Unique Critiques

Archive for the category “Math and Science”

Designing your Life

Science / Biz Book Review

Bill Burnett and Dave Evans designed a pretty amazing book with Designing your Life.  They are both professors at Stanford but each of them had pretty amazing careers pre-Academia.  The way they write and the way they use their own goals comes across as two guys who have figured out quite a few things about life.  At least their own lives.  Not only does their communication style come across as very comfortable, both authors have that tone of calm competence that you always get from people who have mastered their craft.  The book comes from concepts that were pioneered and tested in the classroom and the boardroom.  The class they offered had the same title and it quickly became one of the most popular classes at the school.

You can see why this would be so popular.  So many kids get their first taste of freedom when they head off to college/university.  With this freedom comes some new accountabilities that can easily pile up to a massive oh shit question.  What the hell am I going to do with the rest of my life?

Up until this point, most kids have a pretty clear idea of what they are supposed to do next.  There is a fairly unambiguous scorecard that comes in the form of grades or scoreboards or even social pecking order.  Once you get into college, your previous standing in all these things becomes irrelevant.  Not only do you have to recreate who you are, you typically have to do it by yourself.  Sure, you have advisors throughout the process, but the road ahead is no longer obvious and your parents aren’t there for the day to day stuff.  Burnett and Evans help kids figure this incredibly difficult transition out.  Now that all this knowledge is in a book, they can help you figure it out too.  I don’t want to leave you with the impression that this is just for kids.  No matter how old you are, if you are contemplating any type of change in career, relationship, health, etc. the knowledge in these pages will help.  We should all actively work to design our lives no matter where we start in the process because the alternative is to let the world do it for you.  That’s how the victim mindset begins.

Our authors start with sharing some facts.  First, only 27% of college grads end up working in something related to their majors.  Second, “two-thirds of workers are unhappy with their jobs.  And 15% actually hate their work.”  With just those two statements it becomes obvious we are not doing a good job of designing our lives.

They then take us through their definition of design.  Design requires radical collaboration, talk with many people from many disciplines to design something amazing.  Designers are also great tinkerers.  “Designers don’t think their way forward.  Designers build their way forward.”  To design your life effectively, you’re going to need “curiosity, bias to action, reframing, awareness, and radical collaboration.”  They also take on the passion mindset a bit and that you can’t just fall into it, “people actually need to take time to develop a passion.  And the research shows that, for most people, passion comes after they try something, discover they like it, and develop mastery – not before.  To put it more succinctly: passion is the result of a good life design, not the cause.”

Step 1: Start where you are

They outline an amazing roadmap of how to start this design.  Step 1:  Start where you are.  This is figuring out how to place the ‘you are here’ pin.  They ask you to break down where you stand in four critical pillars of life: health, work, play and love.  They walk you through creating a dashboard of how you stack up in each of these pillars.

Step 2: Building a compass

In this stage, they ask you to define true north.  They ask you to build a Lifeview by asking some fundamental questions: “What gives life meaning? What makes your life worthwhile or valuable? How does your life relate to others in your family, your community, and the world?  What do money, fame, and personal accomplishment have to do with a satisfying life?  How important are experience, growth, and fulfillment in your life?”  None of these questions have easy answers and each of them deserves serious introspection.  It’s worth it.  They ask you to do the same for your Workview which is a similar exercise but focuses on your craft.  The goal of both of these exercises is coherence.  You want to be able to articulate an internal compass to guide you through the many shades of gray that life tosses your way.

Step 3: Wayfinding

In this stage, the goal is to understand what makes work fun.  One of my favorite quotes from the book came from this chapter: “Flow is play for grown-ups.”  Wayfinding takes you through a set of exercises to understand what flow means for you.  In their words, “Work is fun when you are actually leaning into your strengths and are deeply engaged and energized by what you’re doing.”  They provide you with a good time journal that asks you to track what you’re doing at work for a couple of weeks.  When you scribe the task, they ask your engagement level while the activity was happening.  They then ask you to record your energy level for the activity when it was complete.  This starts identifying those tasks that bring you to flow already or point the direction for the work that can take you there.  If this does not become obvious after a couple of weeks, you can dive deeper using the AEIOU method.  You can look at each task/experience then ask: what Activities were actually involved?  What was the Environment like?  What was the Interaction like – people or machines, new or old?  What Objects were you interacting with?  What other Users were involved?

Step 4: Getting Unstuck

This section was all about brainstorming where they walk you through effective ways to build out a mind map which is essentially a post-it note guided brainstorming session.

Steps 5 & 6: Designing your life and Prototyping

They then ask you to take some of your results from the brainstorming exercises and to build out three five year plans.  These are three completely different things that you could see yourself doing over the next five years.  “We call these Odyssey Plans.”  Once you build these plans, it’s time to start doing some prototyping.  A lot of prototyping involves just getting out there and talking to people that have done something similar to what you’re trying to do.  Figure out why these folks love or hate what they’re doing.  Get their story and try to superimpose some of it on yourself.  Is this something you could really see yourself doing?

These first steps are the ones that resonated for me.  Like a lot of these personal development books, it started very strong but faded a little as it went on.  The authors continue with really good advice on designing and landing a dream job, but most of this was not as fresh or new as the earlier parts of the book.

They close with some great thoughts on how designing your life will actually create an immunity to failure.  If you are constantly designing your life, if you are constantly self-improving, any failure you experience is just part of the process.  That’s what life is after all, a constant trial and error experiment.  The big difference is that if you choose to design your life, you’ve decided to own that experiment.  You’ve decided to call the shots and play an active role in it rather than passively let your external stimuli control it for you.

The choice seems obvious to me.

Advertisements

Tinker, Dabble, Doodle, Try

Science Book Review

Tinker, Dabble, Doodle, Try hits you like a firehose of knowledge.  Dr. Srini Pillay looks into the depths of the brain and asks the central question – what are our brains doing when they are not focused?  Why is unfocused time important?  The zeitgeist, at least in Western culture, is that focus is king.  If you haven’t started down the path of focused world domination by the time you’ve finished that first cup of coffee, you’re doing it wrong.  And if you are not still focused on that goal of complete self-improvement by the time you’ve finished you’re second power scotch of the evening then you are an utter failure.  How we acquired this attitude is the subject of countless other books.  This book talks about why focusing all the time is a bad idea.

Fair warning: this book is not light reading.  Dr. Pillay does his best to sprinkle antidotes and lightness throughout the book, even adding little sidebars that have the smell of a ‘for dummies’ book.  For Dummies it is not as any green Jedi master might tell you.  When reading the book it feels as if the author has too much to say and was told by a publisher somewhere that he had to fit all of these cool ideas into a book that’s under 200 pages long.   This makes the transitions from chapter to chapter a little stilted.  The flow from idea to idea disjointed.  Please don’t let this discourage you from the read though because Dr. Pillay has a lot to teach.  I took more notes in this book than I have in a long time.

Pillay opens the book by taking on the ‘cult of focus’.  One of the examples he brings up is the famous gorilla suit experiment.  This is the one where participants are asked to focus on a team passing a basketball back and forth and is asked to count the number of passes.  Almost all participants miss the dude in the gorilla suit that walks right through the basketball game because they are so focused on counting passes.  Dr. Pillay posits the right questions here: “If focus makes you miss seeing a gorilla, what else are you missing in life?”

Another interesting fact shared is that when we are hyper-focused we lose the ability to care.  “Hyperfocus depletes the brain’s prefrontal cortex (PFC), which helps us make moral decisions.”  I can’t imagine a scenario where that is a good thing.  Pillay goes on to talk about the importance both focus and unfocus have on the brain with a great analogy.  “Focus and unfocus are two different settings.  Focus is the close and narrow beam that illuminates the path directly ahead.  Unfocus is the beam that reaches far and wide, enabling peripheral vision.”  Both are important to living a valuable life, so why don’t we give ourselves the chance to let go more often?

One of the things I liked about the book is that Pillay had zero hesitation about diving into the science.  The part of the brain that manages unfocus is called DMN or the default mode network.  At first we did not understand much about this circuit and before the value of unfocus was discovered it used to be referred to as the ‘do mostly nothing’ circuit.  After quite a bit more study, we discovered that this DMN circuit is actually one of the greatest consumers of energy in the brain.  Pillay shares a laundry list of things that it is used for:

  • It acts as a distraction filter
  • It builds mental flexibility
  • It connects you more deeply with yourself and others
  • It integrates the past, present and future
  • It helps you express your creativity
  • It helps you dredge up intangible memories

These are all traits we would be lost without.  Pillay’s advice is take the focus with the unfocus.  His personal experiments have led him to “strive for fifteen minutes of unfocus for every forty-five minutes of focus.”

He next dives into creativity and our first of the title topics, dabbling.  He starts by talking about two of the great polymaths in recent history, Einstein and Picasso.  Both men were great dabblers.  “Einstein was strongly influenced by aesthetic theory and was fascinated by Freud’s work.  Picasso was strongly influenced by photography and X-ray technology.  Neither man felt he had to become expert in these side interests.  Both indulged their curiosity, mulled over their responses, and discussed the resulting ideas with their respective think tanks.  The results changed the world.  Deciding to dabble can be a profound choice.  It means being willing to try something out and be a student again.”  Who doesn’t want to go back to beginner’s mind?  Anytime you try a new sport or hobby, you typically gain huge strides early in the process.  More importantly, trying something new opens the brain to new experience and lets a tsunami of new thoughts in.  This is where breakthroughs are made.  If you’re not trying new stuff, you’re not learning, you’re not expanding.  Being static in this day and age is a recipe for disaster.

He dives more deeply into learning, specifically dynamic learning.  Dynamic learning is “to own up to, talk about, learn from, and correct errors rather than following a hypothetical ‘right’ way.”  If anyone thinks that there is only one right way to learn these days, they are eons behind the times.  We have even started acknowledging failure as a big part of that learning – “As long as you ‘fail forward’, ‘fail fast’, and recognize that ‘done is better than perfect.’  When you do, you ostensibly avoid intellectual stagnation and overcome fear of failure.  Put more simply. Talk is cheap, so keep on doing what you’re doing until you get it right.”  This is more of his tinkering mindset shining through.

He dives into doodling through the side door of multitasking.  Multitasking is not something I believe is ever effective but he makes an interesting argument about doodling.  “One way to activate your unconscious brain and release yourself from the clutches of focus is to doodle.  As we have previously seen, it activates the DMN and gets your focused, conscious brain out of the way.”  He segues this nicely into play by talking about how play actually helps your brain become less distracted.  Play is where we figure stuff out without the risks of commitment.  Play is basically just another form of doodling.

He also draws some interesting parallels between authenticity and possibility.  This naturally contrasts intrinsic rewards with external rewards.  When we are naturally curious and solve things using that curiosity, the rewards we gain are often deeper than an external pat on the back.  Yet we cannot find what will bring these intrinsic rewards without tinkering and finding what is meaningful to us.  That’s where authenticity comes in.  You’ve got to tinker your way down enough paths to find those that are authentic to you.  This is also a great way to find purpose.  He quotes Lao Tzu – “Lao Tzu once said, ‘When I let go of what I am, I become what I might be.’  Possibility is about being and letting go; tinkering is the process of becoming.”  Powerful stuff.

 

 

 

Sapiens: A Brief History of Humankind

To understand who we are, it’s always a good idea to look at who we were.  It’s certainly cliché but that doesn’t make it any less true.   Yuval Noah Harari has written a masterpiece on the history of our species in Sapiens: A Brief History of Humankind.  He brilliantly takes us on an anthropological journey that defines who we are as a people.  This book has taken its place on my shelf as one of the all-time greats.

He starts from the very beginning.  2.5 million years ago, the humans evolve into being in Africa.  We were weird: big brains, skinny, we walked upright, we used tools.  The world didn’t know what it was in for.  Since we walked upright, women had a really tough time of it when it came to giving birth.  The upright gait required much narrower hips which constricted the birth canal.  Big brains required big heads and death in childbirth was a huge problem.  So we evolved to give birth to very premature babies.  If you look at other species, like horses, or even giraffes, they start walking within days.  It takes us over a year, but we’re vulnerable for far longer than that.  This required us to evolve communication and communities to take care of our young.  That’s what got the ball rolling towards world domination.

Harari breaks the book down into four sections: the Cognitive Revolution, the Agricultural Revolution, the unification of humankind and the Scientific Revolution.  There are a ton of insights in each section of the book so I’ll do my best to capture the ones I found most interesting in this quick review.  There is so much more in there though, so please do yourself a favor and read the book.

Cognitive Revolution

The Cognitive revolution started about seventy thousand (70K) years ago.  This is my back of the napkin math, not Harari’s, but if we consider that over history there was roughly five generations per century, this means that we started serious cogitation about thirty five hundred (3,500) generations ago.  That’s a lot of chance for evolutionary mutations but nothing compared to the roughly 2.4 million years before that time started that it took for us to figure out the tools and weapons to take us from the middle of the food chain to the top.  During that much longer period of time, sapiens weren’t the only kids on the block.  There were the Neanderthals, Homo erectus, Homo rudolfensis, Homo ergaster and several others.  The evolution to sapiens wasn’t a serial progression from these other species.  There is DNA evidence that we did the nasty with Neanderthals and we didn’t drive them to extinction until about thirty thousand(30K) years ago.  It wasn’t until about thirteen thousand years ago that Homo sapiens were the only humans left.

So why did sapiens make it when the rest of the competing human species didn’t?  The conclusion that Harari draws is fascinating.  He claims that our big edge was our ability to create fiction.  In his words, “Large numbers of strangers can cooperate successfully by believing in common myths.”  There are natural laws like the law of gravity that would exist even if humans were not on the planet, but “There are no gods in the universe, no nations, no money, no human rights, no laws and no justice outside the common imagination of the human beings.”  All of those things exist only because we made them up.  Our ability to create these fictions allowed us to “revise our behavior rapidly in accordance with changing needs.  This opened a fast lane of cultural evolution, bypassing the traffic jams of genetic evolution.”  When everyone believes in a similar idea or concept, it builds trust, which allows us to work effectively in much larger groups than chimps or Neanderthals.

The other really big step we took in the Cognitive Revolution was when groups of sapiens near Indonesia figured out how to build ships and leave Afro-Asia.  This was a monumental advantage over other creatures because we didn’t have to wait to evolve flippers and fins.  Instead, we built boats and sailed to Australia.  “The moment the first hunter-gatherer set foot on an Australian beach was the moment that Homo sapiens climbed to the top rung in the food chain on a particular landmass and thereafter became the deadliest species in the annals of planet Earth.”  As soon as we got there, we wiped out 90% of the megafauna.  All of the big animals there didn’t see us as a threat until we stuck them full of spears.  They never had the chance to evolve a fear of sapiens and they were destroyed, by us, long before that could happen.  Sadly, this was true with every other landmass we migrated to.  We migrated there and wiped out all of the big animals.  This is a disturbing trend of our species.  We move in, we pillage and destroy, and we completely change the ecological environment.

Agricultural Revolution

The Cognitive Revolution was followed by the Agricultural revolution which started around 9500-8500 BC.  Harari calls the Agricultural Revolution the biggest con job in history.  “The average farmer worked harder than the average forager, and got a worse diet in return…Moreover, the new agricultural tasks demanded so much time that people were forced to settle permanently next to their wheat fields.  This completely changed their way of life.  We didn’t domesticate wheat.  It domesticated us.”  Farmers got a raw deal and were pretty miserable.  Bigger communities meant a lot more violence and a ton more disease.  As a species though, it was great.  We banged like rabbits and our population went through the roof.

The Agrarian society also had us thinking about the future for the first time.  Since we were no longer foraging, one bad crop could wipe everybody out.  This drove us into planning for the future and accelerated things like trade with other communities.  With that many humans now living together there was a ton of bloodshed.  “The problem at the root of such calamities is that humans evolved for millions of years in small bands of a few dozen individuals.  The handful of millennia separating the Agricultural Revolution from the appearance of cities, kingdoms and empires was not enough time to allow an instinct for mass cooperation to evolve.”  This made fiction and the shared myths even more important, especially when it came to organized violence like armies.  “At least some of the commanders and soldiers must truly believe in something, be it God, honor, motherland, manhood or money….How do you cause people to believe in an imagined order such as Christianity, democracy or capitalism?  First, you never admit that the order is imagined.  You always insist that the order sustaining the society is an objective reality created by the great gods or by the laws of nature.”

The other big advance that came out of the Agricultural Revolution was writing.  “The human brain is not a good storage device for empire-sized databases, for three main reasons…. First, its capacity is limited.  Secondly, humans die, and their brains die with them.  Thirdly and most importantly, the human brain has been adapted to store and process only particular types of information.”  These were things like what plants and animals it was safe to eat.  With all these people living together it became important to process large amounts of data.  Writing and math were an inevitable progression so the whole system didn’t come crashing down.

The Unification of Humankind

The next stage he covers is the unification of humankind which started about 5,000 years ago.  Harari posits that the three great unifiers were money, empires and religion.  “Money is based on two universal principles: a. Universal convertibility: with money as an alchemist, you can turn land into loyalty, justice into health, and violence into knowledge. b. Universal trust:  with money as a go-between, any two people can cooperate on any project.”  There was a serious dark side that came with money.  “When everything is convertible, and when trust depends on anonymous coins and cowry shells, it corrodes local traditions, intimate relations and human values, replacing them with the cold laws of supply and demand.”

Our current liberal societies don’t relish the idea of Imperialism.  However, empires were incredibly effective in unifying people.  “Ideas, people, goods and technology spread more easily within the borders of an empire than in a politically fragmented region.  Often enough, it was the empires themselves which deliberately spread ideas, institutions, customs and norms.”  They did this for two reasons.  This made life easier for those running the empire but a common culture also brought legitimacy to their rule.

Religion was the final unifier.  This is how Harari defines religion, “Religion can thus be defined as a system of human norms and values that is founded on a belief in a superhuman order.”  All religions had two big rules, “First, it must espouse a universal superhuman order that is true always and everywhere.  Second, it must insist on spreading this belief to everyone.  In other words, it must be universal and missionary.”  Two pretty powerful rules, they knew their marketing.  It’s not a huge surprise that the idea of religion became such a unifier.

The Scientific Revolution

The Scientific Revolution started about 500 years ago.  Science was very different from the traditions that came before it in three primary ways, “The willingness to admit ignorance…The centrality of observation and mathematics….The acquisition of new powers.  Modern science is not content with creating theories.  It uses these theories in order to acquire new powers, and in particular to develop new technologies.”  This led to my favorite quote of the book, “The Scientific Revolution has not been a revolution of knowledge.  It has been above all a revolution of ignorance.  The great discovery that launched the Scientific Revolution was the discovery that humans do not know the answers to the most important questions.”

One of the kickers for science is that it needs an alliance with an ideology to flourish.  The ideology is necessary to justify the cost of research.  The two big allies for science were imperialism and capitalism.  One of the primary reasons why Europe dominated the Scientific Revolution was, in Harari’s words, “The key factor was that the plant-seeking botanist and the colony-seeking naval officer shared a similar mindset.  Both scientist and conqueror began by admitting ignorance – they both said, ‘I don’t know what’s out there.’  They both felt compelled to go out and make new discoveries.  And they both hoped the new knowledge thus acquired would make them masters of the world.”  This quote reminded me of the Patrick O’Brian books where Captain Jack Aubrey was always accompanied by Dr. Stephen Maturin, conqueror and naturalist going hand in hand to take over the world.

This ultimately led to the Industrial Revolution.  “The Industrial Revolution turned the timetable and the assembly line into a template for almost all human activities.”  This led to a great story he told about time.  All local communities used to track time in their own unique way.  Based on how they calculated time, It might be 8 AM in London but 8:04 AM in Liverpool.  This was true until trains starting making their way across Britain and the train timetables were getting all screwed up.  So, in 1847, the train companies set all of their timetables to Greenwich time  Thirty years later, the British government followed suit and that is how the world got Greenwich Mean Time.

The Industrial Revolution came with a serious downside.  “Yet all of these upheavals are dwarfed by the most momentous social revolution that ever befell humankind: the collapse of the family and the local community and their replacement by the state and the market.”  Neighbors used to work on barter agreements.  Your fence falls down, I help you fix it.  My wall topples, you help me.  With the Industrial Revolution all of this changed.  “In order really to break the power of family and community, they needed the help of a fifth column.  The state and the market approached people with an offer that could not be refused.  ‘Become individuals.'”  Study after study shows that when we are surrounded by family and community we are happier.  We love to describe ourselves as rugged individuals but the cost turned out to be a whole lot of happiness.

Harari is a bit of a cynic when it comes to happiness.  He broke happiness down into three theories.  The first is that happiness is in the hands of our biochemical system.  Once we can regulate that machine like a well-tuned air conditioner we can engineer our way into happiness.  Meh.  The second is that “perhaps happiness is synchronizing one’s personal delusions of meaning with the prevailing collective delusion.  As long as my personal narrative is in line with the narratives of the people around me, I can convince myself that my life is meaningful, and find happiness in that conviction.  This is quite a depressing conclusion.  Does happiness really depend on self-delusion?”  He didn’t like that idea either but this seems to be the Facebook fallacy.

Know Yourself

His third theory comes down to ‘Know Thyself!’.  This is the one I prefer.  He uses Buddhism as a way to describe this knowledge.  In Buddhism, “People are liberated from suffering not when they experience this or that fleeting pleasure, but rather when they understand the impermanent nature of all their feelings, and stop craving them.”  He goes on to add, “In contrast, for many traditional philosophies and religions, such as Buddhism, the key to happiness is to know the truth about yourself – to understand who, or what, you really are.  Most people wrongly identify themselves with their feelings, thoughts, likes and dislikes.  When they feel anger, they think, ‘I am angry.  This is my anger.’  They consequently spend their life avoiding some kinds of feelings and pursuing others.  They never realize that they are not their feelings, and that the relentless pursuit of particular feelings just traps them in misery.”

I like his systematic approach to analyzing happiness.  He seems to come to no conclusion on what theory is the best approach allowing us to draw our own.  He closes by bemoaning that we really don’t have any historical study of happiness and that is a huge gap in our collective knowledge.  “Most history books focus on the ideas of great thinkers, the bravery of warriors, the charity of saints and the creativity of artists.  They have much to tell about the weaving and unraveling of social structures, about the rise and fall of empires, about the discovery and spread of technologies.  Yet they say nothing about how all this influenced the happiness and suffering of individuals.  This is the biggest lacuna in our understanding of history.”  Lacuna, cool word.

Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies and Companies

Math and Science Book Review

Scale is an impressive body of work authored by one of America’s top scientists, Geoffrey West.  Dr. West recently headed up the Santa Fe Institute which is a think tank in the true sense of the term.  This is a bunch of scientists with the goal of advancing science unencumbered by some partisan political stance.  They bring in a ton of different scientists from many different disciplines and try to tackle the tough problems of the age.  One of their big targets has always been complex systems and building on an overall complexity theory.  In his book Scale, West takes on the big question of what happens to things when they grow.  He draws parallels between biological systems, cities and companies using a scientific approach backed with a good amount of layman’s math and illustration.

This is a wonderful book but it does require a pretty high level of concentration to get through all of the concepts.  While you don’t need a mathematical background to enjoy it, having a bit of that background makes the first read through a little easier and I would guess a little more enjoyable.  I found that as he dove into scaling and power laws I was able to draw a bunch of parallels to other scientific adventures I had taken in school or independent study.

He does a craftsman’s job of explaining what nonlinear growth means – “nonlinear behavior can simply be thought of as meaning that measurable characteristics of a system generally do not simply double when its size is doubled.”  He gives some solid definitions for what sublinear and superlinear growth mean and then starts hitting you with examples.  One of the most important example to understand is what happens to a structure when it grows.  If you are building a rudimentary square shed that is 10′ X 10′ X10′ and you decide to increase the length of each side by a factor of 10, the area and strength to support that area increases by a factor of 100.  So your 100′ X100′ shed now has an area of 10,000 instead of the original 100.  The volume increase and the strength to support it is even worse, you go from a volume of 1,000 to a volume of 1,000,000 which is a massive increase required in the strength to support the structure.  Another example is the Richter scale for earthquakes which is a logarithmic (exponential) scale.  So an earthquake that registers as a 6 on the Richter is 10 times more powerful than one that registers as a 5 and 100 times more powerful than one that registers as a 4.

This concept of Scale and it’s nonlinear growth make up the central questions answered by the book.  His first exploration of scale is through biology where we learn why larger animals live longer than smaller animals on average.  “Because larger animals metabolize at higher rates following the 3/4 power scaling law, they suffer greater production of entropy and therefore greater overall damage, so you might have thought that this would imply that larger animals would have shorter life spans in obvious contradiction to observations.  However…on a cellular or per unit mass of tissues basis metabolic rate and therefore the rate which damage is occurring at the cellular an intracellular levels decreases systematically with increasing size of the animal-another expression of economy of scale.”  The main takeaway then being, “So at the critical cellular level cells suffer systematically less damage at a slower rate the larger the animal, and this results in a correspondingly longer life span.”

He dives deep into the scaling of cities and finally the scaling of companies but through all three of these systems he comes up with a universal theory of how we scale ‘allometrically’:  “the generic geometric and dynamical properties of biological networks that underlie quarter power allometric scaling are: (1) they are space filling (so every cell of an organism, for instance must be serviced by the network); (2) the terminal units, such as capillaries or cells, are invariant within a given design (so, for instance, our cells and capillaries are approximately the same as those of mice and whales); and (3) the networks have evolved to be approximately optimal (so, for instance, the energy our hearts have to use to circulate blood and support our cells is minimized in order to maximize the energy available for reproduction and the rearing of offspring).”

He then ties this directly to cities and companies.  In a city, our road and transportation networks must fill space to service every region as do all of the utilities that must service homes and buildings.  This is also true of social networks, we collectively fill the socioeconomic space available to us.  As far as the terminal units go, he uses the plug as a great example.  A plug is the same standard size regardless of what you plug into it.  Finally, we will always try to optimize these systems for both biological and economic reasons.

One other point that I found fascinating and is worth highlighting in this review is around what happens when we get too big.  “In this scenario demand gets progressively larger and larger, eventually becoming infinite within a finite period of time.  It is simply not possible to supply an infinite amount of energy, resources, and food in a finite time.  So if nothing else changes, this inextricably leads to stagnation and collapse,”  The key here is ‘so if nothing else changes’ because this is where innovation comes into play.  He addresses innovation with, “A major innovation effectively resets the clock by changing the conditions under which the system has been operating and growth occurring.  Thus, to avoid collapse a new innovation must be initiated that resets the clock, allowing growth to continue and the impending singularity to be avoided.”  Sounds good right?  If we just keep innovating we’ll be fine.  Not so fast.  “There’s yet another major catch, and it’s a big one.  The theory dictates that to sustain continuous growth the time between successive innovations has to get shorter and shorter.  Thus paradigm-shifting discoveries, adaptations, and innovations must occur at an increasingly accelerated pace.”  So, to keep growing we have to innovate faster and faster but it seems inevitable that we will eventually hit this limit and stagnate.  Scary stuff.

There are many more beautiful nuggets of wisdom within these 500+ pages but it does tend to get dry at times.  Stick with it because it is a brilliant, innovative way to look at what happens when things get bigger.

How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics

Math and Science Book Review

Math and Science Book Review

Eugenia Cheng takes on the ambitious task of trying to bring the excitement of math to the lay person through the study of category theory.  This is a long shot that requires truckloads of metaphors.  Luckily, she has a deft hand at metaphor and she does an admirable job of bringing her excitement about the subject matter to the page.  She starts simple with, “Mathematics is the study of anything that obeys the rules of logic, using the rules of logic.”  For you Vulcans out there, this means that math can study damn near anything, except for maybe teenage girls.  One of the really cool aspects of math is that it is based on that very simple premise, math can take us to crazy new places.  Another one of her great metaphors, “Do you know that feeling of climbing to the top of a hill, only to find that you can now see all the higher hills beyond it?  Math is like that too.  The more it progresses, the more things it comes up with to study.”  This certainly brings to mind an internal exploration of logic and reason that can seem almost limitless in it’s scope and breadth.  As long as you have the tools, there really are no limits to where math can take you and that really is exciting.

Two of the major tools to start this exploration are abstraction and generalization.  Abstraction begs the budding mathematician to ignore some details so that the situation becomes easier to understand.  In Cheng’s words, “Abstraction is like preparing to cook something and putting away the equipment and ingredients that you don’t need for this recipe, so that your kitchen is less cluttered.  it is the process of putting away the ideas you don’t need for the present purposes, so that your brain is less cluttered.”  She goes on to acknowledge that abstraction is also dangerous and where we lose a lot of people in the weeds.  “Abstraction is the key to understanding what mathematics is.  Abstraction is also at the heart of why mathematics can seem removed from ‘real life’.  That detachment from reality is where math derives its strength, but also its limitations.”  She emphasizes that one of the keys to the mathematical method is being very clear about your assumptions.  This reminded me a lot of Nate Silver’s book, The Signal and The Noise, that dove deep into mathematical modeling.  One of his major premises was that mathematical models need sunlight shone on their assumptions from the very beginning to be successful.  You can tell that Cheng loves the process of abstraction because it opens up so many crazy doors, “Part of the process of abstraction is like using your imagination.  Mathematical abstraction takes us into an imaginary world where anything is possible as long is it’s not contradictory.  Can you imagine transparent Lego blocks?…Four dimensional Lego blocks?  Invisible Lego blocks?”

Before she dives into generalization she spends some time on mathematical rigor.  This is another area where I, as a physics major, always had a problem with math in school, mathematicians seemed to get all tied up in the minutia of the process which, in my mind, didn’t relate to the real world.  Cheng poses that math really is all about the process and that’s what makes it interesting, “Math is a world in which the end does not justify the means: quite the reverse.  The means justify the end; That’s the whole reason it’s there.  It’s called mathematical proof,…”  I’m starting to come around.

Generalization is the other major tool in a mathematicians toolbox.  “This is the point of generalization in mathematics as well – you start with a familiar situation, and you modify it a bit so that it can become useful in more situations.  It’s called generalization because it makes a concept more general, so that the notion of ‘cake’ can encompass some other things that aren’t exactly a cakes but are close.”

With these tools, imagination starts to become a mathematician’s friend.  “The key in math is that things exist as soon as you imagine them, as long as they don’t cause a contradiction….Do you think it’s cheating to solve a problem by inventing a whole new concept and declaring it to be the answer?  For me this is one of the most exciting aspects of math.  As long as your new idea doesn’t cause a contradiction, you are free to invent it.”  How many art majors would have become mathematicians with a teacher like Cheng?  It’s a shame that we teach math in this painful, rote methodology that squeezes all of the excitement out of what rigor and logic have to offer.  Math has been called a lot of things, but creative is rarely one of those things.  How do we bring this excitement back to the classroom?

She never gets into the nitty gritty of category theory, but instead she alludes to it through many different examples.  Here is one of them, “Whatever mathematics does to the world, category theory does for mathematics.  It’s a sort of meta-mathematics like Lego Lego…Category theory is also an organizing principle, just one that operates inside the world of mathematics.  It serves to organize mathematics.”  I never truly understood category theory from the book, just that it is worth looking into in more detail.

I thoroughly enjoyed reading the book, especially the actually mathematical examples that took me out of my comfort zone.  Those things that make you think beyond what you can see are what seem to bring true knowledge and this book is full of those things.  Overall though, it’s her joy of the subject matter that makes the book work.  It’s worth your while.

Post Navigation