By Professor Lance Linke

Yale Center for Emotional Intelligence

I’ve wondered for quite some time if there is a relationship between mathematics and morality. These fields have often been considered to be distinct, with adherents dismissing the possibility of a bridging rationale that could unite the two in common language. However, there seems to be historical precedent for suggesting this union is possible or even probable. For example, Pythagoras’ world view was imbued with a sacred appreciation for number and geometry that esteemed the fundamental nature of mathematics. This appreciation crossed from geometry and harmonics to a praise of certain equations and frequencies as fundamentally good. The a priori nature of mathematics suggests to many that mathematical relationships are part of the essential structure of reality (Penrose, 2004). Max Tegmark (2014) similarly argues mathematics as being a comprehensive language adept at describing reality, introducing the possibility that the world is in some sense fundamentally understandable from a mathematical perspective.

My line of inquiry here questions whether we may begin to address more precise connections across these two domains. Specifically, whether mathematical algorithms or information theory may offer any additional explanatory power to various moral behaviors. This is merely a thought experiment to consider whether moral thoughts and behaviors are distinct from immoral ones in a manner that is mathematically discernible or describable. I find this reflection akin to Gregory Chaitin’s (2012) elucidation of metabiology, a computational theoretical approach to evolution. Chaitin suggests that we can model biology algorithmically, identifying essential mathematical components of evolutionary change. In a similar fashion, I wonder if it is possible to employ this algorithmic perspective to the nuanced and often ambivalent field of moral philosophy by utilizing his basic tenets and introducing features of information exchange.

Following Chaitin’s logic and applying it to mimetic evolution – the study of how memes as opposed to genes evolve – there may be essential features of moral behavior that are distinct from immoral behavior, for example, truth telling versus lying. These in turn may be mathematically decipherable. Therefore, the mimetic evolution associated with moral psychology and behavior may have a corresponding mathematical structure.

Moral behaviors require different costs to initiate and maintain compared to immoral ones. They are structured in distinct ways from an information exchange standpoint. For example, truth telling is fundamentally an information exchange. It requires a perception of our environment and then the communication of this info to someone else. Lying twists the information we perceive about the world in order to transmit it again to effect a desired end. This alteration of the original perception of events requires a change in information processing and thereby makes that information qualitatively, and perhaps quantitatively, different. In turn, these various renditions of events may likely follow different patterns of adoption and replication, like adoption and replication in biological evolution. When mimetic selection pressures act on these structural differences between honesty and lying, it may be they have varying and predictable trajectories of operating in the world. That is, these structural differences may alter the way the meme is culturally reproduced. Employing this logic, honesty may have a quantitatively different mathematical signature from lying from an information theory perspective in a manner that may be eventually discernible or definable algorithmically.

Naturally, perspectives such as these are rife with caveats, however, the intent here is merely to consider the plausibility of defining moral behavior such as truth telling within a mathematical domain. What is important here is that from an information exchange viewpoint, truth telling looks qualitatively distinct from deception. Truthfulness ‘matches’ objective perspectives of the world more fully and numerously than do lies. That is, a veridical rendition of events – or a description of reality that is in fact accurate – is more likely to be corroborated by other perspectives, especially as the number of perspectives grows. Even within conversations between two people, honesty will allow for more congruencies than dishonesty. This ‘congruence’ of perspectives allows for heightened and more efficient exchange of information. The information exchange is heightened because there are more similarities across the reference points of the two sources of information. It is more efficient because peculiarities associated with dishonesty do not need to be accounted for in order to make the two versions of events match. This is because the truthful rendition of events is manipulated the least to correspond to what actually happened. Therefore, truth would be the most internally consistent and most efficient means of communicating information. It would also be the most flexible in terms of uniting numerous viewpoints and perceptions of the world since truthful exchanges would most easily match other truthful statements in a manner that would produce the most organized network of reported events. This interactive structure of honest statements would have a degree of internal consistency that could not be matched by intentionally manipulated stories (lies) about what actually transpired.

While efficiency and consistency do not necessarily equal moral virtue, they are certainly hallmarks of profound mathematical theories. Is it possible that even our everyday social exchanges are imbued with logic patterns that are discernible from a mathematical vantage point? Could it be the case that truthful information exchange is quantitatively, as well as qualitatively, distinct from deception? Perhaps moral virtue is indeed a fundamental facet of the nature of reality also written in the language of mathematics.

Prof. Lance Linke (Yale University) Lance is an Associate Research Scientist at the Yale Center for Emotional Intelligence. He completed his initial graduate studies in philosophy exploring the dimensions of moral decision making. Thereafter, he trained as a developmental and educational psychologist studying the influences of emotions on learning and decision making. His research investigates interpersonal functioning from a prevention science perspective, early assessment and prevention strategies for building resilience, and emotion regulation skills in parents and children.