Arithmetic, Population Energy and
Money
This Is my second blog
and I would like to take you through some math and the importance of numbers in
life especially percentages and doubling time with some psychology and news
reading skills. As many of you know, I’m a math and Science enthusiast but now
I’m inclined towards psychology too. First of all, we must understand that math
is more than just numbers and it should be rightfully defined as the science of
computing. When math is represented with discrete values it is called
arithmetic and algebra when we use alphabets or symbols when you represent
something broader, say a law or a theorem. We were all taught basic of
mathematics in our schools and colleges, but we merely study them as subjects
which are a part of our curriculum. We sometimes fail to recognize or
acknowledge some simple relations we come across in our daily life that are
governed by the same mathematics that we learnt, which if seen from the right
perspective, is easier than you thought it was. I would like to inform you that All Global Problems are connected by Arithmetic.
The article would also touch upon today’s speculative news market and how to
read news article, though not in detail. The way I write will be very direct
and I use only simple English, albeit, you may have to read a few sentences
twice to understand what I mean to say.
Do not understand what
you want to, but, what I want you to. I hope you like it.
The greatest short coming of the human race is our
inability to understand the arithmetic exponential function. Yes..!!! Logarithmic and Exponential functions, by
far the best means available in mathematics used to forecast or predict future
trends and values are not understood by most of us. When an information passed
from one person to another the quality
of information is maintained only when all the necessary data in the message is
understood and interpreted by the listener. Most of our information that we
depict today, are in terms of percentages. I hope everyone is well aware of
percentages. Percentage merely describes
anything that grows with time, increase by a fixed fraction for a fixed period
of time. Even though the information travels in a very crisp manner, the
listener/reader should still compute as to how much increase or decrease it actually
is.
And then there is
doubling time. Doubling time is the
time taken for a particular quantity to become twice its magnitude. Lets
take 3 examples
1. “A baby grows to twice its height if 2 – 3 years”.
2. “You will have twice
the amount of homework to do if you spend the weekend watching movies and
playing video games”.
3. “The world oil
consumption doubled in the sixties”.
Now these are just mere examples which depict what a Doubling time is …. Or wait..!! Are they …???
NO. !!!
Doubling time needs to be specific. It’s a measure of time. You need to
quantize the time period for a quantity to double in its magnitude. The first
statement somewhat tentatively conveys the message regarding the starting and
the ending period. Start when the baby is born and end somewhere between 2-3
years.
The
second example however does not talk about time period at all. You have to
assume a lot of things to understand this. Firstly, you should be given home
work on weekends and you should be given homework after the weekend. Third, you
should be given the same amount of homework after the weekend. The third
example is even more disastrous. It only has the word doubling time. It does
not compare the consumption pattern to a previous time scale. It did not speak
about what oil. It did not specify a particular time period as to when it
actually doubled.
Now
re-consider your thought process if you happened to be convinced with those
three examples when you read it for the first time. Most of the news you see on
TV or read on the papers today are baseless as the examples stated above. Now
why do people fall for these news anyway?
Express
it in percent, no one cares. Represent it as doubling time, and everyone is awestruck.
Yes ..!!!!!
Invest in BANK A and your money will double in 6 and a half years.
Invest in BANK B and you will get 11.50% interest per annum.
Which statement catches your eye ?? Well,
for all the effort I’ve put in, I hope it is the first one.
However, the truth is
that Bank B gives you slightly more than double the amount you invest in the same time period. All said
and done, how do you calculate doubling
time ? You do not want to sit with a calculator when you read the news, do you?
It is easier than you thought. Just divide 70 by the interest rate. 7% interest
takes 10 yrs to double (70/7 =10).
So if you have Rs 100
today growing at 7%, it grows by another Rs 100 in 7 years and you end up
having Rs 200 at the end of 10 years. The average world economy for the past
400 years has been steadily growing at something under 7%. I’m pretty much sure
about this as I’ve read it somewhere sometime ago. Anyways, let us assume it to
be so and let us go back 300 years. The Indian princely states had to pay an
amount equivalent to Rs 100 at that time, as a yearly tax to the British.
Rs 100 at 6.8%,
doubles 30 times in 300 yrs,
2 ^ 30 x 100 . It is something more than
100 Crore Rs or something less than $20 million. Now there was more than one princely state falling under the
British rule in 1713 and the British made a lot of money. And $20 million per
annum per state is sumptuous. Another piece of information Manhattan was purchased in 1626 fr 24$. Assuming a steady growth of 6.8%, Do the math.
Legend has it that the
game of chess was invented by a mathematician who worked for a king. The king
was very pleased with the invention of the game that he wanted to reward him.
The mathematician said, “Well my king, my needs are modest. If you just take my
chess board and on the first square place one grain of wheat. On the next square
double the one to make two and on the next, double the two to make four. Just
keep doubling till you reach the 64th square and that would pretty
much suffice my needs and my family’s”. The king thought he was a fool and said
“You fool, I was going to give you a real reward and you resort to some grains
of wheat? “. Well let’s work it out and find whether the mathematician was
actually a fool or not.
The table below is
pretty simple to understand. The first column numbers the squares, the second
column tells you how many grains are in the square and the third column shows
the total number of grains in the chess board.
Square # Number
|
Grains on Square
|
Total Grains on the Board
|
1
|
1
|
1
|
2
|
2
|
3
|
3
|
4
|
7
|
4
|
8
|
15 (24
– 1)
|
5
|
16
|
31 (25
– 1)
|
.
|
.
|
.
|
.
|
.
|
.
|
63
|
262
|
263 – 1
|
64
|
263
|
264 – 1
|
Again I hope you
don’t have any difficulties in understanding the table above. Let us identify a
pattern here. Every new square has one
grain more than the total number of grains on the entire chess board. The 2nd
square has 2 grains which is one more than the total number of grains which
were there, which was one. The 5th square has 16 grains which is one
more than 15 which happens to be the sum of all grains till the previous
square. And so the relation is obtained where n happens to be the Square#
number and “ 2n – 1 “ is the number of grains n the square. So every
time a quantity doubles it takes more than all that you’ve used before
So you have to
understand that the whenever something doubles, it means that the production/consumption
of that particular item is going to be more than what existed till date. Going
back to the news which said, “The world oil consumption doubled in the
sixties”, which actually meant crude oil, this statement says that the amount
of oil consumed in the 1960s was more than what was consumed in the entire
history of the earth till 1959.
The
word population today is around over 7 billion. The population was 3.5 billion
in 1968. So, in just 45 years, human beings have produced more off springs than
the total number of off springs ever produced in the history of mankind which
runs to 10s and 1000s of years. The frightening fact is that, we still continue
to grow at close to 2% p.a. This means that we have also produce more food than
what we have produced in the history of mankind. And also the space available
per person on land has shrunken by slightly more than half and all of this has
happened in just 45 years. The picture
depicts a rough timeline just for the sake of understanding it is not perfect
to scale.
Consider the black patch to be the timeline from 10000BC to
today, it is to be noted that the first billion was achieved only in the
starting of the 19th century and now we have a whopping 7 billion
people in our planet. The thin blue line in the end depicts the last 45 years in
which our population doubled.
Now,
going back to the king and his chess master, exactly how much was the total
amount of wheat grains on the chess board. “
264 – 1” is just a little more than
400 times the 1990 world harvest of wheat. Oooooohhhh yeaahhh … !!!!
IT IS .
Well this should feed
his family till eternity.
Well, I think, this is
precisely the reason why people are AWESTRUCK when something is depicted in
terms of doubling time.
I’d
like to finish this off with one more explanation. Bacterium multiplies by
dividing into two. The two become four and the four become eight, sixteen and
so on. Suppose you put them in a jar and the bacteria doubles every minute, the
jar gets filled up in one hour. Say, you
place one bacterium inside a jar at 11 a.m in the morning, the jar gets filled
at 12 noon. Easy to understand and I hope you are clear. The growth is constant
and occurs in a finite environment.
Now I’d like to ask you 3 questions:
1. When is the jar half full?
Some of you may be surprised by the answer. It is exactly
at 11:59 a.m. Just one minute before 12 noon, because, they double in number
every minute and so, if you reduce a minute you’ll arrive at exactly half of
what you had.
2. If you were the bacterium in it, at what time
would you have realized that you’re running out of space?
Well coming to think
of this, a minute before 12 noon, the bottle is half full. Two minutes before,
it’s a quarter full. Three minutes, 12.5% full. Well, jus 5 minutes before 12
noon, there is tremendous scope of growth as there is approximately 97% free
space in the jar and how many of you are going to predict that you are going to
be choked up in the next five minutes .????
Well then, let us
consider that there are a few brainy bacteria inside the jar who predict this
short coming and set to launch a search mission for new bottles. They are
successful enough to find 3 new bottles. Now question 3.
3. How long do you think the bacteria
can sustain after these bottles have been identified?
Well, at 12 noon you
will have one bottle filled. At 12:01 p.m. the other bottle gets filled and at
12:02 p.m. all the four are filled.
Well then Folks..!!! I know you have already figured out the moral behind this
article. Keep an eye on percentages. Always look for specific details, just the
percentage without time scale is just speculation. Doubling means not only
increase in production or extraction, but also depletion. And at the rate in
which our population is rising, we are already in the last minutes like those
of the bacteria. Looking at the timeline diagram again I wonder whether we are
in the last minutes or last seconds...!!!
Keep thinking until I get back to you, hopefully, on something more interesting.
NOTE:
The “easy to understand”, “ I hope you understood” are all psychological impact
statements that I have experimented with you. These statements are supposedly
used to ease your head and help you convince yourself that the data is easy to
comprehend. I hope it worked.
