Hick’s law

The Paradox of Choice – Why More Is Less is a 2004 book by American psychologist Barry Schwartz. In the book, Schwartz argues that eliminating consumer choices can greatly reduce anxiety for shoppers. Autonomy and Freedom of choice are critical to our well being, and choice is critical to freedom and autonomy. Nonetheless, though modern […]

The Paradox of Choice – Why More Is Less is a 2004 book by American psychologist Barry Schwartz. In the book, Schwartz argues that eliminating consumer choices can greatly reduce anxiety for shoppers.

Autonomy and Freedom of choice are critical to our well being, and choice is critical to freedom and autonomy. Nonetheless, though modern Americans have more choice than any group of people ever has before, and thus, presumably, more freedom and autonomy, we don’t seem to be benefiting from it psychologically.

—?quoted from Ch.5, The Paradox of Choice, 2004

Hick’s law, or the Hick–Hyman Law, named after British and American psychologists William Edmund Hick and Ray Hyman, describes the time it takes for a person to make a decision as a result of the possible choices he or she has: increasing the number of choices will increase the decision time logarithmically. The Hick–Hyman law assesses cognitive information capacity in choice reaction experiments. The amount of time taken to process a certain amount of bits in the Hick–Hyman law is known as the rate of gain of information.

Hick’s law is sometimes cited to justify menu design decisions. For example, to find a given word (e.g. the name of a command) in a randomly ordered word list (e.g. a menu), scanning of each word in the list is required, consuming linear time, so Hick’s law does not apply. However, if the list is alphabetical and the user knows the name of the command, he or she may be able to use a subdividing strategy that works in logarithmic time.[1]

Studies suggest that the search for a word within a randomly ordered list – in which the reaction time increases linearly according to the number of items – does not allow for the generalization of the scientific law, considering that, in other conditions, the reaction time may not be linearly associated to the logarithm of the number of elements or even show other variations of the basic plane.

Exceptions to Hick’s law have been identified in studies of verbal response to familiar stimuli, where there is no relationship or only a subtle increase in the reaction time associated with an increased number of elements,[4] and saccade responses, where it was shown that there is either no relationship,[5] or a decrease in the saccadic time with the increase of the number of elements, thus an antagonistic effect to that postulated by Hick’s law.[6]

The generalization of Hick’s law was also tested in studies on the predictability of transitions associated with the reaction time of elements that appeared in a structured sequence.[7] [8] This process was first described as being in accordance to Hick’s law,[9] but more recently it was shown that the relationship between predictability and reaction time is sigmoid, not linear associated with different modes of action. [10]

The power law of practice states that the logarithm of the reaction time for a particular task decreases linearly with the logarithm of the number of practice trials taken. It is an example of the learning curve effect on performance. It was first proposed as a psychological law by Newell & Rosenblom.[1] Delaney et al. showed that the power law fit better than an exponential if the analysis was performed across strategies, for a mental arithmetic task.[2]

However, subsequent research by Heathcote, Brown, and Mewhort suggests that the power function observed in learning curves that are averaged across participants is an artifact of aggregation.[3] Heathcote et al. suggest that individual-level data is better fit by an exponential function and the authors demonstrate that the multiple exponential curves will average to produce a curve that is misleadingly well fit by a power function.

The power function is based on the idea that something is slowing down the learning process; at least, this is what the function suggests. Our learning does not occur at a constant rate according this function; our learning is hindered. The exponential function shows that learning increases at a constant rate in relationship to what is left to be learned. If you know absolutely nothing about a topic, you can learn 50% of the information quickly, but when you have 50% less to learn, it takes more time to learn that final 50%.

Research by Logan suggests that the instance theory of automaticity can be used to explain why the power law is deemed an accurate portrayal of reaction time learning curves.[4] A skill is automatic when there is one step from stimulus to retrieval. For many problem solving tasks, reaction time is related to how long it takes to discover an answer, but as time goes on, certain answers are stored within the individual’s memory and they have to simply recall the information, thus reducing reaction time. This is the first theory that addresses the why of the power law of practice.

Power function:

RT = aP?b + c

Exponential function:

RT = ae?b(P-1) + c


RT = Trial Completion Time
P = Trial Number, starting from 1 (for exponential functions the P-1 argument is used)
a, b, and c, are constants

Practice effects are also influenced by latency. Anderson, Fincham, and Douglass looked at the relationship between practice and latency and people’s ability to retain what they learned. As the time between trials increases, there is greater decay. The latency function relates to the forgetting curve.[5]

Latency Function:

latency = A + B*Td


A = asymptotic latency B = latency that varies T = time between introduction and testing d = decay rate

humans are animals

The Moral Status of Animals First published Tue Jul 1, 2003; substantive revision Mon Sep 13, 2010 What is distinctive about humanity such that humans are thought to have moral status and non-humans do not? Providing an answer to this … Continue reading

The Moral Status of Animals
First published Tue Jul 1, 2003; substantive revision Mon Sep 13, 2010

What is distinctive about humanity such that humans are thought to have moral status and non-humans do not? Providing an answer to this question has become increasingly important among philosophers as well as those outside of philosophy who are interested in our treatment of non-human animals. For some, answering this question will enable us to better understand the nature of human beings and the proper scope of our moral obligations. Some argue that there is an answer that can distinguish humans from the rest of the natural world. Many of those who accept this answer are interested in justifying certain human practices towards non-humans—practices that cause pain, discomfort, suffering and death. This latter group expect that in answering the question in a particular way, humans will be justified in granting moral consideration to other humans that is neither required nor justified when considering non-human animals. In contrast to this view, many philosophers have argued that while humans are different in a variety of ways from each other and other animals, these differences do not provide a philosophical defense for denying non-human animals moral consideration. What the basis of moral consideration is and what it amounts to has been the source of much disagreement.

The species Homo sapiens share a genetic make-up and a distinctive physiology, but this is unimportant from the moral point of view. Species membership itself cannot support the view that members of one species, namely ours, deserve moral consideration that is not owed to members of other species. Humans are morally considerable because of the distinctively human capacities we possess. But which capacities are only human? There is no activity that is uncontroversially unique to humans. Both scholarly and popular work on animal behavior suggests that many of the activities that are thought to be distinct to humans occur in non-humans. Darwin brought us closer to the animal world, but equally brought animal nature closer to us. (http://plato.stanford.edu/entries/moral-animal/ ).

The notion of personhood identifies a category of morally considerable beings that is thought to be coextensive with humanity. Historically, Kant is the most noted defender of personhood as the quality that makes a being valuable and thus morally considerable. Yet Kant’s view of personhood cannot distinguish all and only humans as morally considerable. Some humans are not persons, i.e. infants, children, people with advanced forms of autism or Alzheimer’s disease or other cognitive disorders—do not have the rational, self-reflective capacities associated with personhood.

More to the point, rationality itself is suspect as a basis for moral right. On one hand, human rationality is bounded by lower level instincts and mechanistic behavior, and on the other, non-humans exhibit behavior that can be deemed moral. Thus morality is orthogonal to rationality. As a matter of fact, individuals that are hyper rational and lack lower level motional control of their behaviors are nor deemed highly moral, but rather are characterized as psychopathic (http://scienceblogs.com/cortex/2010/04/29/psychopaths-and-rational-moral/ ).

Al Dunlap [That would be “Chainsaw” Al Dunlap, former CEO of Sunbeam and notorious downsizer.] effortlessly turns the psychopath checklist into “Who Moved My Cheese?” Many items on the checklist he redefines into a manual of how to do well in capitalism. There was his reputation that he was a man who seemed to enjoy firing people, not to mention the stories from his first marriage — telling his first wife he wanted to know what human flesh tastes like, not going to his parents’ funerals. Then you realize that because of this dysfunctional capitalistic society we live in those things were positives. He was hailed and given high-powered jobs, and the more ruthlessly his administration behaved, the more his share price shot up.

Some models of human behavior in the social sciences assume that humans can be reasonably approximated or described as “rational” entities (see for example rational choice theory, or Downs Political Agency Models). Many economics models assume that people are on average rational, and can in large enough quantities be approximated to act according to their preferences. The concept of bounded rationality revises this assumption to account for the fact that perfectly rational decisions are often not feasible in practice because of the finite computational resources available for making them.

Bounded rationality is the idea that when individuals make decisions, their rationality is limited by the information they have, the cognitive limitations of their minds, and the time available to make the decision (http://en.wikipedia.org/wiki/Bounded_rationality ).

If morality is defined in terms of social behavior, non-humans exhibit different moral behavioral modes (http://www.ted.com/talks/frans_de_waal_do_animals_have_morals?%ca&language=en ). Social life may be regarded as a sort of symbiosis among individuals of the same species: a society is composed of a group of individuals belonging to the same species living within well-defined rules. When biologists interested in evolution theory first started examining social behavior, some apparently unanswerable questions arose, such as how the birth of sterile castes, like in bees, could be explained through an evolving mechanism that emphasizes the reproductive success of as many individuals as possible, or why, amongst animals living in small groups like squirrels, an individual would risk its own life to save the rest of the group. These behaviors may be examples of altruism. Revengeful behavior has been reported in non Homo sapiens (http://en.wikipedia.org/wiki/Ethology ).

Humans are animals in ways so subtly that we are unaware of it. Humans are subject to the same instinctual drives and influences as other animals are; it’s only human arrogance that would ever lead us to think otherwise. Fifty to seventy percent of the variation between individuals – in intelligence, in personality, in political leanings, or just about any other mental character you care to name – derives from the genes; zero to ten percent derives from the home environment; and the mysterious remainder is due to chance or to non-parental environment. (The Blank Slate: The Modern Denial of Human Nature by Steven Pinker)

The understanding that other people’s emotional states depend on the fulfillment of their intention is fundamentally important for responding adequately to others. Psychopathic patients show severe deficits in responding adequately to other people’s emotion. Psychopaths can teach us a lot about the nature of morality. At first glance, they seem to have perfectly functioning minds. Their working memory isn’t impaired, they have excellent language skills, and they don’t have reduced attention spans. In fact, a few studies have found that psychopaths have above-average IQs and reasoning abilities; their logic is impeccable. But the disorder is associated with a severe moral deficit. (http://scienceblogs.com/cortex/2010/04/29/psychopaths-and-rational-moral/ ).

So what’s gone wrong? Why are psychopaths so much more likely to use violence to achieve their goals? Why are they so overrepresented in our prisons? The answer turns us to the anatomy of morality in the mind. That’s because the intact intelligence of psychopaths conceals a devastating problem: the emotional parts of their brains are damaged, and this is what makes them dangerous.

When normal people are shown violent imagery or other painful stimulus, they automatically generate a visceral emotional reaction. Their hands start to sweat, and their blood pressure surges. But psychopaths feel nothing. When you peer inside the psychopathic brain, you can literally see this absence of emotion. After being exposed to fearful facial expressions, the emotional parts of the normal human brain show increased levels of activation. So do the cortical areas responsible for recognizing faces. As a result, a frightened face becomes a frightening sight; we naturally internalize the feelings of others. The brains of psychopaths, however, respond to these fearful faces with utter disinterest.

I am more inclined to take the position of Schopenhauer. For him, all individual animals, including humans, are essentially the same, being phenomenal manifestations of the one underlying Will. The word “will” designated, for him, force, power, impulse, energy, and desire; it is the closest word we have that can signify both the real essence of all external things and also our own direct, inner experience. Since everything is basically Will, then humans and animals are fundamentally the same and can recognize themselves in each other. For this reason, he claimed that a good person would have sympathy for animals, who are our fellow sufferers (http://en.wikipedia.org/wiki/Arthur_Schopenhauer ).

Schopenhauer emphasizes the necessity of finding a basis for Ethics that appeals, not to the intellect, but to the intuitive perception (http://en.wikisource.org/wiki/On_the_Basis_of_Morality/Translator%27s_Introduction ). According to Schopenhauer, the end of Ethics is not to treat of that which people ought to do (for ” ought ” has no place except in theological Morals, whether explicit, or implicit)