Linear Feedback Shift Registers and What They Can Teach Us About Free Will
In this essay, I will define free will, what it means for a sequence of actions in the world to be deterministic, examine the relationship between the two concepts, and finally use the example of linear feedback shift registers to illustrate how free will is incompatible with determinism and not a real property of the world.
Free will describes the ability of conscious beings to act freely in accordance to their will, unfettered by externalities to the self. There are two basic tenets that free will requires which allows us admit agency to a conscious being:
- The ability to choose to perform an action, and importantly, the ability to do otherwise; and
- Consciousness itself being the wellspring of an agent’s action in the world.
Taken together these properties of free will align with intuitions about how we navigate the world. Agents do not exist in isolation however, they are constituents of the world, and can be influenced by it in many ways. (Kane, 18)
Determinism is the logical conclusion of the assumption that the world is bound by natural laws that are universally consistent. In a causally-closed deterministic system, any past state of the system, met with the internal and external events that act upon it, can elicit only a single possible future state. A deterministic view of the world therefore is a doctrine that posits that nature is made up of interconnected, and wholly deterministic systems. The “compatibilism debate” examines the implications of a deterministic world to the consciousness within it. (Kane, 19)
If we exempt consciousness and view the world as a causally-closed system where the laws of nature are consistent, it’s intuitive that the insentient matter in this world would interact in ways that are predictable, and the events that transpire in this exclusively material world would do so in ways that are mechanically determined. All the events in such a world can only have one possible future for a given past and present. We don’t live in such a world that is unattended by consciousness, nor do we yet know if, excluding consciousness, all other events in our world are deterministic. But we can recognise that there are degrees to which the world can influence consciousness, and therefore impinge on our agency in ways that we might not be privy to.
For an agent to possess any free will about the world, there is a corollary assertion that the world does not completely determine an agent’s actions. P. Strawson, analyses how human beings tend to possess “reactive attitudes” that reveal our intuitions about the existence of free will in the actions of an agent. Reactive attitudes are the set of cognitive and emotional reactions to another person’s action — attitudes that only make sense on the assumption that agent is in control of their own agency. We accord the actions of an agent as if they are free, and importantly, as if they are free to do otherwise.
The attribution of free will to an agent underwrites our approach to moral accountability. Moral responsibility and free will have a special relationship here as we can soundly justify apportioning penalty or reward for an action upon its author, so long as they have demonstrable agency. This notion of agency is fundamental to a Lockean theory of self that takes an objective view of identity. Locke considers identity to be an evanescent concept in society that visits moral actions. This same theory, when examined from a subjective locus, posits that the self exists insofar as a person can recall their attendance to past events. The question of whether or not agents can have free will in a deterministic world necessarily implicates the subjectivity of our conscious experience, or what we mean when we use the word “self” with regards to agency. (Law, 301–2)
Compatibilism asserts that even in a wholly deterministic world, conscious beings can exert their free will about it. These doctrines take a view of conscious experience as the animus of desires, emotions, appetites and compulsions, and this makes it amenable to a Lockean understanding of self. Both the Lockean theory of self and compatibilist theories of free will commit the same error in cementing an abstract concept as if it were a feature of reality. For Locke, this is the claim that personal memory makes an adequate substrate for the reality of identity. And for compatibilists who ruminate on alternate possibilities, this is the assertion that an agent somehow possesses events that are not authored by her — the hypothetical “freedom to do otherwise”.
The argument for compatibilism continues with ever-increasing nuance, yet still fails to explain why consciousness should be exceptional in an otherwise deterministic world. Modern theories of compatibilism, as advanced by Frankfurt, attempt to stratify the wills of an agent in order to introduce a vehicle for freedom. These argue that because the compulsive wills of an agent can be overridden by aspirational wills, we as human beings routinely exert a freedom of will. This begs the question — does free will only exist when the overriding will prevails? It looks remarkably like the hypothetical “can do otherwise” argument, redressed as novel and bearing a uniquely anthropocentric slant. Yet, viewed with an incompatibilist lens, these actions seem to be determined by whichever will that an agent is most sympathetic to at the time, regardless of their position in some arbitrary hierarchy. (Kane, 21–24)
Proponents of free will who agree about its incompatibility with determinism follow libertarian theories that apply their scrutiny to nature. Classical theories such as these extol the idea of a disembodied soul to grant exception to the laws of nature upon consciousness. Divinity features in other libertarian theses, where the actions of the divine upon nature are not bound by natural law. Such claims remain uncontaminated by evidence, and their property of being unfalsifiable make them impossible to advance in a modern scientific purview. (Kane, 24)
More modern libertarians look to quantum mechanics to conclude that the world of Newtonian predictability promised by the 19thcentury physicist, Pierre-Simon LaPlace, loses its predictive properties at very high speeds or at very small scales. The Heisenberg uncertainty principal is frequently recruited as evidence of us inhabiting a non-deterministic world. Despite the conflation of predictability with determinism, physicist Laurence Krauss explains the problem with this analysis:
To measure the position of a particle you have to bounce light off the particle, and to resolve the position with great precision requires light of a wavelength small enough to resolve this position. But the smaller the wavelength, the bigger the frequency and the higher the energy associated with the quanta of the radiation. But bouncing light with a higher and higher energy off the particle clearly changes the particle’s energy and momentum. Thus, after the measurement is made, you may know the position of the particle at the time of the measurement, but the range of possible energies and momenta you have imparted to the particle by scattering light off it is now large.
For this reason, many people confuse the Heisenberg uncertain relation with the “observer effect,” as it has become known, in quantum mechanics.
(Krauss, 90)
Concluding that the world is non-deterministic because we cannot predict the outcome of events merely begs the question and reveals an epistemic error. A more modern species of this confusion between predictability and determinism argues that because interaction between the physical world and what we demarcate as its emergent properties, such as consciousness, is reciprocal, the world is indeterminate. To illustrate why feedback between strata in natural science is non-problematic, and hence why this fails to advance non-determinism, I look to an example from computer science to demystify the nature of complexity using linear feedback shift registers.
Linear feedback shift registers (LFSRs) are finite state machines used in cryptography to synthesise randomness. Given a sequence of “random enough” numbers — say, sampling the one millionth fractional digit from monitoring the thermal noise of a modern CPU — a LFSR will transform that sequence of numbers into an ostensibly more “random” sequence. To generate this pseudorandomness, the LFSR uses a confluence of current data and historical data such that any subsequent entries will be transformed by the LSFR in ways that are unique to the past sequence and exact position of the supplied digit. Any semblance of geometric pattern that is present in the input sequence will be rendered unintelligible after its transformation.
LFSRs are vital to information security. They’re designed to simulate chaos, and yet they produce a causally deterministic output. Any complete sequence of input numbers that are fed into two identical LFSRs will produce the same output. However, you would be forgiven for arriving at the halfway point in the output of a LFSR and thinking that there is neither rhyme nor reason to the sequence that emerges. Armed with the exact sequence of input data and the programming of the LSFR, you would have perfect predictive capability of its future output.
There seems to be a concordance between new compatibilists and incompatibilists about the pursuit of science. Scientific experimentation assumes that we live in a deterministic world. This tenet is falsifiable but has nonetheless prevailed throughout the history of modern science. The objects of scientific experimentation are merely sophisticated but naturally-occurring machines that are not unlike LFSRs: systems for which a set of experimental and environmental factors determine a singular possible outcome. Nobody argues that the proton beams colliding at near light-speed in the Large Hadron Collider had the ability “to do otherwise”. The exemption from determinism seems to be a unique hankering of consciousness.
David Hume, despite himself being a compatibilist, held the key to how we can think about the self, or the subjective experience of consciousness, in a way that is consistent with determinism:
[the experience of humankind is] … nothing but a bundle or collection of different perceptions, which succeed each other with an inconceivable rapidity, and are in a perpetual flux and movement.
(Hume, 534)
What Hume is arguing for is the illusory nature of “self”, and how attempting to resolve one in the real world is not possible because no such thing exists. And this perspective of self lends us tremendous insight into how we deliberate on the choices we make and also the animus of our actions about the word — the two properties of consciousness on which we predicate our free will. (Hume, 534)
Like the sequence of “random enough” numbers that are received by an LSFR, it may be tempting to think that the deliberations of conscious beings are somehow indeterminate until an action is observed. If you elevate imagined alternative choices to the status of reality then it would be tempting to think that we live in a world that is constantly at the behest of our deliberations. But armed with the complete bundle of experiences and environmental factors, along with the programming of the wetware on which a consciousness operates, you may find yourself with perfect predictive capability of the future actions of an agent, as if they were deterministic. This would reveal free will, in accordance with the self, to be an illusory feature of humankind.
References
Hume, D., 1874. Of Personal Identity. In: T. G. a. T. Grose, ed. A Treatise on Human Nature. London: Longmans, Green, and co., pp. 533–543.
Kane, R., 2009. Free Will. In: E. S. a. G. S. R. Jaegwon Kim, ed. A Companion to Metaphysics. 2 ed. s.l.:Wiley-Blackwell, pp. 18–27.
Krauss, L., 2017. The Greatest Story Ever Told … So Far. 1 ed. London: Simon & Schuster.
Law, E., 1794. A Defence of Mr. Locke’s Opinion Concerning Personal Identity. In: The works of John Locke, in nine volumes.. 12th Edition ed. London: Cambridge, pp. 301–319.
Schechtman, M., 1994. The Truth About Memory. Philosophical Psychology, 7(1), pp. 3–18.
