γυμνὸς or γυμνοὶ in Clement's Letter to Theodore?

[RandyHelzerman]

For convenience of reference, here is the same treatment given to the collection of sigmas and iotas which PeterKirby kindly collected for us, in post viewtopic.php?p=169090#p169090

Here I will comment a bit: In general, the iota's appear to be written with one stroke which have at most one continuous, rounded curve, like a candy-cane. In either stick form, or candy cane form, the pen does not seem to be making sharp angles.

The sigmas appear to be composed of 3 discernable parts: an angled line, a horizontal line, and another angled line. The pen appears to be making 2 changes of direction, one or both of which are acute and sharply pointed.

There are two interesting examples which stretch these characterizations, one iota and one sigma. Both of these seem to be suffering from an unfortunate ink blob. It is imaginable that if the ink blob were not there, they would fit very nicely into the above characterizations.

I hazard a theory: Both letters can be written without taking the pen off of the paper. But, iotas all can be written by a continuously moving pen. The sigmas, however, cannot. The most stereotypical sigmas are written such that the pen must stop moving at two points. Sometimes it looks like the scribe has cheesed it around one of the corners, but I don’t see a sigma which could be written without stopping the pen at least one time.

[Ken Olson]

I experimented around with some image processing/edge detection/contour detection algorithms. Results posted here w/o comment.

I think you may need to comment on what you think your image processing shows. It's not clear to me that it shows anything we didn't already know - that some examples of the same letter (Iota or Sigma) provide comparanda that resemble the letter in question more than others do.Do you think it shows something more than that?

Best,

Ken

[RandyHelzerman]

I think you may need to comment on what you think your image processing shows

i didn't say much because I didn't want to prejudice the issue, but yeah, its probably a good idea if I explain a bit what these pictures show and what information you can extract from them.

Q. What is the context? Where would these images be used?
A. Generating images like this is the first stage in computer algorithms which read handwriting. When looking at a blob of pixels, and trying to figure out what letters it spells, the computer generates a list of what are called "features" of that blob. These features are then fed into later stages of the algorithm.

Q. What are these features?
A. They are pretty much what you would guess you would want when interpreting handwriting: You would want to know:
* What path the nib of the pen traced.
* At each point along the path, how fast was the nib moving, and in what direction?
* how thick or thin the stroke was.

These are the kinds of things a computer can extract from these pictures. And humans can extract them too, once they know what to look for

Let's take a look at how this is done. To illustrate, I'll compare Ken's defeater example with a more stereotypical final sigma, because it illustrates the difficulties with handwriting recognition very well. *We* know that it is a final sigma, but we know that from higher-level contextual issues, like grammar and semantics, which the computer doesn't have accesss to. The computer just has a blob of pixels. Lets see how far we can push it:

First, we run a so-called edge detector:

sigmas.jpeg (48.43 KiB) Viewed 314 times

I've scaled up the image so you can just see the pixels. The original blob of pixels is on the left---the transformed image on the right shows 2 things;
1. The outline of the blob, in white
2. Inside of the outline, is the "skeleton"" of the blob, which in our case is the path where the pen went.
Both of these things tell us cool stuffs we want to know.

Think of how a dip pen works....the slower you move the pen, the more ink can leak out of it---which means the fatter is the outline! So the width of the outline can be used as a measure of how fast the pen was moving. For example, our stereotypical sigma:

outline_good_sigma.jpeg (17.7 KiB) Viewed 314 times

the outline is pretty much the same thickness throughout. There is a *slight* bulge at the two points where the pen changes direction--like any other physical object, the pen cannot instantaneously change the speed its moving, so it has to slow down, around the bends, and then then it speeds again on the straightways. The scribe here has drawn effortlessly, with confidence.

Ok, it's important to clarify here exactly how strong these conclusions are. Are they sober, objective fact, which any two reasonable people can agree on? Are the high probability inferences? that most observers will agree on, or are they subjective judgement calls which (however frustrating secret alias finds it) reasonable people can and will disagree over?

Going forward, I will color code all the conclusions I report accordingly. Thus:

1. The outline is pretty much the same thickness throughout the stroke is an objective feature of this blob of pixels. The pixels are the pixels, the data is the data, and any two observers, equipped with a ruler, will agree.

2. The pen moved at pretty much the same speed throughout the stroke is a probabilistic inference from the data. These days, computers are very good at assigning these sorts of probabilities--as long as you give them enough training data. Any two observers who know statistics will *very likely agree* on the probability of the feature, given the data. However, the conclusion is defeasible. Consistent speed of the pen is a very likely explanation for the consistent thickness, but it could just be by coincidence. Reasonable people can and will disagree on whether the putatively most likely explanation is the correct explanation.

3. The pen changed directions twice during the stroke is also a probabilistic inference. We know the pen's path is very likely to be inside the outline, but the exact path it took is also something probabilistically inferred from the data.

4. The scribe here has drawn effortlessly, with confidence, like those stern nuns with knuckle-rapping rulers taught him to is obviously a subjective judgement call. Reasonable people can and will disagree about theses kinds of conclusions all the time.

I'm trying very hard not to prejudice the case, so I will try to color-code the conclusions correctly, but since I make mistakes all the time please double check me.

So on to our other sigma. it was not drawn so effortlessly. Notice how the outline width changes here:

funny_sigma_outline.jpeg (51.38 KiB) Viewed 314 times

It is thicker at the beginning of the stroke, and thinner towards the end. It makes sense, because we know that this is a sigma, and yet it is a very funny looking sigma..

The scribe was moving slower at the beginning of the stroke than at the end of the stroke.Perhaps the scribe was looking back at his exemplar, and accidentally let his hand linger a bit too long. Or perhaps he was forging it!!!

Continued next post.......

[RandyHelzerman]

Now when computing the probabilities of what this letter is, the computer will make its best guess as to what the path was that the pen made. It will do so on the basis of which pixels are the darkest, as they have the most probability of being on the path. It will also try to figure out whether the path is straight or curved, where the pen stopped, etc. In all likelihood, the path went something like this:

The scribe started moving the pen straight down for a short distance:

stroke1.jpeg (51.99 KiB) Viewed 303 times

Then the scribe changed directions:

stroke2.jpeg (53.01 KiB) Viewed 303 times

And then finally completed the stroke:

stroke3.jpg (54.58 KiB) Viewed 303 times

[RandyHelzerman]

OK, lets put that result next to what would be the same processing done to the stereotypical sigma:

processed_sigmas.jpg (54.62 KiB) Viewed 275 times

And, if you look at it abstractly, after processing, the two don't look as much different as they started!! In both cases, we have 3 lines. Two of the lines in both pictures meet at a similar angle. Really, the only difference is the angle at which the top yellow line meets the cyan line. And the length of the lines, of course. .

What with all these newfangled deep-learning neural networks if you gave it enough training samples, which cover enough of the screwy cases which people end up warping their letters into in real-world writing, the computer would be able to tell with a very high degree of confidence that *BOTH* of these are a final sigma..

So, *that* is the value of these edge-detected pictures. Even though the two blobs of pixels we started out with look very different from each other, nevertheless, with the right image processing techniques, a computer can analyze them down to their essences, and---it can reconstruct the pen motions which the scribe most likely used to draw the glyph. It can then use that to make very high quality inferences. For a language like English, of which there are zillions of exemplars, exceedingly accurate handwriting recognition systems can be built.

I hope the utility of these processed pictures is now apparent. With a little practice and imagination, you can look at an outline and do the processing yourself. If a portion of the outline is thicker, you can guess that the pen was moving slower. By tracing out the darkest pixels inside of the outlines, you can get a pretty good reconstruction of the path which the scribe used to create the glyph. Is the path a series of strait line segments? Or is one of the segments a curved line. Actually, let me just give an example of a curved line glyph:

curve_exammle.jpg (137.84 KiB) Viewed 275 times

*chuckle* next to the sigmas, that was easy. The glyph appears to be written in one continuous, but curvy stroke.The outline width is consistently pretty near the same.which indicates so was the speed of the pen. To me, anyways, that looks like the scribe was relaxed and on automatic pilot when he was writing that.

Now, I could go on and do the same analysis for our favorite gymnastic example, but, again, I really don't want to prejudice the issue any more than I already have. Look at them and see what you come up with.

(this is the end of the posts in this series)

[Peter Kirby]

I think you should include the final sigma in ἔχοντος from page 2, line 16 among the comparanda.

Theodore 2.16 ἔχοντος.png

Here's an image of just the same final sigma cropped from Hedrick's / Viklund's bitmap file (uncompressed).

2.16_sigma.png (14.75 KiB) Viewed 286 times

[Peter Kirby]

And here's the character we've been talking about on the third page, which isn't a sigma.

the_character.png (19.74 KiB) Viewed 275 times

In the previous example, of a sigma, we can see at the top a stroke that goes down and slightly left before breaking direction.

In this example, which is not a sigma, there is a single unbroken curved stroke, which curves from going down and slightly right, gradually becoming a stroke that goes down and slightly left (although I would need to consult with an expert to know whether it's drawn down or up). This unbroken curved stroke is something we see in some other iotas but not in the final sigmas.

I will grant that we have seen some lower-quality images that can play tricks on the eyes because of their poor quality, but on closer examination, none of these examples break the clear pattern here. The conclusion has been strengthened by this testing.

When I have time, I can assemble all the relevant examples from all three pages.

I do understand wanting to get feedback from scholars with relevant paleographic expertise for their comment.

[RandyHelzerman]

Here's an image of just the same final sigma cropped from Hedrick's / Viklund's bitmap file (uncompressed).

Just for fun:

other_sigma.jpg (193.66 KiB) Viewed 260 times

Just a rough cut. the image quality isn't as good, but this is a good indication of how robust these are to image quality. We still get a discernable outline, and, if you look in the center, outline version, you can kinda see a vaguely sigma-shaped region of darker pixels.

[RandyHelzerman]

And here's the character we've been talking about on the third page, which isn't a sigma.

I posted the edge-detected version of this one earlier. But after reading the above it probably makes more sense now, so I'll post it again for convenience:

letters.jpg (31.11 KiB) Viewed 245 times

Can you pick it out of a line-up

Each glyph has two outlines, one from a standard edge detector and one through a sobal filter. Its a good read on how robust the method is for varying quality of outline generators.

I will grant that we have seen some lower-quality images that can play tricks on the eyes because of their poor quality, but on closer examination, none of these examples break the clear pattern here. The conclusion has been strengthened by this testing.

THIS. word. Amen. Selah.

And we should keep in mind that even the best pictures we have fall far short of the original, so we may have to once again re-evaluate.

[AdamKvanta]

How about this?

paint.net -> Effects -> Stylize -> Outline... -> Thickness = 4, Intensity = 100

sigma.png (100.92 KiB) Viewed 234 times