It should be acknowledged that this research project was funded by the Canada Pension plan - it's not peer-reviewed science. However, keeping a diary¹ seems unlikely to hurt anyone, so you are welcome to peer-review it yourself.

YOUR TIME CONSTANT - YOUR KEY TO SUCCESS
The initial drop that the author measured followed a standard decline curve. One might expect a straight line drop as shown, but it followed the sagging curve² below it.

Two constants nail down a decline curve; the horizonal green line; called the asymptote, and a time constant that he measured at just over one year.

A quirk: the slope³ of this function multiplied by the time constant ends somewhere⁴ on the horizontal⁵ line shown.

LET YOUR BODY SET THE PACE
Your body re-cycles its cells continually, pulling them apart and refreshing them after a little more than a year. This is a tightly regulated process, and if you try to force your weight down faster, "Famine Mode"⁶ will set in. People who diet commonly trigger plateaus - diets appear to disrupt normal regulation; needlessly stretching out the rate of drop.

Instead we use the body's one-year rate of drop as our guide. To achieve it, adjust habits to maintain the two parameters above by holding the projection on goal. The math then duplicates⁷ what "growlies" did for the author.

The second chart shows this process: if you hold the xxx Lb One Year From Now signal near goal, that tugs the blue dotted one down.

There is pleasure in eating, leading people to eat more than is required to balance the recycling process. Hunger pangs are one-sided feedback - sadly there is no natural "stop" signalⁱ. Thanks to the quirk above, we now have one.

If Recycling Is Damaged

When someone is very overweight - all too common these days - the body's recycling system itself may have been damaged. A lot of muscle builds up to support high BMI, and that happened to the individual whose chart appears to the right.

The total drop is almost 40% if one was to follow the sagging curve from the beginning to its end, which would approach a horizontal green line. Instead he chose to make the green line slope downward, which straightened out⁸ the blue line:

Plan B: hold the one-year projection 15% below present weight.
You should find that any steady rate of loss should help hold blood sugar levels down, because blood sugar is the middle-man between fat and breathing out carbon dioxide. Your muscles pull it out of the blood stream if you keep them healthy and busy.

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FOOTNOTES: ¹ Don't assume one needs math to understand and use the app. The core idea is to manage the projection on the data entry page daily. This page may not be relevant to you - just those who maintain the app.

² The curve is an exponential with a negative growth rate. A person who starts losing weight tends to assume he/she is on a linear curve like the one above the sagging one. That sets up false expectations because the slope of an exponential drops off as time passes.

³ The slope is obtained from linear regression over 58 days of strongly filtered scale weights. (Two menstual cycles to balance the slope.) First a weight corresponding to a BMI of 17 is subtracted from scale weight.

Then the remainder is further coordinate-transformed into the LN() domain. An EMA8 or EMA32 is extracted for each weight; for EMA32, 3% of scale value is added to 97% of the previous EMA32.

Then the standard Least Squares Fit yields a slope that gives the Time Constant and an Intercept that gives a point for a straight line to go through. The coordinate transformed straight line becomes the sagging curve when the transformations are reversed. Thus what the app extracts is an exponential that your habits have achieved, not the ideal one.

⁴ Starting with the fact that the slope of e^x is simply e^x, we can use calculus to show that the horizontal green line (asymptote) is located at this slope times the time constant. We can use the above coordinate transformations to approximate this situation by simply adding 365.25 days to the time in the slope-intercept formula y=mx+b and then reversing the coordinate transformation process above.

That is near the asymptote for a least-squares fit exponential through the user's actual scale weights, and is called a "projection" in the description for the BioFeedback process. If it is off the goal (red signal), it becomes the user's task to adjust habits until the above slope changes to turn the signal green again. The resulting mathematical series converges on the goal at about the body's natural rate.

⁵ The red/green signal leads to a green line that does not go straight sideways. It would be possible to extract the actual asymptote, which is below the one year projection, but simply calculating a point on the sagging curve a year ahead gives a weight that is close enough to the asymptote to get the job done.

⁶ One explanation for plateaus was "set points". Testing eliminated that hypothesis. It now seems that arrested cell replacement may cause them. Note that this is only a hypothesis, but if this app consistently works faster than more aggressive dieting, that is evidence for the hypothesis.

⁷ While the math is the same when fed-back habits are in control, its implementation is reversed. Applying a step function to a first-order feedback control system will produce a chart that reveals the time constant and asymptote described above. (The feedback was provided within the body, using the "growlies" signal.) The time constant was measured by trying various candidates until it was found visually that one year sent the asymptote sideways.

In the spirit of BioFeedback, the natural control loop has now been replaced by keeping the projection via. that measured time constant near the goal weight.

ⁱ There used to be a natural stop signal. Having food meant hoeing weeds, so over-eating was limited naturally. Fortunately the Green Line can do the job.

⁸ It is best to shed muscle, which burns calories, at the same rate you shed fat cells. For that reason, this individual chose to start his BioFeedback number at about 15% below his declining BMI and then keep lowering the goal along the green line. Then the blue scale weight line is a straight line - no curvature.

There is a second reason for doing that; a Standard Decay Curve (the lower of the two blue weight curves; sagging and fainter.) requires the whole 40% shift in one's habits right from the start. Instead, the straight-line graph above required only 15% change in habits at any one time.