Learning Mathematics in College

# States of Consciousness

These pages composed and maintained by Greg McColm, Department of Mathematics, University of South Florida.

If you are going to do homework, you have to be in an appropriate state of consciousness. Let's think about states of consciousness. A ``state of consciousness'' simply refers to the sort of awareness you have of mental operations you are consciously doing.

In a given state of consciousness, you have some awareness about the world around you, you have some awareness of what your mind is doing (and you are doing it at some level of seriousness), and so on. Your state of consciousness should be appropriate to the given situation: the state of consciousness of a soldier on guard duty is (hopefully) different from his state of consciousness while partying on leave. Some states of consciousness are very relaxing; others require a constant effort to maintain.

Here are some familiar states of consciousness:

• Alertness. One is aware of what is physically in front of onesself, and one reacts to that. For example, when driving a car, one is (hopefully) aware of what is in the road ahead, and what the cars ahead (and beside and even behind) are doing.
• Concentration. This is akin to alertness, except that it involves continuous effort, usually involving an attempt to achieve something. Solving a word problem is an example; so is threading a needle (if needle-threading is not among one's acquired skills).
• Daydreaming. One is aware of some semi-scripted drama which one plays out, perhaps with frequent revisions. For example, the James Thurber story The Secret Life of Walter Mitty is about a man who takes every spare moment he can to imagine himself a ship captain, a rocketeer, etc.
• Flow. This is also akin to alertness, but unlike concentration it seems effortless while one is in the state, and it is possible to remain in this state for hours. (Afterwards, comes the fatigue.) It is the primary state when at play, and it is also a state allowing considerable creativity.
• Mindfulness. This is also akin to alertness, except that it is awareness of what the mind is doing. Unlike daydreaming, there is no effort maintained to control what the mind is doing, or even to keep the mind doing things. One just maintains awareness of what the mind is doing.
• Obsession. One is aware of one thing, often with an overwhelming compulsion to act on it. The standard example is enraged grief, accompanied by a powerful desire for vengeance.
• Stress. Sometimes something overwhelms one, making thought or action impossible. The classic example is pain, which in extreme situations make it impossible to do anything except writhe. A milder example is ``anxiety,'' which can be distracting or, if severe, become paralyzing or shift into an obsession.
• Subconsciousness. We should mention this state, which is poorly understood. One can be awakened from sleep to a state of (bewildered) alertness by a loud noise or a blow, and one will not remember being in asleep (although one may remember going to bed). Whether this means that one was unconscious when asleep, or merely does not remember being asleep, is not known.
Notice:
• This list is not exclusive, and amateur psychologists can easily imagine a different categorization. (Alas, many professional psychologists are not very interested in consciousness.)
• These categories are like primary colors: one can be in a sort of composite state (daydreaming while driving, to give an alarming example).
• The Mind and the Self seem to be two different things. The Self is what is aware; the Mind is what presents perceptions to the Self. This is clearest when considering Mindfulness, in which (ideally) the Self is completely passive, neutrally observing the Mind scurrying about, doing this and that. But in other states of consciousness, like stress, the distinction between the Mind and the Self is less clear.
• Different categories involve different levels of effort. But these levels are not necessarily what they might seem, given the difference between the Self and the mind. If one is not tired, daydreaming is easy. Concentration is always hard and always seems hard. Flow does not seem hard, but afterwards one is tired. Alertness, the predominate state of consciousness when one is working, is in between, for the Mind always is ready for an excuse to wander. Stress and Obsession are very hard, but it is very hard to get out of them: one of the great acts of self-control is to force onesself into a state of Mindfulness (or even Alertness) when something terrible happens.
• It is not clear which states people would prefer to be in. Some could easily daydream all day long; others prefer a sort of obsession provided by big game hunting. A few even seek stress.
This suggests a strategy to deal with our attitude.

When one is preparing to do some mathematics (or other) homework, one is preparing to spend a lot of time in one of three states of consciousness.

• Concentration. This means continual effort, focus on something, like trying to force your way through a fence. This is quite difficult to sustain: I know of one member of the National Academy of Sciences who refuses to concentrate for more than five minutes at a stretch. Others can concentrate for up to an hour, or even (so it was said of Isaac Newton) several hours.
• Flow. Since this state is seems effortless when you are in it, and since even afterwards, it seems to consume little more energy than alertness, it is often best to try to get into this state. This is the state of consciousness that small children are in when they are dismantling and (if we are lucky) reassembling mechanical alarm clocks. Approach the topic with a positive attitude and perhaps a sense of play (try to develop a curiousity about the topic). For an extended discussion of flow, see Mihaly Csikszentmihalyi's book Optimal Experience.
• Alertness. Most research in the library, most prose writing, and (face it) most routine math exercises only require alertness. It is a matter of being aware of the situation and doing the right thing, and these are situations in which the right thing is not too difficult to figure out. It is a bit like flow, but a without wind beneath your wings, and one is ... aware ... of ... the ... clock. Most people can spend hours each day being alert (although many of us require breaks every few hours or so).
This suggests:
• We should schedule homework time so that we will be able to maintain alertness during that time, and perhaps ration time for concentration.
• To get into a state of flow, or at least alertness (which is not easy when we plan to do something that we feel may not be fun), we may do best by clearing our mind first, and then turning to the subject. In otherwords, enter a state of mindfulness first, and from mindfulness, go into a state of alertness. Many writers develop a ritual that helps them enter a state of mindfulness, e.g., reviewing notes from the previous day, sharpening a handful of pencils, or a brief reverie about sitting down and writing about whatever they are to write about that day.
One way to learn about manipulating one's own states of consciousness is to practice traditional (i.e., Buddhist) meditation techniques.. For more on what the more and less useful states of consciousness are (as far as doing homework is concerned) see the page on doing homework versus thinking about doing homework. For more on what to do once one gets into the most useful state of consciousness, see the page on doing homework.