# The Soulmate Statistic

A bureaucracy of immortal beings, all as enamored with data collection as we are, could use our lives as data points to run an experiment on us.

And on The Good Place, they did.

)Michael the Architect, a demon, designs his bit of hell, a fake heaven, to get four humans to torture each other forever.

He works hard on it.

He needs a cast of hundreds of demons to help.

Stakes are high but Michael is confident the experiment will work.

His boss, Sean, is not.

Michael: ‘I think that we can get them to torture each other for 1,000 years.

'Sean: ‘I think you’ll be lucky to get six months out of this insane gambit.

’ (¹)The first attempt fails when Eleanor, one of the human test subjects, catches on to the lie a few days in.

Sean gives Michael a second chance to run the experiment.

This attempt also fails so Michael secretly reboots it again.

And again.

He runs the neighborhood 802 times.

Eleanor figures it out almost every single time.

(Jason the idiot figures it out once.

” “THIS is the Bad Place.

” “This is the Bad Place!” (²)Michael’s cast of demons get sick of the endless iterating and turn against him.

He allies with the humans and comes clean about his data collection.

When Eleanor asks how many times they have been ‘rebooted,’ Michael pulls up the plot below.

He tells her that the longest run was 11 months and the shortest was 8 seconds.

(³) Later he tells her that they spent about 300 years total in all the versions of the neighborhood.

(⁴)Michael’s attempt log.

There is no shot in the episode of the plot without the left side cut off, but we can see the pattern with what we’ve got here.

Many attempts of many lengths.

With so many numbers to compare, how would Michael and Sean know whether their guesses about the neighborhood were right?An insane gambitA statistical test could compare their guesses to the actual average length of the experiment.

Michael unwittingly generates a sample large enough to run such a test.

I wanted to gather all the data on the show to rebuild Michael’s attempt log and run the test, so I built a web scraping tool in Python to search the show’s scripts for dialogue mentioning the relevant hard numbers.

(⁵)In the attempt log screen shot above it looks like the longest run, 11 months, is an outlier.

The next highest value is around 9 months and 1 week.

I used NumPy to generate a random distribution of 800 values with a max at 9.

25 months and then injected the true max and min values.

#The parameters for a distribution like Michael's attempt logMinimum value: 8 secondsMaximum value: 11 monthsPopulation size: 802 valuesSum of all values: ~300 years#min: 8 seconds at 556th attemptmin_ = 8 / 86400 (seconds in a day)#max: 11 months at 770th attemptmax_ = 334 (days)My reconstruction of Michael’s attempt log.

The 11-month attempt sticks out like in his plot.

The sum of the values in my distribution was around 309 years, close to what Michael said.

The mean value was 142 days; from this we can say that Michael’s neighborhood lasted on average between four and five months.

He guessed it would last 1000 years which is so wrong as to be either sad or hilarious.

Sean’s guess, six months, was much closer.

Sean could effect policy changes in the Bad Place if he were shown convincing data.

He might like to know if his guess about Michael’s experiment was close enough to suggest that more of these new-fangled torture set-ups would not be worthwhile.

“You’ll be lucky to get six months” is like saying “I predict you will get less than six months.

” A proper experiment would test against this guess with a ‘null’ hypothesis: “You will get six months or more.

” If Sean’s guess turns out to be far above the ‘observed mean’ (the average neighborhood length) in a statistically significant way, then we’d reject that null hypothesis and infer that Sean’s guess was right.

# "You will get six months or more"# (Accept or reject)Null hypothesis: mu ≥ 6 months# "You will get less than six months"# (Infer if null is rejected; otherwise do nothing)Alternative hypothesis: mu < 6 monthsWith the whole set of 802 attempts as a distribution we can run a one-sample ‘t test’ with one ‘tail’ and an ‘alpha’ at 0.

025.

(⁶) I ran the test with SciPy’s one-sample t test module.

Test statistic: -15.

789063286858525P value: 4.

268684972679036e-49Sean's mean: 181 daysObserved mean: 139 daysP < alpha = TrueThe results: Sean’s guess is far enough above the observed mean that we reject the null hypothesis.

(⁷) We can see how high it is with a histogram.

All the reasonable neighborhood lengths are clustered about the observed mean.

The upper bound separates the lengths that are unreasonably high.

Sean’s guess falls above it.

He was right to say that Michael would be lucky to get six months: the vast majority of the attempts did not last that long.

Here the attempts are resampled 1000 times in batches of 30.

The means of these batches form a new, ‘normal’-shaped distribution with the same observed mean as in the original.

Tell the boss, then: our hypothesis test suggests that the scheme to get four humans to torture each other could not work for longer than six months.

Torture should last forever so the demons should stick to tried-and-true methods, e.

g.

torturing William Shakespeare by explaining to him in excruciating detail the plot of the Entourage movie.

(⁸)Statistics tells us that Sean’s guess was right but it does not tell us why.

Michael agonizes over this.

He chose four humans who seemed suited to annoy each other forever.

What kept going wrong?“This is truly the saddest day of my life.

” (⁹)People = GoodI’d offer Michael the Architect some encouragement by pointing out that we could not have asked for better experimental design.

He has held all the variables constant every time to reproduce the torturing behavior for 1000 years.

It doesn’t go how he wanted but the experiment still yields an insight: people are good.

The demons who run the Bad Place assume that humans are bad.

Neither Michael nor Sean anticipates that the four humans meant to torture each other would instead help each other.

The idea that humans might be good takes Michael most of the second season to grasp.

But he gets there.

(¹⁰)Sean, on the other hand, still isn’t buying it at the end of the third season.

Sean: “Counterpoint: humans are terrible.

Limp Bizkit, slavery.

The prosecution rests.

” (¹¹)Despite that solid rebuttal, the evidence to support people’s goodness is resounding.

Eleanor asks Michael in how many of the reboots Chidi did not help her:Michael: “Never.

He always helped you.

.

.

Now his agreeing to help was part of my plan.

What wasn’t part of my plan was it actually working.

Drove me nuts.

Pesky little nerd.

” (¹²)In attempt after attempt, afterlife after afterlife, Chidi and Eleanor showed goodness.

In one of those attempts, #119, something even more surprising happens.

(¹³)Michael: “I put you and Chidi in close proximity because I needed you to drive each other crazy.

But I never intended for you to fall in love.

” (¹⁴)Love?.It must be a fluke.

How could Eleanor and Chidi possibly fall in love in Michael’s neighborhood when the whole point was for them to torture each other forever?.Probability may give some perspective.

In the first 801 attempts they fall in love once: 1 out of 801, or 0.

124% of the attempts.

Success in less than 1% of the attempts sounds low.

The distribution of all attempts would show 800 ‘failures’ and 1 ‘success.

’A real probability distribution for this event would be difficult to interpret.

Here we can get a sense of how rare the event was by showing it with all the ‘failed’ attempts.

We don’t know if one success in 801 tries is lucky, unlucky, or expected.

The probability of success in one trial is 50%.

You would be exceedingly unlikely to get heads just once in 801 tosses.

We don’t know the probability of Eleanor and Chidi ‘succeeding’ once in one lifetime, so we cannot build a distribution to tell us how likely it was to happen once in 801 lifetimes.

The probability of falling in love with a person in one lifetime is unknowable but common sense tells us that it cannot be 50%.

It must be lower — very low — or else love would be as ordinary as friendship.

If it were, say, 1 out of 81, then it is tragic that it only happened once in 801 attempts.

You’d expect them to revel in romance 10 times: the universe here is cruel.

But if the probability were, say, 1 out of 8,001, then they were fortunate to fall in love once in only 801 tries: the universe smiled on them.

1 success is what actually happened.

Was that unexpectedly lucky, unexpectedly unlucky, or expected?.At a soulmate statistic of 1/81, you could expect 10 successes.

You would be unlikely (and unlucky) to get just 1, as shown by the diminishing area under the golden curve where X = 1.

At a soulmate statistic of 1/8001, you would be unlikely to get any successes in 801 attempts.

Getting 1 would be very lucky, as shown by the diminishing area under the gray curve where X = 1.

And of course at a soulmate statistic of 1/801 you would expect 1 success in 801 attempts.

To the lovers this is beside the point.

It happened once; it could happen again.

The version of Eleanor from attempt 119 believes that it is not a fluke:Eleanor: “We know this is, like, the hundredth time you’ve tried to torture us, but this time it’s different, because we’re in love.

And love is stronger than anything you can throw at us.

No matter what he does, we will find each other, and we will help each other, because we’re soulmates.

” (¹⁵)It is, she believes, inevitable.

Michael’s machinations may stack the odds against them but they will still succeed once in every 801 attempts.

A soulmate statistic of 1/801 is not so bad for two lovers who get hundreds of chances.

It’s bad news for those who only get to live life once, i.

e.

the rest of us.

You have a less-than-1% chance of falling in love with your soulmate before you die.

Even Eleanor and Chidi with all their hundreds of lives only get it right one time.

Until it happens again.

I call it my Lookin’ HoleThey fall in love a second time, after a look through Mindy St.

Clair’s Lookin’ Hole (¹⁶), and a third time, after Michael guiltily shares some wiped memories with Eleanor.

(¹⁷) But these are not independent love-fallings-in; if they were, their probability would be simple to calculate, like getting heads three times in three coin tosses.

#Getting heads three times in three tosses(1/2) * (1/2) * (1/2)= 0.

125#Falling in love three times in three lives(1/801) * (1/801) * (1/801)= 1.

945819053721303e-09 (Basically zero)The second and third events depend upon Eleanor learning about the first.

She would not see in herself the capacity to love if she were not shown a recording of it.

(¹⁸) Chidi, too, has to be convinced that memories of love from previous lives can fold into his sense of self hundreds of iterations later.

(¹⁹) Once they’re finally in love at the same time and on the same plane, they go on a perfect first date in a mail depot.

Even with this new information, 1/801 is still the only probabilistic data we have.

But it may be enough.

It reveals an astonishing coincidence: the two fake soulmates who were put together to torture each other are real soulmates.

How could the ‘perfect system’ built by immortals to treat humans as data produce this flaw?.(²⁰) If their holy algorithm can throw such an error then these immortal coders are not infallible.

Before whom might they fall?Well, if an immortal layer of management works above us then why not another, two layers up?.Maybe an unseen hand, manipulating Michael the way he has manipulated the humans, seeks to bring Eleanor and Chidi together across lifetimes and time frames not in damnation but in salvation.

Maybe this hand wants to mate their souls; maybe it just throws the cosmic dice.

(²¹) Eleanor and Chidi don’t know how many more lives they’ll get to live but with each new life a 1-in-801 chance to get it right looks less bleak.

Success now and then: soulmates once every 801 lives or thereaboutsIn fact, if the angels and demons have unlimited computing power then Eleanor and Chidi may get infinite lives.

And if the pattern of lives without a soulmate stretches from zero to infinity then the pattern of lives with a soulmate does, too.

The soulmate statistic assures the lovers a smaller but still infinite number of lives to succeed in finding each other.

If the price they pay is to wait forever, their reward is to be together in a smaller version of forever.

Two infinities: zero-to-infinity and zero-to-infinity divided by 801It is easy to hear in The Good Place a warning about our near-religious fervor for data.

It is timely to remember that our built systems have flaws because we are flawed builders.

And it is humbling to consider that we cannot account for all phenomena by counting them.

But I surprised myself to find in the show a more hopeful message: there is a measure of probability to use when probability no longer serves, a soulmate statistic to ensure that when you distribute all your chances across a boundless multiverse, even the smallest chance will become a sure thing.

Take heart, then.

Even if you don’t find your soulmate this time, you are finding them in 1/8 of 1% of all the other lives you lived, the lives you’re living, and the lives you will live, here and everywhere, now to forever.

Everything is fine.

(²²)NotesTitle image: Season 3, ‘Pandemonium’:A moment from the ‘Forgotten Memories’ video montage.

Season 1, ‘Mindy St.

Claire’ In dialogue taken from the scraped scripts I’ve left number words written as they were, whether in digits or spelled numerals, e.

g.

‘1000 years’ v.

‘six months.

’ For numbers under 10 in my writing I’ve used spelled numerals where it looks more natural and I’ve used digits with other digits, e.

g.

‘falling in love in one lifetime’ v.

‘1 out of 81.

’Season 2, ‘Dance Dance Resolution’:A montage of Eleanor figuring it out.

Eleanor’s intelligence is underestimated again and again on the show.

Season 2, ‘Team Cockroach’:Eleanor: ‘How many different versions of this place have we been through?’Michael: ‘Uh, let’s see.

802.

The longest one was 11 months.

Uh, this current one has only been going for one week.

Boy, you guys barely know each other.

It’s gonna make this tough.

’Chidi: ‘What’s that super tiny line?’Michael: ‘That’s the shortest one, eight seconds.

It was a butt reboot.

I sat on the activator by mistake.

’Season 3, ‘Jeremy Bearimy’:Eleanor: ‘So all the attempts you made to torture us we must have been in the afterlife for 100 years.

’Michael: ‘Almost 300, actually.

’Web scraping: I got the scripts from the website Springfield!.Springfield!.Thanks to them.

My Jupyter Notebook contains flexible functions to search the scripts for dialogue on any topic.

You can use it to do your own investigations if you like.

e.

g.

What is Janet, really?.Or, how many points does it really take to get into the Good Place?.(I spent a lot of time trying to figure this out.

The writers of the show are clever about it.

)Why a one-sample t test with one tail?.The distribution isn’t ‘normal’ (bell-shaped,) we don’t know the standard deviation, and we don’t have separate treatment and control groups.

The test would have one tail at the upper bound, the region where the observed mean was so much higher than Sean’s guess that there was little chance that the difference in means was due to random chance.

I chose an alpha of 0.

025 to mark the upper bound before I ran the test.

Check out my glossary for definitions of more statistical mumbo jumbo.

If the observed mean had hovered somewhere nearer to Sean’s mean, the p value might slip above the alpha value and the result would not be significant.

Visually it would look like Sean’s mean had slipped ‘below’ the upper bound.

Season 3, ‘Chidi Sees the Time-Knife’:Sean: ‘And then Turtle makes a bet with Ronda Rousey, and if she loses, she has to…’Season 1, ‘Michael’s Gambit’:Just including this image for its hilarious set-up.

Season 2, ‘The Trolley Problem’:Michael: ‘People = good.

People = good.

People .

.

.

what is it?’Chidi: ‘“Good.

”’Michael: ‘“Good.

”’Season 3, ‘Chidi Sees the Time-Knife’Season 2, ‘Team Cockroach’Season 3, ‘Pandemonium’:Not an image from when they fell in love the first time; it’s just the image that hit me the hardest.

I wept all over again when re-watching the episode to get screen shots.

This is the first heterosexual love story that hasn’t bored me.

Season 3, ‘The Worst Possible Use of Free Will’Season 3, ‘The Worst Possible Use of Free Will’Season 2, ‘Dance Dance Resolution’:Eleanor: ‘Mindy, you pervert!’Season 3, ‘The Worst Possible Use of Free Will’Season 3, ‘A Fractured Inheritance’:Eleanor: ‘I never even told a boyfriend I loved him.

’Season 3, ‘Janet(s)’:Chidi: ‘If I can’t remember what happened because it happened to a Chidi from another timeline, it’s not a unified me.

’Jason: ‘Just because you don’t remember doing something doesn’t mean you didn’t do it.

I have no idea how it happened, but there is definitely a tattoo on my butt that says “Jasom.

”’There are references to the ‘perfect system’ throughout the show.

Most come from Michael, who eventually turns against the system he once espoused.

One clear interpretation of the show is that it critiques our reliance on and faith in systems, algorithms, and numbers.

Season 1, ‘Everything Is Fine’:Michael: ‘…we calculate the total value of your life using our perfectly accurate measuring system.

… Again, it’s an incredibly selective system.

… See, that’s the trouble with these perfect systems.

’Season 1, ‘Most Improved Player’:Michael: ‘Our system has never made a mistake before.

It’s just not possible.

’Season 2, ‘Everything is Great!’:Michael: ‘Now, normally, our omniscient system perfectly analyzes each person’s profile…’Season 3, ‘Janet(s)’:Accountant: ‘The system is flawless, and tampering is quite impossible.

’Or maybe it’s holding the Time-Knife.

Season 3, ‘Chidi Sees the Time-Knife’:Chidi: ‘Ah!.Ha!. More details