Visual Aid Volunteers of Florida, Inc.

You've stopped at your preferred grocery store to quickly grab a few items. You've chosen to pop in at exactly the wrong time, just after work hours, when harried people swarm to purchase supplies, be it for the weekend, a holiday, or simply for the week. All the checkout lanes are full, brimming with curving lines of incommunicative and unsmiling shoppers that crest at the beginnings of the grocery aisles themselves. Shoppers still entrenched in their struggle politely "Excuse me" as they exploit the occasional gaps between the carts to negotiate through the maze of disgruntlement and continue their trek through the store, seeing in each grim visage a harbinger of their own pending commercial purgatory. However—Eureka!—there is a convenient 15-items-or-less line that seems to be moving along rather briskly and isn't too encumbered by those meandering lines of dour, frustrated shoppers. You glance down to your cart and quickly tally the items tossed in. Bag of potatoes, bread, six-pack of single-serving yogurt, and so on. You begin to overthink it—is that sweat starting to bead at your brow? One bunch of bananas, surely that counts as one item and not each individual banana? The concept of the word, "bunch," to say nothing of its singular usage in grammar, certainly implies a singularity. But—Tragedy!—the bananas have been split into two bunches by an errant bag of broccoli crowns (also itself a single item, you tell yourself) haphazardly tossed into the cart in your haste to escape the carnival of frustration that a grocery store at rush hour invariably produces. That would make it a sum total of 16 items. Definitely sweat on the brow now. You risk it anyway. The cashier does not seem to notice—or artfully pretends not to, whether through apathy or kindness. You escape the tumult with a palpable sense of relief and your dignity intact.

Which brings me, by circuitous route not dissimilar from those winding lines, to the purpose of today's article. What constitutes a single item in UEB math/science? Because, just as those potatoes, bread, and yogurt were prepackaged to each be a single item, so too must ungrouped elements found within a technical expression be "bagged" to fully represent the extent of the item being modified. While a split bunch of bananas may count as one item at the grocery store, in UEB, regardless of similarity, they would need to be bagged, as it were, in braille grouping indicators.

Let us begin with numbers, as they are relatively easy to determine whether they constitute a single item or a collection of individual units needing grouping indicators. As UEB defines it, any number is a single item so long as it contains only decimal points and commas, or is a simple numeric fraction. Thus, if we wanted to place a bar over the entire number 2.367 (for whatever reason), we could, using the contracted symbol for a bar over, simply show it as:

#b4cfg:

Naturally, that won't be a common occurrence. Most frequently, we would see the bar over a part of a number to represent a repeating decimal. As such, if our number were 2.367, the pertinent numbers would need to be enclosed in braille grouping indicators to define what elements of that single item number have the bar over it:

#b4c<#fg>:

You will also note in the above example that the opening braille grouping indicator terminates numeric mode, so the numeric indicator must be repeated after it. If any numbers fall after the closing braille grouping indicator, a numeric indicator would likewise be required there.

In some instances, other braille grouping devices replace the need for the grouping indicators because they create a single item, such as opening and closing parentheses, the general fraction indicators, or the open and close radical expression indicators. In the example x ^y⁄₂, where the fraction is in the superscript position, you will note that no grouping indicators are needed because the general fraction indicators have packaged this nicely into a single item:

;;x9(y./#b)

Were this a simple fraction in the superscript position, such as x¹⁄₂, no grouping indicators are needed, as a simple fraction likewise constitutes a single item:

x;9#a/b

Moving on to letters, only a single letter constitutes an item unless it is enclosed in either braille grouping indicators or if print shows the letter sequence enclosed in other grouping devices, such as the aforementioned parentheses, brackets, etc. In its simplest form, a barred capital A, A, would not require braille grouping indicators and would use the contracted form of a bar directly above (and would likewise need a grade 1 indicator before the bar over symbol):

,A;:

(As a side note, when undergoing transcriptions, always be aware of the possibility of mistranslated characters. The above example is a bar over capital a, but some files may read it as a macron above an A, Ā, an entirely different symbol sequence and meaning. The same should be noted for underlining versus the bar under. This points to the necessity of carefully checking translations and never solely relying on the transcription software used and file provided.)

Anything more than a single letter will need to be grouped in some manner. As such, ray AB⟶ would need to be enclosed in braille grouping indicators:

;;<,,ab>^:

In the examples above, note that the contacted form of a "simple right-pointing arrow over previous item" is being used. When these contracted forms of symbols are utilized, the directly under and directly over symbols are not necessary. Once we get into symbols outside the list shown at the beginning of Section 12 in the UEB Guidelines for Technical Materials, we will need to begin to introduce those additional symbols. Suppose Ray AB was suddenly transformed into Line AB, and would be represented in print as AB⟷. UEB has no contracted form for a common bidirectional arrow over previous item, and so we would need to utilize the "expression directly above" indicator—in addition to braille grouping indicators—to properly transcribe this item:

;;<,,AB>.9\wro

In the same manner as before, though, if it were represented in print as (AB)⟶, no grouping indicators would be needed:

;;"<,,ab">.9\wro

Following this logic, our prepackaged potatoes, bread, and yogurt from before acted in much the same manner as print grouping devices do when considering the extent of an item. On the other hand, our wayward banana bunches would need to be bagged to be truly considered a single item, much as many common elements of technical material need the addition of braille grouping indicators to avoid confusion and properly represent print mathematics. Unlike checkout lane guidelines that may allow for some wiggle room, these rules must become ingrained and adhered to closely. To pretend otherwise is not a luxury at our disposal.