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.
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.