Tag Archives: complex numbers

An engineers approach to diet and work-outs (part 1)

This is the first in what I hope will be an interesting blog post series on my attempts at fighting obesity through the means of applying control theory to dieting and working out.   Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behaviour of dynamical systems with inputs. My first attempts at trying to harness my body’s use of nutrients with control theory failed miserably in a way not dissimilar to how my first attempt at creating an amplifier  while studying electronics failed miserably. In folow-up posts I will talk about different aspects that went wrong, but in this post I shall focus on the most essential aspect of applying control theory to any system: picking the proper parameters to use in the feedback loop.

As many people coping with obesity do at first, I too made the horrible mistake of focusing on my scale and my Body Mass Index (BMI), thinking these numbers were somehow indicative of my health.  The body mass index is basically an index that describes the relative weight for someone of a certain height. The problem is, the body weight however is composed of multiple components, including:

  • Muscle mass
  • Fat mass
  • Water mass

What we mostly care about with respect to obesity is not the total mass, but mostly the size of the fat mass compared to the bodies total mass, or the total body fat percentage (TBFP). The current use of the BMI by nutritional professionals and throughout the medical profession and throughout society stems from the statistically significant correlation between the BMI and  TBFP within populations.  The problem is however that ‘improving’ ones BMI does not necessarily imply any improvement to the TBFP.  You could for example under specific conditions loose weight, basically eating your muscle mass while actually gaining  fat mass, or you could loose weight by dehydration, both leading to a higher TBFP.

In the end, and I realize this is difficult as the idea is so deeply rooted, we should stop believing that weight is a useful measure for individual body compositional and health goals. Instead of the BMI we need to look at different numbers. So what parameters are a good measure of our general health and of a healthy or unhealthy body composition. As stated, the TBFP is an important and relatively undiluted  number. Lets star by creating a simple scale that most likely will yield a number between 0 and 10 for most probably anyone who is struggling with obesity tendencies.  Lets define the Body Fat Index as:

BFI = \frac{TBFP - LBFP}{5}

That is, we take your total body fat percentage, subtract from that the lowest number from the dark green section of the below chart, and divide the result by 5.


So a 43 year old male with a body fat percentage of 46% would end up with:

BFI = \frac{46 - 11}{5} = 7

There is a second dimension we need to look at regarding a healthy and stable body composition. You may have heard the phrase “use it or loose it”, well basically that’s how your body works when you start starving yourself, especially if you are also eating the wrong things while starving yourself.  If you don’t exercise all of your muscles regularly, are on a calorie deprived diet, but at the same time are bombarding your body with insulin by getting much of your calories from fruit juices, you leave your body no other option than to start consuming muscle mass. You weren’t using those muscles, and the fructose induces insulin spikes will make sure you won’t be using your bodies fat as an energy source, so your body will basically start eating your muscles. And to make things worse, with less muscles your body will burn less calories, further reducing your chances of loosing fat.

You need to use these muscles, grow them if possible so they help out at burning calories, and you need to monitor them to make sure you aren’t eating them by starving yourself. The best way to do the later is by keeping track of your strength. Carbs are bad if you don’t work out, but if you are getting into sports, you will need sufficient pre-workout carbs to fuel your workout. If you eat to little calories all together, or to little protein for muscle repair. your strength will suffer. If you start cutting to fast for your body to keep up with, your strength will suffer. If you eat well, you will get progressively stronger from your exercises. As such, your strength is a good indication of how well your body is doing. So in addition to our BFI above, we shall define a Body Strength Index (BSI) that we also aim for should have a value that for the most of us is between 0 and 10. We define:

BSI = 14 - 2\frac{S + B + D}{W}

That is, we first add up your squat, your bench and your dead lift strength and divide that by half your body weight. Than we subtract that number from 14. So if for example you weigh 100kg, your bench is 125, your dead lift 225 and your squat 275, the result would be:

BSI = 14 - 2\frac{125 + 225 + 275}{100} = 14 - 2\frac{625}{100} = 14 - 12.5= 1.5

With the BSI, your strength training becomes a measuring tool for measuring how well your body is doing. How well your diet is working an if you aren’t taking your diet beyond the point where is helping you.

Now we come to the interesting part, how do we combine the BFI and the BSI in a useful way that can help us apply control theory to our work out and dieting routine? We combine the two by defining a Generic Body Health Index that is complex number:


The absolute value of GHBI is defined by Pythagoras’s theorem:

|ghbi| = \sqrt{BFI^2 +BSI^2}

While this absolute value is the value we are aiming to ultimately reduce, if there is a large difference in the values of the two components, its probably wisest to focus on the component that’s contributing most to the absolute value first. If we subscribe to the idea that its a good idea to not focus to much on either component but to balance the two, a way to find a good balance in our projected goals for body improvement  would be to define a circle segment that starts at  the point in the complex plain defined by GBHI and that ends at 0 +0i under an angle of exactly 45 degree.



As the above example shows, our ideal path may warrant for one of the two components to suffer slightly in order to more effectively address the one that needs most attention, and, and this is just as important, to allow us to be able to define a smooth line suitable for critical dampening. In this case our individual is rather strong and extremely fat so he/she should allow a little loss of strength in order to loose fat first. Other individuals may need to allow gaining some fat to easier allow for gaining substantial strength. The basic idea is that we define a circle segment that aims for both a balance between strength and leanness and for providing a smooth path to an ultimate attainable goal.

I hope this post has shown how my GBHI makes sense as an alternative to the over used BMI, and how projecting a circle segment on the complex plain defines a desirable path towards a healthier stronger and leaner body.  In part two of this series I’ll try to address how and why combining a basically low-carb diet with substantial complementary pre-workout carbs seems to be a good basis to base our control system input on. How low-fat high carb destabilizes the BFI part of our control system while low-carb high-fat interferes with  progress on the BSI part.  Basically both the low-carb and the low-fat approaches lead to sub optimal results at best, my personal experiences with applying control theory to my diet have made me come up with what I think is a reasonable yet somewhat cumbersome middle ground where timing of different calorie sources is essential. I’ve been able to trace back any lapse I had to failure of applying strict timing discipline. More on that in my second post in this series.