How does the measurement of time impact your progress toward success? Have you ever wondered what is so special about December 31 that all success hinges on the values of your securities in relation to exactly 365 days, 5 hours, 48 minutes, and 20 seconds earlier?
Dear Family, Friends, and Clients,
Does time exist? If you sit and ponder this question in a quiet room alone it could cause deep enough thought to stimulate a little anxiety. “Of course, it does- I can see the clock ticking right there.” But time is not consistent, it is relative. Due to gravitational time dilation, a watch on your ankle will eventually fall behind a watch on your wrist given sufficient ticking years- which means that technically, your head ages faster than your toes. Furthermore, due to relative velocity time dilation, an atomic clock on the International Space Station will fall behind an equivalent clock down on the ground because of the high speed at which it travels around the Earth; astronauts return home ever so slightly younger than they should be. In this case, the magnitude of the relative velocity time dilation is greater than the impact of gravitational time dilation, because the closer one is to the center of the Earth, the slower time moves. Time passes faster at the top of a mountain than it does at sea level. These are all minute effects that accumulate over many passing seconds, but it begs the question: Does time exist?
An even more important question is whether what we perceive as time requires observation to manifest. According to the relationalists, time is really a measure of motion; it prevents everything from happening at once. It prevents the motion of particles viewed by us as events from occurring simultaneously. In a sense, there is no motion without time- and is there time without an observer? Quantum Physics has shown that subatomic particles only exist as probabilities until they are measured. St. Augustine of Hippo (354-430 AD) concluded that “time is all in our heads” after a lifetime of pondering, and many physicists and philosophers agree with him.
So how does the measurement of time impact your progress toward success? We are told that average annual returns, as compared to an index, are the way we should judge our success. Some even wring their hands over quarterly returns or even shorter periods of time. Have you ever wondered what is so special about December 31 that all success hinges on the values of your securities in relation to exactly 365 days, 5 hours, 48 minutes, and 20 seconds earlier? Determining the validity of this last premise will be our purpose in this exploration.
Alfred Korzybski was a Polish American academic who developed a discipline called General Semantics. His theory was that no human can directly experience reality because we are limited by our senses and by our language. There are certain concepts and emotions that we simply lack the words to express, so we are forced to use the words we have available to give an estimate of what we think, or how we feel. “The map is not the territory”, was his famous mantra. Looking at a map of Germany does not allow the viewer to experience Germany, even though it can help one understand the structure of the country. We can never truly think outside of abstractions, because of the physical limits of our nervous system and the structure of our lexicon. I bring this up because we will discuss time as an abstraction, and we may never truly understand the nature and reality of time.
Base Units of Time
Let us consider whether time is continuous or discreet. In other words, is there a measure of time that is a still frame, like a movie, or is it infinitely divisible? The smallest theoretical unit of time is Planck Time, which is 10-43 seconds. That is a decimal, followed by 42 zeros, 1. The smallest unit of time that has been measured is the zeptosecond. A zeptosecond is a trillionth of a billionth of a second, and it measures how long it takes for single photon to travel the length of a hydrogen atom. Apparently, it takes 247 zeptoseconds for this journey, but we will have to take their word for it. An even larger measure is the attosecond, which is 1,000 zeptoseconds. 100 attoseconds is to 1 second as 1 second is to 300 million years. 24 attoseconds is the atomic unit of time. It appears that the search for an infinitesimal tick of time is still currently beyond our ability to measure it, so we will have to consider time continuous given the information that we have.
“You’re splitting hairs, Allen, who cares about this, let’s talk about stocks!” A perfectly rational opinion on the subject- but putting time into perspective is an important key to the emotional aspect of investing. Spinoza said that you must “measure all things in the aspect of calamity”, but I have also read that same quote translated as “measure all things in the aspect of eternity”, the latter I like better, but they are both poignant statements. Understanding the massive scope and scale of time allows us to find our exact location in the Universe. As Tennessee Williams wrote in The Glass Menagerie, “time is the longest distance between two places.” If we define distance in terms of difficulty and effort required to reach, imagine how far you are from any day in your past, even when you are standing in the same spot. Our longest measures of distance are the time it takes for light to travel.
Time feels like a river of motion that moves us from one “now” to the next. If you think about your life, you spend 100% of it living “now”, but you probably spend 98% of it thinking of sometime in the past or the future that isn’t “now”. Yet each successive “now” is the culmination of all the decisions you’ve made in a period of time that was not “now”. Each “now” you experience is dependent on your decision making at a point in the Universe that has become impossible to reach. This is why we put so much emphasis on good decision making; there are no do overs for reality. Once we have made a bad decision, all future moments are shaped by the impact of that error. It would be just as difficult to change something that happened 1 minute ago, than it would be to change Julius Caesar’s crossing of the Rubicon on January 10, 49 BC, which if you read on you will find that even locating that day may be impossible given the difficulty inherent in measuring our trips around the sun.
The current best estimate of the age of the Universe is 14 billion years. To put that into perspective, according to Carl Sagan, “if the cosmic calendar is the size of a football field, all of human history would be the size of my hand”. If the Big Bang occurred during the first second of January 1, all of human history would be the last 10 seconds of December 31. Modifying Spinoza’s advice to view things in the aspect of eternity seems punitive in this case, so we will limit ourselves to relevant eternity. But what amount of time is relevant?
Tracking, Measuring, Naming
The first possible observation of a hominid tracking time was found in the Dordogne Valley in France. Archeologists found an eagle bone with hash marks estimated to be about 30,000 years old. While there is no proof that the carvings are meant to track the passing of moon phases, the pattern and number of tallies is consistent with a 29.5-day month and contains 2.5 months of data. There is also the possibility that the carvings are counting hunting kills, or simply used for knife sharpening. 24,000 years later, in the Neolithic Period, large stone structures called megaliths were being built so that position of the sun would indicate what time of year it was. As the rising sun made its way around the ring of stones, it would reveal within a few days how far away time to plow, sow, or reap was at any given time, when animals would migrate, and when the leaves on the trees would return. There are even some funerary megaliths that focus light on a back wall only on the day of the winter solstice. Tracking the seasons allowed primitive humans to gain their bearings on what time of year it was and allowed them to reliably practice agriculture. The winter solstice let them know that the days were about to get longer, and that winter had arrived.
Once civilization progressed to the point of standardized spoken languages and written words, they turned their eyes to the sky and began making observations of the stars to have a clearer view of exactly what time in the cycle of life it was, and what that meant for weather, crops, animal migration, and eventually religious holidays. As early as 1600 BC the Babylonians were making observations of Venus, and not much later the Egyptians were finding repeating patterns in the sky that correlated with the annual flooding of the Nile, a critical event in their farming cycle. Around 700 BC, Greek writer Hesiod wrote, “when the Pleiades, daughters of Atlas, are rising, begin your harvest, and your plowing when they are going to set”. The first true calendar predates these astronomical observations and was created by the Sumerians in around 2000 BC. The Sumerian Calendar was a lunisolar calendar that broke the year (solar cycle) into 12 months (lunar cycle). The Sumerian calendar was followed by the creation of calendars by the Egyptians, Assyrians, Hebrews, and Chinese.
Our modern calendar is descended from the Roman calendar. The original Roman calendar had 304 days, broken down into 10 months, which meant that it consistently deviated from the tropical year. Our months of September, October, November, and December mean 7th, 8th, 9th, and 10th months, respectively, and oddly enough, the new year began in March for many centuries. By the time of Julius Caesar, the year had expanded to 355 days, and in order to rectify the drifting seasons, magistrates or priests (depending on the source) would decree additional months of varying degree to restore synchronization with the solar year. Unfortunately, as is true of human nature, political motivations soiled this process, and favored Senates would get extra days and unfavored Senates would get fewer days, and various other schemes ensued to personally enrich the lords of the calendar. Caesar attempted to clean up the political machinations involved in keeping the calendar by bringing together scholars to study the heavens and implement the new Julian Calendar. The first year of implementation, 46 BC, had 445 days and he called it “the last year of confusion” (ultimus annus confusionis).
Alas, the poor Julian calendar only had 365.25 days in the year and was consistently running short by 11 minutes per year. That doesn’t sound like much, but by the 16th century, the calendar was 11 days behind reality, and it was starting to push Easter into the summer. A travesty in the mind of Pope Gregory XIII. So, a new commission was formed, and our current calendar, the Gregorian Calendar, was devised with the help of a physician named Aloysius Lilius, and a few other Jesuit priests and astronomers. The new calendar was 365 days, 5 hours, 48 minutes, and 20 seconds. Unfortunately, still 26 seconds short of reality. Our current calendar gains a day every 3,300 years.
To catch the Gregorian Calendar up to reality from the Julian Calendar, 11 days had to be skipped. Most of the predominantly Catholic nations adopted the new calendar soon after October 15, 1582- the day after October 4, 1582. However, England held out until 1752, and on September 14 of that year, mass protests ensued to “give us back our 11 days”. Seems the peasants were under the impression that their life had been shortened by the skipped days, and merchants and landlords were afraid of losing interest and rent. Russia joined us in 1918, and the last holdout, China, relented in 1949.
With the invention of the lunisolar calendar, the year was neatly broken down into 12 months and weeks were broken down into 7 days, which is mostly likely because the 29.5-day lunar cycle has 4 phases of 7.375 days each. Saturday, Sunday, and Monday are named after Saturn, Sun, and Moon, respectively. Tuesday through Friday are named after German gods: Tiw, Woden, Thor, and Freya.
Even after the advent of a neat and tidy calendar that perfectly tracks the heavens, the days themselves are amorphous. There is morning, and mid-day, and evening, but at what exact point in time on a certain day should you show up for an important meeting? The Egyptians had obelisks and the Babylonians and Greeks had sundials, but these could only approximately calculate the time, and only during the day, and the length of the hours depended on the seasons. The Romans were especially uninterested in time, which is illustrated by a story of a sundial being captured by general Valerius Messalla in the Greek colony of Catana. Due to differences in latitudes the dial was especially inaccurate in Rome, which they did not discover for over a century.
The number of hours in a day comes from the Egyptians, who used a set of 24 stars at night to track the passage of time, the final 12 of which marked the passing of the night. The day was also broken down into 12 increments, but because the day extends and shortens with the seasons the hours of the day were significantly shorter in the winter than they were in the summer. The Greeks were the first to standardize the day into equal hours through out the year, but there were some parts of Europe that still used variable hours until the 14th Century. As luck would have it, the Earth is 24,901 miles in circumference at the equator, which means that our 24-hour day breaks neatly into 24 time zones of approximately 1,000 miles each. Time zones were not implemented until November 18, 1883, because of frustration by railroads. It seems that since all time was kept local, in relation to the sun’s position at high noon, a person traveling from Boston to New York would have to change his watch no fewer than 12 times; nearly impossible circumstances under which to keep railroads timely.
The number of seconds and minutes in a day can most likely be attributed to The Babylonians, who were on a sexagesimal, or base 60, number system. 60 has 12 factors and can be easily divided into halves, thirds, fourths, fifths, and sixths. In fact, 60 is the smallest number that is divisible by all numbers from 1 to 6. The Greeks were the first to codify this system, using Babylonian math. Sundials and water clocks were the most useful system for tracking time for thousands of years. Water clocks, or clepsydra, were used by the Greeks and Romans to limit the time of a lawyer’s speech. The passage of time could finally be tamed and control the functions of daily society, such as churches, courts, Universities, and meals.
The first mechanical clock was invented around 1300 AD. There are scant records about this invention, but there is mention of a device owned by King Philip the Fair of France who died in 1314. Once the mechanical clock was available, all churches and town halls had them commissioned to control the regulation of the city’s activities, and the bells would wake you in the morning, ring to end your day at work, and remind you to say your prayers in the evening. Centuries later, every man in Europe was walking around with time in his pocket, and this was the beginning of how our lives became dominated by the passage of time.
It is important to note, that while for the most part the measurement of time is standardized across the globe, there is a wide variance in the approach to and respect for time. There are countries in South America, where showing up an hour late is no concern. There are cities in Japan where showing up 2 minutes late is a great insult. Dan Falk tells a story in “In Search of Time” about a man trying to make a phone call in Nepal that took the clerks 4 days to connect, which was no big deal to the inhabitants around him, because that’s just how long it takes to make a phone call. One study has shown a correlation (not causation) between the growth of an economy and the local respect for time. The faster paced, more disciplined economies seem to grow larger and be more efficient than countries with an easier pace of life. But that anecdote makes me wonder, which ones are happier?
The Time of Newton
Newtonian time is absolute time. It ticks on in the background incessantly, regardless of what goes on in space. Newton saw time like an unseen metronome that ticked away the progression of the heavens. He wrote, “Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly.” To Newton, time could be relied on as infallible. He was greatly disturbed by the discrepancy in manmade timekeeping devices, and this may have been the impetus for his insistence on the sanctity of “real time”.
Newton’s equations for the motion of heavenly bodies requires constant time in order to produce meaningful results, and the motions of large-scale bodies were significantly more accurate than clocks at the time. At the scale of heavenly bodies, a zeptosecond here, and an attosecond there are rounding errors, but most clocks of the age were only accurate to a few minutes over an entire day. Even during his day there were detractors from his vision of time as an absolute. Gottfried Leibniz was a proponent of relational time, which posits that time is simply a method of comparing one event to another, and like a flowing river, requires a bank to be measured; a reference point is needed to truly measure the passing of time. It is the motions of the bodies that define time, not time that defines their motion; it is their consistency that creates the magic.
The Time of Einstein
By the time Albert Einstein was working in the patent office of Bern in 1905 the laws of Newton were producing spurious results when measuring electricity and magnetism. James Clerk Maxwell had developed workaround equations to facilitate the measurement of electromagnetism and waves, which were required for the new electronic equipment that Einstein was evaluating for patent applications. But why did Newton’s laws hold so true for nature, but breakdown in the realm of electromagnetism? It seems that speed is a contributing factor when utilizing Newtonian physics. At everyday speeds the approximations made by Newton were accurate enough to produce predictive results. But at the high speeds involved with electricity and magnetism, the equations were too dependent on absolute time to hold true.
Einstein discovered that time is not absolute, it is relative. Time can dilate to preserve the absolute speed limit of light at 300,000 km/sec (denoted as c). He explains this process in “On the Electrodynamics of Moving Bodies” in a theory called “Special Relativity”. Imagine a person standing on a train traveling at 100 km/hr. If this person throws a tennis ball at 80 km/hr the ball will appear to move at 180 km/hr to an observer on the ground. The total velocity is equal to the sum of the two velocities, which is in line with Newtonian Physics. When high speeds are involved, this process no longer holds true. A person walking on a beam of light will still move at “c” when measured by a stationary observer. To the person on the light beam, time will physically slowdown in order to facilitate the process. Time will dilate to preserve the universal speed limit.
The crux of the matter here is that “now” no longer exists as a common experience. What I experience as now could be completely different to an observer traveling at higher or lower speed. In Newtonian Absolute Time, “now” is a common experience. Two people could be completely sure that moments are simultaneous. They can measure all things in relation to space, time, or both. In Einstein’s world of small particles at high speed, all predictions of reality become probabilistic, instead of deterministic. We can measure location or speed, but not both, and it even turns out that the position of a particle is not exact until we measure it. The act of observation causes the wave function to collapse and the position to become real.
I can hear the bets being placed now on how any of this can possibly be relevant to investing. Going back to our friend Korzybski, let us use the preceding narrative as an abstraction by thinking about bonds in terms of Newtonian physics and stocks in terms of Einsteinian physics. Bonds pay a fixed coupon, usually semi-annually, and usually for a fixed term. The physics of motion are appropriate for measurement because for a bond bought at par, the coupon can simply be clipped twice a year and put in your pocket. Any appreciation or depreciation will be settled when the bond matures, so being fully invested is paramount, and time is absolute. Annual returns are an appropriate measure in fixed income investments, and determinism applies, except in the case of defaults. The returns in fixed income are discreet, and the zeptosecond is a spurious measurement criterion.
Equities, on the other hand, are not so simple. They follow more closely the laws of probability and quantum mechanics when measured in terms of price. The dividend can be considered a coupon, but it is not fixed, can be eliminated at any time, and does not take into consideration the earnings retained by the company to fund future growth. Stock price fluctuations are stochastic and can go up or down at any time. With equities, it is as if the arrow of time doesn’t exist at all. Equities are a continuous pricing system, and taking a measurement at an instant in time gives us some idea of how much cash we can create, but does little to tell us how much value has been created or destroyed.
We run into trouble when we try to use the physics of Newton to measure stock returns. When we look at stock price fluctuations as coupons to be clipped, and put in our pocket, we are being misled. Stock prices are simply a matter of psychology in the short-term and they tend to get way ahead of themselves and then revert violently. A stock can increase for years without increasing profitability, only to be brought back to Earth in a single day. It is said that stocks take the stairs up and the elevator down.
Time in equity investment is relative, not absolute. There is no law of physics that says that stocks in motion will remain in motion. There is, however, a law that states that all shareholders in combination cannot take out more money from a company than goes into it. If you buy a security at $1,000 that is only worth $100, it is quite possible you will find someone to take it off your hands at a much higher price, but gravity eventually does apply to equity prices, especially when interest rates rise.
Even more disconcerting is the way that we measure equity prices. Neolithic man used megaliths to properly determine when to put the seeds in the ground to grow food. This measure of a year was extremely relevant and important to his survival. Equity prices were not marked to market annually until the late 1960’s. Before this time, investments were carried at their purchase prices and the return was measured in dividends and interest. Gains on sales were profit items added to the income statement. It is entirely possible for the value of a company to increase while the price declines, and even more common for a company to remain the same value while the price increases wildly. We try to pay attention to the value of what we own, not how much cash we can convert it into. At minimum, a measurement period should provide some tangible value to be relevant.
Have you ever wondered what exactly a trip around the sun has to do with the value of your portfolio? Why is December 31 such a special date that we add up all your stock price fluctuations and measure your success? What does a single year have to do with your success over a lifetime? A year is an infinitesimal and arbitrary measure of time in comparison to a human life, however, we put so much emphasis on how stocks have fluctuated over this period; some even wring their hands from quarter to quarter. It is as though we are counting attoseconds just because we have the technical capability.
Stock prices are indeed a cyclical system, but a single year has no meaningful impact on their progress. In fact, just like the Egyptians had variable days when measured by sundials, stock market cycles can be as short as 28 months, and as long as 12 years. But measuring progress over an entire cycle is much more relevant that a year or a quarter. The issue with annual performance measurement is that as you reach the later stages of a cycle, if you use annual performance, you will be pushed into riskier and risker investments at exactly the wrong time. Purchasing securities at a discount to fair value is the only methodology that will protect you from meaningful downturns through every stage of the market cycle. The downside is that at the end of the cycle, when irrationality begins to become prevalent, wise investing will produce meaningfully lower price-based returns until after the market corrects. You get to choose whether you look dumb before the end of the cycle, or after; we always choose before.
Your market returns over a lifetime are the sum of all the good and bad decisions you make. We try to make consistent decisions because market time is not absolute, and the physics of Newton are a poor methodology of measuring stochastic returns. All measures and tendencies are a collection of rules of thumb passed down over hundreds of years, and not all of them are relevant, or even useful. We ask that you measure our impact on your success over an entire market cycle and include all of the additional return we provide by being efficient on taxes, managing expenses, helping you plan for liquidity events, and preparing an adequate estate plan. These items add much more to your return over a market cycle than picking the hottest stocks.
Thank you, as always, for the trust you give us. We are focused on protecting your assets first, and maximizing return second. This is not to say that high returns are not a priority for us, it simply states that not messing up is much more key to your success than shooting out the lights. We use financial planning to determine what rate of return you need to facilitate your success, and we only take an amount of risk appropriate to produce that level of return with the retirement portion of your capital.
As the lead quote states, there are two powerful warriors, and time is a poor soldier on its own; the companionship of patience makes time much more effective.
Falk, Dan. In Search of Time: The Science of a Curious Dimension. Thomas Dunne Books, St. Martin's Press, 2009.
Mazur, Joseph. The Clock Mirage: Our Myth of Measured Time. Yale University Press.
MONDSCHEIN, KENNETH C. On Time: A History of Western Timekeeping. JOHNS HOPKINS UNIV Press, 2020.
Yourgrau, Palle. A World without Time: The Forgotten Legacy of gödel and Einstein. Penguin Books, 2007.