Pseudo-Time Arrow

The Pseudo-Time Arrow is a proposal for how phenomenal time (i.e., our felt sense of time) is constructed. In other words, it's a proposal to explain why we perceive time to move forward. The core idea is that states in the present include a backward integration of information from states in the past. This article derives primarily from the QualiaComputing blog post by QRI president and co-founder Andrés Gómez Emilsson.

Problem Necessity and Time Ontology

Given that physical time appears to move forward, it's tempting to argue that we simply perceive the flow of time as it is, so no further explanation is required for our felt sense of time. Consequently, one way to motivate the topic is to deny this assumption, i.e., to claim that physical time does not move forward. This is a position called eternalism, which states that the universe is a single, four-dimensional "block" in which time is an internal axis. Since there is no flow of physical time under eternalism, it becomes clear that our felt sense of time requires an explanation.

That said, while Eternalism makes the need for an explanation intuitively apparent, this need likely exists either way. This is because eternalism and presentism propose identical laws governing the causal structure of the universe, and thus, if one assumes that brains operate within the laws of physics, it follows that our sense of phenomenal time is independent of the nature of physical time. In other words, even if physical time does move forward, the fact that we perceive it to move forward remains a separate fact requiring its own explanation.

Another question about physical time is whether it is discrete or continuous. The pseudo-time arrow assumes the former, i.e., that one can decompose a span of consciousness into a finite set of discrete moments, or "slices". Note that this assumption of discreteness is related to the thing vs. process distinction that underlies much of QRI's thinking about consciousness.

Backward Integration

A depiction of a quale (e.g., a visual percept) containing remnants of past slices. Note that the extent of backward integration (and hence the length of the "trace") shown in the picture is exaggerated for illustrative purposes.

The core idea of the pseudo-time arrow is that a typical slice of consciousness contains a remnant of moments from the immediate past (as shown in the figure to the right), thus creating a discernible direction within the slice. In other words, the brain performs "backward integration" to construct moments of consciousness, such that any one slice contains information about its predecessors.

Note that each slice can only contain partial information from past slices since the amount of information would otherwise be infinite. An exponential decay (i.e., a fraction $q<1$ such that each slice contains $q$ times the information from the previous slice, $q^{2}$ times the information from the slice before that, $q^{3}$ from the slice before that and so on) yields a finite amount of total information as formalized by the geometric series. For example, if $q=80\%={\frac {4}{5}}$, then the total amount of information contained in each slice is $\sum _{k=0}^{\infty }({\frac {4}{5}})^{k}=5$ times as large as it would be without backward integration.

The existence of backward integration explains how individual slices can be sensitive to input data with a temporal component. For example, the fact that people can enjoy music is only possible with backward integration (at least under the assumption of discrete time) since the properties that people enjoy in music always have a temporal component. If the Symmetry Theory of Valence is true, then such cases correspond to symmetrical configurations across the entire consciousness slice, including the components containing information from past slices. This is also called "symmetry across the pseudo-time arrow".

The thickness of a slice (i.e., how much time it spans) is unknown but unlikely to be above 10ms, and possibly far smaller.

Algorithmic Implementation and Exotic Phenomenal Time

Three networks of local binding corresponding to different perceptions of phenomenal time. See the text for details.

In the blog post introducing the pseudo-time arrow, Andrés suggested an algorithmic specification of how backward integration is implemented. The details have been skipped up to this point because the concept can be understood without them, but they are included now since they are required to explain "exotic phenomenal time", i.e., cases in which one perceives time to move differently than usual.

In the proposal, a slice of consciousness is modeled as a directed graph in which the nodes are qualia, the edges are connections between them, and the x-axis denotes time. Thus, the nodes on the very right correspond to the present moment, whereas all other nodes contain information from past slices that are still included in the current slice.

At room-temperature consciousness (top row), the nodes gradually disappear over time, corresponding to the exponential decay discussed in the previous section. Since a graph contains enough information to infer the direction of causality, the resulting network is sufficient to explain the felt sense of time moving forward.

A common effect under psychedelics is the perception that time moves more slowly. This is depicted in the second row, in which nodes decay by the same principle but at a reduced rate. Note that this scenario results in tracer effects, which can be used to classify and even quantify the effect, such as by using QRI's toolkit.

A (much rarer) experience is that of a time loop, which occurs when the network forms a closed circle rather than moving only from left to right, as depicted in the third row. Note again that the existence of this state does not imply anything about physical time, but merely about the felt sense of time within a slice of consciousness.

Other exotic states include timelessness, temporal branching, or moments of eternity; see the blog post for details.

Finally, note that exotic states may exhibit much greater levels of regularity and symmetry than the regular perception of time (e.g., compare the first and third networks on the right). This may explain why nonstandard perceptions of time tend to be combined with highly intense experiences.