The Importance of Considering a Spherical Cow

In the post — “Don’t believe everything you hear–even on TED” — I instinctively rejected the claim that it takes the energy equivalent of a lump of coal to transport one MB of data on them internets. I said that I would do the back of the envelop calculation upon request. Here it is for your kind information.

First the estimation. Consider a spherical cow. No, scratch that. Let me get serious here for a moment. Follow me carefully, if you please, Mr Karma Yogi.

The maintained assumption is that all this is a rough calculation done to estimate something. As long as one is making reasonable estimates, the answer is robust and well within an order of magnitude.

1. One pound of coal has 1 kwh of energy [Source], or 3.6 mega Joules (mJ). One lump of coal is one ounce, say. Its energy content is therefore 225 kilo Joules (kJ).

2. Assume, as claimed in the TED presentation, that it takes the energy equivalent of one lump of coal to move one MB of data across the internet.

3. So combining (1) and (2), we get that it takes 225 kJ to transport one MB.

4. “As of March 2010, the global monthly Internet traffic is estimated to be 21 exabytes.” [Source: Exabyte.] Annual traffic is therefore 250 exabyte (250×10^18 bytes.)

5. Combining (3) and (4), the total energy required to transport bytes annually is 5.63×10^16 kJ.

6. The total annual world energy consumption is 43.7×10^16 kJ. [Source.]

7. Combining (5) and (6), we see that transporting bytes on the Internet takes around 13 percent of the total energy consumed by humanity.

8. World energy consumption by sector:

Industrial users (agriculture, mining, manufacturing, and construction) consume about 37% of the total 15 TW. Personal and commercial transportation consumes 20%; residential heating, lighting, and appliances use 11%; and commercial uses (lighting, heating and cooling of commercial buildings, and provision of water and sewer services) amount to 5% of the total.

9. In light of (8), the fact arrived at in (7) makes no sense at all.

10. Therefore by reductio ad absurdum, (2) is patently untrue. QED.

(You are welcome, Mr Karma Yogi.)

I have not done the calculations on exactly what percentage of total energy use is used in transporting bits. My sense is that it is of the order of 1 percent or so — which is an order of magnitude lower than the TED presenter’s claim.

Now here’s a more serious point that I want to make. I have noticed that in Indian schools and colleges, they do not teach people how to estimate quantities.

If I were to ask the average engineering graduate, for instance, what is the total market value of cars sold in India, I don’t think they will be able to give me a rough figure. Or say the size of the market for shampoo in India. Or how many pairs of shoes are sold, etc.

Once I asked a bunch of students at a very highly rated MBA school in India these sort of estimation question. Some did not even understand the question. One said, “But how can we know what the answer is without looking it up in the data bases?”

They don’t understand the notion of “order of magnitude” or the importance of “significant digits.” That innumeracy is quite widespread, unfortunately.

I have read stuff like this in newspapers:

“It is estimated that by 2014, the number of NRIs returning to India will be 205,473.”

How the heck do they know that it will not be 205,472? Or 205,474?

Recently seen on a billboard related to one construction site (weight lifting event site, if I recall correctly) for the CWG in New Delhi:

“Total project cost Rs 65,37,29,452.”

Thoroughly retarded. They don’t understand that the significant bits are just the 65 crores bit, not even the lakhs bit.

(With that kind of brains, is it any surprise that the CWG preparations were a mess.)

Anyhow, I think people should be taught these things. They should be able to consider a spherical cow. Too often we have to quickly decide if what we are reading or hearing is plausible or not. If these things are not taught, society ends up being overrun by gullible people — which of course is a sure recipe for disaster in a democracy.

Author: Atanu Dey


15 thoughts on “The Importance of Considering a Spherical Cow”

  1. Very good post. This also happens to be one of my favourite topics. In the software engineering community, estimation is only done for project deadlines and done (usually) without a basis. Though we keep hearing terms like ball-park figures etc. they are used mostly to say “I am going to give you a number and you can’t hold me against it”. Way back in college I had read a wonderful article by Jon Bentley about back of the envelope calculations (chapter 6 in his Programming Pearls collection). Yes, most people today lack that. Sad…


  2. To be quite fair, it is not retarded, or even surprising that the project cost was stated as Rs. 65,37,29,252. It is a contractual necessity that you bid an exact amount, and that the amount and other project details be displayed outside the project site. Certainly simpler to have some objective rules like these, and leave it to passers-by to glean the significant numbers from that gargantuan figure.

    All that aside, your point on the necessity of order of magnitude estimates is well taken.


  3. Take a look at this: China is spending money on high speed rail, bio technology, electric cars, electric rails and solar energy, ultra-modern airports. Friedman complains America is lagging behind and is competing with Mid East dictatorships while China is competing for the top spot in the world in terms of innovation and technology. Imagine if America is lagging behind according to Friedman, India is just going backwards–caste based census, affirmative action for colleges (diminishing whatever standards India even has in its few inisitutions with any standards), is the stupidity of those running things even curable? Indians read and take heart about India incurable slide towards even more backwardness with ignorant people and degenerates ruling the country….


  4. Atanu,have you considered the 30% thermal efficiency in converting coal to electricity? So, out of the energy content in coal you can consider only 1/3 as useful energy. Conversely, you need 3 times the heat energy of coal to produce 1 unit of electricity ( on heat energy terms).


  5. To add to my previous comment: Atanu, your broad point on “order of magnitute’ calculations is very valid. Until we develop that ability, we will accept any hype that passes off as information.


  6. Atanu,

    Cant agree with your claim that Indian colleges dont teach guesstimates. Yours truly is from one of the reputed MBA colleges in India and we were taught these guesstimates and back of the envelope calculations ad nausea, something like the number of pot holes in Calcutta 😉


  7. Good to know that you see TED talks. Given that TED has less to do with economics than with science, your viewing of TED talks must be due to seeds planted in you at IITK than those at Berkley at a much later stage of life. I assume you view TED frequently and write blog pieces on them. It would be good to see someone like you commenting on different TED talks.


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