Jesuit Education and Science in the Spanish Imperial Context, 1859-1898: a talk by Dr. Aitor Anduaga of University of the Basque Country

The Institute of Philippine Culture (IPC)
School of Social Sciences
cordially invites you to a lecture on

Jesuit Education and Science in the Spanish Imperial Context, 1859-1898

by

Dr. Aitor Anduaga
University of the Basque Country Leioa, Spain
Visiting Research Associate, IPC

on

February 13, 2012 (Monday)
4:30 to 6:00pm
IPC Conference Room
Rm 203, Frank Lynch Hall
Social Development Complex

*Please call local 4651 or e-mail ipc@admu.edu.ph for inquiries.

Abstract

Although the Royal Decree of 1852 by the Spanish Queen Isabel II  assigned to the Jesuits a strictly missionary function (i.e., to  evangelize the pagan tribes of Mindanao and Jolo), activities soon  extended to education and science. The history of this development is  well known. In 1859, Jesuits took charge of the ?Escuela Municipal.  In 1865, they extended primary education to the secondary one, and  turned the Escuela into a private school, the Ateneo Municipal de  Manila?. That year, they found the Meteorological Observatory as an  auxiliary centre for teaching. Twenty years later, it became the most   important geophysical Observatory in the Far East.

Many historians have placed those achievements within the framework of apostolic spirituality. The ideological structure of the Society of  Jesus would house a spirituality at its core whose values of  diligence, learning, etc. would explain the legitimacy of this study  of empirical sciences. Reality, however, is much more complex. In this  lecture, we shall examine the institutional (not the ideological)  structure of the Society in the educational field, and the influence  that it exerted on the promotion of science. We shall also see that
there was strong interaction between religious and socioeconomic  factors that help to understand those achievements. Last but not  least, the Jesuit experiences in the Spanish dominions of Cuba and  Puerto Rico will help us to better understand the Philippine reality.

Imperfections in image formation: astigmatism, coma, and distortion

by Quirino Sugon Jr.

There are several imperfections or aberrations if you use lenses to form images:

1.  Astigmatism

An optical system with astigmatism is one where rays that propagate in two perpendicular planes have different foci. If an optical system with astigmatism is used to form an image of a cross, the vertical and horizontal lines will be in sharp focus at two different distances. The term comes from the Greek α- (a-) meaning “without” and στίγμα (stigma), “a mark, spot, puncture”. (Read more in Wikipedia)

2.  Coma

Coma is an inherent property of telescopes using parabolic mirrors. Light from a point source (such as a star) in the center of the field is perfectly focused at the focal point of the mirror (unlike a spherical mirror, where light from the outer part of the mirror focuses closer to the mirror than light from the center–spherical aberration). However, when the light source is off-center (off-axis), the different parts of the mirror do not reflect the light to the same point. This results in a point of light that is not in the center of the field looking wedge-shaped. The further off-axis, the worse this effect is. This causes stars to appear to have a cometary coma, hence the name. (Read more in Wikipedia)

3.  Distortion

Distortion can be thought of as stretching the image non-uniformly, or, equivalently, as a variation in magnification across the field. While “distortion” can include arbitrary deformation of an image, the most pronounced modes of distortion produced by conventional imaging optics is “barrel distortion”, in which the center of the image is magnified more than the perimeter (figure 7a). The reverse, in which the perimeter is magnified more than the center, is known as “pincushion distortion” (figure 7b). (Read more in Wikipedia)

Vector addition and subtraction: component and parallelogram methods

by Quirino Sugon Jr.

The sum and difference of vectors a = (3,4) and b = (6,0)

Suppose we choose two points on the Cartesian coordinate system: and .  If we interpret these points as tips of the rays–which we shall now call as vectors–drawn from the origin at $(0,0)$, then we write down our vectors as

The sum and difference of these two vectors is given by

The parenthesis-and-comma notation for vectors is not amenable to algebraic manipulation. To solve this problem, we introduce two unit vectors (vectors of unit length) and . The unit vector points in the direction of positive axis, while points in the direction of positive axis. Using these two unit vectors, let us rewrite Eqs. (1a) and (1b) as

Hence,

It feels natural, doesn’t it?  You add only like terms: those with are added to those with ; those with are added to those with .  If you have a bag containing 3 apples and 4 oranges and another bag containing 6 apples, then putting all these in a single bag results to 9 apples and 4 oranges.  This is an interpretation of .  What do you think is the corresponding interpretation for ?

The sum and difference of vectors a and b using parallelogram method

The apples-and-oranges interpretation, though helpful, is not really precise.  The proper interpretation is geometrical.  In order to interpret and geometrically, we need to draw them together with and (see Fig. 1).  Notice that if we construct a parallelogram with as two of the parallel sides and as the other two parallel sides, then corresponds to one diagonal and corresponds to the other diagonal.

Let us write down some rules.  To draw , connect the tail of to the tip of , then draw  as the vector  from the tail of vector to the tip of .  On the other hand, to draw , connect the tails of vectors and , then draw as the vector from the tip of to the tip of .

In general, we can let the coefficients of and to be any scalar, and we can even include a new unit vector along the positive axis.  If we do this, then

so that

Equations (6a) and (6b) are the algebraic rules for vector addition and subtraction in three dimensions.  The geometrical interpretation is still the same as that for two dimensions.

Scientific method as drama: setting, characters, conflict, climax, and denouement.

by Quirino Sugon Jr.

Scientific method is a method for knowing the relationship between different physically measurable concepts.  There is no one way to do science, but its essential parts can be gleaned from the example of falling bodies.  You will notice that it has all the ingredients of a drama: setting, characters, conflict, climax, and denouement.

A.  Setting and Characters: Observation

For example, if you throw a stone upwards and video the result, you can measure both the height of the rock  and also the time it took for the rock to reach a particular height.  From this two data, you can plot the position vs time function and obtain a parabola.  Then you can find the instantaneous rate of change of position with respect to time to obtain velocity.  You can do likewise for velocity and obtain acceleration.  And you obtain a constant acceleration equal to .

The main characters of the story are time and position.  The supporting casts are velocity and acceleration.  The setting is free fall motion.

B.  Conflict:  The Search for Universals

Then you ask: is this value of acceleration constant for all objects on the surface of the earth?  Is the constant gravitational acceleration a universal law that governs the relationship between position and time?

And you find out that it is not true: a feather falls slower than a stone.  So you ask yourself why.

If you are Aristotle, you shall propose the following universal law in two statements:

1. All matter can be broken down into four components: earth, water, air, and fire.
2. The heavier elements goes toward the center of the earth; the lighter elements goes away from the center of the earth.
3. The speed of the body is proportional to its weight.

People tend to scoff at Aristotelian physics, but there are some truths in it.  Replace earth, water, and air by our concepts of solid, liquid, and gas.  Replace fire by temperature.   Plotting the pressure vs temperature of a substance leads to the classification of different phases of solid, liquid, and gas.

Aristotle’s third statement is also true, provided we assume that the speed is what we call as the terminal speed.  Raindrops fall faster and faster then slower and slower until they travels at a constant speed, due to friction with the air.  This constant speed is the terminal speed.

But what happens if the speed is not the terminal speed?  Then Galileo showed that Aristotelian physics collapses.  Galileo dropped a small and large cannonball from the top of the Tower of Pisa and showed that they arrived at the ground at the same time.  We need a new physics.

C.  Climax: The Scientific Laws

The endless struggle by scientists to find universals in the physical world resulted to the many laws of Physics.  But we must always remember that these laws have a certain range of validity.  Newton’s law of Universal Gravitation may be valid for the falling apple, for the moon around the earth, for the earth around the sun, and for other planets around the sun.  But when we go to the level of galaxies, things go awry.  Newton’s theory predicts that stars near the center of a galaxy travel faster than those far from the center.  But it turns out that in many galaxies, the stars near the center and away from the center have the same orbital speeds.

To resolve this problem, scientists propose a new kind of matter–not anymore earth, water, air, and fire–but something else, something dark and mysterious because we can’t observe it.  So they simply call this thing as “dark matter”, which permeates the voids between the stars.  Other scientists don’t like this idea.  They propose instead that the equation for Newton’s law of Gravitation should be modified.

D.  Denouement: Application of Universal Laws

Once the scientific law has been found, scientists apply them to different problems, instead of a smooth cannonball, we can have the whole London bridge falling down or an airplane flying up.  To do this, we cannot anymore rely on one universal.  We have to use others.

We first make a survey of what has been done before, define the concepts needed, determine the known values or imposed parameters,  write down the universal equations that relate these concepts and their values at certain conditions, describe the method for measuring the known and knowable parameters, present your results, write your conclusions, and list your references.  These are the parts of a scientific paper, which is published so that other scientists can duplicate what you did, learn from your mistakes, and use your results in proposing a new universal law.

Science and Logos: In the beginning was the Word

by Quirino Sugon Jr.

A.  Science and words

Science is rooted in the Latin word scientia meaning “knowledge”.  Many sciences ends in “logy” which is rooted in the Greek word logos meaning “word”.  The act of naming something is to give a word for it, and in doing so we know it.  But in order to do this, one has to distinguish that something from another.  In the Book of Genesis (Gen 1), for example, we read the account of Creation.  Notice how things are created out of formlessness by separation, by distinguishing one from the other.  Here is the process of separation by day of Creation:

1. Light from darkness, day from night
2. Sea from sky
3. Sea from land; fruit-bearing trees from non-fruit bearing trees
4. Sun for day; moon and stars for night
5. Swimming creatures from flying creatures
6. Land animals: creeping things, cattle, and wild animals. Male and female
7. Sabbath: rest from work

Once the objects are distinguished and named, the next step in science is to find their relationships to one another.  One way is to arrange them into groups and subgroups according to structural similarity.  This is the method used by Carolus Linnaeus in his taxonomy system.  He grouped all living things into a hierarchy: kingdom, phylum,  class, order, family, genus, specie.  So if the genus and specie the living thing is known, then its family, order, class, phylum, and kingdom is known.  For example, we are animals (kingdom Animalia) with backbones (phylum Chordata).  Our females have breasts that produce milk (class Mamalia).  We belong to the first among animals (order Primata) and we look like humans (Family Hominidae).  We are indeed humans (genus Homo), but we distinguish ourselves from other humans because we think–or so we thought (specie Sapiens).

Thus, a single word is not enough.  We have to clarify and clarify by adding additional words.  Treebeard in Lord of the Rings says it best:

For one thing, it would take a long while: my name is growing all the time, and I’ve lived a very long, long time; so my name is like a story.  Real names tell you the story of the things they belong to in my language, in the Old Entish as you might say.  It is a lovely language, but it takes a verly long time to say anything in it, because we dop not say anything in it, unless it is worth taking a long time to say, and to listen to. (Two Towers, p. 66)

B. Relationships between words

Another way to arrange living things is to construct a food chain by drawing an arrow from the eater and the food.  As stated by Charles Elton (1927):

The herbivores are usually preyed upon by carnivores, which get the energy of the sunlight at third-hand, and these again may be preyed upon by other carnivores, and so on, until we reach an animal which has no enemies, and which forms, as it were, a terminus on this food cycle. There are, in fact, chains of animals linked together by food, and all dependent in the long run upon plants. We refer to these as ‘food-chains’, and to all the food chains in a community as the ‘food-cycle. (Wikipedia)

The relationship between different animals in a food chain is an abstraction.  The animals are visible; their relationships are not.  It is like looking at your wrist watch.  You only see the hour, minute, and second hands.  But you guess there is something inside the watch that you cannot see which relates these three hands of a clock.

In the Bible, matter (visible) is distinguished from spirit (invisible).  Matter, according to our grade school definition, is anything that occupies space and has mass.  Spirit, on the other hand, is the binding force of matter that once removed, the living thing dies and disintegrates.  Man was made from dust.  And once his spirit is removed from man, man goes back to dust.

In Physics, matter (visible) is distinguished from fields (invisible–except for visible light in the rainbow).   Particles are the protons, electrons, neutrons, etc.  These are the building blocks of matter. Fields are the forces that bind particles: gravitational force, electromagnetic force, strong nuclear force, and weak nuclear force.  Gravitational force is responsible for the fall of Newton’s apple and the never-ending fall of the moon towards the earth in circular motion.  Electromagnetic force is displayed by lightning strikes, global positioning systems, auroras, and cellular phones.  Strong force binds the nucleus together, preventing protons from flying out.  And weak force is responsible for the decay of subatomic particles.

Naming fields into gravitational, electromagnetic, strong, and weak, makes them objects that may be represented mathematical quantities governed by equations. For example, gravitational force is represented by the symbol F and is governed by Newton’s law of gravitation. The electric and magnetic fields are represented by the symbols E and H and their interaction are governed by the four Maxwell’s equations. There are also similar symbols and equations for the strong and weak nuclear forces.

C.  In the beginning was the Word

The Holy Grail of Physics is to find the single relationship between the four forces in the universe, this one relation that shall rule them all.  This relation is called GUT (Grand Unified Theory) that shall explain everything there is to know about the universe and everything that shall ever be.  This requires more and more powerful mathematical concepts.  For example, Maxwell’s equations are originally expressed in terms of 8 scalar equations.  Then the mathematical concept of a vector as an ordered triple of numbers interpreted as a ray was invented.  Using vectors, the Maxwell’s equations was reduced to 4.  With the invention of geometric algebra which combines imaginary numbers and vectors, the 4 Maxwell’s equations can be reduced into one: the Maxwell equation, which states that “the space-time derivative of the electromagnetic field is proportional to the charge-current density”.

Physicists may succeed in finding the GUT equation, but there are still so many things that cannot be unified in the GUT: metaphysics.  What is goodness?  What is truth?  What is beauty?  Physicists see beauty in a single equation that describes so many things yet one and unchanging.  Physicists see also truth in this equation because it describes the physical world.  Physicists may also good in this equation, for the universe may not exist without this equation.  Yet these are but glimpses of things that transcends the physical order.  What is a good man?  How do you know that I am not lying?  Why is a rose beautiful?  The answers to these questions cannot be expressed as an equation with the predictive power of Newton’s laws or Maxwell’s equations.  Between physics and metaphysics lies an insurmountable barrier, a chasm as deep as the abyss.  Who shall bridge this abyss?

The Christians proposes the following answer: Christ.  Jesus Christ who is the Way, the Truth, and the Life (c.f. Jn 14:6) is also the Word of God who created all things, visible and invisible:

In the beginning was the Word, and the Word was with God, and the Word was God.2 He was in the beginning with God. 33 All things came to be through him, and without him nothing came to be. What came to be 4 through him was life, and this life was the light of the human race; 54 the light shines in the darkness, and the darkness has not overcome it. (Jn 1:1-5)

Christ is the Alpha and the Omega, the beginning and the end (c.f. Rev 22:13). Science began in the Creation of the universe. Science shall end in the destruction of the universe.  Science began when the Logos ordered all things. Science shall end when the Logos puts everything under His feet (c.f. Heb 2:8). As Christ said: And when I am lifted up from the earth, I will draw everyone to myself. (Jn 12:32).  And that includes scientists.