Instantaneous Vs Distributional Self
- Ethan Smith
- 27 minutes ago
- 8 min read
I'd like to make two distinctions. An Instantaneous You and a Distributional You.
The Instantaneous You represents a singular point encapsulating all that is needed to render you for a frozen moment in time—like observing a single paused frame of a movie.
This could be analogized to Neural Manifold representations, though rather than specific neurons in a very high-dimensional space, we'll imagine more abstract and general features. It is a vector, a single point, describing a state of a system at any given moment, in this case the system of you. This is always on the move. If I recite in my head "Mary had a little Lamb", every step taken to mentally enunciate the next word may correspond to a change in state, even if relatively small; this being the reason we can use neural decoders to retrieve images and soundbytes from brains. It depicts a frozen snapshot of yourself.
The Distributional You reflects not a frozen moment in time but a history of you over an interval. As you move from state to state, we can measure how frequently a state is visited. For example, you in an idle state might be pretty frequent; you in an angry state may be less frequent. Here, You is described as patterns of behavior rather than a fleeting moment.
Here we can see a plot of the amount of time spent in certain mental states, and by proxy, states of You. Though I stress this is mainly for a rough visual model of imagining how mental states can move continuously between each other and have a probability of how frequently they show up. This is to be taken with a grain of salt; there's a lot of nuance not showcased in the 2 dimensions we have and these are random labels. Mental states are far more complex than the simple labels I used, and I’m sure multiple here could even occur simultaneously.
All we've really described here is a Markov Chain system. A system of variables that can take on different values, have different probabilities of transitioning between those values, and an overall probability of being in a state at all, which can be derived from the transition probabilities. To move forward in time, all we need is the current state of the phenomenon of interest and the rules of the system itself. It can begin at any moment and doesn’t require a history to propagate.
When the rates of transition are constant, so are the resulting probabilities of being in any state and thus overall distribution, thus having reached something of a "steady-state equilibrium". Despite the Instantaneous You keeping on the move, we'd say the Distributional You remains constant. In other words, Instantaneous You is an exact state in time while the Distributional You is a history of patterns.
We have a Markovian experience, and more broadly, this applies to the universe as well. This is to say, for all we know, the universe could have started right now, just blinking into existence, with all the atoms perfectly arranged to form this exact moment and all of your memories and so forth. All things you’ve written or done could have never happened, but with the universe coming into existence, your brain appeared with all of the memories of doing so. More on this can be seen with theories on the Boltzmann Brain.
In this way, the Instantaneous You and Distributional You are intimately related. If we lived in a vacuum, never affected by the external world, the Instantaneous You would be sufficient to extract a picture of the Distributional You. Everything that is needed to estimate your future states and actions lies entirely in your body at that given instance; there are no other variables to be concerned with. In practice, this prediction remains incomplete because you exist within a larger system. The environment continuously shapes your trajectory, influencing which states you'll transition to next. Your Distributional You emerges from this constant interplay between your internal state and external forces—family dynamics, cultural pressures, random encounters, even cosmic radiation affecting neural firing patterns. In this sense, You becomes a dance between internal consistency and environmental influence, between the snapshot of who you are in a fleeting moment and the probability cloud of who you tend to be across time.
There are other kinds of distributional lenses we can view this through. For example, we can consider conditional distributions such as "Given the present state, where will we go next?" In the diagram above, these are just the transition probabilities. This would be fixing ourselves to a given state, say, cheerful, and assessing the probabilities of where we could go next.
Another example could be, “What is the distribution of states I may be in given that I have just arrived at the front door of my house?” Perhaps it is most common for me to feel relaxed to be back home from a long day, but other times I may be bored, gloomy, or excited for whatever reason, with lower probability.
Intriguingly, this is something we are estimating all the time without realizing it. When choosing between different brands of a snack at a grocery store, we may make decisions based off how we imagine the experience of eating each snack, essentially gathering insight by running mental simulations. Given the current mental state, which encapsulates your past experiences to reference, all your beliefs, assumptions, and biases on snacks, how do I imagine snack X tasting? And thus we model a set of possible imagined future experiences or states, sampling different imagined outcomes from a hypothesized posterior. Another case may be if we're looking forward to going out with friends later, we may model scenarios in our heads of how the night may play out, implicitly or explicitly. These can be inaccurate models, skewed by spurious correlations and tainted by wishful thinking, though it is our best attempt at modeling nonetheless. This constant distributional reasoning shapes not just our decisions but our very sense of self.
We may also like to counterfactual model of all the states you could be in for the present moment. These represent the "what could have been" scenarios: if we rewound time by 10 minutes and let events unfold again, what different versions of the present moment might we arrive at?
However we can’t know this directly, we’ve only witnessed one continuation from that past moment, only one Instantaneous You materializing into the present moment. Those alternate timelines are sealed away from us. So how can we know what actually “could have been?”
We settle for an estimation the a distribution of outcomes from our accumulated priors: the library of all that we’ve seen historically and everything we have ever learned and experienced. As mentioned, it’s fallible, but it still often holds weight and can provide insight in how we make decisions. If I have previously not liked the taste of cilantro the 30 past times, it’d be a bit ridiculous to imagine myself suddenly loving it on the 31st try. Or for very impactful flashbulb memories, we might wonder, “What if I left the house just 5 minutes earlier?” We can revisit past moment and imagine them how they could have played out differently with respect to how our world model believes it could have gone. That historical data is useful.
So we've suggested that the Instantaneous You is always on the move, the paths it takes leaves behind the Distributional You.
If the Instantaneous You cycles through all the same locations with unchanging frequency, we would say the Distributional You remains static.
If the Instantaneous You is veering off, spending more time in rarer states and making them more probable, while also less frequently hitting its usual spots, the distribution begins to morph, and thus the Distributional You as well.
You is something that changes. At a high level, this probably makes sense. You may feel like a different person than you did years ago, or when you were a kid.
Whether this makes you a fundamentally different person is possibly less of a yes/no and more of a "how different?" Assuming though we had these distributions in a tangible form, a possibility for neural manifold studies, you could use distribution distance metrics like KL Divergence or Earth Mover's Distance to quantify how much things change.
But the fact you can identify yourself across different periods of time should speak to the change being relatively slight as opposed to having your neural pathways totally scrambled. Though after something like head trauma, this isn't unheard of. There are cases of people forgetting their pre-injury self and exhibiting drastic personality changes like Benjamin Kyle.
Since we're talking about how your experience changes with time, another interesting thing to talk about here is how you recall memories of the past. I find this interesting for two reasons.
Firstly, if an episodic memory is a state of experience (an Instantaneous You) or a set of states defined by the firing rate of all your neurons, you could feasibly lack the circuitry to even reproduce that state as it were. Neural connections change with time. They are strengthened and inhibited, rerouting signal propagation. Reliving a past moment may be fundamentally unreachable. The way a memory is stored may have to change with you to survive, or accessing it may mean making a less accurate projection onto the way you are wired to experience now.
Secondly, it's been discussed that retrieving a memory and using your imagination are both handled in large part by the hippocampus and are not easily distinguishable. Your brain uses similar mechanisms whether you're recalling last Tuesday's lunch or imagining tomorrow's dinner. Memories in general are infamous for having a false sense of fidelity, and may vary depending on the context in which they are recalled. The notorious unreliability of memory stems partly from this shared machinery. Each time you recall a memory, you're not simply retrieving a stored file but actively reconstructing the experience. This reconstruction is influenced by your current emotional state, recent experiences, social context, and countless other factors. The memory becomes contaminated by the very act of remembering it. Context-dependent recall further complicates this picture. The same memory can feel dramatically different depending on when and where you access it. Recalling a childhood birthday while alone in your apartment versus discussing it at a family gathering can yield subtly, or not so subtly, different versions of the "same" event.
A change in the Distributional You may also reflect changes in wiring that have strengthened some states or given them more pathways that lead to them, and weakened others.
Memory appears to be stateful. It appears to be intertwined the current state you're in, with nearby or related states being ways you can be reminded of something. It appears to be related the present way you are wired or the distribution of states you frequent. Consider the common example of chewing gum while studying and chewing gum while studying a test. Or those moments where you walk into a room and forget what you were doing but remember as soon as you walk back, further highlighting how you change moment to moment and the blurred lines of the ever changing Instantaneous You's. If our memories fundamentally shape who we are and how we model the world, then forgetting isn't just losing information, it's becoming a subtly different person. When you can't access a particular memory, the version of yourself that exists in that moment lacks a piece of the experiential foundation that normally defines your identity. On a micro-scale, you've shifted to a different point in the space of possible selves.
I believe deja vu may be something along the lines of revisiting a past You, landing yourself in the same thought pattern or state you were in a prior time.
The Instantaneous You and Distributional You each can represent a level of self, creating the illusion of continuity while allowing for constant change. We are simultaneously the same person (through distributional patterns) and different people (through instantaneous states) at every moment.