It's been one year since Jonas Burgos was abducted from a Mall in broad daylight. I for one, don't believe that this despicable act can just be blamed on a few bad elements in the military (or even the government). It takes a certain kind of Society to make this possible, one that is populated with individuals who possess a mindset that is on full display in this fortright (but anonymous) comment over at Expectorants:

*"It's a simple question of the lesser evil. Who are the aggressive power brokers/stakeholders in the Philippines ba? Military, CPP/NPA, oligarchs.*

Pick one. How you might say? Well, let's stop picking on Arroyo for one and start supporting her. She's killing the commies and bribing the soldiers. So stop those middle-class rallies against GMA and support the parliamentary referendum to prolong her and her party's rule.

If the communists or military sweep to power tomorrow and be a little less corrupt than the oligarchs, I would have to agree that there would be an exponential improvement in the lives of the hungry and destitute.

But if helping a lot of poor means that the new military or communist overlords would take away the accumulated wealth of the present rich, then I'm afraid I would have to side with the evil oligarchs.

As much as I can sympathize with the predicament of the poor, I wouldn't allow a power shift that would uplift their standard of living while at the same time lower mine, that is, my middle class way of living.

It may sound selfish, but I've thought this through. I don't want to spend the rest of my life "starting over" to accumulate again the real estate, big savings account, stocks, and bonds from which my I derive my (rent, interest, dividends, coupons) income from. At the moment, I don't work, but I live like semi-royalty because of that accumulated wealth. I'm afraid if commies or military take over then they'll tax me to the hilt or be forced to go overseas where I'll become a common tao (my wealth would be worth less if liquidated, converted to foreign currency, and moved overseas)."

The banality of evil, alive and well in 21^{st} Century Philippines.
Using the information found on the Genographic Project website's Atlas of Human Journey, i have drawn a Family Tree based on the Y-DNA Haplogroup classifications:

Figure 1: Human Family Tree Y-DNA

Click on image to enlarge

I encourage you to browse the image above as it has some interesting relationships.

**Update April-25-2008:** Based on the Family Tree above, i have measured the degree of separation of each Haplogroup to every other Haplogroup by working out a route via the nearest common ancestor which i then tabulated below.

Table 1: Degree of Separation between Haplogroups

Click on image to enlarge

For example, as shown below, the degree of separation between Haplogroup O3.M122 (i.e. a marker associated with China's first rice farmers who spread throughout China and Southeast Asia) and Haplogroup O1A.M119 (i.e. associated with the Austronesians, a linguistic group that includes present day Filipinos) is '2'. Both the Austronesians and China's first rice farmers share a common immediate ancestor i.e. Haplogroup O.M175 (i.e. the 'East Asian Clan').

Example 1: China's First Rice Farmers and the Austronesians

By way of comparison, the degree of separation between Haplogroup O3.M122 (i.e. China's first rice farmers) and Haplogroup C3.M217 (i.e. the Mongols with *Genghis Khan's Marker*) is farther with a value of '6'. In this case, we need to go back a few steps further up the family tree to find their common ancestor Haplogroup M168 (i.e. the 'Eurasian Adam').

Example 2: China's First Rice Farmers and the Mongols

This can be contrasted with the much smaller degree of separation between Haplogroup C3.M217 (i.e. the Mongols or *Genghis Khan's Marker*) and Haplogroup C.M130 (i.e. the 'Coastal Clan' from where the Australian Aborigines came from) which is '1'. This is because Haplogroup C3.M217 is a direct descendant of C.M130.

Example 3: The Mongols and the Australian Aborigines

It is also interesting to observe that the *Coastal Clan* Haplogroup C.M130, which includes the Australian Aborigines is more closely related to Haplogroup I.M170, known to be the ancestors of the Vikings...

Example 4: The Australian Aborigines and the Vikings

...than Haplogroup I.M170 is to the *Cro-Magnon* Haplogroup R1B.M343 to which many of today's Western Europeans belong.

Example 5: The Vikings and the Cro-Magnon

It is clear from the preceding examples that the previously established major racial categories (e.g. Caucasoid, Negroid, Mongoloid, and Australoid) are no longer scientifically valid.

**Update April-28-2008:** At the comments section, do check out a critique of the Genographic website's Haplogroup descriptions, which according to the commenter, is less accurate than the equivalent entry found in Wikipedia.
As explained by Nagel and Newman in their classic introduction to Kurt Gödel's landmark Incompleteness Theorem,*"...given any consistent set of arithmetical axioms, there are true arithmetical statements that cannot be derived from the set."*

A Mathematical System is based on a limited set of axioms, i.e. assertions or statements that are assumed to be true without the need for any proof.

Figure 1: Axioms as Self-evident Truths

Using the internal rules of the Mathematical System, these axioms can then be used as basis to determine whether other assertions within such a system are true or false. Assertions that are proven to be true are accorded the status of Theorems.

Figure 2: Proving Assertions

These theorems can in turn be used (together with axioms or other theorems) to prove or disprove other assertions via the same method of Deductive Reasoning. One would therefore expect that such an ongoing process of generating assertions and proving them would result in a mathematical system that is able to extend itself by uncovering or constructing more mathematical truths while, at the same time, avoiding false assertions that would allow inconsistency(-ies) to creep into the System. Gödel found out that this is not the case.

Figure 3: Consistent and Complete Mathematical System

(Click on image to enlarge)

What Gödel proved in 1931 was that avoiding inconsistency within the system comes at the expense of *completeness*, i.e. the system's characteristic of being *self-contained* (in other words, '*complete in itself*'). In a mathematical system based on axioms, there will always be assertions that are *true*, but whose truth cannot be proven from within the system on the basis of its axioms (or by way of the system's theorems). The truth of these assertions can be determined from outside the system [aka the 'Environment'], but not from within.

Figure 4: Consistent but Incomplete Mathematical System

(Click on image to enlarge)

Gödel's Incompleteness Theorem has a number of implications that have been explored at length, but i believe that one of the most significant, as explained by Douglas Hofstadter* is that:

*"...***provability is a weaker notion than truth**** no matter what axiomatic system is involved."

A timely reminder to those who count on a given system to always come up with *evidence* to establish *truth*. There are situations when lack of evidence does not negate the truth of an assertion. Sometimes, you just have to step outside the system to see that this is indeed the case.

**Update April-16-2008:** Here's an excellent discussion on Douglas Hofstadter's book Gödel, Escher, Bach (also known by its shortname *GEB*).

**Update April-25-2008:** It is also important to emphasize what Gödel **does not prove**, i.e. Gödel **does not** prove the romantic and anti-rationalist notion that "There are true things which cannot be proved".

*in his book Gödel, Escher, Bach: an Eternal Golden Braid

**Emphasis mine.
I just finished reading Lisa Randall's book Warped Passages, which i highly recommend especially now that the Large Hadron Collider (LHC), where many of the theories she discusses in the book will be tested, is about to start operating.

While Randall's main focus is on theories involving extra-dimensions, she explains a lot of related topics along the way, and for me, one of the most striking details she reveals has to do with the varieties and relative proportions of matter and energy in the Universe. Randall explains...

*"Dark Matter is the nonluminous matter that pervades the universe and has been discovered through its gravitational influence. Even though about ***one-quarter (25%) of the energy in the universe*** is stored in dark matter, we still don't know what it is...

...The universe contains dark energy** (energy not carried by any matter), that **constitutes seventy percent (70%) of the total energy of the universe**...No theory [is able to] explain dark energy."

By contrast, ordinary matter from which we are made of makes up **the remaining five percent (5%)**.

**Update April-20-2008:** Via 3Quarksdaily, an experiment that claims to detect Dark Matter in the form of Weakly Interacting Massive Particles (WIMPs).

Also, here's the web page for NASA's Wilkinson Microwave Anisotropy Probe (WMAP) that i mentioned in the comments section. It has further interesting information including this Timeline of the Universe.

**Click on image to enlarge**

In the above diagram, the acceleration of the Universe's expansion due to Dark Energy is noticeable.

**Update April-25-2008:** Over at Cosmic Variance, blogger-physicist Sean Carroll explains that the famous equation e=mc^{2} does not apply in the case of Dark Energy.*"Interestingly, the dark energy that makes up 70% of the energy of the universe doesn’t really have “mass” at all, since it’s not made up of objects (such as particles) that can have a rest frame — it’s a smooth field filling space."*

*Matter and energy is intergchangeable via e=mc^{2}.

**This mysterious Dark Energy is also known as Vacuum Energy and was first proposed by Einstein as the Cosmological Constant and more recently theorized as a new substance called Quintessence. Its presence is inferred by the observation that the expansion of the universe seems to be accelerating.