Thursday, April 18, 2013

The Most Important Scatterplot Since Hubble?

In 1929, the astronomer Edwin Hubble published the following scatterplot based on his most recent astronomical measurements.

Figure 1. Edwin Hubble's original scatterplot

It shows the recession velocity of the "stars" (in km/s) on the y-axis and their corresponding distance (in Megaparsecs) on the x-axis. A Megaparsec is about 3.25 million light-years. This scatterplot is important for several reasons:

  1. The distances proved to be greater than the dimensions of our local galaxy, the Milky Way, at a time when the Milky Way was generally thought to be the entire universe.
  2. The slope of the linear fit gives the rate of expansion of the universe and therefore lent support to early notions of the whole universe arising from a single Big Bang event.
  3. The inverse of the linear slope (i.e., inverse of the expansion rate) corresponds to the time the universe has been expanding.
  4. Hubble's original calculations, based on the linear regression in Fig. 1, produced an age for the universe of about 2 billion years, when it was already well-established that the oldest rocks in the earth's mantle are on the order 5 billion years.
  5. This paradox arose because Hubble's data were wrong! More precisely, his measurement accuracy was relatively poor, by today's standards. However, it was the best available data that Hubble could produce at the time.
In spite of the inaccurate data, Hubble's linear model was correct, as the more recent scatterplot in Fig. 2 demonstrates. The adjusted slope corresponds to a correct age for the universe of about 15 billion years. Note the tiny red square at the origin. It corresponds to Fig. 1. That's what verification looks like.

Figure 1. Hubble scatterplot updated with 2003 measurements

Hubble's scatterplot and its implications helped to change the then existing view of the universe and our place in it. Arguably, that makes Fig. 1 the most important scatterplot in history.

Guerrilla mantra 1.16: Data comes from the Devil, only models come from God. That means it's helpful to be able to talk to God. But God, she does babel, sometimes.

At least, that's how things stood until a few weeks ago when the scatterplot in Fig. 3 appeared on the arXiv e-print server under the captivating title, Life Before Earth.

Figure 3. Log-linear scatterplot of organism evolution

Note that the y-axis is logarithmically scaled because it represents exponential evolution (the tree of life, as it were) rather than linear evolution, as in Figs. 1 and 2. The complexity of organisms is measured by the length of functional non-redundant DNA per genome counted by nucleotide base pairs, which increases linearly with time. Time, −t, is counted backwards—indicated by the negative sign—in billions of years starting from the present at −t = 0.

The interesting aspect here is not so much the slope of the regression fit (as it was for Hubble) but where it intersects the t-axis. The regression line intersects near −t = 10 billion years or 5 billion years before the earth had formed! (the vertical line in Fig. 3) I find the similarity between this paradoxical result about the age of life in the universe, and Hubble's paradoxical result about the age of the universe, to be quite striking.

The idea that life did not originate solely on the earth but derives from simple-cellular organisms that arrived here on board interstellar debris, is highly contentious—mainly due to lack of extraordinary evidence. But the idea that the entire universe somehow started with a single explosive event was also highly controversial during Hubble's time. Indeed, the notion of an expanding universe only began to take hold when the theoretical physicist, Monseigneur Georges Lemaître, rediscovered such an expanding solution in Einstein's (16-dimensional tensor calculus) equations of gravity. He proposed that if Hubble's expansion of the universe was projected backwards in time, that the volume of the universe would be smaller, until at some finite time in the past all the mass of the Universe would be concentrated into a single "primeval atom" from whence came the fabric of 4-dimensional space-time.

When Lemaître presented this mathematical solution to Einstein himself, he responded by telling Lemaître that although his solution was mathematically correct, his physics was abominable. This reaction was probably evoked, in part, because a decade earlier Einstein had been forced (by the math of the tensor calculus) to introduce an extra term to prevent his theoretical model of the universe from collapsing in on itself due to gravitational attraction. After all, everyone "knew" that the universe was in steady state, neither collapsing nor expanding. This extra term was known as the Cosmological Constant and it's what kept Einstein's mathematical universe in balance. After the publication of Hubble's scatterplot (Fig. 1), however, Einstein was forced to eat his words and ultimately confessed that introducing the cosmological constant had been the biggest blunder of his life. (I wouldn't mind owning such blunders) In another ironic twist, astrophysicists are now reconsidering the role of the cosmological constant as a possible explanation for so-called dark energy effects.

Controversial though it may be, the Panspermia hypothesis is not new. I first became aware of such an idea from the work of the British astrophysicist, Fred Hoyle. That work is cited in the Life Before Earth preprint as

Wallis, M. K., and Wickramasinghe, N. C. 2004. "Interstellar transfer of planetary microbiota," Monthly Notices of the Royal Astronomical Society, 348(1): 52-61.
The earlier joint work of Hoyle and Wickramasinghe can be found in
Fred Hoyle, Chandra Wickramasinghe and John Watson (1986). Viruses from Space and Related Matters. University College Cardiff Press.

In yet another ironic twist of fate, it was Fred Hoyle who coined the term "Big Bang" (in a moment of British sarcasm) because he favored a competing cosmological model called the Steady State model. That model was actually more consistent with Einstein's original equations that included the cosmological constant (well after Einstein had dropped that requirement). The Steady State model was finally eliminated from contention with the serendipitous observation of the microwave echo of the Big Bang in 1964.

In summary, we have from Hubble (the person and the telescope) that the universe came into existence as a consequence of the Big Bang roughly 15 billion years ago. The earth formed in the last third of the universe's life. Read that again: the entire universe is only three times older than the earth! And now we have this new DNA-based analysis indicating that life came into existence during the first third of the universe's life. That analysis lends support to the panspermia hypothesis that carbon-based life is not unique to the earth. Incredible, if it holds up under further scrutiny. Even though there's quite a high likelihood of significant errors in the analysis based on the DNA data in Fig. 3, it's worth keeping in mind that Hubble's data were also wrong, but his model was right.


AnneH said...

Both equations show that the distance of galaxies moving away and Genome size are exponential functions of time, if you realize that the same linear differential equation governs both. The difference may be subtle. In the case of the Genome, complexity is proportional to complexity at a infinitesimal earlier time; in Hubble, recession velocity is proportional to an infinitesimal earlier distance.

I don't know what the conclusion should be.

Neil Gunther said...

Good thinking but, unfortunately, the real conclusion is that there isn't one because there's an understandable flaw in your logic.

The Hubble plot (Fig. 1) shows velocity (v) on the y-axis vs. distance (d) on the x-axis. That the relationhship is linear, and not exponential, follows from simple kinematics: d = v * t. The regression line(s) on the plot exhibits that relationship as v = (1/t) * d. That's why the slope of the line gives the inverse of the age of the universe.

What may have derailed your thinking is the sloppy notation used on the y-axis of Fig. 1. It shows the velocity units as "KM" instead of "KM/S" as I do in my text. To compensate for the poor units notation is does say "VELOCITY" in sideways print along that axis. I don't know if this sloppiness was due to Hubble or the publisher. The modern plot in Fig. 2 shows the correct units.

By contrast, the genome plot (Fig. 3) shows "distance" on the y-axis vs. time (t) on the x-axis. That relationhship is nonlinear of the form d ~ exp(t) up to constants, viz,, exponential growth. However, by transforming to a log scale on the y-axis, the regression line becomes linear of the form log(d) ~ t, up to constants.

Neil Gunther said...

And de-bate goes on. If you can temporarily tolerate Robert Krulwich's patronizing tone (to get down to your dumb-arse level), he reports on January 2013 that analysis of certain Australian rocks (zircons) indicate the presence of water on the planet 4.4 billion years ago. That's within 100 million years of earth's formation, as determined by the most accurate radiometric dating. It also suggests that life appeared earlier than generally thought.

Amazingly, both Krulwich and Zimmer seem to miss the possible explanation that water (and life?) arrived on comets, or similar extraterrestrial bodies.

Neil Gunther said...

Big Bang Paternity in Question, Physics Today, June 2013.

Neil Gunther said...

Curiouser and curiouser. World's Biggest Virus May Have Ancient (and non-terrestrial) Roots.

Neil Gunther said...

The weirdness continues.

We all may have a little Martian in us. New research suggests a mineral found only on Mars may have been crucial to the origin of life on Earth.