if dy/dx = x, then y = x^2/2. That's obvious. If, however, dy/dx = y, that means y' = y, which obviously means y = e^x, since the derivative of e^x is e^x.

In this case, dx/dt = ax. That means that x' = ax, which means that, uh, x = e^at, since the derivative of e^at = ae^at, because chain rule.

And hey, that's exactly what Eifwen said. Good job, Celene.

So if you get 100 bits per day in interest, compounded continuously, and you have 1000 bits, then that means you actually get 105.17 bits per day.

...the average person with a bank account cannot do this math? Most people who are minimally financially literate understand the concept of continuous compounding and why 2% interest a year might be more than 2% if compounded more often than yearly.

Also, uh. You can not in fact perform infinite transactions per second?? Most bank accounts compound daily although some do it monthly or even yearly and then some people buy $5 bills for $4 but you can only spend them a year later, and some people buy certificates of deposits which you can't withdraw until later, and some people buy bonds that pay interest like yearly or biyearly or something and mature in 30 years. And of course some people just invest in a hedge fund or a stock market or an index fund.

Also we tax capital gains in most countries so our math budget is spent on optimizing that with special investment vehicles that are tax exempt or deferred and whatnot and thus we don't have room for continuous compounding.

Anyways you didn't answer my question about whether if I selected monthly it would be paid upfront or if I would have to wait a month!!!

...I guess I'm talking in first person now? Side effect of all the "we"s in this tag.

y' = y, which obviously means y = e^x

Hey, don't forget the y = 0 solution!

So if you get 100 bits per day in interest, compounded continuously, and you have 1000 bits, then that means you actually get 105.17 bits per day.

Well, if you're getting 100 bpd at the start of the day, and you have 1000 bits at the start of the day, then over the course of that particular day you'll end up getting 105.17 bits.

...the average person with a bank account cannot do this math? Most people who are minimally financially literate understand the concept of continuous compounding and why 2% interest a year might be more than 2% if compounded more often than yearly.

Yeah, confirming the "Earth is bad at math and Celene is half-competent at basic math" theory.

You can not in fact perform infinite transactions per second?

Why... not? What's stopping you? Transfer however many bits per second for however many seconds?

Also we tax capital gains in most countries so our math budget is spent on optimizing that with special investment vehicles that are tax exempt or deferred or whatnot and thus we don't have room for continuous compounding.

That sounds deeply horrifying and you probably should not attempt to explain it in further detail we're already getting sorta distracted here. Speaking of which...

Anyways you didn't answer my question about whether if I selected monthly it would be paid upfront or if I would have to wait a month!!!

You'd typically have to wait a month though in your particular circumstance it wouldn't be unreasonable for me to file a request for you to get last month's basic income as a lump sum right now, or something?

Hey, don't forget the y = 0 solution!

Yes, if she has no money in her bank account she gets no interest. This is true.

Well, if you're getting 100 bpd at the start of the day

She loves it when she gets 100 bpd at the start of the day! Great way to start off the day (Not really. At least, she suspects. She doesn't have bpd so she wouldn't know).

Yeah, confirming the "Earth is bad at math and Celene is half-competent at basic math" theory.

Celene is better than the average Earthling at math. This is true. She is definitely not better than the average Earth professional mathematician at math, though.

Why... not? What's stopping you? Transfer however many bits per second for however many seconds?

You're at least gated by your computer's clock speed! You could just approximate it but you might as well just go with the straightforward daily compounding solution, then.

That sounds deeply horrifying and you probably should not attempt to explain it in further detail we're already getting sorta distracted here. Speaking of which...

Yeah as much as she'd love to she does not in fact remember the details of IRAs and Roth IRAs and 401ks and aaaaaaaaaaa

Why would you do it discretely when you could do it continuously. That's deeply silly. There is one obvious simplest option, and it's the continuous one? Having to keep track of how often it's compounded sounds like such a pain?

...Do you want last month's basic income. Whatever strange thing is going on with you, it does sound like you don't particularly have any savings?

It's handled automatically!!! What do you mean "a pain." You just compound at the rate of the transaction instead of doing continuous compounding and having to keep track of the original amount you put in???

...No, she doesn't have any savings. But like, she doesn't want to inconvenience anybody and go through a whole process, and—

actually wait is it a whole process here or is it very easy and simple?

It's handled automatically!

But surely you want to understand the math?

having to keep track of the original amount you put in

You don't have to do that?

actually wait is it a whole process here or is it very easy and simple?

It'd probably take the officer just a couple minutes.

But surely you want to understand the math?

I don't think most people care that much as long as they can easily find the APY. Also the math is more complicated this way? It requires calculus? Most people do not know calculus? Celene's knowledge of calculus was not enough that she could do it easily without thinking a whole bunch? Eifwen's author's knowledge of calculus was not enough that she could do it easily without messing up at the start?

You don't have to do that?

Oh. Nevermind, you don't, you can just correct for it without doing that. But then you might as well just tell them how you corrected for it. She supposes that with this you don't have to send out the transactions on a fixed schedule but you'd probably want to do that anyways.

Most people do not know calculus?

...Okay that's bad. That's pretty bad. They do not have well-formed opinions on societal systems subject to that horrifying constraint.

Eifwen's author's knowledge of calculus was not enough that she could do it easily without messing up at the start?

It was FOUR AM

...Sure.

They will do that then :3

It was FOUR AM

Yeah, and you could've easily done the normal discrete compounding calculation at 4 am :P

She clicks on "► PRIVACY AND DATA HISTORY"

There's no link with that title.

Why is this form SUBTLY CHANGING THE TITLES OF PAGES BASED ON WHICH ONE SHE'S ON

...Oh, probably that happened after you okayed benign deception.

no it DIDN'T because it CHANGED on the PERSONAL PREFERENCES page BEFORE she OKAYED it unless your BENIGN DECEPTIONS involve TIME TRAVEL

it would've been really funny if it did though, she'll grant that. would've been an incredible troll.

...How does she know it did that? Does she have a video?

Very funny. Just show me the page, please.

Okay fiiiine.

If you had a neck I would be wringing it right now.

What is video record? are they. are they recording her right now???

Well, there are cameras on earth in government buildings but the tapes aren't typically... linked to someone's identity?

Is this... permission for the government to view it, or just anyone? She's... uncomfortable having her DNA out in the open for "that would probably be a bad idea on Earth," and fingerprints are commonly used for logging into devices on Earth as well, so if it's the latter she'll select "Require Permission." Wait, what does "Emergency Override Only" mean?

Is the notification going to be a physical letter sent to her, or just an update in her email or something? Even if she doesn't select "require notification," will the access be logged somewhere she can check? That seems to be implied.

Is the case-by-case review a review for her? Is data only going to be shared in cities she stays in? What if someone creates a city for the purpose of gathering people's information maliciously?

So like, broadly the sort of question you should be asking here is "are you okay with people that work closely with Providence analyzing your conversation and stuff today if they have reason to think it'd be helpful to you and society, or do you want to negotiate explicit permission first?" They'll probably ask before doing anything serious using the data but like, maybe I want to ask one of my coworkers a couple questions about what they make of something you said about Earth, for example.

Even if she doesn't select "require notification," will the access be logged somewhere she can check? That seems to be implied.

Any time your data is accessed in any way will be logged, and you'll be able to access that data online.

Is this... permission for the government to view it, or just anyone?

You... could... just post it all publicly, but that's not one of the default options listed here, no.

Is the notification going to be a physical letter sent to her, or just an update in her email or something?

Notification would be through your preferred contact method, which is currently "texting Summer". You'll probably want to change that once you like, own a phone.

Is the case-by-case review a review for her? Is data only going to be shared in cities she stays in? What if someone creates a city for the purpose of gathering people's information maliciously?

Yes, that's "ask permission from Celene each time." Probably only cities you're staying in would access your data. They think they saw a movie about such a city once, but it seems rather unlikely for that to happen in real life.

Wait, what does "Emergency Override Only" mean?

If you just generally don't want to be bothered with access requests, but do want them to go access the data if there's some pressing emergency, you can pick that.

...ok. She'll... leave biometric access and video access blank, since there doesn't seem to be a space to require none? Wait, it's blank by default? So until you fill out your preferences people could hypothetically access it? Surely they haven't registered her yet. But the "recent data collection" section is definitely getting that information from somewhere .

She'll do case-by-case for inter-city sharing. Wait, is that each time a city wants to view her data, or can she just grant permission going forwards for a given city to view it? Is "data sharing" separate from biometric and video access?

Something something ludonarrative dissonance, it defaults to requiring permission each time. If a city asks for permission you'll probably see an option to just approve that city permanently. Biometric and video access... fall under... data sharing? If you go online later you could do more granular settings for individual data files.

....ok, she'll check "Require Notification" for both, then. And case-by-case is fine.

That all?

Well, was there anything else you wanted to do?

"Summer, is there anything I'm missing?"

She doesn't think so?

Oh. Ok, that's all then!