Those who are interested in the mathematical aspects of ideas expressed in *Foods That Lie* might wish to see the elegant formulas that have been proposed to track reward predictions across time. A formula published in 1955 by Robert Bush and Frederick Mosteller, for example, provides a way to mathematically predict whether a particular action is likely occur in a given circumstance (i.e., the probability that Pavlov’s dogs might salivate when a bell is rung):

This formula considers not only the current value of an anticipated reward but the value of past engagements. As such, it more accurately simulates the way a brain might track survival value across time.

**Please note**: The following are simply my own musings about how things might work. I am not implying that this is precisely how the body does things.

If we adapt Bush and Mosteller’s equation to represent flavor, we might arrive at something like the following:

**PN _{next_meal }= PN_{last_meal} + **

**α**

**(AN**

_{current_meal }**–**

**PN**

_{last_meal})This appears complicated, but it is much simpler than it seems. Here, **PN** stands for *predicted nutrition* after consuming a particular flavor, **AN** stands for *actual nutrition *received, and ‘**meal**’ in this case represents a single eating episode (whether a snack, biteful, or full meal) during which a particular flavor is consumed.

This formula essentially says that the predicted nutrition the next time you eat a particular flavor is a function of what happened the *previous* time you ate that flavor, with the new prediction modified by what happened at the previous meal.

Here, the symbol **α** represents a constant that alters how heavily past engagements are weighted in the formula. In the case of flavor, the outcome of very recent engagements is likely to be critical, especially if a toxin or beneficial nutrient is ingested. **α** might also adjust to reflect the variance expected in outcomes. For example, in an intermittent reinforcement environment, where outcomes are highly variable, perhaps lower α value might be used to smooth out fluctuations and prevent overreaction to any single event. On the other hand, if outcomes are generally consistent but suddenly change (like encountering a toxin in a continuous reinforcement environment), a higher **α** value might be beneficial.

Let’s use an example to show how this might work. We will take a particular flavor and assume that one unit of this flavor reliably delivers **10 units** of a particular nutrient every time you eat it. For the sake of simplicity we will set **α** = **0.5** (which means that the new prediction is based on half of the prior prediction value, plus half of the nutritional outcome at the current meal).

In a reliable flavor-nutrition environment where the outcome of engaging with this flavor is always 10 units per unit of flavor, the formula looks like this:

**PN _{next_meal }= PN_{last_meal} + **

**α**

**(AN**

_{current_meal }**–**

**PN**

_{last_meal})** = 10 + 0.5**** ****(10****–**** 10)**

** = 10 + 0.5 x 0**

** = 10 + 0**

** = 10 units of nutrition**

In other words, as you might expect, when the amount of nutrition is reliable across time, the predicted nutrition at the next meal remains constant.

Now let us see what might happen if a deceptive food is consumed (containing a combination of genuine flavors and counterfeit flavors as is typical in modern flavor-enhanced foods). In this case we will assume that the deceptive food contains 6 units of nutrition per unit of flavor (four less than the genuine counterpart).

**PN _{next_meal }= PN_{last_meal} + **

**α**

**(AN**

_{current_meal }**–**

**PN**

_{last_meal})** = 10 + 0.5**** ****(6****–**** 10)**

** = 10 + 0.5 x -4**

** = 10 + -2**

** = 8 units of nutrition**

In this scenario, with a **α** value of 0.5, the predicted nutrition at the next encounter with this flavor drops to **8 units**.

Every time a genuine food is consumed, the predicted nutrition per unit of that flavor returns closer to the original value of 10. Every time a deceptive food is consumed, the predicted nutrition per unit of that flavor drops.

Because this prediction is updated after every encounter, the formula elegantly maintains a running record of *all prior outcomes *within a single number.

It is also important to note that the implication is not necessarily that the brain is running a ‘formula’ so to speak. Rather, this may illustrate the kind of logic the body uses when adjusting taste and smell sensitivity, so that after every engagement, sensitivity dials up or down by a certain weighting based on the outcome of the previous meal.

With this approach, the brain doesn’t need to execute a formula nor store data anywhere. All historical data is elegantly stored in the current sensitivity value of the receptors, reducing the brain’s computational load.