[From Bill Powers (960213.1145 MST)]
Here is an attempt to get some real data into the conversation. The
subject is "square wave disturbances," which Hans Blom mentioned some
time ago. In the experimental program that is appended, a target jumps
up and down by 150 pixels in a square wave with a period of 1 second (up
for 30 frames, down for 30 frames). The human participant tries to make
the cursor track the target, by moving the mouse along its y axis. The
run length is 60 seconds with 60 samples per second, so the data arrays
are 3600 items long.
This is a bare-bones program with no data analysis and no modeling. The
point is to give us some experience with tracking square-wave target
movements, so we know what it is we're trying to model. As it stands,
the half-period of the square wave is 30 units, where 1 unit is 1/60
second on a VGA screen. This is therefore a 1 Hz square wave.
There is a narrow range of square-wave frequencies over which I can
track fairly well by generating my own up-down movements and trying to
match them in phase and amplitude to the target movements. Below about
1/2 Hz, my ability to synchronize my movements to the target movements
deteriorates badly, and for still lower frequencies I just have to wait
for the target to jump. There is a distinct change in mode of control;
the independent generation of cursor patterns seems to be possible only
for frequencies above 1/2 hz (approx). If I try to maintain my
independent pattern generation below 1/2 Hz my "tracking" becomes very
poor. Of course my tracking is also poor for disturbance frequencies
much above 1 Hz.
Generally, my tracking in this mode is not as good as it is when just
following the target, particularly at lower frequencies. Perhaps with
more practice I would improve.
I invite all who want to discuss square-wave tracking to set up this
program and practice with it using various durations of half-period (I
suggest 15, 20, 30, 60, and 120 as the values of "jumpdel" in the
initialization routine). This assumes a frame rate of 60 per second. One
caution: the mouse and mouse-pad should be clean and the mouse should be
centered on the pad so it never has to be lifted up and reset during the
run. My setup requires a mouse movement of about 1.5 inches peak to peak
to get 150 pixels of cursor movement (i.e., 100 counts per inch).
I will be interested in your observations.
Following is the program for taking the data. The data are output to a
file "square.dat" as ascii integers, in the sequence
target,cursor,target,cursor ... with 7 pairs per line followed by a
carriage-return-line-feed after each line. My 12th practice run is
appended after the program.
I hope that everyone who tries this experiment will post the data for a
run after some practice, so we can all try out our own models and
analyses.
···
-----------------------------------------------------------------------
Best,
Bill P.
program modelctl;
uses dos, crt, graph, grutils, mouse;
type datatype = array[0..3599] of integer;
var cursor,target: integer;
c,t: datatype;
oldc,oldt,maxx,maxy,graphmode: integer;
i,j,jmp: integer;
jumpdel: integer;
d: integer;
ch: char;
sqrdat: text;
procedure initial;
begin
jumpdel := 30;
jmp := jumpdel;
d := 150;
oldt := 0;
oldc := 0;
mousex := 0; mousey := 0;
initgraphics;
graphmode := getmaxmode;
setgraphmode(graphmode);
end;
function getdist: integer;
begin
if jmp <= 0 then
begin
jmp := jumpdel;
if d = 150 then d := 0 else d := 150;
end;
dec(jmp);
getdist := d;
end;
procedure showcursor(c: integer);
begin
setcolor(black);
line(maxx div 2 - 30,oldc,maxx div 2,oldc);
oldc := maxy div 2 - c;
setcolor(lightgreen);
line(maxx div 2 - 30,oldc,maxx div 2,oldc);
end;
procedure showtarget(t: integer);
begin
setcolor(black);
line(maxx div 2,oldt,maxx div 2 + 30,oldt);
oldt := maxy div 2 - t;
setcolor(lightred);
line(maxx div 2,oldt,maxx div 2 + 30,oldt);
end;
procedure runexpt;
begin
for i := 0 to 3599 do
begin
readmouse;
c[i] := mousey;
t[i] := getdist;
retrace;
showcursor(c[i]);
showtarget(t[i]);
end;
end;
begin
initial;
maxx := getmaxx; maxy := getmaxy;
runexpt;
assign(sqrdat,'square.dat');
rewrite(sqrdat);
for i := 0 to 3599 do
begin
if ((i mod 7) = 0) and (i > 0) then
writeln(sqrdat);
write(sqrdat,t[i]:5,c[i]:5);
end;
close(sqrdat);
end.
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0 6 0 21