The Drive Home You Don't Remember: Why Being Yourself Takes Effort

You pull out of the parking lot at work. Twenty-five minutes later you're sitting in your driveway with the engine off, and you can't remember any of the drive.

Think about what was in it. Red lights, and you stopped at every one. A left turn across traffic, signalled and timed. A cyclist, and you gave her room. Somebody did all of that. It was you, because you were the one in the seat.

But when you go looking for the trip, it isn't there. The driving got done, and you have nothing to show for it.

Now try the opposite. Sit somewhere quiet and think about yourself. Who you are, what you're doing with your life, why you said that thing at the party in 2014. Then notice that you're thinking about yourself. Then notice that you noticed.

That one is heavy. After a few minutes it feels like carrying a couch up the stairs.

It's the same you both times. So why does the first cost you nothing you can feel, and the second wear you out? Why would being yourself take any effort at all?

It does. And the effort has an exact size.

The short answer

Being yourself takes effort in a precise sense: it has a price. It's a price in reality's own accounting, not in calories, and you can work it out on a calculator. Here's the whole answer in five steps. The rest of this post takes them one at a time and shows how we know each one. (Ticks and moments come from Part 1. They're recapped right after the list.)

1. Following along is free. Every tick of a moment compares an amount posted with an amount felt. When the two match, the price is zero, so a moment can follow each tick as it happens for nothing.
2. Holding the whole costs. A self is a moment that also holds itself as a whole, which sets one tick against the total of all eight. For an even moment, one with 1 on every tick, that's 1 against 8, and the price is exactly 49/16, about 3.06.
3. Lumpy moments cost less, and none are free. That even moment is the most expensive one there is. Let one tick dominate and the price falls. For every complete moment, whatever its shape, the price stays above zero.
4. Below the price, the self goes first. A moment that can't afford its price still follows along tick by tick, and nothing holds the whole.
5. Noticing that you noticed costs more again. In the even moment, holding a record of your own experience brings the price to 2303/240, about 9.60. Each step up costs more than the one below it, and there's always another step.

Why this matters: it pulls apart two things that feel like one. A process can run perfectly, every tick followed, with nothing in it holding the whole. A self is that process plus the holding, and the holding is the part that costs. Part 1 told you what you are. This post tells you what it costs to be it, one moment at a time.

I'll use the drive home and the quiet room as my drawings of two parts of this result: a moment that follows along with nothing holding it whole, and a self that keeps looking at itself. They're drawings. The arithmetic behind them is exact, and I'll keep the two apart.

You need two facts from What You Are, Part 1 of The Universe Writes in Pen.

A moment of consciousness is eight ticks in a row, none of them silent. Reality's record is written one tick at a time. A silent tick is a gap: nothing goes round, so the tick posts no amount. Eight ticks with no gap make one complete moment. Eight, because space has three dimensions and 2 × 2 × 2 is 8. (Gary, the drummer who flips a coin before every beat, is the one who leaves gaps. A moment with a gap isn't complete.)

Every event has two sides: what it does, which anyone can measure, and what it's like, which is experience. A tick is an event, so every tick has both sides.

Here's the route. We'll stop after each step to zoom out. The Ledger keeps the map. The Ledger is how I draw reality's permanent record: a book with a deadpan face and one word, "Noted."

Step 1: Following along is free

Every tick compares two amounts, and a perfect match costs nothing. A moment can follow along tick by tick for free.

Here's how we know, starting with the two amounts.

Every tick of a complete moment posts an amount to the record. Say it posts 1. That's the outside of the tick, the side anyone can measure. The inside is what the tick is like, and that has an amount too: the amount felt. Both amounts are always positive. So every tick is a comparison between two positive amounts, one from each side.

A comparison has a price, the price of the mismatch. To work it out, subtract one amount from the other, square the answer, and divide by twice the product of the two amounts:

price = (posted - felt)² ÷ (2 × posted × felt)

Try it:

Keep an eye on the last row. It's the star of this post.

Three things about this price:

• It's zero only when the amounts match. 1 against 1 costs nothing. Anything else costs something.
• It's the same either way round. 1 against 2 costs what 2 against 1 costs.
• It only cares about the ratio. 2 metres against 1 metre costs the same as 200 centimetres against 100 centimetres: 1/4. Change the units and the price stays put.

That price is forced. Ask for a price that has no jumps, is zero at a match, doesn't care which amount is bigger, and follows one rule for how the prices of comparisons combine (the One-Price Law of Distinction). Fix how sharply it curves away from a match, and exactly one price is left. This is it. In the research papers it's called J. A paper in the journal Mathematics proves it.¹

One word about "price." It's the cost of a mismatch in reality's own accounting. It isn't calories, and it isn't money.

Now take a moment that just follows along. Tick 1 posts 1 and feels 1. Tick 2 posts 1 and feels 1. All eight ticks: 1 against 1, price 0 each, total 0. Call this tracking: every tick feels exactly what it posts. A moment can track all eight ticks for nothing.

The Ledger writes eight entries and finds eight matches. It's the most boring bill in the universe. The total is zero.

Zoom out. Step 1 is done. Every tick is a comparison of an amount posted with an amount felt, a mismatch has one exact price, and following along tick by tick costs nothing. Next, and why: a moment that's yours isn't only eight ticks following along. Somewhere in it, the whole moment has to show up. That's where the price comes in.

Step 2: Holding the whole costs

A self is a moment that follows along and also holds itself as a whole. In an even moment, with the same amount on every tick, holding the whole costs exactly 49/16, about 3.06.

Start with why the whole.

A moment that's yours is one act, not eight flashes that happen to sit side by side. What makes eight ticks one act, and an act that belongs to someone? Somewhere in the act, the act shows up as a whole. A moment that only tracks has eight ticks, and nowhere in it does the whole moment appear as one thing. A self is a moment where it does.

What is "the whole"? Add up all eight ticks. For 1 on every tick, that's 8.

Yeah-But, the voice at the back of your head that has never let anything big go by without a question, clears his throat. "Why the total? Why not the average?"

Because a whole adds up. Walk 3 kilometres, then 5: the whole walk is 8 kilometres. The average of the two legs is 4, and that isn't the length of anything you walked. A number that stands for the whole of a stretch has to give a single tick's amount when the stretch is one tick, and it has to add when you glue two stretches together. The total does both. The average fails the second test: a stretch of 1s averages 1 however long it is.

So here's the requirement. Somewhere in the moment, one tick feels the whole. That tick posted 1 and feels 8.

The price of that tick is 1 against 8: 7² = 49, divided by 2 × 1 × 8 = 16. That's 49/16, about 3.06. The other seven ticks still track, 1 against 1, price 0 each. Add the eight prices and the moment's price is 49/16.

Seven ticks match perfectly. One tick feels more than it posted, and that one lopsided tick is the whole bill.

You can't do it for less. In an even moment every tick posted 1, so whichever tick holds the whole is 1 against 8, and no other way of holding the whole is cheaper. The paper behind this post proves it for moments of every shape, not only the examples here.²

The Ledger notes seven matches. Noted. Noted. Noted. Noted. Noted. Noted. Noted. Then it clears its throat. Noted. That'll be 49/16.

One catch. A moment's total doesn't exist until its last tick has posted. In the drawing, tick 3 holds the whole, and ticks 4 to 8 haven't happened yet. Read once, front to back, only the last tick can know the total.

To hold the whole from any other tick, the moment has to be recorded and then played back with the total in hand. From here on, a moment's price is the least it costs to hold the whole with the total in hand. (Hold it from the last tick with no replay, and the price depends on what that tick posted. It can be higher.) Recording and replaying cost something too, and this number doesn't count them.

Zoom out. Step 2 is done. A self is a moment that follows along and also holds itself whole. In an even moment, holding the whole is 1 against 8 and costs exactly 49/16. Next, and why: not every moment is even. If the ticks differ, the price changes, and we find out whether any moment gets to hold itself for free.

Step 3: Lumpy moments cost less, and none are free

Every complete moment pays above zero to hold itself, whatever its shape. The even moment pays the most: exactly 49/16. The more one tick dominates, the less the moment pays, and it never reaches zero.

Here's how we know. Picture eight friends splitting a dinner bill. (That's a drawing of the real thing: the friends are the ticks and the bill is the total.) One of them has to put the whole bill on their card. Compared with what that friend ordered, how big is the bill? The friend who ordered the most has the smallest gap. If everybody ordered the same, whoever pays is fronting 8 times their own share. If one friend ordered the lobster, the lobster friend fronts the bill and barely notices.

A moment works the same way. The cheapest tick to hold the whole from is the biggest one. Call the biggest tick's share of the total p: the biggest tick divided by the total. The price of the moment is:

price = (1 - p)² ÷ (2 × p)

In the even moment, p = 1/8, and the price is (7/8)² ÷ (2/8) = 49/16 again. Now make the moment lumpy.

Moment A posts 4, 4, 1, 1, 1, 1, 1, 1. The total is 14. The biggest tick is 4 of it, so p = 4/14 = 2/7, and the price is 25/28, about 0.89.

Moment B posts 5, 2, 2, 1, 1, 1, 1, 1. The total is 14 again. The biggest tick is 5 of it, and the price is 81/140, about 0.58.

Same number of ticks, same total, different prices.

Push it to the limit. A moment that posts 100, 1, 1, 1, 1, 1, 1, 1 has one enormous tick. The total is 107, the lobster friend ordered 100 of it, and the price is 49/21,400, about 0.0023. That's almost nothing.

Almost. Not zero. Every tick of a complete moment posts something, so there are always other ticks, so the biggest tick is always smaller than the whole, so p is always below 1, and the price is always above 0. The whole is bigger than any one of its parts, and that gap is the price.

Try your own. Pick any eight whole numbers above zero, say the digits of pi: 3, 1, 4, 1, 5, 9, 2, 6. The total is 31, the biggest tick is 9, so p = 9/31 and the price is 242/279, about 0.87. Whatever eight numbers you pick, the price lands above 0 and no higher than 49/16.

So there are two separate facts here. The even moment is the most expensive moment there is: exactly 49/16. And no complete moment, however lumpy, is free. The self is never free.

Zoom out. Step 3 is done. A moment's price depends on its shape: the more one tick dominates, the less it costs, and it never reaches zero. Next, and why: a price is something you can fall short of. What happens to a moment that can't pay?

Step 4: Below the price, the self goes first

Give a moment a budget: the most mismatch it can pay for. Tracking costs 0, so every budget covers it. Holding the whole costs the moment's price. A moment whose budget is below its price still tracks every tick, and nothing holds the whole.

Here's how we know. It's arithmetic. Tracking is posted-equals-felt on every tick, so its bill is 0, and no budget is below 0. Holding the whole costs at least the moment's price. So any budget below the price pays for tracking and can't pay for the self. In that gap, the self fails first, and the tracking carries on.

Try a budget of 3/4. Moment A's price is 25/28, about 0.89, which is over budget. Moment B's price is 81/140, about 0.58, which fits. Same number of ticks, same total, same budget. B holds itself. A follows along, tick after tick, and can't pick up the whole tab.

Silence is a different way to lose the self. Gary's moments have gaps, and a tick with nothing posted has nothing to compare, so a moment with a gap can't hold the whole at any budget. Gary is still not getting the gig. A complete moment on a tight budget has no gaps: every tick is there and every tick is felt. Only the holding is missing.

That brings us back to the drive home.

Here's the drive home, drawn with every moment's budget below its price. In every moment of the drive, all eight ticks follow along, each feeling exactly what it posts. No tick holds the whole. The driving gets done, and nothing holds it. That's my drawing. The bill beside it is the exact result.

Putting a real person's moments on this scale means finding their ticks, what each tick posts and what sets their budget. That part is still being worked out.

Zoom out. Step 4 is done. Following along is free, so it survives every budget. The self isn't free, so when the budget falls below its price, the self is the first thing to go, and the ticks carry on. Next, and why: the quiet room. If being a self costs something, what does it cost to hold a record of being one?

Step 5: Noticing that you noticed

In the even moment, hold a record of your own experience and the price rises to 2303/240, about 9.60: a little over three times the price of being you. Each step up costs more than the one below it, and there's always another step.

Here's how we know. Go back to the even moment that holds itself. What did it feel, tick by tick? 1, 1, 8, 1, 1, 1, 1, 1. Add those up and you get 15. That's the record of the moment's experience: everything it felt, in one number. It's bigger than 8, because holding the whole is itself felt. The 8 is part of the record.

To notice that you noticed, a moment has to hold that record too. So another tick, one that posted 1, has to feel 15. That's 1 against 15: 14² = 196, divided by 2 × 1 × 15 = 30, which is 98/15, about 6.53. And the moment still has to hold itself, so it still pays 49/16 for the 8. Add them:

49/16 + 98/15 = 2303/240, about 9.60

That's 47/15 times the price of being you, a little over three times.

The staircase doesn't stop, and here's why. Holding a record is itself felt, so the holding adds a new amount to the record: the one that does the holding. That makes the record at the next level bigger than the record you just held. A bigger record against one tick is a bigger mismatch (1 against 15 costs more than 1 against 8), and a bigger mismatch costs more. So each step up costs more than the step below it.

The same move works at every level. Whatever record you hold, a moment can hold that one, and its own record is bigger again. There's always another step. It's one of the three plain facts Part 1 started from: checking a record is a new event, and the new event joins the record.

Yeah-But has one for the top of the staircase. "Yeah, but what if I think about how much it costs to think about myself?"

That's the next step up. It costs more. The Ledger has noted the question.

The quiet room is my drawing of this staircase: each extra look at yourself is one more step, and every step costs more than the last. The staircase itself is the arithmetic above.

Zoom out. Step 5 is done. Holding a record of your own experience costs a little over three times what being you costs, each step up costs more than the last, and there's always another step. Next, and why: that's the whole staircase. What's left is what it adds up to.

What this changes

Being you isn't something that just happens for free. A moment is a self when it holds itself whole, and holding costs, every time. The cost can be tiny, because a lumpy moment holds itself for almost nothing, but it is never zero. Nobody sends the bill. It isn't money and it isn't calories. It's what reality charges for a moment that holds itself whole.

Following along is the part that stays free. Every tick of a complete moment is felt whether or not anything holds the moment whole. The self is the expensive part.

And the price has an exact size. For an even moment it's one tick against all eight: seven squared over two times eight. That eight is Part 1's eight, one doubling for each of the three dimensions of space. You can check the whole thing on a calculator in the driveway.

The whole trip, in one breath

Every tick compares an amount posted with an amount felt, and a mismatch has one exact price. Following along is 1 against 1, and it's free. A self is a moment that also holds itself whole, which puts one tick against the total: 49/16 in an even moment, less in a lumpy one, never zero. Below its price a moment still follows every tick, and nothing holds the whole. Hold a record of that experience and, in the even moment, the price climbs to about 9.60, and there's always a next step. Being you is something reality does, moment by moment. At its cheapest it's seven ticks in perfect balance and one that holds all eight, and even that has a price, with a number.

(The Ledger would like you to know that it noted you reading this far. If you noticed that you noticed, it noted that too. It's keeping a tab.)