Hi Shaq! First of all, congratulations on the work you’ve done. As an architect, I know very well what it means to spend time on this kind of thing, the hours just fly by without you even noticing!
I also wanted to share an interesting video with you about the famous Zodiac composite sketch. It includes some thoughts on the possibility that the sketch may not fully reflect what the survivors actually saw.
Here’s the link: https://www.youtube.com/watch?v=taL5qoQtlp8
The interesting part starts at around 57:15. Unfortunately, the video is in Italian, but you should be able to use automatically translated subtitles.
Have a great day!
Given that we now have determinable eye-to-subject distances and angles obtainable from our model, we can go on to make some broad deductions about what degree of feature detail we might accept as having been realistically discernible by the Robbins witnesses. Specifically, we might want to ask whether the viewing conditions were such that we can have confidence in the rendering of the composite sketches that were produced and, if only so to a limited degree, then to what limit.
As our research above led us to note, a common standard for the minimal angle of resolution (MAR) for 20-20 vision under ideal viewing conditions is 1 arcminute (1′), or a sixtieth of a degree. As pointed out, however, we cannot assume such ideal viewing conditions as being those experienced by our witnesses, but what we can do is perform a graded analysis to steadily introduce degrees of visual separation degradation, taking this down to, say, 2′ and even 4′.
For our modelling, then, we will introduce something we can call a ‘Resolution Factor’ (RF). For any given feature of our scene, we can calculate an RF using:
Using this formula, we will be able to extract precise measurements from within our model, deduce a resolution factor for each of our key features of interest under the various minimal angles of resolution and then grade them according to a deterministic set of interpretive bands, which we can define next.
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)
For our interpretive banding of the extent to which specific features may be clearly discernible under our chosen visual conditions, we will make use of the following classification:
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)
Here, then, are the results we would obtain for our three candidate MARs of 1′, 2′ and 4′ for a figure of height 5′ 8′′ standing 45.70 ft away in an unobstructed face-on view.
Idealised 1′ resolution
| Feature | Angular extent | RF at 1′ | Interpretation |
|---|---|---|---|
| Full figure height | 425.7′ | 425.7 | Clearly shaped |
| Maximum body width / build | 166.8′ | 166.8 | Clearly shaped |
| Shoulder width | 144.4′ | 144.4 | Clearly shaped |
| Head height | 56.0′ | 56.0 | Clearly shaped |
| Head width | 50.1′ | 50.1 | Clearly shaped |
| Glasses — overall width | 43.6′ | 43.6 | Clearly shaped |
| Eye-to-eye centre spacing | 19.8′ | 19.8 | Clearly shaped |
| Mouth width | 18.3′ | 18.3 | Clearly shaped |
| Nose length | 13.0′ | 13.0 | Clearly shaped |
| Nose width | 12.7′ | 12.7 | Clearly shaped |
| Spectacle lens/frame height | 10.0′ | 10.0 | Clearly shaped |
| Single eye aperture width | 7.4′ | 7.4 | Coarsely shaped |
| Lip vertical thickness | 3.2′ | 3.2 | Distinct mark |
| Spectacle-frame/temple thickness | 1.5′ | 1.5 | Marginal |
Baseline 2′ resolution
| Feature | Angular extent | RF at 2′ | Interpretation |
|---|---|---|---|
| Full figure height | 425.7′ | 212.9 | Clearly shaped |
| Maximum body width / build | 166.8′ | 83.4 | Clearly shaped |
| Shoulder width | 144.4′ | 72.2 | Clearly shaped |
| Head height | 56.0′ | 28.0 | Clearly shaped |
| Head width | 50.1′ | 25.1 | Clearly shaped |
| Glasses — overall width | 43.6′ | 21.8 | Clearly shaped |
| Eye-to-eye centre spacing | 19.8′ | 9.9 | Coarsely shaped |
| Mouth width | 18.3′ | 9.1 | Coarsely shaped |
| Nose length | 13.0′ | 6.5 | Coarsely shaped |
| Nose width | 12.7′ | 6.4 | Coarsely shaped |
| Spectacle lens/frame height | 10.0′ | 5.0 | Coarsely shaped |
| Single eye aperture width | 7.4′ | 3.7 | Distinct mark |
| Lip vertical thickness | 3.2′ | 1.6 | Marginal |
| Spectacle-frame/temple thickness | 1.5′ | 0.7 | Not separately resolved |
Degraded 4′ resolution
| Feature | Angular extent | RF at 4′ | Interpretation |
|---|---|---|---|
| Full figure height | 425.7′ | 106.4 | Clearly shaped |
| Maximum body width / build | 166.8′ | 41.7 | Clearly shaped |
| Shoulder width | 144.4′ | 36.1 | Clearly shaped |
| Head height | 56.0′ | 14.0 | Clearly shaped |
| Head width | 50.1′ | 12.5 | Clearly shaped |
| Glasses — overall width | 43.6′ | 10.9 | Clearly shaped |
| Eye-to-eye centre spacing | 19.8′ | 5.0 | Coarsely shaped |
| Mouth width | 18.3′ | 4.6 | Distinct mark |
| Nose length | 13.0′ | 3.2 | Distinct mark |
| Nose width | 12.7′ | 3.2 | Distinct mark |
| Spectacle lens/frame height | 10.0′ | 2.5 | Distinct mark |
| Single eye aperture width | 7.4′ | 1.9 | Marginal |
| Lip vertical thickness | 3.2′ | 0.8 | Not separately resolved |
| Spectacle-frame/temple thickness | 1.5′ | 0.4 | Not separately resolved |
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)
Taking this data, we can go one step further and offer it in visual representation, one rendering for each MAR of 1′, 2′ and 4′, respectively. It needs to be clearly noted, however, that the following images are not in any sense intended to convey how our figure would appear to our witnesses’ vision. Rather, they convey the specific degradations we have identified in visual acuity and the ability to distinguish and describe specific features.
For the three cases considered, we have:
“This isn’t right! It’s not even wrong!”—Wolfgang Pauli (1900–1958)