Monthly Archives: January 2014

The Role of Emotions in Knowledge

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In a previous post, I discussed the idea of objectivity as a method of avoiding subjective error.  When people say that an issue needs to be looked at objectively, or that science is the field of knowledge best known for its objectivity, they are arguing for the need to overcome personal biases and prejudices, and to know things as they really are in themselves, independent of the human mind and perceptions.  However, I argued that truth needs to be understood as a fruitful or proper relationship between subjects and objects, and that it is impossible to know the truth by breaking this relationship.

One way of illustrating the relationship between subjects and objects is by examining the role of human emotions in knowledge.  Emotions are considered subjective, and one might argue that although emotions play a role in the form of knowledge known as the humanities (art, literature, religion), emotions are either unnecessary or an impediment to knowledge in the sciences.  However, a number of studies have demonstrated that feeling plays an important role in cognition, and that the loss of emotions in human beings leads to poor decision-making and an inability to cope effectively with the real world.  Emotionless human beings would in fact make poor scientists.

Professor of Neuroscience Antonio Damasio, in his book Descartes’ Error: Emotion, Reason, and the Human Brain, describes several cases of human beings who lost the part of their brain responsible for emotions, either because of an accident or a brain tumor.  These persons, some of whom were previously known as shrewd and smart businessmen, experienced a serious decline in their competency after damage took place to the emotional center of their brains.  They lost their capacity to make good decisions, to get along with other people, to manage their time, or to plan for the future.  In every other respect, these persons retained their cognitive abilities — their IQs remained above normal and their personality tests resulted in normal scores.  The only thing missing was their capacity to have emotions.  Yet this made a huge difference.  Damasio writes of one subject, “Elliot”:

Consider the beginning of his day: He needed prompting to get started in the morning and prepare to go to work.  Once at work he was unable to manage his time properly; he could not be trusted with a schedule.  When the job called for interrupting an activity and turning to another, he might persist nonetheless, seemingly losing sight of his main goal.  Or he might interrupt the activity he had engaged, to turn to something he found more captivating at that particular moment.  Imagine a task involving reading and classifying documents of a given client.  Elliot would read and fully understand the significance of the material, and he certainly knew how to sort out the documents according to the similarity or disparity of their content.  The problem was that he was likely, all of a sudden, to turn from the sorting task he had initiated to reading one of those papers, carefully and intelligently, and to spend an entire day doing so.  Or he might spend a whole afternoon deliberating on which principle of categorization should be applied: Should it be date, size of document, pertinence to the case, or another?   The flow of work was stopped. (p. 36)

Why did the loss of emotion, which might be expected to improve decision-making by making these persons coldly objective, result in poor decision-making instead?  It might be expected that the loss of emotion would lead to failures in social relationships.  So why were these people unable to even effectively advance their self-interest?  According to Damasio, without emotions, these persons were unable to value, and without value, decision-making became hopelessly capricious or paralyzed, even with normal or above-normal IQs.  Damasio noted, “the cold-bloodedness of Elliot’s reasoning prevented him from assigning different values to different options, and made his decision-making landscape hopelessly flat.” (p. 51)

It is true that emotional swings can lead to very bad decisions — anger, depression, anxiety, even excessive joy — can lead to bad choices.  But the solution to this problem, according to Damasio, is to achieve the right emotional disposition, not to erase the emotions altogether.  One has to find the right balance or harmony of emotions.

Damasio describes one patient who, after suffering damage to the emotional center of his brain, gained one significant advantage: while driving to his appointment on icy roads, he was able to remain calm and drive safely, while other drivers had a tendency to panic when they skidded, leading to accidents.  However, Damasio notes the downside:

I was discussing with the same patient when his next visit to the laboratory should take place.  I suggested two alternative dates, both in the coming month and just a few days apart from each other.  The patient pulled out his appointment book and began consulting the calendar.  The behavior that ensued, which was witnessed by several investigators, was remarkable.  For the better part of a half-hour, the patient enumerated reasons for and against each of the two dates . . . Just as calmly as he had driven over the ice, and recounted that episode, he was now walking us through a tiresome cost-benefit analysis, an endless outlining and fruitless comparison of options and possible consequences.  It took enormous discipline to listen to all of this without pounding on the table and telling him to stop, but we finally did tell him, quietly, that he should come on the second of the alternative dates.  His response was equally calm and prompt.  He simply said, ‘That’s fine.’ (pp. 193-94)

So how would it affect scientific progress if all scientists were like the subjects Damasio studied, free of emotion, and therefore, hypothetically capable of perfect objectivity?  Well it seems likely that science would advance very slowly, at best, or perhaps not at all.  After all, the same tools for effective decision-making in everyday life are needed for the scientific enterprise as well.

As the French mathematician and scientist Henri Poincare noted, every time we look at the world, we encounter an immense mass of unorganized facts.  We don’t have the time to thoroughly examine all those facts and we don’t have the time to pursue experiments on all the hypotheses that may pop into our minds.  We have to use our intuition and best judgment to select the most important facts and develop the best hypotheses (Foundations of Science, pp. 127-30, 390-91).  An emotionless scientist would not only be unable to sustain the social interaction that science requires, he or she would be unable to develop a research plan, manage his or her time, or stick to a research plan.  An ability to perceive value is fundamental to the scientific enterprise, and emotions are needed to properly perceive and act on the right values.

The Role of Imagination in Science, Part 3

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In previous posts (here and here), I argued that mathematics was a product of the human imagination, and that the test of mathematical creations was not how real they were but how useful or valuable they were.

Recently, Russian mathematician Edward Frenkel, in an interview in the Economist magazine, argued the contrary case.  According to Frenkel,

[M]athematical concepts and ideas exist objectively, outside of the physical world and outside of the world of consciousness.  We mathematicians discover them and are able to connect to this hidden reality through our consciousness.  If Leo Tolstoy had not lived we would never had known Anna Karenina.  There is no reason to believe that another author would have written that same novel.  However, if Pythagoras had not lived, someone else would have discovered exactly the same Pythagoras theorem.

Dr. Frenkel goes on to note that mathematical concepts don’t always match to physical reality — Euclidean geometry represents an idealized three-dimensional flat space, whereas our actual universe has curved space.  Nevertheless, mathematical concepts must have an objective reality because “these concepts transcend any specific individual.”

One problem with this argument is the implicit assumption that the human imagination is wholly individualistic and arbitrary, and that if multiple people come up with the same idea, this must demonstrate that the idea exists objectively outside the human mind.  I don’t think this assumption is valid.  It’s perfectly possible for the same idea to be invented by multiple people independently.  Surely if Thomas Edison never lived, someone else would have invented the light bulb.   Does that mean that the light bulb is not a true creation of the imagination, that it was not invented but always existed “objectively” before Edison came along and “discovered” it?  I don’t think so.  Likewise with modern modes of ground transportation, air transportation, manufacturing technology, etc.  They’re all apt to be imagined and invented by multiple people working independently; it’s just that laws on copyright and patent only recognize the first person to file.

It’s true that in other fields of human knowledge, such as literature, one is more likely to find creations that are truly unique.  Yes, Anna Karenina is not likely to be written by someone else in the absence of Tolstoy.  However, even in literature, there are themes that are universal; character names and specific plot developments may vary, but many stories are variations on the same theme.  Consider the following story: two characters from different social groups meet and fall in love; the two social groups are antagonistic toward each other and would disapprove of the love; the two lovers meet secretly, but are eventually discovered; one or both lovers die tragically.  Is this not the basic plot of multiple stories, plays, operas, and musicals going back two thousand years?

Dr. Frenkel does admit that not all mathematical concepts correspond to physical reality.  But if there is not a correspondence to something in physical reality, what does it mean to say that a mathematical concept exists objectively?  How do we prove something exists objectively if it is not in physical reality?

If one looks at the history of mathematics, there is an intriguing pattern in which the earliest mathematical symbols do indeed seem to point to or correspond to objects in physical reality; but as time went on and mathematics advanced, mathematical concepts became more and more creative and distant from physical reality.  These later mathematical concepts were controversial among mathematicians at first, but later became widely adopted, not because someone proved they existed, but because the concepts seemed to be useful in solving problems that could not be solved any other way.

The earliest mathematical concepts were the “natural numbers,” the numbers we use for counting (1, 2, 3 . . .).  Simple operations were derived from these natural numbers.  If I have two apples and add three apples, I end up with five apples.  However, the number zero was initially controversial — how can nothing be represented by something?  The ancient Greeks and Romans, for all of their impressive accomplishments, did not use zero, and the number zero was not adopted in Europe until the Middle Ages.

Negative numbers were also controversial at first.  How can one have “negative two apples” or a negative quantity of anything?  However, it became clear that negative numbers were indeed useful conceptually.  If I have zero apples and borrow two apples from a neighbor, according to my mental accounting book, I do indeed have “negative two apples,” because I owe two apples to my neighbor.  It is an accounting fiction, but it is a useful and valuable fiction.  Negative numbers were invented in ancient China and India, but were rejected by Western mathematicians and were not widely accepted in the West until the eighteenth century.

The set of numbers known explicitly as “imaginary numbers” was even more controversial, since it involved a quantity which, when squared, results in a negative number.  Since there is no known number that allows such an operation, the imaginary numbers were initially derided.  However, imaginary numbers proved to be such a useful conceptual tool in solving certain problems, they gradually became accepted.   Imaginary numbers have been used to solve problems in electric current, quantum physics, and envisioning rotations in three dimensions.

Professor Stephen Hawking has used imaginary numbers in his own work on understanding the origins of the universe, employing “imaginary time” in order to explore what it might be like for the universe to be finite in time and yet have no real boundary or “beginning.”  The potential value of such a theory in explaining the origins of the universe leads Professor Hawking to state the following:

This might suggest that the so-called imaginary time is really the real time, and that what we call real time is just a figment of our imaginations.  In real time, the universe has a beginning and an end at singularities that form a boundary to space-time and at which the laws of science break down.  But in imaginary time, there are no singularities or boundaries.  So maybe what we call imaginary time is really more basic, and what we call real is just an idea that we invent to help us describe what we think the universe is like.  But according to the approach I described in Chapter 1, a scientific theory is just a mathematical model we make to describe our observations: it exists only in our minds.  So it is meaningless to ask: which is real, “real” or “imaginary” time?  It is simply a matter of which is the more useful description.  (A Brief History of Time, p. 144.)

If you have trouble understanding this passage, you are not alone.  I have a hard enough time understanding imaginary numbers, let alone imaginary time.  The main point that I wish to underline is that even the best theoretical physicists don’t bother trying to prove that their conceptual tools are objectively real; the only test of a conceptual tool is if it is useful.

As a final example, let us consider one of the most intriguing of imaginary mathematical objects, the “hypercube.”  A hypercube is a cube that extends into additional dimensions, beyond the three spatial dimensions of an ordinary cube.  (Time is usually referred to as the “fourth dimension,” but in this case we are dealing strictly with spatial dimensions.)  A hypercube can be imagined in four dimensions, five dimensions, eight dimensions, twelve dimensions — in fact, there is no limit to the number of dimensions a hypercube can have, though the hypercube gets increasingly complex and eventually impossible to visualize as the number of dimensions increases.

Does a hypercube correspond to anything in physical reality?  Probably not.  While there are theories in physics that posit five, eight, ten, or even twenty-six spatial dimensions, these theories also posit that the additional spatial dimensions beyond our third dimension are curved up in very, very small spaces.  How small?  A million million million million millionth of an inch, according to Stephen Hawking (A Brief History of Time, p. 179).  So as a practical matter, hypercubes could exist only on the most minute scale.  And that’s probably a good thing, as Stephen Hawking points out, because in a universe with four fully-sized spatial dimensions, gravitational forces would become so sensitive to minor disturbances that planetary systems, stars, and even atoms would fly apart or collapse (pp. 180-81).

Dr. Frenkel would admit that hypercubes may not correspond to anything in physical reality.  So how do hypercubes exist?  Note that there is no limit to how many dimensions a hypercube can have.  Does it make sense to say that the hypercube consisting of exactly 32,458 dimensions exists objectively out there somewhere, waiting for someone to discover it?   Or does it make more sense to argue that the hypercube is an invention of the human imagination, and can have as many dimensions as can be imagined?  I’m inclined to the latter view.

Many scientists insist that mathematical objects must exist out there somewhere because they’ve been taught that a good scientist must be objective and dedicate him or herself to the discovery of things that exist independently of the human mind.  But there’re too many mathematical ideas that are clearly products of the human mind, and they’re too useful to abandon merely because they are products of the mind.