dimensional shuffles

[AntonioLao]

Given 3 points abc there exist 6 permutations or shuffles: abc, acb, bac, bca, cab, and cba. Given 2 points a and b, there exist only 2 shuffles: ab and ba. Both these 2p and 3p shuffles hide two distinct directional invariance properties, say the left (L) and the right (R) property. For the 2p configurations, ab indicates direction to the right and ba direction to the left. For the 3p configurations, abc, bca, and cab indicate direction to the right, while acb, bac, and cba to the left. In these cases, linearity implies one dimensionality and for all 1-dim shuffling configurations there exist two and only two directional invariance properties: L and R. For 4p 1-dim shuffles, there exist 24 configurations: abcd, abdc, acbd, acdb, adbc, adcb, bacd, badc, bcbd, bcda, bdac, bdca, cabd, cadb, cdad, cbda, cdab, cdba, dabc, dacb, dbac, dbca, dcab, and dcba. Among these there are 4 4-cycles of R: abcd, bcda, cdab, and dabc. There are 4 4-cycles of L: adcb, badc, cbad, and dcba. However, there are 10 2-cycles of both R and L: abdc, acbd, bacd, bdac, cabd, cdba, dacg, dbac, dbca, and dcab. On the other hand, there are 3 2-cycles of L: acdb, bdca, and cbda. There are also 3 2-cycles of R: adbc, bcad, and cadb.

These imply that the number of directional invariance properties (Q) is directly proportional to the double exponential growth of the dimension: Q=2ͩ where d denotes the dimension. Excluding d=0, for d=1, Q=2; d=2, Q=4; d=3, Q=8; d=4, Q=16; d=5, Q=32; d=6, Q=64; d=7, Q=128; d=8, Q=256. For d=2, the Q’s are derived from L, R, F (forward), B (backward): LF, LB, RF, and RB. For d=3, the 8 Q’s are derived from: L, R, F, B, U (up), and D (down): LFU, LBU, RFU, RBU, LFD, LBD, RFD, and RBD. By these, the dimensional shuffles is defined as the product of Q and the point factorial.

[labelwench]

In riding the fully schooled horse, one has three sets of aids: the seat bones, the lower legs, and the hands. These are complimented by proper use of breathing and the eyes.

By combining these aids, a proficient rider may guide the trained horse through the following movements:

Collected walk
Medium Walk
Working Walk
Extended walk

Collected Trot
Medium Trot
Working Trot
Extended Trot

Collected Canter
Working Canter
Hand Gallop or Extended Canter

Full Gallop

Back up (Walk Only)

Side Pass (To left and to right)

Leg Yield at the walk
Leg Yield at the trot
Leg Yield at the canter

Leg Yield in reverse (To left and to right, walk only)

All of the movements can be done while traveling to the left or to the right.

In upward transitions, a horse may depart from the standstill into any of the walk, trot or canter.

In downward transitions, a horse may go from the canter to the trot, the walk, or even a sliding stop.

The horse maintains balance by a change of lead when changing direction, but the horse can also be schooled to take the counter-balance on cue from the rider, and travel with the body counter arced to the direction of travel.

The change of lead can also be performed while traveling in a straight line, and very advanced horses can change on every stride.

All of this and more, is conveyed to the horse by means of movements so subtle that only another skilled in equitation may detect the aids in use.

Perhaps some of Antonio's math could be used to describe the correct proportion of signal that is conveyed to the horse by each aid, in that the horse is clearly able to distinguish the difference in the task requested by the permutations involved.

What do you figure, Antonio? Have you got a formulation for a direct rein, indirect rein, open rein, leading rein, supporting rein etc.? Perhaps we can rewrite the equitation instruction texts in a whole new format....

[AntonioLao]

Since horses live a a world of three dimensions, their dimensional shuffles can be a lot more complicated than the ones I described. But I noticed that the elbows of the hind legs of horses are bending in the opposite directions to that of human knees while combined with hand elbows, ours seem to point away while those of horse seem to point toward each other which could provide more degrees of freedom and consequently more dimensional shuffles.

[labelwench]

Since horses live a a world of three dimensions, their dimensional shuffles can be a lot more complicated than the ones I described. But I noticed that the elbows of the hind legs of horses are bending in the opposite directions to that of human knees while combined with hand elbows, ours seem to point away while those of horse seem to point toward each other which could provide more degrees of freedom and consequently more dimensional shuffles.

Another interesting aspect of the movement of the horse, is that the sequence of the footfalls is different in each gait. The walk is a four beat gait, the trot is a two beat gait, bounding from diagonal to diagonal, which is why it is bouncy to sit for a novice rider, lol. The canter is a three beat gait, and the gallop is once again a four beat gait.

The following link goes to a brief article that well describes the pattern of footfall for each of the above.

http://www.helium.com/items/1189569-...nded-collected

[AntonioLao]

My question is what exactly does a horse whisperer says to the horse?

[labelwench]

My question is what exactly does a horse whisperer says to the horse?

Thank you for the question.

A 'horse whisperer' is akin to a horse psychologist. From the position of empathy, they seek to understand and communicate with the horse by means of body language, and once the horse is willing, through gentle touch. Horses are very tactile creatures, and in the herd, they groom each other, and stand close when in need of confidence or comfort, not that different from humans, really.

Horses, like people, vary in personality. Some are bold, others timid, and all variations between. The horse has been our ally since domestication, and we would not have made the progress we have nearly so quickly without the aid of this noble and forgiving creature.

In answer to your question, then, a 'horse whisperer' thinks like a horse, and while some verbal articulation and tone may be used, most of the communication is by means of subtle body language, some eye contact, and concentrated thought. Not quite telepathy, lol, but the next thing to it. Even with my youngsters, I could give a demonstration of their understanding that would appear like 'magic' to the average, and even fairly advanced horse person.

Marvelous creatures, horses, and excellent diplomats when one learns their style of communication. It truly amazes me that more people do not get seriously injured when I contemplate some of the situations that the inexperienced place themselves and their horses into.

Of course, there's only one way to truly gain experience.......wet saddle blankets, as we say in the horse business, meaning you've got to ride plenty of miles and work up a sweat in the pursuit of such understanding.

http://en.wikipedia.org/wiki/Daniel_...er%22_Sullivan

[AntonioLao]

Do you think there are human whisperers? Would this be our alter ego? It is a fact that people do talk to themselves whenever they perform mental shuffles.

[labelwench]

Do you think there are human whisperers? Would this be our alter ego? It is a fact that people do talk to themselves whenever they perform mental shuffles.

I elect to answer your question, firstly, from the perspective of 'empathy'. In that regard, I would suggest that there are human whisperers; people who are able to meet one or several of the following uses of the term 'empathy', taken from Wikipedia.

Theorists and their definitions

Empathy is an ability with many different definitions. They cover a broad spectrum, ranging from feeling a concern for other people that creates a desire to help them, experiencing emotions that match another person’s emotions, knowing what the other person is thinking or feeling, to blurring the line between self and other.[5] Below is a list of various definitions of what empathy means:
Daniel Batson: A motivation oriented towards the other.[6]
D. M. Berger: The capacity to know emotionally what another is experiencing from within the frame of reference of that other person, the capacity to sample the feelings of another or to put oneself in another’s shoes.[7]
Jean Decety: A sense of similarity in feelings experienced by the self and the other, without confusion between the two individuals.[8][9]
Nancy Eisenberg: An affective response that stems from the apprehension or comprehension of another’s emotional state or condition, and that is similar to what the other person is feeling or would be expected to feel.[10]
R. R. Greenson: To empathize means to share, to experience the feelings of another person.[11]
Alvin Goldman: The ability to put oneself into the mental shoes of another person to understand her emotions and feelings.[12]
Martin Hoffman: An affective response more appropriate to another's situation than one's own.[13]
William Ickes: A complex form of psychological inference in which observation, memory, knowledge, and reasoning are combined to yield insights into the thoughts and feelings of others.[14]
Heinz Kohut: Empathy is the capacity to think and feel oneself into the inner life of another person.[15]
Carl Rogers: To perceive the internal frame of reference of another with accuracy and with the emotional components and meanings which pertain thereto as if one were the person, but without ever losing the "as if" condition. Thus, it means to sense the hurt or the pleasure of another as he senses it and to perceive the causes thereof as he perceives them, but without ever losing the recognition that it is as if I were hurt or pleased and so forth.[16]
Roy Schafer: Empathy involves the inner experience of sharing in and comprehending the momentary psychological state of another person.[17]
Wynn Schwartz: "We recognize others as empathic when we feel that they have accurately acted on or somehow acknowledged in stated or unstated fashion our values or motivations, our knowledge, and our skills or competence, but especially as they appear to recognize the significance of our actions in a manner that we can tolerate their being recognized."[18]
Edith Stein: Empathy is the experience of foreign consciousness in general.[19]
Simon Baron-Cohen (2003): Empathy is about spontaneously and naturally tuning into the other person's thoughts and feelings, whatever these might be [...]There are two major elements to empathy. The first is the cognitive component: Understanding the others feelings and the ability to take their perspective [...] the second element to empathy is the affective component. This is an observers appropriate emotional response to another person's emotional state. [20]
Khen Lampert (2005): "[Empathy] is what happens to us when we leave our own bodies...and find ourselves either momentarily or for a longer period of time in the mind of the other. We observe reality through her eyes, feel her emotions, share in her pain.."[21]


Since empathy involves understanding the emotion states of other people, the way it is characterized is derivative of the way emotions themselves are characterized. If for example, emotions are taken to be centrally characterized by bodily feelings, then grasping the bodily feelings of another will be central to empathy. On the other hand, if emotions are more centrally characterized by a combination of beliefs and desires, then grasping these beliefs and desires will be more essential to empathy.The ability to imagine oneself as another person is a sophisticated imaginative process. However the basic capacity to recognize emotions is probably innate and may be achieved unconsciously. Yet it can be trained, and achieved with various degrees of intensity or accuracy.

The human capacity to recognize the bodily feelings of another is related to one's imitative capacities, and seems to be grounded in the innate capacity to associate the bodily movements and facial expressions one sees in another with the proprioceptive feelings of producing those corresponding movements or expressions oneself.[22] Humans also seem to make the same immediate connection between the tone of voice and other vocal expressions and inner feeling. See neurological basis below.[23]

http://en.wikipedia.org/wiki/Empathy

From my Mother, I have inherited an empathetic nature. When people meet me, they either take immediate liking to me, or they wish to avoid me. No 'in between'. My personal thought is that when one is observant, there is nowhere to hide, and such is recognized, even if unspoken.

The interesting thing about communicating on the inter-net, is that I am not able to use this skill in the traditional way. There is no body language and no verbal inflection.

Yet, even in the written word, one can begin to sense where there is consistency in the replies of those doing the posting.

The concepts of some of the maths and physics do not come to me well in this medium. I am tactile. With my senses, do I enjoy exploring the world. Theories are fascinating, even when they contradict each other, but I am not satisfied unless there is something that I can actually 'experience'.

However, I can easily understand that there are people who are as enamored of the possibilities of these theories as I am about experiencing the world from horseback, looking for signs of wildlife activity after a new fallen snow.

It's all different, and very interesting, whether I ever 'get it' or not, lol.....

Thank you for your patience.

[AntonioLao]

Then in light of falling academic achievement at the elementary, secondary, and college level education what the United States need are more empathic teachers.

[SB_UK]

Then in light of falling academic achievement at the elementary, secondary, and college level education what the United States need are more empathic teachers.

We need an explanation of the point of learning; unfortunately neither the carrot of having more money nor the stick of having less money than most (so we shall shortly see)
will be enough.

ADDF:meadd823 alluded to the point of learning by her description of her 'mind appearing to have a mind of its own'.

The mechanism which underlies Tammy's statement provides us with the point of education; the point of education is nothing to do with money; in fact, money (ironically currently) prevents us from real-izing the purpose of proper education.

A very personal journey of understanding which leads the individual (who follows the white rabbit) into everything we've been seeking, occurring alongside an understanding of morality; this ~idea~ works ... ... ...

... .... we could (indeed), could indeed call, could indeed call the journey, call the journey 'an inquiry into morals' ... ... ...

[the point of education]

R.P.Bi Bra(hman) and he know it, know it well.