Impossible Theorem (Guide)
On Theorising About the Impossible
Created by Hannah
Reviewed & Improved by tirerim
This guide will go over the two ways to obtain an Impossible Theorem, with cost analysis and ways to optimize the process.
Impossible Theorems are used in various places, sometimes expended, sometimes not. Of course, for spoiler reasons I won't mention them here, but if you are curious, you can find the list of actions which require an Impossible Theorem.
There are two different methods to create an Impossible Theorem currently in the game: researching it in your lab, or locating one outright. It is almost always better to go with the former, unless you have an incredible excess of 
Searing Enigmas, endgame levels of 
Watchful, no care for profitability, and no fear of death. However, both methods will be included in this guide for sake of completeness.
Researching[edit]
Requirements[edit]
Naturally, researching something known to be "Impossible" will have a few prerequisites:
7 x Both of these are covered in this (quite comprehensive) guide.
Additionally, you will require
- a source of
Parabolan Research
Speeding up the Research[edit]
13000 
Laboratory Research is a lot… if only there was a way to speed up the progress?
It turns out, there is! 
Review the Prior Literature > Relate this problem to a past Enigma will trade 1 Searing Enigma for 500 Laboratory Research (so long as you have more than 500 research left to go). While it is technically possible to spend up to 26 Searing Enigmas to trade directly for 13000 Laboratory Research, this requires drawing Review the Prior Literature 26 times in a row. Rather, ~20 Searing Enigmas is safer bet on how many will be utilized, though this of course will depend on how lucky you are with card draws.
This does raise the question, though: Is it worth doing the trade in the first place? The answer depends on how efficiently you can grind Searing Enigmas.
Each Searing Enigma takes 1 action to convert into 500 Laboratory Research. As such, if S is the number of actions per enigma, 500/(S+1) is the equivalent Laboratory Research per action. For example, if it takes 20 actions to get a Searing Enigma, that's 500/(20+1) = 500/21 ≈ 23.8. Compare this to the typical research you get by using your lab cards (for most lategame labs this will be in the 20~25 range, if well-optimized it can get closer to 30). If the number you get through Searing Enigmas is greater than the typical number through Laboratory cards, then it is worthwhile to trade in research.
Hunting[edit]
Requirements[edit]
Hunting is much simpler than researching—however, that's not to say it's easier. The requirements are straightforward:
- Access to
The University - 49 x Searing Enigma
9 x Sudden Insight (10 x if you're using one to increase your chances)- and a dream that RNG favours you in that moment
Considerations[edit]
One important thing to be aware of is you are extremely likely to die at least once through this method and, additionally, it costs almost twice as many Searing Enigmas as researching does even if you succeed first-try.
Here is a calculator that will give the expected results of trying to gain an 
Impossible Theorem through hunting, given your Watchful and if you are using Sudden Insights for second chances:
name = Average Hunting Results per Theorem module = ActionCost modulefunc = calcCost form = hunting1Param result = hunting1Result suggestns = 0 param = act | Action Cost | 9 | hidden param = stat | Stat Value | 100 | int param = chance | Second Chances? | DISABLED | check param = ctype | Second Chance Name | | hidden param = diff | Difficulty | 500 | hidden param = sucs | SuccessParams | 3 | hidden | 3 | 1=squal1,snum1; 2=squal1,snum1,squal2,snum2; 3=squal1,snum1,squal2,snum2,squal3,snum3; 4=squal1,snum1,squal2,snum2,squal3,snum3,squal4,snum4; 5=squal1,snum1,squal2,snum2,squal3,snum3,squal4,snum4,squal5,snum5; 6=squal1,snum1,squal2,snum2,squal3,snum3,squal4,snum4,squal5,snum5,squal6,snum6 param = squal1 | Quality/Item/Menace Name 1 | Impossible Theorems | hidden param = snum1 | Quality/Item/Menace Gain 1 | 1 | hidden | -Infinity - Infinity param = squal2 | Quality/Item/Menace Name 2 | Sudden Insights | hidden param = snum2 | Quality/Item/Menace Gain 2 | -9 | hidden | -Infinity - Infinity param = squal3 | Quality/Item/Menace Name 3 | Searing Enigmas | hidden param = snum3 | Quality/Item/Menace Gain 3 | -49 | hidden | -Infinity - Infinity param = squal4 | Quality/Item/Menace Name 4 | | hidden param = snum4 | Quality/Item/Menace Gain 4 | | hidden | -Infinity - Infinity param = squal5 | Quality/Item/Menace Name 5 | | hidden param = snum5 | Quality/Item/Menace Gain 5 | | hidden | -Infinity - Infinity param = squal6 | Quality/Item/Menace Name 6 | | hidden param = snum6 | Quality/Item/Menace Gain 6 | | hidden | -Infinity - Infinity param = fals | FailureParams | 5 | hidden | 5 | 1=qual1,num1; 2=qual1,num1,qual2,num2; 3=qual1,num1,qual2,num2,qual3,num3; 4=qual1,num1,qual2,num2,qual3,num3,qual4,num4; 5=qual1,num1,qual2,num2,qual3,num3,qual4,num4,qual5,num5; 6=qual1,num1,qual2,num2,qual3,num3,qual4,num4,qual5,num5,qual6,num6 param = qual1 | Quality/Item/Menace Name 1 | Sudden Insights | hidden param = num1 | Quality/Item/Menace Gain 1 | -3.5 | hidden | -Infinity - Infinity param = qual2 | Quality/Item/Menace Name 2 | Searing Enigmas | hidden param = num2 | Quality/Item/Menace Gain 2 | -1 | hidden | -Infinity - Infinity param = qual3 | Quality/Item/Menace Name 3 | Echoes | hidden param = num3 | Quality/Item/Menace Gain 3 | -100 | hidden | -Infinity - Infinity param = qual4 | Quality/Item/Menace Name 4 | trips to the boatman (+72 CP wounds each) | hidden param = num4 | Quality/Item/Menace Gain 4 | 1 | hidden | -Infinity - Infinity param = qual5 | Quality/Item/Menace Name 5 | CP Nightmares | hidden param = num5 | Quality/Item/Menace Gain 5 | 7.5 | hidden | -Infinity - Infinity param = qual6 | Quality/Item/Menace Name 6 | | hidden param = num6 | Quality/Item/Menace Gain 6 | | hidden | -Infinity - Infinity
