Actual / Expectation

The Quadrivium of Reality, Information, Surprise, and Boredom: Unveiling the Universal Formula


The complex interplay between reality, information, surprise, and boredom may not be immediately apparent. However, a closer look at Claude Shannon’s foundational 1940 paper on information theory reveals an underlying mathematical structure. This article introduces the universal formula—actual divided by expected—that unifies these seemingly disparate concepts, providing a holistic understanding of human perception, communication, and experience.

Information Theory and the Mathematics of Surprise

Claude Shannon’s groundbreaking work in the field of information theory gave us the concept of information entropy, a quantifiable measure of “surprise.” According to Shannon, the value of information is directly proportional to its level of unpredictability or surprise, encapsulated in the formula:

The absence of surprise means the absence of information, making the two practically synonymous within the framework of information theory.

The Universality of the Formula in Reality and Boredom

The formula’s utility extends beyond information theory, influencing our very perception of reality and, interestingly, boredom. Our sense of reality hinges on how our actual experiences align with our expectations. The formula applied here is identical:

When the value equals one, it signifies a state of equilibrium or harmony. A value less than one implies discord or dissatisfaction, while a value greater than one indicates euphoria or excessive joy.

In the context of boredom—a state where actual and expected align perfectly—the formula also holds:

Here, boredom serves as a cognitive reset button, providing a mental break that enables introspection and creativity.

Interconnection of Reality, Information, Surprise, and Boredom

The universal formula serves as a connecting thread between these diverse concepts. Surprising outcomes adjust our understanding of reality by serving as new information. Conversely, boredom offers a break from constant stimuli, allowing for mental rejuvenation. Whether encountering an unexpected event or settling into a state of boredom, the same mathematical formula governs our cognitive and emotional responses.


The universal formula of actual divided by expected is not a mere academic construct; it is a holistic framework that captures the essence of human experience in various dimensions—reality, information, surprise, and boredom. This unified theory transcends disciplinary boundaries, offering a comprehensive lens for understanding communication, expectation, and the human condition.

Author: John Rector

John Rector is an AI Futurist who predicted the next word in business™, starting with his notable paper from 2015, "Mommy, What's a Cashier?" Drawing upon 40 years of experience in the practical applications of high technology, he assists clients in converting uncertainty into strategic advantages within a one-to-six-year framework. With leadership roles including IBM executive and co-founder of e2open, he has a diverse and impactful background. In the AI sector, he has set benchmarks through his contributions to Mind Media Group and Florrol, pioneering AI-based services and content generation. His investment initiative, Waterway Ventures, is committed to advancing promising AI startups. His creative ventures include founding Bodaro and graphic design studio Palm ❤️. In education, he has launched Nextyrn, which uses AI for personalized learning experiences, and in art, he leads Potyn, an initiative using AI to create bespoke pieces. His ever-expanding portfolio features companies like Nozeus, Infinia, Blacc Ink, and Maibly. Operating from Charleston, SC, his current focus involves partnering with individuals and enterprises to develop innovative business models and processes for the rapidly approaching age of AGI.

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