# D&D.Sci(-fi): Colonizing the SuperHyperSphere [Evaluation and Ruleset]

This is a followup to [the D&D.Sci post](https://www.lesswrong.com/posts/T3iG4MQ76988JBfkq/d-and-d-sci-fi-colonizing-the-superhypersphere) I made ten days ago; if you haven’t already read it, you should do so now before spoiling yourself.

[Here](https://h-b-p.github.io/d-and-d-sci-SuperHyperSphere/) is the web interactive I built to let you evaluate your solution; below is an explanation of the rules used to generate the dataset (my full generation code is available [here](https://github.com/H-B-P/d-and-d-sci-SuperHyperSphere/blob/main/gen.py), in case you’re curious about details I omitted). You’ll probably want to test your answer before reading any further.

Ruleset
=======

By default, a ZPPG will produce 100% of Standard Output; however, various phenomena will affect this, usually for the worse. Each phenomenon multiplies the expected output by a given quantity; these multipliers are applied cumulatively.

Actual output is expected output multiplied by N(1, 0.0057); a negligible randomness nudging guesses off by half a percentage point.

Coordinates
-----------

### Longitude

ZPPG output is greatest when Longitude=52.46, and decreases as you move away from that angle.

![](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/78419f28c025b10e0d89d256b798f2902b51234b06413a99.png)

### Latitude

ZPPG output decreases by sharply when Latitude is within 36 degrees of the equator.

![](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/30dc26510588f18defbb56a24a1c4bc02751f38ba6813830.png)

### Shortitude

ZPPG output decreases slightly when Shortitude>45 degrees.

![](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/a6202e8813eda721bdce7ce02505f97534ab77fdfa645b86.png)

### Deltitude

Deltitude has absolutely no effect on anything.

Smells
------

Somewhat weird smells greatly decrease expected output; extremely weird smells only decrease it by ~6%.

![](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/455ffb221698279cd09e833a36f50ed8a1400347e0884ac5.png)

Tastes
------

Bizarre-tasting air is to be expected on the SuperHyperSphere: air with no taste suggests one of the cleverer native lifeforms is trying to lure you to build there so it can siphon power. (Conversely, burning air suggests the presence of a dimensional distortion which actually helps ZPPG performance.)

![](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/a88eb642cd373f1fc023ce90ec7e03573923c11981d649af.png)

Feng Shui
---------

ZPPGs work better in places with good Feng Shui.

![](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/254a16330029e685966b1433979d18d47d21d078dbd26bbe.png)

Sounds
------

Sounds are always bad news: they mean native lifeforms are present and will impair a ZPPG built on that site.

(There is one apparent exception, Otherworldly Skittering; this is because the Multiversal Spiders who cause this noise reliably rid the area of the more damaging Time Flies and their Unnatural Buzzing; however, Silence is still preferable to every sound.)

![](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/d66fa835d545843bd19b84fb48b14a677acb2364a1c69a5d.png)

Pi
--

ZPPGs function optimally when Pi=3.15; moving away from that optimum decreases ZPPG effectiveness linearly.

![](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/e9319a99b6864d748c9274cb42909f370330ae5464ec5e1e.png)

Murphy
------

ZPPGs function optimally when M=0; increasing from that optimum decreases ZPPG effectiveness cubically.

![](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/7feaa144bcfb98a604a291635fa375632c5d9e3a05a85730.png)

Strategy
========

There are 40 sites in cleared\_sites\_data.csv which have >100% of Standard Output, and the tiny amount of randomness between explanatory and dependent variables means that it’s possible to identify most of these from patterns in ZPPG\_performance\_data.csv; therefore, it’s reasonable to try and make your point to your superiors in the Empire.

Reflections
===========

This game centered on a simple, cruel trick: most of our more common tools (computational, statistical and conceptual) implicitly assume that all feature effects can and should be modelled as additive. When applied to a problem where feature effects multiply – or use any other non-additive linkage – these tools predictably screw up, systematically mis-estimating extreme values and/or adding endless epicycles in an attempt to make up for using the wrong paradigm.

Congratulations to aphyer, simon and Unnamed for dodging my planned pitfall and separately reaching perfect answers: if you want to know how they managed it, their comments on the original post are impressively thorough and refreshingly reflective (in particular, aphyer has an [excellent](https://www.lesswrong.com/posts/rAnS5jCQ5r87eMvus/d-and-d-sci-hypersphere-analysis-part-1-datafields-and) [series](https://www.lesswrong.com/posts/F5nkk9dtypicyJY5M/d-and-d-sci-hypersphere-analysis-part-2-nonlinear-effects) [of](https://www.lesswrong.com/posts/gs9yhwB3LW2CM8rvS/d-and-d-sci-hypersphere-analysis-part-3-beat-it-with-linear) [posts](https://www.lesswrong.com/posts/tFYec8tBHQbLZ72ES/d-and-d-sci-hypersphere-analysis-part-4-fine-tuning-and) walking readers step-by-step through his analysis). Congratulations also to everyone who figured out that they couldn’t figure things out, and selected the safer option. (Congratulations and commiserations to Yonge, who managed to produce an answer which *would* have achieved >100% average performance, but was misled by the aforementioned systematic mis-estimations into thinking it wouldn't.)

This challenge was small, obnoxiously straightforward[^41vav9lm4dy] once you know the gimmick behind it, almost actively hostile to players who couldn’t figure that gimmick out, and contained one (thankfully, not game-ruining) outright mistake on my part[^pn8xsmzrbn]. Despite all this, I think it’s my best work in the genre since [Voyages of The Grey Swan](https://www.lesswrong.com/posts/S3LKfRtYxhjXyWHgN/d-and-d-sci-april-2021-voyages-of-the-gray-swan): to my mind, there’s no educational tool quite like a puzzle built to trip you up for making a (important, prevalent) false assumption. Feedback on this point, and all other points, is greatly appreciated.

Scheduling
==========

~~My hope is to run the next game from Feb 2^nd^ to Feb 12^th^; my significantly more tenuous hope is to run a game starting on the first Friday of every month until I run out of points to make and axes to grind. Unfortunately, my current circumstances make these hopes, not plans or promises; still, I’d put subjective probability you’ll get something at the start of next month above 70%; watch this space.~~

Best-laid plans did as they do; the next one will be out when it's out.

[^41vav9lm4dy]: I here extenuate myself on artistic and pedagogical grounds; the toyishness of the scenario means a player approximating a solution with a max_depth=6 additive Decision Forest will later get to look at the generation code and discover that there are no interactions whatsoever when viewed through the correct lens. 

[^pn8xsmzrbn]: While I can justify it in-universe as the Empire having a weird coordinate system and/or the SuperHyperSphere being non-Euclidean, the Doylist explanation for the dearth of sites near the Equator(s) is just “the GM screwed up”. Sorry!