On Celebrating Birthdays

There could be many reasons to celebrate a birthday:

  • came a year closer to adulthood
  • survived one more year
  • chance to party!
  • gifts! Cake! food! Drinks!
  • chance to get b’day bumps without fear of being labeled a masochist

But several months ago, an old person remarked to me, “I hate celebrating my birthday because it means being a year closer to the end”. That reasoning looked irrefutable. I mumbled something about surviving another year, and slunk away. Although this happened several months ago, the thought stayed with me. I felt there had to be something wrong with this argument. And then, a few days ago, I realized how a refutation was possible. That is what I want to cover in this article.

“A year gone, hence a year closer to the end” — is based on the assumption that the end is fixed, that the moment of death is destined, frozen in advance. But in fact, the future is not frozen — it holds many possibilities. For example, one may become a centenarian, or one may die in a freak accident tomorrow. However, one can use statistics to estimate one’s chances of survival. Now, it turns out that by following this statistical reasoning, one can show that “a year closer to the end” is wrong thinking. However, before I develop this argument properly, we must take a detour into some necessary concepts: lifespan, life expectancy, mortality rate, and life table.

Lifespan is simply the number of years a person lives. Obviously, it can only be determined post facto, after he or she is gone.

Life Expectancy is the average lifespan of a population, again measured post facto, after every single individual is gone.  Note that a “population” may be chosen in different ways — e.g. all individuals in a state or country, or only the females in a region, or only females within a certain income range, or only Japanese females within a certain income range, and so on. Once such numbers are collected for a large sample size, interesting patterns emerge. For one thing, one can determine how many people died between age n and n+1. This number, generally expressed as a count per 100,000, is called mortality rate.

It turns out that mortality rate is not constant. See the chart of age versus mortality rate below (males, USA, 2010)  [9]. There is a blip of high child mortality, then a long tail that builds into a tall peak in ripe old age. The area under the bars equals 100,000. Notice that had the mortality rate been constant, the curve would have been flat at height ~1000 (assuming max age of 100 years).


C(n) = Conditional life expectancy at age n is the average lifespan of a population that has already survived to age n. Clearly, life expectancy = C(0). In the chart, C(0) is 79. Visualize it as the point along the horizontal axis where the blue shape will balance on a knife edge.

Now we come to something interesting: how does one calculate C(n) for various values of n? Notice that with increasing values of n, one discards the individuals that did not survive to age n. That is, the blue bars to the left of n are to be discarded. It is obvious that the knife edge has to be shifted to the right to keep the truncated shape balanced. That is, C(n) keeps increasing with n.

One can also understand why C(n) rises by using an analogy. Consider a pile of pebbles of various sizes. Each pebble represents a person, and the pebble’s weight represents the person’s lifespan. Say, a 5 gram pebble corresponds to a lifespan of 5 years, a 100 gram pebble corresponds to 100 years. Of the initial pile, the average pebble weight represents life expectancy. Now, to find C(n), we remove all pebbles weighing less than n grams. Then C(n) is the average weight of the remaining pile. It should be obvious that as we keep increasing n, that is, keep throwing out the lighter pebbles, the average weight keeps on increasing.

Life table is simply a table of C(n) for different values of n. An abbreviated table adapted from [4] is given below (note: sampled population is different than that of the previous chart).

Table: Conditional Life Expectancy C(n) versus age

AGE C(n) AGE C(n) AGE C(n) AGE C(n)
0 76.33
1 76.81 26 77.58 51 79.79 76 86.51
2 76.84 27 77.65 52 79.94 77 86.93
3 76.86 28 77.72 53 80.11 78 87.36
4 76.88 29 77.79 54 80.29 79 87.81
5 76.89 30 77.86 55 80.47 80 88.28
6 76.90 31 77.93 56 80.67 81 88.76
7 76.91 32 78.00 57 80.87 82 89.27
8 76.92 33 78.07 58 81.09 83 89.80
9 76.93 34 78.15 59 81.32 84 90.34
10 76.94 35 78.22 60 81.55 85 90.91
11 76.94 36 78.29 61 81.79 86 91.50
12 76.95 37 78.37 62 82.04 87 92.11
13 76.96 38 78.44 63 82.30 88 92.74
14 76.97 39 78.52 64 82.57 89 93.40
15 76.99 40 78.60 65 82.84 90 94.08
16 77.02 41 78.68 66 83.12 91 94.79
17 77.05 42 78.76 67 83.40 92 95.52
18 77.08 43 78.85 68 83.70 93 96.27
19 77.13 44 78.95 69 84.01 94 97.05
20 77.18 45 79.04 70 84.32 95 97.85
21 77.24 46 79.15 71 84.66 96 98.68
22 77.30 47 79.26 72 85.00 97 99.53
23 77.37 48 79.38 73 85.36 98 100.39
24 77.44 49 79.51 74 85.73 99 101.27
25 77.51 50 79.64 75 86.11 100 102.15

A full plot of C(n) vs n is given below. It is obvious that life expectancy rises with age, especially after age 60.

Conditional Life Expectancy C(n) vs age

So now it is time to refute “passing of one year brings one a year closer to the end”. Why is this incorrect? First of all, the future is not fixed and there is no fixed predestined lifespan for a particular person. Rather we only have statistical estimates, which change as new information comes to light. Thus the very fact that one has survived another year is new information that pushes out the endpoint. This yearly push amounts to a substantial fraction of a year for super senior citizens!

So one can celebrate a birthday not only to celebrate having survived another year, but also for having pushed out one’s life expectancy by the very fact of having survived another year.

Further Reading

[1] Life expectancy https://en.wikipedia.org/wiki/Life_expectancy

[2] Life table https://en.wikipedia.org/wiki/Life_table

[3] Mortality rate https://en.wikipedia.org/wiki/Mortality_rate

[4] Actuarial Life Table https://www.ssa.gov/oact/STATS/table4c6.html

[5] Mortality Database http://www.who.int/healthinfo/statistics/mortality_rawdata/en/

[6] country life tables http://apps.who.int/gho/data/?theme=main&vid=60740

[7] World life table http://www.worldlifeexpectancy.com/world-life-table

[8] Health Inequality Project https://healthinequality.org/data/

[9] Life Expectancy is misleading https://understandinguncertainty.org/why-life-expectancy-misleading-summary-survival



Hidden Persuaders

Everybody knows that advertisements are designed to persuade you to buy the product. It’s also well-known that the ads work better when they appeal to your emotional side, to your subconscious, rather than to your rational side.  The adman will not hesitate to arouse your sexual desire, or feelings of guilt,  or leverage  feelings of low self-esteem,  to sell his product.  Consider the ads that have scantily clad women, or authority figures saying that you must do the best for your children, or when the actor in the ad transforms from a loser to a confident, attractive person by a single application of some substance. In fact, you may rationally reject the message but the ad has still reached your subconscious mind.
I recently realized that getting people to buy that product is just one of the goals. There seems to be another hidden goal, especially with consumable products . Here are some examples, try to spot the hidden goal:

  • Toilet Soap: boy standing under a running shower, rubbing a bar of soap on the skin.  Notice that  a lot of soap is being wasted as it comes in contact with  running water. Further,  vigorous rubbing of the soap bar abrades away a lot more soap than is really used.  Note how this ties into being able to adulterate the soap, the soap is loaded with fillers like sodium silicate which have no cleaning action.
  • Toothpaste: Close-up shot of at least an inch of toothpaste being lovingly applied along the whole length of the toothbrush. Do you know how little toothpaste is really needed?  The manufacturer is also eager to shaft the customer in two remaining dimensions – the diameter of the tube orifice is much larger than needed, so that the maximum amount of toothpaste is consumed (wasted) per application.
  • Deodorant: The 90 pound weakling puts on  this brand of deodorant, then goes out. He is immediately attacked by several attractive girls. Locations differ but the result is the same – a happy, satiated, 90 pound weakling. You may not have noticed consciously that the weakling has sprayed about half the whole bottle of deo on himself and the room. But your subconscious is getting trained that it takes half a bottle of deo per use to attract gorgeous girls.
  • Cologne/Aftershave: Every notice that the handsome man splashes a huge amount of cologne on his face? Some ads show this action several times, to make sure the message sinks in. http://www.youtube.com/watch?v=9aRIyxh_yKk

The second hidden goal should be clear now– it is to get people to consume MORE. More, more, more. More than really needed.

But now that you are aware of this subtle persuasion, you can first of all realize that you cannot trust what is being shown in the ad. And then you can figure out yourself the correct quantities to be applied per use of such consumable products. It may be harder to convince the children, however.
I will try to guess where this trend might go – one might see some “improved” products or packaging with improved “wastage  coefficients”.

  • Toilet soap with sponge-like structure. Dissolves faster under running water. Although it will be marketed as being gentler or with special enzyme action etc.
  • Toothbrushes with increased surface area.
  • Toothpaste tubes with a square orifice (square cross section has higher area than a circular cross-section).
  • Deodorant or cologne bottle with a spring loaded dispenser that always delivers a big squirt.

If you come across more such ads, please do post a link or a description in the comments.

Sitting Can Kill You

Recent research indicates:

Sitting, it would seem, is an independent pathology. Being sedentary for nine hours a day at the office is bad for your health whether you go home and watch television afterward or hit the gym. It is bad whether you are morbidly obese or marathon-runner thin. “Excessive sitting,” Dr. Levine says, “is a lethal activity.”

Everybody (except people working on a farm), and especially all cubicle dwellers, should carefully read the New York Times article “Is Sitting a Lethal Activity?” by James Vlahos: http://www.nytimes.com/2011/04/17/magazine/mag-17sitting-t.html?_r=2&src=me&ref=homepage#

Acknowledgments: Thanks to SDR  for link to the article.

Life’s Little Mysteries

We are lucky to be born in this century. The history of Humankind seems to have reached a turning point. Knowledge explosion, population explosion, global warming, nuclear proliferation, terrorism, … Life in the next century promises to be completely different — if any humans survive. Or if they remain human.

At the same time, especially during a quiet walk or the daily shave, one is apt to ponder on life’s little mysteries. Here are my favourites.

1. Why a mirror reverses left-to-right and not top-to-bottom

2. Why a T-shirt reverses front-to-back when turned inside-out

3. Why buses come in pairs or threes at a bus stop

4. Why, sometimes, you get a  call from a person just when you are thinking of them

5. Why a woman of unexceptional looks become the subject of the most famous painting in the world (Mona Lisa). Compare the two pictures below:

Classic Modern
original modern-monalisa

6. Why some pictures fool the eye into seeing motion.

7. Why a safety razor with four blades gives a better shave than one with three blades

8. Why one never sees baby pigeons (pigeon chicks, to use the correct word).

9. All elementary particles are fundamentally identical, yet Hans Dehmelt of the University of Washington has a positron named Priscilla.

10. Why the majority of people throughout history have remained in slavery, ruled over by small elites — including today. I use the wide definition of slavery: economic or mental slavery as well as physical slavery. Hmm … maybe this not a small mystery.
(note: fixed broken link to modern mona lisa)

Cabbages And Kings

Some authors have an insidious effect on the reader – the reader’s thinking patterns change, at least for a while. Here is a very short story. the author has been clearly dazed by The Alchemist. Or maybe Jack Welch. 

“Nothing in the world is ever completely wrong. Even a stopped clock is right twice a day.” – Paulo Coelho (Brida)

“People never learn anything by being told, they have to find out for themselves.”-Paulo Coelho (Veronika Decides to Die)
“My main job was developing talent. I was a gardener providing water and other nourishment to our top 750 people. Of course, I had to pull out some weeds, too.”- Jack Welch

Cats, Dogs, and Bacteria

A software engineer working in a product company was chatting with his son on what the son wants to do after growing up.
“If you are a cat, you can become a consultant. If you are a dog, you can work in a services company.”
Son: “but I want to be like you Daddy, and work in a product company.”
Engineer: “Oh, to work in a product company, you must be a bacterium.”
The engineers wife, listening to this conversation, was getting annoyed.
“What nonsense are you putting into his head now?”
Engineer: “I attended a talk by a great man who told us that we were bacteria. And it must be true, because all the engineers laughed and clapped and greatly appreciated the point.”
Wife: “And who is this great man?”
engineer: He calls himself a gardener.”
“Huh, a gardener.” said his wife. “What do you think a gardener thinks about all day long? He is naturally concerned with small animals, insects, and soil bacteria– what else would one expect from a gardener?”
She paused, and then said thoughtfully, “In fact, I believe he paid you a compliment — he didn’t say you were manure. My grandfather was a gardener you know, and he used to talk manure all the time.” she said, and walked away.
Strangely, the engineer’s heart no longer felt heavy. He was cheerful again.
He went out to play cricket with his son.
“Don’t worry about what you will do when you grow up, son, even if you turn out to be a monkey there will be jobs in several cities for you.”
“Which cities, daddy?”
“Pune and Chennai, most certainly”, said the engineer, “just tell them that monkeys are naturally good at climbing trees.”
“Now mind the ball” he warned, as he bowled a good length to his son.
The son was clean bowled on the first ball.
— by E. Vexedococcus