This was originally posted by Kent Thune at The Financial Philosopher.

Whether you are an investment trader, a music fan, a mathematician, a curious observer wishing to learn more about human nature, or any combination thereof, you will appreciate this lesson on the Fibonacci Sequence (more on this after the YouTube link):

The video, created by a college student to help explain the Fibonacci sequence, features images of space from the Hubble Telescope and music from the cerebral and progressive hard rock band Tool.  What makes the video and song incredibly compelling is the lyrics, which teach a lesson on pattern recognition.

For those non-traders and non-mathematicians out there, a Fibonacci sequence is a series of numbers where, after two starting values, each number is the sum of the two preceding numbers.  For example, the number sequence 2, 3, 5, 8 and 13 are a Fibonacci sequence (2+3=5, 3+5=8, 5+8=13, and so on).

Making the video and song more interesting is that the cadence of the lyrics (number of syllables of succeeding verses) follows a Fibonacci sequence.  What’s more, the meaning and lesson of the lyrics implies that humans are hopelessly addicted to looking for patterns everywhere they turn:  The “over-thinking” and “over-analyzing,” as the lyrics suggest, have an effect of dulling intuitive thought and often results in missed opportunities.

Pattern Recognition: Strength, Weakness or Both?

Philosopher and mathematician, T.L. Fine, once said, “A keen eye for pattern will find it anywhere.” This profound statement is neither a compliment nor an affront to humankind but it suggests that a fundamental awareness of the human tendency for pattern recognition allows for a healthy balance of intuitive thought and science.

Pattern recognition is a means of making sense of randomness.  This search for understanding, which is rooted in the desire for control and safety, can be self-defeating.   Wanting to find patterns can be considered thinking “inside the box,” but the answers are not always in the box.  Additionally, being comfortable without having answers can often open doors to new ideas, new opportunities and success.  Therefore asking questions is more important than having answers.  As 19th century philosopher and spiritual leader Jiddu Krishnamurti once said, “Freedom from the desire for an answer is essential to the understanding of a problem.”

Balance Linear And Lateral: Seek But Remain Open to Discovery

Returning to the message within the Tool song, aptly named Lateralus, too many people think and live linearly (in straight lines, black and white, inside the box), whereas thinking and living laterally (randomness, color, outside the box)–embracing the unknown–is healthy.

Perhaps the wisest solution is to balance the linear with the lateral.  There is no stopping your nature to seek and find patterns; and to eliminate this nature is nothing less than attempting to become something other than a human being.  Just be aware of your nature, and its potential limitations, and you’ll open doors to intuitive thought–expand beyond the narrow-minded linear thought–balance responsibility with adventure–seek but remain open to discovery.


Kent Thune is an investment adviser, free-lance writer and blog author of The Financial Philosopher, where his philosophical musings guide readers to think independently and to place “meaning before money, purpose before planning.”

Category: Philosophy, Psychology

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10 Responses to “Tool’s Lesson on Fibonacci: Think ‘Laterally’”

  1. dead hobo says:

    Fortunately, computers programmed with HFT algos don’t know any of this. Their only ability is to look for predetermined points and react in specified ways if those points are met or exceeded. Thus, magic charts become self fulfilling prophecies that tend towards rising markets over the short term, and, thus, become predictable if enough liquidity is available to give them something to work with. As a byproduct, the algo + liquidity combination causes excruciating pain and a wall of worry for ‘professional investors’ who often seem totally confused by it. While oil is the wild card that might monkey things up, the Fed plus the Japanese money dumps should provide enough fuel for the algos for a few more months.

  2. cthwaites says:

    For a fascinating chapter on Fibonacci sequences and the Golden Mean see Alex Bellos’ Alex’s Adventures in Numberland

  3. Rouleur says:

    Apophenia is the experience of seeing patterns or connections in random or meaningless data. The term was coined in 1958 by Klaus Conrad, who defined it as the “unmotivated seeing of connections” accompanied by a “specific experience of an abnormal meaningfulness”.

    Conrad originally described this phenomenon in relation to the distortion of reality present in psychosis, but it has become more widely used to describe this tendency in healthy individuals without necessarily implying the presence of neurological or mental illness.

    In statistics, apophenia would be classed as a Type I error. Apophenia is often used as an explanation of paranormal and religious claims. It has been suggested that apophenia is a link between psychosis and creativity.

    (sorry, [])

  4. @ Dead Hobo: Yes, when enough people are aware of certain patterns, self-fulfilling prophecy becomes an influence. Nothing attracts a crowd like a crowd.

    @ cthwaites & Patrick Neid: Thanks for the links.

    @ Rouleur: I’ll check out Apophenia…

    Cheers to all and thanks to Barry for keeping the door open at TBP…

  5. Bruman says:

    Like to write
    Poetry using
    Fibbonaci sequences too.

  6. DeDude says:

    Pattern recognition is sort of the lazy alternative to understanding the underlying mechanisms and creating models based on those mechanisms. As with most lazy alternatives it is not as good as the real deal. Unfortunately for investors the multivariate model of most markets would have so many hard to define and obtain parameters that nobody have come up with one that is better than guessing or drawing lines through point. I think that is why so many investors find comfort in the crowds (at least I won’t be crushed alone).

  7. @ Bruman: Nice Fibonacci sequence!

    @ DeDude: I agree. The brain (and the crowd) prefers to find answers in patterns, which is arguably lazy behavior, but patterns are like word phrases that need to be interpreted correctly. The problem is that some phrases send false signals. Personally, I am not a “trader” but I am drawn to the psychology and philosophy sides of finance.

  8. Greshams-law says:

    There is perhaps an even more rudimentary reason for patterns in finance, maths, music etc. The great insights about the philosophy of perception by Kant are very relevant here.

    That which we perceive is subject to – not necessarily the laws of things in themselves – but rather the criterion and laws of our own capacities to perceive. That is, that which we perceive is – to be sure – perceivable. And for things to be perceivable, they must be subject to the criterion of our apparatus of cognition and perception. Thus, the world as we know it should be patterned and ordered to align with the laws intertwined with our apparatuses of thinking and perceiving.

    This is particularly interesting for financial markets. They are – themselves – products of perceiving beings who perceive the world as ordered. It would seem natural that they might be patterned (not necessarily ‘mechanically’ patterned, but patterned nonetheless).

  9. @ Greshams-law: Well said. What we perceive and what we prefer as humans are patterns. This may explain why a dissonant chord or out-of-tune musical instrument sounds so terrible. Unless messages of any kind (visual, audible) are harmonious they are simply “noise” to our human ears.

    On a lighter note, perhaps those who love jazz music, such as myself and our gracious host, Barry Ritholtz, enjoye the randomness of improvisation because it is a kind of “organized chaos.” Capital markets are not different than this…