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Wandering Towards a Goal
How can mindless mathematical laws give rise to aims and intention?
December 2, 2016 to March 3, 2017
Contest Partner: The Peter and Patricia Gruber Fund.
read/discuss • winners

Trick or Truth: The Mysterious Connection Between Physics and Mathematics
Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation
Media Partner: Scientific American

read/discuss • winners

How Should Humanity Steer the Future?
January 9, 2014 - August 31, 2014
Contest Partners: Jaan Tallinn, The Peter and Patricia Gruber Foundation, The John Templeton Foundation, and Scientific American
read/discuss • winners

It From Bit or Bit From It
March 25 - June 28, 2013
Contest Partners: The Gruber Foundation, J. Templeton Foundation, and Scientific American
read/discuss • winners

Questioning the Foundations
Which of Our Basic Physical Assumptions Are Wrong?
May 24 - August 31, 2012
Contest Partners: The Peter and Patricia Gruber Foundation, SubMeta, and Scientific American
read/discuss • winners

Is Reality Digital or Analog?
November 2010 - February 2011
Contest Partners: The Peter and Patricia Gruber Foundation and Scientific American
read/discuss • winners

What's Ultimately Possible in Physics?
May - October 2009
Contest Partners: Astrid and Bruce McWilliams
read/discuss • winners

The Nature of Time
August - December 2008
read/discuss • winners

Review Of FQXi Essays Wandering Towards a Goal

By Harry H. Ricker III


The purpose of this essay is to discuss my impressions and comments resulting from reading the submissions to the 2017 FQXi Essay Contest. The title of this contest is Wandering Towards a Goal: How Can Mindless mathematical laws give rise to aims and intentions. In my essay I took issue with the thesis and asserted that mindless mathematical laws can not give rise to aims and intentions. The essay topic was sufficiently vague and ill defined that it allowed for a number of different interpretations.

Essays That Took Issue With the Topic

Here I will address the essays that tried to define the problem as it relates to the essay topic. There was one outstanding essay in this regard. That is the one by Dave Bruiger. Dave answers the question this way: ”The blunt answer is that mathematical laws cannot give rise to anything but other mathematics!” I really think that this is correct, but the implication is not actually the issue of mathematics, or laws, but about whether scientific method is capable of solving the problem of biological behavior. What is important to the reader is that it is recommended that Dave’s essay be read before reading mine or the others since it sets the issues into perspective. One interesting part of Dave’s conclusion is:”In this context, the paradox of mathematics is that it transcends physical reality while derived ultimately from it by conscious agents. I take the position that mathematics, like science, is a form of human cognition.” I don’t put it that way in my essay. My view is that mathematics is a human invention that serves human goals. The main flaw is the thesis that the contest is aimed at discussing, is that goal oriented behavior is essentially that defined by human beings who desire that nature is describable by mathematical law rather than designed by a cosmic agent such as God. Dave concludes his essay as follows: “To account formally or mathematically for natural goal seeking behavior, in a logically consistent manner, requires re-instating the fundamental notion of agency.” He sidesteps the issue of God as deity and substitutes for it the concept of the fundamental notion of agency. It is obvious that such a concept is needed, but why it ought to be couched in such nebulous terms instead of the more common terms of understanding is disappointing.

Chris Ransford takes a viewpoint different from Dave’s. His essay Where The Question Leads addresses the issue that the topic needs refining, but he asserts conclusively: “Although some still hold this assumption as controversial, the evidence that the universe is indeed purely mathematical is overwhelming.” That being the opposite of Dave’s essay. Quite frankly I thought Chris’ claim to be unsupported and not convincing by the evidence he offered. Others may disagree with me and find his argument convincing. The section where he parses the question is however of greater interest. The conclusion is worth noting: The question of ‘How mindless mathematical laws may give rise to intentions’ may not have been fully legitimate as originally stated, and we examined both the term ‘mindless’ and the phrase ‘give rise’ to parse evidence of possible prior cognitive bias in the way the question was put. Doing away with any possible bias, we then sought to answer a new, more neutral version: ‘How can mathematics enable mindful intentions?’ Chris doesn’t give us any answer however, and so the essay falls short there.

Stefan Weckbach’s essay In Search Of The Meaning Of Meaning is recommended as it sets up the issues and their problems very well. I liked this essay very much since it addressed the real issues head on. For example he says: “Firstly, consciousness aims to be not merely a cosmic accident but has an inner desire to be the intentional result of a meaningful process. Secondly, this meaningful process is traditionally attributed to have its roots within a greater consciousness (god) that should have the power to bring such a process at all into existence. If there are goals and intentions in the universe that are independent of living creatures, then only another, more potent conscious agent can be the author of these goals.” That is a surprise. But he writes god rather than God, or deity and puts god in parenthesis as if it is merely a side topic. As to whether this problem has a solution within science he says: “By equating objectivity with mathematical formalizability, it is no wonder that science at one point tends to eliminate the very actor of science, namely the scientist including his goals and intentions. But nowhere in nature there is a guarantee that nature has to be completely formalizable. Nonetheless, science, in many ways, acts as if the opposite is guaranteed by some universal law.” Regarding the ability of mathematics to produce a solution he says: “Another argument against the complete formalizability of all that exists is that even some simple mathematical systems like first-order arithmetics cannot reliably decide between a necessity and a possibility. For Kurt Gödel’s incompleteness theorems to be true, it is necessary that one assumes this system to be consistent, but incomplete.” His conclusion then follows: “The results of this essay are that goals and intentions, as they are traditionally understood by us humans, cannot be reduced to merely mathematical patterns or mere fictions without reinterpreting them from what was originally meant by these terms.” Finally although avoiding the God word he ultimately concludes: “If there is goal-oriented behaviour in the universe independent from all the pettiness of living creatures, this behaviour should have its roots in a more knowing and more potent conscious agent than we are and least of all in a dead universe. “ I do wish he had said God, but it is a good essay.

Paul Butler’s essay Are Mathematical Laws Truly Mindless? addresses the issue from a different perspective than asking whether mathematics can provide the solution, he addresses the bigger picture of the evidence that bears on the problem. His essay takes on one of the main issues, that I address in my essay, as follows: “It is true that once the laws have been written down either in the form of ink on paper or in the form of the real world entities that have them written into them, so that they perform according to those laws, the laws themselves do not possess a mind of their own, but they are the output expressions of the mind that created them and, therefore, are an image of the intelligence that is behind their construction.” Exactly right. He then proceeds to analyze why a creator is needed in steps. “The conclusion at this point is that the universe likely was created by a very intelligent living being.” After further analysis he arrives at his conclusion: “Much more information is given in both the Old and New Testaments, which all leads me to conclude that the universe was not created by chance, but by God.” Note that Mr Butler doesn’t evade the concept of deity as in the previous essays, he says it right out in the open.

Essays That Assumed That Mathematical Laws Do Solve Goal Oriented Behavior

The essay by Jack Hamilton James dives right into the problem and doesn’t pause to question whether the question has a solution or not. He is sure he has the answer. Unfortunately his analysis is tedious and difficult to follow in its intricate details. He says regarding a mathematical model: “what is required to satisfy a mathematical account of intention is an internalist account that aligns with external mathematic and scientific descriptions. Of course, no known mathematics is internal, which is where the missing piece of the formation of intention might hide. Perhaps the only conceptual option for the internal is computational interactions (at least we can conceive as such, e.g. a robot governed by internal programming giving it intention). Therefore, an Ecorithm 5.b.3 is the only conceivable internal mechanism for aligning with the recipe/arrangement 4.b facilitating the science of abiogenesis” Curiously, after proceeding confidently that there must definitely be a mathematical solution he ends by saying this: “We are descriptively stranded, and so whilst we may reveal a math of intention I doubt that it will provide a math of consciousness.” This result is significant because in the end there is no result, so mathematics does not provide any solution to the posed problem, when all through the essay it appeared that there would be a solution.

Essays That Presented Arguments Based Upon Quantum Mechanics

Primary in this category is the essay by Biswaranjan Dikshit It is difficult to make sense of what is being discussed since the author is not presenting a thesis based upon mainstream quantum mechanics but upon his theory called free will theory, or biased will of nature theory. The idea behind it being to solve the well known difficulties in the accepted mainstream quantum mechanics. “After discovery of first quantum mechanical formalism by Schrodinger in 1926, quantum physics has established itself as a robust and accurate theory of nature explaining nearly all the physical phenomena observed in the universe both at the micro and macroscopic level. But most important limitation of quantum mechanics is that it is a stochastic theory providing only a probabilistic prediction of experimental results.” The essay purports to solve the problem of how goal oriented systems arise in the following way: “… since all processes occurring in the universe are governed by quantum physical laws which incorporate the biased will of the nature (as demonstrated in this paper), every system is inherently goal oriented whether we are able to perceive it or not….some amount of goal oriented behavior is there in every system since the time of creation. It is purely a physical/cosmic trend, not accidental. That’s why repeated generations during evolution of living organisms have made them more and more fit to be adaptable to the changing environment….biased will theory of this paper indicates that in addition to causality, result is also affected by teleology i.e. a purpose in future… So, I think, living bodies have life in them because of quantum coherence among their constituent parts… Thus, all living organisms are intelligent since they pursue self preservation because of quantum coherence.” This is an interesting thesis but is really evading the problem by creating a cause, which is obscure, to explain the unexplained. So it is not really a cause in the sense of Aristotle’s Final Cause. It attempts to implant into the basis of microscopic behavior, a material cause that explains the other three causes of Aristotle. So it does follow in the tradition of modern science in trying to discover the Final Cause by removing the need to have a Final Cause, by substituting a mechanical cause for the action of inanimate matter.

The essay by Steve Agnew Math Laws and Observer Wandering seems to have taken the problem literally and turned wandering into a primary physical cause in nature. The conclusion of the essay seems to be that mindless mathematical laws is not a solution to the problem posed. Here is what he says: “In conclusion, matter and action represent a fundamental duality of the universe and a neural mind made up of matter is also a neural mind made up of action as well. Instead of the overly simplistic duality of just mind and body or spirit and material, the universal duality of matter and action is true for all observers and sources and even for the mindless mathematical laws of neural memory. There is no sense in separating the universe into mindless mathematical laws for the actions of sources versus mindful observer aims and intentions. We can only know that the decreasing entropy of increasing source order flows to the increasing entropy of decreasing observer action, but we must simply believe in the mystery of that action.” There really is no conclusion at all, other than the expression of doubt as to the success of the suggested essay contest enterprise. Maybe I missed the point entirely when he was talking about quantum phase noise.

The essay The Irrational Side Of Reality by Gerold Grundler, is probably the only one I recommend reading, where the primary argument is based upon quantum mechanics. Dr Grundler answers the main question up front by saying: No, mindless laws do not give rise to aims and intentions. But it seems to be an answer which is a “NO, BUT” and that leads into a complicated argument based upon experiments in quantum mechanics. The essay is technical and ends up as follows: “Aims and intentions, and free will, can evolve in these irrational aspects of reality. They can evolve, but we can not prove that they do. We vividly feel that they do, but as physicists we are not used to accept feelings as proofs. On the other hand, as the irrational aspects of reality are not subject to the laws of physics, we will definitively never be able to compile a sound physical proof for the existence of free will, aims, and intentions, and their effects onto the course of objective events. The violation of Bell’s inequality merely proves that there really is an irrational aspect of reality, and that consequently free will, aims, and intentions, which may impact the course of objective events, can not be excluded.” It is a ambiguous ending, which perhaps is the correct ending for an ambiguous question, but it is unsatisfying. However, the reader learns something about the scientific issues. In the end I was struck by the fact that this essay captures the dilemma of the scientist. He is sure that there is an answer, and that science can discover what it is, and produce useful knowledge, but unfortunately the tools that a scientist uses are inadequate to accomplish the intended task.


If the purpose of this essay contest was to beat the woods of science and philosophy and find someone out there who was a genius, and had some hidden secret answer, then the contest failed to find him. What did I find in reading the essays? Basically I found that almost all of the essays agreed that there was no positive answer to the question. So mindless mathematical laws are not a solution to the problem of life in the universe. I however, was unique in proposing that the question was an ill posed one and that the solution did not come from science, but from a different sort of philosophy, and I recommended religion as a better answer than science.


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