[Paper Review] Quantum Structure in Cognition: Human Language as a Boson Gas of Entangled Words

Diederik Aerts, Lester Beltran|arXiv (Cornell University)|Sep 15, 2019

Quantum Mechanics and Applications130 references19 citations

TL;DR

This paper proposes a quantum model of human language by treating words as bosons in a gas state, where word frequency corresponds to energy levels. Using Bose-Einstein statistics, the model fits empirical word frequency distributions in stories (e.g., Winnie the Pooh) with high accuracy, revealing a deep connection to Zipf’s law and offering new insights into conceptual identity and indistinguishability in cognition.

ABSTRACT

We model a piece of text of human language telling a story by means of the quantum structure describing a Bose gas in a state close to a Bose-Einstein condensate near absolute zero temperature. For this we introduce energy levels for the words (concepts) used in the story and we also introduce the new notion of 'cogniton' as the quantum of human thought. Words (concepts) are then cognitons in different energy states as it is the case for photons in different energy states, or states of different radiative frequency, when the considered boson gas is that of the quanta of the electromagnetic field. We show that Bose-Einstein statistics delivers a very good model for these pieces of texts telling stories, both for short stories and for long stories of the size of novels. We analyze an unexpected connection with Zipf's law in human language, the Zipf ranking relating to the energy levels of the words, and the Bose-Einstein graph coinciding with the Zipf graph. We investigate the issue of 'identity and indistinguishability' from this new perspective and conjecture that the way one can easily understand how two of 'the same concepts' are 'absolutely identical and indistinguishable' in human language is also the way in which quantum particles are absolutely identical and indistinguishable in physical reality, providing in this way new evidence for our conceptuality interpretation of quantum theory.

Motivation & Objective

• To develop a quantum-theoretic model of human language based on the statistical behavior of words as bosons.
• To explain the emergence of Zipf’s law in word frequency distributions through Bose-Einstein statistics.
• To introduce the concept of the 'cogniton' as the quantum unit of human thought, analogous to a photon in a light field.
• To investigate the role of quantum superposition and entanglement in linguistic structures, particularly in narrative texts.
• To provide empirical validation of the model using real texts, including short stories and novels, showing strong fit with Bose-Einstein distribution.

Proposed method

• Assign energy levels to words based on their frequency of occurrence in a text, with the most frequent word at the lowest energy level E₀.
• Model the text as a Bose gas in thermal equilibrium, using the Bose-Einstein distribution: N(Ei) = 1 / (A·e^(Ei/B) - 1).
• Calibrate parameters A and B using two constraints: total word count and total energy, derived from word frequencies.
• Map word frequencies to energy levels using a linear energy scale: Ei = i for i ∈ [0, 1, ..., n], where n is the number of distinct words.
• Apply the model to real texts (e.g., 'In Which Piglet Meets a Haffalump') and compare predicted frequencies with empirical data.
• Use quantum harmonic oscillator and particle-in-a-box models as analogies to explain wave-like and quantized behavior of linguistic concepts.

Experimental results

Research questions

• RQ1 Can the statistical distribution of word frequencies in human language be accurately modeled using Bose-Einstein statistics?
• RQ2 What is the physical and conceptual meaning of assigning energy levels to words based on their frequency?
• RQ3 How does the quantum model of language explain the emergence of Zipf’s law in linguistic data?
• RQ4 To what extent do quantum phenomena like superposition and entanglement underlie the structure of narrative texts?
• RQ5 What does the concept of 'indistinguishability' of identical concepts in language reveal about the nature of quantum particles?

Key findings

• The Bose-Einstein distribution provides an almost perfect fit to word frequency data in the story 'In Which Piglet Meets a Haffalump', with a total of 2655 words and total energy E = 242891.
• The model successfully reproduces Zipf’s law: the Bose-Einstein graph of word frequency versus energy level closely matches the empirical Zipf graph.
• The most frequent word, 'And', appears 133 times and is assigned the lowest energy level E₀ = 0, while rarer words like 'Able' (1 occurrence) are assigned higher energy levels.
• The energy level E₅₄ = 54 corresponds to the word 'Thought', which appears 10 times, contributing 540 units of energy to the total.
• The model demonstrates that linguistic structures exhibit quantum-like features such as superposition and entanglement, with deep non-classical correlations violating marginal laws.
• The concept of the 'cogniton'—a quantum of thought—emerges as a fundamental unit, analogous to a photon, with different energy states corresponding to different linguistic concepts.