Book Review: Imagined Life by James Trefil and Michael Summers

 

This blog has had several posts linking how we use math to answer questions about space. 

Math Vacation: Book Review: Twenty Worlds by Niall Deacon (jamesmacmath.blogspot.com)

Math Vacation: How Many Black Holes are there in the Universe? (jamesmacmath.blogspot.com)

Math Vacation: Number of Planets in the Universe (jamesmacmath.blogspot.com)

Math Vacation: Can We Reach Another Star? (jamesmacmath.blogspot.com)

Math Vacation: How Far is it to the Next Nearest Planet with Interstellar Communication? (jamesmacmath.blogspot.com)

Math Vacation: One Equation - One or Many Worlds? (jamesmacmath.blogspot.com)

Authors James Trefil and Michael Summers put together a very good summary of the types of planets that exist in our universe that could support life. They classify these planets in the following ways:

Goldilocks – those planets like Earth that are just right distance from their star to have liquid water. This is our only confirmed source of life in the universe, so this very Earth-centric view is valid. However, they bring out that many other planet types could support life.

The other planet types explore in the book include:

Planets with surfaces of only solid ice.

Planets with surface ice and having liquid oceans below the surface.

Planets entirely covered with liquid water.

Planets that are in a tidal lock with their sun as our moon is with Earth.

Earth-like planets bigger than Earth but smaller than Neptune (none in our solar system, but very common elsewhere).

Planetary systems like those orbiting Trappist-1 where several planets are orbiting in close proximity to their star.

Most interestingly, are the rogue planets. These are planets that formed in solar systems and were ejected from the system by violent encounters during the solar system’s formation. Some believe that the number of rogue planets may far outnumber traditional planets. While they would not bathe in sunlight, they still have the source of energy from the cooling of their initial formation and from radioactive decay. Therefore, it is possible that these rogue planets could harbor life.

The book also discusses life forms that may exist outside of usual experience, including artificial intelligence and life based on electromagnetic basis versus a chemical basis.

Another important idea discussed is what other liquids, other than water, could be supportive of life. The main candidates include liquid methane, ammonia, and hydrogen sulfide.

Also explored is the possibility of life based on elements other than carbon, such as a silicon-based life.

Imagined Life: A Speculative Scientific Journey among the Exoplanets in Search of Intelligent Aliens, Ice Creatures, and Supergravity Animals: Trefil, James, Summers, Michael: 9781588346643: Amazon.com: Books

 

Salute to Stephen Timoshenko (Тимошенко, Степан Прокофьевич, 1878-1972)

 

(Photo credit: Timoshenko, Stephen, 1878-1972 (aip.org) - original source unknown)

As I make this post, Russia is in their second month of the invasion of Ukraine. I think back to my college days trying to remember anyone I might know from Ukraine, and I recall the premier textbook on Applied Engineering Mechanics was written by Stephen Timoshenko.

Born in Ukraine and settled in the United States, teaching at Stanford for over forty years (Timoshenko | Mechanics and Computation (stanford.edu)).

In his honor and for the benefit of the besieged Ukrainians, I pledge to donate any advertising income of my blog to a vetted Ukrainian relief organization (My vetting will be through Fidelity Charitable: https://www.fidelitycharitable.org/guidance/disaster-relief/how-to-help-ukraine.html?_ga=2.119746766.759715814.1649212022-1817714618.1634856305).

μαθηματικός

 

It’s been two years since I started my blog about mathematics. Originally, I wanted to share some my views on mathematical concepts. Over time, as I researched each new post, the quest shifted to the expansion of my own learning. To share a mathematical concept, one must really learn the basis of how that concept works.

It is appropriate for my 100^th blog posting to be on the etymology of the word “mathematics” or shorten to “maths” or for North Americans, “math.”

The English word mathematics is derived from the Greek, μάθημ, or mathema, which translates to “what one learns.” I’ve also seen the translation derived from μαθηματικός (mathēmatikós) which mean studious. These all seem appropriate for the those who enjoy learning about mathematics.

David Hilbert Problems

 

By Unknown author - Possibly Reid, Constance (1970) Hilbert, Berlin, Heidelberg: Springer Berlin Heidelberg Imprint Springer, p. 230 ISBN: 978-3-662-27132-2., Public Domain, https://commons.wikimedia.org/w/index.php?curid=36302

In 1900, a renowned German mathematician, David Hilbert, published 23 problems for the mathematical community to work on for the 20th century. At the time of the publication, the problems had not been solved. A link to the English translation of the problems: S0002-9904-1902-00923-3.pdf (ams.org)

To date, 8 of the problems have been resolved, meaning the problem was solved or a proposed proposition was proven or disproven. Another 9 have been partially resolved, meaning there exists some controversy as to whether the proposed solution fully resolves the question. Six problems remain unsolved.

A breakdown of the problems' status is given here: Hilbert's problems - Wikipedia.

Problem 2 was written about in a prior post about Kurt Gödel's incompleteness theorem.

Problem 18 sought a proof for the densest sphere packing which wasn't resolved until 1998. Also see this blog's post on sphere packing in higher dimensions.

The Very Small and the Very Big

In a prior post we considered how many digits of pi are required for a calculation, and I recently listened to a Lex Fridman podcast with guest Tim Urban, where they discussed if man is smaller than we are large or larger than we are small (Lex Fridman podcast).

Let's explore both extremes of small and large. 

Starting with the characteristic size of a human, 1 meter. Most humans are taller than a meter but are thinner and not at wide as a meter so for this discussion 1 meter will be the scale of comparison we use.

Moving up in scale:

10 m            About the size of a garage or apartment

100 m          The length of athletic field or pitch

1000 m        The span of a large bridge (The New York George Washington bridge has a span of 1067 m)

10,000 m     A 10k race that in which many runners have competed

100,000 m   A distance typically traveled by automobile at highway speeds 

10⁶ m            A full days driving on a long trip or traversing the north-south extent of California

10⁷ m            The distance from the north pole to the equator through Paris (by definition of meter)

10¹¹ m          The distance from the Earth to the Sun (One AU = 1.5 10x11m)

10¹² to 10¹³ m   The  orbit of Neptune is 30 AU

10¹⁶ m          The distance to the Oort cloud (the furthest extent of our Solar system)

10²¹ m          The diameter of the Milkyway Galaxy

10²⁷ m          The radius of the observable universe

View this animation on the large scale of the universe: (1535) your mind will collapse if you try to imagine this | UNIVERSE SIZE COMPARISON - YouTube

Another good visualization is given here: https://bigthink.com/starts-with-a-bang/logarithmic-view-universe/

Moving down in scale

0.1 m            A human hand width

0.01 m          A small finger width

0.001 m        1 mm or about the thickness of a credit card

0.0001 m      A fine human hair or diameter of a human egg cell (the largest human cell)

0.00001 m    Diameter of a human capillary vessel

10^-6 m           (one micron) Low end of the size of a bacterium

10^-9 m           (one nanometer) Size of a molecule

10^-10 m          Angstrom - approximate size of hydrogen atom

10^-15 m           Size of proton

10^-19 m           Upper limit of theoretical size of a quark

10^-35 m          The Planck length is 1.62 x 10^-35 m (smallest possible dimension)

Now, let’s consider the ratio of the very largest thing, the observable universe, to the vary smallest, theoretical size, the Planck length. The ratio is approximately:
10²⁷ m: 10^-35 m or 10⁶² to 1. Humans are somewhat in the middle but closer to large end in the comparison given above. If we only venture down to the size of a quark, then we closer to small end.