(a somewhat dense blog post, created largely because I wanted somewhere to record my musings)

Now is a difficult concept. It's one I've thought about a lot over the years and, like science in general, got nowhere with.

I've been thinking about it recently because it's still niggling at me after cropping up in my Impossible Times series:

Simply put, "now" doesn't exist in the equations that to the best approximation science can come up with, govern existence.

If you write an equation to describe a system - like a ball being thrown - it will tell you at each time (t) where the ball is, how fast it's moving etc. But there is no special time (t=T) that corresponds to any "now". The system has been described and no one value of t has any significance over any other. Moreover there's no direction to time: the equations work equally well in both directions.

And this doesn't just apply to a ball being thrown, it applies to every equation describing every system ever.

There are vague arm-wavy explanations for the direction of time, relying on statistical arguments (entropy increases). But for "now" … nothing. Just Einstein pointing out that "now" isn't universal. One person can experience (according to space-time equations, not because they are crazy) two events being simultaneous, and another may experience them happening one after the other.

But this experience of "now" - this singular point moving forwards at 60 minutes an hour, a special divider between past and future... that does not crop up in any of the mathematics over the past few centuries that have described the universe ever more accurately and delivered all our technology.

Of course you can point at the failings of current theory to explain certain very significant components of the universe - primarily dark energy and dark matter. And you can say that maybe when such things are encompassed within the latest theories then "now" will also pop up. And I guess it may.

However, for now I am forced to hunt for someway of reconciling my subjective experience of existing with the science that so accurately describes everything I can see, and an vast amount that I can't.

And I've found a way that at least seems plausible to me and scratches the itch. It's not a scientific break through. I haven't solved any equations. It's just a way of thinking about it that for me has let me move on.

Consider the often drawn space-time cube. It's a diagram where 3-dimensional space is shown as a 2-dimensional plane and the third axis is time. The cube captures all existence, all space and all time. Our lives can be plotted on it (I show a section in green) as can a truck moving along in a straight line (I show a section in red). At each time the thing (me, or the truck) is at given coordinates (x,y). We can imagine the coordinates expanded to include the full parameter space we exist in, so that everything about the entity in question is fully described from its beginning to its end.

From this perspective there is no "now". Everything exists in one block. The old you in a care home, the baby you being born, and all the stuff in between are just points along the line that describes you.

You don't follow this line as time moves. Time is static and exists. The line exists. All the you's that we can examine by looking at a particular t=T … exist.

So … why do we strongly believe that there is a "now"?

Those with a science background may be familiar with the reformulation of classical (or quantum) mechanics into a Hamiltonian (thanks to Mr Hamilton in 1833) vector field where the evolution of the system through time is just given by following the slope of the field.

Basically if we go back to the thrown ball: its trajectory is the solution of the equations of motion given the starting parameters. At any point along the trajectory we can examine the parameters that describe the ball (primarily its position and velocity) and deduce its parameters at the next point.

For a ball it's pretty simple.

A person is also the solution to an equation. A far more complex equation. But the solution is their trajectory through the parameter space that describes them, and one axis of that parameter space is time. We can just think of the planes in the above diagram as not only the contraction of 3-D space into 2-D but of a huge parameter space into 2-D. That parameter space describes not just x & y coordinates, but temperature, posture … brain state … in fact the coordinates of every atom in the person's body, the chemistry of the brain … everything.

Now consider the Hamiltonian: given a ball at time t = t1 we can deduce the ball's state at time t = t2 by considering its position in the relevant parameter space, which is (IIRC) momentum space.

The Hamiltonian for a person is obviously vastly complicated. Their next action will be constrained by things like gravity and momentum but also by state of mind. The solution that delivers their trajectory in the space-time cube is one that includes a constantly changing state of mind (just as the ball's trajectory includes constantly changing x,y-coordinates.

In other words, the solution that is us, necessarily includes a changing state of mind that is dependent on stored versions of earlier events (memory) - they can only be earlier because of causality - and a model of future events (planning/anticipation etc), and as a consequence/by product of that solution there is in a self-aware system (one that models itself) a sense of now.

The solution that is us exists at every point on the space-time trajectory (we don't follow that trajectory any more than a ball does - it's the entire solution, there's no following - that's just an artefact of playing around with one of the parameters (t)). And at every time on the solution there is a local solution (us) which by necessity maintains a sense of now as a consequence of the nature of its formulation - the solution included solving for the mind state since this is part of the parameter space of the Hamiltonian. We exist at all times from our creation to our destruction - all those times are equally important points on the line joining our birth to our death. At all those points (at least when we are conscious) our minds retain memories and plans, and an artificial sense of "now" that is a necessary component of linking the two. But there is no now. Just a quadrillion Marks along a certain stretch of my trajectory all with a brain state that equates to wrestling with the concept of "now" because that is part of the solution of me given my starting conditions and the equations that govern us.

Ta da.

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