CICO denial

— Last summer I gained 5 kg of muscle mass
— How did you do that?
— I consistently ate more than I expended
— That’s not a way to gain muscle, bro
— What are you, a CICO denier? Increasing your muscle mass is an energy balance problem: when people gain muscle mass, it’s always because more calories were consumed than were expended. This is a hard fact, man
— You are right. No one can break the Laws of Thermodynamics


The simple, unavoidable fact of human physiology is that you can’t increase your muscle mass without creating a calorie surplus. Whether you do this by eating more, moving less or a combination of the two, is a matter of preference.


Making up a physiologic behaviour from a physics constraint

(versión en español: pinchar aquí)

When you eat more calories than you burn, the excess calories are primarily shunted into your adipose tissue. Your adiposity, or body fatness, increases. It really is as simple as that (Stephan Guyenet, PhD)

No, it is not as simple as that. As a matter of fact, that idea is a perfect example of the energy balance pseudoscience. The laws of physics do not tell you how things work, but rather the constraints under which they work. Whatever happens in a system, its behaviour cannot violate nature laws: matter cannot be created from nothing, an object will not accelerate unless a net force is applied or energy can not be created nor destroyed. Nevertheless, those limitations are often irrelevant in practice. For example, according to the Law of Conservation of Matter, you cannot accumulate matter in your body unless more matter enters the body than exits. But that fact is irrelevant for understanding growths in a living being.

What I want to explain in this blog entry is that the fraud in the energy balance theory does not lie in the maths —since this theory is indeed compatible with the physics constraint imposed by The First Law of Thermodynamics—, but in the physiologic behaviour that this theory makes up by using language tricks.

I am going to use a water tank as an analogy. Water is poured regularly into the tank and part of its contents is lost through a drain. We know that water cannot accumulate in the tank unless more water comes in than is lost through the drain. That is a true as useless, because it is just saying accumulation with different words. But, do you think that when more water comes in than goes out, the excess water is accumulated in the tank?

I am going to present two simple models based on a water tank. Both of them are compatible with the physics laws, since water is not created nor destroyed in any of them, but they behave differently. I insist: my point is that the energy balance theory is a fraud not because of its maths but because it makes up a physiologic behaviour.


Model #1


Let us assume, for example, the following behaviour of the drain: the rate at which water flows from the tank is constant. In this case, if the rate of water flowing into the tank is bigger than the drain rate, water will accumulate in the tank. We could say “excess water” accumulates in the tank.

But let us assume that the drain rate is adaptative and equal to the rate of water poured into the tank. Would you say that, in this case, “when more water comes in than goes out, excess water accumulates in the tank“? No it does not and, in this case, there is no such thing as excess water. Not always it is correct to say that “when more water comes in than goes out, the excess water is accumulated in the tank“.

It is our physiology knowledge what would lead, where appropriate, to talk about “caloric excess”. From the First Law of Thermodynamics we cannot deduce a physiologic behavior, which is what the fraudulent energy balance theory does.

For example, the storage of carbohydrates as glycogen cannot be caused by an intake that exceeds their oxidation, because that would mean that by increasing our carbohydrate intake we could gain as much weight as we wanted. But physiology says it is not like that.

a chronic imbalance between carbohydrate intake and oxidation cannot be the basis of weight gain because storage capacity is limited and controlled, conversion to fat is an option which only occurs under extreme conditions in humans, and oxidation is increased to match intake (Broskey et al.)

Physiology determines if it is correct to speak of a specific “excess” as a cause of a specific accumulation.

Model #2

In this model part of the contents of the tank is lost through the drain, but part is lost because it overflows the walls of the tank.


Please note that our body has physiologic mechanism that can dissipate unnecessary nutrients as heat. One of these mechanisms are the uncoupling proteins, which can be found in several organs and tissues in our body.

Moreover, in this model the walls of the tank are not fixed, but they can dynamically expand or contract, changing the total volume of the tank. In this model the position of the walls is regulated by the concentration of specific substances in the water.


Let us assume that a specific substance is present in the water and it makes the tank expand. As a consequence of that expansion, the total volume of water stored in the tank increases. Would you say that, in this case, “when more water comes in than goes out, excess water accumulates in the tank“? No, this not correct. The use of the term “excess water” is unwarranted.

Water is not accumulated because more water comes in than goes out, although more water will come in than go out when water accumulates.

This model does not violate universal laws of physics —water is not magically created nor destroyed— and the existence of another model that is also compatible with the physics laws, but with a behaviour different from that of the energy balance theory, clearly shows that this theory goes beyond the physics constraint that the First Law of Thermodynamics establishes: it introduces an unwarranted physiologic behaviour. As I said before, the fraud of the energy balance pseudoscience does not lie in the maths but in the unwarranted physiologic behaviour that it makes up.

Fundamentally, obesity is a problem of energy imbalance, which only develops when energy (food) intake exceeds total energy expenditure (Schrimpton et al.).

Obesity is not a problem of energy imbalance: it is a problem of excessive triglyceride accumulation in the adipose tissue. There is no physiologic basis for talking about “energy” or “energy excess” in regard to weight changes in the human body.

Energy Balance Pseudoscience and Causality Hoax (2/2)

The messages I want to convey with this second part of the blog post are as follows:

  • To complete the explanations from the first part, which can be summarized as that the energy balance theory does not rightfully derive from the laws of thermodynamics. Energy intake and energy expenditure are not necessarily neither the cause nor the solution to the obesity problem
  • To clarify the causality fraud and its consequences in practice by means of a simple mathematical model of body weight dynamics, but also to explain the limitations of mathematical models.

I will use a very simple model of body weight dynamics, taken from an article (see) from Kevin Hall, a well-known promoter of the energy balance pseudoscience. In the past I have criticized the pretensions of this gentleman to interpret the forecasts of his mathematical model as scientific evidence, something always reprehensible but it is especially so in his case because he uses his results to blame the victims, the obese, for not being able to lose weight (see, see).

Please, do not bother criticizing the modifications I’m going to introduce in the mathematical model: I do not intend to propose an alternative model nor to improve the model. The ideas I want to convey are others and the model I use seems quackery to me, because instead of modelling the phenomenon of interest, which is the accumulation of triglycerides in the adipose tissue, what the model does is model the terms of the energy balance. Any model that is based on the energy balance theory is, in my opinion, insurmountable quackery (see first part of this entry).

Model #1: A model that lacks a physiological adaptation

I assume hereafter that the daily energy intake is as the picture below shows (it is the relatice change with respect to the baseline, which is supposed to be a point of intake&weight equilibrium):

The model is very easy to understand. The energy intake is the input (on the left side) and the body weight is the output (on the right side). Each day we calculate (yellow block) the difference between caloric intake and energy expenditure and, in this model, that value determines the daily weight gain. The body weight is calculated as the cumulative sum (orange block) of all these daily changes.

This model does not include a physiological adaptation mechanism.

In the graph below, on the left I show the body weight evolution with time and on the right the energy expenditure evolution. By design of this model, when the energy expenditure is reduced around 200 kcal/d the body weight will stabilize. It can be shown that when the energy intake is a constant the model stabilizes its output at weight=intake/epsilon, which in this case is -200/25.8 =-7.75 kg. There is no need to run the model to know that result because, as I said above, it is part of the design of the model.

We are not seeing a rebound effect (i.e. a physiological adaptation) because in the Model #1 we do not include a physiological adaptation mechanism.

Do we deduce from this simulation that the physiological adaptation does not exist in real life and that what happens is that obese people simply eat more than they tell us? (see).

Model #2: A model that does include a physiological adaptation

Let us suppose that, triggered by the food restriction, our physiology has changed. In Model #@ we maintain that there is a certain tendency to lose body fat, driven by the fact that we are eating too little, but now our adipose tissue has become especially prone to accumulate body fat (see the lightgray block and a new yellow block that adds these two effects in the figure below):

In this new version of the model, the body weight evolves as shown in the pictures below (blue curve on the left side). The energy expenditure is reduced as shown by the blue curve on the right side. The graph on the right shows that the simulated energy expenditure has been gradually reduced by around 50 kcal/d additional to what we expected (which would be the red curve):



In this model, the body weight is not regained by “eating more than it is expended”, but rather by the opposite, because the physiological adaptation that has been modeled is caused by the food restriction, i.e., for “eating an insufficient amount of food” in a sustained way. Does this model violate any laws of physics? Please consider that for our body functioning with the substrates that have not been stored is like we’ve just consumed a few grams less of food each day. It is not that hard to understand that Model #2 does not violate any law of physics or suppose an impossible situation for our body.

I believe there is no point in explaining how I implemented the physiological adaptation mechanism in Model #2. What I want to explain is that when I believe that there is a physiological adaptation and, therefore, I include an adaptation mechanism in the model, the model shows a physiological adaptation. And Model #2 is not doing anything clearly impossible: we are talking about an additional reduction of the energy expenditure of 50 kcal/d after two years. Note that the Hall calculations were that the CALERIE2 participants were consuming around 37 kcal/d more than they actually consumed (difference between black and white bars in the graph), which is a difference of the same order of magnitude of those 50 kcal/d that I have simulated. What the Hall model attributes to an increased energy intake when compared with actual data is probably caused by the physiological adaptation whose effects Hall despises.

In short, the message here is that when Hall argues that there is no physiological adaptation in reality because his model does not show a physiological adaptation, his argument is fallacious: if he included the appropriate mechanism in his model, his model would show a reduction of the energy expenditure that goes beyond his present prediction. Just as I have done. In short, his argument can be summarized as follows: “the physiological adaptation does not exist in real life because I did not want to include it in my mathematical model”.

This simulation illustrates the very long equilibration time for weight loss in obese subjects and demonstrates that the weight loss plateau observed after 6 mo cannot be a result of physiological adaptation (source)

Model #3: An “energy” model that does include a physiological adaptation

Model #3 is, mathematically speaking, identical to Model #2. It also includes a physiological adaptation mechanism, but the magnitude of that reaction now changes directly the total energy expenditure and the energy balance equation is applied to compute the magnitude of the daily body fat accumulation.

Note that the evolution in time of intake, energy expenditure and body weight are identical to those of Model #2, because mathematically models #2 and #3 are identical (it has only changed at which point of the feedback loop the physiological adaptation is applied). What is different between these two models is the assumed causality.

  • Model #2. Your adipose tissue stores more fat–> Your body has less fuel to spend–> your body reduces its energy expenditure
  • Model #3. Your body reduces its energy expenditure–> your body has more fuel to store–> your adipose tissue stores more fat

In Model #2 the adipocytes have changed their behavior and they seek to recover the lost body fat, and the rest of the body can not spend what has already been stored in the adipose tissue. Therefore, as a consequence of gaining weight, the energy expenditure is reduced exactly like in Model #3. A reduction in the total energy expenditure would only be a consequence of the underlying physiological process that is actually causing the changes in the accumulated body fat.

For the sake of clarity, these are the  weight (blue curve on the left) and energy expenditure (blue curve on the right) for Model #3:

The energy balance pseudoscience assumes that if you are regaining weight this is caused by an energy imbalance. What I am showing here is that other causalities are compatible too with the first law of thermodynamics: it is possible that the cause of gaining weight is a physiological adaptation regardless of the calorie intake or the energy expenditure. The adaptation can be driven by starvation, by losing weight, by a change in the mean size of the adipocytes or by another physiological cause. In this case, the energy expenditure would be an irrelevant possible symptom of the underlying physiological process that is indeed being caused by food scarcity. Model #2 does not violate any law of physics but it does highlight the causality fraud of the pseudoscientific energy balance paradigm.

it can be calculated that a weight loss of 20-kg body weight in an obese patient will result in an obligatory average reduction of 400 kcal in daily EE. Besides this obligatory or passive energy economy, further reductions in daily EE can also be expected as it has repeatedly been demonstrated that the fall in EE is greater than predicted by the loss of body mass, thereby underscoring the operation of mechanisms that actively promote energy conservation through adaptive suppression of thermogenesis. (source)

May be it doesn’t happen “through” suppression of thermogenesis: they are assuming that an effect is the cause.

How to avoid the physiological adaptation

From the point of view of the energy balance theory, if there is a physiological reaction equivalent to 50 kcal/d, if you eat 50 kcal less you will compensate for the physiological effect. But understanding the process requieres understanding causality: if the cause of the physiological adaptation were an excessive intake, reducing the energy intake would make the reaction disappear and the weight would remain stable. But the cause of that reaction is not necessarily that you eat “too much”, but rather the opposite. The adaptation may be caused by losing weight “eating of less”, i.e. by scarcity of food. If we confuse energy expenditure, a symptom, with the cause of weight regain, we will not prevent that weight regain.

What does the model predict if we even consume 50 kcal/d less? That the physiological reaction will continue to exist, because its cause is not an excessive energy intake. Reducing the energy intake is treating a symptom, the “energy balance”, not fixing the actual cause of that reaction.

I do not intend to draw any conclusions as if in real life there is or not a physiological adaptation similar to the one that I have included in the model. My message is exactly the opposite! What I try to explain is that no useful conclusion can be drawn from a simulation, about the existence or inexistence of such adaptation, because a mathematical model simply does what we command it to do.

And the other conclusion has to do with causality: if a factor makes us fatter, it has to make us fatter, not necessarily have a direct effect on our energy intake or on our energy expenditure. We save money for reasons that can not be deduced by examining the factors that affect our incomes or expenses.

Further reading:

Energy Balance Pseudoscience and Causality Hoax (1/2)

(versión en español: pinchar aquí)

Let us assume that your family unit saves 300 euros/month, the difference between the 2000 euros you earn at your job and the 1700 euros that you spend.

Savings = incomeexpenses

300 = 20001700

The above equation is correct, but “maths” tell us nothing about why you’re saving that amount each month. Income, expenses and savings are just numbers I can observe, but unless I know how your family thinks, unless I know your interests and motivations, I will not understand why you are saving 300 euros per month. The real cause can not be deduced from the knowledge of incomes and expenses.

Your savings are determined by your incomes and expenses. If you have no incomes you can not save!

This is a fallacy because it deceives drawing conclusions from conditions in which your behavior would be different. Of course if you have no incomes you can not save, but that is not the situation that we are talking about. We are talking about a situation where your incomes are 2000 euros/month and in that case saving is not mathematically impossible nor unrealistic.

Your  savings are determined by your incomes and expenses

It is typical of pseudosciences to use ambiguous terms (misleading language). These terms are introduced in the arguments with one meaning but, without prior notice, they are used to imply a different one. What you save each month can be “determined” (meaning “calculated“) from the knowledge of incomes and expenses, e.g. in the same way that the expenses can be computed by using a mere subtraction of incomes and savings. But, without prior notice, “determined” stops meaning that and it deceitfully starts to imply that changes in certain parameters cause changes in others. We should notice the difference between the following two statements:

You save because your incomes are bigger than your expenses

What you save can be calculated from incomes and expenses

The first one is correct but the second one is not necessarily so.

Why are you saving 300 euros/month? Maybe it is because your goal is to buy a car in the middle term. Is it possible that without that goal in mind your expenses could simply raise and match your incomes? Is it possible that if you planned to have a big expense in the future, you would accordingly reduce your expenses and increase your savings? The reasons why you save may have nothing to do with the magnitude of your incomes and expenses, unless you think of particular or extreme cases that are quantitatively different from the case under discussion. You normally save for other reasons and you consequently adjust your expenses.

Of course, it is also a possibility for a family to pay no attention to how much they save each month. In the absence of control, in the absence of regulation, the savings would be indeed determined by the difference between incomes and expenses. It is not impossible, but it is just a particular case, one where the parameter of is unregulated. It is only a possibility that may or may not happen, not the will of gods.

Of course I am drawing an analogy with the pseudoscientific energy balance theory. The defenders of this stupid theory believe that their ideas derive from an inviolable law of physics, but the reality is that what they defend is the idea that if suddenly your family starts saving 400 euros/month instead of 300/month, to understand why this change happened what we need to study is what determines your incomes or what determines your expenses. They even build mathematical models based on that stupid idea to try to understand obesity, instead of studying the physiological processes of triglycerides’ absorption and release (lipogenesis and lipolysis). Common sense tells us that the reasons why you save now more money can not be understood by means of studying the symptoms of that change.

The factors that determine the body fat accumulation may have no direct effect on energy intake nor in energy expenditure. A mathematical model of obesity based on the energy balance equation is just pseudoscience.

You visited recently a friend who has been hospitalized and as a result of that experience you changed the amount of money that you save per month. But, according to the “economic balance” theory, that visit can’t play a relevant role in your savings because it barely affected your expenses (a couple of euros of public transportation) and that visit doesn’t affect your salary

Even if we made a very detailed mathematical model of what determines the changes in incomes and expenses, we would be modeling the symptoms, not the phenomenon of interest, that would be the savings and the real causes of its behaviour. That mathematical model would be pure pseudoscience.

An imbalance between energy intake and energy expenditure will lead to a change in body weight (mass) and body composition (fat and lean masses). (source)

For example, the incidence of obesity and its co-morbidities has increased at a rapid rate over the past two decades. These conditions are characterized by changes in body weight (mass) that arise from an imbalance between the energy derived from food and the energy expended to maintain life and perform work.(source)

Mathematical models are beginning to provide a quantitative framework for integrating experimental data in humans and thereby help us better understand the dynamic imbalances of energy and macronutrients that give rise to changes in body weight and composition (source)

Obesity could be due to excess energy intake or decreased energy expenditure (source)

for insulin to cause fat gain, it must either increase energy intake, decrease energy expenditure, or both (source)

The fraud of the energy balance theory does not lie in the maths, it lies in the causality. The hoax is not the violation of universal laws, since the energy balance theory does not violate those laws, but the unwarranted assumption that the adipose tissue’s behaviour is passive or not physiologically regulated. Note that we know that there is a physiological regulation of the adipose tissue (see).

Why does no one propose to study muscle hypertrophy by using the energy balance pseudoscience? Is that so because the energy balance theory does not apply to energy accumulated in muscle mass? Is to eat more than you expend the way imposed by the laws of physics to increase our muscle mass? (see)

This is the end of the first part of this article. Read the second part.

Further reading:

Why the Energy Balance Theory is pseudoscience

Why the Energy Balance Theory is pseudoscience

First of all, its basis is a mere tautology (i.e. needless repetition of an idea) referred to the adipose tissue:

if the adipose tissue accumulates energy, in that tissue more energy comes in than gets out

This is just a truism, because that is what “accumulation” means, since energy can’t come out of nothing nor can it disappear, but this tautology tells us nothing about why the accumulation of triglycerides is happening. The tautology (in its correct form) is useless. The false sense of utility provided by the Energy Balance Theory comes from a deceitful transformation of the useless tautology: the trick is that the boundary for the application of the First Law of Thermodynamics is unjustifiably considered to be the whole body’s boundary, instead of the correct boundary, which is the adipose tissue’s boundary. Understanding this deception is crucial: if you want to apply the First Law of Thermodynamics, you must have a clearly defined physical boundary in its use. The Energy Balance Theory violates that principle and that fact makes this theory a hoax.

A thermodynamic system is that part of the world to which we are directing our attention. Everything that is not a part of the system constitutes the surroundings. The system and surroundings are separated by a boundary.

Internal energy is the totality of all forms of kinetic and potential energy of the system

When the “Calories In” and “Calories Out” terms are used, the physical boundary is the whole body’s boundary. This is mandatory. And, therefore, the totality of all forms of energy in the body have always to be taken into account. It is unjustifiable and deceitful to only consider the energy stored in a specific tissue (e.g. the accumulation of triglycerides in the adipocytes).

Calories In = Calories Out + Change in FAT DEPOSITS

Calories In = Calories Out + Change in ALL ENERGY STORES

Any energy that’s left over after the body has used what it needs is stored as body fat (source)

That is a theory that doesn’t derive from physics’ laws.

The faux causality problem

Moreover, the Energy Balance Theory relies on an unfounded attribution of causality. It is easy to understand this point, just by comparison with any other growth in a biological system. What does the Energy Balance Theory tell us about conditions such as fatty liver, muscle hypertrophy, giantism or a tumor’s growth? What does it tell us about how anabolic steroids work? All of those situations represent the growth of tissues inside of the body, and therefore they represent energy accumulation in one or several tissues, just as obesity does.

Fatty Liver

Fat accumulates in the liver, therefore

it is an incontrovertible fact of physics that fatty liver happens when calorie intake exceeds expenditure […] the laws of physics ensure that any person will reverse its fatty liver if calorie intake is reduced sufficiently

it is an incontrovertible fact of physics that weight increases when calorie intake exceeds expenditure […] the laws of physics ensure that any obese person will lose weight if calorie intake is reduced sufficiently


Your body can’t grow unless you eat more than you expend:

An imbalance between energy intake and energy expenditure is the primary etiology for giantism.

An imbalance between energy intake and energy expenditure is the primary etiology for excess weight gain.

Muscle mass

Muscle tissue can’t grow unless there is a caloric inbalance:

Muscle hypertrophy is defined as a state of increased muscle mass resulting from chronic nutrient excess, where energy intake significantly exceeds energy expenditure

Obesity is defined as a state of increased adiposity resulting from chronic nutrient excess, where energy intake significantly exceeds energy expenditure


A tumor can’t grow unless more energy comes in than gets out:

A key determinant of a tumor’s growth is the balance between ingested calories and the body’s basal energy expenditure. The tumor’s growth therefore results when small positive energy balances accumulate over a long period of time

A key determinant of obesity is the balance between ingested calories and the body’s basal energy expenditure. Obesity therefore results when small positive energy balances accumulate over a long period of time

Anabolic steroids

Do anabolic steroids increase your muscle mass by making you hungry or sedentary?

if anabolic steroids don’t increase energy intake […], and don’t decrease energy expenditure, then how exactly are they supposed to cause energy accumulation in the body as fat? There is no energy fairy

if insulin doesn’t increase energy intake [… ], and doesn’t decrease energy expenditure, then how exactly is it supposed to cause energy accumulation in the body as fat? There is no energy fairy

Your energy expenditure is not a controllable input of the system

The Energy Balance Theory hoax is supported with rethorical fallacies where the energy expenditure is alluded as if it were a controllable input of the equation. It is not. If both energy intake and energy expenditure are considered inputs of the system, and if the decepcion explained above is used (i.e. considering only the energy stored in a specific tissue), a false impression of causality is created:

When calorie expenditure decreases and calorie intake increases, the energy balance equation leaves only one possible outcome: fat gain (source)

When calorie expenditure decreases and calorie intake increases, the energy balance equation leaves only one possible outcome: fatty liver or muscle hypertrophy or giantism or a tumor’s growth or you are pregnant and the fetus grows

As explained above, to assume a result for an output (“calorie expenditure decreases”) is cheating. It is not an input we can control.

When calorie intake increases, in the case where the calorie expenditure decreases the energy balance equation leaves only one possible outcome: fatty liver or muscle hypertrophy or giantism or a tumor’s growth

The energy balance equation can NEVER be used to predict the response from a living tissue to a stimulus, because that law has nothing to do with biology. Its use related to the study of obesity is based on rethorical fallacies and it is, therefore, unwarranted.

Does this mean that the First Law of Thermodynamics is not valid in a biological system?

That idea is not correct: the First Law of Thermodynamics is always fulfilled, and, therefore, it is also fulfilled in biological systems. It is the Energy Balance Theory what is a fraud, because it is both a misapplication and a misinterpretation of what the First Law of Thermodynamics says.

The pseudoscience is the pretension that the Energy Balance Theory is rightfully derived from the First Law of Thermodynamics and that, therefore, it must be used to deduce causes and solutions for obesity. The Energy Balance Theory is a hoax and it can’t be used for that purpose, just as it is clearly inappropriate to deduce how to cure your fatty liver, how to increase your muscle mass or how to treat a kid that suffers from giantism. Obesity is not a special condition.

Ultimately, obesity reflects energy imbalance, so the major areas for intervention relate to dietary intake and energy expenditure, for which the main modifiable component is physical activity (source)

Giantism also reflects energy imbalance, right? What are the major areas for intervention in that case? A tumor’s growth also reflects energy imbalance, right? What are the major areas for intervention in that case?

Further reading:

Sugar-sweetened beverages and obesity

DAILY calories from sugar-sweetened beverages among U.S. adults (1980-2010):

imagen_0462 (source,source)

CUMULATIVE TOTAL increment in the percentage of obese adults (orange stars) versus CUMULATIVE TOTAL calories from sugar-sweetened beverages (blue line; numerical data not shown in the figure):

Are these data consistent with an important effect of sugar-sweetened beverages on body weight? Do they suggest, on the contrary, that sugar-sweetened beverages are highly unlikely to be an important cause of obesity?

Further reading:

If your sugar intake today is lower than yesterday’s, do you slim down?


This article is an extension of an article that I posted a few days ago. The idea that I want to discuss is the one below:

We have data from the time evolution of two parameters, named A and B. Some people believe that there is a dependence relationship between A and B so that A has a significant effect on B, but we know that A suffered a trend change and B didn’t, so other people say that this fact suggests that it is highly unlikely that A has a significant effect on B.

For the purpose of explaining the failures in the previous idea, I will assume a very simple model of obesity: we gain 3 g of body weight for every 100 g of sugar consumed. Please, don’t bother to criticize this model: I will only use it as a tool to explain the errors in the idea explained above. What we will see is that, under the premise that sugar is determining our body weight gain, the correlation between sugar intake and body weight may be low. That is the main conclusion and the specific model used for the explanations is irrelevant.


As said above, our assumption is that we fatten 3 g for every 100 g of sugar consumed. If our intake of sugar were 50 g, we would fatten half that amount: 1.5 g.


Given a specific sugar intake, the DAILY increase in body weight will be directly related to that DAILY sugar intake.

If I’ve consumed a certain amount of sugar PER YEAR, the PER YEAR increase in body weight would also be directly related to the PER YEAR sugar intake. For example, if one year’s sugar intake were 33 kg, our body weight would increase by 1 kg that year. Had I consumed only one third of those 33 kg, my body weight would have increased that year one third of 1 kg.

Let’s say that over the years our DAILY sugar intake has changed according to the blue curve in the graph below. In this scenario, our DAILY body weight gain would change as indicated by the red curve (calculated according to the hypothesis of that we fatten 3g per each 100 g of sugar consumed).


DAILY sugar intake and DAILY body weight gain are directly related variables. Their correlation, i.e. the mathematically-computed resemblance between them, is maximum.

If we compute (in blue) the CUMULATIVE TOTAL sugar intake since 1980 (i.e. for each year we compute the total amount of sugar consumed since 1980 until that year), versus (in red) the CUMULATIVE TOTAL body weight increase since 1980 until that year, we get this:


Again, as we saw with DAILY body weight increase and DAILY sugar intake, there is a direct relationship between CUMULATIVE TOTAL sugar intake and CUMULATIVE TOTAL body weight gain. This is also to be expected: under the premise that body weight gain is directly proportional to the sugar intake, if the CUMULATIVE TOTAL sugar intake over the past X years gets bigger you are expected to gain more weight, and if it gets smaller you are expected to gain less weight.

In order to clarify what comes next, let’s assume we are filling a bucket by pouring into it daily glasses of water. Every day we pour into the bucket the contents of one glass of water. Let’s assume that the volume of water in the glass has been progressively rising, day after day, until reaching a peak at 110 ml, and then, for the last 15 days we have gradually reduced the volume of water in the glass until reaching 95 ml. Is the cumulative total water in the bucket expected to be reduced at the end of those 15 days? Does anyone think that if I reduce the volume of water poured daily, the volume of water in the bucket has to decrease? When we confirm it doesn’t decrease, do we conclude that it is highly unlikely that the volume of water in the glass has an important effect on the volume of water in the bucket?

Let’s get to the point, but first remember that the correlation between DAILY sugar intake and DAILY body weight gain is maximum, and remember, too, that the correlation between CUMULATIVE TOTAL sugar intake and CUMULATIVE TOTAL body weight gain is also maximum. Now, what kind of relationship exists between the DAILY sugar intake at a given year and the CUMULATIVE TOTAL body weight gain at that same year? A direct relationship is not to be expected: if the DAILY sugar intake is reduced, the CUMULATIVE TOTAL body weight is not expected to be reduced, in any case that year the body weight will go up by a smaller amount, but it will continue to increase, and the effect of a smaller DAILY sugar intake will also be small in relative terms, since we have only changed the data for one year that has to be accumulated to the rest of the years in the CUMULATIVE TOTAL: we have been accumulating body weight for years and the sugar intake during the last one of those years is expected to have a small effect in the CUMULATIVE TOTAL.

From another point of view, the CUMULATIVE TOTAL sugar intake —including the contribution from last year, but with a weight that depends on how many years are being considered—, is the variable which determines the CUMULATIVE TOTAL body weight gain to that year. It is nonsense to expect a direct relationship between DAILY sugar intake and CUMULATIVE TOTAL body weight gain. And, in fact, that relationship is not a direct one. Assuming that a man weighed 80 kg in 1980, the graph below shows his CUMULATIVE TOTAL body weight (red curve) versus his DAILY sugar intake (blue curve):


We know that the red curve is completely determined by the blue curve, but they don’t have a good correlation. Or in other words, we confirm that a low correlation tell us nothing about the existence of a dependence relationship between two variables. If for the same situation, we had chosen the two previous graphs, we would have concluded that the relationship between sugar intake and body weight gain is undeniable.

If we recall the idea at the beginning of the article, A (blue curve) has changed, and the effect on B (red curve) is apparently small, but we know for a fact that A completely determines B.

What are we seeing?

In the last graph I presented above, the red curve is completely determined by the blue curve and the correlation between them is low. How is that possible? Because these two variables, while they are completely related, they don’t have a direct relationship. One variable is the CUMULATIVE TOTAL body weight gain, the effect of several years of fattening, while the other variable is just the DAILY sugar intake for one of those years. The fact that one of them goes on rising, albeit more slowly, when the other one decreases DOES NOT suggest that a cause-effect relationship between them is unlikely. The CUMULATIVE TOTAL body weight gain is not supposed to go down when the DAILY sugar intake is reduced: a “negative consumption of sugar” would be needed to produce such an effect on body weight. And, in any case, it would be the level, i.e. the fact that sugar intake is negative, what would produce a decrease in the  CUMULATIVE TOTAL body weight gain, not the change, i.e. the fact that sugar intake decreases. Even if it were possible to consume negative amounts of sugar, neither there would be a direct relationship between both variables nor a high correlation would be expected.

anyone who defends that sugar intake is a main cause of obesity and diabetes is proposing that there is a direct relationship between those variables

That’s a fallacy. The hypothesis that sugar is fattening means that the DAILY sugar intake affects the DAILY body weight gain. Nobody says that the DAILY sugar intake is directly related to the CUMULATIVE TOTAL body weight gain to that date: it is stupid to expect that when your DAILY sugar intake goes down your CUMULATIVE TOTAL body weight has to go down. This is not mathematics: it is just common sense.

Does the data presented by Guyenet in his graph suggest, as he says, that “sugar is highly unlikely to be the primary cause of obesity“? No, it does NOT suggest that. His graph is absolutely consistent with a direct effect of the DAILY sugar intake on the DAILY body weight gain: it can easily be seen that when the DAILY sugar intake was decreased, the DAILY body weight gain also decreased.



The main Guyenet’s mistake, or the base of his attempt of deception, is that he assumes that the CUMULATIVE TOTAL body weight gain and the DAILY sugar intake are directly related, and that hypothesis is both nonsense and inconsistent with the hypothesis that he is trying to refute. No one proposes that the DAILY sugar intake has a direct relationship with the CUMULATIVE TOTAL body weight gain: this specific relationship is expected to be non-linear! Had he compared DAILY body weight gain with DAILY sugar intake, he would have found a direct relationship (consistent with the hypothesis that sugar is fattening). Had he compared CUMULATIVE TOTAL body weight gain with CUMULATIVE TOTAL sugar intake, he would have found a direct relationship (consistent with the hypothesis that sugar is fattening).

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We have seen in this article, with help from a simple model of obesity, that although CUMULATIVE TOTAL body weight gain and DAILY sugar intake are not well correlated, that doesn’t suggest that there isn’t a causal relationship between both variables.

On the other hand, Guyenet confuses a lower intake of sugar with a negative consumption of sugar. Logic says that if sugar is fattening, reducing its consumption doesn’t make us slim down.


  1. When in this article I use the term “direct” what I’m saying is that when one variable goes up the other variable also goes up and that when one variable goes down the other variable also goes down. Note that a direct relationship is not necessarily one of proportionality.
  2. the data used by Guyenet as support for his hypothesis is epidemiological. This is relevant, since when part of the population chooses to decrease their sugar intake, they probably take additional measures related to improving their health, such as not eating grains/flour, not consuming processed products, cooking more at home, less frequently eating out, etc. And, in addition, those who make these decisions have not been chosen at random: they are the ones who have decided to take care of themselves, so we’re not just comparing sugar intake: we are comparing lifestyles. That is an important difference with respect to a randomized controlled trial (RCT), where participants can’t decide if they decrease their sugar intake (and perhaps its replacement by another product). In the case of a RCT that reduction is supposed to be the only difference between goups. Guyenet’s data is far from being that case.
  3. We are talking about total sugar intake, regardless of its format, regardless of when it is consumed, regardless of which products accompany it in the mouth. A lot of information is missed.
  4. We are talking about the average sugar intake of a population and the percentage of adults above a specific level of obesity. The interesting data would be to compare individualized DAILY sugar intake and DAILY body weight change, and we would want to have this data for a large number of people.
  5. Guyenet says the variation in the percentage of obese adult has been small —he even expected a decrease! — but, actually, the change has been bigger than expected from the small reduction in the DAILY sugar intake (gradually decreasing the intake from 110 g/d to 95 g/d is an average reduction of 9% relative to the baseline: it is not an 18% decrease!). May be people who have decreased their sugar intake have also taken, at the same time, other measures to improve their health, and those additional measures could be contributing to the undeniable trend change perceived from year 2000 in the percentage of obese adults.

Further reading: