I read this book after really enjoying reading the speech Hamming gave called You and your research. If you’re unsure if you want to give the whole book a read (it is a hefty tome), then start with that.

The speech summarises the idea of the whole book, namely, using the one shot you get at life to make significant contributions to humanity. It emphasises a style of thinking more than a boilerplate approach. It uses example from various areas of his career in scientific research to hammer home the points, and some of that can get quite technical. But as Hamming mentions at the start, they are anciliary to the main idea of the book, so no need to get too bogged down in the maths if you don’t want to. It’s simply a way of showing how some the great minds he encountered approach problems.

A final note that is important, dont try to internalise all the ideas of the book. Some will work for you, and others wont. Research and problem solving is a fundamentally personal activity, so see what resonates with you and build on that.

Style of Thinking

Innovation

Thinking about the future

• Questions for the future
  • What is possible
  • What is likely to happen
  • What is desirable to happen
• How will the future be different from now?
• How will it be the same?
• Think about the future to anticipate change (passive to active)

Thinking about new technologies

• When you encounter a new technology, think in what new areas and ways can it be used? How will this be used in the future?
• Always thinking of related concepts – how can this be applied elsewhere?
• “What are the real world uses of this idea?”

Affecting change

• If you do not occasionally doubt accepted rules, you will not be a leader
• Sometimes things that are technologically feasible and economically desirable are prevented for political, social and legal reasons
• Innovation in a field usually comes from an external source/individual

Independent Thought

• “Believe nothing, no matter where it comes from, unless it agrees with your own sense of logic and common sense”
• See a technology – have a hypothesis – think of an experiment to test the hypothesis
• Take a lot of time to think – come up with opinions, theories and hypotheses
• Think about something until “you are fairly clear what you believe and why you believe it”
• Do your own work instead of spending all your time in lectures
• Make time to turn ideas over in the mind
• Do not just drift along, think of what you want to be and how to get there
• Have theories on lots of things
• If you look around your organisation there are many things that should not happen but do because they are customary
• Develop the ability to quickly learn new fields

Working Diligently

• Software chapter – Have care and diligence, think before you write code
• Prove all of your assumptions, this way you
  1. Don’t make bad ones
  2. Have a deep idea of what is going on
  • Am I satisfied this is correct?
• Do the proofs yourself
• How will you convince yourself that you have not made a mistake somewhere
• Question your assumptions: “Why do I believe whatever I believe?”
• Working calmly gives you longevity, but the breakthroughs come after frustration and emotional struggle

Problem Solving

The problem

• Be very clear on what the problem is
• Complex idea –> what does it look like?
• How does this fit into the whole picture?
• When thinking of complex systems –> is it stable?
• Think of how a system converges or diverges
• Don’t just think what a function is, what class is it from? What functions are similar to it?

Your toolbox

• Multidisciplinary (all the sciences)
• Awareness of cognitive biases
• Have a broad scientific/mathematical toolbox from which to draw
• “How can other subject areas apply here?”
• A key skill in mathematics is abstract pattern recognition
• The lab and the field are two very different things
• Mathematics requires application to be useful
• Prepare your mind for the future, do not just memorise, but truly understand things
• Be aware of the limitations of certain measures and methods
• Flexibility should be a part of modern systems and processes
• Different skills matter at different levels in a field

Techniques

• Start simple and build from there
• Always start from the basics and build up from there
• Back of the envelope calculations
  • Retain information better
  • Keep sharp the ability to model situations

Fundamentals

• Focus on these
• They:
  • Have stood the test of time
  • Can derive the rest of the field
• If you know the fundamentals well, the fancy parts follow easily

Working with Others

• Understands that most others don’t think like him
• Teamwork is a necessity when working on complex projects – know and understand that others have different views to you

Great Work

• There is no shortage of opportunities to do great things. The more prepared you are the better
• Take pride in your ability to do great work, it will be important when confidence is needed
• Creating new things requires self confidence
• We are nothing more than the sum total of our habits

Engineering

• Digital revolution
  • Continuous signals –> discrete pulses
  • Helped by transistors
• Hardware chapter similar to Feynman computing book
• L1 and L2 regularisation come from simplifications of n dimensional spaces. They are distance functions
• Coding theory
• Information theory should have been called communication theory
• Quantum Mechanics
  • Heisenberg’s uncertainty principle
• Data is rarely as accurate as you think
• Systems engineering = high level thinking on a project/system
  • Optimising the components of a system regularly ruins the performance of the whole system
  • Systems approach to learning – being intelligent as opposed to just passing many individual exams
• You get what you measure
  • The method of measurement impacts the result you get