Think Better: An Introduction to Thinking Tools

The philosopher and computer scientist Bo Dahlbom stated that “You can’t do much carpentry with your bare hands and you can’t do much thinking with your bare brain.”  Why? Our bare brains are full of cognitive biases. If left untrained in wielding the right tools for thinking, appropriate solutions will be harder to find.

Since the earliest times, thinkers are fond of creating thinking tools. Some of them are simple and intuitive. Some of them are complex and as Dan Dennett calls them–thinking tools par excellence.

Of these, he mentioned Rene Descartes’ Cartesian coordinates, the x- and y-axes. Without such tool, calculus wouldn’t likely to have been invented by two great thinkers independently: Isaac Newton and Gottfried Wilhelm Leibniz. Pascal gave the world a plus one with his probability theory. The Reverend Thomas Bayes contributed his eponymous theorem which is the foundation for Bayesian statistics. Now, Bayesian inference is used in cognitive science and decision-making theory. Calculus is used in disciplines from physics to economics.

I know that many people do not have the time to study much of them (just like me) but don’t be disheartened. There are other simpler tools that people can use to extend their imagination and hold their focus longer. Dennett shared his favorite thinking tools in his book Intuition Pumps and Other Tools for ThinkingSome of them and others that I have encountered will be featured in this column.

So, what’s the best thinking tool?

In all the tools that I have come across (some I use daily) from studying philosophy, science and mathematics, the best thinking tool for me is the concept of thinking tools. This may sound like a mysterious Zen koan but let me explain why.

There is an art and wisdom in choosing which tool to use for a task. If you want to cut down a tree, an ax would be helpful. A chainsaw will be better. A toothpick? A nail filer? Not so much.

This is also the same in wielding conceptual tools: thought experiments in philosophy and science, the abstract apparatuses of math, and how they go together. If we fail to cultivate the wisdom of when, how and for what we use them, we’d likely miss the mark. Many times we go way off.

Let me give you a quick example.

Same Tool. Similar Problems. Different Results: Neptune and Mercury

Neptune, Wikimedia Commons

The discovery of Neptune is an excellent example of how many tools come into use. From around 1821 to the 1840s, scientists have found the planet Uranus to have some irregularities in its orbit. It was observed that it deviates from its orbit as predicted by the prevailing theory at the time. This has either of three causes: (1) the observations were flawed, (2) the prevailing theory was lacking or (3) Uranus is being perturbed by another celestial body.

Urbain Le Verrier, a French mathematician, labored exhaustively to pin point the exact location or position of this undiscovered object just using mathematics. He shared his calculated coordinates to astronomer Johann Gottfried Galle of the Berlin Observatory.

On one fateful night of September 1846, a planet was observed within one degree of Le Verrier’s coordinates by Galle. This discovery was seen as a powerful confirmation of Newton’s gravitational theory in the 19th century.

Mercury, Wikimedia Commons

Mercury’s orbits have also peculiarities. Le Verrier, because of his previous success, was assigned to work on them by Francois Arago, director of the Paris Observatory. He used the very same methods and hypothesized that there is another undiscovered mass in an orbit between Mercury and the Sun.

He called this Vulcan.

This time his predictions, using the same tools, did not match the observations. Later, it was found out that the perturbations in Mercury’s orbit was solvable not by Newton’s gravitational theory but by Einstein’s theory of relativity.

The latter is a more powerful tool in both explaining and predicting things studied in celestial mechanics. A better tool came a long.

Conclusion. Right now, you may have intuit that scientific, mathematical, and philosophical concepts are best thought to be as “just tools” we use to approximate the world and our place within it. In a Buddhist context, these are just “fingers pointing to the moon”. They are not the moon themselves. Some may, like Le Verrier’s, point to the right direction for one thing but is less useful for another.

There is an art and science to choosing the right tools, using them the most efficient way, and the wisdom & humility not to use them and wave them around like a master key.

What to Expect Next? In the next iterations of this column, we will be introduced to simpler tools for thinking, how to use them, and how to think about them.


Dennett, D. C. (2013). Intuition pumps and other tools for thinking. WW Norton & Company.

Encyclopaedia Britannica. (2018, March 4). Urbain-Jean-Joseph Le Verrier | French astronomer. Retrieved from



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