Preview of Dynamics
in the Flow of
Differences in Differences

On the webpage that sent you here, we are examing the until now not-rigorously-explored consequences of considering mental process as taking differences in differences.

We are searching for a formal meaning for the phrase "differences in difference." As a way of provoking curiosity and getting a sense of where the search is taking us, this page will show examples of the dynamic patterns that can emerge from recursively taking the differences in the flow differences within a dynamic system.
(Press browser back button to return to referring page.)
Detailed Intructions for using the the applet.

Using the applet.

Delay between iterations. For most new computers it will be useful to check "Use Delay" radio buttton and use the Delay Slider to set the delay between iterations to about 10 ms. What works depends on your particular computer's speed and video card. If the your computer runs the pattern too fast, make the delay longer. If the your computer runs the pattern too slowly, uncheck "Use Delay." We recomend adjusting the delay so that the speed (next to the Play controls reads around 20 to 30 iteratins per second (ips) [see instructions].

Press Play (GREEN ARROW).

Discussion is found below the Applet.

Discussion

You should see a series of columns with a dynamic pattern in each column. The first, left-most, column is the flow of differences in the original (0) basin (TAO-0). The second column (1) shows the flow of differences in the differences in the first column. Put another way, the second column shows the first derivative or TAO-1. The third column (2) shows the differences in the differences of the flow of differences (second derivative). And so on up to TAO-16.

Experiment: Change "Window Size". For example set Window Size to 11 iterations.

MAIN POINT. With Window Size set to 15 (default) or to 11 or to whatever value you like you should experience the flow in the differences in differences from Sensory basin up through all levels of TAO not as static things but rather as processes that in order to exist must be ongoing. There are no things here, only ongoing processes.

Standing Waves for Basin Lenght L=8. If you set Window Size to factors of 8 (16, 24, 32, ...), you will see what appears to be a static image. It is not. If you check the iterations per second (ips) you will notice that your computer is running the dynamic system at some high rate and whatever that rate of the process may be it has been tuned in a way that stabilizes pattern. So even when pattern appears static it is not, it is a STANDING WAVE in the process that looks static by is in fact a dynamic stability.

The Standing Waves happen because the system is in a basin that has length L=8 and when the Window Size equals basin length, the representation of the dynamics of the system are frozen, even though the system is running and differences are flowing. In contrast, if Window Size is set to values other than factors of five, you will experience apparent motion in the flow of differences. These apparent motion effects and their implications for human pattern perception are discussed in depth on Apparent Motion page of this web site. For now, notice the difference in your perception of pattern when the image is static and when it is moving (dynamic).

Observe: With the Window Size set to 8 the image is static, notice that it is apparent that each derivative (TAO level) has its own pattern. When you change the Window Size to 9 or 10 or 11, these patterns become dynamic and you will notice new aspects of the dynamic flow. At Window Size = 10 certain dynamic relations (subbasins) are extracted from the flow to appear as standing waves. This allows easy perception of these dynamics. Shifting window size extracts different as apects of the flow of process to be standing waves.

Instructions Top

Window Size (iterations). [BLUE HIGHLIGHTS].

This is the most important control conceptually because it adjusts the phase relations between basin length and the processing of the basin (and this allows the extraction of different aspects of the dynamic patterns portrayed here.

Drag the Slider (highlighted in blue) from its default setting of 60 down to whatever size is suggested above for using the particular applet you are viewing. In this case the slider has been dragged down to 11 iterations.

Click the Slider Bar. Optionally you may click on the Slider Bar and the Window Size will slowly scroll in the direction (to right of slider or to the left of slider) you want. You can easily get a change of one unit by clicking on the slider bar. This gives you a finer degree of control over window size than does dragging the slider.

Read the Window Size. To the right of the Window Size area is a number (highlighted in blue) that tells you exactly what the Window Size is. Top

Setting Delay. [YELLOW HIGHLIGHTS].

WHY?: Adjusting your Computer's speed to your Monitor's speed: Most monitors cannot paint accurately faster than 66 to 77 times per second. In this class dynamic systems, we ask the computer to paint each iteration of the system to the screen. Depending on the how fast your computer is (it's clock speed mega-Hz or giga-Hz and what type of video card it has) this software may send requests to paint images 1000 or more times per second. Once the iterations per second is higher that 65 or 70 iterations per second (ips) what you see on the screen is some undetermined interaction between your monitor hardware and the behavior of the dynamic system. In other words, you aren't seeing the behavior of the system any more, you are seeing that part of the behavior that the screen happens to capture.

Solution. Click on the Use Speed radio button (higlighted in yellow). Then drag the Delay (between iterations) Slider (highlighted in yellow) from its (very slow) 250 millesecond delay between iterations down to some lower value that gives you a good sense of dymanic motion in the output. As we said, you generally want the the iterations per second (ips) to between 20 ips and 60 ips, although it seems to work well in this case as low as 6 to 8 ips. You your judgment as this is about your perception.

If your computer is slow, you may not need to use the Speed control. Top

Interations per Second (ips). [HIGHLIGHTED IN LAVENDER].

When you push PLAY, you generally want to have the iterations per second indicator (just to the left of the double black arrow on the control bar) to be between 20 and 60 ips. This range allows you to perceive apparent motion effects but is within your monitor's ability to paint the screen. Obtaining this range may require setting the delay (see below) between iterations.

Sizing the Viewing Area. [ORANGE HIGHLIGHTS].

Resize Viewing Area. [ORANGE HIGHLIGHTS]. The dimpled bar between the Controls and the Output Frmae (Viewing Area) can be dragged in either direction (as indicated by black arrows). This allows you to adjust the viewing area to see more or less TAO levels.

Full-Interface Viewing Area. [ORANGE HIGHLIGHTS (Top)]. Once you have the controls set as you like them you can eliminate them and see more derivatives by clicking on the little left-pointing arrow at the top of the bar dividing the controls from the output frame. Clicking the right-point arrow will return the controls to veiw. You can also grab the dividing bar and drag one way are another to size the parts of the interface the way you want.

Viewing the Iterations per Second (ips) indicator. To see the number indicating the iterations per second (ips), it may be necessary to drag the dimpled bar to the right. This is usually not the case, but when it is true it is minor and easy to do but it is an annoying adustment that makes these instructions appear to more complicated than necessary. We are working on fixing that.

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