Roger's Equations

Introduction

"When hearing something unusual, do not preemptively reject it, for that would be folly. Indeed, horrible things may be true, and familiar and praised things may prove to be lies. Truth is truth unto itself, not because [many] people say it is." Ibn Al-Nafis, Sharh' Ma'na Al Qanun.

Do you remember when you were in grade school, first learning about science and the scientific method and were told about the Islamic Golden Age? How about the day when you were introduced to algebra and learned its name was Arabic for "restoration"? Do you remember how your teacher told you about the great Islamic scholars of Baghdad and Cairo who translated Sanskrit, Persian, Greek, and Latin into Arabic, and stored the works in libraries larger than even the Great Library of Alexandria of classical times? Do you remember learning how the city of Baghdad had been the largest city in the world for centuries, with over a million people at a time when London had at best 20,000?

For me, unfortunately, none of the above things ever happened. The thousand years between the fall of Rome and the Renaissance was at best rushed through, and mostly with Western highlights. I learned about the Goths, then the Muslim Conquest, then the Franks and Charlemagne, then the Vikings (counting Normans here, too), then the Crusades (the ones the West won in detail, the others - there were nine - in less detail), then the Mongol Conquest, then Marco Polo, then the Black Death, which is presented in an "it's always darkest before the dawn" sort of for way, and then finally the Renaissance, at which point we slowed down again and started learning names and dates in earnest.

For many of us, there is a giant hole in history we like to call the "Dark Ages". The Dark Ages were anything but dark in the Islamic world. I can't hope to cover the history of the Caliphates in this blog. It would pull the discussion way off topic from my desired goal of examining the development of Epistemology, specifically the Scientific Method. If, however, you someday find yourself bored and are looking for something to do, I recommend reading about the Golden Age of Islam. To help understand how the Islamic advancements to the scientific method were possible, I will provide a brief historical overview to bring us up to speed, but my 300 words below barely scratch the surface.

The Golden Age of Islam

The Islamic Golden Age is generally considered to have begun in 750 AD after the Battle of the Zab and the establishment of the first Abbasid Caliphate and to have ended with the burning of Baghdad by the Mongols in 1258 AD. With the ascension of the Abbassid Caliphate (so named because they were descendents of the prophet Muhammad's youngest uncle, Abbas ibn Abd al-Muttalib), the capital of the Islamic world was moved from Damascus to the newly-built Baghdad in 762 AD. Baghdad quickly became a significant cultural, commercial and intellectual center for Islam. A unique characteristic of the Abbasid Caliphate, often considered a trait derived from Persian influence, was a rapacious desire to collect knowledge. Works in Greek, Latin, Persian, and Sanskrit were translated meticulously into Arabic, cataloged, and then housed in libraries. The newly-learned technology of paper was used instead of fragile papyrus or expensive parchment. Many libraries were built in Baghdad, including a great library called the House of Wisdom.

The House of Wisdom, through the sponsorship of the Abbaisid Caliphs, grew to become the premiere learning center in the world. In the beginning it concentrated on acquiring and translating (into Arabic) any and all works that could be found. Soon, however, the works started to be those of Arab scholars who built upon and extended the knowledge of the classical works. For over 400 years the House of Wisdom in Baghdad and later the House of Knowledge in Cairo (founded in 1004 AD) were centers of learning. Scholars from every country would travel to these cities to study and learn, much as they had to Alexandria and its great library a thousand years earlier. Scholars associated with the House of Wisdom were Sahl ibn Haroun, Muhammad ibn Musa al-Khwarizmi (Mathematician), Mohammad Jafar ibn Musa and al-Hasan ibn Musa (Engineers), Sind ibn Ali (Astronomer, Mathematician), Yaqub ibn Ishaq al-Kindi (Physician, Mathematician), Hunayn ibn Ishaq (Translator), and Sabian Thabit ibn Qurra (Mathematician).


Alhazen

How do we see? This was a subject upon which ancient greats had disagreed. Ptolemy and Euclid believed that the eyes emitted light to see. Aristotle believed objects emitted particles into the eyes. To resolve this issue, Alhazen (Abu Ali al-Hasan ibn al-Hasan ibn al-Haythan) systematically employed experiments and mathematics to confirm or reject these hypotheses.

In Part III of this series, it was shown that Aristotle combined induction and deduction to derive truths. Induction was used primarily as a method of determining first principles which could be used as premises. Then new truths were acquired bv deductive reasoning from these premises. As was stated in that blog entry, this was a monumental step forward for the acquisition of knowledge.

Alhazen realized that induction could be used for more than just determining first principles to be used as premises; induction could also be used to support or disprove premises. In other words, induction could provide truths like deduction. The one caveat is that the truths obtained through inductive methods, though highly probable, could never be definite. Deductive truths, on the other hand, can be definite. One, however, could minimize the uncertainty of inductive truths by controlled scientific observation (as opposed to just scientific observation - collecting empirical evidence). Controlled scientific observation seeks to reduce variables and focus on particular aspects of a problem. The idea being that any single, controlled observation itself was useful only as a part of a corpus of many controlled observations. Today we call controlled scientific observation "experiment".

Alhazen constructed many experiments. Some were used to contradict the theory that light was emitted by the eyes, some were used to contradict the particle theory of light, and some were used to observe the properties of light. Eventually, and after many years of experiments, Alhazen concluded that light reflected off objects to the eyes, a brand new theory born from his careful systematic inductive method.

Scholars of Alhazen's day and later refined the experimental approach to obtaining truth. Al-Biruni developed methods to prevent systematic errors and observational biases and advocated repeating experiments to qualitatively arrive at a "common sense value of measurement" (if you measure 5 times and you get 5.9, 5.8, 6.2, 6.2, 5.9, then a commonsense value would be around 6.0). Avicenna emphasized that hypothesis should come before experiments, not after. This would prevent observational bias.

Al-Jabr

"That fondness for science, ... that affability and condescension which God shows to the learned, that promptitude with which he protects and supports them in the elucidation of obscurities and in the removal of difficulties, has encouraged me to compose a short work on calculating by al-jabr and al-muqabala , confining it to what is easiest and most useful in arithmetic." - Al-Khwarizmi, Al-Kitab Al-Mukhtasar Fi Hisab Al-Jabr Wa'l-Muqabala

Muhammad ibn Musa al-Khwarizmi died about 100 years before Alhazen was born. He was a Persian scholar in the early days of the House of Wisdom in Baghdad. The term "Algebra" comes from his 820 AD book "al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala", in which he provides known rules (at the time) for solving quadratic equations. This is considered to be the foundation of modern algebra.

Why is this significant? Well, we all know mathematics is important to modern science. To the ancient Greeks, mathematics was for the most part geometry and number theory. If you showed Greek mathematicians a formula, they would ask what in geometry it corresponded to. Algebra separates the formulas from the geometry. In algebra, the formulas are the "thing". They are analyzed, characterized, and systematically solved. That is not to say that they aren't connected to geometry, but in algebra the formulas aren't studied for a geometric end; they are studied in their own right.

As I described earlier, the Islamic scholars were translating everything they could get their hands on into Arabic. This meant Sankrit (India) works as well as Greek and Latin. The result was the combination of many different cultures' mathematics into a single, more useful mathematics. The efficient was kept (Hindu numerals and decimals from Sanskrit and Persian) and the cumbersome was discarded (roman numerals, greek numerals). The math born in the Islamic golden age was much more expressive and flexible that earlier math. It was at this time that it began to be thought of in the modern sense. With better mathematics, better theories could be derived.

Alhazen also used geometry to explain the optical phenomenon he saw through his controlled observations (experiments). It wasn't the first time science and math had been tied together, but because of the significant advances made by Islamic scholars in mathematics, Alhazen and other Islamic scientists had many more mathematical tools with which to describe the world.

Conclusions

Significant advances in mathematics, especially the untethering of mathematical formulas from geometry, the adoption of Arabic-Hindu numerals, and the incorporation of decimals, altered the nature of mathematical inquiry and provided scientists with more mathematical tools with which to understand nature. The consolidation of knowledge from four massive cultures (Hindu, Greek, Persian, and Roman) into libraries in Baghdad and Cairo created an easily accessible and deep knowledge base that could be built upon and extended. As a result, scholars began to expand the knowledge obtained during the classical period. As knowledge was expanded, the methods by which knowledge was obtained were reexamined and improved.

The scholars of the Islamic Golden Age introduced systematic experimentation as a method to find truth. Hypotheses were determined before experiments to prevent observational bias. Repetition of experiment was used with common sense selection of the best observed measured value in order to minimize instrumentation error. This systematic inductive procedure of experimentation, applicable to more problems than purely deductive reasoning, greatly expanded the breadth of scientific inquiry and discovery and laid the foundation of the modern scientific method.

In Part V we will see how a friar and some others brought the scientific method back to the West and built upon it.

Useful Links:

http://fourriverscharter.org/projects/Inventions/pages/muslimworld_algebra.htm
http://en.wikipedia.org/wiki/Islam_and_science
http://www.ms.uky.edu/~carl/ma330/project2/al-khwa21.html

Introduction: A brief biography

"πάντες ἄνθρωποι τοῦ εἰδέναι ὀρέγονται φύσει." - Ἀριστοτέλης
("All men by nature desire to know" - Aristotle*)

Aristotle was born in 384 BC in Stageira, Chalcidice, which was considered part of Macedonia at the time, but today would be considered part of Greece. Aristotle's father was the court physician to King Amyntas of Macedon, which allowed Aristotle to be educated like an aristocrat. At age 18, Aristotle was sent to Plato's Academy to continue his education. He stayed there for 20 years, leaving only when Plato died and control of the Academy passed to Plato's nephew, Speusippus.

It is important to understand that Plato's Academy was not a school or university in the modern sense. It was more of an intellectual club, with junior and senior members, that tackled a wide range of philosophical problems using the dialectic method. The senior members would choose the topics that were to be discussed and then all members, junior and senior, participated in trying to obtain the truths in that topic. The idea was that, in the pursuit of truth, the person gains education. This is like how we might say today that someone who joins the armed forces gains discipline, although one wouldn't suggest the goal of the armed forces is discipline.

Upon leaving the academy, Aristotle traveled with another Academy member, Xenocrates, to Asia Minor, where they stayed as guests of their friend Hermias of Atarneus in his court (when one attended Plato's Academy, one tended to have powerful friends). A few years later, King Philip II of Macedon invited Aristotle to become the tutor to his son, Alexander the Great, who was approximately 12 at the time. For the next 7 to 8 years, Aristotle was head of the royal academy of Macedon, teacher to the future kings Alexander the Great, Ptolemy the Savior, and Cassander, as well as many other Macedonian aristocrats.

After the death of Phillip II and the ascension of Alexander the Great to the Macedonian throne, Aristotle returned to Athens, where he established his own school (to compete with the Academy) known as the Lyceum. Aristotle lectured at the Lyceum for the next 12 years. It is during this time that many of his works were supposedly written. The subject of this blog entry is Epistemology, however, so I will not digress into the multitude of subjects to which Aristotle contributed. If you're interested, I suggest starting at the Wikipedia page for Aristotle and going from there.

With the death of Alexander the Great, the crowds in Athens started to express anti-Macedonian sentiments. Aristotle, being a Macedonian, wisely made a hasty retreat to his family lands in Chalcis, where he died shortly thereafter of natural causes (in 322 BC).

*I was able to get this in the original Attic Greek from the Perseus Collection


Aristotle the Epistemologist

It is hard to describe the importance of Arisotle to someone who is unfamiliar with the history of Epistemology. Aristotle was/is to Science what farming was to the establishment of civilization, what antibiotics were to the establishment of modern medicine, what steam power was to the Industrial Revolution, what the telescope was to astronomy, etc. Arguably, Aristotle founded Science as we know it (although the Scientific method we use today wasn't fully formed until over a thousand years after his death). He systematically studied the act of "reasoning to obtain truth" and developed a discipline called Logic that standardized it. His students conquered most of the known world and established the Library of Alexandria, an institution that became synonymous with knowledge long after its final destruction. Aristotle's death began a golden age of scientific discovery that lasted centuries and only went into hibernation when the Roman Empire started to fall apart.

Why? What did Aristotle do that led to this explosion in knowledge?

Basically, Aristotle combined empiricism and reasoning in such a way that they complemented each other. Logic could be used to eliminate misconceptions caused by those deceptive senses that Socrates distrusted; Empiricism could give Logic a starting point and direction, making it much more efficient and reliable. Aristotle accomplished this by carefully examining the entire process of obtaining knowledge. Where some might take the sentence "Is this statement true or false?" as self-evident and try to answer it, Aristotle dissected the sentence systematically, asking "What is a statement?", "What is true?", and "What is false?" Aristotle took nothing for granted and carefully built a framework from which truth could be obtained.

Before we dive into that framework, let us first examine his feelings about The Plato/Socratic Forms model that he learned at Plato's Academy.

Aristotle and the Theory of Forms

Aristotle was practical to a fault and so had trouble with Plato's theory of Forms. This is most apparent in Metaphysics Part 14, where he says (italicized):

"…For if the Forms exist and 'animal' is present in 'man' and 'horse'…

(1) if the 'animal' in 'the horse' and in 'man' is one and the same, as you are with yourself, (a) how will the one in things that exist apart be one, and how will this 'animal' escape being divided even from itself? (cwarner7_11 in his comment from Part II regarding the Möbius strip provides an analogy to illustrate how single objects might appear to exist apart, which contradicts Aristotle's argument)

(b) if it is to share in 'two-footed' and 'many-footed', an impossible conclusion follows; for contrary attributes will belong at the same time to it although it is one and a 'this'. If it is not to share in them, what is the relation implied when one says the animal is two-footed or possessed of feet? But perhaps the two things are 'put together' and are 'in contact', or are 'mixed'. Yet all these expressions are absurd. (As an analogy of how such a thing is possible, I point to the Flatland example from the comments in part II where a cylinder tangent to a two dimensional plane can be both a circle or a sphere on that plane, depending upon orientation.)

But (2) suppose the Form to be different in each specie. Then there will be practically an infinite number of things whose substance is animal'…that other would be an element in 'man', i.e. would be the genus of man…. (Aristotle, based on the "fact" that something can't be in two different places (1a) at the same time and appear differently in different things yet be the same thing (1b), therefore suggests that Plato's theory of Forms leads to a contradiction, stated definitively in the final paragraph of Part 14 given below).

"Further, (3) in the case of sensible things both these consequences and others still more absurd follow. If, then, these consequences are impossible, clearly there are not Forms of sensible things in the sense in which some maintain their existence.

It hardly matters that Aristotle's proof above against Plato's theory of Forms was full of holes. In general, the more you read Aristotle, the more you realize he was terrible at proving the necessity of his approach of acquiring knowledge or disproving Plato's. It must have been terribly frustrating, because he must have been painfully aware that his method of obtaining knowledge was far superior to Plato's and Socrates "remembering", but he simply couldn't prove it through pure abstraction. If you think I'm being unfair to Aristotle, remember that he wasn't chosen to succeed Plato; after Plato's death, he was never associated with the Academy again.

In the end, it is best Aristotle left the academy at 38 (for whatever historical reason you choose to believe, I choose to believe it was because of the change in management), because Aristotle didn't belong at the Academy anymore. He was a counter-revolution born out of the Socrates/Plato revolution against the Sophists. He took the ideas that worked for him from the Academy and discarded those that didn't to form a new way of understanding the world.

The Epistemology of Aristotle

Aristotle's ideas are often portrayed as in opposition to Plato's Theory of Forms. This would make a lot more sense if he hadn't attended Plato's Academy in Athens for 20 years and left only when Plato died. In fact, if one truly understands the Theory of Forms presented by Plato, and the concept of universal truth that it creates, one realizes that Aristotle meant not to change the theory of forms, but rather to reconcile it with what he instinctually believed to be correct, his Theory of Universals.

Whereas Plato and Socrates believed that knowledge of the forms could only be learned through "remembering" (rationalizing), Aristotle insisted that if one looked around carefully, and used logic to prevent the senses from misleading you, that observation by the senses could greatly assist one better being able to know the Forms. In other words, Aristotle was advocating empiricism combined with rational thought rather than just rational thought for obtaining the Forms. Also, Aristotle did not believe in a hierarchal structure to truth, where a single principle led to all other principles (called Supra-philosophy in Part I). Instead, he believed that there were many truths that were parallel to each other (for example: Fire is warm, Water is wet are two truths not born from a single superseding truth). That is not to say some truths weren't directly derived from larger truths; it just meant there wasn't a universal truth that lead to every truth. This is an important concept because much of the Pre-Socratics and even Plato and Socrates Epistemology clung to this idea of a fundamental truth from which all other truths are derived. Aristotle was advocating the search for lots of little truths rather than an epic quest for a universal truth which he felt didn't exist.

From these ideas Aristotle set about developing a method of obtaining knowledge so thorough that it basically represents the invention of Science. Before Aristotle, humanity was fumbling around in the dark and occasionally getting lucky and learning things about nature. After Aristotle humanity was systematically investigating the universe to unveil its truths. When it comes to Epistemology, Aristotle was the single most important philosopher (and by a lot) because he taught the world how to accurately reason with the introduction of the field of Logic.

Logic

The term logic comes from the Greek term logos, meaning reason. Webster's dictionary definition of Logic is "a science that deals with the principles and criteria of validity of inference and demonstration: the science of the formal principles of reasoning". Aristotle formalized reasoning in a way that had never been done previously. Aristotle's formalized reasoning is laid out in six works called collectively the Organon.

It is no accident these 6 books of Aristotle were later grouped and called the Organon (which literally means "a tool", as in "a tool for acquiring knowledge") because that is precisely what they are. The Organon is a critical moment in man's search for knowledge because it is the first time a system was developed and standardized. The works are Categories, On Interpretation, Prior Analytics, Posterior Analytics, Topics, and Sophistical Refutations.

Categories

In Categories, Aristotle lays out a ten-fold classification scheme consisting of substance, quantity, quality, relation, place, time, situation, condition, action, and passion. These ten things represent everything that can be the subject or the predicate of a proposition. In other words, this book is basically a "how to" guide to formulating "the question". This is essential, since if "the question" is not clearly stated, what hope can there be of a sensible answer? Aristotle is explaining that asking the right question is the first step to obtaining knowledge, and the only way to be able to consistently "ask the right questions" is to be aware of how questions are structured and their potential pitfalls and nuances.

On Interpretation

What is a word? Nouns and Verbs alone cannot be true or false. Only sensible word combinations have meaning and thus can be right, wrong, etc. Simple prepositions lead to single facts; complex prepositions are many simple propositions compounded. Nouns carry with them no sense of time, but verbs do. What is possible of affirmation, or what is possible to deny?

In "On Interpretation", Aristotle further breaks down the Subject and Predicate of Categories in more detail to discover the precise structure of statements.

Prior Analytics

Why was Aristotle so obsessed with language in the first two books above? Because Aristotle believed that language was both the means by which we express our premise(s) and the means by which we systematically express the logical steps used to obtain our conclusion(s). In "Prior Analytics", Aristotle lays out the structure for obtaining truth. Start with a premise that is either a) known to be true, or b) has been proven to be true. Then rational steps are followed to obtain a new truth (deductive reasoning).

Aristotle suggests that one should start from what is known to be true as first principles in order to obtain truths. But since limiting premises to what can be "known to be true?" greatly limits what can be investigated (I will cover this in a future entry involving Descartes), how does one obtain first principles? Plato would have said they had to be remembered (in the Forms sense). Aristotle said that known truths or "First Principles" are patterns that we discern over time through our senses and have come to expect (Induction), colloquially referred to as intuition. This is captured today in the maxim, "There is nothing in the understanding which was not prior in the senses".

Posterior Analytics

In Posterior Analytics, Aristotle presents an overall view of his method of obtaining truth. He describes the "demonstration", which is logical reasoning (syllogism) and the "definitions", the prepositions from which the logical reasoning starts (premise(s)) and the conclusion(s) reached. Aristotle speaks also of "form" (logical reasoning) and "matter" (premises and conclusions), describing ways the form can be incorrect (circular reasoning, infinite intermediate steps, etc.). He also talks about how even with perfect form, incorrect conclusions can be reached if the matter is flawed, either because the premise was stated unclearly or the conclusion was poorly stated.

Aristotle also explains the difference between knowledge obtained by purely deductive reasoning (Apodeictical ) and knowledge that is obtained as some combination of inductive and deductive reasoning (dialectical (fourth paragraph in linked pdf)). He points out that the derived truth is always less certain that the premises it is built from. He discusses the relative strengths of deductive arguments; for example, that the demonstration of a universal proposition is preferable to a particular preposition. Here's an example:

4+3= Odd (Particular)
Even+Odd= Odd (Universal)

Also examined are the types of truth obtainable, such as the truth of properties associated with objects, as well as some other ideas that have collectively come to be known as quiddity (from the Latin Quidditas, meaning "What it is"). Essentially, quiddity is the definition of something. For example, one can say "the number 2", but the quiddity of 2 could be "First Even Number" or "Second Prime Number". This is literally what it is, not what it is called. Basically, Aristotle describes what truths looks like. It's what we have come to call "science".

Topics

In Topics, Aristotle discusses the art of the dialectic, where prepositions are developed from empirical knowledge (common knowledge, commonly held beliefs). He presents a systematic (Aristotle = systematic) approach to evaluating this empirical knowledge (what's right and what's wrong or superstition). This systematic approach includes "the senses of a term" (what people mean when that say the term), understanding correlations and non-correlations (called by Aristotle "accidents"), understanding the essential and nonessential properties of a subject, etc.

This is basically a handbook for separating "good" common truths (good common knowledge) from "bad" common truths (bad common knowledge).

Sophistical Refutations

In this book, Aristotle discusses how seemingly sensible sounding arguments can be completely incorrect. He describes verbal fallacies such as Equivocation.

For example, the following is not a logical argument:

A feather is light
What is light cannot be dark
Therefore, a feather cannot be dark

In the above deductive argument, the verbal fallacy of equivocation is demonstrated. Two different meanings of the word "light" are equivocated to produce an erroneous conclusion. This may seem simplistic, but it can get complicated and difficult to catch quickly, for instance:

All heavy things have great mass
This is a heavy fog
A heavy fog has great mass

Some might accept the idea that "a heavy fog has great mass" as the conclusion states; however the proof is invalid because of the intermediate statement, "This is a heavy fog" in which the word "heavy" means "opaqueness". Thus, the conclusion was erroneously formed from equivocation (heavy=high mass, heavy=high opacity).

Other verbal fallacies detailed by Aristotle are Accent, Amphibology, Composition, Division, and Figure of speech. Aristotle also points out "Material Fallacies" in which the actual structure of the premise-logic-conclusion has been subtly subverted. For example, the material fallacy of "Begging the question" where the conclusion is placed in the premise:

All animals are opportunists
A dog is an animal
Therefore a dog is an opportunist.

What is structured as a proof above is actually a statement, a categorization, and another statement. The conclusion presented was not "deduced" in any way, it just is a more specific restatement of the premise. Other material fallacies are described by Aristotle are Accident, Affirming the Consequent, Converse Accident, Irrelevant Conclusion, False Cause, and Fallacy of Many Questions.

It should be noted here that Aristotle is not commenting on the "truth" or "untruth" of the statements I presented in those examples. What he is saying is that the logical arguments used to obtain them are flawed.


Conclusions

Thus Aristotle, student of Plato, student of Socrates, completely changed the way we acquire knowledge. Accepting the concept of "truth", he developed a systematic method for acquiring knowledge that utilized vetted empirical data as premises and well-structured and self-consistent rational arguments (logic) as a means of using those premises to discover new truths. These new truths collectively would be come to be known as "scientific knowledge".

This method represents several breaks from previous Epistemology. Rejected was the idea that there was a single over-arching "truth" from which all other truths derived. Instead, many truths exist and are things that one accumulates. Gone is the concept of a separate world from which objects were imperfectly projected into the real world (Plato's Forms). Objects are what they are and their properties only have meaning within the context of the object. The "memory" approach of Plato and Socrates for obtaining truths is now replaced by a inductive/deductive hybrid approach where observation and rationalizing work together to produce truths. Careful examination of language informs the structure of questions, arguments, and conclusions and standardized approaches and clearly expressed pitfalls are described.

As this is a blog about Epistemology, we aren't getting into the multitude of other things Aristotle did, especially those vast contributions to knowledge he was able to make with his new method. In essence, this blog entry is more concerned about his contributions to the acquisition of knowledge. What Aristotle did, to borrow from the proverb, was to teach us how to fish. It was a climactic moment in Epistemology that created the concept of "science" and sent humanity down the path of discovery. What Aristotle laid out became the blueprint for acquiring knowledge for over 50 generations. Even now the echoes of his ideas resonate in our most modern theories.

In Part IV we will move forward in time to the Islamic golden age to see how the next steps towards our modern conception of the scientific method were taken.

Introduction

"Man is a being in search of meaning" - Plato

Socrates was a short, ugly, and generally annoying man who lived in Athens from 470 BC to 399 BC. He spent the first half of his life as a sculptor, which made sense since he was the son of a sculptor. Legend has it that he became a philosopher sometime after age 40 when the Oracle at Delphi indicated he was the wisest man in the world. The news of this surprised Socrates who, though educated in literature, music, and rhetoric, felt strongly that he wasn't very wise at all. It was only after he started interrogating the greatest thinkers of Athens that he came to realize that nobody really knew the things they supposed they did. This thus verified the oracle since he seemed to be the only person aware of the fact that nobody (including himself) seemed to truly know anything, which made him the wisest person in the world.

Socrates escaped execution a few times during his life. Finally, as an old man of roughly 70, he was found guilty of corrupting the youth of Athens and not believing in the gods of the state and was executed by being forced to drink poison (hemlock). When asked to flee by his followers, he responded that no true philosopher feared death and besides, where ever he ended up he would probably annoy them so much that it would lead to the same result (Crito).

It is popular to portray Socrates' trial and punishments as unjust, and there were a lot of politics at work in the trial and sentencing. Still, it is worth noting that twice previous to the trial there had been overthrows of Athens democratic government by students of Socrates (Alcibiades and later Critias). It's not surprising that his students would try to overthrow democracy since Socrates was a strong critic of it and said it made "Equals of everyone, including unequals".

What we know of Socrates today comes from his student Plato, the historian Xenophon, and the playwright Aristophanes. The first two exalt Socrates in Euthyphro, Phaedo, Sophist, and many other works; and the last satirized him in the play "Clouds" and briefly describes him as an instigator of sedition in "Birds." Socrates himself wrote nothing as far as we know. Thus the specific ideas of Socrates and those of Plato are hard to separate, since Socrates spoke but didn't write and Plato says he wrote only what Socrates spoke. Rather than worry about what was said by whom, lets combine the two and treat them as one person and examine their contributions to epistemology relevant to our discussions.

Theory of Forms - The Epistemology of Socrates as Expressed by Plato

The epistemology of Socrates (and Plato) is defined by the theory of Forms. The theory of forms essentially states that the objects of the world we perceive empirically (through our senses) are only imperfect aspects of more complete, idealized "Forms." The famous shadow on the walls of a cave story from The Republic does a good job of explaining this idea of "Forms;" here is the Wikipedia summary of the allegory:

In the dialogue, Socrates describes a group of people who have lived chained to the wall of a cave all of their lives, facing a blank wall. The people watch shadows projected on the wall by things passing in front of a fire behind them, and begin to ascribe forms to these shadows. According to Socrates, the shadows are as close as the prisoners get to viewing reality. He then explains how the philosopher is like a prisoner who is freed from the cave and comes to understand that the shadows on the wall do not make up reality at all, as he can perceive the true form of reality rather than the mere shadows seen by the prisoners.

The Forms are essentially abstract concepts that were more complete than the aspects of them that are perceived in the real world. Try thinking of it this way:

Imagine you were tasked with determining whether or not an object placed in front of you was a dog. Chances are you'd feel fairly confident that you'd recognize a dog if you saw one standing in front of you and the task wouldn't be too difficult.

Now imagine someone else is tasked with determining whether or not an object placed in front of them is a dog, except they have no idea what a dog is. You are allowed to explain to them what a dog is, but then must leave them to complete their task. Now the task is much more difficult.

We all think we know what a dog is, but when pressed to describe one to someone who has never seen one, it becomes difficult due to the variety of characteristics of dogs. This is a classic characteristic of the Socratic Dialogues. In these Dialogues, Socrates is constantly asking the person he's interacting with to define something and refine that definition. For Socrates, part of the problem was that people took for granted they knew what an object, virtue, emotion, etc. (dog) was, but when pressed to describe one would often fail miserably (since describing one is much harder than it sounds).

The fact that we recognized whether or not it was a dog standing in front of us was evidence to Socrates that we possessed an innate understanding that was deeper than the objects we came across in the real world. Socrates believed that there is a "Form" that was "dog" that we knew inherently so that when a dog was placed in front of us, we recognized it as such. This was also true for beauty, courage, table, fire, house, anger, etc. What we encountered in the real world were not these Forms themselves, but rather a shadow of these Forms (or if you like the book Flatland, a projection). Socrates felt that since the world we live in is filled only with shadows of the Forms, Forms themselves couldn't be fully appreciated (understood) by the senses. One must resort to rational thought (reasoning) to understand the Forms.

Socrates (and Plato) believed these idealized concepts (Forms) couldn't be learned, but rather had to be remembered. This is completely consistent with the theory of Forms, but may strike us in the modern world as strange. Basically Socrates reasoning was that all Earthly things are imperfect shadows of perfect Forms corresponding to those things. All varieties, shapes, and sizes of dogs were but imperfect shadows of the idealized Form "Dog." All varieties of courage were but imperfect shadows of the Form "Courage." Socrates thus believed that all of us were just imperfect shadows of the Forms of "Ourselves." The Forms of "Ourselves," being ideal and perfect, could perceive the Forms of all other things (Courage, Dogs, Beauty, etc.). Thus in order to understand the Forms of other things, we must somehow access that knowledge we forgot (lost) when we were projected from our perfect Form of "Ourselves" to that flawed shadow which inhabits the real world. Socrates believed rational thought (reasoning) allowed us to remember the things we forgot. Naturally, based on this way of looking at things, Socrates believed any outside stimulus was unimportant since when one used rational thought to discover Forms, one was remembering, not learning.

This link has an example of Socrates approach.

I have used the term "shadows" above in my explanation, but that is just a metaphor. A more accurate description of what Socrates believed would be Perfect Ideals (Forms) and that which exists in reality (Shadows). To summarize, Socrates believed there were perfect ideals (Forms) that corresponded to those imperfect or incomplete things that we come across in the real world (shadows). Socrates believed that we "ourselves" were no exception, and there existed an ideal version (Form) of "Ourselves" that knew the idealized versions (Forms) of everything else. Thus to understand the ideal version of everything else, we needed only remember that which we forgot when we were projected into the real world. This remembering was achieved with rational thought.

Consequences of the Theory of Forms to Epistemology

First and foremost, Socrates believed that absolute truths existed (Forms). He believed that empirical data were incomplete and distorted aspects of these absolute truths were thus irrelevant. The absolute truths (Forms) could only be learned through reasoning.

Socrates believed that Forms could have no self-contradiction. For example, if you say "all dogs are large" and then acknowledge "some dogs are small" then your original definition is wrong. Socrates consequently developed a method for disproving misconceptions through contradiction. The misconception is stated as a premise. Other short premises that are easily agreed upon are presented. Through a series of logical steps, a contradiction emerges that disproves the original misconception. This created a process of elimination by which one could move closer to the absolute truths (Forms) being examined.

"If particulars are to have meaning, there must be universals" - Plato

The next point is profound and it is hard to determine whether it came from Socrates or Plato. Basically it says "The whole of everything has a corresponding Form." What that means is that it is not enough that a definition be consistent with respect to a particular Form; it must be consistent with respect to all Forms since all Forms correspond to a single Form "the Universe." There can be no contradictions in general. A proof need only be proven incorrect once to be incorrect. This is a fundamental tenet of mathematics and science today.

In Part 3 we will see examine how Aristotle took the theory of forms and modified it in such a way as to create a foundation on which modern thinking was built. Link to Part 1.

Introduction

"Thy Godlike crime was to be kind, To render with thy precepts less, The sum of human wretchedness, And strengthen Man with his own mind" - Lord Byron, Prometheus

One of the defining features of human beings is the ability to acquire and pass along ideas. Actually, it is less a feature than a pathological obsession. Hundreds of thousands of years ago at least, there is evidence that our ancestors passed ideas and technology on to later generations. This idea of continuity, of the passing on of ideas and technology by a group of individuals, is really what is meant by the term culture. Other animals have been said to have distinct cultures; however, no animal cultures are as complex, versatile, and quick-to-adapt as human cultures. In fact, the very name of our species, Homo sapiens, emphasizes this point.

The Latin word sapien means "wise" or "learned" and the Latin word homo means "man". For billions of years, life came into being, lived, reproduced, and died. Over thousands of generations, small changes in the biology of the animals, combined with external conditions, resulted in natural selection. Natural selection is a process by which the organism best suited for the existing conditions survives while other "less suited" organisms are marginalized or even go extinct. The problem with natural selection is it can take (though not always) a long time to produce an organism adapted for a particular environment. A more efficient system would be an organism that has evolved the ability to adapt, rather than an organism that adapts by evolving. Thus it was only a matter of time before intelligent life evolved.

The term "intelligent life", of course, is a vanity. There is a joke that says that everyone who drives faster than you is a maniac and anyone who drives slower than you is a moron. By "intelligent life", we literally mean "our species". This is evident by the constant revision of what constitutes "intelligence". For instance, the defining characteristic of intelligence was, for a long time, considered to be the use of tools. Implied in this statement was that the use of tools must originate from within the species, not from human training. At any rate, it was found that some primates use tools in the wild - and so the definition was shifted to "has culture", as in "intelligent life has the characteristic of culture". Of course, further study showed that some primates displayed distinct cultures. Another popular definition was "self-awareness", but mirror experiments have shown many species share that trait with us as well.

Clearly there is no line one can draw and point to where intelligence suddenly emerges, but our vanity demands it, so we try anyway. Somewhere over the last 100,000 years since our species evolved, we have come to view ourselves as separate and superior to the other organisms found in the world. It's understandable but ultimately illogical, mainly because our criteria for "superiority" are based on the things we're good at (such as learning). If superiority were instead based on, say durability, or strength, or quickness, or survivability, or longevity, we would score quite low. Some argue that our superiority is self-evident due to the things we've produced; the problem with that argument is that whoever said the point of existence was to produce things? Really in the end it is our vanity as a species that presupposes our superiority, but there is nothing wrong with that. The instinctive urge for survival of a species must necessarily produce a certain level of conceit if that species is self-aware.

With that background, it should not be surprising then that one of the earliest branches of philosophy to emerge was that of epistemology. Epistemology is the branch of philosophy concerned with the acquisition, validity, and limits of knowledge. To better understand what that means, we should probably define knowledge. Merriam-Webster's dictionary defines knowledge as the body of truth, information, and principles acquired by humankind. So epistemology tries to figure out the validity and limits of the "truths, information and principles" acquired by human beings. Epistemology also investigates the methods and means by which knowledge (truths, information and principles) are acquired. To understand modern branches of Epistemology, we should first review its history.

The Pre-Socratics

"Everything has a natural explanation. The moon is not a god but a great rock and the sun a hot rock." - Anaxagoras

When giving a brief history of any type of philosophy, it is always popular to start with the Pre-Socratics. Certainly there have been philosophers as long as there has been man, and undoubtedly the Pre-Socratics of Greece borrowed heavily from other cultures that came before them (I'm looking at you Egypt, Crete, Phoenicia, and Mesopotamia), but we need a starting point and the Pre-Socratics will do. The Pre-Socratics, when it came to Epistemology, had many different schools of thought. Among the Pre-Socractics are, in roughly chronological order, the Milesian, Pythagorean, Eleatic, Pluralist, and Sophist schools.

The Milesian school was significant because of the (supposed) break from the belief that events were the result of the will of gods. Instead, the Milesian School sought a fundamental material from which everything was made and gave it its properties. They believed that through observation one could deduce this fundamental material. Although they disagreed amongst themselves what the fundamental material was, what is significant for our conversation is their implicit Epistemological belief that nature followed logical rules and could be understood through careful observation.

The Pythagorean School was significant because it was the first to tie philosophy and mathematics. The Pythagoreans believed that the world was inherently mathematical. That is not to say "being able to be described by mathematics", but rather "is mathematical in nature". This belief was taken to an extreme (to mysticism). To reconcile the idea of the infinite continuum and discrete world we live in, the Pythagoreans turned to the idea of harmony. Here is an excerpt from an explanation from Wikipedia explaining this idea:

"A musical scale presupposes an unlimited continuum of pitches, which must be limited in some way in order for a scale to arise. The crucial point is that not just any set of limiters will do. One may not simply choose pitches at random along the continuum and produce a scale that will be musically pleasing. The diatonic scale, also known as "Pythagorean," is such that the ratio of the highest to the lowest pitch is 2:1, which produces the interval of an octave. That octave is in turn divided into a fifth and a fourth, which have the ratios of 3:2 and 4:3 respectively and which, when added, make an octave. If we go up a fifth from the lowest note in the octave and then up a fourth from there, we will reach the upper note of the octave. Finally the fifth can be divided into three whole tones, each corresponding to the ratio of 9:8 and a remainder with a ratio of 256:243 and the fourth into two whole tones with the same remainder. This is a good example of a concrete applied use of Philolaus' reasoning. In Philolaus' terms the fitting together of limiters and unlimiteds involves their combination in accordance with ratios of numbers (harmony). Similarly the cosmos and the individual things in the cosmos do not arise by a chance combination of limiters and unlimiteds; the limiters and unlimiteds must be fitted together in a "pleasing" (harmonic) way in accordance with number for an order to arise."

In the above example we see the seeds of the concept of Musica universalis. The above paragraph has subtly introduced math into a philosophical discussion.

"The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things." - Aristotle, Metaphysics 1-5 , cc. 350 BC

The Eleatics insisted simply observing the world wasn't enough to determine truths. They demanded truths have logical consistency. From this school of thought sprang the process where one starts with a sound, indisputable truth and through progressive logical steps obtain another truth. Also emerging in this school of thought was the process of disproving a truth through progressive logical steps that lead to a contradiction (Modernly referred to as reductio ad absurdum). That last method was made famous by Zeno (of Elea) and his paradoxes. This method also emerges later often in Socrates' dialogues (Socratic dialectic method).

At this point, I need to inform any and all reading this that I am picking out aspects of these schools of philosophies corresponding to Epistemology. At that time, the branches of philosophy weren't really separated into things like Epistemology, Metaphysics, Politics, Ethics, and Esthetics. What these Pre-Socratic schools of philosophy did was develop a sort of "supra-philosophy", a straight forward philosophy from which all phenomena were explained. That's why you get mathematical mysticism with the Pythagoreans and some Milesians trying to explain how fire may be made up of water. When we read the Pre-Socratics today, it is easy to get distracted by the "supra-tenets" at the heart of these supra-philosophies and miss the subtle, unconscious epistemological breakthroughs that emerged when they were forced to validate or defend their supra-tenets. For instance, the Milesian idea of nature being governed by principles and these principles being acquired through observation was a huge epistemology breakthrough (probably unfairly attributed to them when mostly likely such ideas occurred to mankind much earlier, but alas our knowledge of history is limited to written history). The Pythagorean idea linking mathematics with nature andthe Eleatic idea of logic superseding the senses as a way of determining truth were epistemological advances that formed the foundation of Socrates, Plato, and most especially Aristotle, who were in their turn the foundation of western Epistemological thought.

Continuing with the Pre-Socratics we come to the Pluralist School, which is notable for replacing the supra-tenet idea escribed above (reducing nature to a single principle) with the idea that nature consists of many principles. One of the lasting ideas of the Pluralists was the idea of the four roots (fire, air, water, and earth) that when combined in different proportions created everything in the universe. An important concept introduced by the Pluralists was that human beings never see the entirety of anything in one glance. For truth to be fully achieved, something must be examined from many angles. This supported the Eleatic view that observation alone wasn't sufficient to determine truth.

This summarizes the Pre-Socratic schools of philosophy contributions to epistemology. I've omitted the Sophists because much of our understanding of them comes in criticism of their work and such biased accounts make it difficult to determine their contributions. Already we start to see bits and pieces of something familiar in the Pre-Socratics in their approach to obtaining knowledge. The ideas that nature is governed by rules, learned through observation and validated through logic, particularly mathematics, are ideas we still hold today.

In Part II of this series, we will examine Socrates, Plato, and Aristotle and how Epistemology matured under their watch and set the stage for the development of the scientific method.

Part II - Wherein extraordinary events and post cold war politics conspire to set particle physics back 25 years. The following is a fictitious account littered with facts.

"If you give me six lines written by the hand of the most honest of men, I will find something in them which will hang him" - Cardinal Richelieu

Scene 2: 10 years have passed since the events detailed in Part 1. Our heroes, Scientist #1 and Scientist #2, find themselves on the verge of realizing a scientific triumph. Already, some $2-billion has been spent on the construction of the Superconducting Super Collider (SSC), a wondrous instrument that will reveal countless secrets of nature and advance the knowledge of our ever-curious kind. Top scientists from around the U.S. have relocated to Texas in the hope of participating in what will undoubtedly go down in history as a golden age of particle physics. Yet all is not well. Fate is capricious and much has changed in 10 years. Our heroes work as they await the tidings of a messenger (Scientist #3) sent to determine what budget cuts to expect from Congress.

Scientist #3 now arrives at the door to the director's office at SSC headquarters. Scientists #1 and #2 are standing in the office, reviewing blueprints on a table. They're having an animated discussion; neither has slept well for weeks.

Scientist #3: [quietly] I see my noble friends hard at work. Such industry does not deserve the reward I bring. [louder] My friends, I come from Congress with bad news. My mission has failed.

Scientist #2: Be at ease. I'm certain whatever difficulty you've encountered can be overcome. Please, sit and tell us what you've learned.

Scientist #1: Yes, let us know so that we might plan our response. What is most important is that we continue to move forward.

Scientist #3 walks toward the other two but cannot bear to sit, stands and hesitates for a moment, then begins.

Scientist #3: [in despair] Dear friends, I see that you do not yet comprehend the depth of our undoing, and it pains me a great deal to reveal it.

Scientist #1: Why do you speak this way? Have we not overcome much already? Do we not dedicate our lives to removing the veil of nature so as to reveal the truths that lie underneath? How difficult could it be to sell that which will so greatly advance us as a nation to those who are charged with making it great?

Scientist #3: I fear you assign virtues to others and expect like-mindedness where neither exists, especially in Congress where compromise is compromising.

Scientist #1: It is a singular aspect of our race – to endeavor – that separates us from the lesser species. I assign no virtue that isn't inherent to all people. If it is not readily found, then it is buried by fears that we must dispel.

Scientist #3: If it is fear, as you say, then it is a powerful terror. They are quite turned against the SSC. I suspect in fact it is a lack of fear that unmakes us.

Scientist #2: Please tell us in detail what has happened.

Scientist #3 falls dejectedly into the previously offered chair. Scientists #1 and #2 exchange worried glances and seat themselves opposite Scientist #3.

Scientist #3: I've spoken with a number of our advocates in the lesser and greater chambers and all indicate the cause is lost. There is a tide of frugality and meanness sweeping over Washington that targets anything deemed wasteful. As you know, the SSC has been criticized by the Project on Government Oversight for high costs and poor management. The $12-billion that this will now cost is far beyond the original $4.4-billion originally estimated. Our inability to draw international funding to help offset costs hasn't helped either. Since the cost is equivalent to that of funding the International Space Station (ISS), most representatives have decided it can be only one or the other.

Scientist #2: Oh! Such a false choice! The ISS is a political machine to encourage cooperation with the newly formed democracy of Russia. Its scientific merits are far less than those of the SSC. It is foreign policy over science.

Scientist #3: The ignorant know not the difference and are arrogant in their folly. They all agree that the stability and encouragement of the nascent democracy of Russia is tantamount and that the ISS must proceed.

Scientist #1: Then we must make them see the value of the SSC. We must make them understand that it will be as when Galileo peered through his telescope and noticed the satellites of Jupiter and saw that Nebulae were composed of stars. The SSC will do far more than that political toy, the ISS, will ever do.

Scientist #3: [shaking head, sadly] You dream. Congress answers to the people, and the people don't care for Galileo. They only cared for science itself when there was a USSR to fear. Now that this adversary is gone, they care not.

Scientist #2: But surely they desire the comforts of new technology that come from such scientific endeavors?

Scientist #3 rises and walks to the window. Below, construction continues on the SSC. Scientist #3 strains to see something in the distance, then failing, shrugs and still staring out the window responds to Scientist #2.

Scientist #3: The people create their own myths as to how our existing technology came to be. This is just as the Greeks created Prometheus to explain fire, having long-forgotten the prehistoric scientist who invented it. From these myths they will derive justification for cutting science from their budgets. They will lionize free enterprise as the source of invention and deride scientists as ivory-tower pedants. Already the whispers grow to murmurs, and I fear this next election we will witness the roar.

Scientist #1: [shaking head slightly side to side] I don't believe it. One would have to ignore the last 75 years of history to believe such things.

Scientist #3: History is easy to ignore, especially with no adversary with which to compete and keep one honest (so to speak). Remember how after Athens fell, Sparta faded away? Should we really be so surprised that with the threat of communism receding, that the people should become shortsighted and selfish?

Scientist #1: I don't share your cynicism. People are good and do the right thing when given the opportunity.

Scientist #2: It's true that people are good, almost all people, but only as individuals. Put them together as a group … well … remember what Seneca said, "It is proof of a bad cause when it is applauded by the mob."

Scientist #1: We mustn't pretend their arguments are without merit. Our cost overruns have been unacceptable and we should have better anticipated public sentiment in the post-Cold War world.

Scientist #3: Those are merely the excuses. To respond to them is to hug the pickpocket. The truth is that they never understood the science, and without the Soviet Union to scare them, they now feel they don't need it. They have a bottomless pit of condemnations that could have been applied to thousands of projects over the past 50 years – and never were.

Scientist #1 gets up and walks to the window. Scientist #2 follows. All three stare down at the construction below. The workers are on break now, laughing at some unheard joke. Scientist #1 stares off into the distance straining to see something, but cannot. Scientist #2 watches #1. Scientist #3 stares blankly, lost in thought.

Scientist #1: [searchingly] Perhaps they merely wish to embrace frugality after years of reckless spending.

Scientist #3: [sighs] If that were truly the case, there are much bigger projects than ours that they seemed to have missed. No, their actions reveal their true motives. They target those things that they feel they no longer need for political gain. There is no Sputnik to rally them to our cause.

Scientist #2: [resigned] I am beginning to understand. This has nothing to do with this project. The world has turned and we are left behind. How can we convince the people to invest in their future when the Cold War has been won?

Scientist #1 is still searching far out in the distance, even as he answers

Scientist #1: [vacantly] Certainly they must know that there will be other wars.?

Scientists #2 and #3 turn back and return to their seats. Scientist #2 tenderly rolls up the blueprints they had been examining earlier. Scientist #1 remains at the window staring outward.

Scientist #3: Not for a long time. The world is weary of war. Someday – maybe – they will clamor for us, but that day may be a long time off. For now, they will forget what we have wrought and discard us instead. I fear this is only the beginning.

Scientist #1: [stubbornly] There's no question that we thought the most important science project over the next twenty years would happen here. This is a tremendous disappointment. Still, I will continue to fight and try to convince the people that this is needed.

Scientist #2 finishes rolling up the blueprints, realizes there is no place to put them, searches for a rubber band to bind them and cannot find one and finally lays them back on the table where they proceed to unroll themselves.

Scientist #2: [dejectedly] I fear what this means for the future of science in this country.

Scientist #3: With good reason, for the very fools who have undermined this endeavor are, at this very moment, congratulating themselves. Today our country, a beacon of scientific endeavor, that noble shining city on a hill, has turned down its light in the name of frugality. But I tell you that it is not frugality but rather meanness that has brought about this calamity.

[Anger is replaced with despair] Ah! What we could have learned! What wondrous discoveries were waiting for our intrepidity? I understand now how Archimedes must have felt as that gladius plunged into his breast, or how Socrates felt as he drank his fatal tea. It seems the hoi polloi will tolerate only so much progress before their baser instincts demand a respite. I do not fear for science; other countries will fill the vacuum we create. But I fear for my country, which embraces decline with such vigor.

Scientist #1 finally turns from the window but remains standing at the window regarding Scientists #2 and #3, notes the half rolled blueprints on the table, hears the shouts of the construction workers below, and for a moment feels overwhelmed. Then seems to find purpose again, walks to a desk, pulls out some rubber-bands and walks to the table and hands them to Scientist #2. Scientist #2 gratefully puts the blueprints back in order. Scientist #1, still standing, addresses the two other sitting scientists.

Scientist #1: There is always hope, and even if it is as you say, we will labor on and weather the storm, accomplishing less than we could have, but still pushing forward.

And so that most excellent project that would have brought about a golden age of particle physics was cancelled. Even today, 17 years since the cancellation, there has been little progress made since there was no collider powerful enough to probe the energy regions necessary for discovery. There is hope that this decade, the LHC in Europe may achieve half the energy of collisions that the SSC would have achieved more than a decade ago if it had been allowed to be built. Costly were those 10 billion dollars saved. Today the U.S. ranks 25th out of 34 countries in math and 17th in science. Many are the reasons given, but they are all nonsense. The cause is quite simple, children imitate adult's attitudes. Woe to our nation if we continue to turn our back on reason.

The End

Relevant Links:

http://www.hep.net/ssc/new/history/appendixa.html
http://en.wikipedia.org/wiki/Superconducting_Super_Collider
http://www.damninteresting.com/americas-discarded-superconducting-supercollider
http://en.wikipedia.org/wiki/Atom

Part I - In which the U.S., in the midst of the Cold War, aspires for greatness in science and arranges to build a particle accelerator of incredible power. The following is a fictitious account littered with facts.

"Things on a very small scale behave like nothing that you have any direct experience about. They do not behave like waves, they do not behave like particles, they do not behave like clouds, or billiard balls, or weights on springs, or like anything that you have ever seen." - Richard Feynman

Scene 1: A High Energy Physics Advisory Panel (HEPAP) hearing (Department of Energy (DOE)) for the consideration of the construction of a 20 TeV Supercollider. It's 1983.

Scientist #1: Originally, the atom was conceived to be a fundamental unit of matter. The name "Atom" is literally greek for "indivisible". At the turn of the 20th century, with the discovery of the electron, it became clear that the atom was in fact made up of smaller parts. The idea of atoms consisting of electrons and a nucleus was developed in the 1910s. In the 1930s it was determined that these nuclei consisted of protons and neutrons. In the 1960s we figured out these protons and neutrons were made up of quarks and in the 1970s we finalized something called the Standard Model that explains more things than I have time to relate. Suffice it to say that in 70 years we've come a very long way in our understanding of the fundamental particles that make up matter.

Scientist #2: Yes, we now know that an atom consists of electrons orbiting a nucleus. A nucleus consists of protons and neutrons bound by the nuclear force (a residual strong force analogous to the van der Waals force, except involving the strong force between nucleons). Protons and Neutrons are made of quarks, three each to be exact, up-up-down for the former and up-down-down for the latter. The quarks are held together by the strong force. Then the details become much more complicated involving concepts such as total angular momentum, baryon number, electric charge, isospin, charm, strangeness, bottomness, topness, and color charge. From this a particle zoo ensues, hundreds of unique hadrons.

Panel Member #1: How confident are we in our understanding as it stands today?

Scientist #1: To directly answer your question, we think we pretty much understand what's going on, but we have reached certain limits in how much we can test what we think we understand. That, of course, is why we are here today.

Scientist #2: Last summer leading particle physicists attended a meeting in Snowmass, Colorado to discuss elementary particle physics and future facilities. For 5 years there has been talk for the need of a 20 TeV proton-proton collider. A workshop from Cornell on accelerator technologies and another workshop on detector technologies from Lawrence Berkeley Laboratory made it apparent that such collider is now possible.

Scientist #1: That's why today we are urging the immediate initiation of a multi- TeV high-luminosity proton-proton collider project at the earliest possible date. Details are provided in the reports submitted to your office.

Panel Member #2: We will evaluate your recommendations and decide how to proceed. Thank you for your time.

Scientist #1: Please do, and when you do, please consider this. When J.J. Thomson discovered the electron, a subdivision of the indivisible atom, scientists were surprised. At that time, the periodic table was well established and although there were inconsistencies regarding atomic weight, scientists didn't imagine something as small as an electron would be found inside atoms. Everyone at that time thought they pretty much understood what was going on, just as we think we do today. It's not that they were wrong mind you, it's just they found when they looked more closely there was much more detail than they expected.

Scientist #2: And when Bohr suggested the energy of an electron in orbit about a nucleus is quantized in 1913 to solve the problem of electrons spiraling into the nucleus, it led to a brand new field of science called quantum mechanics. Something no one could have anticipated resulting from studying atoms.

Scientist #1: That's true, and who could have imagined peering into the nucleus of an atom would lead to the atomic bomb with force far beyond any other weapon in history? We urge you to remember that this science, seemingly without practical purpose, inevitably revolutionizes the world through it's discoveries. It is no different from the first time man worked with Bronze, or Iron, or Plastic. We cannot be certain of what we will discover, but we can be reasonably certain it will change the world.

Panel Member #1: My friends, rest assured we understand the importance of maintaining a lead in scientific discovery. Certainly we will never allow ourselves to fall behind the Soviets in developing new science and new technologies. It is essential we maintain our technological and scientific lead.

Scientist #1: Rest assured, the SSC is critical for future progress in particle physics and technology in general.

Over the next year the HEPAP chartered preliminary studies regarding the technical and economic feasibility of a 20 TeV collider. Three designs were developed, each with their own costs. After much work with National Laboratories and collaborating Universities, the technical details were worked out and a design was selected and presented in a Conceptual Design Report written in 1986. This was by no means a finished product, many details regarding the accelerator and detectors needed to be worked out, but the Department of Energy was satisfied it could be done, and in January 1987, the DOE recommended the Superconducting Super Collider (SSC) project proceed. President Ronald Reagan signed off on the project and after a very complicated and political selection process, in 1988 Texas was selected to be the location of the SSC. The total construction of the SSC was estimated to cost 4.4 Billion dollars.

End of Part I

Relevant Links:

http://www.hep.net/ssc/new/history/appendixa.html
http://en.wikipedia.org/wiki/Superconducting_Super_Collider
http://www.damninteresting.com/americas-discarded-superconducting-supercollider
http://en.wikipedia.org/wiki/Atom