I am Andres Aravena

• Assistant Professor at the Molecular Biology and Genomics Department, Istanbul University
• Mathematical Engineer, U. of Chile
• PhD Informatics, U Rennes 1, France
• PhD Mathematical Modeling, U. of Chile
• not a Biologist
• Applied Mathematician who can speak “biologist language”

Generic goals

We want to help you to become

• Better molecular biologists
• Better scientists
• Better professionals
• Better citizens

Better molecular biologists

• Lower failure rate in your experiments

• Do better experiments

• Ask better questions

• Achieve larger impact

Better scientists

• Ask better questions

• Propose better answers

• Create Knowledge, not only Data

Better professionals

• Perhaps you will change your career later in life

• Whatever you do, do your best work

• Always follow good practices

Better citizens

Perhaps you will win the lottery
(or inherit many million dollars from a distant uncle)

and you do not work anymore

Still, you need to understand the world

Enough so big companies cannot fool you

We need to see the Big Picture,
How did we get to here and now?

Course plan (first part)

• Asking good questions
• Observing nature
  • Estimating
  • Measuring
  • Evaluating uncertainty
• Finding reasonable theories
• Testing theories with experiments

Key words

• Estimation and Guesstimation
• Order of magnitude
• Confidence Intervals
• Error propagation
• Uncertainty budget
• Dimensional Analysis

Lab Notebook

One of the essential good-practices of laboratory work is the Lab Notebook

They are essential if you want to get a patent for something you create

They are essential to carry long term experiments

We encourage you to use a good quality notebook every day

Do not trust your memory

Course’s Homepage

Our homepage is at https://www.dry-lab.org/blog/2024/msr/

It is part of my blog https://www.dry-lab.org/

Homework and class slides are published there

I also have a YouTube channel https://www.youtube.com/@dr.andresaravena

Two systems of thinking

The priority of our organism is

1. Survival
2. Save energy

So System 1 is the default mode

Most of the time we use the cheap intuitive system

Rational thinking (i.e. math) is not spontaneous

Intuition vs Rationality

One option is to be like Spock, and suppress all intuition

The other option is to train our intuition

Guesstimation trains our gut

This is why we have been practicing estimating magnitudes

• Not let our intuition fool us

• Get a gut feeling about numbers

This last part is important, because we make decisions based on our feelings, and often we do not know what to feel about a number

Powers of 10

At first, we estimate by powers of 10
(after choosing the appropriate units)

We even have names for some of them them:

• deci, centi, milli, micro, nano, pico

• deca, hecto, kilo, mega, giga, tera, peta, exa

Upper and lower bounds

When estimating a value, we usually can guess that the real value is somewhere between two values

In other words, we guess lower and upper bounds \(L\) and \(U\)

Choose the smallest value that seems right,
then the largest one

Order of magnitude

The order of magnitude of a value is its power of 10

More precisely, is the integer part of the logarithm base 10

We say that two quantities are in the same order of magnitude if their ratio is between 0.1 and 10

i.e. if each one is less than ten times the other

Compare populations

Which of these populations are of the same order of magnitude?

• Istanbul
• Ankara
• Tokio
• USA
• UK
• China
• India

Half order of magnitude

Instead of going \[10^{-1}, 10^{0}, 10^{1}, 10^{2}, 10^{3}\] we can increment the exponent by 0.5 \[10^{-1}, 10^{-0.5}, 10^{0}, 10^{0.5}, 10^{1}\]

Since \(10^{0.5} = \sqrt{10}≈ 3.16≈3\) we can say \[0.1, 0.3, 1, 3, 10, 30, 100,…\]

How many trees?

Our campus has a park, near Astronomy department

How many trees are there?

Writing large numbers

The speed of light is about 300000000 m/s

It is easy to miscount the number of “0”

Instead, we write 3×10⁸ m/s$

Better, in computers we write 3E8

(This is called exponential notation)

Here 3 is called mantissa and 8 is the exponent

The “billion dollars problem”

In USA, a billion is a thousand millions

In the rest of the world, a billion is a million millions
(often called “a milliard”)

There are two conventions: short scale and long scale

To avoid confusion, better use giga or tera

or use scientific notation: 10⁹, 10¹²

Homework

Please read The Library of Babel by J.L.Borges