Yes, it’s time for a science post again. For this installment, I’m basically going to continue the discussion that began in a previous post from a couple of years ago, and take one step further in trying to quantify one of Daredevil’s superhuman senses, namely the sense of touch. Or rather, try to figure out specifically how good a person’s sense of touch would have to be in order to be able to read standard print.
Before we start, a disclaimer is in order: The ability (and the inability of us ordinary humans) to read print by touch is limited by two factors.
One is the ability to register a signal at all, i.e. for something printed on a page to be perceivable, it needs to actually be raised and give the overall surface some kind of texture. The underlying assumption with Daredevil is, of course, that his threshold for registering, say, the layer of ink on a page is much lower than that of an ordinary person. However, some kind of texture still has to exist or it will feel like an even surface even to someone with an enhanced sense of touch.
A problem (for Daredevil, that is) with many modern printing techniques is that they yield surfaces that are perfectly smooth or very nearly so. This was something that Mark Waid brought up in a recent interview where he talked about how modern technology is making life increasingly difficult for Matt. It doesn’t matter how good your sense of touch is if there really isn’t anything for you to feel.
For the purposes of the discussion below, we’re going to have to assume that we are talking about an ink layer that actually does have some measurable thickness to it, enough for someone like Matt to pick up.
However, there’s also a second limiting factor in print reading by touch. Because, even provided that the ink layer is thick enough, the spatial resolution of a person’s fingertips also limits wether a line of print, for instance, can be discerned or register as nothing more than an indecipherable smeared line. The topic for today will be to address this second issue. Given that a line of print can be felt, how good does the spatial resolution of the fingertip need to be to be able to perceive individual letters and words?
To help answer this question, we’re going to turn to an exciting paper by K.O. Johnson and J.R. Philips from 1981 that was printed in the Journal of Neurophysiology and which seeks to examine tactile spatial resolution.
Out of the four sub-sets of experiments, one specifically addressed the ability of test subjects to correctly identify raised (by 1.5 mm) letters that varied in size from 3 mm to 8 mm in height. On this test, the subjects were able to correctly identify 30 % of the letters at 3 mm, close to 50 % at 4.5 mm, 60 % at 5.5 mm and just over 80% at 8mm.
Since the result of this experiment was fairly linear, we can assume that the test subjects would have come close to 100 % for letters 10 mm high. Interestingly, even getting 30 % correct at 3 mm is pretty impressive and well above chance since this test used all 26 letters of the alphabet and the correct response from just guessing would have been 3.8 %.
Also, to the extent that people guessed incorrectly, those responses weren’t random either but were confined to a finite set of letters similar in shape to the target. This means that a persons ability to correctly identify whole words and sentences would be higher than their ability to identify individual letters at all letter sizes, since knowledge about which letters and words commonly appear together would come in to play and improve this result.
In a sense, this is analogous to lipreading (more appropriately termed speechreading) in which a person uses his implicit knowledge of the language itself to make statistical inferences when the signal is ambiguous.
Given that standard printed letters in a book are around 3 mm in height (at least in the one I grabbed at random from my bookcase), it would seem that even an average person might conceivably do a half-decent guess job if trying to read it, had the thickness of the ink been high enough. Of course, one can easily imagine just how slow and inefficient this would be. For print reading to be worthwhile at all for Matt, his sense of touch would have to be quite a bit better than this.
Interestingly, in the discussion section of this particular paper, the authors are able to use these and other findings to compare the senses of touch and sight, in terms of spatial resolution. This gives us a better idea of the amount of effort that goes into reading small print by touch versus doing so visually.
For obvious reasons, tactile spatial resolution can easily be measured as a matter of distance, i.e. by simply giving the dimensions of the smallest discernable letters, for instance.
Vision doesn’t quite work this way. You may be able to comfortably read tiny letters from one foot away, but if you move that same piece of text to ten feet away you’d fail miserably because the same piece of visual information at a greater distance takes up a smaller portion of your visual field. Consequently, visual spatial acuity is commonly measured by giving the visual angle.
The smallest line on a standard eye chart (also known as a Snellen chart) corresponds to 20/20 vision, which in turn is the equivalent of having a spatial resolution of one minute of arc (= 1/60th of a degree). The height of the letters of that bottom row actually covers five minutes of arc, but you need to be able to see the individual features of the letters in order to recognize them.
In terms of comparing vision and touch, Johnson and Phillips conclude that 2.2 mm on the skin is roughly equivalent to one minute or arc perceived visually. This means that you can decipher a 10 mm letter by touch with roughly the same ease as you are able to discern a 0.45 mm letter from one foot away. 0.45 mm (app 1/60th of an inch) sounds awfully small, but if you (like me) have normal vision, you should be able to do this, the same way you are able to read an 8.9 mm high letter at 20 feet on a Snellen chart because they correspond to the same visual angle.
In the image above, you see the relative (these are not to scale) sizes of letters of various sizes. On the far left, very tiny, is the 0.45 mm letter that represents the smallest letter a person with 20/20 vision can reliably (i.e. without error) see at the distance of one foot. Next, you see letters representing the average text in a standard book, followed by four Braille letters (that spell “matt” incidentally) at the correct relative size for standard Braille. On the far right is the 10 mm letter size which represents the tactile equivalent of reading the tiny letters on the far left, more or less.
One thing I want to point out here is how relatively economical Braille is in how it maximizes the sense of touch. Before the invention of Braille, they actually did make books for the blind that had large raised letters. The problem, as we can infer from the picture above, was that they had to be quite large and reading the text was very slow. Add to that the fact that Braille can easily be written (yes, even by hand) as well as read efficiently, and it’s easy to see why Louis Braille and his fellow students took to the new system like a duck to water.
So, with the relationship between vision and touch sufficiently established, we should be able to figure out how much better your sense of touch (in terms of spatial resolution) has to be in order to read print of standard size.
Since the vast majority of people can reliably identify raised letters with a height of 10 mm, but errors (though not necessarily major ones right away) start to crop up below that point, we need to get Matt from that 10 mm limit down to roughly 3 mm. This means that we need to boost his acuity by a factor of just over three in both dimensions of the surface of the fingertip. Using some quick math, we can conclude that his (fine) touch receptor density would have to increase approximately ten times compared to the norm.
However, most of us wouldn’t want to read text so tiny that the letters are just barely legible (i.e. the equivalent of visually reading 0.45 mm letters at a distance of one foot) because it’s uncomfortable and tiring. If we expect Matt to be able to read standard letters by touch with the same level of ease as someone with 20/20 vision is able to, his actual tactile acuity would have to be better.
If his fingertips are supposed to be the equivalent of 20/20 vision he should be able to read even those tiny 0.45 mm letters by touch. This means that his spatial resolution would have to be roughly twenty times better (10 mm ~ 20 x 4.5 mm), in both dimensions. Twenty squared is 400, which means that he’s need 400 times as many touch receptors in his fingertips as a normal person.
However, there is a practical problem with this scenario. Since the average person has around 100 touch receptors per fingertip (of different types, not just those specific to detecting fine touch, but 100 is a nice even number…), Matt would need 40 000 touch receptors in order for his fingertips to more or less do nearly the same job as the central portion of the retina.
Using the Meissner corpuscle (one of the types of touch receptors in the skin) and it’s 50 micrometer diameter as a reference point, all of those receptors would actually take up 78.5 square millimeters of fingertip real estate. That is several times larger than the actual surface of the fingertip.
Being just barely able to spatially resolve raised print by touch (with ten times as many receptors as normal) makes sense in a world of superpowers, but extreme “vision-like” tactile acuity is impossible, even by Marvel Universe standards.
Add to this the fact that the layer of ink on most printed material is very thin (and, as we’ve noted, steadily getting thinner), and you’d be hard-pressed to imagine why Matt would rely on print as anything other than a last resort, when possible. Then again, I always thought that his voluntarily shunning Braille (way back in the Silver Age) made very little sense.
If you made it to the end of this post, congratulations! You’re officially as much of a geek as I am!