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Summary

In the first part of this series, I explored a primitive ‘quantitative diet’ idea. In the second part, I showed how to use a simple model and some differential equations to estimate the effect of a diet on weight loss, and ‘derive’ a diet to acheive a weightloss goal. In the third part, I discussed how I track my diet using ChatGPT-4. In this part, I can share some pitfalls, including local fluctuations, model fitting, and so on.

Reducing uncertainty

While tracking weight and calories, I’ve noticed a problem.

When you decrease your calorie intake sharply (from a fast or beginning of a new diet), of even change the spread of fat vs carb vs protein significantly, I’ve notice an immediate change in weight.

When beginning a diet, this early loss vastly outstrips the predicted loss. These two factors were something I previously attributed to just poor caloric estimates, or, shall we say “food accumulation in my guts” (or rather, the loss of accumulated recent meals causing sharp weight changes).

Here’s my wow plot:

Predictions (See dieting-differential-equations-2)
   (Y)     ^
      Lbs: |
      >228 | ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
      >226 | ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
      >224 | ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
      >222 | ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
      >220 | +-----start weight⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
      >218 | ⡏⠙⠳⢶⢦⡤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
      >216 | ⡇⠀⠀⠀⠉⠙⢕⣒⠬⢍⡒⠒⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
      >214 | ⣇⢀⠀⠐⠀⠀⠀⠐⠑⠢⢌⡑⠢⠤⣀⡈⠉⠑⠒⠢⠤⢄⣀⡀⠀⠀<---sedentary⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
      >212 | ⡇⠀⠉⠀⠊⠐⠒⠀⠂⠀⠀⠈⠑⠢⣀⡈⠑⠒⢄⣀⠀⠀⠀⠈⠑⠒
      >210 | ⡇⠀⠀⠀⠀^wts ⠀ ⠀⠀⠀⠀⠈⠢⠤⡀⠀⠉⠑⠢⠤⣀⡀⠀⠀⠀
      >208 | ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀  ⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠈⠑⠢⢄⣀<--light
      >206 | ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀        mod--->⠈⠑⠤⢄⠀
      >202 | ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀
      >200 | ⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
      >198 | ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀GOAL
      >196 | ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
      >194 | ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
      >192 | ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
      >190 | ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
-----------|-|---------|---------|---------|--------
           | >0        >15       >30       >45       >60
           | Days

On the first couple days of the diet, I lost about 8 lbs, and then levelled off for the next week. Plotting the rest of the weights out for two months would clutter it, but let’s just say it’s mostly level.

So, there’s two curiosities. First, what’s with the early loss? Second, why did I level off?

Early loss

Any random on the internet will call this “water weight”, but what does that mean? (By the way, the opposite effect holds too: after cheat days I can gain 5 lbs easily.)

The answer allegedly is that the body stores energy in the form of glycogen, which is a carbohydrate. Glycogen is stored in the liver and muscles, and is used for quick energy. It’s also stored with water, which is why it’s so heavy. When you start a diet, you would think your body uses up the glycogen stores, and the water is released. That would explain some early loss, except I’m not in a total energy deficit. In fact, I only cut 10% of my calories.

From what I can tell, the liver stores 2000 calories or so. It should take me days to deplete that, unless I’m completely fasting. Even depleting 10% would be 200 calories, which is 50g of glycogen, maybe accompanied by 200g of water. That’s 0.5 lbs, not 8.

It turns out that as soon as I switched to my reduced calorie load, I also switched what I was eating - I wanted to go higher fat/protein so I would not feel so hungry all the time.

It turns out switching from mostly carbs to mostly protein can cause an immediate and severe dip in weight.

Here’s what I think is going on. First, look at how much water is retained to store each gram per macro:

grams of water
------------------
Carbs ........ 3-4
Protein ...... 2
Fat .......... 1

This just means that every gram of carbs causes you to retain 3-4 grams of water, etc. If the “weight” you have to carry is the gram of macro + its water, then we have 5 for carbs, 3 for protein, and 2 for fat.

"Carry" grams
------------------
Carbs ........ 5
Protein ...... 3
Fat .......... 2

However, not all calories are the same:

calories per gram
------------------
Carbs ........ 4
Protein ...... 4
Fat .......... 9

Therefore:

grams to carry per calorie
--------------------------
Carbs ............... 1.25
Protein ............. 0.75
Fat .................. 2/9

Take my word for it that 117 g each of protein, carbs, and fat is 2000 calories. Then that’s 117*5 + 117 * 3 + 117 * 2 = 1170 grams to carry. For a given calorie load, you carry C/2000 * 1170 ~=0.6 * C grams, or 0.0006 * C kg. That’s around 2.5 lbs just to hold your food.

Corollary: Every 80 carbs you eat is +1 lb of carry weight.

However, a high carb diet might have 500g of carbs, which is up to 2500g = 5.5 lbs. Vs a high fat diet, for which 2000 calories requires 222g of fat, which is 444g of carry, or just over 1 lb. So switching macros can cause a 4-5 lb drop in weight. And presumably this happens basically instantly, not over time. Body composition hardly changes, but the weight swings based on macro balance.

If you’re like me, and you go out swinging before the first day of the diet, you can go from 3000 calories carb-heavy pizza and beer, to below 1000 calories, mostly protein on day 1. (trust me I’ve done this a lot). It wouldn’t be unreasonable to see a 10 lb drop in weight in the first few days. And believe me you feel smaller, but it’s not fat loss.

Leveling off

It’s probably obvious now why I “level” off. The question isn’t “Why doesn’t the weight loss continue”, because there is no early functional weight loss. Just a macro balance change causing changes to water content in my body.

The more subtle problem is that my expected rate of weight loss is based on starting weight. And my calorie deficit and predicted weight all come from that.

So I’m basically completely misrepresenting my weight as too high, then expecting a steeper slope down from a given deficit. That is, my basal metabolic rate (calculated from weight) is much lower than I think because my weight is 5-10% higher from water due to pizza and beer binges before my diet.

All that to say, maybe third time is the charm.

Closing

To ensure that yes, this year I will actually do it, I mailed a large check to a friend who can cash it if I do not stand on a scale in front of him by the end of July and clock in at 200 lbs. I’m cautiously optimistic.