We normally assume that memories fade with the passage of time. The more time has elapsed, the more our memories decay. This is only partly true. The opposite is true as well: the more one repeats a memory, the more deeply is it etched into one's mind and the more easily is it accessed. Thus time can either weaken or strengthen memory.
In regards to the levels of memory mentioned earlier this implies that the more transient types of memory can become more enduring ones through repetition. Hence Iconic/Echoic memory can become part of working memory by repeating the sounds or images again and again. It may continue onto short term memory as well, especially if in addition to repetition one makes intellectual sense of it. It may even penetrate long term memory if one finds a way to effectively integrate it with information/experiences already stored in long term memory. The layers of memory are thus dynamic, and through repetition and understanding one can transform even the most fleeting and short lived memories into long term ones.
One factor that determines how deeply a memory will be absorbed is one's level of desire to internalize it. The stronger one's drive to bond with it, the more one will repeat it over and over in an attempt to perpetuate it within one's being. This is visible as a vice in the mental state of 'obsession' where one cannot banish certain thoughts out of one's mind and repeats them consummately. King David referred to the virtuous parallel of this state when he said, "I delight in Your laws, hence I will not forget Your words." He links memory with his level of delight in the subject matter he seeks to remember, knowing that his desire to bond with the teachings will result in their internalization into his long term memory.
The expression 'practice makes perfect' is thus only partially true. For 'practice makes permanent' as well...
A RABBI, HIS SKATEBOARD, AND HIS DIARY
Sunday, November 27, 2011
Wednesday, November 23, 2011
On Memory I
Every trick has many aspects: foot placement, application of pressure on the right parts of the board, jumping with the board in the direction it moves, timing, clearing the stairs or ledge on which a trick is being performed, etc. When learning a trick I often forget which elements I've already worked on and which still require my attention and end up working on the same elements again and again. Sometimes I forget errors that I've corrected in the past and thereby revert to former mistakes. This makes my manner of learning tricks highly inefficient. Clearly, memory plays an important role in the trick learning process.
People typically conceive of memory as the ability to bring previous experiences to mind. In truth, memory involves much more than that. Psychologists and cognitive scientists divide memory into several forms (though the boundaries between them are often elusive): iconic/echoic memory, working memory, short term memory, and long term memory:
a) Iconic/echoic memory are the impressions of visual or auditory sensations lasting for a few fleeting moments after they're experienced. It is this memory that allows one to perceive a series of actions as one cohesive sequence.
b) Short term memory is the ability to remember ideas from a minute to extended periods, without any ongoing conscious effort to sustain the memories. However, the memories are not so deeply impressed upon the psyche as to become permanent.
c) Long term memory is the ability to store information permanently.
d) Working memory is the capacity to consciously 'hold' information while manipulating it. Working memory can draw on all the other forms of memory. For example, while reading this post your working memory draws on your memories of English reading skills (long term memory), remembers the chain of ideas mentioned earlier in the post so that the present ideas are seen in context (short term memory), and it draws on the sensory impressions of the words being read. To hold ideas in working memory, people often repeat words or concepts in their mind over and over. It has been demonstrated that intelligence strongly hinges on the effectiveness of working memory, for in order to make sense of information one must be able to juggle many ideas/skills within the mind from all levels of memory.
Let's apply these memory types to skateboarding:
When skating, it is necessary to see the sequence of movements involved in a trick's performance as one coherent continuum. This requires firm attention to the iconic/echoic (tactile, vestibular, etc) impressions. Of course, to carry out movements correctly and to sense where in a trick's series of steps one is holding at any given moment one must draw on long term memory of how the trick is performed (or short term memory if the trick still hasn't become ingrained). One may then compare present performance with one's memory of how the trick should be performed.
Working memory allows one to keep both memory types in mind for the comparison to be made. When one finds a discrepancy between the two memory types, it may be that either one's present performance requires correction so that it aligns with long term memory, or that long term memory requires modification. Alternatively, both memory types may require improvement. One's 'theories' of what requires correction and why must be kept in mind in order that their merit be tested. Short term memory offers the storage needed for the theories.
Memory can also work at a subconscious level. In one relevant study, a group of people were shown a list of names famous only in highly specialized circles. Several months later they, alongside another group that hadn't been shown the list of names, were shown another list of names and asked to identify the prominent ones. Some of the names on the second list appeared on the first list. The group exposed to the first list were remarkably more capable of identifying prominent names even though they'd long forgotten the names from the first list. They seemed to remember names from the first list subconsciously.
This has promising implications for skateboarders who feel that a lack of any obvious progress renders a skate session a waste of time. For during every session one subconsciously assimilates information and experiences which transfer as subconscious memory to subsequent skating. A skater thus continues to progress even when unaware of the memories underlying his growth...
People typically conceive of memory as the ability to bring previous experiences to mind. In truth, memory involves much more than that. Psychologists and cognitive scientists divide memory into several forms (though the boundaries between them are often elusive): iconic/echoic memory, working memory, short term memory, and long term memory:
a) Iconic/echoic memory are the impressions of visual or auditory sensations lasting for a few fleeting moments after they're experienced. It is this memory that allows one to perceive a series of actions as one cohesive sequence.
b) Short term memory is the ability to remember ideas from a minute to extended periods, without any ongoing conscious effort to sustain the memories. However, the memories are not so deeply impressed upon the psyche as to become permanent.
c) Long term memory is the ability to store information permanently.
d) Working memory is the capacity to consciously 'hold' information while manipulating it. Working memory can draw on all the other forms of memory. For example, while reading this post your working memory draws on your memories of English reading skills (long term memory), remembers the chain of ideas mentioned earlier in the post so that the present ideas are seen in context (short term memory), and it draws on the sensory impressions of the words being read. To hold ideas in working memory, people often repeat words or concepts in their mind over and over. It has been demonstrated that intelligence strongly hinges on the effectiveness of working memory, for in order to make sense of information one must be able to juggle many ideas/skills within the mind from all levels of memory.
Let's apply these memory types to skateboarding:
When skating, it is necessary to see the sequence of movements involved in a trick's performance as one coherent continuum. This requires firm attention to the iconic/echoic (tactile, vestibular, etc) impressions. Of course, to carry out movements correctly and to sense where in a trick's series of steps one is holding at any given moment one must draw on long term memory of how the trick is performed (or short term memory if the trick still hasn't become ingrained). One may then compare present performance with one's memory of how the trick should be performed.
Working memory allows one to keep both memory types in mind for the comparison to be made. When one finds a discrepancy between the two memory types, it may be that either one's present performance requires correction so that it aligns with long term memory, or that long term memory requires modification. Alternatively, both memory types may require improvement. One's 'theories' of what requires correction and why must be kept in mind in order that their merit be tested. Short term memory offers the storage needed for the theories.
Memory can also work at a subconscious level. In one relevant study, a group of people were shown a list of names famous only in highly specialized circles. Several months later they, alongside another group that hadn't been shown the list of names, were shown another list of names and asked to identify the prominent ones. Some of the names on the second list appeared on the first list. The group exposed to the first list were remarkably more capable of identifying prominent names even though they'd long forgotten the names from the first list. They seemed to remember names from the first list subconsciously.
This has promising implications for skateboarders who feel that a lack of any obvious progress renders a skate session a waste of time. For during every session one subconsciously assimilates information and experiences which transfer as subconscious memory to subsequent skating. A skater thus continues to progress even when unaware of the memories underlying his growth...
Tuesday, November 15, 2011
Of noise and silence
One frequently sees skateboarders react in opposite ways when landing a trick successfully. Sometimes they exhibit immense excitement, give their friends a high-five, or repeat the trick in front of their friends to impress them. And sometimes, they'll perform the same trick with no obvious reaction to it, they simply continue skating. I call the first type of reaction 'noisy', and the second type, 'silent'.
What accounts for the different reactions?
Let us explore a few possible explanations:
a) If a bottle full to the brim with coins is shook, it makes no noise. A bottle containing only a few coins, however, produces a loud rattle. One who is deeply confident with his skateboarding ability doesn't feel the need to show off, he knows that people appreciate his ability without him having to actively draw their attention to it. In contrast, one who feels rather empty of value and ability, feels that people will not automatically appreciate his skating, he thus actively makes them notice him through noise and pomp.
b) A feather makes little noise on landing; a brick lands with a thud. A skater who is aware of how amazing professional skateboarders are and compares his own abilities to theirs, or who senses that relative to his own potential, he's only actualized a tiny fraction, feels quite small - 'light'. Hence, he makes little noise about himself when he lands a trick. On the other hand, a skater who loses sight of his true place may exaggerate his own abilities, seeing them as more substantial - 'heavier' - than they really are. As a result, he is inclined to make noise when he lands a trick.
c) Compare three types of fuel: moist wood, straw, and oil. Moist wood crackles heavily when consumed; straw is quieter; olive oil burns silently. The reason for the decreased noise in each successive fuel type is the fuel's decreased resistance to consumption. Moist wood is coarsest and most resistant to consumption and thus makes much noise. In a sense, it puts up a big fight. Oil, in contrast, is exceptionally refined and perfect for consumption. It is thus consumed silently.
A skater who feels he's attempting a trick well beyond his level, and whose body and psyche resist performing the trick, is apt to make much noise as he comes closer and closer to landing it. On the other hand, a skater who has the physical and psychological preparedness to perform a trick, does so with greater ease - less resistance - and hence more quietly.
d) Novelty tends to be exciting. What one is accustomed to, he tends to take for granted. Hence, when a skater first lands a trick, he is inclined to feel excited and joyful. However, having performed the trick many times - and has continued to attempt more skillful feats - he has typically habituated to the trick and thus performs it without the whistles...
What accounts for the different reactions?
Let us explore a few possible explanations:
a) If a bottle full to the brim with coins is shook, it makes no noise. A bottle containing only a few coins, however, produces a loud rattle. One who is deeply confident with his skateboarding ability doesn't feel the need to show off, he knows that people appreciate his ability without him having to actively draw their attention to it. In contrast, one who feels rather empty of value and ability, feels that people will not automatically appreciate his skating, he thus actively makes them notice him through noise and pomp.
b) A feather makes little noise on landing; a brick lands with a thud. A skater who is aware of how amazing professional skateboarders are and compares his own abilities to theirs, or who senses that relative to his own potential, he's only actualized a tiny fraction, feels quite small - 'light'. Hence, he makes little noise about himself when he lands a trick. On the other hand, a skater who loses sight of his true place may exaggerate his own abilities, seeing them as more substantial - 'heavier' - than they really are. As a result, he is inclined to make noise when he lands a trick.
c) Compare three types of fuel: moist wood, straw, and oil. Moist wood crackles heavily when consumed; straw is quieter; olive oil burns silently. The reason for the decreased noise in each successive fuel type is the fuel's decreased resistance to consumption. Moist wood is coarsest and most resistant to consumption and thus makes much noise. In a sense, it puts up a big fight. Oil, in contrast, is exceptionally refined and perfect for consumption. It is thus consumed silently.
A skater who feels he's attempting a trick well beyond his level, and whose body and psyche resist performing the trick, is apt to make much noise as he comes closer and closer to landing it. On the other hand, a skater who has the physical and psychological preparedness to perform a trick, does so with greater ease - less resistance - and hence more quietly.
d) Novelty tends to be exciting. What one is accustomed to, he tends to take for granted. Hence, when a skater first lands a trick, he is inclined to feel excited and joyful. However, having performed the trick many times - and has continued to attempt more skillful feats - he has typically habituated to the trick and thus performs it without the whistles...
Monday, November 14, 2011
Love and fear: the petals and thorns of skateboarding
Love and fear are the fundamental emotions within the human heart. They pretty much underpin all human behaviour. When one gravitates toward something, 'love' is the driving force, when repelled by something, fear is behind the scenes.
These qualities have many ways of expressing themselves: strong or weak, selfish or selfless, passionate or mellow, etc. Thus sometimes love is termed 'attraction', and fear, 'repulsion'; sometimes love is called 'interest', and fear, 'disinterest'; and at other times love is 'appreciation' and fear, 'reverence'. When one's repulsed by something it's because he fears the discomfort the object may cause him. When one is disinterested, he fears that engaging the object will cause him to miss more important and desirable things, to waste time, or be bored. Appreciation and reverence are more refined and civilized forms of the two qualities.
Love and fear are entwined and virtually inseparable. There can be no fear without love. A person fears injury because he loves himself and desires his own well being. One fears for the safety of his own children because he loves them. This is one reason that he feels more fear when his own child crosses the road than when an other's child does: simply, he loves his own children more.
Often one love is in conflict with another love. When a person has a choice between chicken and beef main courses and finds it difficult to decide which he'd prefer, it is because he 'loves' both and fears that in choosing one he has to miss out on the other. A similar process takes place on a higher 'octave' when one desires to give charity to one of two favoured organizations but can't decide which to donate to.
Sometimes specific fears conflict with each other. Should one visit the dentist or suffer from a toothache? Both alternatives evoke fear in many people. Often an individual procrastinates making a choice until he feels compelled to take one. Many people engage in diversions in order to avoid dealing with fear/fear conflicts.
Sometimes love and fear are in conflict. One may love and fear the same object, albeit different aspects of it. Take the rose for example. Its charm and beauty is alluring and attractive, yet its prickly thorns arouse caution. In approaching a rose one feels both love and fear. As a general rule, the further an individual is from an object or event the weaker are his love and fear of it. And, as he comes closer, his feelings swell more and more. However, love tends to predominate when one is still at a distance, while fear increases more sharply as one comes closer, often overriding love and resulting in the abandonment of the object of love.
This is a much repeated experience when skateboarding, for skateboarding tricks are at once highly alluring and desirable, yet also dangerous. From a distance one may imagine oneself executing an amazing trick and feel strongly motivated to do so in actuality. Yet, as one rolls up to perform the trick, the height of the stairs or the solidity of the concrete cause one's fears to escalate and pressure one to bail. This process reinstates itself almost every time a skater wishes to progress to a more difficult level of performance. Indeed, skateboarding comprises elegant petals and prickly thorns. To skateboard is to approach a gorgeous rose.
These qualities have many ways of expressing themselves: strong or weak, selfish or selfless, passionate or mellow, etc. Thus sometimes love is termed 'attraction', and fear, 'repulsion'; sometimes love is called 'interest', and fear, 'disinterest'; and at other times love is 'appreciation' and fear, 'reverence'. When one's repulsed by something it's because he fears the discomfort the object may cause him. When one is disinterested, he fears that engaging the object will cause him to miss more important and desirable things, to waste time, or be bored. Appreciation and reverence are more refined and civilized forms of the two qualities.
Love and fear are entwined and virtually inseparable. There can be no fear without love. A person fears injury because he loves himself and desires his own well being. One fears for the safety of his own children because he loves them. This is one reason that he feels more fear when his own child crosses the road than when an other's child does: simply, he loves his own children more.
Often one love is in conflict with another love. When a person has a choice between chicken and beef main courses and finds it difficult to decide which he'd prefer, it is because he 'loves' both and fears that in choosing one he has to miss out on the other. A similar process takes place on a higher 'octave' when one desires to give charity to one of two favoured organizations but can't decide which to donate to.
Sometimes specific fears conflict with each other. Should one visit the dentist or suffer from a toothache? Both alternatives evoke fear in many people. Often an individual procrastinates making a choice until he feels compelled to take one. Many people engage in diversions in order to avoid dealing with fear/fear conflicts.
Sometimes love and fear are in conflict. One may love and fear the same object, albeit different aspects of it. Take the rose for example. Its charm and beauty is alluring and attractive, yet its prickly thorns arouse caution. In approaching a rose one feels both love and fear. As a general rule, the further an individual is from an object or event the weaker are his love and fear of it. And, as he comes closer, his feelings swell more and more. However, love tends to predominate when one is still at a distance, while fear increases more sharply as one comes closer, often overriding love and resulting in the abandonment of the object of love.
This is a much repeated experience when skateboarding, for skateboarding tricks are at once highly alluring and desirable, yet also dangerous. From a distance one may imagine oneself executing an amazing trick and feel strongly motivated to do so in actuality. Yet, as one rolls up to perform the trick, the height of the stairs or the solidity of the concrete cause one's fears to escalate and pressure one to bail. This process reinstates itself almost every time a skater wishes to progress to a more difficult level of performance. Indeed, skateboarding comprises elegant petals and prickly thorns. To skateboard is to approach a gorgeous rose.
Sunday, November 13, 2011
Knowing, Knowing...Known
What does it mean to know something?
Philosophers have distilled three basic types of knowledge:
1.Propositional knowledge: a knowledge of facts or statements about existence. For example, 'the Sun rises in the east and sets in the west'; 'David and Debbie are happily married'; 'Einstein formulated the theory of relativity'. An Intellectual knowledge.
2.Personal knowledge: a sense of connection, familiarity, sympathy, or intimacy with something or someone. For example, 'I know David well'; 'I know that park, I've been there many times'; ' I know what you mean'. An Emotional Knowledge.
3.Performative knowledge: one's knowledge of how to perform tasks or activities. For example, 'I know how to ride a bike'; 'I know how to speak french'; 'I know how to maintain an orderly home'. A Functional Knowledge.
In Kabbalah, personal knowledge is strongly admired. In one episode from the rich chassidic repertoire of stories passed down through the generations, a devout Torah scholar left his family and travelled to a distant town to study mysticism from a chassidic master. On his return home after several months of absence, his father in law protested, 'What did you learn there that you couldn't have learned right here?' To which he replied, 'I discovered that God exists!' Annoyed, the father in law pointed at some trees and asked his simple maidservant, 'Who created these?' Without hesitation she answered, 'God of course!' Turning back to his son in law, he pressed, 'For that you travelled such a great distance?!' The scholar replied, 'What the maidservant says, I know!'
The scholar and the maidservant both possess knowledge of God. However, while the maidservant had propositional knowledge, the scholar attained personal knowledge. When the scholar said he 'knows' God exists, he meant that he senses this as a palpable reality; he can point his finger at the trees and genuinely proclaim, 'these are manifestations of God!'
When God provided Adam with a partner, He said, 'It is not good for man to be alone; I shall make a helpmate for him'. Then, when describing Adam's sexual union with his partner, Eve, the verse states, 'And Adam knew Eve'. Why does the verse employ the term 'knew' rather than a more explicit expression? Additionally how does 'knowing' repair the 'not good' of being alone? These questions are indeed difficult to answer if we understand 'knowing' as propositional knowing. For indeed, if Adam simply knew many facts about Eve, how does that indicate marital union? In truth, however, in 'knowing' Eve, Adam attained personal knowledge of her; he become psychologically entwined with her, and felt her to be a part of his own being; caring for her as he naturally cared for himself. Their sexual union was a physical expression of their deeper sense of oneness.
Skateboarding incorporates all three types of knowledge, the most obvious being performative knowledge. Skaters watch trick tips or develop their own understanding of how to perform tricks. Indeed one often hears skaters explaining the sequence of steps necessary to execute a manoeuvre. Of course skaters also have propositional knowledge about their art. From knowledge of what an Ollie is, to which skater originated the Ollie (In 1976 Allen Gelfand - whose nickname was 'Ollie' - was the first to perform it in a pool, and in 1982 Rodney Mullen was the first to perform it on flat ground), to the record holder of the highest ever 'Ollie' (Aldrin Garcia - 45'' - in February of 2011). Most importantly, however, skaters can develop personal knowledge of skating, where through much experience skateboarding, the skater feels that his skateboard is part of his own being, and performs tricks naturally and automatically as though the board was an extension of his self, under the direct control of his will as are his arms and legs.
Personal knowledge is 'good' for a skater in at least two ways:
Firstly, it brings a skater to feel that his skateboard is his 'friend'. When he picks up his board, he senses how much depth, joy, challenge, adventure, and potential lies beneath its plain wooden veneer. Additionally, it is through personal knowledge that one becomes a good skater, exhibiting such incredible control that it becomes difficult to discern where the skater ends and the skateboard begins. It also seems that skating is an intrinsic part of his being. Thus on several occasions, when watching pro skaters sharing trick tips, I was shocked to hear them describe how they learnt the trick and the difficulties they had in doing so. Because of how ingrained skating is in their being, it seems as though they were always capable of skating as well as they do.
Philosophers have distilled three basic types of knowledge:
1.Propositional knowledge: a knowledge of facts or statements about existence. For example, 'the Sun rises in the east and sets in the west'; 'David and Debbie are happily married'; 'Einstein formulated the theory of relativity'. An Intellectual knowledge.
2.Personal knowledge: a sense of connection, familiarity, sympathy, or intimacy with something or someone. For example, 'I know David well'; 'I know that park, I've been there many times'; ' I know what you mean'. An Emotional Knowledge.
3.Performative knowledge: one's knowledge of how to perform tasks or activities. For example, 'I know how to ride a bike'; 'I know how to speak french'; 'I know how to maintain an orderly home'. A Functional Knowledge.
In Kabbalah, personal knowledge is strongly admired. In one episode from the rich chassidic repertoire of stories passed down through the generations, a devout Torah scholar left his family and travelled to a distant town to study mysticism from a chassidic master. On his return home after several months of absence, his father in law protested, 'What did you learn there that you couldn't have learned right here?' To which he replied, 'I discovered that God exists!' Annoyed, the father in law pointed at some trees and asked his simple maidservant, 'Who created these?' Without hesitation she answered, 'God of course!' Turning back to his son in law, he pressed, 'For that you travelled such a great distance?!' The scholar replied, 'What the maidservant says, I know!'
The scholar and the maidservant both possess knowledge of God. However, while the maidservant had propositional knowledge, the scholar attained personal knowledge. When the scholar said he 'knows' God exists, he meant that he senses this as a palpable reality; he can point his finger at the trees and genuinely proclaim, 'these are manifestations of God!'
When God provided Adam with a partner, He said, 'It is not good for man to be alone; I shall make a helpmate for him'. Then, when describing Adam's sexual union with his partner, Eve, the verse states, 'And Adam knew Eve'. Why does the verse employ the term 'knew' rather than a more explicit expression? Additionally how does 'knowing' repair the 'not good' of being alone? These questions are indeed difficult to answer if we understand 'knowing' as propositional knowing. For indeed, if Adam simply knew many facts about Eve, how does that indicate marital union? In truth, however, in 'knowing' Eve, Adam attained personal knowledge of her; he become psychologically entwined with her, and felt her to be a part of his own being; caring for her as he naturally cared for himself. Their sexual union was a physical expression of their deeper sense of oneness.
Skateboarding incorporates all three types of knowledge, the most obvious being performative knowledge. Skaters watch trick tips or develop their own understanding of how to perform tricks. Indeed one often hears skaters explaining the sequence of steps necessary to execute a manoeuvre. Of course skaters also have propositional knowledge about their art. From knowledge of what an Ollie is, to which skater originated the Ollie (In 1976 Allen Gelfand - whose nickname was 'Ollie' - was the first to perform it in a pool, and in 1982 Rodney Mullen was the first to perform it on flat ground), to the record holder of the highest ever 'Ollie' (Aldrin Garcia - 45'' - in February of 2011). Most importantly, however, skaters can develop personal knowledge of skating, where through much experience skateboarding, the skater feels that his skateboard is part of his own being, and performs tricks naturally and automatically as though the board was an extension of his self, under the direct control of his will as are his arms and legs.
Personal knowledge is 'good' for a skater in at least two ways:
Firstly, it brings a skater to feel that his skateboard is his 'friend'. When he picks up his board, he senses how much depth, joy, challenge, adventure, and potential lies beneath its plain wooden veneer. Additionally, it is through personal knowledge that one becomes a good skater, exhibiting such incredible control that it becomes difficult to discern where the skater ends and the skateboard begins. It also seems that skating is an intrinsic part of his being. Thus on several occasions, when watching pro skaters sharing trick tips, I was shocked to hear them describe how they learnt the trick and the difficulties they had in doing so. Because of how ingrained skating is in their being, it seems as though they were always capable of skating as well as they do.
Personal knowledge in skating is thus 'good' for a skater's psychological well being, and 'good' in terms of how impressive his skating appears to onlookers.
Monday, November 7, 2011
Saturday, November 5, 2011
Sacrificing beauty: a beautiful sacrifice II
In its wider application this principle is common. An individual who sees beauty in loving-kindness will part with objects of beauty in order to bestow their friends with gifts. Some incredible people even forgo living in luxury and move to a third world country in order to offer aid to its underprivileged citizens. Rather than barbarically destroying beauty on account of an inability to appreciate it, such individuals surrender it for the sake of attaining a loftier and nobler form.
This brings us to a specific form of such sacrifice, also visible in skateboarding. The top of a skateboard would look more appealing if it's smooth varnished wood was exposed, without coarse black grip tape covering it. Yet, for the sake of having more traction between one's board and feet, beauty is again sacrificed.
This form of sacrifice - beauty for traction - is pronounced in teaching. A teacher, especially one expert in highly abstract concepts, often couches his understanding in more concrete and sensually stimulating analogies and parallels in order to grip his students with the ideas. Certainly in high school, many students are overcome with lethargy when teachers discuss highly technical or rarefied concepts. The discussions simply fail to grip the attention of the class as if they are so smooth that the students 'slip off' them. The teachers that manage to express concepts in coarser and more tangible ways - though adding something foreign and relatively crude to otherwise elegant and fine mathematics or formulae - are most successful at grabbing and maintaining their students' interest...
This brings us to a specific form of such sacrifice, also visible in skateboarding. The top of a skateboard would look more appealing if it's smooth varnished wood was exposed, without coarse black grip tape covering it. Yet, for the sake of having more traction between one's board and feet, beauty is again sacrificed.
This form of sacrifice - beauty for traction - is pronounced in teaching. A teacher, especially one expert in highly abstract concepts, often couches his understanding in more concrete and sensually stimulating analogies and parallels in order to grip his students with the ideas. Certainly in high school, many students are overcome with lethargy when teachers discuss highly technical or rarefied concepts. The discussions simply fail to grip the attention of the class as if they are so smooth that the students 'slip off' them. The teachers that manage to express concepts in coarser and more tangible ways - though adding something foreign and relatively crude to otherwise elegant and fine mathematics or formulae - are most successful at grabbing and maintaining their students' interest...
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