D&D.Sci(-Fi) June 2021: The Duel with Earwax

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Initial impressions:

Even though Janelle probably always uses Beta and Maria probably always uses Delta, we can get an idea of the characteristics of each resonance type by comparing their hypothetical results against heteropneums weak enough for them to overwhelm.

From eyeballing graphs of strength v. heteropneum amplitude for each resonance type and both pilots:

The qualitative behaviour of each resonance looks similar between Janelle and Maria, but quantitatively different (likely a simple multiplicative factor, but I should check!). The multiplier per pilot is different for the different resonance types (so, e.g, Janelle is about as strong as Maria with Beta resonance, but weaker with other resonance types).

And for the different resonance types the graphs are as follows:

Alpha does not depend on enemy strength and maybe has two clumps.

Beta does not depend on enemy strength.

Gamma's points seem to line up on straight, mostly slanted lines from a more-or-less common origin at zero enemy strength. Suggesting a strong dependence on enemy strength but one of the lines is flat and too low, so need to find a way to find out which line you'll end up on.

Delta has a gentle upward trend for Maria (too noisy to detect for Janelle). This does not appear to be a selection effect as Maria is always handily beating the heteropneums.

Epsilon has a curve that looks like a parabola at first, but then slows down, so maybe a sine curve? It is very consistent looking (not noisy) so should be possible to have an accurate fit for it. The curve looks a bit distorted in places for Janelle but this is likely just rounding due to her very low values at this resonance.

Zeta and Eta have points lined up on flat lines. For Zeta one of those lines is at zero.

Based on this, some candidate responses:

- If we can figure out which line we'll end up on, possibly Gamma as used by Janelle. We need to be confident however that we'll end up on a good line.
- Ditto for Zeta as used by Corazon, but with the additional caveat that we need to know that her past hypothetical results of 1.98 were low tier results (and she'll get high tier this time). If the 1.98's were high tier, she'll lose.
- If we can't figure out the information needed for either of the previous, the safe choice appears to be...Epsilon as used by Will. This may seem surprising at first glance since Will's only hypothetical result with Epsilon resonance was a measly 0.21. However, this result was at Heteropneum amplitude 0.57, near the bottom of the Epsilon power curve as seen for Maria and Janelle. If Will has the same Epsilon power curve but with a multiplier, he is around twice as strong as Maria with Epsilon resonance (but check rounding error bars!), and should confidently beat Earwax as long as the Epsilon power curve doesn't take a surprisingly sharp turn to decline between 3.12, where Maria last overwhelms heteropneums with Delta, and Earwax's amplitude of 3.2. However, Will will not overwhelm Earwax, and either option 1 or 2 could do so if successful, so if we can figure out the necessary information for either of those options, they would be preferable.

Since time is pretty much up, summarizing where I'm at:

Afaict each resonance pilot strength result is a multiple of the result of a pilot-independent, resonance-specific rule times a pilot-specific power level with that resonance. (though, tbh, I haven't checked this that closely).

With Maria out, the highest pilot power levels per resonance appear to be:

Alpha: Corazon. This resonance has apparently random variation about a constant value that jumped slightly somewhere around Floorday 500. It is too weak to save us.

Beta: Janelle. This resonance has apparently random variation about a constant value. It is too weak to be likely to save us.

Gamma: Janelle. Credit to GuySrinivasan for finding the specific formula of (1+k*amplitude) (times pilot gamma power level). The integer k is from 0 to 5 with 1 being slightly more common than 0 (could be random variation) but dropping off beyond that. Though that isn't the most expected random distribution and may hint at something non-random, I haven't found the pattern if there is one. Janelle needs k to be 1 or higher to save us or 2 or higher to overwhelm Earwax. Without knowing a pattern for the k value, this seems too risky.

Delta: Amir. This resonance has apparently random variation along with a moderate upward slope with heteropneum amplitude. It is too weak to save us.

Epsilon: Will. This resonance follows a cubic formula (credit to GuySrinivasan for reporting the cubic dependence first, though I hadn't read his comment when I reported it). Though GuySrinivasan expresses low confidence in Epsilon, it seems to me that, assuming the assumptions of the cubic formula plus the multiplicative relationship between power values for different pilots is correct, there is no way the coefficients could possibly off by enough for Will not to beat Earwax. And these assumptions seem to me more solid than for Zeta below, so I see this as the safe choice (but not my current choice, because Epsilon will not overwhelm).

Eta: Will. This resonance has a non-random constant value with several jumps over time. One of the jumps appears to coincide with Alpha's jump. Without any reason to expect a further jump since the last observed data, it is not strong enough to save us.

Zeta: Corazon. Zeta is either zero, or one of two non-zero values. Afaict whether it is zero is random, except that no zero values have been observed for heteropneum amplitudes above 2.27, so I weakly infer that there will not be a non-zero value against Earwax. It seems that which non-zero value occurs depends on which of two or more populations the heteropneum belongs to. The large majority of heteropneums belong to a population with amplitudes that are (before rounding) multiples of 0.142 or something very close to 0.142. These always get a low Zeta value if they get a non-zero result. The minority that are not in this population always get a high Zeta result if they get a non-zero result. Earwax's rounded 3.2 value cannot be obtained by rounding a multiple of 0.142, so we can expect a high Zeta result and for Earwax to be overwhelmed. Thus, I pick this choice, despite my uncertainty as to whether I have enough evidence against a zero result.

A potential wild card is that we don't know Flint's power levels except for alpha, since he never overwhelmed any heteropneums. If there is a way to predict power levels without seeing a strength result with that resonance, this could reveal further opportunities with Flint.

Update on Epsilon resonance:

It's cubic not sine; I can fit Maria's Epsilon data so that the curve rounds to the exactly correct value for every data point, and also for Janelle's data (separately) to round to the exactly correct value; I still need to check if I can make a single curve and multiplier between Maria and Janelle to round exactly for both, but it does look like the curves are at least fairly close to exact multiples of each other.

Interestingly, no x-value rounding needs to be assumed, at least to get the correctly rounding values for Maria and Janelle separately.~~ So, perhaps the x (heteropneum amplitude) values are exact?~~ *No, see below*

The cubic curve *does* take a big dive at high heteropneum amplitudes, but fortunately not until after Earwax's ~3.2 amplitude. Also, the fit for Maria's 0.57 amplitude result of 0.1 is actually around 0.096. Will getting 0.21 suggests he is at least around 2.13 times stronger than Maria using Epsilon and is projected to get at least about 3.85 against a 3.2 amplitude heteropneum. So, Will using Epsilon still looks like a safe pick to survive if we can't find guaranteed survival another way.

edited to add: ~~note that the speculation that the x-axis values might be exact should only apply to the overwhelmed heteropneums - there are the these are the only ones we have epsilon data on and also the only ones we have data to 2 decimal places on.~~* Irrelevant, see below*

All overwhelmed heteropneums that are duplicates in power of another overwhelmed heteropneum is a multiple of an integer from 2 to 22 times 0.142 (the integers probably go higher than this, but Maria stops overwhelming them at that point). This value of 0.142 might not be the exact value, but it makes the numbers round correctly, whereas the rounded values are not exactly the right ratios, so presumably the amplitude values are rounded.

update on Eta resonance:

Eta is simply a multiplication of a character-dependent Eta power level and a date-dependent Eta strength. The date-dependent Eta strength is constant except occasionally it jumps. The lowest strength was from floordays 2-253, then second lowest from 280-297, then next level from 316-~~395~~**495**, then it jumped to the highest level from 516-746, and then dropped to the second highest level from 749-804. (no relevant data in the time gaps). It has never jumped back to a level after going to a different level.

Will's sole eta value of 0.9 occurred on floorday 110 when Eta was at its lowest strength. This means Will is almost as strong as Maria at Eta (everyone else for whom we have Eta data is lower). Unfortunately, this is still not strong enough to beat Earwax if the Eta strength remains, now at floorday 814, at the same level it's been from 749-804.

edited to add: Alpha also shows a jump between floorday 495 and floorday 516. (This is the reason for the bimodal appearance of its distribution). Since this jump occurred in both Alpha and Eta, but the others only occurred in Eta, this suggests that it might have a different cause than the other jumps.

update on Zeta resonance:

Though duplicate amplitude values are common, all verifiably high-tier Zeta values so far have been against heteropneums with unique amplitudes. Admittedly, this is only 5 datapoints.

The good news: Corazon got her Zeta results against duplicate-valued heteropneums, so if the pattern holds true for her, her results have been low-tier so far and she is strong enough to overwhelm Earwax if she gets a high-tier result.

~~The bad news: Earwax has a duplicate amplitude value (as long as the formatting including rounding if applicable is consistent between Earwax and the other entries) so if the pattern holds true for Earwax, there will be no high-tier Zeta result against Earwax. ~~*Wrong, see below*

Edited to add: ~~Earwax and the "duplicate" (Divisor, floorday 389) have not been overwhelmed and are likely rounded to 1 decimal place, but all of our zeta data is from overwhelmed heteropneums, reducing the likely relevance of the "duplicate". ~~*More detailed info below.*

Further addition: I failed to mention earlier that all the non-duplicated entries have either high-tier or zero Zeta results (whereas all the duplicated entries have zero or low-tier Zeta). So, this is very likely significant.

On reviewing the relationships between the duplicated entries for which we have overwhelm results, all are equal to 0.142 multiplied by an integer from 2 to 22 (when that is rounded to 2 decimal places). The 0.142 might not be the exact value but it makes them round correctly. The 22 is probably not the highest but is simply where Maria last overwhelms heteropneums (3.12 amplitude).

Importantly, Earwax's value of 3.2 *cannot* be rounded from a multiple of 0.142 (3.12 is too low, and the next value would be 3.266, which would round up to 3.3). If I try to lower the base value to 0.1419, this already prevents correct rounding of the known values (it would predict the 18x number would round to 2.55 but the 18x number needs to round to 2.56), and this too-low base value still predicts 3.2637 for the next multiple). Thus, Earwax is not from this population of heteropneums, which accounts for all the low tier Zeta results!

However, we still need to find a way to predict if we will get a zero result. Of the 9 non-duplicated overwhelmed heteropneums, there was a zero pilot strength Zeta result in 4 of these cases.

Still further addition: For amplitudes above 2.27, we have no cases of zero zeta. Among the overwhelmed heteropneums (which is all we have Zeta data for) we have 27 total cases of zero Zeta among 150 data points, and there are 41 cases with more than 2.27 amplitude. So, if all are statistically independent, then the probability of this happening by chance is (123/150)x(122/149)x...x(83/110)=0.00006457.

There are a variety of reasons not to be too impressed by this probability number.

- We don't have a very good reason to believe that the results are statistically independent. Duplicates in amplitude values do vary in whether they get zero Zeta (if amplitude less than or equal to 2.27), so they
*might*be statistically independent, though. - I came up with the hypothesis (that Zeta is never zero above some amplitude) after seeing the data, not before, and need to adjust for the prior with possible hindsight bias.
- Even if there is a non-random pattern causing the results, it doesn't necessarily imply that it will hold for Earwax.

That being said, my expectation is that abstractapplic did leave us a way to overwhelm Earwax, so I'm confident enough (barely) to switch my proposed response to Corazon with Zeta. In real life, I'd stick with Will and Epsilon, which I am far more confident in.

The "safe" bet is to have Janelle use Gamma. The distribution has a long tail and she already has a few (3/36) BLA results in the viable range. I give this strategy about 8.3% chance to succeed and at least some chance to dominate.

We could instead have Corazon use Gamma. We only have a few data points, but they could easily be from the same distribution as Janelle's. Possibly a better chance to succeed/dominate, but could also be worse.

My third reasonable-sounding plan is to have Corazon use Zeta. Zeta is weird. Everyone has a very consistent "base" result, except sometimes they get zero instead, and sometimes they get an anomalously high result. E.g. Maria usually gets exactly 2.16, but sometimes gets 7.53 (or zero) instead. Janelle has a "base" of 0.93 and sometimes gets 3.24 (this would be a success, but I think using Gamma gives a better chance). Corazon appears to have a "base" result of 1.98, which is higher than Janelle's and almost as high as Maria's. Janelle got her high result 2/36 times, and Maria got hers 2/104 times. These are different enough that I think it's likely that each pilot has a different chance of getting a high result, so maybe Corazon+Zeta would give a better chance than Janelle+Gamma.

I really hope that the Corazon+Zeta strategy is the best one. I think the puzzle would be better if the "obvious" Janelle+Gamma strategy is not optimal, but past experience with these has taught me that I shouldn't over-think things, so I'm going to go with my first choice and **have Janelle use Gamma Resonance**. If it turns out that Corazon is better, then I'll be pleasantly surprised (and probably dead).

So the 'resonances' are the

Pilot Strength (alpha),Pilot Strength (beta),Pilot Strength (gamma),Pilot Strength (delta),Pilot Strength (epsilon),Pilot Strength (zeta),Pilot Strength (eta)

things, from the data file?

What are floordays?

And how do you distinguish between heteropneums? I.e. how do you know that earwax (weak, benign) and Earwax (powerful, malevolent) are the same?

So the 'resonances' are the

Pilot Strength (alpha),Pilot Strength (beta),Pilot Strength (gamma),Pilot Strength (delta),Pilot Strength (epsilon),Pilot Strength (zeta),Pilot Strength (eta)

things, from the data file?

Correct.

What are floordays?

The Sphere has an idiosyncractic timekeeping system, as regular 24-hour days have been found not to be optimally conducive to keeping your colleagues' souls in their most useful state.

And how do you distinguish between heteropneums? I.e. how do you know that earwax (weak, benign) and Earwax (powerful, malevolent) are the same?

This is achieved via [long, technobabble-laden pseudo-explanation which uses the words 'pneuma', 'resonance', 'fingerprinting', and probably 'quantum' for good measure]. As GM, I can confirm that no heteropneum was ever misidentified.

Did we not record which resonance each pilot *actually* used each time? Usually it's clear

and holistically it's even more clear, but

it'd be nice to have confirmation in those cases where we have all the counterfactual EFS's and I'm pretty sure that data should be available.

I hereby affirm that observations of EFS derived via Branch-Loop Analysis are just as reliable as those gained via direct observation. As such, distinctions based on 'what actually happened' - itself a slippery concept for people who regularly work with multiple timelines - are irrelevant.

To check understanding: if in the first timeline, we use a radiation that doesn't exceed double the heteropneum's EFS, then there remains one timeline. But if we do, there are multiple timelines that aren't distinguishable ... except that the ones with <2x the EFS can't have been the original timeline, because otherwise there wouldn't be branching. I guess I'm confused

If your EFS is more than double a heteropneum's amplitude, you can get a (perfectly accurate) recording of what your EFS would have been had you used a different resonance on it. The in-universe justification for this is that Sphere scientists can observe - and infer things about - alternate timelines under the right conditions.

It seems implausible that all fights would have resolved in the heroes' favor so far. Are there failures that were not recorded, or do we really have that strong of plot armor? It seems like the strategy of "do whatever we've been doing" has a very high prior for success, but on the other hand, we haven't seen multiple attacks in the same day before yet here we are.

Why does it seem implausible? Does this set of 'heroes' not seem like a strong set of pilots for which that is reasonable, or is it something else?

Mostly it's just the conjunction of so many events. Even if each battle has a 99% chance of success (which seems high), the chance to win 291 battles in a row is 5.4%.

The record is a complete list of all fights. Usually heteropneums can be detected, predicted and managed such that the Sphere never needs to have more than one fight per floorday, and they can send a pilot they feel confident will win; Earwax's actions are unprecendented.

Spolier protection

Where we have access to data for Maria for all resonances the amplitude that would have been produce is roughlyn in the same ballpark except for the gamma resonance which is highly variable and is not obviously correlated to anything. The ordering is:

- delta

- alpha

- beta

- zeta ( except for a few where zeta generated 0)

- epsilon

- eta is a little erratic, sometimes above beta, sometimes below zeta, othertimes in between.

Which would suggest that delta should be used, except this pattern clearly doesn't hold for all the other pilots, so assumming the data for one pilot will help us work out what wuld be best for another pilot to use looks dubious.

Janelle has consistently generated higher amplitudes than the other candidates.

With the gamma resonance she generates > 3.2K 3/36 time with a number of other close calls (7 > 3.15 11 > 3)

With the beta resonance she generates > 3.2K 2/96 times (Though a number of others were close 4 > 3.15 10 > 3)

With the zeta resonance she generated > 3.2K 2/36

She has never generated > 3.2K with any of the others.

All the other candidates except Will do best with the alpha resonance, though there is nothing to suggest any of them are likely to generate > 3.2K regardless of which resonance they use.

So Janelle is going to have to try her luck with the gamma resonance and good luck to her, she'll need it.

I am liking this one a *lot*. There are enough hints, some obvious and others more subtle, that indicate many resonance strengths are simpler than they appear at first. TBD: whether I'm reading too much into the data and seeing more hints than actually exist.

What do you think has the best chance of getting in a strike that's double the amplitude of Earwax? (And otherwise ignoring chances of survival - I'm suggesting this partially because if Earwax has suddenly gotten stronger once, if it does so again, then a smaller chance of a larger magnitude seems like a better play.)

The phrase "previously considered benign" was intended to convey an unexpected change in attitude, not amplitude; Earwax did not and will not become stronger. Apologies for the confusion.

Summary: Send Janelle, using Gamma Resonance. Great chance of winning, maybe 60-70%, and half the time you win you double also. Honorable mention to Will's Epsilon Resonance, which if we had more data or a better theory we might be convinced could win 100% of the time, but we just don't have the data or theory to justify it yet.

Alpha: Maria does not show any real amplitude-dependent EFS, and no potential pilot shows 3.2+ EFS. Reject.

Beta: No amplitude-dependence. Maria and Janelle look pretty similar, but all the trainees do far less well, so this is person-dependent. As such probably Janelle's chances of winning are probably best estimated using only her data? Either way, I get somewhere between a 2%-3.5% chance of winning for Janelle and nothing for trainees. We can do better.

Gamma: Very clear dependence on amplitude A, which is good. Each person has some base value B; Maria's is 0.66, Janelle's is 0.89. The EFS generated is of the form B x (1 + k x A), for observed values of k from 0 to 4, and maybe one day we'll see higher. I don't see a way to predict k, but this is quite promising for Janelle. k=0 loses, k=1 wins, and k=2, 3, or 4 wins and doubles. That's a 64% chance of winning overall, with 39% (60% of the time given that we win) of doubling. Going off of observed frequency of Janelle hitting various k; the relative ratios are different enough from Maria's that it's not clear we can combine them in any nice way. They both show large k=0,1,2 and small k=3 and tiny k=4. (None of the trainees has a higher B.)

Delta: Maria's EFS shows a linear upward trend dependent on amplitude. Janelle's is too low to be interesting, and the trainees' are all very low and none suggest having a super-positive slope. Reject.

Epsilon: Ooookay this one's interesting. I didn't get sin to fit as well as a cubic, and I did get a cubic form that can be described with just one parameter varying per Maria vs Janelle, which I thought was likely given how Gamma worked, which means we can generate the entire cubic for Will and check how it does at A=3.2 and... it predicts 3.31 EFS. The Epsilon Resonance is *entirely predictable* given an amplitude. *However*, there are two big problems with simply sending Will to use Epsilon. First, even if our model is precisely right, the precision of our instruments is not perfect, and once we take that into account, Will's Epsilon EFS predictions vary a fair amount, leading to only about a 60% chance of winning. Second, our model is almost certainly wrong, because we haven't found a simple model. So Janelle's Gamma is better than Will's Epsilon in every way according to our current uncertainty.

Zeta: You might get 0, or your base Z, or rarely 3.5 x Z. The problem is that Janelle's 3.5 x Z only just barely beats 3.2 (and doesn't beat 3.25!), and she gets 3.5 x Z maybe like 5% of the time which is << 64%. While Corazon's 3.5 x Z would handily double, it loses otherwise. Again << 64%.

Eta: Janelle's too small here, but Flint has a 2.3, and it looks like the possible EFS's are a base E, or x1.5, or x1.5x1.5, or x1.5x1.5x1.125, or 1.5x1.5x1.125x1.25. If Flint's E=2.3, this might be promising. Unfortunately it seems much more likely that 2.3 is one of the multiples, and if there *is* an amplitude dependence, it's probably one of the high multiples.

I *completely forgot* that since Earwax's actions are unprecedented, we're not entirely confident of its amplitude remaining constant either! Janelle's Gamma has basically the same characteristics at various amplitudes. Will's Epsilon works significantly less often if the new amplitude becomes smaller. A bit more reason to stick with Janelle here.

I think the only big remaining two things that could convince me to switch to Will are (a) figuring out a time-based/less-significant-digits-based pattern which tells us that Janelle's Gamma will have a poor k today/at 3.2 amplitude, or (b) figuring out a simple theory giving the cubic (or whichever) for Maria and Janelle that predicts Will's Epsilon will always win, removing the model uncertainty and the precision uncertainty.

If someone wanted to work on this collaboratively or just let me watch you work for a bit, HMU! I'm an experienced programmer, but fairly inexperienced with data analysis.

Using Python in a Jupyter notebook. Seaborn has a fantastic little function to quickly see pairwise graphs, it's great to begin with. Here's what Maria looks like after sns.pairplot(df[df.name=='Maria N.']): https://drive.google.com/file/d/12Q_11ZTPnyak87EXO89Vbg4am3TXc4px/view?usp=sharing

Documenting my process as I go along:

Step 1: open the csv file. You can do this with programs, or you can use a spreadsheet application.

Step 2: I opted to do this via spreadsheet. Literally copying (the text from the link) and pasting it in worked. (The application added missing rows and columns automatically (no extras of any though. I'll have to add some for analysis).)

Step 3: Saving it. I don't want to mess things up by sorting one row or column by itself and get things out of sync.

Glancing through things, floordays are incremental not cyclical. I.e. day 1, day 2, etc. If you want to

check whether resonances are affected by days of the week, you're going to have to create days of the week

as well as come up with your own mapping between days of the week and 7 resonances. Is this number a coincidence?

First of all, I'm sorting by Pilot, via right clicking the column. This seems to scramble the floornight column, so everything seems to be working right, to figure out who has what resonances down. (Sorting a resonance column to bring the days to the top that maximize it is isn't super simple. Sorting by maximum values, however, is.)

Glancing at Will on non-double events, makes it seem as though it isn't likely the best resonance. Except on double events it looks...best one time, second best the other. Alpha came out higher the other time though. The time it didn't it was narrowly third best. There's an argument to be made for having Will use Alpha,

Nevermind, I was reading an entry from the next pilot. Will, beta resonance seems the way to go (not a lot of data). Best (out of six): 1.7. Best out of overloads: 1.6.

Maria. Does a lot more missions. Seems strong with delta, harder to confirm across all data points considering there's so many. Best out of first 7 is 6.01. Highest probably around 7.

Janelle is tricky. Beta? Gamma? Those 2 seem higher than the others, either way. Highest seems to be 4.66, with gamma.

The rest are short, like Will.

Corazon, alpha. Highest: 2.3, and is an order of magnitude worse with everything else.

Amir, as likely alpha as beta. Overall slightly better with alpha, though the difference is like 0.0x, where x is a number. Highest 2.something.

assuming you can use multiple people at once, but each can only have one resonance

Alpha, corazon

Beta, Amir

Gamma, Janelle

Maria, delta

If you can only send one, in order:

Maria

Janelle

Corazon

Amir

I could write a function to tell if, say, delta is max, and then paste it in, and count how many that's true for versus not...or I could move on. What if floordays are the secret? Chances of survival due seem higher than usual - ish - given the circumstances.

Three hours ago, ace pilot Maria N. returned from heading off a possible attack, exorcising the offending heteropneum so swiftly and thoroughly that your superiors saw fit to posthumously assign it the official designation “Toast”. Two hours ago, while Maria was still catatonic, a heteropneum previously considered benign (amplitude: 3.2 kCept, designation: “Earwax”) teleported onto the Sphere, flooding half of the base and injuring 21% of active personnel before dispersing. Sixteen minutes ago, sensor readings indicated that Earwax is reforming. Your communications are down, and there is no time to evacuate.

Maybe today is a supercharge day, so everyone is stronger, heterpneums and pilots alike! Maybe.

Are some resonances better on some days? Maybe. A formula to check for the best resonance (for days where all resonances are available can work like this: (F2>E2)+(F2>G2)+(F2>H2)+(F2>I2)+(F2>J2) + (F2>K2)

Name the column appropriately, [resonance name] is max, and if it is it will say 6 if it is, and the heteropneum gets overloaded in that row. Repeat as necessary, then move the floor day row over to see if there's a (simple) matchup. If it's a function also involving the pilot, then things are going to get complicated.

Beta resonance is best if Janelle, or (unclear subset of even numbered days which just happens to coincide...). Also happens with Will, once...

And it's also happened on odd numbered days. Doesn't seem to be about days.

Floor day doesn't seem to matter (for beta resonance). Though perhaps a plot of when one resonance is best will yield a different equation, more complicated than day of week?

There's also the possibility of trying to:

- figure out conditional probability of overload (independent of heteropneum strength)

- try plotting the distributions

- try calculating the distributions for the pilots with only a few datapoints, and figure out who to send out on the small chance they will succeed today like they've never succeeded before.

--figure out relationships between resonances, and heteropneum strength, in case that helps

--relationships between days and pilots and resonances

The part I'm not clear on, is, if you were to try to send more than one pilot (say, multiple people on one resonance) how would that work (or could multiple resonances be used in conjunction. This seems unlikely, but the prompt seems to hint at 'you need to try something wild'. Really, at the moment I think

None of these people are likely to beat this thing. Here's a shot in the dark: you go. We have no idea what your resonance is, or how powerful it will be. This suggests 'figure out the most likely/most powerful resonance.' There's also 'don't evacuate everyone just throw who you can in the sub, and hope they can warn ??? about anomalous heteropneums. Maybe a team can be dispatched, that will be able to take it out (and then some) and build your new theory.

Or maybe the submarine has some sort of charge, based off of its last use, that you can make use of. What to look for: effects based on last use.

The other possible analysis change, would be: don't just focus on overload days to try to figure out the distribution, for the best combination.

How did you want to collaborate?/What application did you have in mind for screen sharing?

Feel free to PM me.

It is dark in the submarine, and Maria isn’t ready.

Maria isn’t ready at

all. Maria is in her usual post-battle fugue, disoriented, dissociated, checked-out, can’t come to the phone right now. Sending her to fight in this condition would be both homicide and suicide; also, your boss wouldn’t let you.Janelle, the backup pilot, is ready. That is, she’s physically/psychologically/pneumatologically prepared to go toe-to-toe with a soul-eating monstrosity, throw Beta Resonance at it, and almost certainly die. But in the sense of having a >5% chance to successfully protect herself and her colleagues from the aforementioned soul consumption, Janelle is not ready.

There are four other viable volunteers: Amir, Corazon, Flint, and Will. None of these pseudo-under-understudies have so much as a double-digit number of missions under their belt, and none of them have ever faced an adversary half as strong as the one you’re dealing with. In other words, they’re not ready either.

You are Ratio Tile, a scientist working at the Sphere, a deep-sea research facility dedicated to studying mysterious – and frequently aggressive – accumulations of soul energy called heteropneums.

Youare ready. Or, at least, you’d better be.Three hours ago, ace pilot Maria N. returned from heading off a possible attack, exorcising the offending heteropneum so swiftly and thoroughly that your superiors saw fit to posthumously assign it the official designation “Toast”. Two hours ago, while Maria was still catatonic, a heteropneum previously considered benign (amplitude: 3.2 kCept, designation: “Earwax”) teleported onto the Sphere, flooding half of the base and injuring 21% of active personnel before dispersing. Sixteen minutes ago, sensor readings indicated that Earwax is reforming. Your communications are down, and there is no time to evacuate.

Dr. Cept was incapacitated in Earwax’s first attack. Cecelia is on her annual visit to the surface, visiting friends and family, unaware of her colleagues’ peril. In their absence, the decision of which pilot to send and which type of Resonance they should use falls to you and you alone.

Your boss seems to think that you can use Soul Coherence Theory to choose the pilot/Resonance combination most likely to produce >3.2 kCept of Effective Field Strength and therefore save everyone. Unfortunately, Soul Coherence Theory straightforwardly predicts that you’re almost certainly all going to die; though it also rules out such observed phenomena as Pseudo-Refraction, heteropneums with amplitudes over 4.92 kCept (no, Cept, the instruments are

not‘potentially unreliable’), and – topically – heteropneums vanishing and reappearing the way Earwax did. So instead, you’re going to look at the data for all fights thus far with fresh eyes, treating this as a pure analysis problem.There is one other relevant factor. (Really, Ratio? You’re pulling this

now?) When a pilot overwhelms a heteropneum by generating an Effective Field Strength of more than double its amplitude, you get readings of much greater precision, and can use Branch-Loop Analysis to determine how much EFSwouldhave been generated if the pilot had used a different Resonance. Earwax is exhibiting previously unseen behaviours and abilities; if you can not only defeat but dominate it, you justknowthat data will help you construct an alternative to Soul Coherence Theory. And this isn’t (just) your (boundless, inappropriate, potentially lethal) curiosity talking: figuring out how this creature works could be key to protecting the Sphere against future attacks.You are Ratio Tile. You have five possible pilots, seven known Resonances, one functioning submarine, and one chance. You are ready. Who will you send, and how will you have them fight?

Notes:

I’ll be posting an interactive letting you test your decision, along with an explanation of how I generated the dataset, sometime next Tuesday. I’m giving you a week, but the task shouldn’t take more than a few hours; use Excel, R, Python, the Summer Diary, or whatever other tools you think are appropriate. Let me know in the comments if you have any questions about the scenario.

If you want to investigate collaboratively and/or call your decisions in advance, feel free to do so in the comments; however, please use spoiler tags or rot13 when sharing inferences/strategies/decisions, so people intending to fly solo can look for clarifications without being spoiled. Please also spoiler or rot13 any Floornight plot points.