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The Mathematician Rat—An Evolutionary Explanation

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JG is a rat, a Cricetomys gambianus or Giant Gambian Pouched Rat; she is also a Hero Rat, a landmine detector at Apopo in Tanzania. In December 2009, she performed uncharacteristically badly and puzzled everybody as Hero Rats don’t make mistakes. What was the problem with JG? Had she lost it? Had the trainers made a crucial mistake?

Apopo in Morogoro, Tanzania, trains rats to detect landmines and tuberculosis and the little fellows are very good at what they do. In Mozambique, Apopo has so far cleared 2,063,701 square meters of Confirmed Hazardous Areas, with the destruction of 1866 landmines, 783 explosive remnants of war and 12,817 small arms and ammunition. As for tuberculosis, up until now, the rats have analyzed 97,859 samples, second-time screened 44,934 patients, correctly diagnosed 7,662 samples and discovered 2,299 additional cases that were previously missed by the DOTS centers (Direct Observation of Treatment, Short Course Centers in Tanzania). More than 2,500 patients have since been treated for tuberculosis after having been correctly diagnosed by the rats.

In December 2009, I was working full time at Apopo in Morogoro. I wrote their training manual, trained their rat trainers, supervised the training of the animals and analyzed standard operating procedures. At the time of writing, I still do consultancy work for Apopo and instruct new trainers from time to time. Back then, one of my jobs was to analyze and monitor the rats’ daily performance and that’s when I came across the peculiar and puzzling behavior of JG in the LC3 cage.

 

Problem

LC3 is a cage with 10 sniffing holes in a line and the rats run it 10 times. On average, 21 holes, randomly selected by computer, will contain TNT samples. We train rats in LC3 every day, recording and statistically analyzing each session. We normally expect the rats to find and indicate the TNT samples with a success rate of 80-85%. Whenever the figures deviate from the expected results, we analyze them and try to pinpoint the problem.

On December 19, we came across a rat in LC3 that did not indicate any positive samples placed from Holes 1 to 6. She only indicated from Holes 7 to 10. In fact, from Hole 1 to 6, Jane Goodall (that’s the rat’s full name) only once bothered to make an indication (which was false, by the way). From Hole 7 to 10, JG indicated 10 times with 9 correct positives, only missing one, but also indicated 11 false positives. Her score was the lowest in LC3 that day and the lowest for any rat for a long time. What was the problem with JG? She seemed fine in all other aspects and seemed to know what she was doing. Why then did she perform so poorly?

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Giant Gambian Pouched Rat searching TNT in a line cage (photo by Silvain Piraux).

Analysis of searching strategies

Whenever an animal shows such a behavior pattern, and it appears purposeful rather than emotional, I become suspicious and suspect that there is a rational explanation.

In order to analyze the problem, I constructed simulations of two searching strategies: (1) searching ALL HOLES, and (2) SKIPPING Holes 1 to 5 (I didn’t want to be as radical in my simulation as JG). In addition, I ran simulations with two different sample placement configurations: (1) evenly distributed between the two halves, i.e. two positives in Holes 1 to 5 and two positives in Holes 6 to 10; and (2) unevenly distributed — one positive in the first five holes and two positives in Holes 6 to 10.

In order to run the simulation, I needed to assign values to the different components of the rat’s behavior. I chose values based on averages measured with different rats.

  • Walking from feeding hole to first hole (back walk) = 3 seconds.
  • Walking from covered hole to covered hole = 1 second.
  • Walking from uncovered hole to uncovered hole = 2 seconds.
  • Analyzing a hole = 2 seconds.
  • Indicating a positive = 4 seconds.
  • Walking from last hole to feeding hole = 1 second.
  • Eating the treat = 4 seconds.

All time variables were converted into energy expenditure in the calculation of energy payoff for the two strategies and the different configurations. Also the distance covered was converted into energy expenditure. The reinforcers (treats) amounted to energy intake. In my simulation I used estimated values for both expenditure and intake. However, we could measure all values accurately and convert all energy figures into kJ. 

 

The results

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In terms of energy,  (in this simulation I make several assumptions based on reasonable values, e.g. the total energy spent is a function of distance covered and time spent), the results show that when the value of each treat is high (E gain is close to the sum of all treats amounting to the sum of energy spent for searching all holes), it pays off to search all holes (the loss of -5.50 versus -7.88). The higher the energetic value of each treat, the higher the payoff of the ALL HOLES strategy.This is a configuration with four positives (x) and six negatives (0). The results show that neither strategy is significantly better than the other. On average, when sniffing all holes, the rat receives a treat every 31 seconds, while skipping the first five holes will produce a treat every 31.5 seconds. However, there is a notable difference in how quickly the rat gets to the treat depending on which strategy the rat adopts. ALL HOLES produces a treat on average 5.75 seconds after a positive indication. SKIPPING produces a treat 3.5 seconds after a positive indication. This could lead the rat to adopt the SKIPPING strategy, but it’s not an unequivocally convincing argument.

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However, when the energetic value of each treat is low, skipping holes will reduce the total loss (damage control), making it a better strategy (-17.88 versus -25.50).

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However, if we run a simulation based on an average of three positives per run, with one in the first half and two in the second half  (which is closest to what the rat JG was faced with on December 12), we obtain completely different results. This first analysis does not prove conclusively that the SKIPPING strategy is the best. On the contrary, it shows that, all things considered, ALL HOLES will confer more advantages.

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The energy advantage is also detectable in this configuration, even when each treat has a high energetic value (a gain of 3.13 versus a loss of -0.75).With this configuration, the strategy of SKIPPING is undoubtedly the best. On average, it produces a reinforcer every 27.5 seconds (versus 28.7 for ALL HOLES) and 2.5 seconds after an indication (versus 5 seconds).

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Conclusion

This second simulation proves that JG’s strategy was indeed the most profitable in principle. However, the actual results for JG are completely different from the ones shown above, as they also have to take into account the amount of energy spent indicating false positives (which are expensive).

It is now possible to conclude that the most advantageous strategy is as follows. Whenever the possibilities of producing a reinforcer are evenly distributed, search all holes. It takes more time, but on average you’ll get a reinforcer a bit quicker than if you skip holes. In addition, you either gain energy by searching all holes, or you limit your losses, depending on the energetic value of each reinforcer. Don’t be fooled by the fact you get a treat sooner after your indication when searching all holes then when skipping.

Whenever the possibilities of producing a reinforcer are not evenly distributed, with a bias towards the second half of the line, skip the first half. It doesn’t pay off to even bother searching the first half. By skipping it, you’ll get a lower total number of reinforcers, but you’ll get them quicker than searching all holes and, more importantly, you’ll end up gaining energy instead of losing it.

Finally, avoid making mistakes by indicating false positives. They cost as much as true positives in spent energy, but you don’t gain anything.         

 

An evolutionary explanation

Of course, no rat calculates energetic values and odds for certain behaviors that are reinforced, nor do they run simulations prior to entering a line cage. Rats do not do this in their natural environment either. They search for food using specific patterns of behavior, which have proven to be the most adequate throughout the history and evolution of the species. A certain behavior in certain conditions, depending on temperature, light, humidity, population density, as well as internal conditions such as blood sugar level etc., will produce a slightly better payoff than any other behavior. Behaviors with slightly better payoffs will tend to confer slight advantages in terms of survival and reproduction and they will accumulate and spread within a population; they will spread slowly, for the time factor is unimportant in the evolution of a trait. Eventually, we will come across a population of individuals with what seems an unrivalled ability to make the right decision in circumstances with an amazing number of variables, and it puzzles us because we forget the tremendous role of evolution by natural selection. Those individuals who took the ‘most wrong decisions’ or ‘slightly wrong’ decisions inevitably decreased their chances of survival and reproduction. Those who took ‘mostly right’ or ‘slightly righter’ decisions gained an advantage in the struggle for survival and reproduction and, by reproducing more often or more successfully, they passed their ‘mostly right’ or ‘slightly righter’ decisions genes to their offspring.

This is a process that the theory of behaviorism cannot explain, however useful it is for explaining practical learning in specific situations. In order to explain such seemingly uncharacteristic behaviors, we need to recur to the theory of evolution by natural selection. This behavior is not the result of trial and error with subsequent reinforcers or punishers. It is an innate ability to recognize parameters and behave in face of them. It is an ability that some individuals possess to recognize particular situations and particular elements within those situations, and correlate them with specific behavior. What these elements are, or what this ability exactly amounts to, we do not know; only that it has been perfected throughout centuries and millennia, and innumerable generations that accumulate ‘mostly right’ or ‘slightly righter’ decisions—and that is indeed evolution by means of natural selection.

Featured image: Giant Gambian Pouched finds a landmine (photo by Xavier Rossi).

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My Last Love Letter—We Love Too Much and We Love Nothing

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These days we seem to love a lot. We love food, clothes, iPhones, dogs, cats, horses, houses, cars, hairstyles, tunes, movies, apps, sushi, coca-cola and much, much more. We also love our spouses, partners, kids, family, and friends. Everything goes together in the same pot. In short, we love everything and nothing, too quickly and too easily—but what comes easily goes just as easily.

I still remember when we reserved the word “love” for only the very, very special. It appears that either we have devalued the meaning of “love,” (as swiftly as we do with a currency when it reflects our poor financial resolutions), or that we simply don’t know what love is.

We seem to be terribly confused about love. Maybe, it is this dark age of ideological decay and disillusion, in which we live, that compels us to beg for and crave love. It prompts us to see love everywhere and to mistake it for what it is not, namely passion, infatuation, obsession. Though, as far as I’m concerned (and, of course, you may disagree), love is none of the above. Love is, in its essence, incompatible with passion.

We regard the love between two lovers as the epitome of love itself. Our literature and movie industry give us plenty of examples thereof. We are flooded by thousands of love songs and romantic movies. And yet, despite the fact we depict this romanticized love as the pinnacle of our aspirations, it often turns sour and gives way to despair and tragedy. The “forever clause” love promises, often falls painfully short. The USA has a divorce rate of 53%, which equates to one divorce every six seconds (with 73% of third marriages ending the same way). Italy has the highest rate of unhappily married women: 52%. These figures alone beg the question: do we know what love is?

The problem, as is often the case, is how we define (or do not define) the concepts our mind uses to think. If feelings and emotions influence our thoughts, so do thoughts leave their mark on our feelings and emotions—and ultimately on who we are.

When we fall in love, we aim for completion: an escape route from the crushing feeling of loneliness entrapping us, from our deficiencies. Do we fall in love with the other person or with the enhanced image of ourselves in our lover? That is a pertinent question for, as I see it, to begin a deeper relationship simply to escape our shortcomings and satisfy our needs is extremely selfish and disrespectful to both parties. It will not bring us peace and harmony either, both inherent parts of love. We love best when our need to see our loved ones happy exceeds any need we may have of them.

Falling in love is not love. It is an infatuation, a passion, a very strong feeling of excitement and anticipation. It hurts so bad that it must be good, or so we think. Anger and sexual desire are equally strong feelings of excitement and anticipation, yet I doubt anyone would regard them as love. “Making love” is a misleading term used to describe sex. You don’t need to love the one you make love to, and you can love someone to whom you don’t make love. In other words, “making love” is just a romanticized way to describe sex or a subtle way to distinguish between casual sex and sex with someone for whom we care.

The confusion results from the fact that passion and love are similarly strong attractions to one person. The fire of passion gets its oxygen from our unsatisfied needs. It comes with many strings attached. It is highly conditional. “I love you, you make me feel a better person,” “You’re mine, I love you,” “I need you, I love you.” Passions rise and fall like a rollercoaster and often at the same speed. They depend on how the other person treats us and how we perceive ourselves in the relationship. Passions are full of doubt and questions: “Do you still love me?,” “What can I do so you keep loving me?” Passions are strong, often irrational attachments to the object, which generates them.

The essence of love, or at least as I understand it, is a far cry from the essence of passion. True love (not to be confused with falling in love or making love) is unconditional, no strings attached, no expectations. I scratch your back, and I don’t necessarily expect you to scratch mine. True love is to want the other person to be happy, irrespective of what it makes us. That does not imply that if we love someone, we must accept and endure disrespectful treatment. I can love someone and genuinely wish that person to be happy—and contribute to it, no strings attached—though not at the cost of being miserable. There is no contradiction in saying, “I love you, I want you unconditionally to be happy, but it’s not right for me to live the way you want.” True love can only grow and thrive in freedom. We cannot entrap love, for if we do, we kill it. True love is a free bird that we can’t cage. All we can do is to rejoice seeing it fly around freely, being fully aware that one day it may not come back, and contemplating that prospect with no trace of fear.

All relationships are a trade—a give and take. Passions survive if there’s a balance between the two. We keep (consciously or unconsciously) accurate accounts on what we give and what we take. Love also requires balance though not depending on particular give and takes. We give what we can, and we are grateful for what our loved one offers us.

Passions wane if we don’t get what we need. Love does not because it does not depend on our needs. Passions are selfish, calculated and manipulating. Love is not. In our times, what most resembles true love is probably our love for our children. We want them to be happy, and we give without expecting anything in return. Still, many parents sacrifice the happiness of their kids for what it makes them, compelling them to follow determined paths. That is not love, but merely a selfish projection of one’s ego and shortcomings. One thing is teaching to the best of our knowledge; another thing is to impose our norms and to project our ambitions onto our children’s lives.

“If I don’t get what I need, I walk away”—that’s passion. “You took away from me something I needed, and I didn’t walk away on you”—that’s love.

Passions are by nature unreliable. They ignite as easily as fuel, are as volatile as fire, and are dangerously unstable. Crimes of passion are, alas, too frequent. Passions are a poor foundation for true love, peace, and happiness. Being in love feels great as long as it lasts, and we can certainly enjoy it as long as we are well aware that it will end one day and that it may hurt. Being in love is an infatuation and, as with all obsessions, it is capricious and shallow.

We fall in love for many reasons, but mostly out of some degree of desperation, either because we feel lonely, we have an immense craving for affection or the need to be re-affirmed. We see ourselves through the eyes of the person with whom we fall in love. We identify ourselves with a picture, a fata morgana. To define ourselves by means of anything but who we are (that is, what we think, we feel and we do) is inviting suffering to bed. It is like having a beautiful dream, but all dreams come to an abrupt end for we will we wake up eventually. Deep inside, lovers know that. Clinched in a profound embrace, they look into each other’s eyes and whisper, “I want to stop time, to keep this moment frozen forever.” It is the realization that it will end one day that makes it hurt so badly. What makes us suffer is the inevitable loss of the illusion, to which we cling in vain, pinning on it all our hopes for happiness. When it’s over, we feel we have lost love, but we haven’t really lost it, for we never had it in the first place. What we had was an illusion, as we failed to realize that we can only find our peace and create our happiness from within and through our own thoughts and actions. Nobody, not even a lover, can give it to us.

True love is completely different in essence and manifestation. We cannot lose what is real, only what is an illusion. Therefore, true love does not leave scars when we lose it because we can never lose what is real. When the free bird flies away, we don’t lose it because it was never ours, and we never claimed it. What is ours forever and is true is the pleasure of seeing it fly freely and wish that it will fare well. Passions live in anticipation, love in what is real.

Love is fragile and, like a bonsai, we must nurse it and take good care of it. A bonsai requires a reliable measure of water, light, and temperature, not when we have the time for it or feel like doing it, but when the bonsai needs it. We need to take care of it every day no matter how busy we are with other chores. Love requires a reliable dose of dedication, unselfishness, and affection, not when we have the time or the need to give it, but when the other person misses it. A bonsai grows into a beautiful little tree we can rejoice in if we treat it correctly. Its strength and imperceptible growth fills our heart with joy for we have given without expecting anything in return—for what can a little bonsai give us but joy? Equally, love flourishes and enriches our lives if we take good care of it without keeping account of what we get back. The happiness of our loved one will fill our hearts with joy—and what can happiness give us but happiness?

Are you ready for love? Nurse a bonsai for five years. If you can, the chances are you are ready for love. “There’s no remedy for love than to love more,” Henry Thoreau wrote. I’d say, “There’s no remedy for love than to love right.”

Loving is not an apparition. It is the process of having the courage of facing our weakness and turn it into strength. The moment we expose our vulnerability to another person, we face our egos, desires, demons and illusions. If it is the right person, we may challenge ourselves toward creating an open-minded and genuinely honest relationship—one marked by a pure, unselfish, and unconditional love. Only then, an everlasting connection may emerge between two wholesome individuals who don’t depend on one another but willingly and lovingly give and take in mutual support.

You know true love when you gaze into the eyes of your loved one, and you catch a glimpse of a new world, an unconditional promise of freedom from the boundaries of your confined self, the ultimate journey into the timeless and the boundless—reasoning and being, giving and taking seamlessly merged—like tears in the rain.