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Haeckel's Mistakes: Measuring Idealization Between Two Registers

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Haeckel's Mistakes: Measuring Idealization Between Two Registers

The same hand drew the same radiolarians twice: once as science, once as art. The plan is to train a LoRA on each register to isolate the idealization between them, turning "Haeckel exaggerated symmetry" from a century-old argument into a measurable vector.

ConceptStage: Not Yet Built
2Registers, Same Hand
1887Challenger Report
1899–1904Kunstformen
n-foldSymmetry Metric

Why Not the Embryo Plates

The famous Haeckel controversy is about a different corpus entirely: the 1874 embryo grids in Anthropogenie and Natürliche Schöpfungsgeschichte. Michael Richardson's team re-photographed embryos of the same species and ages Haeckel drew and found they often looked strikingly different: Haeckel had exaggerated the similarity and hadn't drawn to scale. It's genuinely contested, though: Robert Richards argued in 2009 that the comparison wasn't fair, since Haeckel's drawings explicitly excluded yolk sacs and maternal material that Richardson's photographs included, which alone would make the embryos look more different than they are.

That's not this project's corpus, and it doesn't need to be. Trying to adjudicate a century-old fraud allegation from photographs on both sides of a real methodological dispute is a bad use of a portfolio project, and most of what's discoverable about it online has been colonized by creationist framing anyway. What's actually usable is a much cleaner version of the same underlying question, did Haeckel idealize, sitting entirely inside the existing, uncontested Kunstformen/radiolaria corpus.

Haeckel vs. Haeckel

Haeckel drew the same radiolarians twice, in two registers, twelve years apart. Once for the 1887 Challenger Report: a scientific monograph, drawn to document specimens collected on HMS Challenger's survey voyages. Once again for Kunstformen der Natur (1899-1904): the same organisms, redrawn for an art/nature-philosophy audience, radially symmetric and lithographed onto a warm cream background.

Same artist, same species, two different jobs the drawing was doing. That would give a clean, license-free way to isolate an idealization signal: train one LoRA adapter on the Challenger plates and a second on the Kunstformen plates, both against the same Stable Diffusion base, then treat the vector between the two adapters' weights as the aestheticization direction (the specific stylistic push from "documenting a specimen" to "composing a plate"). No modern photography, no embryo controversy, no licensing question: both corpora are public domain.

The Measurement

The hypothesis worth testing: diffusion models regress toward the mode of their training distribution, so a LoRA trained on Kunstformen should produce radiolarians that are more symmetric than Haeckel's own Kunstformen plates ("more Haeckel than Haeckel"). If idealization is really what separates the two registers, sampling from a model trained on the more idealized register should push past it, not just match it.

The plan is to measure this directly rather than by eye: segment each specimen out of its plate, then compute its rotational symmetry order and its radial deviation from perfect n-fold symmetry, run across three distributions (the Challenger plates, the Kunstformen plates, and a batch of model samples from the Kunstformen-trained LoRA). If Challenger comes out least symmetric, Kunstformen sits in the middle, and the model's own samples land past both, that would be a monotonic result and the one graph the whole project needs to make its point.

Steering Back

Once the idealization direction is identified as the vector between the two adapters, the natural next step is to run it in reverse: negate it and apply it to the Kunstformen-trained model's generations, pushing samples back toward the Challenger register instead. If the direction is real, that should produce de-idealized plates: specimens that look measurably closer to a field report than to a decorative print, generated from a model that was only ever trained on the decorative print.

Sources are the same public-domain material haeckel-lora already used, plus the Challenger side: 300 dpi scans of all 100 Kunstformen plates are on the Internet Archive (via BioLib), and the Biodiversity Heritage Library holds both the original 1887 Challenger volumes and the 1899–1904 Kunstformen volumes with full JP2/PDF downloads.

PyTorchDiffusersLoRAscikit-imageOpenCV

What This Will Prove, Once Built

Task-Vector / Adapter Analysis

Scoped around isolating a stylistic direction by training two LoRA adapters on the same subject in two registers and taking the vector between their weights, rather than hand-engineering a symmetry-idealization filter.

Quantifying a Qualitative Claim

Designed to turn "Haeckel idealized his subjects" from an art-historical argument into a measurable pipeline (segmentation, rotational symmetry order, radial deviation, run across three distributions) instead of an eyeballed comparison.

Responsible Framing of a Contested Source

Recognizes that the well-known embryo-fraud controversy is a separate, genuinely disputed corpus, and scopes the project to a cleaner question inside uncontested material instead of wading into a dispute it doesn't need.

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