled. And, for reference, a dollar in 1979 is worth $2.25 in today's inflation-adjusted currency.

The spreadsheet was nothing new, and referred to 'spreadable' sheets that were unfolded in ledgers to keep track of transactions. Computer calculations had been invented as well, and researches used columns or rows of numbers to simplify calculations. However, it was Dan Bricklin and Bob Frankston that combined the two and packaged it for the first time on a micro-computer: the Apple II.

By creating a tool that allowed users to rearrange numbers and text on a 2D grid, and hide the formulas that outputted some of those numbers, VisiCalc allowed for an entire new way of thinking about business 'what if' scenarios and projections. And, thanks to American law and their quasi-monopoly on the Apple II, VisiCalc became the first 'killer app' - software so good people would buy the hardware just to run it. And the founders of VisiCalc were able to profit from their notation tool by becoming the best-selling piece of software in history.

Of course, the story doesn't end there, as they become entangled in legal trouble and allowed Lotus 1-2-3 to improve their system and take over the DOC operating system, before Microsoft Excel took the lion's share of the market by betting on the Mac and the Windows operating systems. Spreadsheets are the foundation of modern business, and have been since the 1980s. However, the system is not perfect and will only be king until a new form of notation emerges.

Notation today

Today, one brand of notation tools is back in the limelight: note-taking tools. Products offered by Airtable, Notion, and Roam Research allow for new ways to display, organize, and link information. Airtable offered a custom database, allowing users to build 'blocks' without needing to code. Notion built an intuitive display of information with easy nesting, hosting, and collaborating on pages (like this one!). Roam Research abstracted away the links between bodies of text with their once-novel bidirectional links.

But notation tools extend far beyond the realm of 'productivity tools,' because notation goes far deeper than personal note-taking and record-keeping. Bear in mind that mathematical notation is deeply intertwined with the advance of the academic field and ensuing applications.


Musical notation allowed for centuries of cultural flourishing in the West. Spreadsheets literally created the analyst role on Wall Street, and a whole new way of thinking about capital allocation. In every instance, a specific space of information was revolutionized by a new way of engaging with that information.

So what makes a great notation tool?

The VisiCalc spreadsheet makes for a great case study, especially given its rapid adoption and massive impact on our society.

A spreadsheet on the early VisiCalc [
A spreadsheet on the early VisiCalc [link to a great data visualization site]

These are obviously broad strokes, but hopefully shed light on the characteristics of excellent notation tools:

  1. Unconstrained uses: the spreadsheet was designed to help with financial projections, but was soon hijacked (in the best of ways) by users with novel use cases. They were specifically use cases that Bricklin had never imagined, like designing office layouts in the grid, or managing hospital patient throughput. It was the lack of specialization that allowed for such creative applications, which in turn propelled the spreadsheet to markets that were never even considered markets. This is obviously at the risk of confusing customers ('what exactly does this do?') at first, but with a high potential reward.
  2. Graphical display: the 2D array adopted by Bricklin was based on the tables drawn on the whiteboards in his HSB classes, and centuries of 'spreadsheets' before that. However, the name itself, short for 'visible calculator,' hints at its massive value in visualizing certain pieces of information to allow for useful layouts. This is obviously a hallmark of mathematical as well, but emphasizes the visual nature of human thinking over other potential mediums (even with music, which is inherently audial). This is similar to the idea of curation as focused contextualization.
  3. Simplify computation: early VisiCalc users didn't grasp that the program could do its own arithmetic, and some even glued calculators to the side of their keyboards. Automatic re-calculation for new edits meant that the spreadsheet could save workers hours if they found an error early in the process. Arabic numerals allowed for simpler addition and subtraction on paper, and Mendelev's table meant that chemists could quickly place an element by understanding its atomic mass and number.

At the end of the day, what births enduring notation is a simpler way to engage with more complex information. And as long as humans keep compounding knowledge, we can be sure that raw information will continue to grow more complex, and that we will need such tools to match them to our constrained mental abilities (until those can be augmented, too).

Software allows for more reorganization and retooling of information than has been possible in millennia. Not all notation is helpful, and not all software will survive. But as new tools emerge for the information banks of our world, they will inevitably continue to knock down the dams and barriers to human knowledge and innovation. And I am personally very much looking forward to seeing new notation emerge in areas that have or will have complex information.

Enter Causal

One example I'm particularly excited about it Causal.app, which is attempting to be just such an example of superior notation for modeling numbers. If you've never tried it before, I suggest jumping into and enjoying a simple model, like the rent vs buy template. Even a few minutes will give helpful context to the next few paragraphs.


Causal brings a few key features to the table, which go a long way to address some of the ideas listed above:

  1. Ranges and distributions: easy to express uncertain assumptions, create Monte Carlo simulations
  2. Readable formulas: create and name variables instead of depending on column and row references
  3. Time-series: easy and fast create time-series models, automatically display monthly or annual summaries
  4. Connected models: bring shared variables, datasets, and visuals into a ‘single source of truth’
  5. Data integrations: for real-time data imported from Stripe of Google Sheets
  6. Interactive dashboards: for easy sensitivity analysis and presentations

Fundamentally, every one of these is an attempt to create simplified tools for complex computation, leaning on user-friendly visuals. And though Causal is wonderfully suited for financial modeling, the truth is that it can be used for any number of use cases requiring the manipulation of numbers. And there you see the pillars of good notational tools: unconstrained use, graphical display, and simplified computation.

Causal is not the only player in this space. Dozens of 'visualization tools' have emerged, trying to address business analytics, data visualization, or complex modeling. But few of these are built on the same foundations of good notation, and play a role that, while helpful and necessary, will not turn an opaque body of knowledge into a malleable tool that can be taught at any level.

Remember, calculus used to be the cutting edge of mathematics, and today it is taught in high schools. It is the role of notation (among others) to help cut the distance between engaging with a model, and understanding it.

edit: in March someone shared a piece with me titled 'Excel never dies,' which covers some of the same areas and may be of interest for further reading.