... Why does a "sensory" memory hang around at all? Why would there need to be a third structural kind of information along with the short and long term kinds? ...
It is not a "need" and it is not "structural" IMHO. Just a consequence of how nerves encode information. Most who know that information is encoded by specific sets of nerves and their "rate of discharge" do not know that it is by the CHANGE in rate of discharge. I.e. all nervers are constantly with their normal "not in use" discharge rates, which can be a couple of hundred pulse per second.
Probably both short term and long term memory do involve some sort of "structural change" but probably not "sensory memory." I think that is more accurately described as a "metabolic excursion." Sort of like the complimentary color effect is. (Stare at red spot for few minutes and then look at white paper and see same shape green spot.) The more fascinating "waterfall effect" is also due to metabolic fatigue, in V3 nerves, I think, from memory. If after watching a set of parallel, evenly-spaced, lines move at constant speed (New line appearing as old one leaves the display screen, so it is always filled with lines.)* the motion of the lines is stopped, then they will be perceived as moving in the opposite direction. It is really a strange sensation. You can put your finger on one of the lines, firmly fixing it in space, yet you sense it is moving despite remaining at that one location. (Their "regular spacing" is essential as there is something like a Fourier transform also being done to process and understand images and you need this transform to be sharply peaked - driving some small set of nerves hard. It may seems strange, but it is true, that we quickly get rid of the 2D representation of V1 and work in the transform space, just as I will now explain for color also.)
All three (sensory memory, after image, and waterfall effect) and several others are due to the way information is encoded in neural impulses. For example, after some well known algebraic transformation (I am too lazy to dig the equations up for you.) the activity in the three different color sensitive retina cells (R,B,G - the same three colors you will see if you examine dots of color TV screen up close) are in V5 encoded onto three "axis" (BW, RG, & BY or Black white, Red green, and Blue yellow). The same set of V5 nerves indicate, for example, both blue and yellow. (Another set, both red and green, and the BW axis gives the intensity.)
This is the way almost everything is encoded in the brain. I.e. by a
change in the rate of neural discharge. I forget which way it goes, perhaps a high rate in the RG set of nerves corresponds to "red" and a low rate corresponds to "green" (or conversely - as I said, I forget which now, but to continue my discussion, assume red is rapid discharge, pink less rapid, but still more rapid than white, etc.)
Thus, when you are looking at red spot the RG set of nerves in V5 is discharging rapidly (compared to looking at a white sheet) and becomes slower as the metabolic resources immediately available are used more rapidly than if looking at white paper. So immediately after switching to look at an only white paper the rate drops below the appropriate discharge rate for "white" - I.e. you see green.
I think this is what is happening in "sensory memory" also, but the name is a little wrong. The metabolic depletion is more central than the peripheral nerves. To pick up my previous example with Dichotic listening, where the unattended, male voice said: "I will hit John." the sound pattern of the word hit (its phonemic structure) was ""looked up" in your "lexicon" to retrieve the meaning** and this used up some of the metabolic potential of those "lexicon nerves" slightly. - Use made their firing at less than their normal "not in use" rate. So for a small fraction of a second, with switch of attention to the male voice the mention of your name (john) caused you can still recover the fact that the sentence with "John" has also the word "hit" and by automatic amazing processes rebuild that now gone sentence.
This is why I called "sensory memory" a "metabolic", not a "structural" memory mechanism.
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*Easy program to write. - I made one in Quick Basic years ago of only about 20 lines of code which moved the set of displayed lines until I hit the space bar. (used it as wanted to keep looking at the screen.) It had input data parameters to control line width, color, velocity, motion direction and spacing and a simple test to create a new horizontal line at top of screen (if lines were moving down) from the one disappearing at the bottom.
**And many other "lexicon facts", such as fact "hit", if usually plays the role of a verb*** in whatever sentence the brain should construct from this string of phonemes. Furthermore, the lexicon also contains the fact that some other subsection of the sentence (actually still just a "phonetic stream") to be constructed is hit's mandatory object (Hit is a transitory verb).
***Hit can also play the role of an adjective as in "The party was a hit." Building a sentence from the string of phonemes is quite a complex task especially when there are many different roles some strings looked up in the lexicon can play. Even the printed word (verbalized silently as you read) is sometimes difficult to correctly construct. This also has to do with the "7 limit" to short term memory. I.e. if as the sentence is read, the compination of the number of "possible roles" some of the words can play gets too large to keep in short term memory, you will automatically throw out some of the less probably possibilities to keep the remaining ones active.
There are some famous "garden path" sentences (as in "lead down the garden path") where most people will discard the correct role prematurely and thus not be able to make any sense of the string of words read. For example, the following is a perfectly good English sentence, but I have not put in the normal punctuation signs to help you read it correctly:
The horse raced past the red barn on the hill fell.
