I will start my comments to the two target papers [Gruber et al., 2022 (GBM) and Buonomano and Rovelli, 2022 (BR)] with two uncontroversial premises, stressed in particular by BR:

By referring to the two target papers, I will focus on the first two questions¹ by briefly sketching three possible avenues of research: physical, ontological, and neurocognitive.

One physically necessary condition for C is that events “keep on happening” one after the other along worldlines. IGUSs rely on this presupposition too: our brains register the objective temporal succession of physical events, where the objectivity is given by the invariance of proper time. GBM agree: “the experience of happening is part of our experience of the flow of time” (p. 6). In BR, Rovelli insists that spacetime is replete with processes and therefore is “dynamic”.

The ontological way to “explain” or describe this succession of physical events is to postulate a “locally growing block (Ellis, 2014), where local is added to prevent objections raised by relativity”². I claim that evidence for this model are facts that do not involve our momentary experience of time that IGUSs³ are meant to simulate but my knowing that, as I write at T, each passing day I am 1 day “closer” to the moment of my death D. Relatively to T, every minute the number of heartbeats separating T from D for me decreases in average by sixty: time for me passes in average one heartbeat per second!

The problem with the locally growing block is, as GBM correctly note, that it seems to be unable to shed light on the two-times problem from an empirical viewpoint. Yet, it is difficult to account for the facts above just by postulating a tenseless, “static” relation between T and D. I grant that this explanation can be given and that physics, obviously, does not require a privileged now. However, despite the following spatial metaphors, the claim that, relative to T, the temporal distance between T and D decreases seems much more plausible: this fact calls for a locally growing block regarded as a primitive, fundamental ontological asymmetry or as a “irreducible intrinsic asymmetry in the temporal structure of the universe” (Maudlin, 2007, p. 109).

A first difficulty is that, contrary to C, IGUSs work only for events that are closer to our present experience by including our short-term memory: as such, they do not seem capable to simulate the essentially predictive capacity of our brain (see 1 above). If anything, IGUSs can only refer to short-term anticipations (Dorato and Wittmann, 2020). Neither can “premonitions about the future” (p. 3) solve this problem.

More in general, the IGUSs presented by GBM seem too simple to account for the complexity of our experience of time. Evidence for this claim is that whenever some discrepancies between the IGUSs and our experience arise, the former must be supplemented with additional “gadgets” (GBM, p. 3). On the one hand, the simulation must be faithful. On the other, IGUSs cannot be too complex since this would imply providing them with too many contraptions⁴. Faithfulness and simplicity pull in opposite directions. In addition, the mere possibility to fabricate various IGUSs by using VR headsets to show that our experience of flow might be illusory does not imply that our actual experience is not veridical. If “the experiential flow component of the FOT is attributed to the utilizing system of the robot and not to the time of physics” (p. 2), the illusions that it generates are themselves “real” even if subjective, because the robot itself is physical. Furthermore, a thorny conceptual difficulty is generated by the widespread use in physics of the vague epistemic term “information” (which enters the definition of IGUSs): given that the notion contains a semantic feature that seems irreducible, what is information in physical terms? “To be informed that…” has a propositional content (a “that clause”) and propositions are abstract, non-physical entities.

GBM hold that FOT presupposes “dynamism of change/motion” (p. 4). The problem raised by this quotation depends on the meaning of ‘dynamism and change’. Correctly denying any motion of the now does not rule out some minimal form of tenseless becoming: the caption of Figure 1 tells us that “the robot experiences a stack of cards labeled a, b, c, d, e, f, whose top member changes from time to time” (GBM, p. 2). However, this sequence can more plausibly be interpreted as a worldline-dependent coming into being of events at instants of proper time, as suggested by the above argument concerning the decreasing distance between T and D. The anticipation of an event in the distant future and its later experience in the present presupposes some stronger kind of dynamism consisting in the addition of previously non-existing events in an unrestricted sense of existence⁵ that cannot be explained away by the momentary experience of flow allegedly allowed by the IGUSs.

Within neurophysiology, if 1 above presupposes a capacity for mental time travel (a projection in different moments of time) it also requires an enduring self. Mental time travel has been the subject of intense experimental study (Suddendorf et al., 2009). For instance, the use of spatial metaphors in our talking about time may depend on the fact that “Time Travel and Mental Space Navigation could be consistently explained by similar cognitive mapping principles, namely: egocentric mapping and coordinate system conversion” (Gauthier and van Wassenhove, 2016, p. 66). Egocentric mappings are representations of time (and space) from our temporal perspective (like the “here” in a map). Coordinate transformations are self-projections maintaining “egocentricity of the map when adopting a viewpoint differing from the ‘here and now”’ (Gauthier and van Wassenhove, 2016). It seems to follow that the possibility of keeping the egocentric character of the map entails an enduring self.

It has also been stressed that within a subjective, agential perspective, the self must be regarded as an enduring entity (Paul, 2017)⁶. The agential viewpoint implied in our temporal projections is directly called into play by 1: the capacity to predict a future event has been selected by evolution and serves the subject's need to act in view of an anticipated event.

I agree with BR that time is a multilayered concept. The list from i) to ix) (p. 5) is an inventory of key temporal notions apportioned between physical and neuropsychological time: in this respect, I argued that the main bridge between them is an ontology of events (Dorato, 2015). Since this plurality of senses holds even among the various branches of physics (Rovelli, 2004, p. 58–62), progress in the two times problem depends on disentangling the various elements in the list.

First, a radical pluralism about time and a “dappled view of science” in general (Duprè J., 1993; Cartwright, 1999) would dissolve our problem: within this framework we shouldn't even try to reduce or unify notions of time belonging to very different “levels of reality”. If physical time and experiential time have a limited, domain-relative range of validity, they cannot conflict. However, the two-times problem ought to be regarded as an attempt to bridge an explanatory gap and I take it that BR implicitly assumes that explanation need not entail reduction.

Second, reliance on the oft-invoked but unclear notion “open future” requires attention. BR identify “open” with “indeterministic”: “Neuroscience builds on the existence of macroscopic traces and on the openness of macroscopic future produced by the thermodynamic arrow of time. The second, in particular, underpins the possibility of our experience of being ‘free to choose’, since different macroscopic futures are compatible with the same macroscopic past, choice depends on what happens in the organism” (BR). Also for compatibilists choice “depends on the organism.” The existence of different possible futures all compatible with the same past requires indeterminism but the thermodynamical arrow of time depends on the initial state of the system. The fact that statistical mechanics is both deterministic and time-symmetric implies that the indeterminism in question is epistemic like the probabilities involved in the theory. In addition, the incompatibility between freedom and determinism is very controversial⁷.

Also the expression “four-dimensional block” must be handled with care. Analytical philosophers usually argue that the block, regarded as the sum total of events and changes in four dimensions, is static, since changes and events happen in the block. Rovelli correctly reminds us that general relativity implies a different account of the “block” because its main novelty is that spacetime itself (i.e., the block) is dynamical: “The 4-dimensional universe is not an entity, it is a process…. a complex network of changes, not a static 4-dimensional block”. I am sure that Rovelli agrees that in some sense the (observable) universe is an entity and that, unlike any other process, it does not occur in time, but has time as one of its dimensions.

Finally, Buonomano stresses the fact that the function of our brain, shaped by evolution (see 1 above) creates unavoidable limitations to the task of interpreting those physical theories referring to layers of reality that are very remote from our experience. He claims correctly that physics does not force us to adopt any particular temporal ontology and that, possibly as a consequence of the fact that our brain mainly relies on visualization, we cannot picture quantum jumps caused by photons hitting electrons in the nucleus. Yet, these limitations do not imply that realism about the ontological claims of physical theories is unjustified. The undeniable cognitive “inadequacies” of our brain are not a safe guide to ontology: both the discovery of inertia and of the relativity of simultaneity clearly show that the naïve physics implanted in our brain by evolution can be conquered.