The Roman civilization was one of the largest the world has known. At its height, the Roman empire included most of western Europe, all of Britain except Scotland, parts of Northern Africa, Egypt, Greece, Turkey, and the region around Jerusalem known as Judaea. The civilization had a big impact which lasts to this day. The towering columns in the entrance of the White House in Washington D.C. are based on that of Roman temples. Everyone knows the sayings: “All roads lead to Rome”, and “When in Rome, do as the Romans do.”

The Romans are famous for grand buildings, engineering, aqueducts, amphitheatres, baths, roads, military organization, vast empire, and gladiatorial games. At its height around 100 AD, the population of the empire was around 56 Million, which constituted around one third of the then world population. Some famous people of Rome include – the great general and dictator Julius Caesar; Brutus, the senator who led the assassination of Caesar; the statesman and orator Cicero; the despotic emperor Nero; the conqueror Trajan; Marcus Aurelius, emperor.

The Roman empire came into being with the founding of Rome ca. 753 B.C., by the twins Romulus and Remus on the banks of the Tiber river. Romulus was the first king of Rome. He was followed by a succession of kings, the last of whom was overthrown around 500 B.C., and Rome became a republic. The republic was run by a group of senators who acted as the government. They framed the laws and dictated policy. Some senators had specialized roles – some were judges, some were governors of provinces, some were in charge of finances, some managed public activities and events, some were in charge of civic infrastructure. There were around 100 senators in all.

Rome conquered Greece around 200 BC. The Romans were heavily influenced by the Greeks in various ways. Their grid-like town layout is influenced by that of the Greeks. The famous Roman columns are inspired by those found on Greek temples. Several Greek statues made originally in bronze survive today only as copies made in stone by the Romans.

How did the Roman empire become so powerful? Romans were very good at engineering and organization. Their roads and bridges are prime examples of their skills in engineering. Roads enabled the army to march quickly to cover vast distances, something that is of essence in a war. Their military organization and tactics were superior to that of their opponents. One can see similarities between the Roman military, and modern corporations. The military stressed on training and process, rather than individual bravery. Soliders were not born; they were made. Each new soldier underwent rigorous training as part of his induction into the army. As the army marched to war, every night a camp was made. These camps were extremely well organized. Every camp was laid out in the same way, so that anyone could make his way around them easily. Soldiers had to know how to build a fence and pitch tents. Every soldier carried a shovel as part of his standard equipment. In battle as well, training trumped individuality. Soldiers were taught how to fight. They were trained to defend and conserve energy, and attack when the opponent was vulnerable. Contrast this with the dash and slash heroic depictions of soldiers in popular movies.

Around 50-45 B.C., Julius Caesar became a very powerful man in Rome. He was a great military leader, and was also a consul, who was a special senator and had more powers. There were two consuls at any time. As Caesar became more powerful, his designs became grander, and finally he declared himself dictator of Rome. This obviously didn’t go down too well with the senators, who always thought of Rome as a republic. In fact, Rome became a republic by overthrowing a despotic monarch. Caesar had crossed the line. In 44 B.C. a group of senators led by Brutus and Cassius assassinated Caesar. Brutus and others intended to restore the republic, but their plan was not made well. Rome plunged into a civil war for several years. In 31 B.C., Caesar’s heir Octavian defeated Mark Antony and Cleopatra (the Egyptian queen) in the Battle of Actium. Octavian went on to become the first emperor of the Roman Empire, and took on the name of Augustus.

Augustus was followed by a succession of emperors – Tiberius; Caligula; Nero (ca. 64 A.D. fire of Rome); Vespasian (ca. 70-79AD), in 70 AD commissioned the building of the Colosseum; Titus, conquered the Jews in 70 AD (commemorated by the arch of Titus in Rome); Trajan, conquered new regions, the empire was at its largest extent in his reign; Hadrian, built a wall around the borders of the empire (now known as Hadrian’s wall); Marcus Aurelius (ca. 161 – 180 A.D.). After the rule of Marcus Aurelius, Rome was increasingly attacked by barbarian tribes – Visigoths, Ostrogoths, Vandals, Gauls. Constantine (ca. 330AD) shifted the capital from Rome to Constantinople (present Istanbul, Turkey). The empire was split into two parts – an Eastern empire and a Western. The Eastern empire went on to be called the Byzantine empire (Justinian, ca. 500 A.D.). The Western empire was overrun by barbarians. In around 470 A.D., the last Roman emperor (also called Romulus) was deposed. This event is conventionally thought to signify the end of the Roman empire.


Posted in Uncategorized | Tagged , , | Leave a comment

When To Postpone Tasks And When Not To

We saw earlier a number of reasons why we postpone tasks. Some of them are reasonable, while others belong to the procrastinators. Here, we’ll look at some valid reasons to postpone a task, as well as when we should not postpone a task.

First, some valid reasons to postpone a task:

  1. The task is not worth accomplishing. Completing it requires more effort than its benefits deserve. In this case, the right thing to do is to strike the task off the list.
  2. Postponing will enable accomplishing the task in a better way. For example, you might obtain more information.
  3. Postponing will result in lesser effort. For example, the task might be combined with another task which will have to be done in the future. Or, in the procrastinator’s viewpoint, someone else might complete the task, resulting in you avoiding any effort altogether.

Some reasons why you should not postpone tasks:

  1. Postponing causes a fixed cost to be incurred. For example, forgetting to pay a bill on time and incurring a penalty.
  2. Postponing causes gradually increasing loss. For example, if a library has a penalty for each day of delay in returning a book.
  3. Postponing causes an increase in probability of incurring a high cost. For example, the greater the number of days you don’t service your car, the higher the chances that some component gets damaged.
  4. Postponing increases the chances that you will forget to complete the task for a while. This will in turn increase the costs either in manner of points 1, 2, or 3 above.
  5. By far a big reason to not postpone, is that while the task is not done, there is a cognitive load that the task imposes. You have to carry around the task in your head, lest you might forget and invoke point 4. This again is a gradually increasing loss of the type of point 2.
  6. For an alternate viewpoint (and one opposite to that of the procrastinator in point 3 in the previous list), postponing might result in the task being called off, or someone else accomplishing it. This results in you losing the credit of accomplishment, as well as the experience gained while accomplishing it.

Both the above sets of viewpoints have to be taken into account while deciding whether to postpone a task.




Posted in Uncategorized | Tagged , , , , | Leave a comment

Travel Pricing

Let’s look at a simple example of travel pricing. Say there is a train route from Bangalore to Mumbai. Tickets are two way, for simplicity, with the onward journey on Friday, and the return journey on Sunday. Such tickets are an example of perishable inventory. If a seat is not occupied on a certain day, it is a waste. It cannot be stored for a future date. In this case, tickets are non-transferable, and non-cancellable. To keep things simple for the analysis, assume for now that there is only one seat. The cost of a two way train run is Rs.500 to the train company (say FastTrack), and the minimum fare is set at say Rs.1000. Hari wants to travel there each week. He derives a benefit of Rs.1500 each trip, and is ready to pay upto Rs.1000 for the ticket. If he pays a fare of Rs.1000 and travels, he gets a net benefit of Rs.500, and FastTrack makes a profit of Rs.500. Over a period of 10 weeks, Hari travels 10 times, pays a total of Rs.10,000, with a net benefit of Rs.5000 to him, and Rs. 5000 to FastTrack. The overall benefit in our toy economy is Rs.10000.

Ganesh is a different type of traveller. Everytime he travels, he gets a benefit of Rs.3000, and so is willing to pay upto Rs. 2000 per trip. However, he is not sure if he will travel or not in a given week. All he knows is that he will travel roughly half the time. He will come to know only on Wednesday, whether he is travelling that week. However, the ticket booking opens on Monday. What happens now?

Since the ticket price is only Rs.1000, Ganesh can anyway book 10 tickets, one each Monday, for a cost of Rs.10000. The benefit to FastTrack remains the same, Rs.5000. Ganesh travels 5 times, with a total benefit of Rs. 15000. Net benefit to Ganesh is Rs. 5000. Again, the total benefit in the economy is Rs.10000. But what about the other 5 times when Ganesh doesn’t travel? The seat that Ganesh booked is vacant, while Hari is willing to travel. This is surely a wasteful situation which can be improved. But how? On the other hand, Hari can also the book the same ticket each week ahead of Ganesh. Hari gets to travel 10 times, and Ganesh none. The total benefit is Rs.10000. However, notice that Ganesh’s travel is more beneficial to the economy than that of Hari’s. This suggests that we should look for a scheme that allows Ganesh to travel when he wants, and Hari otherwise. Such a scheme is likely to increase the total benefit.

One possibility is to have two classes of ticket. Let’s call them ‘preferred’ and ‘regular’. Preferred tickets are priced at Rs. 2000, and regular at Rs. 1000. When the booking opens on Monday, there is only 1 preferred ticket, and 0 regular tickets. Any available preferred tickets on Thursday morning are changed to regular tickets. On Monday, Hari doesn’t book the preferred ticket, since he can’t afford it. Ganesh waits, since he’s not sure at this point, if he is going to travel. On Wednesday, he comes to know. If he’s travelling, he books the preferred ticket at Rs.2000. He doesn’t wait till Thursday for the ticket to become regular, since he can’t be sure then if he will get the ticket. Hari doens’t travel that week. On the other hand, if Ganesh is not travelling, then he doesn’t book the preferred ticket on Wednesday. On Thursday morning, the ticket becomes regular, and Hari now books the ticket.

Let’s compute the benefit now. Ganesh travels 5 times paying Rs.2000 each time. His benefit is Rs.15000, and cost is Rs.10000, for a net benefit of Rs.5000. Hari travels 5 times, with a net benefit of Rs.2500. FastTrack makes Rs.1500 on each of 5 of Ganesh’s tickets, and Rs.500 on each of 5 of Hari’s, for a net benefit of Rs.10000. Now we see that the net benefit in the economy has risen to Rs.17500. This is made possible by the ticket scheme that we came up with. Of course, other schemes are possible. In reality, there are a lot more factors to consider, and more people wanting to travel, each with varying requirements. We will analyse more such situations in a later article.


Posted in Uncategorized | Tagged , , , , , , | Leave a comment

Quotes on Inquiry


  • It is error only, and not truth, that shrinks from inquiry. -Thomas Paine, philosopher and writer (1737-1809)
  • Basic research is what I am doing when I don’t know what I am doing. – Werner von Braun
  • They know enough who know how to learn. – Henry Adams
  • Every discovery opens a new field for investigation of facts, shows us the imperfection of our theories. It has justly been said, that the greater the circle of light, the greater the boundary of darkness by which it is surrounded. – Humphry Davy
  • The aim of an argument or discussion should not be victory, but progress. – Joseph Joubert, essayist (1754-1824)
  • A teacher affects eternity; he can never tell where his influence stops. – Henry Adams
  • It is not because the truth is too difficult to see that we make mistakes. It may even lie on the surface; but we make mistakes because the easiest and most comfortable course for us is to seek insight where it accords with our emotions — especially selfish ones. – Aleksandr Solzhenitsyn
  • To teach is to learn twice over. – Joseph Joubert
  • My own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose. – J. B. S. Haldane
  • We suffer primarily not from our vices or our weaknesses, but from our illusions. – Daniel Boorstin
Posted in Uncategorized | Tagged , , , , , , | Leave a comment

Bad Visualization

Have a look at this graph, which depicts the money raised in awareness campaigns for various health problems, and the number of deaths from the same problems.


Donations vs Deaths - Bad Graph

Donations vs Deaths – Bad Graph


Is there something seriously wrong with this graph? There is. I’m not going to analyse the subject matter here, but use this graph as a fine example of bad visualization.

Look at the first two circles under ‘Deaths (US)’. Heart disease kills around 600,000, whereas Chronic Obstructive Pulmonary Disease kills 142,000. This is a ratio of about 4:1. Now look at the two circles again. Are their sizes in the ratio of 4:1? Not at all. The first circle looks incredibly bigger than the second. It’s tough to compare the areas, but one would guess at a ratio of atleast 10:1. This is true of all circles on the graph. The issue here is that although the quantities are represented as circles, the radius of the circles, and not the area, is proportional to the quantity. Since the area is proportional to the square of the radius, the ratios appears much more than they actually are. So a ratio of 4:1 visually appears as 16:1! When a quantity is represented as an area, one naturally expects that the area of a figure is directly proportional to the quantity, not the square of the quantity, which misleads us in this case.

Consider the figure below for an illustration:



Are the quantities really in the ratio 1:2:4? The correct way to represent these quantities is as below:



Now they really appear to be in the ratio 1:2:4.

Graphs are useful, and visualizations are a powerful way to depict information in a way that can be easily grasped. But this example shows how it can be misused, and that one needs to be careful while choosing a suitable visualization of the data. Also as a reader, one needs to be careful while reading such graphs, lest we are misled, intentionally or unintentionally.

This is a better way of showing the above data:

Donations vs Deaths - Better Graph

Donations vs Deaths – Better Graph



Posted in Uncategorized | Tagged , , | Leave a comment


The Colosseum is a vast amphitheater in Rome, built to host gladiatorial events. It was commissioned in 70 AD by the Roman emperor Vespasian. After 10 years of building, it was inaugurated by the emperor Titus in 80 AD. What made this amphitheater different from the earlier ones was that this was meant to be permanent, and hence was made of stone (mostly travertine) and concrete, whereas the previous ones were temporary, made in wood.




An audience of around 50-70,000 could be seated at the Colosseum. For comparison, the Lord’s cricket ground in London seats 28,000, and the ‘Bird’s Nest’ Beijing National Stadium, which was used to host the 2008 Olympics, seats 90,000. The seating in the Colosseum was surprisingly well organized. People got clay tickets to view the event, although the entry was free. There are 76 entrances. People would use a particular entrance based on their social standing. The ticket had the entrance number, the level of the stand, and the seat number inscribed on it.




The above picture shows an inner view of the Coloseum. The Colosseum showcases the engineering and architectural skills of the Romans. There are five levels of seats. Over the topmost level, a moveable canvas, known as ‘velarium’ stretched out as a shade against the sun and rain. Sailors were specially enlisted to work this canvas. The upper classes of society sat on the lower levels, which offered a closer view of the arena, whereas the commoners had to make do on the upper levels. On the far side of the arena, we can see a partially reconstructed wooden ground. The original arena was also made in wood, and covered with sand. The sand served to absorb the inevitable blood shed in combat. In fact, the English word ‘arena’ is derived from the Latin ‘arena’, meaning sand. One can also see a basement level, below the wooden floor. This level is filled with passageways. These housed any items required for the show. For example, animals were made to appear out of the ground, by lifting them out from the basement level out of trap doors built into the wooden floor. The presence of aqueducts leading to the Colosseum has seeded the theory that in the earlier days of the Colosseum, these passageways didn’t exist, and the basement level was empty. This enabled water games to be conducted, by removing the wooden floor, and filling the basement level with water. Later on, the passageways were constructed, after which water games could not have been conducted.

A 100 days of games were held to inaugurate the building. There were two types of events. The morning sessions had events involving animals and hunters, whereas the afternoons had fights between gladiators. These fights (and more about the period) are graphically depicted in Ridley Scott’s 2000 movie, ‘Gladiator’. Events were held around once a month, and lasted for a few days at a time. Gladiators consisted of prisoners and slaves – men who had little to lose. They served a contract with their leaders or managers to fight for a fixed period of time, say 10 or 15 years. If they managed to survive the contract, they were free. Some even managed to become rich.

The last games were held in the Colosseum sometime in the AD 500s. An earthquake in the 1300s led to partial destruction of the building. The Colosseum eventually became a quarry of sorts. The travertine stone blocks were removed to be reused elsewhere. The decorations on the walls were also removed, probably stolen. A huge bronze statue of Nero nearby led to the current name of the building (colossal = huge). The name doesn’t have anything to do with gladiatoral events. Supposedly the Romans had a different name for the building when it was in use.

Why was the Colosseum built at all? It didn’t generate any revenue, since the tickets were free. The emperors surely had good reason to dedicate a vast amount of resources – building material and manpower – to such an undertaking. Partly the reason might have been political. The emperors did it to gain favour with the public, knowing that such an arena would be very popular.


Posted in Uncategorized | Tagged , , , , , , , | Leave a comment

Chess in Russia

Looking at the list of world chess champions over the years, one can’t help noticing a large number of Russians. The breakup by nationality is as follows:

  • USSR – 8 (Alekhine, Botvinnik, Smyslov, Tal, Petrosian, Spassky, Karpov, Kasparov, Karpov, Khalifman, Kramnik)
  • Germany – 1 (Lasker)
  • India – 1 (Anand)
  • USA – 1 (Fischer)
  • Austria-Hungary – 1 (Steinitz)
  • Cuba – 1 (Capablanca)
  • Netherlands – 1 (Euwe)
  • Bulgaria – 1 (Topalov)
  • Norway – 1 (Carlsen)
  • Ukraine – 1 (Ponomariov)
  • Uzbekistan – 1 (Kasimdzhanov)

I’ve always felt there were a lot of Russians there, but the actual number is surprising – each of the other countries has only 1 champion, while Russia has 8! This is no coincidence. It stands to reason that Russia produces good chess players.

What factors can be at play here? One is geography. This factor exhibits itself in several ways. Almost any sport requires a local community of players. Clubs encourage people to play more. Discussions are an essential aspect of learning. Competition motivates players to improve their gameplay. Further, simply having more players improves the chances of discovering players with great talent. Having world champions also helps motivate people into playing.

The above are advantages of having a large local community. How does such a community get formed in the first place? Why chess and not other sports? One contributing factor might be that winters being especially harsh in most of Russia, people would spend more time indoors playing chess, than outdoors playing football (so to speak). I also know that Russia has world class mathematicians. (Many results of American mathematicians were later shown to have been obtained by Russians at an earlier time. Most Russian work being written in Russian, it was all but inaccessible to Americans.) Russian literature is of course, well known around the world. Who hasn’t heard of Tolstoy, Dostoevsky or Chekov?

How much of a role do genetic factors play here? Are there genetic traits which are helpful in chess? Memory surely plays a big role. Are Russians especially good at remembering? Creativity and risk-taking are surely lower on the list of essential qualities. Becoming a great chess players demands a lot of perseverance. One has to play hours on end for years together. Talent is only part of the requirement. A greater requirement is practice. One needs focus and patience to become a great player. Ability to visualize possibilities in the mind is another important quality. How much of these traits can be attributed to genes?


Posted in Uncategorized | Tagged , , , , , | Leave a comment