Outline History of Life and Human Evolution

The following Outline of the History of Life on Earth, and Human Evolution was written by my friend HWPTRA, a Life Sciences scholar. This outline history is a list of some of the significant events during the 4.5 billion years of Earth’s history. Any one of the entries in this list is itself a vast topic with an enormous literature (both scientific and popular) behind it; the brief descriptions here are little more than labels pointing the interested reader toward that literature (as on the Internet) for all the details.

The years and periods listed for the events are always to be taken as very approximate. As science advances, the time or period estimated for a listed event can be found to be different than previously thought, sometimes significantly different, and the sequence of events can even change as a result of new knowledge. So, this list is a snapshot of our knowledge today, where we understand that there are limits to the precision of that knowledge. Even so, it is a fascinating and enlightening presentation, which can help us gain a bare-bones yet integrated overview of the natural history that eventually produced us, Homo sapiens sapiens.

Following the outline history of life on Earth, I post a Histo-Map of human civilizations, compiled by John B. Sparks in 1931. To help the reader, I have posted six images of this map: one of the entire map, and five of sequential sections of the map. Also, I list a link to a website that shows a “big” version of the entire map. In all cases you will find lots of tiny print, and may wish to expand an image for easier reading (until it becomes fuzzy due to the low resolution of the original). The Histomap covers the interval of 2000 BC to 1930 AD, perhaps half of human history, and a very late 0.86 millionths of Earth’s history. Enjoy.


Outline of the History of Life on Earth, and Human Evolution

If the entire 4.5 billion years of Earth’s history were compressed into a single year:

1. January and February: it was too hot for any life to evolve.

2. March 1st to July 25th: bacteria were the only life forms on the planet.

3. July 25th: oxygen in the atmosphere was finally at near modern levels, and oxygen-using eukaryotic cells evolved.

4. November 20th: animals with backbones appeared.

5. December 22nd: first placental mammals appeared.

6. December 29th: the first apes appeared.

7. December 31st, 6:00 PM: Homo erectus appears.

8. December 31st, 11:46 PM: Homo sapiens (modern man) appears.

9. December 31st, from 11:59 PM to 12:00 AM (midnight): all of human history.











Histomap 2000BC-1930AD


Addendum (1 March 2017)


Earliest evidence of life on Earth ‘found’
1 March 2017

A Lifetime of Heartbeats

“I believe every human has a finite number of heartbeats. I don’t intend to waste any of mine running around doing exercises.”
– Neil Armstrong (5 August 1930 – 25 August 2012) (1)

There are 86,400 seconds/day, and 31.536 million seconds/year (365 days).

The normal resting adult human heart rate ranges from 60 to 100 beats-per-minute (bpm). Slow heartbeat rates of about 40-50 bpm during sleep are common and considered normal. Medically, heart rates of 50 to 60 bpm in apparently healthy people are taken as a good sign needing no further attention, while heart rates above 80 bpm may be due to some otherwise undetected unhealthy condition, if not caused by stimulants like caffeine, or bursts of exercise. The maximum heart rate a person can safely experience during bursts of strenuous activity decreases with age, being about 180-200 bpm for people in their 20s, 175-190 bpm for people in their 30s, 170-185 bpm for people in their 40s, 165-175 bpm for people in their 50s, 155-170 bpm for people in their 60s, and 145-160 bpm for people in their 70s. A human lifespan that is not prematurely interrupted may experience up to 3.5 billion heartbeats, or even more. (2)

Let us define a characteristic average heart rate, which we shall call the Armstrong Heart Rate (AHR) in honor of Neil Armstrong: test pilot, aeronautical engineer, university professor, and the astronaut who was the first human to step onto the surface of the Moon. Assume as typical an average heart rate of 66+2/3 bpm during three quarters of every day (18 hours), which includes periods of “calm” and periods of “activity” and “stress.” We assume that sleep occupies one quarter of every day (6 hours) with an average heart rate of 40 bpm. The daily average with these assumptions is

AHR = [3/4 x (66+2/3)] + (1/4 x 40) = 50 + 10 = 60 bpm = 1 bps (beats per second).

A human with a heart rate equal to 1 bps will experience 31.536 million heartbeats per year. Given this average heart rate, the total number of heartbeats over periods of time would be as follows.

Longevity - Heartbeat (table)Neil Armstrong’s lifetime of 82 years and 20 days experienced an estimated 2.58768 billion heartbeats.

The United States is listed 38th and ranked 34th among nations as regards average life expectancy. The overall life expectancy in the United States is 79 years. The U.S. is ranked 37th for male life expectancy, which averages 76 years, and it is ranked 36th for female life expectancy, which averages 81 years. (3)

By our AHR model of average heart rate, the average US male lifespan includes 2.396736 billion heartbeats, and the average US female lifespan includes 2.554416 billion heartbeats. The overall average (79 years) is 2.4913344 billion heartbeats.

So, the average US lifetime is one of about 2.5 billion heartbeats, assuming the typical heart rate is the AHR, which we defined as 1 bps.

Of course, heart rate can and will vary over the course of a lifetime, and human variability is wide, so in reality heart rates both above and below the AHR model will occur in the population. The AHR model helps us visualize the order of magnitude of total heartbeats experienced in a human lifetime.

The heartbeats per lifetime for a wide variety of non-human mammals ranges between 0.53-1.5 billion heartbeats; and is 2.17 billion for chickens that live 15 years, and 2.21 billion for humans that live 70 years. (4)

Since many animal species experience lifespans of about 1 billion heartbeats, we can think of them as “dying in our 30s.”

We can describe five stages of human life, based on the summation of heartbeats, as follows:

1 billion heartbeats to develop and grow into seasoned adults in three decades (to 31.71 years),

1 billion more heartbeats to experience three decades of productive adult life (to 63.42 years, 2 billion heartbeats),

1/2 billion more heartbeats over the course of 1.5 decades of retirement and denouement (to 79 years, 2.5 billion heartbeats),

a possible bonus of another 1/2 billion heartbeats and 1.5 decades of advanced old age (to 95.13 years, 3 billion heartbeats),

and a very few may experience another 1/2 billion heartbeats to live another 1.5 decades of extreme old age (to 111 years, 3.5 billion heartbeats).

For most of us who manage to avoid the fatal hazards of bad luck and disease, we can expect to experience lifespans of between 2 to 3 billion heartbeats, and most likely about 2.5 billion heartbeats.

The wise thing to do with your heartbeats is to spend the life they sustain on what you enjoy doing.

The only moral constraint (or aspiration) I would put on that enjoyment is: be kind.


[1] Neil Armstrong, https://en.wikipedia.org/wiki/Neil_Armstrong

[2] Heart rate, https://en.wikipedia.org/wiki/Heart_rate

[3] List of countries by life expectancy, https://en.wikipedia.org/wiki/List_of_countries_by_life_expectancy

[4] Animal longevity and scale, http://www.sjsu.edu/faculty/watkins/longevity.htm


Conformal Mapping of Dickinsonia Costata

Dickinsonia costata

Dickinsonia costata

Dickinsonia costata was one of nine species of Dickinsonia life forms, which resemble bilaterally symmetric ribbed ovals, which lived during the Ediacaran Period (635–542 Mya) and which went extinct, along with all the biota (life forms) of that period, by the beginning of the Cambrian Period (which occurred during 542-488 Mya).


The Ediacaran biota were enigmatic tubular and frond-shaped organisms living in the sea, and are the earliest known complex multicellular organisms. The adult phase of life in most Ediacaran species was spent at fixed individual sites, such as barnacles, corals and mussels do today. In contrast, the Dickinsonia moved around to feed.

My curiosity about Dickinsonia costata was sparked by reading Richard Dawkins’ description of this organism in “The Velvet Worm’s Tale,” which is in his book The Ancestor’s Tale, A Pilgrimage to the Dawn of Evolution (highly recommended).

What intrigues me is the similarity of Dickinsonia costata’s ribbed planform to the mathematical result known as the conformal mapping of a circle in cylindrical coordinates to a line segment in cartesian coordinates. I wrote about my use of this mathematical transformation to solve a problem in electrostatics in the blog entry

DEP Micro-device 2D Electric Field.

Conformal Mapping Circle-Line

Conformal Mapping Circle-Line

The left side of the diagram looks like a very simple model of a Dickinsonia costata planform. Hyperbolas branch out perpendicularly from a central line segment and fan apart, while ellipses of greater circularity with increasing distance from the central line segment cross the hyperbolas at right angles. The right side of the diagram shows a unit circle, which corresponds to the central line segment on the left, and radial rays (corresponding to the hyperbolas on the left) which are crossed at right angles by larger diameter circles.

The equations of the transformation conformally map each point of the radial (radius-angle) two-dimensional geometry, from the unit circle out, to corresponding points in the cartesian (length-width ’square grid’) two-dimensional geometry, from the line segment out. An inverse conformal mapping relates each point in the planar cartesian geometry to a corresponding point in the planar cylindrical geometry. Note that the interior of the unit circle corresponds to the collapsed now infinitesimal ‘interior’ of the line segment, and these spaces are excluded from consideration.

This conformal mapping is very useful in solving the problem in electrostatics of calculating the falloff in voltage from a flat strip electrode (the 2D part is the plane with finite line segment) that is infinitely long in the third dimension (“into” the paper or screen of the diagram). Physically, the ellipses of increasing circularity with distance from the line segment are contours (“surfaces” in a 2D view) of constant voltage. If the line segment (strip electrode) has a positive voltage, then the equipotential ellipses have decreasing voltage with increasing distance. If the line segment electrode has a negative voltage then the ellipses increase in voltage with distance. The rate at which voltage falls off from its value at the strip electrode is most rapid close to that electrode, and decreases (flattens out) with distance. The hyperbolas, which cross the elliptical equipotential contours, are the paths of greatest increase (for +) or decrease (for -) of voltage from the far distance into the line segment. The hyperbolas are lines of electric field, which is high where those lines are steep near the electrode, and which is low where those lines are flat, out at great distance.

It is much easier to arrive at the mathematical formulas for the equipotential ellipses and the hyperbolic field lines by first solving the corresponding problem in cylindrical coordinates, where the equipotentials are circles and the field lines straight radial rays, and then using the conformal mapping to arrive at the 2D cartesian result.

If we now imagine the unit circle and its corresponding line segment (in the above) to be the sensing centers of living and mobile organisms, then we can see that the radial rays and hyperbolas, respectively, are the paths of fastest communication with and reaction to the surrounding environment, and that a bodily bounding circle or ellipse, respectively, is a contour of simultaneous sensation of that external environment. Here, I am thinking of organisms that are flat and that do most of their living and moving two-dimensionally, that is to say more or less perpendicular to gravity.

The cartesian ‘strip electrode’ form of Dickinsonia costata gave it a head and tail (a fore and aft) as well as a left and a right (a bilateral aspect). In fact, the left and right sides of the Dickinsonia organisms were not mirror images of one another, but instead had an alternating pattern according to glide reflection symmetry. That is to say, a boundary rib or ridge or depression line on the right side emanates from the central line segment at a point midway between similar boundary hyperbolas on the left, and vice versa.

The fore-and-aft left-and-right layout of the Dickinsonia species meant that they had an internal coordinate system with which to reference the headings (directions) of sensations of the environment, and reactions to it in the form of motions.

It is probable (that is to say my uneducated guess) that they ingested nutrients by absorbing them (sucking them up) through their undersides from the algal mats they skimmed over in the sunlit shallows of Precambrian seas.

They could have moved straight ahead by alternately expanding the forward part of their bodies while contracting the rear, then contracting the forward segments (between the hyperbolas) while expending the rear ones, to produce a wave-like forward motion. Clearly, some point of contact would be necessary with the surface below Dickinsonia in order to gain traction for motion. Another possibility for motion would be an oscillation of the (nearly) elliptical bounding edge of the body into a wave-train that moved from head to tail (fore to aft), as a flounder, sea ray or skate does today.

Paleontologists have speculated that the Dickinsonia segments between hyperbolas were filled to overpressure with fluid (compared to the seawater exterior), so it is reasonable to speculate that these inter-hyperbola segments were plenums whose volumes (and widths) were modulated hydrostatically, for forward motion and for turning. A left turn could be effected by expanding the forward right side while contracting the forward left side, and simultaneously contracting the aft right side while expanding the aft left side. A right turn would require the opposite pattern of contractions and expansions.

It is possible that improvements in responsiveness and maneuverability were gained through evolution by collapsing an earlier cylindrically symmetric planform into the fore-and-aft left-and-right planform of the ‘strip electrode’ Dickinsonia organisms. If so, then Nature has made elegant use of the conformal mapping of a circular center of life into a linear one.



Correcting Publisher’s Errors in Einstein’s “Relativity”

In 1916, Albert Einstein (1879-1955) wrote a book in German for the general public about his theory of relativity, and he continued to add to it until its fifteenth edition in 1952. That book is called Relativity, The Special and the General Theory, and its English version is an “authorized translation by Robert W. Lawson.” That fifteenth edition has been in continuous publication since, and its copyright is held by “the Estate of Albert Einstein,” dated 1961.

It is a wonderful book. “The author has spared himself no pains in his endeavor to present the main ideas in the simplest and most intelligible form,” and Einstein’s exposition is a model of what every scientist should strive for in the clarity of their writing, and every journal should seek to publish to serve humanity’s interest in the widest dissemination of knowledge.

The particular edition of this book that I will comment on is published by Three Rivers Press, which is a trademark of Random House, Inc., and this edition of the book has the identification code: ISBN 0-517-88441-0. The publisher (NOT Albert Einstein!) — somewhere between the editor and the typesetter — has introduced errors into the text, and the purpose of this article is to show the corresponding corrections (to the three errors I have noticed). Page numbers are cited for the specific edition noted here.

Page 46 (Theorem of the Addition of the Velocities. The Experiment of Fizeau), footnote, in the second sentence (at the third line of text), a second closing parenthesis is needed for the expression for W, which should then appear mathematically equivalent to:

W = {w + v∙[1 – (v∙w)/c^2]}.

Note that the velocity w (of light in a motionless liquid) is much much greater than the velocity v (of the liquid in a tube). The speed of light in a vacuum is c. W is the “addition of velocities,” of light with respect to a liquid that is itself flowing along a tube, where W is observed from the frame of reference of the tube.

Page 129 (The Structure of Space According to the General Theory of Relativity), footnote, in the second sentence (at the third line of text), the symbol (label) “x” should instead be the symbol (label) “ƙ,” the Greek letter kappa. This makes line 3 consistent with the mathematical expressions in the previous lines of the footnote.

Page 124 (The Possibility of a “Finite” and Yet “Unbounded” Universe), the equation shown in the book is multiply wrong. The equation should be a mathematical statement that the ratio [circumference/surface diameter] = [pi] x [sine(nu/R)/(nu/R)], and this is always less than or equal to pi.

π ≥ π∙{ [sin(nu/R)] / (nu/R) } = [circumference/“radial” arc x 2]

The Greek letter “nu” can look like the lower case script “v,” which appears in the denominator of the erroneous formula on page 124. The first error to correct in that formula is to replace the lower case “r,” which is shown in the argument of the sine function, with the same “v” as in the denominator (and which “v” I will call “nu” further below).

The second error to correct is to replace the equal sign (=) with a multiplication symbol (×, or ∙), or to make that multiplication implicit by eliminating that equal sign and enclosing the entire ratio (corrected as above), to the right of the pi, within parentheses or brackets.

The lower case “r” that Einstein uses on page 125 refers to a quantity (an arc length along a “great circle,” my “radial arc x 2”) that is shown as the product 2x[R]x[theta] in the display that follows.

The following display shows what Einstein is describing on pages 124-125, and how the equation shown above comes about. The quantity (ratio) that should be printed on page 124 is shown within a hatched bean-shaped outline in the display. I leave it to you to enjoy that display, and I hope the trustees of Einstein’s legacy can cause future printings of “Relativity” to be free of textual errors.

Finite Unbounded

Finite Unbounded


Albert Einstein's desk

Albert Einstein’s desk, 19 April 1955

This is a photograph of Albert Einstein’s desk on 19 April 1955, the day after he died.

DEP Micro-device 2D Electric Field

I used to have the ambition of being an “artistic scientist,” a physicist and engineer aiming to produce scientific findings that were both useful and elegant, and which I would present in as beautiful a manner as I was able. The type of beauty I sought is a combination of logical simplicity, mathematical elegance, some range and depth of insight provided by the ideas, all communicated with visual and literary crispness in my written reports and other presentations.

I achieved this ideal, to my own satisfaction at least, a few times during my scientific career. One of those proud achievements is my model of the electric field in dielectrophoretic (DEP) micro-devices.

My original report “The 2D Electric Field Above A Planar Sequence Of Independent Strip Electrodes” is available below (a link to a PDF file). The report is dated 4 October 1999, and lists two authors; the second author is the patron who paid my salary during the months I worked on this project.

This paper was sent to a journal and subsequently published, but with egregious errors introduced by the journal’s editors, who “simplified” my math for publishing convenience. Months after I pointed this out to them, they issued an errata. The combination of the published paper and the errata (showing correct formulas) did not include many of the illustrations I had produced for my original report (Version 1), and which I think would help anyone actually thinking of using my mathematical model of DEP electrostatics.

So, this blog entry is similar to the case of a former artist who pulls out an obscure and favorite painting of theirs from storage in an attic or basement, dusts it off, and hangs it up on the wall so he can look at it again, and remember how good it felt to make.

A second report (an excerpt in PDF form) describes how use of the electrostatic model could assist in the development of DEP micro-devices (which are used in DNA sequencing technology).

DEP Device Diagram

DEP Device Diagram

DEP 2D Math Beauty

DEP 2D Math Beauty

DEP 2D Model Version-1

DEP 2D Model & micro-devices