This summer I read Walter Isaacson’s illuminating biography of Albert Einstein, the man who is widely considered to be the greatest thinker of the 20th Century. In 1905, when he was only 26 years old, he published four groundbreaking papers that forever changed the way people understood space, time, mass, gravity and energy.
By the time Einstein turned 40 in 1919, at a moment when he was struggling to devise a unified theory of matter, he complained to a friend that “Anything truly novel is invented only during one’s youth. Later, one becomes more experienced, more famous – and more blockheaded“.
Einstein’s frustration at his diminished capabilities as he aged is a phenomenon that is considered common with mathematicians and physicists who seem to make their greatest contributions to science before they turn 40. Einstein remarked to a colleague that as he got older he felt his intellect slowly becoming crippled and calcified.
Why does this happen? In Einstein’s case, it was partly because his early successes had come from his rebellious traits. In his youth, there was a link between his creativity and his willingness to defy authority and the universally accepted cosmological laws of his day. He had no sentimental attachment to the old order and was energized at the chance to show that the accepted knowledge was wrong or incomplete. His stubbornness worked to his advantage.
After he turned 40, his youthful rebellious attitudes were softened by the comforts of fame, renown, riches and a comfortable home. He became wedded to the faith of preserving the certainties and determinism of classical science – leading him to reject the uncertainties inherent in the next great scientific breakthrough, quantum mechanics. His stubbornness began working to his disadvantage as he got older.
It was a fate that Einstein began fearing years before it happened. He wrote after finishing his most groundbreaking papers: “Soon I will reach the age of stagnation and sterility when one laments the revolutionary spirit of the young“. In one of his most revealing statements about himself, Einstein complained: “To punish me for my contempt of authority, Fate has made me an authority myself“. He found it even harder as he got older acknowledging “the increasing difficulty a man past fifty always has adapting to new thoughts”.
Einstein brilliance is beyond compare, but I can relate to his observation about doing your best work when you are young. When I look back at my personal life and work career, I recognize that I was at my most ambitious and innovative during the decades of my 20’s and 30’s.
My adult life exploded with big events in 1982, the year that I turned 22. In the timespan of that one year I managed to graduate from college, marry my college sweetheart, start my first professional job as an engineer, buy a new house and a new car, and learn that my wife and I were going to become first-time parents. I remember filling out a survey designed to measure the amount of stress in your life during that eventful year and being surprised when the calculated stress numbers registered so high that they indicated I should be dead!
But all of it was exhilarating to me at that point in my life. I was experiencing new things and accumulating knowledge like a sponge. I knew that my growing family would be counting on me to be a good provider – which gave me the incentive I needed to focus on building a stable career.
I was determined to be successful in my engineering role and threw myself into learning everything I possibly could about the company I worked for as well as the electronic test and measurement equipment that they manufactured.
Many of my co-workers had graduated from more prestigious universities than me and I felt that I had something to prove. I wanted to make a name for myself and grow my reputation and value within the company by making important contributions to the projects to which I was assigned.
I took several continuing education engineering classes at night to improve my knowledge of subject areas that I knew would be helpful to me at work, I sought out brilliant co-workers who could mentor me and give me wise advice on how to approach complex technical projects, and I questioned everything – wondering if there might be a better solution to the problems we were trying to solve.
This drive in my early career to be successful enabled me to do my most innovative and important work for the company during the decades of my 20’s and 30’s. In the span of my first 18 years working for the company, I was awarded two patents, helped develop multiple new test products which generated millions of dollars for the company, created automated software regression tests significantly lowering product development times while improving software quality, and published frequent technical articles for industry conferences and trade journals.
By the time I turned 40, I could point to many important career milestones and had achieved recognition as a top performer and leader within the company. The rewards of my hard work were a comfortable home and financial independence. With this success I began to have feelings of contentment that lessened my drive to take on new projects or solve interesting problems. I became comfortable and happy with life as it was – I no longer felt the need to over-extend myself.
I was satisfied to rest on my past achievements and to take on less tasking roles that would improve the product in evolutionary, rather than revolutionary ways. Over time, I became the wise, experienced, older mentor to younger employees who came to me for advice and direction.
I felt okay with that transition as I considered it my good fortune to be in a situation where I was able to share my knowledge with a new generation of ambitious young people who were ready to make their own marks on the world by inventing novel new solutions that were now beyond me. In some ways, being a part of those collaborative efforts made me feel better than my individual personal accomplishments.
The famous journalist Ed Bradley once interviewed Bob Dylan in 1998 on the television show 60 minutes, at a time when he was approaching 60 years old. During the course of the interview, Bradley asked Bob what the source of inspiration was for his famous early songs, the ones that led to him being recognized as the voice of a generation while he was still only in his 20’s.
Dylan replied that his early songs were almost magically written and that he felt some kind of power, outside of himself, flowing through him while was writing them. When Bradley asked if he could still tap into that penetrating magic now in his songwriting, Dylan paused and said; “No, I don’t know how I got to write those songs“. Bradley followed up and asked if that disappointed him, Dylan replied softly; “Well you can’t do something forever and I did it once… and I can do other things now – but I can’t do that“.
That is a healthy way, I believe, of thinking about what is possible for each of us as we age. My days of endless ambition and innovative thinking are past. But I can do other things now that I couldn’t do then. I can indulge hobbies that interest me, I can find new paths to hike and rivers to fish, I can help care for my mother in her old age and I can share what I have learned through my life experiences and pass it on to my grandchildren and the larger community via this blog.
There will only ever be one Einstein, none of us will ever be as brilliant as him – but if you are under 40, get busy by putting your spry young mind and youthful ambition to work! Maybe you too can come up with novel ideas and ways of doing things that will help change the world or someone’s life for the better.
And if you are over 40, you can be like Einstein in his older years; contributing in a positive way to his community and sharing his wisdom, experience and good fortune with the next generation. In the end, many of our late in life pursuits that we share with others can end up being more rewarding and meaningful to us than any personal accomplishments we achieve along the way.
My sleep patterns are a mystery to me. I do not understand why they frequently change or why I so often find myself waking up in the middle of the night, usually at 3 a.m. I have difficulty falling back to sleep even when I practice the usual tricks that have helped put me to sleep in the past (quiet music, meditation, prayer). When those tricks fail me, I eventually rise from my bed to work on some boring task until such a time that my body and mind feel ready to sleep again.
Apparently I am not alone in experiencing periods of interrupted sleep. Sleep experts report that around a third of the population has trouble sleeping and difficulty maintaining continuous sleep throughout the night. I wonder if many of them, like me, have more than a passing familiarity with the 3 a.m. hour.
The author Ray Bradbury had something to say about 3 a.m. in his dark fantasy novel, Something Wicked This Way Comes:
“Three AM. Charles Halloway thought, it’s a special hour. Women never wake then, do they? They sleep the sleep of babes and children. But men in middle age? They know that hour well. Oh God, midnight’s not bad. you wake and go back to sleep, one or two’s not bad, you toss but sleep again. Five or six in the morning , there’s hope, for dawn’s just under the horizon. But three, now, Christ, three A.M. Doctor’s say the body’s at low tide then. The soul is out. The blood moves slow. You’re the nearest to dead you’ll ever be save dying.
Sleep is a patch of death, but three three in the morn, full wide-eyed staring, is living death! You dream with your eyes open… you lie pinned to a deep well bottom that’s burned dry. The moon rolls by to look at you down there, with its idiot face. It’s a long way back to sunset, a far way on to dawn, so you summon all the fool things of your life, the stupid lovely things done with people known so very well who are now so very dead – and wasn’t it true, had he read it somewhere, more people in hospitals die at 3 A.M. than at any other time…?
Ray Bradbury, “Something Wicked This Way Comes”
Why do many people feel afraid or uneasy about the time between midnight and sunrise – especially 3 a.m.? Is it some embedded memory of the horror novels and films we consumed in the past or is it an instinct left within us from our distant ancestors who had to battle nocturnal predators for thousand of years?
For starters, 3 a.m. is sometimes referred to as The Witching Hour, the time of night when some believe the veil between life and death is at its thinnest, allowing spirits and ghosts to travel more easily between the two worlds. The time between 3-4 a.m. is also thought of by some as the Devil’s Hour. The Catholic Church in 1535 forbade activities during the 3-4 a.m. hour because Jesus was crucified at 3PM – and the inverse of that would be 3 a.m. – making it an hour of demonic activity. The number 3 can be used to make a mockery of the Holy Trinity, also making it an ideal time to carry out acts of evil.
Over time, fear of the Witching or Devil’s Hour became common amongst large groups of people, so foul meaning was attached to it. If we’re always waking up disturbed at 3 a.m. then something dark and ominous must be at fault. I have a friend who shared with me that he becomes anxious if he happens to wake up at 3 a.m. and he has to get down on his knees and pray the Rosary in order to calm his spirit . Even those who do not fear spirits or ghosts seem to believe that nothing good really happens at 3 a.m.
My background in engineering has conditioned me to look for scientific explanations to mysterious phenomenon rather than the actions of sinister spirits, ghosts and demons from the shadow world. My research into the topic has revealed that human biology and evolution may have something to do with our often confounding sleep experiences, as well as our tendencies to wake up in the middle of the night.
For most people, 3 a.m. comes along right about the time our body is coming out of a REM phase, the moment of our deepest sleep; when our heart rate slows, our body temperature drops, and our brain turns off as many functions as possible so it can repair itself and so we can get truly deep rest. If we happen to wake up suddenly at the end of an REM phase, we are going to feel very disoriented. The natural reaction to these strange feelings is fear and unease because we can’t help but feel panic when we wake up feeling unlike anything we ever feel when we are conscious.
These nighttime awakenings are distressing for most sufferers, but there is some evidence from our recent past that suggests a period of wakefulness occurring between two separate sleep periods was normal. Throughout history, various medical texts, court records and diaries mention instances of segmented sleep – commonly referred to as “first” and “second” sleep.
In Charles Dickens’ book Barnaby Rudge (1840), he writes:
“He knew this, even in the horror with which he started from his first sleep, and threw up the window to dispel it by the presence of some object, beyond the room, which had not been, as it were, the witness of his dream.”
Anthropologists have documented that bi-modal sleeping was common in preindustrial Europe when sleep onset was determined not by a set bedtime, but by whether there were things to do. Historian A. Roger Ekirch’s book At Day’s Close: Night in Times Past describes how households during this time period retired a couple of hours after dusk, woke a few hours later for one to two hours, and then had a second sleep until dawn.
Ekirch noted that references to the first and second sleep started to disappear during the late 17th century as the Industrial revolution took hold. He believes the practice of consolidated nighttime sleeping started in the upper classes in Northern Europe and filtered down to the rest of Western society over the next 200 years.
Interestingly, the problems of reported insomnia start to appear in literature at the same time as accounts of split sleep start to disappear in the late 19th century. So it may be that modern society is placing unnecessary pressure on individuals to seek continuous consolidated sleep every night – even though there are natural biological tendencies in the human machine towards bi-modal sleep patterns.
Although we aspire to have consolidated sleep, this may not suit everyone’s body clock or work schedule. Perhaps some of us are more suited to the segmented sleep pattern practiced by our pre-industrial ancestors. In fact, some forms of segmented sleep are still accepted in today’s society. Cultures that allow for an afternoon siesta, for instance, acknowledge that our internal body clock lends itself to such a schedule because we naturally experience a reduction in alertness in the early afternoon.
A number of recent studies have found that split-shift sleep schedules provide comparable performance benefits as one big sleep, as long as the total sleep time per 24 hours adds up to around 7 to 8 hours. Several shorter sleeps during the course of a day can be just as beneficial for our health, performance and safety.
So my recommendation for all of you who have trouble sleeping is to forget about demons and witches, forget about manufactured sleep drugs, forget about trying to achieve what society tells you is the perfect consolidated sleep pattern – and simply find a sleep pattern that works for you and one that matches your own unique rhythm.
If you can manage to do that then maybe you will, like me, come to see 3 a.m. less as a foe and more as a friend!
Time is a familiar but mysterious concept. We think about and use it every day, yet it is difficult to describe what it actually is. Saint Augustine puzzled about time when he wrote, “What is time? If no one asks me, I know. But if I wish to explain it to someone who asks, I know not.”
Poets and philosophers throughout the ages have eloquently tried to capture how their senses perceive Time by using phrases such as; “Time is fleeting“, “Time waits for no man“, “Time heals all wounds” and “Time stands still“. None of these phrases, however, succeed in advancing a deeper understanding of the mystery that is Time.
My background in engineering led me to wonder about the concept of Time beyond the typical artistic and philosophical musings – to explore what science actually had to say about the mysterious subject. So, with curiosity and time on my hands, my search led me to an online course called the Physics of Time. In this month’s blog I will share some of the interesting insights I learned about Time from that course.
Time can be examined from two separate scientific perspectives. The first is a biological perspective which deals with internal human body clocks and how the brain processes and perceives time. The second is an external cosmological perspective which has to do with the origin and evolution of time in the known universe.
Human bodies and brains have a natural way to recognize the passing of time because we have predictable biological clocks – like breathing and the beating of our hearts – that exist within each of us .
With a heart rate of about 60 beats per minute and a lifespan of roughly 70 years, the human heart will beat approximately 2 billion times. Chickens have a much faster heart rate of about 275 beats per minute, and live only 15 years – but their hearts, in the end, will also have 2 billion lifetime heartbeats.
Science has observed that the hearts of most animals will beat somewhere between 1-2 billion times but there is an inverse relationship between heart rate and lifespan. In general, the faster the heart rate, the shorter the life span. I wonder if those animals who live fast and die young perceive time any differently than us longer life-span creatures.
Besides the heart and the breath, Neuroscientists have identified three kinds of timekeeping devices inside our brains. One part of the brain keeps track of what time of day it is, another part keeps track of how much time has passed while doing certain tasks and still other parts of the brain serve as alarm clocks for events set to happen in the future.
Different neuron pulses working together in the brain help us to perceive the passage of time. These pulses can be affected by stimulants, such as caffeine, and depressants, such as alcohol which interfere with neurotransmitters in ways that make our internal clocks speed up or slow down.
We experience other biological processes that don’t repeat themselves but still contribute to our awareness of time passing: We age; we think; we make choices; we plan for the future; we remember the past. All these different aspects of time are crucial to what it means to live our lives and be human beings. Perhaps the most important aspect of our awareness of the passage of time is the accumulation of experiences.
People have observed that when they are focused on a task, they don’t pay as much attention to the outside world or to their internal clock. This causes their internal timekeeping devices to slow down while the outside world speeds up. For example, I am surprised how quickly the hours elapse while I am engrossed watching my favorite sports teams compete in a big game.
In contrast, when we are bored and not focused on any one task, the opposite effect happens. Our internal clock seems to go faster while the outside world seems to slow down. For example, when I am stuck on an airplane with nothing to do, the plane trip seems to last forever.
Scientist have reported that subjects in high-stress experiments recollect that time slowed down for them during stressful events. One theory behind this phenomenon is that the more memories we accumulate, the more time we think has passed. Our brains, when we are in a high-stress situation, does its best to record absolutely everything. It accumulates a huge amount of data, so when you think about the situation afterward, you have more memories to leaf through—and, therefore, it seems as if more time has passed.
This theory gets support from the fact that time seems to pass more quickly as we age. Summer seemed to last forever when we were children, but it seems to rush by as we get older. It may be that when we were young in the summertime, such activities as going to the beach were new to us, but as we get older we experience fewer interesting new things. Our brains don’t take in as much new information and we create fewer memories than a child would; thus, time seems to pass more quickly for us compared to when we were a child.
To understand Time from a cosmological perspective is difficult because it requires the human mind to reckon with complex physical laws of the universe that were set in place at the beginning of the universe – and to consider hard to grasp time spans that are billions of years in length.
Most physicists believe Time began approximately 13.8 billion years ago with a singular event known as the Big Bang – the so called “birth” of the universe – a point where space underwent rapid expansion and the laws of physics as we understand them came into being. The Earth is about 4.5 billion years old, so it is a substantial fraction of the age of the universe.
At the beginning, all matter in the universe was densely packed and its temperature was extremely high. About 380,000 years after the Big Bang, the universe cooled sufficiently to allow the formation of subatomic particles and simple atoms. Giant clouds of these primordial elements later coalesced through gravity into matter, eventually forming early stars, galaxies and the other astronomical structures that are observable today.
The feature of matter that is inextricably linked with time is called entropy. Entropy is a way of talking about the disorderliness of “stuff” in the universe. It is the natural tendency of things to lose order over time. For example, a whole egg is very orderly, but if we break the egg, it becomes disorderly; if we scramble the egg, it becomes even more disorderly. A scientist would say that the egg moves from a low entropy state to a high entropy state.
In the long run, nothing escapes the Second Law of Thermodynamics
Entropy is the only quantity in the physical sciences that seems to imply a particular direction of progress, sometimes called an arrow of time. As time progresses, the second law of thermodynamics states that the entropy of an isolated system never decreases over significant periods of time. Entropy measurement can be thought of as a clock and things only happen in one direction of time – not the other. The past is always defined to be the direction in which entropy was lower.
The pull of entropy on matter is relentless. Everything decays. Disorder always increases. The increasing entropy of our universe over time underlies all the ways in which the past is different from the future.
It is the reason why you can disperse the scent of perfume from a bottle into a room, but cannot put the scent back into the bottle; the reason why you can mix cream into your coffee, but cannot un-mix it; the reason why cars eventually break down; the reason you remember the past and not the future; the reason you are born young and grow older; the reason you can make a choice about what to have for dinner tomorrow, but not about what to have for dinner yesterday.
When energy is in a low-entropy form, it can do useful work. When energy is converted into a high-entropy form, it becomes useless. We have fossil fuels sitting in the ground with energy in them in a concentrated form. We can extract the energy to do useful work because the entropy of the fuel is low. Once the fuel is burned it is converted to its high entropy form and it can no longer perform useful work. You can heat a room in your house by burning coal, but you cannot cool off a room in your house by unburning fuel and turning it into coal.
The common thread in these examples is irreversibility: Something happens in one direction, and it is easy to make it happen, but it does not happen in the other direction, or if it does, it is because we put effort into it. It does not spontaneously happen. Things go in one direction of time. They do not go back all by themselves.
It’s not time itself that treats the past, present, and future differently; it’s the arrow of time, which is ultimately dependent on all the “stuff” we have in the universe. It is the arrow of time that gives us the impression that time passes, that we progress through different moments. It’s not that the past is more real than the future; it’s that we know more about the past. We have different access to it than we have to the future.
Stephen Hawking combined the biological and cosmological elements of time into three distinct “arrow of time” components. First, there is the thermodynamic arrow of time—the direction of time in which disorder or entropy increases. Second, there is the psychological arrow of time. This is the direction in which we feel time passes—the direction of time in which we remember the past, but not the future. Third, there is the cosmological arrow of time. This is the direction of time in which the universe is expanding rather than contracting.
At the moment of the Big Bang our universe was in a condition of very low entropy and very high organization. That’s what got time started in the way we experience it in our everyday lives. Ever since the Big Bang, we’ve been living out the process by which the universe increases in entropy. That’s the influential event in the aftermath of which all humans live.
At this point in time the universe is in a condition of medium entropy. It is today that we have galaxies and stars and planets and life on those planets. Complexity depends on entropy; it relies on the fact that entropy is increasing. We don’t have to worry about how complexity can arise in a universe that is evolving. The simple fact that entropy is increasing is what makes life possible.
Scientists have confirmed that the universe continues to expand. Distant galaxies are moving away from us, and the farther away they are, the faster they are receding. The amount of space between us and the other galaxies is increasing.
The second law of thermodynamics predicts that the total entropy of the universe will continue to increase until it reaches equilibrium. The universe will calm down and become colder and colder. Everything will scatter to the winds, evolution will stop and we will have empty space once again. It is speculated by some that after a googol (1 x 10 to the 100th power) years from now, our universe will be empty space and that empty space will last forever.
There are some however who believe instead that multiple universes exist. According to this idea, the Big Bang was an event that is quite small in the history of a much larger multiverse. We see only a finite bit of the universe; perhaps farther away than what we can see, the universe looks very different. The fact that our own universe is inflating gives some credibility to this idea.
Those who talk about the possibility of a multiverse are simply observing that there is a barrier in our universe’s past beyond which we cannot see. Is there a finite amount of stuff out there? Is there an infinite amount of stuff that works exactly like the stuff we can see? Or is there an infinite amount of stuff and conditions that are very different from place to place? Until scientists can answer these questions, they can only speculate.
Regardless of which theory you believe about how the universe will ultimately evolve, we can say that all scientists agree that the universe is a complicated system, embedded in an environment that is far from equilibrium and that there is something called entropy that characterizes the organization or disorganization of us and our environment and results in the evolution of matter.
No discussion of Time would be complete without mentioning one of the most important contributions ever made to science – Albert Einstein’s 1905 publishing of the Theory of Special Relativity. Before Einstein, physicists thought of time as simple and absolute, a steady linear flow separate from the three dimensions of space.
Einstein showed that time is not simple and absolute but is actually influenced by speed and gravity. He stated that there is a link between motion in space and the passage of time. Space and time are fused together in what Einstein called 4 dimensional space-time.
Einstein theorized that Time runs more slowly for an object if it is in motion. Scientists proved this by synchronizing two atomic clocks and placing one clock in a stationary location and the other clock on a plane that was flown around the world. Upon landing, the clocks were no longer synchronized, the one that had been on the plane was milliseconds behind the one that was stationary – indicating less time had elapsed for the moving clock.
With Einstein’s relativity discovery, there is no such thing as one moment of time throughout the universe that everyone agrees on. Space and time are not absolute; they are relative – which means what we call time can be different for different observers.
How much time passes for an object depends on how you move through the universe. The network of satellites in space that carry precision atomic clocks for the global positioning system must be constantly compensated because they “lose” seven microseconds per day compared to ground clocks that are operating in a “slower time stream”.
The faster something moves, the “slower” it ages. Physicists call this effect time dilation. Theoretically, under its influence, a space voyager could return to Earth after a 20-year voyage to find himself hundreds of years in the future. To carry time dilation to its absolute extreme—as we approach travel at the speed of light, it is possible that time stops and immortality begins.
Space-time, Einstein’s four-dimensional reality of our universe, is a collection of an infinite number of events, just as space is a collection of an infinite number of points indexed by the three dimensions of space. Just as we think of all space as being “out there”, Einstein said we should think of all time as also being out there: “The difference between Past, Present, and Future is only an illusion, however persistent“.
I must admit that my deep dive into the science of time raised as many questions as it answered – but that doesn’t mean my study was a waste of my time. On the contrary, I gained some wisdom about life and walk away with a list of important things to remember that will help me make the most of whatever time I have left.
Remember that we are very, very small – Mankind is like a grain of sand in the vast Sahara Desert, occupying an infinitesimally small place in the universe. The astronomer Carl Sagan said that earth is nothing more than “a mote of dust suspended in a sunbeam and our time amounts to nothing more than a blip“. Compared to the enormity of the cosmos and the eternity of time, it is wise for us to keep an attitude of humility, remembering the short duration of our life and the insignificance of our daily struggles.
Be grateful we are alive – In a world full of matter, humans have been fortunate to form over time into a remarkable collection of atoms that are alive, conscious and capable of love and memory. As far as we know, we are the most advanced form of life in the wide universe. In his book Cat’s Cradle, Kurt Vonnegut expresses wonder and gratitude for the gift it was to have become what he called some of the “sitting up” kind of mud in the universe.
“God made mud. God got lonesome. So God said to some of the mud, “Sit up!” “See all I’ve made,” said God, “the hills, the sea, the sky, the stars.” And I was some of the mud that got to sit up and look around. Lucky me, lucky mud. I, mud, sat up and saw what a nice job God had done. Nice going, God. Nobody but you could have done it, God! I certainly couldn’t have. I feel very unimportant compared to You. The only way I can feel the least bit important is to think of all the mud that didn’t even get to sit up and look around. I got so much, and most mud got so little. Thank you for the honor! Now mud lies down again and goes to sleep. What memories for mud to have! What interesting other kinds of sitting-up mud I met! I loved everything I saw! Good night. I will go to heaven now. I can hardly wait… Amen
Kurt Vonnegut “Cat’s Cradle”
Embrace change – Entropy is a natural law, we can’t repeal it or wish it away. Entropy is what helps us to evolve and it is what makes life complex and interesting. So, rather than fight change – which is inevitable – it is healthier for us to embrace the change in our life and determine how we can best use it to evolve in ways that make us better.
Be Mindful of the Present – Sometimes it can be impossible to focus entirely on the present because it comes with an echo of the past and a foretaste of the future. Our minds typically refuse to stay in the present, constantly regretting a past that can never be undone or anxiously awaiting a future that may never arrive. The mind can be trained with Mindful Meditation techniques that teach us how to live “outside of time”, focusing our attention on each passing moment, slowing our perception of time and relieving us of our anxiety over past and future events.
Get busy and try something new – Time moves more slowly for a body in motion and we perceive the passage of time as moving slower during those moments when we are creating new memories. That tells me if I want to make the most out of time I should be pursuing activities that keep me moving and learning new things.
Don’t rule out the Divine – There is agreement among scientists that the universe started in a dense state of very low entropy and that it is expanding over time towards higher entropy. The questions that still puzzle scientists however is what triggered the Big Bang event and why did the universe start in such an unlikely state of low entropy? As a man of science and a man of God, I am somehow comforted when all questions cannot be answered and there is room in the discussions for us to ponder the possibility of a divine hand in the origin of the universe.
May you enjoy your own personal time travel trip – here’s hoping that you live every moment and love every day before your precious time slips away.
One of my post retirement goals is to spend more time reading. After living in my town for 8 years it felt good to finally visit my library last week to request a library card. I have a long list of books that interest me and plan to dedicate at least one hour every day to reading.
My reading list contains novels and biographies but it also includes technical books on engineering and mathematics. There is something profound and beautiful about the laws of mathematics which led Albert Einstein to equate math and logic with poetry and the philosopher Aristotle to observe that the mathematical sciences exhibit order, symmetry and limitation; and that these are the greatest forms of the beautiful.
Math is beautiful because it is governed by proofs, logic and a set of laws that can not be disputed. Mathematical laws properly applied to solve problems lead to insight and truth – solutions that can be trusted. In a world where so much of life falls into areas of gray, it is refreshing to work occasionally in the black and white world of math.
Today’s polarized political environment generates a lot of arguments and misinformation. Too many people purposefully practice the politics of division and fear – spreading select information that matches their personal biases of what is right and wrong; telling people what they want to believe; and keeping a closed mind to alternate facts that contradict their preconceived positions.
Decisions made with insufficient facts always invite danger. At critical moments, people tend to see exactly what they wish to see, rather than objectively considering all the facts. Logic is the beginning of wisdom and without logic bad decisions will be made. The country would be much better off if our governing officials eliminated emotion and party politics from their decision making process and instead used logic, facts, statistics, chemistry and science to craft wise policies that will best solve our nations problems.
I have discovered that there also appears to be health benefits associated with doing math. I recently worked on a book of Math puzzles which occupied and focused my mind over a period of several weeks. I was surprised that working on these puzzles had a positive effect on my mind and body similar to the effects I get when I meditate. While I am working on a math puzzle, all other life distractions temporarily disappear and I find that my mind becomes more focused and my body less stressed. I think a topic on “Mathematics Meditation” would make for an interesting TED Talk and be a good area for future studies in the meditation sciences field.
One last cool thing about math is that it can be used to perform magic tricks that will amaze your friends and encourage them to further explore the mysteries of math and numbers.
Try this Math as Magic trick with one of your friends:
Have a friend give you any 3 digit number [For example, the number 519 – this trick will work with any 3 digit number]
Repeat the digits to make a 6 digit number [519519]
Tell the friend that your magical power leads you to believe that the number is evenly divisible by 13 [519519 / 13 = 39963 : No remainder!]
Now tell the friend that you feel the resulting number is evenly divisible by 11 [39963 / 11 = 3633 : Again no remainder!]
Now, have your friend divide this new number by lucky number 7 and say Shazam when the number that is returned is the original 3 digit number they gave you [3633 / 7 = 519!]
“The laws of nature are but the mathematical thoughts of God” – Euclid
Although we aspire to have consolidated sleep, this may not suit everyone’s body clock or work schedule. Perhaps some of us are more suited to the segmented sleep pattern practiced by our pre-industrial ancestors. In fact, some forms of segmented sleep are still accepted in today’s society. Cultures that allow for an afternoon siesta, for instance, acknowledge that our internal body clock lends itself to such a schedule because we naturally experience a reduction in alertness in the early afternoon.
Words to Live By... 