The Mathematics of Morality

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.


Pythagoras of Samos (570-495 BCE) raised Mathematics itself to the status of the Divine

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-linkeLance 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.

9 responses to “The Mathematics of Morality

  1. Mathematics in my opinion is an objective outlook which exists even if humanity vanished, to the contrary morality is a subjective judgement against rules that would vanish if humanity vanished.


    • Math can describe human morality even if only humans can instantiate it in the world. For instance, math would describe rocket trajectories even if there weren’t any in the future. There is some phenomena or definition at root which the math is getting at, and not the physical objects involved.

      At least, that’s how I understood the article.


  2. This is the direction our understanding is heading. Watch this space for a new intellectual turn: social dynamics as distributed computation. Once we have a general model for adaptive, self-organizing, multi-agent networks, the way we approach many different fields will change drastically.
    A close analogue to the author’s discussion of truth telling is promise keeping. In economic networks, exchange amounts to a communication of information — of subjectively held beliefs and desires that are encoded in the transmission of physical objects. Yet if any two agents cannot rely on each other to keep contract, then error results and no information is shared. Subsequently there is no chance for an economic network to emerge.
    Therefore we tend to see the same sorts of mimetic values in similarly structured social networks. What is “moral” to a given civilization amounts to the set of inter-agent rules that has allowed that society, or organic network, to out-compete its neighbors. Thus the commonality of “thou shalt not steal” and similar codes of conduct to civilizations, as distinct from hunter-gatherer troops. Some moral rules (like the Ancient Greek guest-friend and protection of travelers) allow a more fluid dispersion of information, and, like advantageous genes, then replicate themselves.
    Of course, this is a descriptive account of morality that does not attempt to tell us what is moral. In fact it requires a suspension of the belief that we can know what is moral a priori — we must simply watch and see which moral rules benefit their adherents, and attempt to construct a formal framework (like information exchange) that gives us a deeper layer of explanation.


  3. I read your article with interest. I too am fascinated by the mechanics of morality. I have come up with a mathematical-type formulation of personal morality (from one particular viewpoint). It goes like this.
    When we act, that action affects a number of people, including ourselves. Perhaps it only affects ourselves. We can choose to define a moral action as one that fits the following criterion: each person affected by our action is to receive the maximum benefit and the minimum harm. Of course, to some extent, this involves a balancing act, but it need not be a zero-sum game.
    The “information” exchanged in this case is benefit/harm, or more precisely, what I call The Healing Principle – the drive towards health and quality of life seeking inherent in every living thing, as an evolutionary necessity. This means that benefit/harm is an action rather than a state of being.
    I am putting together a website aiming to give a complete grounding in the basic facts of morality, for reference purposes. Here I describe the Healing Principle and give the above formulation as a diagram showing it in terms of the expansion of the ego from the Self to all concerned in the moral situation. I hope this makes sense.
    This formulation is surprisingly profound when you think about it, and I believe it agrees with the Buddhist definition of acting wisely.
    If you have any comments, I would love to hear them.


  4. Pingback: Philosophers’ Carnival #171 | Nick Byrd·

  5. I believe that there is a profound and fundamental relationship between moral values, emotions and reality and that they can be mathematically defined and calculated, as well as their relationships to one another. Moral values as I see it comes in two varieties, those that are constant within all frames of reference or all realities and those that will vary within each frame of reference or reality that that frame of reference creates. The different factors that define a situation or person or object make up what I call a frame of reference, essentially giving that situation a reality as long as that frame of reference is valid, then it just winks out of existence.
    Morals are a part of the universe as is the electromagnetic force, (perhaps originating with the big bang) not a human invention or unique to the human experience. All creatures, in their own way are subject to it like we are all subject to electromagnetism, and it can be mathematically understood and calculated just as the electromagnetic force is.
    Emotions I believe can also be calculated, and perhaps a good place to start would be to use color and music like a Rosetta stone, both of a mathematical structure, and both able to influence, perhaps create emotions.
    After forty plus years I have developed an idea that might be a useful, perhaps as a structure to mathematicians or anyone interested, but as a layman I am not sure what to do with it and I am perhaps a bit intimidated by academia. Any help would be much appreciated.


  6. I would like to amend my last post with an example of constant and variable moral laws, with a paragraph from my blog The moral value honesty is a good example of this as the natural law or laws that govern this value varies greatly within context or frame of reference, everything from “honey, do I look fat in this dress” to robbing someone of their purse, liberty or life. The old adage about a boy drowning in a pond with a sign in it that says “no swimming”, should I obey the sign and let the boy drown or disobey the sign and save the boy is another example of a variable aspect of honesty. There is however an aspect of honesty that is a constant, valid within all aspects of man’s relationship with the universe, or within all frames of reference, and that is honesty to ones own self. This I believe is a good example of a constant moral law valid within all frames of reference. The following address is to a blog I started some time ago and I hope, health permitting, to become much more active with in the near future. Anyone with an interest may go to brief overview tab at the top and read a brief summery of that idea. Any comments would be much appreciated. Blog address is: Blog name is Revolution of Reality.


  7. I believe the following 7 points are true:
    1)There is a moral force in the universe that is governed by natural laws
    2)This moral force is the same through out the known universe and originated with the other known forces, perhaps at the big bang.
    3)Those moral laws are able to be mathematically defined and calculated
    4)There are moral values that are constant and there are other moral values that are variable depending on the circumstance or frame of reference
    5)That frame of reference gives you a perspective and perception which gives you a reality
    6)That reality through that perspective is able to be mathematically defined and calculated
    7)The validity of a moral issue within that defined, or given reality is able to be mathematically defined and calculated following the natural moral laws of the universe


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