Neighborhood birds – not so ordinary

 kw: book reviews, nonfiction, ornithology, birds, bird watching, photographs

This is how baby robins look the day they hatch. On most monitors this image will be just a little smaller than actual size.

We had the good fortune that a pair of robins built a nest on the kitchen window ledge. They anchored it to the thermometer support. Four blue eggs were followed by four pink nestlings, covered with sparse white fuzz. We kept the window shade down, except when taking pictures, to keep from spooking the parent birds, and later, the fledglings.

I am not much of a bird watcher, but I pay attention to them, particularly the ones in my yard and neighborhood. In Jack Gedney's book The Private Lives of Public Birds: Learning to Listen to the Birds Where We Live, the author wants, most of all, that we all pay attention. Birds are all around us.

When we step outside in the morning (or if we have an open window at sunrise), do we notice the birdsong? When we turn a corner at the end of the house and hear a flutter from a nearby bush, do we bother to look for the rapidly-exiting bird we just spooked? When a catbird is crying nearby, do we crane about, hoping to see it? Do we thrill to see a cardinal in the birdbath?

The book has the stories of 15 common birds of California, where the author lives. A few, the towhee and two species of native sparrow, were new to me. The rest were familiar. Hmm: Chapter 10, on the White-crowned sparrow and golden-crowned sparrow, is two-for-one, so that's 16 bird species.

Although I've lived in California three times, for a total of eleven years, I never learned of the California towhee. Gedney calls it "the brown bird", which reflects its principal characteristic. However, the average songbird is a "little brown thing"—think of common (English) sparrow and wrens—which makes sense. For prey birds, being inconspicuous is a life strategy. So I was probably in the presence of towhees daily and never noticed.

I love the way he writes: lyrically, without being maudlin. In Chapter 6, about the House Finch, he invites us to "reenchant our lives": "You can choose to peel away the concealing layer of quotidian gray and rediscover the brilliant core that's been present all along." From any distance farther than halfway across your yard, it's hard to tell this is a red bird. Particularly in fall and winter, its winter coat is more of a stately pink than this blazing red.

Writing of owls, he remarks on the way they add their own sounds to the night (the stereotypical "Hoo-hoo Hoooo!" is generally a great horned owl; hard to spot in spite of its size). Yet with the spread of artificial light, the monthly cycle of the moon's phases is lost on us, and the changes in owl song that were once so familiar: "[We] lose the evening, erase the quiet time between activity and sleep. Moonlit groves grow lonely in an age of off-and-on." He turns to a poet, Pablo Neruda, to limn the Anna's hummingbird: "You are / a seed in the sun / a fire / dressed in feathers." Although mourning doves have the fastest level flight of any bird, Anna's hummingbirds fly faster relative to their size than any other bird. Put another way, the hummingbird is a bit slower than the dove, but is 1/3rd the length and 1/30th the weight.

I suspect if almost anyone put their mind to it, they could recall at least a dozen birds with which they are at least a little familiar.

I live some 10 km west of the Delaware River, near the PA-DE state line. This is the northern end of the Mid-Atlantic region. The ranges of many populations of northeastern and mid-southern birds overlap, so folks that keep life lists have a rich harvest without going far.

The larger birds we see are typically turkey vultures, such as these two (photographed by my wife), after chopping up some small carcass in our yard, peering in the neighbor's window. I've seen bald eagles in nearby areas, but never from our neighborhood. Even from far away, it's easy to distinguish eagle from vulture. The eagle's wings are held flat and its flight is very steady. The vulture's wings are held in a shallow "V", and it tends to teeter in flight, catching every tiny shift in the updrafts that keep it aloft. The turkey vulture, if close enough, sports long, white triangles on the rear of its wings. Half the tail is also white.

We also have black vultures, with black skin on the head rather than red. Turkey vultures have the best sense of smell of any bird, and black vultures keep an eye on them because they can smell what no vulture can see.

Slightly smaller raptors in the area include this Cooper's hawk, that was sitting our our fence, and both red-tailed hawks and red-shouldered hawks. Cooper's hawks are bird hawks, but one day a friend and I were in the driveway talking, and heard a thump. We turned just in time to see the Cooper's hawk flying off with a squirrel. That's a lot of load for this hawk, for they are smaller than red-tailed hawks.

Middle sized birds are dominated by robins. In certain seasons, it's interesting to see a nearby schoolyard hosting 20 or more feeding robins, which keep 10-20 feet apart, while not far away, a flock of 100 blackbirds, with much closer spacing, could fit in the area of a garage. We also have cardinals—this picture is of two cardinal eggs in a nest in our privet hedge. There are also catbirds, starlings, mourning doves, tree swallows, blue jays, and occasional goldfinches.

Smaller birds include several "little brown things": English sparrows, Carolina wrens, and another wren species I haven't identified. We also have chickadees. Neighbors have reported seeing bluebirds, but I haven't.

That's nineteen. Not much of a life list compared to many folks I know. But for me, it's enough. I can't identify them all by sound, but with observation that ought to improve. I hope Mr. Gedney would approve.

The irresistible impulse to predict

 kw: book reviews, nonfiction, speculation, prediction, futurism

The second chapter of The Skeptics' Guide to the Future: What Yesterday's Science and Science Fiction Tell Us About the World of Tomorrow, by Dr. Steven Novella and his brothers Bob Novella and Jay Novella, begins with a quote by the sage of the ball park, Yogi Berra: "The future ain't what it used to be."

I can think of three facts about the 1969 landing on the Moon by astronauts of Apollo 11, that were not anticipated by science fiction writers, nor by futurists in general:

1. Between 10% and 30% of Americans believe it was all a hoax.
2. The sponsor was not a corporation nor a "rich industrialist" but the Federal government.
3. The world watched Neil Armstrong climb down the ladder on color TV.

It took only 50 years for a few "rich industrialists" to gather both the financial muscle and the personal will to start spaceship companies, and at present there are three! In the golden age of space fiction, mainly pre-1960, nobody dreamed the combined Mercury-Gemini-Apollo programs would cost about a trillion dollars (in current dollars).

What did science fiction get right? Arthur Clarke foretold telecommunications via synchronous satellites in 1945, 12 years before Sputnik 1 surprised the world. On the dystopian side, George Orwell wrote in 1948 of a pervasive surveillance state (he was mixing Stalin with his expectation of immense progress in video technology); now it is upon us. More prosaically, in 1911 Hugo Gernsback wrote of video chatting; of course the inimitable Hugo made dozens of predictions in everything he wrote, so getting it right once in a while is simple statistics in this case.

What approach do the Novella brothers take? I'd call Skeptics' Guide a catalog of futurist ideas sorted by plausibility. I am amused by the title of Chapter 3, "The Science of Futurism." To me, that's an oxymoron. Science is about what we know, or think we know. Stuff that hasn't happened cannot be a scientific subject. To me, futurist speculation is fun, and when folks in a position to know more than most of us about technological and sociological trends speculate that one or another trend "has legs" and is likely to affect all of us, it's worth taking note. Some decent fraction of the time, the speculation turns into fact.

The authors sagely note that it's hard to distinguish robust trends from fads. I look back at a number of things I once thought were "neaty-keen!", that have vanished from the scene, with decidedly mixed feelings. I tried out a Segway at a science park once. I like them. The business model was fatally flawed, though, and my insurance company would probably have charged me more than the cost of the machine...per year. So as much as I hope for the rapid development and spread of self-driving autos, I suspect I won't live to see them "take over" (but I'll get one of they do!).

Or maybe I'll live long enough for many more trends to play out. The next-to-last chapter deals with indefinite life extension. Scale that back to "let's make it possible for most people to live 100-120 years in good health", and I have a decent chance to use or own (if we still own cars in 2040) a self-driving car, and to have not a robot butler but instead several (affordable!) robotic appliances, such as one that can make a decent omelet. Maybe I'll live to see actual, true, artificial general intelligence (AGI). My goal post for AGI is that a mechanism, entirely without "handlers and minders", does research, produces something new, and obtains a patent. A secondary goal post: one that can carry on a discussion on numerous subjects, and hold its own at a meeting of an intelligent, well-read Book of the Month Club.

Of course, artificial narrow intelligence (ANI) is beginning to do some very interesting things. One is the language understanding behind "art generators" such as Dall-E and "text generators" such as ChatGPT, and the object recognition behind image sharpeners such as Sharpen AI. Would life in a settlement on Mars such as the one shown here appeal to you? I prompted Dall-E to create this image. It's a portion of a larger image I "created" with "outpainting". ANI is beginning to push our culture in new directions.

After the introductory part of the book, each of the four sections deals with matters that are less and less likely. The last section discusses the impossible, at least until new laws of physics are discovered: time travel, transporters, and faster-than-light travel for example. My, how prone we are to wrestle against the constraints of the universe!

The point is often made that fiction writers and futurist writers cannot escape putting today's people into their future scenarios. A small number of people are fanatical about "living forever", but do they have a way to predict the social disruption that would result, if even 0.1% of humans became effectively immortal? The authors discuss both positive and negative views of this, and are careful not to draw conclusions. It would be a Black Swan moment for the human race. While I'd like to "not die", I am not willing for evil people to live long enough to get really, really evil. Imagine if Stalin or Mao Zedong were still alive...

As good as the writing is, the book is rather insipid. The authors didn't want to be sensationalists. They succeeded at that.

Yogi Berra also said, "It's tough to make predictions, especially about the future."

Backyard gravitational energy storage

 kw: analytical projects, energy, energy storage, batteries, gravitational energy storage

The Federal subsidy for installing solar panels on houses' roofs continues. I can't take advantage of it because the huge trees in my back yard shade too much of the roof too much of the time. I was told there is an extra subsidy to pay for removing big trees. Hmm, I wonder what the carbon "pollution" balance is between removing several 150-foot trees and using solar power…produced with panels that were manufactured using large amounts of fossil fuel-powered equipment. Is anybody producing solar panels using only solar power?

Anyway, at my latitude, I must use air conditioning about one-third of the year. On the warmest days, the A/C runs periodically all night long, particularly when the overnight low temperature is in the 80's (°F of course; that's about 30°C). It's no longer possible in most states to have the solar panels "run the meter backward" during the day, to build up an energy credit with the utility. Thus, I would have to purchase electricity to run my A/C, and the rest of the house, at night.

I'd like to store energy during the day to use at night. The Tesla Powerwall is one expensive option, and it is probably insufficient. Let's do some figuration.

My electricity bill shows monthly usage between 500 and 1,100 kwh/month. The smaller amount is characteristic of spring and autumn. My A/C unit is a heat pump, so my highest usage is actually in slightly warmer winters, when the heat pump usually runs rather than the backup oil furnace. Let's take 600 kwh/month as the top end of A/C-heat pump usage. That's about 20 kwh/day on the "worst" days, from an energy consumption perspective. Not every day is the same, so there are probably peak days with usage in the 30-40 kwh range. In the summer, more cooling is needed during the day; in winter, more heating is needed at night. Considering that these are very approximate figures, I can begin with the likelihood that an energy storage solution in the range of 20 kwh is appropriate.

First possible option: Tesla Powerwall 2. At a web page for This Old House, I find that the Powerwall 2 has a current (early 2023) price of $11,500 for one battery with a capacity of 13.5 kwh, and $18,500 for a unit with two batteries (27 kwh total). The warranty life is 10 years, with a guarantee of 70% remaining capacity at the end of 10 years. That brings the effective storage of an older unit as low as 9.45 kwh or 18.9 kwh. My benchmark figure of 20 kwh thus requires a two-battery system, with replacement needed 9-10 years down the road. Also, such a unit weighs about 500 pounds (230 kg).

If you're enough of a maker (we used to say "handyman"), what about buying a bunch of car batteries and wiring them together with a charger and a large inverter for converting the DC output to AC at 110 volts (or 220V, for your A/C)? Lead-acid batteries have an energy density of about 40 watt-hours per pound (wh/lb) or 88 (or 90) wh/kg. To achieve 20 kwh we need 500 pounds of car batteries. Hmm, that's about the same as the Tesla unit. Of course, adding the charger and inverter will probably add 100 lbs, and the supporting structure would be another hundred or so. A typical car battery costs $200 or more and weighs 45 pounds; we need 11 of these, perhaps 12 for good measure (even numbers are better for balancing charging and discharge circuits). Not knowing what large, fast chargers cost, nor large inverters, this is still looking pretty good at a battery cost of about $2,400.

That sets some sidebars on direct electricity storage. But I've been wondering about gravitational energy storage. This picture shows one company's proposal for using concrete cylinders and a six-arm crane that uses wind turbine-generated electricity to raise the cylinders, and generates electricity when they are lowered during periods of less wind. They claim overall efficiency of 90%.

The concept is by Energy Vault. The tower is 33 storeys tall (about 100 meters). However, I couldn't make much sense of the numbers in the report, which describes 5,000 concrete blocks with a total weight of 35 tons. That doesn't add up; it works out to 14 pounds per block. I suspect the actual weight of each block is 1,400 lb (640 kg). Such a cylinder would have a volume of a little less than a third of a cubic meter (or about 1/3 of a cubic yard), which is almost twice the volume of an oil drum. From the picture, that looks about right.

What kind of weight would I need to make a backyard gravitational power "tower"? In most neighborhoods, one cannot construct anything taller than a 2-story house; perhaps 30 feet (9 m) at the very most. More figuration is needed, to convert weight and distance to watt-hours.

• One horsepower is 33,000 ft-lbs per minute, or 550 ft-lbs per second
• One kilowatt = 1.36 HP = 738 ft-lbs/s
• 1 kwh = 738×3,600 = 2,692,800 ft-lbs = 372,400 kg-m
• 20 kwh comes to 7,448 Tonne-m (nearly 7½ million kg-m)
• Divide by 9: About 830 Tonnes (910 tons) raised to a 9 m height

Ok, just to run my overnight energy storage, I need to be able to raise and lower upwards of 900 one-ton blocks, using motors that can function as generators with a 4000-watt capacity. Standard concrete weighs 2,400 kg (2.4 Tonnes) per cubic meter, or 4,000 lbs (2 tons) per cubic yard. 830/2.4 = 346 cubic meters of concrete, a mass 18 by 19 meters, one meter thick (English units: 455 cubic yards, about 64 by 64 feet, and 3 feet thick).

My back yard is rather small, only 30 feet deep, though it's 90 feet wide. I do have a side yard that's plenty large enough. I wonder what my neighbors would think if I built a structure as tall as my house, with a footprint of more than 4,000 sq ft. And the big electric motors/generators would most likely whine when in use. I'd probably have to remove some soil and seat it 2-3 feet below grade (with drainage infrastructure for rainy weather) to keep the total height below 30 feet.

Maybe I can use iron (I can't afford 900 tons of lead!). Iron's density is 7,874 kg/cubic meter, or 3.28 times that of concrete. This would shrink the volume needed to 105.5 cubic meters or 138 cubic yards. Reducing the vertical depth to 2 feet means the footprint would be no longer 4,000 sq ft but 1,860 sq ft, or about 43 feet square. My 2,000 square-foot house is two storeys, so it's size is only 25 by 40 feet.

The picture is a bit ridiculous. The primary virtue of such a system is that its energy capacity doesn't reduce over time the way the Powerwall will. But it illustrates the amazing energy density of batteries, even lead-acid car batteries, compared to big blocks of iron or concrete and big motors to lift and lower them.

This is a fun mental exercise. It convinces me to wait for better batteries to be developed. Systems based on something besides lithium, for sure! Sodium-sulfur can have 2-4 times the energy density of lithium-ion, and sodium-ion is in the two-times range. Recent research has produced prototypes that don't have to be kept at 300°C (570°F) to operate efficiently. I can wait.

My Greek NT reference

 kw: book reviews, nonfiction, references, greek new testament, translations, commentaries

A number of years ago I contacted a Bible scholar to ask if there is a reference book that explains the variations between the numerous Greek texts of the New Testament. I was particularly interested to find out if any of the variations—and there are thousands of them among the 5,000 or so Greek manuscripts—had any bearing on the primary elements of the Gospel: The death and resurrection of Jesus Christ, His justification and sanctification of the children of God, and His sonship in the Triune God, in particular. The scholar assured me that Bible truth is not threatened by manuscript variations, and suggested a wonderful resource that I was able to purchase through a used bookstore, A Textual Commentary on the Greek New Testament by Bruce M. Metzger. Published in 1971, it is still in print, but buying a used copy saved me about half the price of a new one.

I used the book on and off for several years, and just before the end of 2021 I decided to use it along with my reading of the Bible, and gradually work through the entire volume of 775 pages. Each year I read through the Bible, using a different plan each time. Sometimes I use different translations (most recently the English Standard Version, ESV, in 2018 and the World English Bible, WEB, in 2020). Most frequently I read the Recovery Version, RcV. I also vary the schedule and criteria for daily selections. For example for a couple of years I would read a certain number of verses daily (plus or minus 15-20% depending on chapter divisions), and in 2022 I used a copy without footnotes and minimal apparatus, and read a set number of pages daily (with some variation), 3 OT pages and 1 NT page daily. I'm doing a similar scheme this year, but reading the New Testament first, followed by the Old Testament. Throughout 2022, after each day's reading, I read the notes in Textual Commentary relevant to the NT portion for the day. Thus over the year I completed the whole book.

This is what a bipage of the book looks like:

At this size it is a bit hard to read. You may click on the image to see it full size (150 dpi).

The longest item on these pages refers to Acts 3:14, "But you denied the holy and righteous One and asked that a man who was a murderer be granted to you". This is from the opening words of Peter's speaking on the day of Pentecost. The word being discussed, which is transliterated 'ern'esasthe, means "denied". It seems that some copyists of early times disliked repeating this word, which had appeared in the prior sentence (3:13), and so substituted ebarunate, which means "oppressed", a rather inappropriate word. The translation committee studied not just the Greek but Hebrew and Syriac versions to winkle out the best explanation for the variation. What looks like an ink smear at the bottom of page 310 and the top of 311 is Syriac text, which is vaguely related to Arabic. Note that later on in the article several Hebrew words are also shown. This book is not for the faint of heart; we may not be able to read the snippets of Hebrew and other languages, and perhaps not even Greek, with any felicity, but we should at least be able to see them in the text without panicking, and trust that the Committee knew what they were doing!

Codex Bezae is a famous manuscript, primarily of the Gospels and Acts, an edited 5th Century text compiled from multiple earlier manuscripts. It has Greek on one page and Latin on the facing page, which makes it valuable to understand what the copyist and translators of the era may have been thinking. Abbreviations such as D and H and Aleph-star (see the 3rd line of the article) refer to manuscripts that would be known to a scholar. The text also frequently refers to groups of manuscripts of different copyist traditions, such as majuscules and minuscules (there are many of each) that were copied using different letter styles. The volume contains about 2,000 such articles of various lengths, covering all the important variations in manuscript texts.

Here is another example I found interesting:

This refers to Revelation 5:10, "And have made them a kingdom and priests to our God; and they will reign on the earth." The word in question, basileusousin, means "they will reign". Greek word endings are numerous and cause difficulty to copyists. The numeric codes refer to Bible manuscripts, and Aleph is a different manuscript from Aleph-star. One more example brings out a couple of important points:

A few manuscripts of Romans 8:1 include one of the most famous glosses in the New Testament. A gloss is a bit of text that a copyist introduced into the body text from a marginal note found in an earlier manuscript. Romans 8:4 reads, "That the righteous requirement of the law might be fulfilled in us, who do not walk according to the flesh but according to the spirit." Some very early manuscripts have the second phrase of this verse copied as a marginal note next to 8:1. In the Textus Receptus, which is the basis of the King James Version of the New Testament, these words were put into the body text. This is a serious error, because it makes the release of condemnation based on the sacrifice of Christ into a result of our performance. The words are appropriate in 8:4, not in 8:1, which properly reads, "There is now then no condemnation to those who are in Christ Jesus." Period. No qualification based on our "walk".

The article also mentions two text types, Alexandrian and Western. About half of all early manuscripts are either Alexandrian or Western. The other half are either Caesarean or Byzantine. These four text-types were current in various regions. The introduction to the book discusses them in an introductory way. Other reference books discuss them more fully. Most later manuscripts are of the Byzantine type, and until about a generation ago, a "near-majority text" such as the Textus Receptus was based primarily on Byzantine manuscripts. The problem is, Byzantine Greek arose as the Greek language changed in the eastern Roman empire in the 4th Century. Byzantine manuscripts containing more than a few scraps of the New Testament date from the 8th Century and later. Significant differences between Byzantine and other text-types indicate that Bible manuscripts were translated into Byzantine Greek, probably before the 5th Century. For modern English speakers, reading Middle English of 600 years ago is a chore. There is a similar difference between Byzantine Greek and First Century Greek (often called Koiné)

My reference library includes four Greek texts of the New Testament, including one that is a full Majority Text, treating words as if they were voters in an election. It is almost entirely Byzantine in character. The United Bible Societies Greek New Testament, Third Edition was published in 1975, based on the scholarship of the Committee mentioned frequently in this volume, which was published in 1971 as a companion volume. Dr. Metzger is the most prominent of the scholars of the Committee.

As a reference, it is unsurpassed. Reading the New Testament with the companionship of this volume impressed me with the wisdom of God in the inspiration and preservation of His book to us.

Numbers too dangerous to imagine

 kw: book reviews, nonfiction, mathematics, number theory

For us ordinary folk, and for most scientists, the numbers on the balance are the limits of practical need. On the right: Avogadro's number, the quantity of protons in one gram of hydrogen. On the left, the long number with lots of leading zeroes is the weight of a proton in grams. Note the little "1/" above it: that makes the quantities balance. I left neutrons out of the discussion because the mass of a neutron is 0.14% greater than that of a proton.

For our more day-to-day experience, we've become accustomed to hearing "trillion" (a million millions) in news about government spending (but I remember a time that the entire Federal budget was much less than one trillion dollars), but few of us ever handle amounts larger than a few hundred thousand dollars, such as writing the check (heavily underwritten by our bank loan) for a house. And we may be familiar with numbers like milligrams or even micrograms (the weight of an average sand grain). That's about it.

Antonio Padilla would like to expand our horizons. A lot. A whole universe/multiverse of a lot. He begins his book Fantastic Numbers and Where to Find Them: A Cosmic Quest From Zero to Infinity by promising to describe a number so compendious that, if it were possible to memorize it in total, the mass of the information would collapse our brain into a black hole. Yes, information has mass. One "bit" of information stored in a computer memory chip has a tiny mass, much less than that of a proton. So does the same information held in our memory. However, the number of neurons available to hold memories (most are used for various thinking tasks), may be a few billion, although the "bits" of memory may be in synapses, at the rate of a few thousand per neuron. So perhaps we have the equivalent of several trillion bits of memory. Some think it is more like a quadrillion (1,000 trillion). Regardless, the mass of our memories is less than the mass of one proton. How many digits must be in a number that "weighs" 67,331,765,482,045,288,639,033,395 kilograms? (I got this number from the Schwarzschild Radius Calculator, using 10 cm for the radius of the "brain".)

Time for a sidebar about scientific notation. We don't readily comprehend numbers written out in full when they have more than 4-6 digits. Zeroing out most of the digits above, we can write that number as 6.733x10²⁵ kg. The exponent 25 tells us how many digits are after the decimal point. Similarly, the number on the left of the scale above is easier to comprehend as 1.672623x10^-24, the mass in grams of a proton. The exponent -24 tells us how many digits, including the leading "1", follow a decimal point far to the left. Its companion on the right is 6.022x10²³.

The "black-hole-in-a-brain" number has so many digits that the exponent has more digits than there are protons in the observable universe. It is called Graham's Number, and is so far the largest number used in a mathematical proof.

Before he gets to Graham's Number, though, Dr. Padilla takes us through some "easy" steps. His first chapter deals with the number 1.000 000 000 000 000 858. There are 15 zeroes in there. Scientific notation doesn't help here! This is the amount of time dilation experienced by Usain Bolt at his peak running speed of just under 30 mph (13.4 m/s). In sub-chapters, we read of various phenomena besides relative velocity that affect the flow of time, such as changing gravitational force on mountain tops or in ocean deeps. Chapters for Googol and Googolplex follow. A Googol is a one followed by 100 zeroes, or 1.0x10¹⁰⁰. A Googolplex has a Googol of zeroes: 1.0x10^Googol or (I have to use a graphic):

Think about that repeated exponent for a moment. It gets one somewhat ready to think about Graham's Number. Using a somewhat different notation, there are 64 levels…or perhaps 64 groups of levels of increasing size. I wasn't too clear, but, I don't want to be swallowed up by a black hole anyway. Graham's Number represents the extreme limit of the number of steps that may be needed to solve a particular problem. Needless to say, no physical computer system will even be able to count the steps, let alone perform them. Perhaps God's computer could do so, but I can't imagine Him being willing to devote the resources to perform the task.

The second section of the book starts with Zero, "a most beautiful number", and goes on to a few special numbers that are very, very close, but not quite there. One is "the most embarrassing number", 1x10^-120 (it has 119 zeroes before the "1"). That is the ratio between the amount of "vacuum energy" we can measure using the Casimir Effect, and a calculation of what the energy ought to be, using quantum theory.

It's the biggest blunder in physics! If quantum theory is true, right down to the smallest scales, no universe larger than a golf ball could exist without immediately collapsing back into a "big crunch". Clearly, we are missing something. Even if we limit the reach of quantum theory to the scale of a proton, no universe larger than the size of Manhattan is possible. The author and others think string theory will rescue the situation. I doubt it; not anytime soon. The last I learned, the number of possible variations of "string theory" is about 10⁵⁰⁰. That's a Googol to the fifth power (Googol⁵). It isn't even possible to make a list of string theory candidates so they can be compared.

So what could come next? Infinity of course! The famous sideways-eight (∞). One chapter is plenty, even though, as we come to find out, there is more than one kind of infinity. Rather than try to explain the difference between Georg Cantor's Aleph-null and Aleph-one infinity—and we don't know if there isn't a "real" Aleph-one, or more, in between!—I'll leave it to you to read this enjoyable, idea-packed book.

-----------

Now I must touch on less pleasant matters. I wish Dr. Padilla had employed a copy editor; if he had one, that person needs a new day job.

1. While discussing time dilation (Usain Bolt's running speed), he dwells on a solar sail that might reach 1/5th the speed of light. Then he goes on to say that time dilation would mean a bacterial stowaway (or an onboard clock) would experience time slowed such that the 20-year journey to Alpha Centauri (4.37 light-years away) would seem to take less than nine years. He slipped a decimal somewhere. The time dilation factor is the square root of [1 - v²/c²], which I calculate to be √[1-0.04] = 0.9798. Now, 4.37x5 = 21.85 years (classical), which time dilation reduces, for shipboard bacteria and clocks, to 21.4 years. To reduce the time to nine years requires about 90% the speed of light, not 20%.
2. Two places I find the phrase, "The precise value of..." something, and a number with two or three digits of precision. The number "precise" should have been left out, or even it should have been stated that "The value of [whatever] is about..." The numbers in question are known to a precision of nine digits. This I attribute to the author.
3. This is a little less consequential: "100 billion neurons in the human brain." An up to date number is 86 billion, plus or minus a couple of billion. Also, 80% of our neurons are in the cerebellum, where they regulate our bodily functions and communicate with the 16 billion (more or less) neurons of our cortex, which is where thinking happens, and where all memories seem to be stored. Our vaunted intelligence primarily resides in those 16 billion.
4. This is a biggie, but it comes down to a simple copy/paste error. On page 190 we find "A quick reference guide to all the particles you'll encounter in this chapter", along with a chart of the Standard Model of particle physics. However, the Lepton portion of the chart is a copy of the Quark portion. The Lepton portion should show the electron, the muon and the tau, and their associated neutrinos. Big oops! I can't believe all the folks who wrote glowing blurbs praising the book (for its back cover) didn't see that. I suspect none of them read the book in full.
5. In the chapter on 10^-120 I find the phrase "external to spacetime", about an "external mechanism". As I understand cosmology, there is nothing external to spacetime. This is nonsense.
6. Finally, a simple typo. At the bottom of a table on page 282, "…infinities of site [Aleph-1]" should read "…infinities of size [Aleph-1]".

This is what I noticed without "looking for trouble." I have edited for others. In "editor mode" I might have found 2-3x as many items needing attention. Now, for those who've read this part, please don't hold it too much against the author. The book is full of wonderful ideas. I still mightily enjoyed the book.