A river flows rapidly down a hill. There’s a stone standing alone in the flow. Downstream of the stone there is an eddy, ever changing, yet always somewhat the same. But the eddy is nothing. It is no thing. Nor is the river a thing. Not even the stone. Not even the hill. All just patterns in the ephemeral flow, for now, for a while. But there is no while, no time, simply static patterns in the sand of reality: spacetime. At last, I see it. But there is no I to see. Just another eddy downstream of a stone in the unmoving stream.
Let’s talk about you and me, in the conventional sense of the terms “you” and “me”. And let’s talk about simulations.
You’ve probably seen those amazing fluid simulations that people do in Blender and similar tools:
Because those simulations are done on digital computers, we can be pretty certain that the computer is calculating discrete chunks, not a truly continuous calculation. It’s somehow approximating what a fluid does. A very small amount of searching and scanning will give us more insight:
Despite all the complication, it all comes down to a repeated “simple” calculation, applied “simultaneously” to a collection of discrete cells or particles. We remember each new set of values and render a picture of the fluid based on them. We either make sure that the cells are smaller than a pixel, or average the values of our cells to get the value of each pixel at each step.
Depending on the size and complexity of the fluid we’re trying to simulate, and the precision we need in our picture, each frame of the resulting video may take much more computation than the time between frames. Most of the amazing simulations we see in films take literally days of computer time to render them. Each individual frame of a typical film can require hours of computer time, and there are 24 frames every second.
Days? Hours? Who cares?
But we don’t care. Watching the film, our eyes just see each frame for a 24th of a second, and one 24th of a second later, we get another frame. We see perhaps 30,000 days of computation in the two hours of watching a typical animated film.
Naturally, the maker of the film applies more than one computer to the task. Otherwise we’d be waiting a long time for Toy Story 3.
But here’s what’s most germane to the umoving river mentioned above:
Movies are integers
The movie is just one very large integer. You download the integer onto your computer, or they send it to you serially over your cable, and your iPad or laptop or cable box decodes the integer, stripping digits out of it and using some scheme to paint colors into another integer, the picture on the screen.
My iPad screen is 2732x2048 pixels, with 24 bit color, or 134,283,264 bits of color. Each frame of video is nothing but a single integer of 134 million bits and change.
The screen of my life is surely more bits than that, although we do know that my eyes, ears, and brain take some amazing shortcuts to enable me to process the information that comes in from the world.
Lots of tiny things. Small bits.
Speaking of my life, current estimates of the number of cells in the human body run around 30 trillion (10^9). There are believed to be more microbes that live inside us than our own cells, perhaps around 40 trillion. There are estimated to be about that many atoms per cell, perhaps as many as 100 trillion. And of course atoms are made of things like protons and neutrons, and those are made of quarks, and so far we don’t know what, if anything, quarks are made of.
Anyway there’s a bunch of stuff in you and me, around 10 to the 19th or 20th power little thingummies spinning about. And at least half of the ones inside us aren’t even really part of our body, they’re just some kind of bacteria and such, coming along for the ride, and coincidentally doing things that our bodies find useful, like digesting our food.
Let’s return for a moment to the movie. There’s a really good bit coming up. Watch what Doctor Strange says.
One big integer
The movie is a big integer. It can be segmented into a long series of smaller but still seriously big integers, each one coloring my iPad’s screen for a fraction of a second.
Sleeping through life.
Suppose that instead of buying the movie, we bought the source code, and compiled it onto our iPad, and set out to enjoy the film. It might take hours, or days, to compute each frame. This would be boring. So what we do is that we connect the power wire from our brain to the iPad. When the iPad starts computing a frame, it drops power to our brain, and we sleep. When the frame is done, hours or days later, the iPad applies power to our brain, we wake up for a fraction of a second, and take in the frame. A few days later, or a 24th of a second later if you’re us, a new frame.
Thousands of days later, the movie has been fully computed, we’ve seen the post-credits scene, and the iPad wakes us up. We’re like “That was a great movie, and why am I so hungry?”
In principle, if we were powered down for a minute or an hour or a day between frames, we wouldn’t know the difference. It would seem like a two hour movie to us.
One sleep? Or many?
But wait. Let’s do it another way. Let’s precompute the movie. Now we have a huge integer that amounts to a huge array of slightly less huge integers, each consisting of one frame.
The movie is just sitting there in iPad memory.
The iPad puts us to sleep. It goes about its business, I don’t know what iPads do in their free time. Somewhere in there, it puts the first frame of the movie on the screen and gives us a 24th of a second to process it, then shuts us back down. The iPad fiddles around for days, doing iPad things, every now and again waking us up to view a frame. It could have shown us the whole movie in two hours. But instead, it only woke us up for a fraction of a second every day and showed us one frame.
The movie is a constant. It’s an integer. It doesn’t move at all. There is some trick going on in our head that makes us think it’s a movie. And it seems credible that if we were only given a fraction of a second per day to process, so long as the picture in front of us was the right one, when we woke up, the movie would seem continuous to us.
Are we real or are we Memorex?
But wait. What if the world itself were a simulation? What if there were some giant iPad somewhere, processing code that represents you, and that represents me, and that represents the cat, and that represents my iPad, showing me the movie? What if it took ages of time to compute the world’s next frame? What if it took a day of computer time to compute a second in our simulation? What if it took a year? What if it took a decade?
We wouldn’t know. Our clocks wouldn’t run in the interim: they’re simulated too. So long as the simulation is dense enough that each frame is convincing to us, it doesn’t matter whether each frame really takes 1/24 of a second, or a decade to compute. We still experiences the 24th of a second every now and then. A century from now, it’s time to go to bed. Better grab a snack.
What is that simulation, the one we’re living in? Well, just like the movie, it amounts to nothing more than a really big integer. We can imagine it being computed incrementally, and each frame given to us as it gets done, as we just did. But we can also imagine it being computed end to end, like the movie, and stored on a cosmic DVD (at least 4K Blu-ray, one hopes). Then, you and I are made aware of the next brain-load integer’s worth of it, every now and then. Could be fed to us full speed. Could be fed to us at one day per frame or a century per frame. It’s the same good life to us.
What is time in this scheme? It’s a subscript. It fetches the next frame from the array or frames. It has nothing to do with time per se. It’s just a view of the next frame.
One more step. If it’s “true” that everything comes down to quarks, then the universe is digital. We can think of it in two ways.
We can consider the universe to be an evolving integer, the state vector of everything, transitioning into another integer according to some rules like the rules of fluid simulation. More complex rules, but same idea. The simulation need not be continuous. “Continuous” may be a mathematical fantasy in the part of your integer and my integer that we call our brains or our minds.
Or … we can consider the entire universe written onto a DVD, one big integer. A constant. Somewhere in that giant integer is the somewhat smaller but still huge integer that we think of as “now”.
When is “now”?
That “now” is gone now, but back then in that integer, the part of the integer that “is” your thoughts, and the part that “is” my thoughts, had a kind of togetherness as you read and I write … despite that I’m writing at 1050 on 22 Feb 2022 and you’re certainly reading at some other time. Yet, your integer in your now has a kind of similarity to the integer in my now.
If your integer is sitting with your partner’s integer, watching a big integer on your wide-screen tv integer, then your partner’s integer and yours have some kind of commonality that enables you and your partner to imagine that you’re talking about the big integer on the screen.
Let’s look at a few frames of you and your partner:
Your integers aren’t really similar at all to the eye. But somewhere in there, there is a kind of commonality that allows your evolving frames to “think” that you understand your partner and they understand you.
We need a debugger.
If we had a really good debugger, we could probably inspect our way down and maybe find the chunk of your integer that says “Why didn’t he just double the resources instead of kill half the people” and the chunk where your partner says “Because it would make for a boring movie”, and the chunk where you say “Yeah, true”. Those chunks are each, of course in different rows of the table above, but the table is just one way of looking at one big integer.
So we see that, “in fact”, there might be no time, no space, no stuff, there could be just a single big integer, and from some odd viewpoint from inside the integer, there are patterns that “we” imagine have meaning like “The Snap” and “The Sandwich” and “Agile”.
It’s OK to pretend.
Now, if you want to think of “time”, setting aside that we “know” that it’s really just a “subscript” into an array, and if you want to think of “you” and “me” as being “things”, spanning a period of time (basically just a longish integer in there somewhere), well, it’s OK with me, and truth be told, I’m happy to think of it that way as well.
Or at least, there are words on this page that seem to mean that.
I hope your part of the big integer is a happy one.