The Broken Pillar Hypothesis

The Broken Pillar Hypothesis states thus: "A structure held up by pillars will soon collapse should the load imposed on it exceed the summation of the load specification of the pillars supporting it. Stated in another way, the summation of the load specification, L = sum of operating load carrying capacity of all pillars + sum of safety margin for all pillars. Once this load limit is exceeded, the pillars will fail in turn, beginning with the weakest pillar, until all the pillars have failed and the structure then collapses. As each of the pillars fail, the remaining pillars will have to take up the load (which remains unchanged). As the load distribution profile changes with each failed pillar, the rate of failure of the pillars rises exponentially".

This concept should be familiar to all students of Mechanics - you would have encountered this in your Statics classes in your A-level/Sixth Form days. However, this concept in Physics can be extended into management theory. This has interesting ramifications, as it opens up a new way of treating human resources.

The modified version of the Broken Pillar Hypothesis can be thus stated: "An organisation or team supported by a group of pillar can only remain in optimal condition if the workload/stress level imposed on it does not exceed the total workload/stress level which can be supported by the team. However, once this workload/stress level is exceeded, the team members will break down in turn, beginning with the team member with the lowest stress tolerance level, followed by other members in turn until all members break down. As the workload/stress profile changes with each member who breaks down, the rate of failure of team members rises exponentially.".

For humans, breakdowns are manifested as low morale, absenteeism, illness, nervous breakdown and at the extreme end, resignation.

With human resources, this problem gets more interesting as the tolerance level of each member is non-constant. This is because the tolerance level is dynamic and depends on a number of factors, both external and internal. Examples of external factors are family pressure, environment, whereas examples of internal pressure are health level, sleep deprivation and mental stamina.

Hence, it will be prudent for team leads/supervisors to be always aware of the state of each team member, and to ensure that workload is effectively dsitributed in a manner that each team member is capable of handling, whilst at the same time ensuring that the team member is sufficiently stretched to enable him/her to grow.

By the way, the Broken Pillar Hypothesis was my own idea. Perhaps it could be further expounded upon into a topic for a thesis and eventually formalised into a proper management theory.

Black Holes

I have been thinking of black holes for the past few days. The more I thought of it, the more fascinating I found black holes to be.

Black holes are sometimes referred to as space-time singularities. This is because matter is concentrated into a small area (which could either be a single point, or a radius of a few kilometers) with infinite density that the space-time fabric around the black hole is so distorted that even light cannot escape it. In simpler terms, gravitational force is infinite, so dominant that even massless particles such as photons are unable to escape a black hole. This is ironic because among the 4 fundamental forces of nature, gravity is the weakest (coming after the strong force, the weak force and the electromagnetic force).

The space-time fabric inside a black hole is so distorted that if any matter were to fall inside a black hole, the gravitational tidal forces will crush it. Imagine a hypothetical scenario where a spaceship went past the event horizon of a black hole (and is thus unable to escape it) and falls into the black hole. As it descends, gravitational tidal forces will rip apart the spaceship and constituent molecules. As it descends further, even the atoms are ripped apart into protons, neutrons and electrons. Further down, even the protons and neutrons get torn apart into quarks.

Now I have a little speculation here. Quantum physicists (especially proponents of the Standard Model) have proposed that gravitational force is mediated by gauge bosons known as gravitons. In the standard model, every particle has an anti-particle version of itself. Thus, if the hypothetical spaceship were to issue a continuous stream of anti-gravitons against the direction of travel, it could be sufficient to counteract the effects of gravity, hence allowing the spaceship to escape from the event horizon and save the crew.

Anyway, back to reality. Black holes cannot be detected directly through conventional optical telescopes as they do not emit light. Thus they are detected indirectly using gravitational lensing or by detecting X-ray radiation emitted by objects when they fall into a black hole. Thus only advanced observatories will be able to detect black holes.

Dr. Stephen Hawking theorized that at the other end of a black hole is a white hole, where matter that is sucked into a black hole is spewed out (albeit in a different form) at the other end. This will then be used to form new universes at the other end. This is another instance of how black holes pose a paradox – an agent of destruction works simultaneously as an agent of creation. Isn’t our universe wonderful?

Memristors - the fourth passive circuit element

I was baffled when I first read of memristors in the October 1-15 edition of EE Time Asia. Conventional wisdom (and many years of studying electronics) have conditioned electrical engineers to think that there are only 3 passive circuit elements, i.e. resistors, inductors and capacitors. Naturally, my curiosity was piqued when I read this feature article on memristors.

Historically, the memristor was postulated in 1971, and named such as an abbreviation for "memory resistor". Technically, a memristor is a passive circuit element that relates flux to charge in the same way resistors relate voltage to current, capacitors relate voltage to charge and inductors relate flux to current.

According to Wolfgang Porod, an electrical engineering professor at Notre Dame University, a resistor relates voltage to current and the memristor relates flux to charge. However, if you sum up flux over time, it becomes a voltage, and if you sum up charge over time it becomes a current. So a device that relates flux to charge, like a memristor, will over time relate voltage to current like a variable resistor, whose resistance changes its value depending on how much and in which direction current has flowed through it.

The nost immediate application for memristors is in the area of memory. As a memristor's resistance changes as current flows through it, it is possible to build an entirely new kind of memory using crossbar switches. Zeroes and Ones can be determined based on the difference in resistivity of each point of the array.

Once this technique has been perfected, it will be possible to produce high-density memory arrays cheaply. Once it has reached critical mass, it could possibly sound the death knell for current solid state memory technologies e.g. NOR and NAND RAM.

Boson and fermions?

Yes, the URL of this blog has drawn many questions. Bosons? Fermions? Some have even thought that this blog is about bosoms and femininity.

Nothing could be further from the truth. Bosons and fermions make up all fundamental and composite particles. Bosons are particles with integral spin, whereas fermions are particles with half-integer spins.

The reason behind their exotic names lie with their inherent behaviour. Fermions obey Fermi-Dirac statistics, whereas bosons obey the Bose-Einstein statistics. All force carriers are bosons. Force in this context refers to the 4 fundamental forces of nature i.e. the strong force, the weak force, electromagnetism and gravity. A commonly observed boson are photons, which are light particles. On the other hand, fermions make up matter. Fermions can be further divided into leptons and quarks. A well-known example of leptons is the electron. However, quarks are not found in isolation in nature. Rather, they are found in groups of triplets to form composite fermions. Protons and neutrons are common examples of fermions.

The subject of fermions and bosons is a large field, too large for single blog posting to encapsulate. Nonetheless, it is my aspiration to shed some light on physics, whilst ocassionally weering off into classical music, philosophy and history. Hopefully it will be of benefit to you, the reader.

The big bang

No, not the big-bang as envisioned by Dr. Stephen Hawking or Edmund Hubble, but more of a way to announce my little step into the world of a blogger.

Watch this space...