Tag: Albert Einstein

Mental Model: Occam’s Razor

The Basics

Occam’s razor (also known as the ‘law of parsimony’) is a problem-solving principle which serves as a useful mental model. A philosophical razor is a tool used to eliminate improbable options in a given situation, of which Occam’s is the best-known example.

Occam’s razor can be summarized as such:

Among competing hypotheses, the one with the fewest assumptions should be selected.

In simpler language, Occam’s razor states that the simplest solution is correct. Another good explanation of Occam’s razor comes from the paranormal writer, William J. Hall: ‘Occam’s razor is summarized for our purposes in this way: Extraordinary claims demand extraordinary proof.’

In other words, we should avoid looking for excessively complex solutions to a problem and focus on what works, given the circumstances. Occam’s razor is used in a wide range of situations, as a means of making rapid decisions and establishing truths without empirical evidence. It works best as a mental model for making initial conclusions before adequate information can be obtained.

A further literary summary comes from one of the best-loved fictional characters, Arthur Conan Doyle’s Sherlock Holmes. His classic aphorism is an expression of Occam’s razor: “If you eliminate the impossible, whatever remains, however improbable, must be the truth.”

A number of mathematical and scientific studies have backed up its validity and lasting relevance. In particular, the principle of minimum energy supports Occam’s razor. This facet of the second law of thermodynamics states that, wherever possible, the use of energy is minimized. In general, the universe tends towards simplicity. Physicists use Occam’s razor, in the knowledge that they can rely on everything to use the minimum energy necessary to function. A ball at the top of a hill will roll down in order to be at the point of minimum potential energy. The same principle is present in biology. For example, if a person repeats the same action on a regular basis in response to the same cue and reward, it will become a habit as the corresponding neural pathway is formed. From then on, their brain will use less energy to complete the same action.

The History of Occam’s Razor

The concept of Occam’s razor is credited to William of Ockham, a 13-14th-century friar, philosopher, and theologian. While he did not coin the term, his characteristic way of making deductions inspired other writers to develop the heuristic. Indeed, the concept of Occam’s razor is an ancient one which was first stated by Aristotle who wrote “we may assume the superiority, other things being equal, of the demonstration which derives from fewer postulates or hypotheses.”

Robert Grosseteste expanded on Aristotle's writing in the 1200s, declaring that:

That is better and more valuable which requires fewer, other circumstances being equal… For if one thing were demonstrated from many and another thing from fewer equally known premises, clearly that is better which is from fewer because it makes us know quickly, just as a universal demonstration is better than particular because it produces knowledge from fewer premises. Similarly, in natural science, in moral science, and in metaphysics the best is that which needs no premises and the better that which needs the fewer, other circumstances being equal.

Early writings such as this are believed to have led to the eventual, (ironic) simplification of the concept. Nowadays, Occam’s razor is an established mental model which can form a useful part of a latticework of knowledge.

Examples of the Use of Occam’s Razor

Theology

In theology, Occam’s razor is used to prove or disprove the existence of God. William of Ockham, being a Christian friar, used his theory to defend religion. He regarded the scripture as true in the literal sense and therefore saw it as simple proof. To him, the bible was synonymous with reality and therefore to contradict it would conflict with established fact. Many religious people regard the existence of God as the simplest possible explanation for the creation of the universe.

In contrast, Thomas Aquinas used the concept in his radical 13th century work – The Summa Theologica. In it, he argued for atheism as a logical concept, not a contradiction of accepted beliefs. Aquinas wrote ‘it is superfluous to suppose that what can be accounted for by a few principles has been produced by many.’ He considered the existence of God to be a hypothesis which makes a huge number of assumptions, compared to scientific alternatives. Many modern atheists consider the existence of God to be unnecessarily complex, in particular, due to the lack of empirical evidence.

Taoist thinkers take Occam’s razor one step further, by simplifying everything in existence to the most basic form. In Taoism, everything is an expression of a single ultimate reality (known as the Tao.) This school of religious and philosophical thought believes that the most plausible explanation for the universe is the simplest- everything is both created and controlled by a single force. This can be seen as a profound example of the use of Occam’s razor within theology.

The Development of Scientific Theories

Occam’s razor is frequently used by scientists, in particular for theoretical matters. The simpler a hypothesis is, the more easily it can be proved or falsified. A complex explanation for a phenomenon involves many factors which can be difficult to test or lead to issues with the repeatability of an experiment. As a consequence, the simplest solution which is consistent with the existing data is preferred. However, it is common for new data to allow hypotheses to become more complex over time. Scientists chose to opt for the simplest solution the current data permits while remaining open to the possibility of future research allowing for greater complexity.

Failing to observe Occam’s razor is usually a sign of bad science and an attempt to cover poor explanations. The version used by scientists can best be summarized as: ‘when you have two competing theories that make exactly the same predictions, the simpler one is the better.’

Obtaining funding for simpler hypothesis tends to be easier, as they are often cheaper to prove. As a consequence, the use of Occam’s razor in science is a matter of practicality.

Albert Einstein referred to Occam’s razor when developing his theory of special relativity. He formulated his own version: ‘it can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.’ Or “everything should be made as simple as possible, but not simpler.” This preference for simplicity can be seen in one of the most famous equations ever devised: E=MC2. Rather than making it a lengthy equation requiring pages of writing, Einstein reduced the factors necessary down to the bare minimum. The result is usable and perfectly parsimonious.

The physicist Stephen Hawking advocates for Occam’s razor in A Brief History of Time:

We could still imagine that there is a set of laws that determines events completely for some supernatural being, who could observe the present state of the universe without disturbing it. However, such models of the universe are not of much interest to us mortals. It seems better to employ the principle known as Occam's razor and cut out all the features of the theory that cannot be observed.

Isaac Newton used Occam’s razor too when developing his theories. Newton stated: “we are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.” As a result, he sought to make his theories (including the three laws of motion) as simple as possible, with the fewest underlying assumptions necessary.

Medicine

Modern doctors use a version of Occam’s razor, stating that they should look for the fewest possible causes to explain their patient's multiple symptoms and also for the most likely causes. A doctor I know often repeats, “common things are common.” Interns are instructed, “when you hear hoofbeats, think horses, not zebras.” For example, a person displaying influenza-like symptoms during an epidemic would be considered more probable to be suffering from influenza than an alternative, rarer disease. Making minimal diagnoses reduces the risk of over treating a patient, or of causing dangerous interactions between different treatments. This is of particular importance within the current medical model, where patients are likely to see numerous different health specialists and communication between them can be poor.

Prison Abolition and Fair Punishment

Occam’s razor has long played a role in attitudes towards the punishment of crimes. In this context, it refers to the idea that people should be given the least punishment necessary for their crimes.

This is to avoid the excessive penal practices which were popular in the past, (for example, a Victorian could receive five years of hard labour for stealing a piece of food.) The concept of penal parsimony was pioneered by Jeremy Bentham, the founder of utilitarianism. He stated that punishments should not cause more pain than they prevent. Life imprisonment for murder could be seen as justified in that it may prevent a great deal of potential pain, should the perpetrator offend again. On the other hand, long-term imprisonment of an impoverished person for stealing food causes substantial suffering without preventing any.

Bentham’s writings on the application of Occam’s razor to punishment led to the prison abolition movement and our modern ideas of rehabilitation.

Crime solving and forensic work

When it comes to solving a crime, Occam’s razor is used in conjunction with experience and statistical knowledge. A woman is statistically more likely to be killed by a male partner than any other person. Should a female be found murdered in her locked home, the first person police interview would be any male partners. The possibility of a stranger entering can be considered, but the simplest possible solution with the fewest assumptions made would be that the crime was perpetrated by her male partner.

By using Occam’s razor, police officers can solve crimes faster and with fewer expenses.

Exceptions and Issues

It is important to note that, like any mental model, Occam’s razor is not failsafe and should be used with care, lest you cut yourself. This is especially crucial when it comes to important or risky decisions. There are exceptions to any rule, and we should never blindly follow a mental model which logic, experience, or empirical evidence contradict. The smartest people are those who know the rules, but also know when to ignore them. When you hear hoofbeats behind you, in most cases you should think horses, not zebras- unless you are out on the African savannah.

Simplicity is also a subjective topic- in the example of the NASA moon landing conspiracy theory, some people consider it simpler for them to have been faked, others for them to have been real. When using Occam’s razor to make deductions, we must avoid falling prey to confirmation bias and merely using it to backup preexisting notions. The same goes for the theology example mentioned previously – some people consider the existence of God to be the simplest option, others consider the inverse to be true. Semantic simplicity must not be given overt importance when selecting the solution which Occam’s razor points to. A hypothesis can sound simple, yet involve more assumptions than a verbose alternative.

Occam’s razor should not be used in the place of logic, scientific methods and personal insights. In the long term, a judgment must be backed by empirical evidence, not just its simplicity. Lisa Randall best expressed the issues with Occam’s razor in her book, Dark Matter and the Dinosaurs: The Astounding Interconnectedness of the Universe:

My second concern about Occam’s Razor is just a matter of fact. The world is more complicated than any of us would have been likely to conceive. Some particles and properties don’t seem necessary to any physical processes that matter—at least according to what we’ve deduced so far. Yet they exist. Sometimes the simplest model just isn’t the correct one.

Harlan Coben has disputed many criticisms of Occam’s razor by stating that people fail to understand its exact purpose:

Most people oversimplify Occam’s razor to mean the simplest answer is usually correct. But the real meaning, what the Franciscan friar William of Ockham really wanted to emphasize, is that you shouldn’t complicate, that you shouldn’t “stack” a theory if a simpler explanation was at the ready. Pare it down. Prune the excess.

I once again leave you with Einstein: “Everything should be made as simple as possible, but not simpler.

Occam’s razor is complemented by other mental models, including fundamental error distribution, Hanlon’s razor, confirmation bias, availability heuristic and hindsight bias. The nature of mental models is that they tend to all interlock and work best in conjunction.

Too Busy to Pay Attention to Life

“You act like mortals in all that you fear, and like immortals in all that you desire.”

— Seneca

Alan Lightman, the physicist who brought us The Accidental Universe, has also written several works of fiction, including Einstein’s Dreams, presented as dreams Einstein might have had while working as a patent clerk in Switzerland in 1905. More philosophy than physics, the book is a collection of thought experiments about the concept of time. Each of the hypothetical scenarios is only a few pages long, but all provide food for thought. What if we knew when our time would end? What if there were no cause and effect to our actions? What if there was no past? No future? If we could freeze a moment in time, what moment would we choose? And, most critically, are we spending our finite allotment of time on this earth wisely?

In one of Einstein’s dreams, people live forever. In this world, the population is divided into the Nows and the Laters.

The Nows note that with infinite lives, they can do all they can imagine … Each person will be a lawyer, a bricklayer, a writer, an accountant, a painter, a physician, a farmer. The Nows are constantly reading new books, studying new trades, new languages. In order to taste the infinities of life, they begin early and never go slowly…They are the owners of the cafés, the college professors, the doctors and nurses, the politicians, the people who rock their legs constantly whenever they sit down.

The Laters reason that there is no hurry to begin their classes at university, to learn a second language, to read Voltaire or Newton, to seek promotion in their jobs, to fall in love, to raise a family. For all these things, there is an infinite span of time. In endless time, all things can be accomplished. Thus all things can wait. Indeed, hasty actions breed mistakes … The Laters sit in cafés sipping coffee and discussing the possibilities of life.

If you recognized yourself or the people in your life in these descriptions, it’s not surprising. People in this world of infinite time are strikingly familiar to us because we live our lives as if we are going to live forever. We bury our awareness of our mortality beneath our busyness or convince ourselves that there will be time to live the lives we want ‘later’.

This is nothing new.

Over two thousand years ago, Seneca wrote:

What man can you show me who places any value on his time, who reckons the worth of each day, who understands that he is dying daily? For we are mistaken when we look forward to death; the major portion of death has already passed. Whatever years lie behind us are in death’s hands.

Too Busy to Pay Attention to Life

The Now personalities, the perpetually-busy, rushers-through of life, can be spotted in several of Einstein’s Dreams. A dream where “one may choose his motion along the axis of time”, illustrates the consequences of moving too quickly.

The woman catches her breath. She is fifty years old. She lies on her bed, tries to remember her life, stares at a photograph of herself as a child, squatting on the beach with her mother and father.

In another world, time passes more slowly for people in motion, but the faster people travel, the less happy they seem to be.

Because when two people pass on the street, each person perceives the other in motion, just as a man in a train perceives the trees to fly by his window. Consequently, when two people pass on the street, each sees the other’s time flow more slowly. Each sees the other gaining time. This reciprocity is maddening. More maddening still, the faster one travels past a neighbor, the faster the neighbor appears to be traveling.

These words strike a chord in today’s hectic, always-connected, world where we race from one commitment to the next, using our electronic devices along the way to maximize our productivity. But, as Seneca observes in On the Shortness of Life, multitasking only takes us further from our ultimate goal.

…no one pursuit can be successfully followed by a man who is preoccupied with many things…since the mind, when distracted, takes in nothing very deeply, but rejects everything that is, as it were, crammed into it. There is nothing the busy man is less busied with than living: there is nothing that is harder to learn.

We don’t slow down long enough to think. We're so focused on what's next that we rarely take the time to ask ourselves whether we’re living the life we want or if we’re even really present in the one we have.

Waiting for Life to Happen

Not everyone in Lightman’s tales is speeding through life. In one world, people get stuck in time.

In another house, a man sits alone at his table, laid out for two. Ten years ago, he sat here across from his father, was unable to say that he loved him…The man begins to eat, cannot eat, weeps uncontrollably. He never said that he loved him.

[…]

The tragedy of this world is that no one is happy, whether stuck in a time of pain or of joy. The tragedy of this world is that everyone is alone. For a life in the past cannot be shared with the present. Each person who gets stuck in time gets stuck alone.

In another of Einstein’s dreams, that will be painfully familiar to some, two couples are having dinner together, their conversation banal and meaningless.

For in this world, time does pass, but little happens. Just as little happens from year to year, little happens from month to month, day to day. If time and the passage of events are the same, then time moves barely at all … If a person holds no ambitions in this world, he suffers unknowingly. If a person holds ambitions, he suffers knowingly, but very slowly.

We can get stuck in the past, unable to let go of regret, or we can get stuck in a rut of routine, too uncertain of what the future might hold to risk chasing our dreams. Like the people in Dr. Seuss’s waiting place, we can end up ‘just waiting’…waiting for life to happen, passing our time in idle pursuits and telling ourselves that we’ll live the life we want when the mortgage is paid off or when the kids are grown or when we retire.

In On the Shortness of Life, Seneca writes:

How late it is to begin to live just when we must cease to live. What foolish forgetfulness of mortality to postpone wholesome plans to the fiftieth and sixtieth year, and to intend to begin life at a point to which few have attained!

Living a Life Less Short

Despite the title of his essay, Seneca argues that life is only as short as we choose to make it.

It is not that we have so little time but that we lose so much…the life we receive is not short but we make it so; we are not ill provided but use what we have wastefully.

In Moonwalking with Einstein, Joshua Foer suggests one way we can stretch out time.

Monotony collapses time; novelty unfolds it. You can exercise daily and eat healthy and live a long life, while experiencing a short one. If you spend your life sitting in a cubicle and passing papers, one day is bound to blend unmemorably into the next – and disappear. That’s why it’s important to change routines regularly, and take vacations to exotic locales, and have as many new experiences as possible that can serve to anchor our memories. Creating new memories stretches out psychological time, and lengthens our perception of our lives.

This also helps explain why time seems to move faster as we age. The older we become, the fewer novel experiences we tend to have.

In Lightman’s fictional worlds, the people who find contentment are those who learn to live in the moment. Staying in the present is surprisingly difficult to achieve, but practicing meditation and mindfulness can help us get there more often, and the reward when we do so is well worth the effort.

In the final dream of the book, time is a nightingale, as fleeting and elusive as the present moment.

On those occasions when a nightingale is caught, the catchers delight in the moment now frozen. They savor the precise placement of family and friends, the facial expressions, the trapped happiness over a prize or a birth or romance, the captured smell of cinnamon or white double violets. The catchers delight in the moment so frozen but soon discover that the nightingale expires, its clear, flutelike song diminishes to silence, the trapped moment grows withered and without life.

Einstein’s Dreams and Seneca’s essay On the Shortness of Life (also available free online) are both very quick reads. Reflecting on what they have to say is time well spent.

Albert Einstein on Education and the Secret to Learning

Albert_Einstein
In 1915 Einstein, who was then 36, was living in wartime Berlin with his cousin Elsa, who would eventually become his second wife. His two sons, Hans Albert Einstein and Eduard “Tete” Einstein were with his estranged wife Mileva in neutral Zurich.

After eight long years of effort his theory of general relativity, which would propel him to international celebrity, was finally summed up in just two pages. Flush with his recent accomplishment, he sent his 11-year-old Hans Albert the following letter, which is found in Posterity: Letters of Great Americans to Their Children.

My dear Albert,

Yesterday I received your dear letter and was very happy with it. I was already afraid you wouldn’t write to me at all any more. You told me when I was in Zurich, that it is awkward for you when I come to Zurich. Therefore I think it is better if we get together in a different place, where nobody will interfere with our comfort. I will in any case urge that each year we spend a whole month together, so that you see that you have a father who is fond of you and who loves you. You can also learn many good and beautiful things from me, something another cannot as easily offer you. What I have achieved through such a lot of strenuous work shall not only be there for strangers but especially for my own boys. These days I have completed one of the most beautiful works of my life, when you are bigger, I will tell you about it.

I am very pleased that you find joy with the piano. This and carpentry are in my opinion for your age the best pursuits, better even than school. Because those are things which fit a young person such as you very well. Mainly play the things on the piano which please you, even if the teacher does not assign those. That is the way to learn the most, that when you are doing something with such enjoyment that you don’t notice that the time passes. I am sometimes so wrapped up in my work that I forget about the noon meal. Also play ringtoss with Tete. That teaches you agility. Also go to my friend Zangger sometimes. He is a dear man.

Be with Tete kissed by your

Papa.

Regards to Mama.

Follow your curiosity and read letters from Hunter S. Thompson, Eudora Welty, van Gogh, Charles Bukowski, and Richard Feynman.

Einstein on the Ideas of Truth, Goodness, and Beauty

Albert Einstein

A reminder from The World As I See It:

A hundred times every day I remind myself that my inner and outer life depend on the labours of other men, living and dead, and that I must exert myself in order to give in the same measure as I have received and am still receiving. I am strongly drawn to the simple life and am often oppressed by the feeling that I am engrossing an unnecessary amount of the labour of my fellow-men. I regard class differences as contrary to justice and, in the last resort, based on force. I also consider that plain living is good for everybody, physically and mentally.

[…]

Schopenhauer’s saying, that “a man can do as he will, but not will as he will,” has been an inspiration to me since my youth up, and a continual consolation and unfailing well-spring of patience in the face of the hardships of life, my own and others’. This feeling mercifully mitigates the sense of responsibility which so easily becomes paralysing, and it prevents us from taking ourselves and other people too seriously; it conduces to a view of life in which humour, above all, has its due place.

[…]

The ideals which have lighted me on my way and time after time given me new courage to face life cheerfully, have been Truth, Goodness, and Beauty. Without the sense of fellowship with men of like mind, of preoccupation with the objective, the eternally unattainable in the field of art and scientific research, life would have seemed to me empty. The ordinary objects of human endeavour—property, outward success, luxury—have always seemed to me contemptible.

I feel very much that Einstein would have described beauty similar to Richard Feynman.

Albert Einstein on Sifting the Essential from the Non-Essential

Albert Einstein on Sifting the Essential from the Non-Essential

Charlie Munger once said: “We have a passion for keeping things simple.”

Albert Einstein says, “I soon learned to scent out what was able to lead to fundamentals and to turn aside from everything else, from the multitude of things that clutter up the mind.” Most of us try to consume more information, thinking it will lead to more signal, without thinking about how we filter and how we process the information coming in.

Knowing some basic principles helps as does knowing how to combine them. As Einstein says “A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability.”

It wasn't because he understood more about the complicated than other people, as John Wheeler points out in his short biographical memoir on Einstein:

Many a man in the street thinks of Einstein as a man who could only make headway in his work by dint of pages of complicated mathematics; the truth is the direct opposite. As Hilbert put it, “Every boy in the streets of our mathematical Gottingen understands more about four-dimensional geometry than Einstein. Yet, despite that, Einstein did the work and not the mathematicians.” Time and again, in the photoelectric effect, in relativity, in gravitation, the amateur grasped the simple point that had eluded the expert.

Where did Einstein acquire this ability to sift the essential from the non-essential? For this we turn to his first job.

In the view of many, the position of clerk of the Swiss patent office was no proper job at all, but it was the best job available to anyone with (Einstein's) unpromising university record. He served in the Bern office for seven years, from June 23, 1902 to July 6, 1909. Every morning he faced his quote of patent applications. Those were the days when a patent application had to be accompanied by a working model. Over and above the applications and the models was the boss, a kind man, a strict man, a wise man. He gave strict instructions: explain very briefly, if possible in a single sentence, why the device will work or why it won't; why the application should be granted or why it should be denied.

Day after day Einstein had to distill the central lesson out of objects of the greatest variety that man has power to invent. Who knows a more marvelous way to acquire a sense of what physics is and how it works? It is no wonder that Einstein always delighted in the machinery of the physical world—from the action of a compass needle to the meandering of a river, and from the perversities of a gyroscope to the drive of Flettner's rotor ship.

Who else but a patent clerk could have discovered the theory of relativity? “Who else,” Wheeler writes, “could have distilled this simple central point from all the clutter of electromagnetism than someone whose job it was over and over to extract simplicity out of complexity.”

Charles Munger speaks to the importance of sifting folly.

Part of that (possessing uncommon sense), I think, is being able to tune out folly, as distinguished from recognizing wisdom. You've got whole categories of things you just bat away so your brain isn't cluttered with them. That way, you're better able to pick up a few sensible things to do.

Albert Einstein to Marie Curie: Haters Gonna Hate

Einstien to Curie

“One never notices what has been done; one can only see what remains to be done.”
— Marie Curie

***

“Few persons contributed more to the general welfare of mankind and to the advancement of science than the modest, self-effacing woman whom the world knew as Mme. Curie.”

That's from the obituary of Nobel winning Marie Curie — the only person so far to win a Nobel in two difference Sciences.

Things, however, were not always easy for her.

In 1911, Curie was facing relentless attacks on her personal life saying that she “tarnished the good name” of her late husband Pierre Curie. She was denied a seat in the French Academy of Sciences in January 1911 for reasons that probably included gender and religion.

Albert Einstein took to the pen and paper and offered her some sage advice that is still relevant today. Not only did Einstein have a big brain, but he had a big heart.

The letter is part of nearly 5,000 of his personal papers that can be found online in The Collected Papers of Albert Einstein.

Highly esteemed Mrs. Curie,

Do not laugh at me for writing you without having anything sensible to say. But I am so enraged by the base manner in which the public is presently daring to concern itself with you that I absolutely must give vent to this feeling. However, I am convinced that you consistently despise this rabble, whether it obsequiously lavishes respect on you or whether it attempts to satiate its lust for sensationalism!

I am impelled to tell you how much I have come to admire your intellect, your drive, and your honesty, and that I consider myself lucky to have made your personal acquaintance in Brussels. Anyone who does not number among these reptiles is certainly happy, now as before, that we have such personages among us as you, and Langevin too, real people with whom one feels privileged to be in contact. If the rabble continues to occupy itself with you, then simply don’t read that hogwash, but rather leave it to the reptile for whom it has been fabricated.

With most amicable regards to you, Langevin, and Perrin, yours very truly,
A. Einstein

The advice reminds me of something Maya Angelou said, “The problem I have with haters is that they see my glory, but they don’t know my story.”

If you're interested in learning more check out Madame Curie: A Biography.

12