October 20th, 2010 by Moti Karmona | מוטי קרמונה · 3 Comments
I have just finished reading a very interesting book (!!!) “Predictably Irrational” by Dan Ariely and came across a very interesting historic story.
“In 210 BC, a Chinese commander named Xiang Yu led his troops across the Yangtze River to attack the army of the Qin (Ch’in) dynasty. Pausing on the banks of the river for the night, his troops awakened in the morning to find to their horror that their ships were burning. They hurried to their feet to fight off their attackers, but soon discovered that it was Xiang Yu himself who had set their ships on fire, and that he had also ordered all cooking pots crushed.”
“Xiang Yu explained to his troops that without the pots and the ships, they had no other choice but to fight their way to victory or perish. That did not earn Xiang Yu a place on the Chinese army’s list of favorite commanders, but it did have a tremendous focusing effect on his troops (as they grabbed) their lances and bows, they charged ferociously against the enemy and won nine consecutive battles, completely obliterating the main-force units of the Qin dynasty”
Prof. Ariely is making a point about the advantage of making a choice to focus by closing other doors/options/opportunities.
Joshua Baer had an interesting allegory to the startup world in his “Necessity is the mother of Invention” post
“This is similar to when a bootstrapper enters the Valley of Death* and commits to their venture, but before they are making money and cash flow positive. They are forced to figure out how to make it work with what they’ve got. The timeline is not completely in their control.
We’re always tempted to leave ourselves an escape route or path of retreat. And usually that’s a good idea. But sometimes there aren’t enough resources to mount the attack and cover the retreat. In order to be successful sometimes you have to commit the resources to what you believe in because the retreat option isn’t acceptable. Sometimes once you head down a path there is just no turning back, so you might as well commit all of your resources to getting to the end”
Well… this is true but since I am a notorious pessimist and usually like my options open, I have continued reading about this fine gentlemen (a.k.a. Xiang Yu)
I learned that indeed in the beginning of the civil war Xiang Yu was winning but with his rude manners, arrogance and lack of political vision, the tide turned against Xiang Yu and in the end he lost the war to Liu Bang.
In 202 BC, when Xiang Yu and his remaining men had their backs against the river while surrounded by Liu Bang’s troops, a boatman on a raft persuaded Xiang Yu to go with him across the river so he can prepare a comeback.
Xiang Yu said, “When I crossed the River and went west, I took with me 8,000 sons and brothers from east of the Yangtze. Now none of them has returned; how can I face the elders east of the Yangtze?” After declining this offer, Xiang Yu turned around, charged against the Han troops, killed over a hundred men, and finally cut his own throat.
Shortly after his death Liu Bang established the Han Dynasty.
Three concluding facts about Xiang Yu:
- Xiang is popularly viewed as a leader who possesses great courage but lacks wisdom, and his character is aptly summarized using the Chinese idiom “Yǒu Yǒng Wú Móu” (有勇無謀) – “Having Courage but No Strategies” (or to be foolhardy or to be more brave than wise or to have reckless courage…)
- Xiang’s battle tactics were studied by future military leaders while his political blunders served as cautionary tales for future rulers
- Xiang Yu is also the kind general that raided the Terracotta** tomb less than five years after the death of the First Emperor – Xiang’s army was looting of the tomb and structures holding the Terracotta Army, as well as setting fire to the necropolis and starting a blaze that lasted for three months.
“Yǒu Yǒng Wú Móu” (有勇無謀) – “Having Courage but No Strategies” – Think about it…! ;)
* Valley of Death – A slang phrase to refer to the period of time from when a startup receives an initial capital contribution to when it begins generating revenues.
During the death valley curve, additional financing is usually scarce, leaving the firm vulnerable to cash flow requirements.
** The Terracotta Army or the “Terra Cotta Warriors and Horses“, is a collection of terracotta sculptures depicting the armies of Qin Shi Huang, the First Emperor of China
The figures, dating from 210 BC, vary in height according to their roles, with the tallest being the generals. The figures include warriors, chariots, horses, officials, acrobats, strongmen, and musicians.
Current estimates are that in the three pits containing the Terracotta Army there were over 8,000 soldiers, 130 chariots with 520 horses and 150 cavalry horses, the majority of which are still buried in the pits.
There is also a legend that the terracotta warriors were real soldiers, buried with Emperor Qin so that they could defend him from any dangers in the next life.
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p.s. Prof. Ariely also recommends another role model for door closing – Rhett Butler for his supreme moment of unpredictable rationality with his astonishing elan, “Frankly my dear, I don’t give a damn”
Tags: Conspiracy · Leadership · People · Psychology · Strategy
October 9th, 2010 by Moti Karmona | מוטי קרמונה · 6 Comments
Well.. Everyone are talking about Location-Location-Location so this weekend was all about Geographical distance
I will quickly preview few basics (geographic coordinate system, earth radius), introduce and compare four distance calculation models (Pythagorean, Law of Cosines, Haversine, Vincenty), finalize with a pragmatic recommendation (use Law of Cosines! :) and random quote for desert.
Start with the basics…
A Geographic Coordinate System Indicate location using lines of longitude and latitude
Latitude is the angle between the equatorial plane and a line that is normal to the reference ellipsoid, which approximates the shape of Earth to account for flattening of the poles and bulging of the equator.
Longitude is the angle east or west of a reference meridian between the two geographical poles to another meridian that passes through an arbitrary point. All meridians are halves of great circles, and are not parallel. They converge at the north and south poles.
The Status of Liberty is located on 40° 41′ 21″ N , 74° 2′ 40″ W with the following Decimal representative: 40.689167, -74.044444
40.689167 = Degrees + Minutes/60 + Seconds/3600 = 40 + 41/60 + 21/3600 = 40.689167
-74.044444 = -1*(74 + 2/60 + 40/3600) = -74.044444 // the minus is used to represent South & West
What is Earth Radius? (hint: we will need later for the calculation)
To cut a *very* long story short, Google, IUGG and Karmona labs thinks it is 6378.137 (3963.19 miles)
Because the Earth is not perfectly spherical, no single value serves as its natural radius.
Distances from points on the surface to the center range and regardless of calculation model, the radius falls between 6,357 km and 6,378 km
Earth Radius (km) based on different models
Geographic Distance Calculation Models
There are quite few geo distance calculation models but I will focus on the four I found most relevant:
* Law of Cosines
I have done a little excel experiment (downloadable here):
- I have compared the distance between “The Empire State Building” and 15 other locations
- I have used three geo distance calculation models (beside Vincenty)
- Modeling this into Excel – I had two locations A (latA, longA) and B (latB, LongB) with R as Earth Radius (coordinates are used in their decimal representative)
- Pythagorean =SQRT((111.2*(latA-latB))^2+(85.2*(LongA-LongB))^2)
- Law of Cosines =ACOS(SIN(RADIANS(latA))*SIN(RADIANS(latB)) + COS(RADIANS(latA))*COS(RADIANS(latB))*COS(RADIANS(longA-longB)))*R
- Haversine =2*ASIN(MIN(1, SQRT(SIN(RADIANS(latA-latB)/2)^2 + COS(RADIANS(latA))*COS(RADIANS(latB))*SIN(RADIANS(longA-longB)/2)^2)))*R
- Additional Notes:
- The reason I have used 111.2 and 85.2 in the Pythagorean equation is the fact that 1° latitude ≈ 111 km and 1° longitude can vary but the average is ≈ 82.2 km (the right thing to do actually is to choose the exact longitude/km conversion base on the degree)
- The conversion from the original Geo Location representative to a decimal one was using this excel formula =IF(Degree<0,Degree-Minutes/60-Seconds/3600,Degree+Minutes/60+Seconds/3600)
- The Results
- Pythagorean is easy to compute but not that accurate
- Law of Cosines and Haversine are almost the same
- See comparison table below…
|Model||Pythagorean||Law of Cosines||Haversine||Vincenty|
|Formula||d = sqrt((X2 – X1)^2 + (Y2 – Y1)^2)||a = sin(lat1) * sin(lat2)|
b = cos(lat1) * cos(lat2) * cos(lon2 – lon1)
c = arccos(a + b)
d = R * c
|dlon = lon2 – lon1|
dlat = lat2 – lat1
a = sin^2(dlat/2) + cos(lat1) * cos(lat2) * sin^2(dlon/2)
c = 2 * arcsin(min(1,sqrt(a)))
d = R * c
|Too long… ;) |
|Assumptions||Flat Earth… :)||Spherical Earth||Spherical Earth||Ellipsoidal Earth|
|Accuracy (Worst | 1-5 | Best)||(1) Estimated distance (good enough for less than 20km)||(4) Good!||(4) Good! + The Haversine formula is more robust to floating point errors||(5) Great! The most accurate…|
|Computability (Slowest | 1-5 | Fastest)||(5) Fastest!||(4) 5-6 trig. calls||(3) 5 trig. calls + SQRT (+ Floating Point)||(1) Requires iteration (+ “The rest”)|
- Simple pragmatic recommendation – Use Law of Cosines to calculate geographic distance – It will be suffice in 90% of your usages !
- Complex pragmatic recommendation – It really depends – Call me…
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Random Quote: “There’s no sense in being precise when you don’t even know what you’re talking about” | John von Neumann