Ironic Flint

On Isolation And Modernity

2011-08-13T18:05:00.000-07:00

An intriguing excerpt lifted from Albert Camus' essay The Minotaur - Or - The Stop In Oran:

There are no more deserts. There are no more islands. Yet there is a need for them.

The desert itself has assumed significance; it has been glutted with poetry. For all the world's sorrows it is a hallowed spot. But at certain moments the heart wants nothing so much as spots devoid of poetry. Descartes, planning to meditate, chose his desert: the most mercantile city of his era. There he found solitude.

From Amsterdam Descartes writes to the aged Guez de Balzac: "I go out walking every day amid the confusion of a great crowd, with as much freedom and tranquility as you could do on your garden paths."

What Is Humor?

2010-11-20T15:47:00.000-08:00

Here's an interesting question: what is the definition of humor? A brief examination of modern dictionaries is a thoroughly depressing, self-referential affair: one offered definition is "something designed to be comical and amusing". This does not seem very descriptive, especially when you consider that amusing is defined as "giving amusement".

My point with this examination is not to say that common understanding of humor is wrong. I would rather communicate that our conception of humor is very often implicit. From a scientific perspective, I think that it would be useful to identify common threads within what is perceived to be humor, in an attempt to quantify the concept. With this in mind, I would like to submit one particular theoretical definition of humor for your consideration.

Humor: An emotion that is grounded in the harmless resolution of unexpected phenomena.

I find that this description gains the most traction with an analysis of several types of humor. Please consider the descriptive power of this definition in the context of the following three examples:

Irony
Generalization: This category of humor relies upon descriptions of reality that diverge from the models that we construct to explain it.
Example: A fire station burned down to the ground.
Specific Explanation: The ability of firefighters to squelch fires appears to share an inverse relationship with distance. Thus, the failure of firefighters to stop a fire at their base of operations conflicts with this mental construct. Furthermore, if any of these three factors were missing (distance does not impact chances of repulsing fire, we are financially invested in the fire station, we weren't paying attention when exposed to the information), then the situation would be less likely to be seen as funny.

Puns
Generalization: Wordplay that diverges from typical linguistic practice; often with its real meaning hidden behind grammatical complexities. A pun can be thought of as an aberration of linguistic rules. Jokes often use equivocation to connect previously unrelated.
Example: I wondered why the baseball was getting bigger. Then it hit me.
Specific Explanation: "Then it hit me" is a common expression for discovery of an idea. The joke is funny because it unexpectedly co-opts this expression as a literal vehicle of communication.

Tickling
Comment: Tickling is not limited to homo sapiens between it dispenses with our specialized development and employment of language.
Generalization: Tickling is an action that invades our personal space. It has been argued that we laugh because we are pleasantly relieved, at a primal even subconscious level, that the offender is not inflicting harm on us.

The above reasoning can be thought as an introduction to the developing theory best known as the Benign Violation Theory of humor. If interested, I would encourage you to explore the entire Wikipedia article as a more complete introduction to the subject.

Finally, I would welcome the reader to produce an alternative or improved definition of humor, and we can discuss its relative merits. I am also interested in analyzing "edge-case" examples which may point to inadequacies of the theory. I enjoy exploring alternative explanations problematic exceptions to this Benign Violation Theory, as I find it a useful way of iterative improve my understanding and presentation of this topic.

The Periodic Table: Orbitals

2009-09-09T22:58:00.000-07:00

In this post, I would like to address the concepts of order and beauty within the Periodic Table. Below I have constructed the Periodic Table as it appears in most textbooks.

This illustration is a nice snapshot of the order that its creator, Dmitri Mendeleev, had found within the elements. Indeed, all textbooks generally say the same thing: that these elements are arranged from left-to-right and then top-to-bottom in order of the amount of protons (the atomic number) in the nucleus. Arranging these atoms into the table produces a startling result: electrons within the same column behave in strikingly similar ways. The well-known elements of copper, silver and gold (located in the eighth column from the right, symbolized by Cu, Ag and Au respectively) illustrate this principle well: they are all strikingly less chemically reactive than nearby metals.

So goes the conventional wisdom. However, this brief synopsis of Mendeleev's discovery is not comprehensive. As we look closer, in fact, we find irregularities that demand an explanation:

Chemists have not discovered a last element; new elements continue to be created.
Hydrogen and helium do not conform to their column's traits as convincingly as other elements.
The Lanthanide and Actinide series are housed apart from the table (the two detached rows fit "inside" the yellow strip on the above table).

This last item means that the Periodic Table is, to a certain extent, oversimplified. The actual table looks like this:

A lot less attractive, right? Well, before you leave dismayed by the chaos of nature, consider that the quantum mechanical approximation of orbitals can afford our table with an interpretation that can be considered beautiful. Let us assume that we are only interested in elements that are not ionized, then the order of an electron-based Periodic Table remains unchanged. Allow me to further reposition helium - one of the exceptional elements mentioned above - alongside hydrogren. Finally, I have added an extended ellipsis at the lower right of the table. This symbolizes our other observation that chemists continue to discover higher-order elements.

Remarkably, we discover that with our light manipulations, we are now able to group our Periodic Table into four separate rectangles. It turns out that these rectangles represent orbitals, which stem from the principles of quantum mechanics. Below we have delineated the four known groups into orbitals s, p, d, and f. These symbols originate from spectroscopy, and are regrettably more historical than meaningful. They stand for sharp, principal, diffuse and fundamental.

We have completely rearranged the Periodic Table into four separate rectangles, each of which represent different orbital types. In effect, we allowed a certain amount of ambiguity with respect to the macroscopic in order to obtain greater clarity in the smaller scale. In fact, we can continue our journey towards the foundations for the periodic table with another reorganization. The following idea (independently rediscovered by myself) was actually discovered in 1928 by Charles Janet.

It is important to realize that this reorganization in no way changes the atomic number ordering of Mendeleev, it simply rearranges it. By moving the s-orbital block to the right, we have further compromised macroscopic interrelationships in order to furnish ourselves with meaningful patterns and predictive power. In my next post, we will pick up Janet's Table and attempt to unearth and understand the mechanisms behind its underlying patterns.

My hope is that you are beginning to experience the periodic table as an dynamic snapshot of physical reality. In this article, I have zoomed in from the common behavior-oriented paradigm towards a more fundamental orbital approximation. For more information, please refer to the following series of video lectures provided by MIT.

Einstein's Puzzle

2009-08-31T19:34:00.000-07:00

Below is fairly well-known puzzle attributed to Albert Einstein. Some claim that 98% of the human population cannot solve it. While this claim is probably unsound, it does point to the severe difficulties people experience when working towards its solution. It is my belief that such difficulties are entirely avoidable. Through an exploration of one illustrative solution, I hope to shed light on the art of learning. Specifically, I intend to show that this puzzle is not inherently difficult; but is interpreted as such because human beings all too often fail to understand the power of abstraction.

The Puzzle

Five men of different nationalities and with different jobs live in consecutive houses on a street. These houses are painted different colors. The men have different pets and have different favorite drinks. The following clues are provided:

The English man lives in a red house
The Spaniard owns a dog
The Japanese man is a painter
The Italian drinks tea
The Norwegian lives in the first house on the left
The green house immediately to the right of the white one
The photographer breeds snails
The diplomat lives in the yellow house
Milk is drunk in the middle house
The owner of the green house drinks coffee
The Norwegian's house is next to the blue one
The violinist drinks orange juice
The fox is in a house that is next to that of the physician
The horse is in a house next to that of the diplomat

Determine who owns a zebra and whose favorite drink is mineral water.

The Solution

1) Extract needless symbolism.

Assigning meaningful variable names not only saves space, but if effectively relieves any symbolic baggage from the problem. Here, numbers differentiate between the five specified characteristic and letters identify individual members of the set.

2) Quantify the problem.

The next phase in our process of abstraction is quantification. Rather than dealing with these extensive logic chains, it is arguably simpler for the brain to visually interpret the data. As we will see, this technique is extremely powerful and reduces this convoluted verbal maze into a straightforward fill-in-the-blank puzzle matrix. So simple, in fact, that I am convinced that anyone determined enough could solve it.

Below illustrates one such quantization. As you can see, the house-trait pairs have been represented in a 5x5 matrix, and puzzle pieces have been fabricated, each labelled with the associated clue. The problem is solved by fitting all of these pieces onto the puzzle and identifying the missing squares. The only complication is that two of the puzzle pieces, the two closest to the matrix, can be mirrored about the y-axis. Note that the ribbons above the puzzle pieces represent the associated clue. Blocks 1E, 2E, and 3C have already been filled out based off of clues 5, 11 and 9 respectively.

All we have done up to this point is clarify and illuminate the problem before us. While the previous simplifications and abstractions take time to implement, they are fundamentally trivial constructions.

I have concealed the next phase of the solution should you choose to attempt the solution for yourself. The purpose to my writing is not to expound a particular implementation of the solution (although the following is instructive), but to discuss the underlying principles behind effective situations.

3) Solve the problem.

While a brute-force approach would be relatively straightforward, I will illustrate the solution via a more conventional logic tree. Note that the following is not necessarily the most elegant path. I have chosen it for its simplicity and its illustrative strategic methodology. One quick note: we will represent puzzle pieces by (clue number) and columns by [column name]. We will also symbolize placement decisions via the notation Place(clue number, column name).

Our working strategy is to find the path of least choice. Here, (8&14) can only fit into only two locations, and is therefore the least complex logical path.

Path 1:

Assume (6&10) is placed in [M&R]. It then becomes apparent that (1) has only one allowed placement:

Place(6&10, M&R).
Place(1, FR).

Here, (8&14) contains the last piece from row 2. Therefore, it must be mirrored about the y-axis and placed. From here, the placement of (4) and then (12) become apparent:

Place(8&14, FL&L).
Place(4, L).
Place(12, FR).

However, we have reached an impasse that can be understood through the Pigeonhole Principle. In the above illustration, (2) and (3) and (7) are mutually exclusive (they all have at least one row in common with another) and may only be placed in [M] and [R]. Just as we know that three pigeons cannot fit into two holes, we can be certain that Path 1 contains no solutions. Since we began our solution by exploring the first possible placement of (6&10), we must know turn to the second.

Path 2:

This path begins with the alternative placement of (6&10) in [R&FR]. As before, (1) and then (8&14) have only one available location:

Place(6&10, R&FR).
Place(1, M)
Place(8&14, FL&L)

We have now reached another fork in our journey. There are no mandated placements, so we search for limitations to our choices. One such limitation is that (4) can only be placed in [L] or [R]. Therefore, we once again branch into two paths.

Path 2a:

We start by assuming that (4) is in [R]. Given this assumption, we can ascertain the implied locations of (2) and then of (3):

Place(4, R)
Place(2, FR)
Place(3, L)

However, in the resultant figure above we simply have no room for (12). We can safely conclude that Path 2a is incorrect and proceed to Path 2b.

Path 2b:

Since (4) cannot be in [R], it must be in [L]. This mandates the location of (12) in [R]. This in turn means that (3) must be in [FR].

Place(4, L)
Place(12, R)
Place(3, FR)

To our delight, we can now appreciate that Path 2b is the only correct logical journey through our puzzle. The concluding steps are given below, and the desired quantities are shown in yellow:

Place(2, R).
Place(7, M).
Place(13, FL&L).

Finally, our symbolic table can decode this information to provide the desired solution: The Norwegian man drinks the mineral water and the Japanese man owns the zebra.

4) Extract significance.

Hopefully, you will have been able to follow the logical journey above. Please note that I explored every logical journey in order to establish the unique nature of the solution. Given the right setup, however, this process essentially becomes a 5x5 jigsaw puzzle.

While there are many legitimate interpretations of our results, perhaps the most useful is the implications of human logical capacity. I would posit that much the human population could easily, albeit not as explicitly, reproduce the logical chain of events required to solve our matrix. The lesson here lies in the reinterpretation of the problem, which transformed the problem from a convoluted mess into a simple puzzle. It is not superhuman ingenuity, but rather this process of chipping away at problems until you uncover their infastructure, that has been the vehicle for the humanity's greatest accomplishments.

Color

2009-08-20T15:15:00.000-07:00

Without light, color has no meaning.

Since visible light is merely a small subset of all possible photon wavelengths, color is more accurately defined as our brain's interpretation of a lack of certain wavelengths. In other words, color is not an autonomous reality, but is rather your interpretation of the characteristics of the light striking your face.

One example to illustrate this reality. Take an object that appears blue when placed under white light. What happens if this "blue" object is placed under a red light?

Let us now take a closer look at the three actors in our story:

White light occurs when there is are equal proportions of small-wavelength (SW) and large-wavelength (LW) photons.
Red light consists of only LW photons.
The "blue" object absorbs LW photons and reflects SW photons.

Given these characteristics, it is easy to analyze the behavior of our object:

Under a white light, the object is barraged by both SW and LW photons. However, it absorbs the LW photons, and only reflects the SW photons toward us. Our eyes interpret these smaller wavelengths as blue.
Under a red light, the object is barraged with only LW photons. It behaves the same way as before: absorbing all LW photons and reflects all SW photons. However, there are no SW photons available to reflect! This translates to our eyes receiving no photons from the direction of the object. The result? The object appears black.

J

2009-08-20T13:30:00.000-07:00

Whenever you encounter a misplaced J in an email or other digital document, you can safely assume that it began its life as a smiley-face.

Apparently, due to some very convoluted translation issues (involving standards for the Dings font series), the original character is, annoyingly, reinterpreted.

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