What is Entropy?

A few days after their successful eradication of a nest of creatures who went to ash so soon as their clothing caught fire Grace receives an email from Samir.

There's a good chance he's stoned. It's the middle of the day when the thing shows up in her inbox.

Hey G: I've been reading about chance and mortality and all that but IDK if I'm getting the hang of it. I get that everything decays over time and with the right program I could alter the Code to exploit things breaking down without having to break them myself etc etc but I'm having trouble applying the concept of probability since probability is, you know, relative.

Like okay I know if you argue long enough then everything becomes relative and we reduce ourselves to solipsistic egomaniacs and I should be able to just make the universe do what I want it to do because that's how this works so who gives a shit why it does what it does (/s) but right now I don't know how to go about coding to account for every single possible random outcome Patterns are capable of introducing to the Tapestry without my head exploding.

-S.

--------------------------------------------------------------------------

Her reply comes back quickly, almost as if she were waiting for this email, somehow. She wasn't. But there's something about the sharing of information that scratches all of Grace's mental itches. We gather, so that we can disseminate. 

Hi Samir. I have some stuff to help you out here. First, I'd like to introduce you to a guy named Claude Shannon. [https://en.wikipedia.org/wiki/Claude_Shannon]. I don't know if he was one of us, but based on the flame-throwing trumpet invention, I'd swear SoE? Anyway, Shannon came up with the idea of the Entropy of Information [https://en.wikipedia.org/wiki/Entropy_%28information_theory%29]

Basically, this has a lot less to do with things 'breaking down' per se, and more to do with the amount of information a thing contains. More information, more entropy.

Take this line:

--------------------

The dashes are constants -- guaranteed to be the same, guaranteed to stay just as they are. You can represent this information as above, or you can represent it like this: -20 as if to say, hey, it's just 20 dashes in a row, pretty simple.

Now take this line:

--.---..---.------

Now, you can't represent this as easily. There's added complexity. You can do it like this: -4.-3.2-3.-6 and there's still less total text required to represent it, but more than the first line. We can probably do a little better by analyzing patterns, and creating symbols:
(--) = a
(.---.) = b
thus our line becomes: a1b2a3

But, that's still a lot more involved than just -20.

The first line has less entropy than the second line. It also conveys a lot less information. A book made of nothing but a's, despite being made of the same number of characters as a dictionary, does not convey nearly the same amount of information as a dictionary. Meaning comes into being by the introduction of entropy.

Imagine the universe as a crystal, unchanging, unperturbed. It would be perfect, but rather devoid of information. Now start breaking pieces off. It suddenly requires a lot more information to represent the universe. Now start inscribing music on those shattered crystal surfaces -- now you've got even more information. All of those operations increase the entropy of the crystal universe. Creation and destruction are both entropic operations, in other words. Sides of a coin. Where you see entropy, you're seeing the effects of change.

Information entropy and physical entropy are the same beast -- an idea that comes naturally to those of us who view the universe as code and data. But it works out like that in realspace as much as it does in mathspace.

So, probability. How does that relate to information entropy? To get probabilities, you must first observe some data. Imagine, for example, that you have a dictionary. You are given the task of guessing a word picked out of the dictionary at random. You're kind of screwed. However, let's start filtering the result set. Each bit of data you can get will help you make a better and better guess. Let's say you're given the first letter of the word. If that letter is "a", you're a little more screwed than if that letter is "z". The z would narrow things down a lot more. So, the letter z carries far more information than does the letter a. Z is more entropy-laden than a, if you will. Z might even hold more information by itself than the letter combination "at" since so many words start with "at".
So, when dealing with probabilities, if you're trying to find something, you need to find enough bits and pieces of information about it to start solidifying your result, but you may never quite make it. Until you have all the information, you can make better and better guesses, but they might not be correct, they can only become more probable. If you're trying to hide something or make it less predictable, you need to scatter your information or encrypt it (basically, hide it within enough random data so that it's indistinguishable from random data). Preferably, both.

Sam
The last Grace heard from Samir was sometime yesterday afternoon when he emailed her to ask her for her thoughts on entropy. Specifically: probability and how to reconcile its objectivity. As is par for the mentorship course she sent back plenty of reading material to get him started.

And then he proceeded to stay up all goddamn night reading about information technology and Shannon entropy and the next thing he knew the sun was up.

Whatever he did between then and now is between him and Kalen. It's later in the evening. Grace is at home in the warehouse. She may start to regret giving him access to the building if he keeps this up. At least he can't teleport yet.

It doesn't take long to find her. He knocks first.

Grace
[Awareness!]

Dice: 5 d10 TN6 (4, 7, 9, 9, 9) ( success x 4 )

Grace
There's a knock at the door to the pantry. At first she's thinking it's Kalen, but then Kalen doesn't feel like a stab. Who feels stabby? Oh yeah.

She shouts his name through the closed door, right before it opens. "I wasn't expecting you. Pleasant surprise. What's up?"

Inside this place is a virtual cornucopia of things which shall not go bad. There's rock candy coffee stirrers, freeze-dried ice cream (along with other freeze-dried foodstuffs), about ten different kinds of coffee and inumerable types of tea. If Samir ever got the idea that their little compound was a bit of a prepper's paradise, he wouldn't be too far off. The kinds of apocalypses Kalen imagines are beyond the wildest dreams of most, however.

Sam
More than once the thought has occurred to him that if civilization collapsed around the warehouse that anyone holed up inside the warehouse might not even realize until the power went out. If the power went out. A house full of Forces Initiates is not necessarily beholden to power grids.

This stabby creature feels like Mind threads wrapped tight around himself. Nothing can get in that isn't already there. He always feels like that though.

He opens the door and pokes his head in. Flashes her a grin that is more uncomfortable than cocky and stays where he is. His eyes are a touch red. She knows that look by now. Cocaine isn't his vice. The pursuit of knowledge though. That's a high he can't sell.

Though it's restrained his hair is a bit of a mess. Shocks have escaped from the knot at the back of his neck. Make of that what you will.

"If I wrote the Code using SIC-POVM probabilities and translated a density matrix into a distro using the SIC-POVMs, do you think I could reproduce the statistical predictions on the matrix from those probabilities instead? That would give me related probability distros instead of a bunch of derivations, right?" A beat. He's hyper but not manic. Grace is the only person in the city who can tell the difference between his mental states. Dubious honor. "I haven't slept in like two days, I feel like I could see through Time if I really put my mind to it."

Grace
She squints at him. The sharp, quick words. The red eyes. The lack of sleep.

"SIC-POVMs. Okay. So. There's many ways to go about this. I think I know what you're talking about? If tangentially? It's a generalized measurement in quantum mechanics. But the IC stands for "Informationally Complete". What if you don't have all the information? If it's incomplete?

Can he think clearly on this much sleep deprivation? It's not improbable.

"Do you need some coffee?"

Sam
"... yes."

Before he lets go of the pantry door to step back and let her out Sam glances around at his surroundings like to make sure the walls are still intact. He holds the door open until she's through. That's the only way he can check and make sure the light is out inside the pantry and check to make sure the door continues to open and shut four fucking times before he goes into the kitchen to wash his hands. Which he does as he continues to talk.

As for his dilemma:

"See that's the problem I keep running into, right, it's that I have so much information I don't know what to do with, like whether it's even relevant or not, so I thought Well what if I just write the Code to account for the fact that I have my head up my ass it can't be that hard! Just because it doesn't mean shit to me or I'm not looking for it doesn't mean it's not there. Right? I mean I'll have to modify the program parameters if I ever get to where I decide I want to be able to influence the--"

His hands are wet. He waggles his fingers around like to give probability a physical interpretation and uses his sleeve-covered wrist to shut off the faucet. Stands there with his hands up in front of him like a surgeon because he can't find something he wants to dry them on.

Then a thought hits him.

"Wait a minute. Wait wait wait." He runs his hands through the escaped bits of hair. That's one way to dry them. "Last night... this morning... whenever, I was reading about this Craft out in east Asia where everyone was born male but raised as women and bound in service to demon kings, or something, I don't know, that's just what it said... anyway, they had to escape their homes because the First Emperor went apeshit and was trying to kill all of them, and on their way to the coast they were like Holy shit, the spring turtles are humble and fierce and shit, we want up on that. So they started adopting the turtles as pets and painting on their shells to... I don't know, impress their psyches onto the animals, and then after a week they would boil and eat the turtle, and the shell would crack in such a way that the dude-lady casting the spell could divine whether or not her his whatever next venture would be successful."

What the fuck are you talking about, Samir.

"It's not like I'm just going to be wandering around trying to metal-detect something I don't know shit about, right? If I'm using this, I'm looking for something in specific anyway. I'll have enough information to get that far. I don't need to account for incompleteness. The program'll do that for me."

Grace
He says yes, and so she goes to set a kettle on the stove, only once running into problems with this because he is standing around with his hands up in the air unaware of what to do with them. Water in the pot, water in his hair, spring turtles...

She's listening. She is also making coffee, turning on the heat, using energy to increase the entropy of the system of heating element, pot, water.

"I think your main problem is that you are attempting to run first before learning to walk," she says, snugging the lid onto the heating pot.

"I like to think of it as a journey. You start off with no information, everything is equally probable as the next. Like, the base Code when you're just looking at the random data of it. It could mean anything. You collect a bit of information about what you're looking for, and you can use that to update your probability set. Another bit, another update. Treat it like a process that never quite finishes, because as you nail your path down, it gets up and walks away again.

"Part of the problem is finding the point at which you cut the process short and say: 'Here, I have a pretty good idea of the information content now.'"

If it sounds less like she is talking about information, and more about the progress of life and death, you wouldn't be entirely wrong. She turns and heads toward the pantry again, opening the door. She doesn't feel the need to close it again four times. Very quickly though, she returns with some coffee beans in an unlabeled bag.

"At first though, you may only be able to tell that there is information there. Like, you don't know what it means -- just that it exists. Sometimes, that is enough."

Sam
Now Grace has a definitive answer in case anyone ever asks her what the worst Sphere to teach to an obsessive-compulsive reality hacker is. Attempting to integrate uncertainty and unknown variables into a paradigm that names Code as the basis of everything is all well and good until you realize all of Sam's weird rituals were born because his brain misfires and that's how he has learned to live with the anxiety his condition causes him. He cannot tolerate uncertainty and unknown variables.

His main problem is that he thinks he ought to be able to make sense of this Right The Fuck Now because the other Spheres came to him easy. Even the spirit world wrote itself into his paradigm without this much effort. The spirit world is straight forward compared to the world of probability.

Information. Life and death. Two sides of the same coin.

It helps to have another person tell him he's got the gist of it. Par it down a bit.

While she embarks on her quest to retrieve the beans Sam unleashes his hair. Runs his fingers through it to return it to some semblance of order. Of course he counts how many times he runs his fingers through it before he secures it again.

"You're right." He almost chews on his thumbnail but then he takes out his yellow plastic pack of hand-rolled cigarettes and his cheap plastic lighter and drops them on the counter instead. "You're totally right."

Grace
[Entropy 1: Viewing the entropic states of the immediate area, Diff 4 - 1 for taking time.]

Dice: 3 d10 TN3 (1, 3, 8) ( success x 2 )

Grace
[Also, should include Corr 1, because reasons, bleh]

Grace
"Okay. I think the act of coffee-making will be a good one to watch," she says, somewhat enigmatically, and pulls out her phone. Coffee bag in one hand, thumbing through her programs with the other.

It starts off with the Code, until she pushes that through a rendering engine, and the room they're standing in (complete with tiny versions of Grace and Sam within it)

"So, what does it look like if I take my 3D representation of the room, and overlay it with a gradient corresponding to the relative levels of information content within the space?" she says, and her eyes flit to Sam.

A few more adjustments, and she has exactly that. When she turns the phone around, Sam can see the heat energy of the stove element dispersing into the water, into the air, carried along by the steam. He can see the twin engines of their bodies, busily converting energy into blue order on the inside, while releasing red chaos into their surroundings. He can see a hairline crack in one of the wooden chairs around the kitchen table, a bright purple against the varigated wood grain. He can see the light in the room, conveying its information in terms of photons. He can see everything, that is, that space can form a boundary for, in rainbow hues depicting their general level of entropy.

"As you can probably see, you can categorize information density without caring much about what that information is trying to tell you. Using this, I can tell if something has a weak spot, if that's what I'm looking for. Shows up as the universe requiring a higher level of information density to bring out the details of where it's weak, as opposed to where it's nice and solid and the same as everything else around it."

Sam
Enigmatic statement begets the lighting of a cigarette. Last time he'd ashed into an empty coffee cup. Smoking doesn't do much in terms of quelling his pursuit of cleanliness and decontamination but it does give him something to do with his hands.

He stuffs the lighter and the cigarette pack into his jacket pocket once it's lit and finds himself a cup before coming to stand behind Grace and peek to see the screen. Their eyes meet brief when she glances over at him after the rhetorical question. A few more adjustments and he leans one hip against the countertop.

"Whoa!" he says when she shows him the screen. Hasn't exhaled yet. The word is tamped down in his throat until he blows the smoke up towards the ceiling. "Is that the only Sphere you're running?"

Cigarette filter wedged between his lips and Sam has his hands freed up again. He has to reach into the inside pocket of his jacket to remove his handheld computer. Inspiration has stricken him.

Grace
She slides her phone onto the counter so Sam can still see it, and goes to grind her beans. They go into a little cup in the machine, and she turns it on. Suddenly, that machine goes to purple high-entropy in its complicated, destructive dance.

"Well, I had to get a representation of the area. For that, I used some Correspondence to map out the spatial dimensions of everything. But the colors and stuff is all information density, completely agnostic of what that information is attempting to convey. It could be the heat from the stove, or the way your cigarette smoke is dissipating, or the way the walls are propped up, making the house frame secure. As far as this program is concerned, it doesn't care. All we've got is order and chaos, known information and uncertainty, stolid and free.

"Now, this is easy to interpret, because we're right here. We do something," she says, and waves, making waves of shimmering gradients on her screen "and we know why the image just changed, right? In unknown arenas, it's going to be more difficult to figure out what is what. You'll get this mess of rainbow gradients that bleed into each other and don't make a lot of sense. You might want to combine the information density calculation with a matter scan, so you can see just the more solid and weaker areas of a pane of glass, so you know where to hit it the right way, that kind of thing."

Sam
[let's just roll grace's mentor thingie now to see what happens]

Dice: 3 d10 TN7 (5, 7, 7) ( success x 3 ) [WP]

Sam
[i might as well do his library while i'm screwing around]

Dice: 2 d10 TN7 (1, 4) ( success x 1 ) [WP]

Sam
Though he doesn't touch the phone he does keep leaning against the counter to watch what the room is doing on the screen. The hand responsible for the cigarette repositions the coffee cup he's appropriated and watches what happens when he slides it across the countertop. When he takes another drag off the cigarette and tips the ash in to join what he's already deposited.

Sleep deprivation will make anyone a bit deranged. He started out deranged though. Hasn't reached the point of staying awake where he is haggard and incapable of focusing. That's a look Grace has seen him wear before.

He doesn't take his eyes off the screen until he hears Grace finish grinding the beans.

"The Internet says you can use Entropy to tell if someone is lying. Is that a different program?"

Grace
"You'd want to do something a lot more focused than what I just did. That's a mess. You wouldn't be able to tell the difference between a lie and the AC coming on..."

She opens a cabinet, and out pops a convenient French press (Kalen's coffee-maker of choice -- they are literally scattered everywhere). She dumps the beans into the pot, and stares at the kettle like it is annoying her with its lateness.

Grace is actually pondering. Lie detection. How would you...

"I suppose if you subjected the sound of their voice to an Entropy analysis, that might work. Not like, the whole room, because then you're also going to get all the cracks in the ceiling and the car noises outside and everything ever. Might work even better if you combined it with a heartrate/persperation scan or a mind scan."

Sam
"I haven't unlocked the Life branch of the tech tree yet."

Oh Samir you're so funny. Funny or not he's gone and distracted himself finding something Grace can't answer super fast. What's left of the cigarette disappears with a quick hard inhale and he tosses the spent filter into the coffee cup.

Thin gray strands of smoke rise up out of the ashes. His eyes glance down at the screen as it changes to reflect the heat of the water extracting the coffee from the beans and the ember slowly dying in the coffee cup.

"Can you try it with Mind?"

Grace
"I could," she says, and the kettle starts whistling.

She slides it off of the burner, and pours the water in, providing a new show of slithering rainbows for Sam to look at. Heat and the exchange thereof is a thermodynamic entropy process after all.

"Want me to do it on myself and tell a bunch of shitty lies?" she asks, as the coffee grounds go swirling in the glass carafe of the French press.

Sam
Thermodynamic entropy processes are fascinating when you've been up all goddamn night and have replaced solid food with cigarettes and energy drinks and junk food from the corner store. They would be fascinating anyway but he's loathe to look away while Things are happening.

But then Grace poses the question the way she poses it and Sam snorts. Phrasing.

"Yes. Yes I do."

Grace
So, coffee started, she slides back over to her phone with a smile, completely missing why Sam just snorted at her. Oh well.

"Okay, let's get rid of Rainbow Road here," she says, and cancels the running program. "And do something else..."

She's never done this, Sam. Working a bit on the fly here. But, she starts by attempting to whittle away at the Data, focusing it to just her own mental state, a thing like a multidimensional snowflake. To that, she will apply a data density function, to calculate the information given and information hidden.

[Mind 1, Entropy 1 -- Lie Detector! Diff 4 - 1 taking time.]

Dice: 3 d10 TN3 (4, 6, 8) ( success x 3 )

Sam
Nothing much to do but wait while Grace instructs the phone to focus on different data arrays. Waiting isn't one of his strong suits. He takes his own handheld computer out of his jacket again and taps a few keys. He won't be able to read the random elements but as long as they're screwing around with rotes they've never done before he might as well see if he can read Grace's aura while she's trying to lie.

Which means he drops the mind shield he always has running as a background process. Ah, trust.

[mind 1: mind empowerment! dialing his perception up to 11.]

Dice: 2 d10 TN4 (1, 3) ( botch x 1 )

Sam
[le backlash!]

Dice: 1 d10 TN6 (10) ( success x 1 )

Sam
[le soak!]

Dice: 4 d10 TN6 (4, 9, 9, 10) ( success x 3 )

Grace
Grace, for her part, does not notice thing things have gone horribly wrong for Sam. She's too focused on her own coding, which goes rather more successfully. On her phone screen, a graphic representation of her mind blossoms into view, followed by a readout at the bottom, showing a deception probability meter.

She slides the phone onto the table again, so Sam can see.

"I enjoy coffee," she says, to her phone. It says there is a 12.58% probability of deception, and she grins.

The probability reading actually goes up a bit, while she is thinking of something decently horrible to say, and then skyrockets when she comes out with: "The Technocracy has the right idea, really."

Sam
Things tend to go horribly wrong for Sam. That will happen when he doesn't put forth any real effort despite all the anecdotal evidence supporting the hypothesis that reality hates Sam and loves backhanding him.

It isn't as impressive a nosebleed as the one he earned the night Elijah wanted to go gallivanting off to a high school football field by himself but he still boasts a thin trickle from his right nostril.

He blinks several times as his vision goes black and white on him. He is frowning as he puts his knuckles beneath his nostrils and pulls them away. The red isn't red. It will go back to normal in a few seconds but for a moment he is as distracted as Grace is.

Then she comes up with a mighty bold statement.

"You," he says before he reaches for a paper towel, "suck at lying."

Grace
Finally, Grace looks up from her work and notices. "Did you?" she says, making a motion about her nose. "Ohh. It happens," she says, and goes to get a mug.

"You should take a caffeine break. It might be the sleep deprivation getting to you."

That having been said, she slides her black mug onto the counter and starts rummaging around for additives. First, the fridge, for some cream. Then, a cabinet for some raw sugar rock candy stirrers. Then, the medicine jar of marshmallows. This stuff is dumped on the counter with her mug, and she goes for the plunger of the French press.

Sam
He blinks a few more times as his vision returns to normal and wipes the blood from his upper lip. Holds the paper towel folded up beneath his nostril in case it decides it isn't done oozing and comes to stand beside Grace to read the screen.

His eyebrows flick up and down once in approval. That answers the question of how in the hell the Sphere responsible for chance handles truth or the absence thereof.

As she cuts him off Sam leans back against the sink and stifles a yawn. Attempts to talk around it.

"If I stop now, the withdrawal might pop a blood vessel in my skull." Yawn over. "Will Entropy tell you the probability of me dying of caffeine withdrawal before I make it home?"

Grace
It says something about their mutual sleeping habits that Grace's answer to sleep deprivation is to prep his caffeine. There's just something about the quest for knowledge that drives one to obsessively talk for hours about That Thing On Your Mind. Grace has been there. He won't be sleeping yet.

"This is good caffeine, man. You won't be dying of withdrawal here," she promises. The lie detection on her phone also promises, with a 15.42% probability of deception.

The plunger settles itself into the bottom of the carafe at last, and she pours herself a cup -- does not get Sam one -- and starts loading it up with the things she likes (which is all of it). There's a candy stirrer and a floating marshmallow on top by the time she's done.