Well, in a theorist's pursuit, it often helps to get some kind of a ballpark figure.
And often we do that by some quick calculations.
These are often called 'back of the envelope' calculations.
Back of the envelope calculations.
The purpose of a back of the envelope calculation is not to obtain exact values, essentially
to get some kind of a order of magnitude calculation.
And in many cases that helps.
The famous physicist Enrico Fermi was a master of this technique.
So, many times these method of calculation is called 'Fermi estimates'.
Because Fermi showed how effectively such very quick calculations can lead to some idea
regarding the order of magnitude of what you are trying to find.
For example, you know that during the Second World War, in the United States a project
called the Manhattan project was initiated which ultimately led to the development of
the atom bomb.
And a large number of European scientists at that time worked in the Manhattan project
because it was at that time believed that the Germans are also working on developing
the atom bombs.
So, as a counter to that, these scientists worked on that.
When it was finally built, it was to be tested.
And it was to be tested in a desert.
And scientists were standing at a distance and the the bomb was detonated.
Fermi was also one of the spectators.
What he did was, he simply had a piece of paper in his hand.
He tore it up into shreds of small pieces and then dropped it from his hand.
And as the blast happened the blast took the pieces of paper to some distance and it fell.
He quickly measured the amount of distance it travelled in the horizontal direction in
absence of any wind and how much did it fall from the vertical direction.
And only based on that, he on a back of an envelope, he calculated the approximate power
of the bomb that was detonated at a distance (assuming that he knew the distance at which
he was standing).
So, these are... and he got something like 10 kilotons as a ballpark figure.
And when it was finally, after a lot of trouble lot of calculation it was calculated how much
was the actual power of that bomb, it was found to be 21 kilotons, which means that
he was right at least to the order of magnitude.
So, these are these are typical Fermi estimates.
As a as a as a fun exercise, I can show you one of this one of such Fermi estimates: for
example, how many barbers are there in the New York City?
How many barbers are there in the New York City?
The moment you are asked this question, you say I have no clue as to how many barbers
can be there.
Fermi would say that, ok, let us try to try to guess with some kind of a ballpark figure.
So, what is the population of New York City?
So, suppose something like 5 million people.
Okay?
So, let us try to figure out the number
in New York City.
Yes, the moment you are asked this question you say I have no clue, no idea how many barbers
shops.
But Fermi would say, suppose the number of people population, which is easy to find of
New York City is say 5 million.
Suppose... okay, out of out of the 5 million people half are women and therefore, they
would not go to the barber shop.
They would go to other places to cut get their hair cut.
So, that 50 percent are women.
So, that brings it down to 2.5 million needing haircut, needing to go to barber shops.
Then out of this 2.5 million some will be babies, too small to need a haircut.
Some will be bald and therefore, they would not need a haircut.
And likewise there might also be some people who cannot afford a hair cut, so poor that
they cannot afford haircut.
So, suppose the number of such people maybe say 20 percent.
So, 20 percent do not need a haircut.
Let me write babies, bald people and say too poor.
So that, they would also not need a haircut.
So, that that brings the number down to about 2 million.
So, 2 million million people would be needing haircut approximately once a month.
So, that is a ballpark figure because people would normally need a haircut once a month.
Now let us look at the barbers perspective.
Normally a barber would cut somebody's hair in about say 15 minutes.
So, one haircut needs 15 minutes.
Okay?
So, how many haircuts does a can a barber perform in a day?
Suppose the barber works for eight hours each haircut needs 15 minutes which means he will
need he will be able to do... a barber can perform around 32 haircuts a day .
A 32 haircuts a day and assuming weekends approximately that would be say into 20.
So, 640 haircuts a month.
So, one barber can perform 640 haircuts a month and there are 2 million people needing
a haircut every month.
So so cutting the hair of 2 million people would need how many barbers?
It will be 2 million, 2 into 10 to the power 6, divided by 640.
So, that that that would come approximately to 3000 barbers.
So, New York City will need around 3000 barbers.
And assume that each barber shop has some 4 barbers.
So, if each has 4 barbers, then the number of barber shops becomes 3000 by 4 would be
about 750.
So, this then is a sort of estimate of the number of barber, barber shops that would
be there in New York City.
Notice that when we started we had no clue.
But if you start arguing properly and if you use some kind of a ballpark figures.
Notice that the way the Fermi estimates go.
This is a figure that we know, but these are sort of this is a figure that we know, but
these are sort of ballpark figure, could be right could be wrong we do not know.
How many can a barber how many peoples hair can a barber cut per day?
We do not know really, but we assume that it would be something like 32.
So, if this ballpark figures are correct then this is more or less correct.
At least this should be correct to an order of magnitude.
So, this this is a typical example of a back of the envelope calculation.
And such 'order of magnitude' calculations are often used by say astronomers.
If you want to look at a particular part of the sky, how many galaxies would be there
in that particular part of the sky?
If you have if you use this kind of a ballpark figure you can estimate the number of galaxy
that might be there in a particular part of the sky as visible to a particular telescope
with a particular strength.
But probably the most famous Fermi estimate was of probably the most famous Fermi estimate
was the estimate of the number of alien civilizations that might make contact with us.
Very interesting calculation.
But in the 1960s, somebody called Frank Drake, somebody called Frank Drake sorry, did a Fermi
calculation of how many many extraterrestrial
civilizations may try to make contact with us.
So, this is the question that was asked.
Drake said, that ok let us do a again a Fermi type calculation where the the inputs that
we need or... he he wrote an equation like this.
N is equal to...
N is the number of extraterrestrial civilization.
So, so this is N. He said that let that be estimated as R star
times f_p times n_c times f_i f_l f_i then f_c then L.
I have to write each of these, what are these?
Well N is the number that we are trying to estimate, but then your R star, R star is
the number of the the average rate of star formation in our galaxy.
We are assuming that the extra extra terrestrial civilizations may try to contact with us,
if they are within our galaxy.
Otherwise they are too far off to be able to do that.
So, within our galaxy.
So, the the rate of star formation in the milky way galaxy.
So, you know more or less the rate at which stars are forming, but after that you need
need to have some kind of a fraction, fraction of stars that have planets, fraction of stars
that have planets.
Okay?
And then we have the n n_c is the average number of planets that that can potentially
support life.
The average number of planets number.
Not number, fraction of planets that can potentially support life.
Then we have f_l.
f_l is the fraction of planets with life that actually go on to develop intelligent life.
The fraction of planets actually actually develop life.
f_i is the fraction of planets with life that develop intelligent life that is f_i.
Then f_c.
f_c is the number of... or the fraction of intelligent civilizations that developed
that developed advanced technology sufficient to contact us.
And finally, the length of time.
The final, the L is the length of time, time for which such civilizations have been trying
to contact us.
This detectable signals have been released into space.
So, notice that each are reasonable things that we try to figure out.
What Drake did was made some ballpark figures for example, this he said let it be 1 per
year, this he said let it be f-p was say 0.2, n_c was say 1.
f_l was so, his point was that if... he he was assuming that the the planet would harbor
life and if they have sufficient time, then they would actually develop life and if life
had sufficient time, then it would develop intelligent life.
So, all these he assumed to be one and f_c is not all that given that to develop high
technology.
He assumed to be say 0.1 to 0.2 and L he assumed that it they existed for say 10000 years 1000
years.
So, alien civilizations have been sending a signal for about 1000 years.
So, if you multiply them out he got the total time n as something like of the order of 20.
Well, there have been enough controversy as to the assumptions, whether the assumptions
are okay or not, there may be enough controversy; but the fact that he got a non zero number
that arouse a lot of interest.
And that is what is at the basis of our search for extraterrestrial intelligence.
Because the he got some non zero number.
So, this is the basis of the what is known as the back of the envelope calculations or
sometimes called Fermi calculations.
And this often helps in formulating models and getting some idea regarding the ballpark
figures.
We will end here today.