Quantitative Performance Improvement Studies in Dance

In the past few days, I have been pondering about how to get my students to perform better.  My training as a Scientist and Engineer drives me to seek an efficient and scientific way to train my students in Classical Ballet.  Qualitatively I have good ideas as to where my dancers need more improvement but I do not feel comfortable not knowing cause and effect relationships at a quantitative level.  Specifically, I seek numerical evidence to determine which aspects of movement and anatomy affect the execution of certain steps in the vocabulary of Classical Ballet.  So far I have not found any good material covering this approach to performance improvement analysis. 

The general approach I plan to take is to get data on  input variables such as the angle of turnout, depth of plie and correlate this with the number of piroutte turns or the height of a grand jete.  The method will involve looking at film images and analyzing the body positioning based on stick models.  Quantitative data from this will then be analyzed using correlation analysis and other experimental analysis methods.  I'd like to know if anyone has ventured into this type of performance improvement research in Dance.  Feel free to comment.

Math Problem Help - Inequalities

Inequalities was a very confusing topic for me when I first learned Algebra.  The key to it really is to remember that < means less than  and > is less than.  Here's my solution to Exercise 4 of College Algebra by Hart.

ECHO - a film on perspectives

At times we make judgements on what we see based on our experience.  More often than not, our experience tends to make us skeptical and critical of what we encounter.  Only if we look closer and deeper do we uncover a new dimensions of something thrust before us.

I recently encountered the film "Echo" in a MOOC on film making.  The story revolves around a 17 year old girl, Caroline, who receives a phone call while walking on the street.  From the conversation, you  deduce that it is about her Dad getting into an accident.  Passersby notice the distraught Caroline and offer to help by getting her a cab and giving her money.  As soon as she takes the cab, her face changes and she stops the cab a few meters away from the scene.  Later you find Caroline at home with her family. Her mom upset about her being late.  In the next scene you find her having the same phone call and a passerby helping her.  This is cut short with the arrival of her brother. He asks who the guy is and how does he know about their dad.   In the final parts of the film, Caroline once again has the phone call experience with people helping her.

At the first sequence  of Caroline's phone call experience, you conclude that she is a fraud, taking advantage of the kindness of other people.  The film shots are taken from a distance, giving you the point of view of an outsider.  The middle part of the film gives you a glimpse of Caroline's family life. You get hints about an incident in the past that the family is coping.  The third part gives you an insight of how Caroline is feeling during the phone call experience.  With upclose camera shots, you find that she is highly emotional as if she were reliving the whole experience of her Dad having an accident.

The use of repetition and variation in this film gives you an insight to the same phenomenon from different angles.  By watching this film, one realizes that a story has many dimensions depending on the point of view you look at it from.  It reminds me of Akira Kurosawa's film "Rashomon" where a single storyline is told from the perspective of many witnesses with the end left for the audience to present a verdict.

I'm curious to know what you think of this film. Feel free to comment.

A look at the campaigns of the the 2016 Presidential Candidates

It has been interesting to observe the different Presidential Aspirants and their varied strategies to garner support.  I don't consider myself an expert in political campaigns but I have been privy to some campaigns giving me enough sensitivity to detect nuances in what the various camps communicate. Instead of doing a politics of obstruction and vote buying, the campaign teams should work on genuine public support by clearly communicating the unique selling proposition of their candidate. Buying votes and obstruction are indicative of the lack of creativity the campaign have.  They should not aim to merely have votes but rather aim to have an army of campaigners.  They should work giving people a powerful "Second Moment of Truth"..

 Here are some of my opinions regarding the various campaigns:

1.) Mar Roxas -  I think the campaign strategist are trying to make him something he's not.  It appears to be a rehash of the "Mr. Palengke" approach that hurt him bad in the last election.  Why do they try to make him a man of the masses when he is not.  There's also the "Tuwid na Daan" message that associates him with the current administration.  It would be better if he built on the tradition of his family.  How his grandfather labored for the independence of your country. How his father stood for the principles of liberty during Martial law. Building on this, he could say that he is ready to lead the country into a new era of economic prosperity, security and stability guided by the principles his family fought for.  The emphasis of his campaign should be more on the economic and financial aspect because that is what he is known for.

2.) Jejomar Binay -  It is quite challenging to manage his campaign because of the corruption allegations looming over his head.  Nevertheless, his campaign should be focused on human rights and social justice. He should highlight opportunities to solve human rights and social justice problems in our current political landscape.  The more radical and difficult the problem, the better.  It has to be good enough to overshadow the  corruption debacle. 

3.) Grace Poe -  Sen Poe's campaign has been put on the defensive because of her citizenship and residency being questioned.  Her campaign should use this to her advantage.  She can use her experience being a foundling and adopted by her parents as a springboard for her campaign. She should cast a vision of a more compassionate administration that takes care of the people.  With her as President,  the Filipino will now have a country that truly is their home.  Our previous women Presidents were not successful in communicating a mother persona for the country. 

4.) Rodrigo Duterte - Among all the candidates, his is a campaign with a clear consistent message.  His campaign is believable and gives the impression that it is intertwined with his person.  Mayor Duterte's campaign is peace and order and the elimination of corruption. It is also backed by a track record that consistently delivered this promise. His cursing the Pope, communicates he does not respect any as far as public welfare in concerned. Flaunting his womanizing appreas to be a strategy to belittle a weakness in order to put focus on the campaign promise.  What the public perceives as faux pas and incidents of miss-speaking are actually opportunities to strengthen Mayor Duterte's eccentricities differentiating himself from the other candidates.  My advice to his people, leave him to direct his own campaign. By doing so he appears more genuine and flawed making him even more credible as a leader to the populace. 

There you have it...I  wish all candidates the best in their campaigns.

Structured Improvisation-How to Dance in your own way

Improvisation is a regular activity I have in my Contemporary Ballet Class.  I find that doing improvisation exercises, improves the awareness dancers have for each other.  It also trains them to notice nuances and movement details which will prove useful in their future training.  The use of improvisation also makes the dancers aware of choreographic elements, enabling them to respond better to instructions and directions during choreography.

This week, I was working on structured improvisation.  In class I had 2 dancers starting off with a mirroring exercise that was being done as each dancer was approaching the other.  At the point of contact, the dancers were instructed to do a walk exercise with poses at moment of their choosing.  On my cue, the dancers then shifted to a unison followed by having them make a shape that they would move and progress through the space.

Mirroring

Walk Exercise

Walks with a pose

Unison

Moving/Developing Shapes

I found that doing this exercise, the dancers were being trained to overcome their discomfort with using space.  The pose exercise also helped them overcome their comfort with certain positions.  A very good lesson in this exercise is that the dancers learned to do their movements based on the demands of the environment and in response to the movements of their fellow dancers.

You may want to try this out for yourself:

1. Get a partner and stand face to face.

2. Start moving in a slow fashion and have your partner follow you.  Use simple and slow movements, avoid movements that remove eye contact with your partner (e.g. turning your back etc.)

3. Switch roles with your partner by taking on the follower role with your partner as leader. 

When you do this, I recommend using slow flowy music.

Math Problem Help : Dealing with Grouping 3

We continue with how to deal with grouping in mathematical equations.  This is a continuation of my solutions for exercise 3 of College Algebra by Hart.

A Compassionate Bureaucracy: Gauchet's "The Mass of Men"

It is not uncommon to find workers in the Government Bureaucracy to act in a condescending manner upon those who seek their services.  While it is unfair to make this as a generalization towards all in  civil service, it remains a fact that rude treatment of their  clientele exists.  It is a constant challenge, therefore, for the leadership of Government agencies to drive and maintain a culture of customer orientation among their agents. 

I encountered a short film by Gabriel Gauchet depicting the plight of jobless individuals in the UK seeking assistance from Government Job Centers.  The film shows the main character showing up a bit late for his appointment.  Despite the fact that the job officer did not notice the tardiness until the main character brought it up, the job officer slaps him with a suspension of his allowance for 2 weeks.  The tension escalates as he refuses to sign the document which prompts the job officer to threaten him with a 4 week suspension of his allowance.  This comes to an end when a guy comes in an shoot the lady with a nail gun, drags her and nails her to the floor.   While this commotion escalates, our main character does what he can to delete the suspension from his records. 

 WARNING : THIS FILM IS VIOLENT!!!

What seems to be put forth here is the attitude of utter disdain the job officer has for her client, who she sees as lazy and irresponsible.  She does not see him as an individual who needs assistance during this stage in his life.  In my own experience, I benefited from the services of a Police Investigator who treated me as a client who needed assistance rather than as a source of information to do his job. By having a high sense of customer orientation ingrained in a civil servants training regimen, Government services are delivered more efficiently and effectively.

Physics Help - Conversion Problems

 Continuing our journey through Physics. Problems solved are from Fundamentals of Physics, Halliday, Resnick, Walker

18. Suppose your hair grows at the rate of 1/32 in. per day. Find the rate at which it grows in nanometers per second. Since the distance between atoms in a molecule is on the order of 0.1nm , your answer suggest how rapidly layer of atoms are assembled in this protein synthesis.

To answer this quesstion we go through the conversion calculations as follows:

(1/32) in/day  x  2.54 cm/in  x 1/100 m/cm  x 10^9/1 nm/m x 1d/24h x 1h/60mins x 1min/60s =

9.19 mm/s

 

Our next problem simply requires us to express the area in the more popular dimensions of square area.  Conversion is as possible

100ft x .305m/ft = 30.5m

150ft x .305m/ft = 45.75m

A = 1395m^2

 

The first task is to express volume in square ft.  By doing conversion calculations we get

131ft x 66ft x 39ft = 337194 ft^3

To get the weight of air we multiply Volume by density to get mass.

337194ft^3 x 0.076lbs/ft^3 =2.5627 lbs

Ballet Physics - The Arabesque and the Center of Mass

In this post, we will look closely at a popular pose in Ballet, the Arabesque.  We will do so from the perspective of Center of Mass as the Arabesque is a pose that requires proper balance in its execution.

Our analysis starts off with a deconstruction of the human body representing each of its parts in terms of line segments.  The photo below shows a sketch of the Arabesque and a line segment deconstruction.  For purposes of simplicity, we will keep our analysis in 2 dimensions.  We will also assume the angle between the legs is 90 degrees and the angle between the trunk the vertical axis as 30 degrees. The standing leg is assumed to coincide with the vertical axis.

We will use representative data on a dancers body, taken from Tozeren, 1999.

Taken from Human Body Dynamics - Classical Mechanics and Human Movement by A. Tozeren, 1999

The first step is to determine the positions of the segment midpoints with respect to the origin.  Once this is determine, we the proceed to calculate the moment for each of the segment midpoints.  A moment is the representative mass of the segment multiplied by the segment midpoint position.  This is done for both vertical and horizontal coordinates.  The moments are then totaled according to axis and divided by the total mass of the segments.  These results in the coordinates of the center of mass.

Going back to our sketch, we find that the center of mass is 4cm away from the vertical axis which in this case is the center of support.  This means the dancer will have to pull the body towards the arabesque leg to bring the body over the center of support.  Another way of managing this is to work on the height of the Arabesque leg to move the center of mass toward the vertical. 

To help the dancer improve balance in Arabesque, numerical simulations would be great sources of information to guide training.  This will likely a subject in a future blog post.

How unison improvisation can improve co-worker relations...

 

One of the most common exercises in improvisation is the Unison.  It trains dancers how to feel each other and move as a group.  Unison exercises develop a heightened awareness in dancers for the movements of their co-performers.


In it's basic form, a unison exercise starts off with a leader in front who moves in a slow fashion.  As soon as the leader faces the sides or turns about, the most forward person in that direction becomes the leader.  The leadership changes as the leader changes  the position he/she faces.  The great thing about unison is that you can also add the elements of variation and succession which we use in mirroring.  If a dancer has learned how to do mirroring, unison should not be that difficult.

While this improvisation exercise benefits dancers a lot, non-dancers have a lot to gain as well.  For one, the awareness to non-verbal cues allows participants to be sensitive to the movement of the group as a whole.  By constant exposure, this awareness can grow to a point that a person can carry that same sensitivity into the work setting and other non-dance environments.  Considering that most communication is non-verbal, an organization with its members  adept in unison and other improvisational exercises would certainly be a highly effective team.  For this to work, it would be great is the whole organization regularly gets into a unison exercise to be able to explore and experiment on interdependency relationships between team members.


Unison exercises train teams to function organically without any verbal communication.  I also teaches how to adjust with leadership changes. In a nutshell a unison activity is a good simulation for developing co-worker interaction.  Perhaps, these exercises are  a great preventive to common place personality clashes in the work place.

Math Problem Help : Dealing with Grouping part 2

In this post, we will be continuing our work on grouping. Specifically, we will work on problems that involve the removal of grouping in equations.  A key thing to remember if a negative number goes before a parenthesis, we are to multiply it to the numbers inside.

On Perseverance and Training...Lessons from Thelma

Training is important to give you consistent technique and stamina.  In most cases in it the difference between victory and defeat.  A lot of us are awed when a talented person comes along.  In the long run however, we find that those who are on top are those who had the consistency and tenacity to go through the daily struggles of their career.

I was fortunate to have my friend, Rino Que, give me a DVD copy of the award winning film Thelma. Rino and his wife Sam were the Executive Producers of this remarkable feature film Produced by Paul Soriano (also the Director)  and Maja Salvador.  The film centers around a girl named Thelma from province of Ilocos in the Northern part of the Philippines.  Thelma is a free spirit who seems untamable.  She goes about doing as she pleases until one day her dear sister gets hit by a car.  Faced with a sibling who may not be able to walk again, she joins a marathon and wins the prize money with which she purchases a wheelchair.   In the process, she catches the eye of a good coach who is determined to get her into a formal athletic programme. She also learns a very important family secret: her mother used to be a champion runner but gave up her career when she got pregnant with Thelma. The coach aslo happened to be her mother's old coach. With the coaching she gets from her mom and her coach, she becomes a champion all the way up to the nationals.  At this point, she is taken under the wing of top caliber coach who trains her for qualifying into the Philippine Track team.  A second challenge comes in her life, when she learns that her mom is taken to the hospital because of Cancer.  She is now torn between going home to be with her family or continuing her goal to finish college and to represent the Philippines in International competitions. Resolution comes when her family pushes her to pursue her goal and she does so as a dutiful daughter.

For me the memorable scenes where the accident which became a turning point in her life and the point of decision she had at the latter part of the movie.  If found the accident scene very moving with sequences cutting back and forth between Thelma and her sister Hannah with the car at the background.  It gave a sense of foreboding, telling you that the accident was going to happen even before it happened.    The decision scene at the end was also well presented.  The sequence was made of shots on Thelma as the camera was moving around giving a sense of dizziness and confusion.

The story does have a good moral in that it states that sacrifices have to be made to fulfill your dreams. This is made clear as the main character is surrounded by characters whose dreams are not fulfilled.  Her mother, her sister and her boyfriend.  What makes Thelma special was that her dreams were not out of selfish ambition but out of a sense of love and duty to her family. 

Physics help : Tips for Dimensional Analysis Problems

It's time for some help for the Scientifically challenged.  Today we deal with problems involving dimensional consistency.  I will be solving problems from my favorite Physics book, "The Fundamentals of Physics" by Halliday, Resnick and Walker 8th ed.






Chapter 1 problem #12.  

To solve this problem we are to considered that all the factors of the numerator are length dimensions so you get a  volume dimension as a result of the multiplication of the cube of a length dimension.  Dividing the numerator with the denominator, you get a length squared dimension which leads to the final result of a length dimension upon taking the square root.

r = [ (s-a)(s-b)(s-c)/s]^1/2

  = ( L^3/L)^1/2
= (L^2)^1/2
= L

the dimensions are consistent.









Chapter 1 problem #13

 First we take note of the dimensions of the quantities called out:

S - length
a - length/length^2, m/s^2
t - time, s

if we were to plug in the values of m = 1 and n =2, the equation would look like this

length = k (length/(time^2))^1 * time^2

with  time cancelling out and not considering the dimensionless k, we find

both sides of the equation reflecting length

Dimensional analysis does not give enough info to determine the value of k









Chapter 1 problem #14

Consider the dimensions of the following quantities:

T - time
l - length
g - length/time^2







the quotient inside the radical results in a time^2 quantity.  Taking the square root results in both sides of the equation having time units.








Chapter 1 problem #15

 

In the case of equation (a), the left hand side of the equation has length/time dimensions. The right hand side of the equation has length/time dimensions for the first term and length^2/time^2 for the second term.  Thus this equation is not dimensionally consistent.  

Equation (b) on the other hand has both length dimensions on either side of the equation making it dimensionally consistent.

Chapter 1 problem #16

 

Force has the units of  kg•m/s^2.  Multiplying this with r^2, and dividing this with kg^2, you get m^3/kg•s^2 for the units of G.

Chapter 1 problem #17

 We first define the first term coefficient A = 1.50 Mft^3/mos.  Converting to ft^3/s we go through the following:

A = 1.5x10^6ft^3/mos x 1mo/30d x 1d/24h x 1h/60m x 1min/60s = 0.579 ft^3/s

in a similar fashion

B = 0.008x10^6 ft^3/mos^2  x (1mon/30d)^2 x (1d/24h)^2 x (1h/60min)^2 x (1min/60s )

   = 0.19 x 10^-9 ft^3/s^2

V = 0.58 ft^3/s t + 1.19 x 10^-9 ft^3/s^2 t^2

The Physics of Ballet- 3 things you need to Achieve Balance

Balance is an important aspect of Ballet.  It is critical to the proper execution of steps and the maintenance of energy through out a performance.  Without balance, the quality of a dancer's movement is severely impaired.  To achieve balance, one must understand the concepts of Physics that govern this phenomena.

Equilibrium

In scientific parlance,  Balance is called Equilibrium.  This is defined as the absence of a net Force in the system, meaning the dancer is not moved by any force in any direction.  Expanding this further, equilibrium in the stronger form includes the absence of a net Torque (a Force acting at a distance from a point of rotation) in the system. This means the dancer is not influenced by a rotational phenomenon.

In Ballet, the issue is really in the area of rotation.  A skilled dancer is able to prevent his/her tipping sideways, forward or backward when posing on one leg.  This is also the case when executing turns, the dancer wants to execute movement along the vertical axis without any rotation in the horizontal ( aka tipping or leaning).  To achieve this, we have to gain a proper understanding of the Center of Mass.

Center of Mass

The Center of Mass is a point of a system that can represent all its equivalent mass.  This is dependent on the weight distribution and geometry of a body.  In the case of a dancer,  the Center of Mass is located at the center lower abdomen above the pubis.  If a leg is lifted to the side a la seconde the Center of Mass shifts toward the extended leg.  When lifting the leg to the back in Arabesque, the Center of Mass shifts towards the front as the leg pushes the torso forward.

While the positioning of the limbs play a big role in the position of the Center of Mass, there are other finer aspects that play important roles.  For one the stability of the internal organs influence the stability of the Center of Mass particularly during turns.  The alignment and stability of the spine also plays a very important role in balance.  To achieve this,  the dancer has to activate the Abdominal muscles particularly the Transversus Abdominis.  This requires  frequent abdominal exercise to condition the abdominals to be contracted for sustained periods. Arms and head positions also have non-negligible effects to the Center of Mass.

Center of Support

Another important concept critical to Balance is the Center of Support.  This is defined as the point which represents all the forces that hold the body up.  When standing on 2 legs with equal weight distribution, the Center of Support is half way of the distance between the 2 legs.  If the dancer leans to one leg, the center of support will move toward the leg supporting more weight.  When one leg is lifted, the center of support is entirely on the supporting leg.  Furthermore, it is confined to the area of contact with the floor.  The Center of Support decreases as one moves from a flat foot to a demi pointe and eventually to full pointe.


Alignment

To achieve Balance, the Center of Support has to be aligned with the Center of Mass.
In dance, the challenge of Balance is usually not the presence of uncontrolled force.  Instead it is the presence of unwanted Torque.    The point of rotation is the Center of Support.  The point of  action of the Gravitational Force (aka Weight) is the Center of Mass.  To eliminate torque and achieve balance, both Centers have to be completely aligned.  While some are able to Balance without complete alignment, they do so with much energy lost as they have to compensate with the excess Torque.

In the leg alone, there are 4 vulnerability points as far as alignment is concerned: 1.) The toes 2.) The ankle 3.) The knees and 4.) The hip joint.  By coaching the dancer to push out the arches of her feet, we usually achieve the alignment at the 1st 3 of the vulnerability points.  The hip joint is trained by Cambre exercises and other conditioning regimen for the hip flexors.

At the end of the of it all, Balance is something a dancer achieves by trial and error.    Learning these concepts will give a good framework to try things out more efficiently.  It does however still require experimentation to tailor fit these concepts into the unique body one has.

To learn more about Ballet join our classes:

 Breathe, Solenad 1, Nuvali, Sta. Rosa, Laguna - MWF 4:20-5:50 (ages 9 and up)
                                                                              W 3-4, Sat 11-12nn ( ages 4-8)

Life 'N Arts, Blk 33 Lot 2 Ph 1, San Lorenzo South, Sta. Rosa, Laguna - T, Sat 3:30- 4:30pm ( ages 4-8)
                                                                                                                      T 6-7pm/Sat 2-3:30pm ( ages 9 and up)

model : Alexandra Gabrielle Obordo, Acts Manila @ Breathe, Solenad 1 , Nuvali, Sta. Rosa, Laguna

Teaching Creativity and Improvisation to Young Dancers - Structured Mirroring with Successions

For the last three weeks I have been working with my students on Mirroring.  The goal is to introduce them to the practice of improvisation in the hopes of developing their ability to express themselves beyond mere technique of Classical vocabulary.

The first week we did our mirroring, I had my students find a  movement phrase by exploring  a door frame with their extremities.  They then rehearsed these phrases and used these as the basis of their phrase when leading the mirroring exercise.  On the second week, I had them start our in a similar fashion looking for a movement phrase from a door frame.  When we did our mirroring exercise, I introduced the concept of variation. I had the leader repeat a phrase 3 times and instructed the follower to vary segments of the phrase according to height, direction,etc.

This week, I had the dancers create their phrases as they were doing the mirror.  The movement they had was completely unrehearsed.  As they got the hang of it,  the concept of succession was introduced.  The leader was instructed to do a segment of a phrase in sharp sudden movement followed by a pause.  The follower then followed the phrase segment to the best of his/her ability.
 
After  a few tries, I introduced my dancers to structured innovation.  I instructed them to start mirroring from one side of the room moving across to the opposite side.  At a certain point, the dancers were to do mirroring with variations and at another point the mirroring with successions.  Below is a video of their first stab at structured improvisation.

Math Problem Help(Algebra) - Dealing with groupings part 1

Today we deal with groupings.  It is not uncommon for the mathematically challenged to be confused when parenthesis are put on some terms of an equation.  The key to solving your problem is to deal with the operations inside the parenthesis first.  A good acrostic to remember is PMDAS - Parethesis, Multiply, Divide, Add, Subtract telling us what operations to do first.  Below is the first installment of solutions to Exercise 3 of College Algebra by William Hart. 

Skyborn - A short film worth watching

I recently encountered a nice short film entitled "Skyborn" in a MOOC that I was working on.  This film by Jamie Stone, supported by the National Film and Television School of the UK, shows the struggle of a Father and Son as they try to free themselves from the life they have in a post-apocalyptic smog filled world.

Our story begins with the father, Gideon, telling his son, Blue, a story of how the smog came to be.   As cities grew, the smog became thicker forcing people to build their cities even higher.  Some were left on the ground facing the challenges of a smog filled world.  Eventually, those on the surface died except for Gideon and his son Blue.  It is with this premise that Gideon casts the vision of building a flying machine so they could rejoin the other humans in the cities above the clouds.  The task of building and trying out flying machines proves daunting, driving Blue to discouragement.  Blues discouragement turns into outright resentment towards his father, thinking that Gideon loves the vision more than his son. Blue acts on his feelings by creating a tree that has plastic bags "growing" from it, in an effort to disprove his fathers idea that the bags are evidence of a city above.   The boy then has a change in conscience and eventually works towards realizing his fathers dream.

What I like about this film is that it has a clear, concise story line that has an escalating level of tension as the story goes.  When you think there is a good ending in sight a twist happens that makes the film memorable and powerful.  Skyborn has a very effective use of drama in the development of a credible emotional experience for our main character Blue.  His father also plays a consistent yet benevolent opposing character which eventually wins the young Blue by the mentioned traits.

A recurring theme in this film is examining the evidence.  Gideon has a hypothesis that there are cities above the clouds as stated by the stories passed on to him from previous generations.  The presence of plastic bags with elaborate markings are considered by him as evidence to support his belief.  Blue tries to dissuade him from his beliefs by fabricating false evidence.  Gideon is saddened at first but responds by closely examines the evidence to address his doubts. 

Watching this film was truly enriching experience for me.  Please share your insights in the comments section below.


Skyborn from Jamie Stone on Vimeo.

Physics Problem Help - Density Problem Solutions 3

We continue our work on solving Physics problems.  I'm working on my favorite text, "Fundamentals of Physics" by Halliday, Resnick and Walker 8th ed.

The first problem we solve, Chapter 1 #8, is to determing the amount of gold that is lost per second from a wedding ring over a 50 year period.

In the next problem, we are tasked to get the mass and number of atoms of an iron cube.

Problem #10 is all about determining the mass and number of atoms of a section of structural I-beam.

Problem #11 seeks to answer the question of how many molecules of water are in a pail of given mass and how many molecules of water in that pail used to be in a puddle of water in a dinosaur's claw print. 

Enjoy!

Ballet Steps for the Young Dancer - The Five Basic Positions of the Feet

Ballet has a rich tradition spanning more than 400 years.  Over the course of it's history,  it has gone through constant innovation and experimentation that has resulted in tried and true practices for the art of dance.  The techniques codified in Ballet syllabi around the world reflect the most effective means of executing dance steps in the context of the syllabus' development.  While one cannot deny that all Ballet has its roots in Italy by way of France, it cannot also be denied that tried and true principles are retained by the different syllabi regardless of its origin.

Today we deal with the basic foot positions in Classical Ballet.  These are the positions from which we start all other gestures and movements.  There are 5 positions universally accepted by all Ballet syllabi from which turned out feet can move.


First Position

1st Position

!st Position Top View

 

This position is aptly called the first position because it is the very first position with turned out feet that is taught to young dancers.  To achieve this, the dancer is taught to line up her feet together toes pointing forward then have her open these up into the widest letter "V" she can form.  The heels remain together and the knees are straight.  Some teachers, like myself,  refer to this as "smiling feet". I even go to the point of having the children smile and wave at their feet.  Some dancers push themselves to form a straight line from the toes of one foot to the other.  This causes unnecessary strain on the knees in terms on torsion and is hard to balance with. Others lift their little toes putting pressure on the big toes.  All toes must be on the floor to avoid any distortions of the toes due to bad habits.   The wide "V" with all toes on the floor is the safest way of executing this position.

Improper 1st Position - Lifted little toe

Second Position

2nd Position

This position retains the same  orientation of the feet in first position with the exception that the feet as 1 -1.5 shoe sizes apart.  Anything wider or narrower than that spacing may result in injury or a diminished quality of dance step execution. Second position is normally used to transition into big jumps or turns. It is also used by male dancers to support or transition into lifts.

2nd Position Top View

Third Position

3rd Position

Third position is not commonly used in Classical Ballet choreography.  It is often used as a transition step to train the young dancer to overlap one foot in front of the other.  It retains the same feet orientation as First position but this time, the heel of one foot is right in front of the middle of the instep of the other foot.

3rd Position Top View

Fifth Position

5th Position

I move straight to Fifth position as I am following the way I teach the feet positions to my students.  When the young dancer becomes comfortable with putting her feet in a proper third position, it is time to introduce Fifth position.  The general concept is for one foot to entirely cover the other foot, the heel of one foot connected to the toes of the other.  This is to be done while keeping the knees straight and all toes on the floor.  It is permissible to have a gap between the little toe of the front foot  and the heel of the back foot if the dancer is unable to keep the little toe pressed down on the floor.  This is an indication that there is significant torsion on the lower leg which may result to injuries on the foot (bunions)  or the knees (ligament tears, etc.). The photo below shows the dancer is still working on turning out her leg properly.  Fifth position is probably the most utilized among the basic positions in Classical Ballet choreography.

5th Position Top View

Fourth Position

4th Position

The last position is Fourth position.  It is very similar to Fourth position, with the exception that there is a 1 shoe size gap between the front foot and back foot.  A variant of this is an Open Fourth which is more of a Third position with a 1 shoe size separation between the feet. Fourth is best known as the preparation position for Pirouettes.

4th Position Side View

4th Position Top View

In general, the proper execution of these position will result in unnecessary torsion and stress on the foot and knees which are very critical areas in a Dancer's physique.  By putting forth these concepts, I do how the young dancers and their parents get a better picture of how to correct themselves when doing these positions.

( Video will be up as soon as I fix issues with it....Apologies)

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Dancers in photos: Angel Grace Baesa, Ma. Clare Assumpta Sison
Dancers in videos: Francesca Faith Walde, Precious Marian Gabrielle Macali, Serafina Claire Villar

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Teaching Creativity and mprovisation to Young Dancers - Mirroring with Variation

Mirroring is one of the most basic ways of exploring what your body can do in terms of movement. It trains dancers to be sensitive to movement quality, pace and direction.  Internally, mirroring also enables the performer to be sensitive to how the body wants to move.  In  a mirroring activity, two dancers face each other, one is the leader while the other is the follower. The leader initiates motion in a slow, sustained manner while the follower replicates the movement similar to a mirror image.  At some point in time, the roles switch as the leader now becomes the follower and vice versa.  As they gain more experience in mirroring, the concept of variation is introduced.  It is at this time they are taught to vary a gesture with respect to direction, level, etc.

Teaching mirroring to young dancers can be quite challenging.  When I first tried to this exercise, I realized that my students did not feel comfortable moving any which way they feel. I guess the years of disciplined training in classical Ballet under me made them so conscious of their technical "correctness".  So when I told them to move in any which way, they were stuck.  Normally the dancers would just move spontaneously,  but in the case of my students, they would just stand there not know what to do or just keep repeating certain steps we learned in class.  These were the very things, Agnes Locsin, former Artistic Director of Ballet Philippines, would be upset about in the classes she taught,  as she wanted to see dancers create movement.

To help my students do mirroring better, I first had them do one dancer exercises for them to create movement on their own.  For one of my nine year old students, I had her write her name on the floor in big letters. After this I had her write on the wall with the same size of letters.  Finally I had her write her name on an imaginary wall at the center of the room.  As you see in the video below, she is already beginning to dance.

For my older students, I wanted something more dramatic than writing their name. So I had them stand by the door frame and told them to find movement and poses related to the door.  Technically, what I had them do is a form of Structural Movement Analysis which I will tackle in a future post (thus no videos yet).  As soon as they found their movement phrase, I had them recreate it at the center away from the door frame.  When they were comfortable with their movement phrases, I had them to the mirroring exercise. ( I have to admit the their movement in the video is a bit faster than in typical mirror exercises.  )

 Ordinary Mirroring = Leader ( Lavender leotard) and Follower ( Red leotard ) have the same leg extended

 Mirroring with Variation = Leader ( Lavender leotard) extends leg forward while Follower ( Red leotard ) extends backward  

For the mirror exercises,  I had the leaders do 3 repetitions of their movement phrases.  As the 2nd and 3rd repetitions, the followers are allowed to vary any segment of the phrase in terms of directions and other parameters.  After completing the 3rd repetition, the role of leader is passed on to the follower with the passive dancer becoming the next follower and the former leader becoming observer.

The dancers really got the concept of variation.  The next step I have for them is to repeat the exercise using spontaneous movement generated.  I will also be introducing the concept of successions in the next session.

Math Problem Help (Algebra)- Operations Involving Signed Numbers 2

Today we continue our journey into the exciting field of mathematics.  While a lot of us may have had bad experiences with math, we cannot deny that it is exciting in that the very laws of the physical universe are  somehow coded in mathematical language.  So we will, retake baby steps in Algebra in the hope that it will create in us a new found joy in Mathematical thinking.

In Arithmetic, we dealt with addition, subtraction, multiplication and division of positive numbers.In this post, we will tackle the addition of signed numbers. Here are some things to consider when working with signed numbers:

1. ) When two numbers have the same sign then you are supposed to add them and retain the sign they carry.  Ex. -28 -9 = -37

2.) When two number have opposite signs, then you get the difference and adapt the sign of the bigger number. Ex. -13 + 5 = -8

3.) Adding or subtracting by 0 results in the identity of a number. Ex, 0 -25 = -25

4.) The negative of a negative is a positive. Ex. -(-3) = +3

5.) It is helpful to associate terms of like signs together before doing the operation.
Ex. -10+17-8+14=-10-8+17+14= -18 + 31 =   13

6.) When solving for products or quotients of two numbers, like signs result in a positive number. Opposite signs result in a negative number .

Below are my solutions to Exercise 2 of College Algebra by William Hart.