Bridges and Tunnels

Very often in mathematics the crucial problem is to recognize and discover what are the relevant concepts; once this is accomplished the job may be more than half done.
— Israel Nathan Herstein (1923-1988)

The challenge of forecasting is concisely captured in the following piece of advice: When presenting a forecast, always observe the first rule of forecasting: “Give them a number or give them a date, but never both.” Indeed, we may know that certain events (e.g., news announcements or periodic release of government statistics) will occur at a precise date and time – down to the second even – but we can never be sure how the market would react. On the other hand, we may know quite a bit about how a particular market might behave, e.g., oscillating in a range-bound fashion, but we are not able to pin down the exact time of reversal. Good forecasting, therefore, requires that we master the movement and rhythm of the market so we can be reasonably sure of the magnitude and direction of occasional big changes, while keeping track of the approximate timing of frequent small reversals.

This brings us to looking at forecasting from the perspective of building bridges and tunnels. Bridges are the plausible relationships that connect concepts together in a domain of discourse; while tunnels constrain the uncertain relationships between two concepts to within a zone of possibilities. By using a “bridges and tunnels” metaphor to understand how a conceptual map can be constructed and applied towards the business of forecasting, we hope to illuminate the somewhat murky picture of trying to discern the future. And that does not come from seeing the future through a crystal ball.

Forecasting by Bridges and Tunnels: Connect and Constrain.

Forecasting by Bridges and Tunnels: Connect and Constrain.

The greatest enemy of knowledge is not ignorance, it is the illusion of knowledge.
— Stephen Hawking


  1. Saffo, Paul (2007). Six Rules for Effective Forecasting. Harvard Business Review. Retrieved from:
  2. Walonick, David (2013). Survival Statistics. Chapter on Forecasting. Retrieved from:
  3. Cheng, Eugenia (2015). How to Bake π: An Edible Exploration of the Mathematics of Mathematics. Basic Books.