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. The price is the cost of a mismatch between two amounts. It isn't calories and it isn't money, 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. (The list uses two words from Part 1. A tick is one step in the writing of reality's record, and a moment of consciousness, also called a complete moment, is eight ticks in a row. The section after the list gives the reasons for both.)

1. Following along is free. Every tick of a moment compares an amount posted (what the tick writes in the record) with an amount felt (what the tick is like). When the two match, the price is zero, so a moment can follow along tick by tick for nothing.
2. Holding the whole costs. A self is a moment that also holds itself as a whole: one tick feels the total of what all eight posted. For an even moment, one with 1 on every tick, that's 1 posted against 8 felt, 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. When the ticks are uneven and one dominates, the price falls. For every complete moment, whatever its shape, the price stays above zero.
4. Below the price, the self goes first. Give a moment a budget, the most mismatch it can pay for. A moment whose budget is below its price still follows along tick by tick, and nothing holds the whole.
5. Noticing that you noticed costs more again. A moment can also hold a record of its own experience, the total of what it felt. In the even moment, that brings the price to 2303/240, about 9.60. Each step up holds a larger record than the one below it, holding a larger record costs more, and there's always another step.

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

Here's the answer to the question this post opened with. The drive home and the quiet room are my drawings of two parts of this result. The drive home stands for a moment that follows along with nothing holding the whole, and following along is free. The quiet room stands for a self that keeps looking at itself: each look holds a larger record than the one before, holding a larger record costs more, and there's no top step. They're drawings. The arithmetic behind them is exact, and I'll keep the drawings and the arithmetic apart. Putting your own drive and your own evening in a quiet room on this scale isn't derived yet. Step 4 says exactly what it takes.

Four facts from Part 1, and why each holds

The answer rests on four facts from What You Are, Part 1 of The Universe Writes in Pen. Each comes here with its reason. Part 1 gives the full version.

1. Reality keeps a record of every event, and nothing in it is ever erased. The basic laws of physics never destroy information. In quantum mechanics this is called unitarity: the present state of a closed system fixes every earlier state exactly, so running the laws backward recovers each one. Two more facts come from how the record is written, and they do different jobs. Each new entry is a comparison, and a comparison needs information about both sides, so every entry is written against what came before. That says what an entry is. Why none is ever lost is the second fact: the record only grows. Each new entry is added with every earlier entry kept, and writing it never alters an earlier one.¹ One link here isn't derived yet: that the physical world's change over time is this record being written, so the information the laws keep is this record.

2. A tick is one step in the writing of that record, and the smallest kind of event is one thing told apart from another, a single yes or no. Reality's record is written one tick at a time. You're doing the smallest kind of event right now: your eyes are telling the dark marks on this page from the white around them. Every measurement and every perception tells one thing from another. Telling two things apart needs information about both of them, and the least information there can be is one yes or no.

3. A moment of consciousness is eight ticks in a row, none of them silent. A silent tick is a gap: the tick posts no amount. Eight ticks with no gap make one complete moment, and a moment with a gap isn't complete. Why eight. Space has three directions: left and right, up and down, forward and back. It has three because loops that last pair up by linking, like two rings of a chain, and linking works only in three dimensions: in two, loops can't wind around each other, and in four or more any two loops slide apart. Each direction has two sides, so each is one yes-or-no. Three yes-or-nos make 2 × 2 × 2 = 8 combinations, the eight corners of a cube. A complete moment is a round that visits every corner once, one corner per tick. Eight corners take at least eight ticks, and eight are enough.

Why none silent. A silent tick posts nothing, so at that tick there is nothing to compare. Step 4 shows what that does to the self.

4. Every event has two sides: what it does, which anyone can measure, and what it's like, which is experience. These aren't two things glued together. They're one event, seen from without and from within. Is Your Coffee Mug Conscious? gives the reason. Every tick that posts an amount is an event, so it has both sides.

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)

The price measures imbalance: it grows as the two amounts move apart. It isn't energy, money or calories, and nobody is paid it. It's the size of the mismatch between the two sides of a tick.

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 meets all of these requirements, and exactly one is left:

• It is zero at a match and has no jumps.
• It grows as the two amounts move apart.
• It is the same whichever amount is put first.
• It follows one rule for combining comparisons, the One-Price Law of Distinction. Two comparisons can be chained by multiplying their ratios or by dividing them. The rule says the price of the multiplied pair plus the price of the divided pair is twice each price, plus twice the two prices multiplied together. For two comparisons of ratio 2, each costing 1/4: multiplied, the ratio is 4, which costs 9/8; divided, it's 1, which costs 0. And 2 × 1/4 + 2 × 1/4 + 2 × 1/4 × 1/4 is 9/8 too.
• It has one calibration: how sharply the price rises as a match starts to break.

Other prices meet the first three requirements and fail the rule; the note at the end gives one, with the rule in symbols.² The one price that meets all of them is the formula above. In the research papers it's called J, and a paper in the journal Mathematics proves it's the only one.³

Now take a moment where every tick feels exactly what it posts. 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 following along. A moment can follow along on all eight ticks for nothing.

Next: a moment that's yours is more than eight ticks following along. Somewhere in it, the whole moment has to show up, and that's where the price stops being zero.

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 a self needs 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 follows along 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 what all eight ticks posted. For 1 on every tick, that's 8.

A fair question: 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 of ticks has to pass two tests. For one tick, it gives that tick's amount. When you glue two stretches together, it adds. The total passes both. The average fails the second: glue two stretches of 1s together and the average is still 1, not 2.

Now, where does the whole show up? A moment's only parts are its eight ticks. What each tick posts is its own amount, so the whole can't show up there. The inside of a tick is what it feels, so the whole shows up as what one tick feels. That's the requirement: somewhere in the moment, one tick feels the whole. In the even moment, that tick posted 1 and feels 8.

The price of that tick is 1 against 8. The difference is 7, and 7² = 49. Divide by 2 × 1 × 8 = 16 and you get 49/16, about 3.06. The other seven ticks still follow along, 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. 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.⁴

One catch. A moment's total doesn't exist until its last tick has posted. In the drawing, tick 3 holds the whole, but 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 first and then replayed with the total in hand. Recording means keeping the moment as it happens, tick by tick. Replaying means playing the recording back, now with the total known. From here on, a moment's price is the least it costs to hold the whole with the total in hand. Recording and replaying cost something too, and this number doesn't count them. If the last tick holds the whole with no replay, the price depends on what that tick posted, and it can be higher.

Next: not every moment is even. If the ticks differ, the price changes, and we find out whether any moment holds 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: each friend is a tick, each order is what that tick posted, 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 putting up 8 times their own share. If one friend ordered the lobster, the lobster friend pays the bill and barely notices, because the bill is hardly more than their own order.

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)

This is the Step 1 price. It only cares about the ratio, and here the ratio is p, the biggest tick against the total. In the even moment, p = 1/8, and the price is (7/8)² ÷ (2/8) = 49/16 again. Now make the moment lumpy, with ticks of different sizes.

Moment A posts 4, 4, 1, 1, 1, 1, 1, 1. The total is 14 and the biggest tick is 4, so p = 4/14 = 2/7. The price is (5/7)² ÷ (4/7) = 25/28, about 0.89.

Moment B posts 5, 2, 2, 1, 1, 1, 1, 1. The total is 14 again and the biggest tick is 5, so p = 5/14. The price is (9/14)² ÷ (10/14) = 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 lobster. The total is 107, and the lobster tick is 100 of it. 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 the other seven ticks always add something to the total. The biggest tick is therefore smaller than the whole, p is below 1, and the price is above 0, every time. 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 first eight digits of pi: 3, 1, 4, 1, 5, 9, 2, 6. The total is 31 and 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.

Next: 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. Following along costs 0, so every budget covers it. Holding the whole costs the moment's price. A moment whose budget is below its price still follows along on every tick, and nothing holds the whole.

Here's how we know. It's arithmetic. Following along means posted equals felt on every tick, so its price is 0, and no budget is below 0. Holding the whole costs at least the moment's price. So a budget below the price pays for following along but not for the self. Between zero and the price, the self fails first, and every tick keeps following along.

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. A silent tick posts nothing, so it has nothing to compare, and a moment with a silent tick can't hold the whole at any budget. A complete moment on a tight budget has no silent tick: 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 as a drawing of this result, 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. The driving gets done, and no tick holds the whole. That's my drawing. The bill below it is the exact result.

Here's exactly what's still open. Putting a real person's moments on this scale takes three things that aren't derived yet: which events in a person are a moment's ticks, what each tick posts, and what sets the person's budget. What is derived is the scale itself: every price on it, and that a moment below its price loses the self first while following along continues.

Next: 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 costs more again

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

Here's how we know. Go back to the even moment that holds itself as a whole. What did it feel, tick by tick? 1, 1, 8, 1, 1, 1, 1, 1. Add those up and you get 15. The record is the total, for the same reason the whole was the total in Step 2: a whole adds up. 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, on top of holding the whole. One tick can't feel both 8 and 15, so a second tick, one that also posted 1, has to feel 15. That's 1 against 15. The difference is 14, and 14² = 196. Divide by 2 × 1 × 15 = 30 and you get 98/15, about 6.53. The moment still has to hold itself as a whole, so it still pays 49/16 for the 8. No comparison costs less than zero, so the least it can pay is the two prices added:

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

So noticing that you noticed costs 47/15 times what being you costs, a little over three times as much.

Each step up holds a larger record than the one below it, and holding a larger record costs more. 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, and a bigger mismatch costs more: 1 against 15 costs more than 1 against 8.

And the staircase has no top. 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. That rests on the fact that holding a record is itself felt: the holding is a new event, and it joins the record.

A fair question for the top of the staircase: what if you think about how much it costs to think about yourself?

That's the next step up. It holds a larger record, so it costs more.

The quiet room is my drawing of this staircase. Each extra look at yourself is one more step up: it holds a larger record, and holding a larger record costs more. The staircase itself is the arithmetic above.

Next: that's the last of the five steps. What's left is what they add up to.

What this changes

Being you is something reality does, moment by moment, and it isn't free. A moment is a self when it holds itself as a 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 the size of the mismatch in a moment that holds itself as a whole: one tick set against the total of all eight.

Following along is the part that stays free. Every tick of a complete moment is felt whether or not any tick holds the 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, which is 49/16. That eight is Part 1's eight, one doubling for each of the three dimensions of space. You can check every number in this post on a calculator in the driveway.