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Programmatically compute similarity between zodiacs - Printable Version

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Programmatically compute similarity between zodiacs - Gioynich - 17-01-2021

Hello everyone!
I have been working on a script that computes a similarity score for pairs of zodiacs.
Unfortunately, I don't have much time to work on this anymore, so I thought I would share everything I currently have with the community in case anyone is interested.

The tl;dr of what I am doing is:
  • There are 11 components, one for each zodiac sign present in the VMS, plus one for generic characteristics (e.g. number of signs per page, type of frames around signs, etc.)
  • For each component, I defined a list of characteristics to be compared (e.g. how many limbs does Scorpio have? Is Taurus eating something? etc.)
  • For 100 zodiacs (thanks Marco for providing the list and for your feedback!) I looked at all the signs and recorded their characteristics.
  • I defined a similarity function that is tuned for each characteristic but, for most of them, it returns 1 if the values are the same, 0 otherwise.
  • I subjectively gave more weight to some characteristics and gave more weight to characteristics that are rare across the whole dataset (e.g. virgo being a woman is pretty common, so it's assigned less weight).
  • For each couple of manuscripts in the dataset, I compute a similarity score for each sign and an overall similarity score (average of the 11 components).
Here are some findings:

The most (overall) similar zodiacs to the Voynich's are, in order:
  1. You are not allowed to view links. Register or Login to view. (1450-1460, Freiburg, Germany)
  2. You are not allowed to view links. Register or Login to view. (1430-1450, South Germany)
  3. You are not allowed to view links. Register or Login to view. (1400-1450, Bavaria, Germany)
  4. You are not allowed to view links. Register or Login to view. (1250, South Germany)
  5. You are not allowed to view links. Register or Login to view. (1450-1499, Iran)
The most similar zodiacs for each sign are:

Aries:
You are not allowed to view links. Register or Login to view. (1200, Soissons, France)
   

Taurus
[font=Tahoma, Verdana, Arial, sans-serif]You are not allowed to view links. Register or Login to view. ([/font]1400-1450, Bavaria, Germany)
   

Gemini
You are not allowed to view links. Register or Login to view. (1250, Amiens, France) 
and (tie)
You are not allowed to view links. Register or Login to view. (1444, South Germany)
[font=Tahoma, Verdana, Arial, sans-serif]     [/font]

[font=Tahoma, Verdana, Arial, sans-serif]Cancer[/font]
[font=Tahoma, Verdana, Arial, sans-serif]A lot of ties, because most of them look the same[/font]

[font=Tahoma, Verdana, Arial, sans-serif]Leo[/font]
[font=Tahoma, Verdana, Arial, sans-serif]You are not allowed to view links. Register or Login to view. (1480, Ahun, France)[/font]
[font=Tahoma, Verdana, Arial, sans-serif]and (tie)[/font]
[font=Tahoma, Verdana, Arial, sans-serif]You are not allowed to view links. Register or Login to view. (1412-1416, France)[/font]
[font=Tahoma, Verdana, Arial, sans-serif][font=Tahoma, Verdana, Arial, sans-serif]     [/font][/font]

[font=Tahoma, Verdana, Arial, sans-serif][font=Tahoma, Verdana, Arial, sans-serif]Virgo[/font][/font]
[font=Tahoma, Verdana, Arial, sans-serif][font=Tahoma, Verdana, Arial, sans-serif]You are not allowed to view links. Register or Login to view. (1230, Sicily, Italy)[/font][/font]
[font=Tahoma, Verdana, Arial, sans-serif][font=Tahoma, Verdana, Arial, sans-serif][font=Tahoma, Verdana, Arial, sans-serif]     [/font][/font][/font]

Libra
A bunch of ties, not really distinctive

Scorpio
You are not allowed to view links. Register or Login to view. (1250, South Germany)
   

Sagittarius
[font=Tahoma, Verdana, Arial, sans-serif][font=Tahoma, Verdana, Arial, sans-serif][font=Tahoma, Verdana, Arial, sans-serif]You are not allowed to view links. Register or Login to view. ([/font][/font][/font]1400-1450, Bavaria, Germany)
[font=Tahoma, Verdana, Arial, sans-serif]and (tie)[/font]
[font=Tahoma, Verdana, Arial, sans-serif]You are not allowed to view links. Register or Login to view. (1425, Lake Constance, Switzerland)[/font]
[font=Tahoma, Verdana, Arial, sans-serif]and (tie)[/font]
[font=Tahoma, Verdana, Arial, sans-serif]You are not allowed to view links. Register or Login to view. (1463, Konstanz, Switzerland)[/font]
[font=Tahoma, Verdana, Arial, sans-serif][font=Tahoma, Verdana, Arial, sans-serif]     [/font][/font]

Pisces
You are not allowed to view links. Register or Login to view. [font=Tahoma, Verdana, Arial, sans-serif](1430-1450, South Germany)[/font]
[font=Tahoma, Verdana, Arial, sans-serif]and (tie)[/font]
You are not allowed to view links. Register or Login to view.[font=Tahoma, Verdana, Arial, sans-serif] (1250, South Germany)[/font]
   

The visualization below instead shows the graph of similarities between all zodiacs, to give you a sense of the "clusters" that exist out there. It's pretty tricky to explain but basically each node is a zodiac, they are connected by an edge if their similarity score is greater than a given value, and they have been laid out using a force-based graph visualization algorithm. The size of the edges is proportional to their strength (similarity).
Note that zodiacs might appear close together even if they are not strongly connected, so make sure you look at the edges.

Full-res image available You are not allowed to view links. Register or Login to view..

   

You are not allowed to view links. Register or Login to view. contains the following files: 
  • 'zodiac.csv': this is a database of all the zodiacs I found. For each of them, you will find the characteristics of each sign, some general characteristics (location, time period, etc.), and a link to the image of each sign. You can open it using Excel.
  • 'similarities.csv': this is the output of my script and it contains the similarity scores for all couples of manuscripts.
  • 'zodiacs_similarities.py': is my (Python) script.
  • 'edges.csv' and 'nodes.csv' are also generated by my script and can be imported using the Gephi software to visualize the network of zodiacs.
A few last notes:
  • I did this analysis without any theories in mind
  • There is a lot of subjectivity going on my script. Feel free to play around with things, change values, add new zodiacs to the database, etc.
  • My code is pretty bad, I wrote it optimizing for speed, but I tried to add as many comments as possible.
  • If you have any questions, I am more than happy to answer them


RE: Programmatically compute similarity between zodiacs - MarcoP - 18-01-2021

Thank you, Gioynich!
I love the idea of a quantitative approach to this kind of analysis. As you say, there still is a large subjective factor, but at least one tries to make their subjective choices more transparent. I hope that sooner or later an art historian will write about the Voynich zodiac in a more extensive way: what authoritative researchers like Ewa Sniezynska-Stolot or Dieter Blume have so far released only are short statements (discussed by Rene You are not allowed to view links. Register or Login to view.).

I am a little surprised to see an Arabic Al-Sufi ms among the top five overall best matches. That tradition includes systematic duplication of zodiac constellations (which are displayed in both the "from earth" and "from heaven" points of view): this results in a double cancer; but then cancer itself is the classical crab, rather than the Northern crayfish. I wonder why your method points out this source as particularly relevant: I can probably find answers in the archive you attached but I haven't tried yet. In the much simpler analysis I posted on You are not allowed to view links. Register or Login to view. in 2016, that ms was ranked 93 among the set of 130 zodiacs I considered.

Seeing now the St Gall Sagittarius, after all the work that Koen has done about costumes and proportions, I find this specific parallel even more striking than I did before. The double circular frame also contributes.

RE: Programmatically compute similarity between zodiacs - Gioynich - 18-01-2021

Quote:I am a little surprised to see an Arabic Al-Sufi ms among the top five overall best matches. That tradition includes systematic duplication of zodiac constellations (which are displayed in both the "from earth" and "from heaven" points of view): this results in a double cancer; but then cancer itself is the classical crab, rather than the Northern crayfish. I wonder why your method points out this source as particularly relevant: I can probably find answers in the archive you attached but I haven't tried yet. In the much simpler analysis I posted on You are not allowed to view links. Register or Login to view. in 2016, that ms was ranked 93 among the set of 130 zodiacs I considered.

Hi Marco,

Al-Sufi is interesting, because it gets very low scores for some signs (e.g. Aries and Gemini), but it ranks pretty high on other components, that is:

- Zodiac: 4th most similar (in a tie with other 5 manuscripts)
- Leo: 3rd (in a tie with other two manuscripts)
[font=Tahoma, Verdana, Arial, sans-serif][font=Tahoma, Verdana, Arial, sans-serif]- Virgo: 6th[/font][/font]
[font=Tahoma, Verdana, Arial, sans-serif][font=Tahoma, Verdana, Arial, sans-serif][font=Tahoma, Verdana, Arial, sans-serif]- Scorpio: 10th[/font][/font][/font]

The 'zodiac' component has just 4 attributes (number of signs per page, which sign starts the zodiac, presence of stars, and shape of the frames around the signs). Two attributes (number of signs per page and presence of stars) match.

For Leo:
- they both have their tongue out
- they are both not crouching
- they both have a front leg raised
- they both have a non-full mane (rare attribute, which means it boosts the similarity score)
   

For Virgo:
- they are both female
- they are both dressed
- they both have a star in their hand (sure, that's subjective, but it's a rare attribute)
- they are both not sitting or crouching (but I am not sure about the Voynich virgo)
[font=Tahoma, Verdana, Arial, sans-serif]     [/font]

[font=Tahoma, Verdana, Arial, sans-serif]For Scorpio, the only reason why they are considered pretty similar is the presence of stars (sure, in a completely different number and configuration), which is a rare attribute, so Al-Sufi's Scorpio doesn't rank as high as non-scorpions, but it ranks very high (if not the highest) among scorpions.[/font]

RE: Programmatically compute similarity between zodiacs - Koen G - 18-01-2021

Given the stylistics, I would assume the Arabic matches are false positives, though who knows.

Is it possible to see which properties are the best regional markers?

RE: Programmatically compute similarity between zodiacs - -JKP- - 29-01-2021

I collected more than 700 zodiacs over the course of a decade (I haven't found very many in the last two years, it's hard to find more when you already have 700+). I didn't use the Warburg site, I went directly to repositories and combed through them.

Of course, just looking at one zodiac-figure is not a good way to see the overall picture (most of these have traditional Gemini rather than affectionate Gemini), but sometimes it's fun to zoom in one figure and study it.

There are about 25 or so that have a tongue together with the tail through the leg, which is not the only way to sort them, but it's one way that's interesting. Here are some of my favorites when selected for those two traits:

[Image: LegtailLeoTongue.png]

The third one on the top row is interesting because it has a crayfish (although it's not explicitly labeled Cancer), a dragon (possibly for Scorpius), and is full of maps and measuring instruments (BAV Pal.lat.1993)


P.S., there are many more Leo figures with the tail through the legs, sometimes it is pointing down or forward. There are more than 80 that have the leg-tail feature that don't have the tongue sticking out if you sort leg-tail together with crayfish-Cancer, for example.

RE: Programmatically compute similarity between zodiacs - -JKP- - 30-01-2021

If you search for leg-tail Leo together with crayfish-Cancer (and ignore the tongue), you get a different subset (about 75 or so):

[Image: LegtailLeoLegRaised.png]


This is why I think combination searches are important (I do a lot of them).

RE: Programmatically compute similarity between zodiacs - -JKP- - 30-01-2021

Gioynich, I don't know if any of these are relevant to your research, but there are many pics and maps on these blogs, along with combination searches on some of the later ones, so perhaps some might be of interest:

July 2013  Intro              You are not allowed to view links. Register or Login to view.
Dec 2015  Sagittarius       You are not allowed to view links. Register or Login to view.
Jan. 2016 Scorpio            You are not allowed to view links. Register or Login to view.
Jan. 2016  Libra              You are not allowed to view links. Register or Login to view.
Feb. 2016  Cancer           You are not allowed to view links. Register or Login to view.
Feb. 2016  Sagittarius crossbow     You are not allowed to view links. Register or Login to view.
Feb. 2016  Leo               You are not allowed to view links. Register or Login to view.
Mar. 2016  Aries             You are not allowed to view links. Register or Login to view.
Apr. 2016  Zodiac Evolution        You are not allowed to view links. Register or Login to view.
Apr. 2016  Taurus            You are not allowed to view links. Register or Login to view.
May 2016 Libra               You are not allowed to view links. Register or Login to view.
May 2016 Gemini           You are not allowed to view links. Register or Login to view.
Mar. 2017 Cancer       You are not allowed to view links. Register or Login to view.
Jul 2017  Aries       You are not allowed to view links. Register or Login to view.
Nov. 2017 More on crossbow       You are not allowed to view links. Register or Login to view.
Jan. 2018 Medieval animal styles and Scorpius       You are not allowed to view links. Register or Login to view.
May 2018 Zodiac patterns       You are not allowed to view links. Register or Login to view.
May 2018 Patterns, Sagittarius       You are not allowed to view links. Register or Login to view.
Jul. 2018 Pisces       You are not allowed to view links. Register or Login to view.
Sep. 2018 Affectionate Gemini       You are not allowed to view links. Register or Login to view.
Sep. 2018 Cancer       You are not allowed to view links. Register or Login to view.
Dec. 2018 Zodiac traditions       You are not allowed to view links. Register or Login to view.
Jul. 2019 Crayfish Cancer       You are not allowed to view links. Register or Login to view.

RE: Programmatically compute similarity between zodiacs - Gioynich - 31-01-2021

(30-01-2021, 12:44 AM)-JKP- Wrote: You are not allowed to view links. Register or Login to view.Gioynich, I don't know if any of these are relevant to your research, but there are many pics and maps on these blogs, along with combination searches on some of the later ones, so perhaps some might be of interest:

July 2013  Intro              You are not allowed to view links. Register or Login to view.
Dec 2015  Sagittarius       You are not allowed to view links. Register or Login to view.
Jan. 2016 Scorpio            You are not allowed to view links. Register or Login to view.
Jan. 2016  Libra              You are not allowed to view links. Register or Login to view.
Feb. 2016  Cancer           You are not allowed to view links. Register or Login to view.
Feb. 2016  Sagittarius crossbow     You are not allowed to view links. Register or Login to view.
Feb. 2016  Leo               You are not allowed to view links. Register or Login to view.
Mar. 2016  Aries             You are not allowed to view links. Register or Login to view.
Apr. 2016  Zodiac Evolution        You are not allowed to view links. Register or Login to view.
Apr. 2016  Taurus            You are not allowed to view links. Register or Login to view.
May 2016 Libra               You are not allowed to view links. Register or Login to view.
May 2016 Gemini           You are not allowed to view links. Register or Login to view.
Mar. 2017 Cancer       You are not allowed to view links. Register or Login to view.
Jul 2017  Aries       You are not allowed to view links. Register or Login to view.
Nov. 2017 More on crossbow       You are not allowed to view links. Register or Login to view.
Jan. 2018 Medieval animal styles and Scorpius       You are not allowed to view links. Register or Login to view.
May 2018 Zodiac patterns       You are not allowed to view links. Register or Login to view.
May 2018 Patterns, Sagittarius       You are not allowed to view links. Register or Login to view.
Jul. 2018 Pisces       You are not allowed to view links. Register or Login to view.
Sep. 2018 Affectionate Gemini       You are not allowed to view links. Register or Login to view.
Sep. 2018 Cancer       You are not allowed to view links. Register or Login to view.
Dec. 2018 Zodiac traditions       You are not allowed to view links. Register or Login to view.
Jul. 2019 Crayfish Cancer       You are not allowed to view links. Register or Login to view.
Thank you, that's super useful! I will add the ones I have missed to the model and see if/how the clusters change.

RE: Programmatically compute similarity between zodiacs - ReneZ - 31-01-2021

I am curious about the 'Lund astro clock' which appears quite close to the Voynich MS in the cluster diagram. I checked and Marco also included it in his earlier study but it seems to not have come out too close.

From some not very detailed images of it, it seems to have two zodiac cycles. Which one was used? Are there close-up images of it?

RE: Programmatically compute similarity between zodiacs - Gioynich - 31-01-2021

(31-01-2021, 07:53 AM)ReneZ Wrote: You are not allowed to view links. Register or Login to view.
I am curious about the 'Lund astro clock' which appears quite close to the Voynich MS in the cluster diagram. I checked and Marco also included it in his earlier study but it seems to not have come out too close.

From some not very detailed images of it, it seems to have two zodiac cycles. Which one was used? Are there close-up images of it?


Hi Rene,

I used this cycle (some of the signs are covered but I was able to extract almost all the features I needed).

[Image: Lund_astronomical_clock.jpg]

I didn't know there was a second one, do you happen to have a picture?

Regarding why it's close to the VMS: they are not similar, in fact they are not connected by a direct edge in the graph, but 'Lundo astro clock' is deemed somewhat similar to Wellcome Library, London, MS 49, Apocalypse (see below)

[Image: default.jpg]

and Ms. Rh. 172, Aurora Consurgens (see below)

[Image: default.jpg]

These three zodiacs are close to each other and loosely connected with the main 15th century German/Switzerland cluster the VMS is part of, this is why they appear close to it.

In general, what represents similarity is the size of edges, rather than position. Since I know you are technical, here is the paper about the visualization algorithm I used, in case anyone is interested and has time to spare: You are not allowed to view links. Register or Login to view.