AfterMath



Hossenfelder on Coincidences and Conspiracies — Posted Saturday June 5 2021
If you have a grid of evenly spaced straight lines on a piece of paper and you toss a bunch of needles on the paper, you can approximate the value of the transcendental number \( \pi \) by counting the number of times the needles land on the lines. Non-mathematicians may wonder how \( \pi \) shows up in this exercise, but it's not a coincidence.

Noted German physicist Sabine Hossenfelder's latest video addresses the coincidence issue via the notions of human pattern identification and false positives, explaining how and why we tend to assign underlying agenticity and conspiracies to purely coincidental events, much like the Peanuts gang's interpretation of overhead clouds:

Hossenfelder's talk is one of the best I've seen, and it explains a lot about the foibles and tragedies of human behavior, in particular the sad predominance of weak-minded right wingers to persistently believe in PizzaGate, the drinking of children's blood by Democratic Party leaders and similar crazy conspiracies actively or passively promoted by the Republican Party.


AI Lincoln — Posted Monday May 31 2021
I have an old book called The Lincoln Reader that I've had forever that relates many personal stories and anecdotes about Abraham Lincoln, my favorite president. Although he lost a chunk of his lower jaw during a molar extraction in the early 1840s, those who knew him said he had a fine set of healthy white teeth and frequently smiled, often when telling an off-color joke. Early photos of the day almost never showed people smiling, a consequence of the proprieties of the times and the fact that early photography usually took several seconds to minutes to capture an image. So people would just sit there, motionless and expressionless, and that's the way we see them today.

With the advancing technology of artificial intelligence we now have relatively accurate ways of showing people in old photos as they might actually have appeared. Here's a new YouTube video that shows a smiling Lincoln, along with varying hair styles. Enjoy.

Sometimes artificial intelligence doesn't work too well. George Washington wore almost full dentures in his later years, sporting false teeth fashioned from human, horse and cow teeth. Here he looks just like Soupy Sales in drag.

Fine Tuning — Posted Saturday May 15 2021
In his latest video, YouTube's "Who Gives a Bleep?" Arvin Ash talks about the fine-tuning argument, which deals with the nature of the fundamental constants of our universe, such as the gravitational constant, the fine-structure constant, the magnitude of elementary electric charge and many other parameters that govern the workings of the observable universe. The problem involves the realization that if these constants were only slightly different (either individually or collectively), the universe would either not exist or would not be capable of creating or sustaining life. It's a short video, and well worth watching:

As I see it, there are only two possibilities: either there is a creator (God or an external entity such as a computer programmer in a simulated universe), or the multiverse theory (or the many-worlds interpretation of quantum mechanics) is valid, in which case there are numerous (possibly infinite) universes each having varying fundamental constants, and we just happen to be living in one in which life is possible.

Perhaps the most important aspect of Ash's talk is his assertion that we cannot talk about the probability of which argument is right, since we have no statistics available to base a probabilistic argument (we observe only one universe, and a sampling size of one is insufficient to do any calculations). This situation perfectly mirrors the familiar "science vs religion" argument, and it's unlikely that we'll ever be able to resolve it (but perhaps both are true).

The Goat Problem \(\ldots\) Again — Posted Friday May 7 2021
If you tie a goat to the outside of a barn and let it graze, how much grass can it clear? This might have been a practical math problem centuries ago, but Quanta Magazine seems to think it's still relevant today.

What's interesting is that the problem becomes much more difficult if the goat is tied to the inside of a closed barn, regardless of the barn's shape. That couldn't have been much of a problem way back when, but it's still occupying mathematicians today. I addressed the problem of a goat in a circular fenced yard on December 11 last year, but now Quanta has upped the ante with a square yard. This time I didn't bite, but you can try it yourself if you have nothing better to do this weekend.

More Geek Stuff — Posted Friday April 30 2021
German physicist Sabine Hossenfelder's views on dark matter vs modified gravity have changed. For the details, you can watch her latest video on the subject here.

For the few who care about such things, back on March 27 I posted some comments on a recent paper claiming that the Mannheim-Kazanas (MK) spacetime metric did not predict flat stellar rotation curves in galaxies. I disagreed, and I've been waiting for Philip Mannheim to publish a rebuttal. But now there's another paper that supports the claim that the MK spacetime does indeed predict flat rotation curves by analyzing the effective potential associated with the metric. In the paper's analysis, the \(\gamma\) term plays an important role in defining the radius at which stellar velocities approach constant values far from their galactic centers. This radius is the same one I came up with.

The MK metric is the only spacetime I've seen that is free from any added parameters (such as scalar and vector fields) that reproduces the predictions of the standard Einstein field equations. Like the Einstein-Hilbert action, that of the MK action (first derived by Hermann Weyl 100 years ago), is pure geometry.

Alien Visitation — Posted Saturday April 24 2021
There are countless YouTube videos depicting UFO sightings, and there's an equal number of people claiming they've been abducted by extraterrestrials for experimental purposes. Writer Devan Taylor talks about the difficulties associated with interplanetary visitation by advanced alien species, perhaps the biggest being "Why the hell would they come here in the first place?"

If extraterrestrials could ever visit Earth, there are only a few possible scenarios. One, they're malevolent, in which case we're already toast, since they would obviously be far more technologically advanced than we are (discounting the entertaining but otherwise preposterous Independence Day film); two, they're benevolent, in which case we'd have already made contact with them; and three, they're just unobtrusive observers, in which case we have today's current situation.

I personally believe there is intelligent life out there, but we'll never make contact with them because they're just too far away and just too darned spread out, so stop thinking about UFOs, aliens and all that nonsense. But meanwhile you can muse over the purely imaginary value of alien visitation, as depicted in this video clip where the Simpsons get abducted (obviously, aliens will need to have powerful tractor beams):


What's Up with the Arizona Ballot Audit? — Posted Saturday April 24 2021
The Arizona Republican Party has hired a right-leaning Florida-based company called "Cyber Ninjas" (I kid you not) to assist in the audit some 2.1 million ballots in the state that were cast during the November 2020 presidential election. Although no irregularities have been reported, the Arizona GOP just wants to be sure that Biden won fair and square.

Reports immediately surfaced that the auditors were illegally using blue and black pens to verify the ballots, in violation of the state's audit rule that only red pens may be employed (only red pens may be used, because computer scanners will falsely count any ballots illegally modified with black and blue pens). When the violation was reported by an Arizona reporter, auditors switched to the red pens, after which the reporter was banned from the audit site.

I bring up this story because on April 20 I posted some thoughts on data fluctuations and their significance. When it comes to counting election ballots, there will always be a few innocent mistakes, such as human and computer counting errors, damaged ballots and other systematic and non-systematic errors. Typically, if these mistakes account for less than a tiny percentage of the total count, then the election is declared fair. If not, one or more recounts may be requested. In the Arizona case, no such irregularity was seen, but Arizona Republicans decided to proceed with a recount anyway, just to be "sure."

Given the fact that the Arizona ballot hen house is now under watch by Republican foxes, it will be interesting to see how the recount ends. They don't have to falsify enough ballots to give Donald Trump the victory in the state, just enough to declare the election invalid. This would then spread to other Red states with anticipated similar results, giving the GOP the chance to declare Biden a fraudulently elected president. I sincerely believe this is their game plan.

America may see a new Civil War after all.

Is It Something I Said or Did? — Posted Thursday April 22 2021
Let us always guard our tongue, not that it should always be silent, but that it should speak at the proper time. — St. John Chrysostom
It was June 9, 1962, the very last day of the 7th grade. Puberty had apparently hit the girls hard earlier that year, as they were all fawning over a classmate who'd been a good friend of mine for as lomg as I could remember. At morning recess the girls were all crowding around him with their cameras, and I felt jealous for the first time in my life ("Get out of the way, Bill, we want to take B's picture!") One girl in particular was practically foaming at the mouth over B, her hormones in overdrive, and in a moment of rage I blurted out "Susan, you make me sick!" Susan wasn't particularly attractive, and I certainly had no interest in her, but I resented her obsequious behavior over my friend. Near the end of the day, Cindy F. asked me why I was so mean to Susan, but I don't recall how I answered her.

I just learned from an old classmate that some years later Susan committed suicide, having been clinically depressed ever since grade school. This news hit me like a sledgehammer, as I instantly recalled that day in 1962 and my heartless remark. Now I'm filled with remorse over something that happened almost sixty years ago and whatever part I might have played in that poor girl's demise.

Watch what you say, because you might not have a chance to make up for it.

An Inspector Calls, 2015.

I'm Still Confused — Posted Tuesday April 20 2021
In 2001 the E821 experiment at Brookhaven National Laboratory in Upton, N.Y., found hints that the muon's magnetic moment diverged from theory. At the time, the finding was not robust enough because it had a statistical significance of only 3.3 sigma: that is, if there were no new physics, then scientists would still expect to see a difference that large once out of 1,000 runs of an experiment because of pure chance. The result was short of 5 sigma — a one-in-3.5-million fluke — but enough to pique researchers' interest for future experiments. — Scientific American
You may have read about "5 sigma," the statistical criterion for determining whether a new scientific discovery is valid or not. Most recently, the magnetic dipole moment of the muon (a heavier but otherwise identical version of the electron) has been measured to great accuracy, but it differs very slightly from the theoretical value determined via quantum field theory. This difference is currently irreconcilable, and the difference amounts to something called 4.2 sigma.

"Sigma" is a just a measure of the standard deviation, computed assuming the applicability of the normal (Gaussian) distribution to experimental measurements. It's just the area outside of the Gaussian curve for a given point on the left of the mean to the same point on the right of the mean, the points being standard deviations. For example, for a standard deviation of 3.3 the area under the curve in the range \(z = -3.3 \) to \( z = 3.3 \) for the Gaussian integral $$ y = \frac{1}{\sqrt{2 \pi}}\, \int_{-3.3}^{3.3} e^{-z^2/2} dz \tag{1} $$ is about 0.99903. The area outside this range ((\(1-y\)) is 0.00097, the inverse of which is 1,030. This is taken to mean that there is only about one chance in a thousand that the measurement is an erroneous, statistical fluke. Similarly, for a standard deviation of 4.2 (based on the latest muon data) the chances are only about one in 40,000 that the measurement is a fluke.

What I don't understand is that all the reports are claiming that the 5 sigma "discovery" statistic means only one chance in about 3.5 million. But a straightforward calculation using (1) shows that this is only one chance in 1.75 million, exactly half of the number being reported. Is this a one-tailed or two-tailed thing?

The answer is: it depends on whether you're calculating sigma or its cousin, the p-value, both of which are used in statistical analysis. So it's basically one-tailed vs two-tailed, no real difference, although I wish to hell they'd be consistent with what they're reporting.

Update: German physicist Sabine Hossenfelder's latest video addresses the issue of sigma significance, noting that even 6 sigma can be misleading.

Math For Fun — Posted Tuesday April 13 2021
For years I've watched the math videos that Steve Chow has posted on his popular YouTube channel Blackpenredpen, which mostly covers undergraduate-level calculus. Chow is an instructor at Los Angeles Pierce College, and while he doesn't have a PhD in mathematics he's the guy I wish I had I when was in school.

Most of his videos present innovative and clever methods and tricks used to do seemingly impossible integrals, but he often changes gears and does purely algebraic problems. One of those that still fascinates me is the infinite tower-power problem $$ x^{x^{x^{x^{\cdots}}}} = 2 $$ (which, to the best of my knowledge, has no practical application whatsoever, but it's a fun problem). It's easy to derive the solution \(x = \sqrt{2}\), but the seemingly easier finite tower-power problem $$ x^{x^{x}} = 2 $$ is far trickier. It turns out that the exponentiation process is not "commutative" in the sense that \( x^{(x^x)}\) is not the same as \( (x^x)^x\). In this video, Chow uses Newton's iterative method to solve for \(x\), getting \( x = 1.476684\ldots\). As is easily shown, however, the solution to \( (x^x)^x = 2\) is just \(x=\sqrt{2}\) (which is also the solution to the infinite tower-power problem), but this disagrees with Chow's solution.

I'm puzzled by this, and I wonder if anyone can show me where I'm going wrong. Chow starts out the Newton's method with the guess \(x = 1\), so perhaps that's a bad start to the process.

Okay, I just found this video that explains everything. It's called tetration, which I knew about (but didn't know there was a rule for it).

My Ignorance — Posted Thursday April 8 2021
Today is my late wife's birthday. She would have been 75, and it still breaks my heart that she is not here today. Here she is on her 60th birthday, as beautiful as ever.

The last few days I've been going through boxes containing many hundreds of old letters that my wife and her brother received from (and wrote to) their parents and friends in Cairo, Egypt and in Kinshasa, Zaire, where my father-in-law taught chemistry. He took the job because it paid in American dollars (not Egyptian pounds), and was therefore a godsend, as it helped finance his adult children's emigration to America. They came to Los Angeles in 1970, as the weather was nearly the same as that in their native Cairo, and because they had a few friends in the church there to help them adjust to their new country.

Munira and I were married 42 years, not counting the 5 years I knew her from before. Outside of some limited and very broken Arabic, I never learned the language, and while looking at the letters (all of which are 40 to 50 years old), I now much regret my ignorance, as I would love to read them now. I will be sending all of them to my wife's brother, the only one remaining in the family who can translate them. Hopefully, with his help I'll learn more about my wife's earlier years, although I also hope to see her again before too much longer.

Is It God, or a "Smelly Hacker"? — Posted Thursday April 8 2021
There's currently a lot of puzzles in the physics world, but two stand out. One is the discrepancy in the Hubble parameter, which has been measured to pretty decent accuracy by two different methods that don't agree with one another, and the other is the measured and calculated magnetic dipole moment of the muon, which are also significantly different.

The Hubble parameter is a measure of the expansion rate of the universe, and it's either about 67 or 73 kilometers per second per megaparsec. There's some error in the observed values, but the error bars don't overlap, hence the discrepancy. On the other hand, the measured and calculated magnetic moments of the muon (a much heavier variant of the electron) are extremely close to one another, but there is a slight difference that physicists cannot explain. It might be experimental error or a statistical fluke, but those explanations are considered highly unlikely. Physicists are hopeful that the difference points to new physics beyond the Standard Model of Physics.

But there's another possibility, one that arises from the famous Simulation Hypothesis, which posits that all reality (including human consciousness) is the creation of an advanced computer programmer or hacker (smelly or not) who resides outside of the simulated universe. Assuming the hypothesis is correct, then even the most advanced programmer (perhaps even God) could not be precisely perfect in creating the simulation, and there would always be glitches that show up in the simulated universe, glitches that might be observable to the universe's inhabitants. This possibility is explored in this recent segment of Closer to Truth:

In view of the large disparity between the calculated values of the Hubble parameter, I highly doubt that it's a glitch of any kind; more likely it's experimental error or an erroneous assumption in the Standard Model of Cosmology. The muon dipole moment problem is far more interesting, as the predicted value is based on highly reliable calculational methods that have been used to fantastic success in other applications. Could the one part in a million difference between experiment and calculation be a glitch, or could it be "new physics"? More advanced experiments are planned, so hopefully time will tell.

PS: Sometimes I imagine that I'm a very old man, getting up in the morning, making coffee, then walking over to my large living room window to watch what's going on out there. What I see today is a fabricated Cretaceous landscape of herbivorous and carnivorous dinosaurs going about their business, thanks to a high-resolution, three-dimensional holographic glass pane that serves as my window to the world outside. Of course, the outside world is the usual boring place of cars going by and neighbors walking their dogs, and by turning off my fully programmable window I can see what's really there. But I prefer to gaze out upon the Grand Canyon, the Eiffel Tower or the Andromeda Galaxy, or if I choose I can watch the pyramids being constructed during Egypt's Old Kingdom. The possibilities are endless, and it makes me also wonder if my own existence isn't also a computer fabrication of some kind.

The Waste Land (Television, Not T.S. Eliot) — Posted Thursday April 8 2021
I just can't watch cable TV news anymore (although I have AT&T TV, not cable), given the non-stop coverage of ugly politics, COVID-19, the ongoing racist treatment of minorities, perpetual mass shootings and all the rest. I put up a flat antenna on my wall and am now watching over-the-air (OTA) television programs, which don't cost anything. The local news is still depressing, but the number of available programs is about as good as basic cable TV.

It's also given me the opportunity to tune into shows that my family and I watched in the 1950s, 1960s and 1970s, which were almost de rigeur viewing in those days because there wasn't anything else to watch.

With the sole exception of The Honeymooners, all the shows are pathetically insipid, with paper-thin plots and nonsensical situations. The family-oriented sitcoms are the worst (Family Affair, The Partridge Family, Donna Reed, etc.), with their well-coiffed, squeaky-clean (and white) children and their invariably highly educated and successful parents (doctors, lawyers, architects, businessmen and engineers) posing as ordinary middle-income folks raising preposterously talented offspring who danced, sang, played instruments and put on fantastic stage shows. And of course no single parent was divorced back then (only widowed), thus preserving the sanctity of marriage. And also all the men had served in the military, which offered plenty of opportunity for the shows to feature patriotic tableaus of one sort or another, always to comedic and heartwarming effect.

Good Lord, how much of that garbage did I consume without thinking in those days? I can only imagine how much better I'd have turned out if my parents had never purchased a television in the first place.

"April is the cruelest month \(\ldots\)"


Enough — Posted Monday April 5 2021
Truth be told, I'm sick to death of the non-stop Derek Chauvin trial coverage on CNN and MSNBC, not to mention the glib commentary by the various hosts of those news networks. The videos and testimonies of eye witnesses pretty much made the case against Chauvin for me, but the extensive trial coverage has become nothing more than a partisanized joke. The liberal-leaning CNN and MSNBC of course are pushing for a murder conviction, while the ultra conservative Fox News, One America Now and other racist networks are either playing the trial down or not covering it at all.

Let's be honest here: if we could replace Derek Chauvin with a black police officer and George Floyd with an addicted white civilian who passed a counterfeit bill, the network biases would be reversed, and the trial would have ended long ago with the black police officer convicted of first- or second-degree murder. Instead, by dragging out the trial ad nauseam the justice system will be forced into a lot of hemming and hawing over who's guilty due to the various legal subtleties and medical minutiae that are being presented, with the result that there's a very good chance that confused jurors will be hung and Chauvin will walk. His police career will be over, but then he'll write a best-selling book and make repeated guest appearances on Fox News, so he won't be hurting financially.

Fortunately, there's still a civil trial pending, and I can only hope that Floyd's family will end up getting a big chunk of whatever money Chauvin earns for the rest of his pathetic racist life.

Come On, Feet, Don't Fail Me Now — Posted Wednesday March 31 2021
It has always killed me when lay people ooh-and-aah over the weightlessness of astronauts aboard the International Space Station, which orbits the Earth at some 17,300 miles per hour. At roughly 200 miles above the Earth's surface, the gravitational attraction is still over 90% that which we all feel here, and it's the orbital velocity and the associated centrifugal force that provides the weightlessness. So it's not outer space we're talking about, people, but the effects of orbital speed. It's easy to calculate that if you were to travel at about 17,700 miles per hour, you could orbit the Earth weightlessly at an altitude of 1 foot, barring collision with buildings, trees, Uncle Jack and other obstacles.

General relativity states that time runs slower the closer one gets to a gravitating mass, a proven feature of the theory that is crucial to the functioning of the Globsl Positioning System (GPS) that our iPhones utilize to enable Google Maps (and for the National Security Agency to monitor our every whereabouts). So don't rob a bank with your iPhone in your pocket, as you'll be easily tracked down and arrested.

It's a miniscule effect at Earth's surface, but as astrophysicist Ethan Siegel writes in his latest article, time really does run slower for your feet than your head because they're closer to the Earth. The effect would be much more pronounced at the surface of a neutron star, but then you'd be squashed flatter than an atom before you'd notice it. In fact, neutron stars are so smooth that even an irregularity the height of a human hair could be observed due to the wobble it would produce on the star's rotation, as explained in this fascinating Sixty Symbols YouTube video.

Say It Ain't So, Matt! — Posted Wednesday March 31 2021
Today's Republican Party—Come for the tax breaks, stay for the paranoia, the lies, the hypocrisy and the pedophilia!

That one may smile, and smile, and be a villain! — Hamlet Scene 1, Act 5
Hey, we've all sinned and fallen short of the glory of God, and I know I'm no different than anyone else. But we tend to hold our political leaders just a tad higher than ourselves, and when they fall short we expect them to come clean, admit their transgressions and repent. Sadly, that's not how it works in the Republican Party, where if you can lie and lie and get away with it, it's the same as telling the truth.

Three days ago, 38-year-old Florida GOP Congressional representative Matt Gaetz appeared on Fox News' Tucker Carlson show to plead innocence over claims that he had sexual relations with a 17-year-old girl and had transported her over state lines for related purposes. I don't know for sure if Gaetz is guilty, but I especially enjoyed how he referred to the unnamed child as a 17-year-old "woman." I suppose that's better than a 12-year-old woman.

Gaetz also claimed that his family was being extorted for $25 million to keep his guilt secret, noting that his father is wearing a wire to record the alleged extortionist's schemes. If true, it must be a pretty stupid extortionist to think that he/she can pull off the crime, given that it's now open to the public. It's also revealing that Gaetz and his family has that kind of money to begin with.

The FBI is investigating both the allegations against Gaetz and the extortion claim, and only time will tell if the Trump-loving Gaetz will find himself in the dock. My guess is that he will, but with a suspended sentence, as it's probably only his fourth or fifth offense. He will then disappear for a while, be forgiven by his Republican backers and faith-based supporters, and then be restored to full Christian forgiveness. Want proof? Just remember the likes of Jimmy Swaggart, Jim and Tammy Bakker and Ted Haggard, just to name a few from a long list of Republican criminals and hypocrites.

Just Nip It, Mr. President — Posted Saturday March 27 2021
"Nip it! Nip it in the bud!" — Some slightly out-of-context (and off-color) advice from Deputy Barney Fife in his currently out-of-print bestseller, Nip It: Barney Fife's Guide to Blistering Hot Married Sex

Pulitzer Prize winner Maureen Dowd's opinion piece in today's New York Times is a reminder to President Biden that the Republican Party despises his guts, and will never agree with any of his policies, regardless of how popular they are with your average Republican voter. Dowd writes "So while you're modulating, Mr. President, here's a suggestion: Ditch that old habit of yours, bending over backward to appease Republicans \(\ldots\) Bipartisanship ain't happening now."

I fully agree with Ms. Dowd. Biden is wasting his and his administration's time with all this talk about bipartisanship. Just look at the Republicans' current voting habits and their ongoing fawning allegiance to Donald Trump, whose lies and anti-democratic antics continue unabated. The current spate of Republican-led voting restriction bills and laws in Red States are proof that the GOP intends to never let the Presidency, House and Senate slip from their grubby hands again. If they could outright block blacks, Hispanics and Asians from voting, period, they'd friggin' do it.

So just nip all that talk of getting Mitch McConnell, Ted Cruz, Rand Paul and their ilk to see the light, Mr. President, and go on an Executive Order rampage.

Geek Saturday — Posted Saturday March 27 2021
The classical Einstein-Hilbert action with a cosmological constant \(\Lambda\) $$ S_{EH} = \int\!\! \sqrt{-g} \, \left( R - 2 \Lambda \right) d^4x $$ has passed every experimental and predicted test of general relativity since Einstein proposed his theory in November 1915. However, in the weak-field limit they do not account for the observed near-constant velocities of stars on the outskirts of their galactic centers, which had led to the proposal that some kind of unobservable dark matter exists around galaxies and galaxy clusters. Assuming that dark matter does exist, then Einstein's theory still holds, so now the search is on for the illusive dark matter. It has been proposed that dark matter may consist of cold neutrinos, axions, massive photons and other exotic weakly-interacting species, all of which have not been detected despite herculean and costly experimental efforts over the past three decades.

Einstein's action is fully Lorentz and coordinate invariant, but it is not invariant with respect to a change in scale, in which the metric tensor is varied according to \(g_{\mu\nu} \rightarrow \Omega(x)^2 g_{\mu\nu} \), where \(\Omega\) is an arbitrary function of space and time. In 1929, the German mathematical physicist Hermann Weyl showed that modern quantum theory demands scale invariance (later recognized as phase or gauge invariance) and that it accounts for the conservation of electric charge. Consequently, many physicists today believe that scale invariance should hold not only at the quantum level but on cosmological levels as well.

In 1989, University of Connecticut physics professor Philip Mannheim and his colleague Demosthenes Kazanas proposed that Einstein's action should be replaced by a scale invariant version of general relativity that reduces to that of Einstein's under less general conditions. Again, it was Weyl in 1921 who derived a unique scale-invariant tensor quantity \(C^\lambda_{\,\,\mu\nu\alpha}\) composed solely of the Riemann curvature tensor \(R^\lambda_{\,\,\mu\nu\alpha}\) and its two contracted variants \(R_{\mu\nu}\) and \(R = R^\mu_{\,\,\mu}\), and Mannheim-Kazanas used the associated action $$ S = \int\!\! \sqrt{-g}\, C_{\mu\nu\alpha\lambda}\, C^{\mu\nu\alpha\lambda} \,d^4x \tag{1} $$ to derive the equations of motion for free space in spherical coordinates. After what must have been laborious effort, they found the Schwarzschild-like solution $$ ds^2 = e^\nu c^2 dt^2 - e^{-\nu} dr^2 - r^2 d\theta^2 - r^2 \sin^2 \theta \,d\phi^2, \quad e^\nu = 1 - 3 \beta \gamma -\frac{\beta(2-3\beta\gamma)}{r} + \gamma r - k r^2 $$ where \(\beta, \gamma, k\) are constants of integration. As is easily seen, for \( \gamma = k = 0 \) the solution reduces to the familiar Schwarzschild line element, where \( \beta\) plays the role of the central gravitating mass. The terms proportional to \(r\) and \(r^2\) serve as acceleration parameters, which initially provided hope that scale invariance would provide an answer for dark energy and possibly for dark matter as well. Indeed, subsequent studies showed that the Mannheim-Kazanas metric accurately predicted the observed flat rotation curves for stars in many galaxies.

Several days ago, a preprint paper appeared on arXiv.org claiming that the Mannheim-Kazanas metric in fact does not accurately predict flat rotation curves under generally assumed galactic conditions. The paper's Cambridge researchers (M.P. Hobson and A.N. Lasenby) showed that a clever coordinate change in the radial parameter \(r\) could be used to eliminate the \(3\beta\gamma\) and \(\gamma r\) terms, thereby reducing the Mannheim-Kazanas metric to $$ e^\nu = 1 - \frac{k_1}{r^\prime} - k_2 (r^\prime)^2 \, \,\,\, * $$ where \(r^\prime\) is the new radial parameter and \(k_1\) and \(k_2\) are constants. This metric is equivalent to that of de Sitter spacetime, in which there is a cosmological constant (proportional to \(k_2\)) but with no matter in the universe (as our universe continues to expand, radiation and matter density will decrease to the point where the de Sitter metric will be perfectly valid). By eliminating the term linear in \(r\) in the Mannheim-Kazanas metric, the Cambridge researchers show that the velocities of stars far from their galactic centers fall off like \(1/r\) (in regions of interest for a typical galaxy) as in the pure Schwarzschild case, resulting in no region for flat rotation curves.

It can be shown that the tangential velocity \(v\) of a rotating star is given by $$ v^2 = \frac{1}{2}\, r e^{-\nu} \frac{d e^\nu}{dr} $$ For the Schwarzschild metric, the velocity decreases inversely with distance, as is classically expected (and in disagreement with observation). However, the situation changes for the Mannheim-Kazanas metric. The velocity will be extremalized (maximized) when its derivative with respect to \(r\) vanishes. With the reasonable assumptions that \( e^\nu \approx 1\), \( \beta \approx GM/c^2\) and \(\beta\gamma \ll 1\), we get the condition $$ \gamma r^2 - 2 k r^3 = \frac{2GM}{c^2} $$ Assuming further that \(k \approx \Lambda\) (and so can be neglected), we find that maximum stellar velocities will occur at the radius $$ r = \sqrt{ \frac{2GM}{\gamma c^2}} $$ Given the expected smallness of \(\gamma\), this will be a very large distance from the galactic center, and is thus in agreement with observation. From this, I judge that the Mannheim-Kazanas analysis does indeed match the effects of dark matter.

I'm studying the various galactic conditions that Hobson and Lasenby used to justify their conclusions but, as I'm not very familiar with galaxy dynamics, I cannot be assured that the assumptions I've made here are legitimate.

I've long been a fan of the work of Mannheim and Kazanas (both their independent and joint research), and I can only hope that they can find convincing arguments rebutting the Hobson and Lasenby paper.

PS: Einstein's full gravitational field equations are given by $$ R^{\mu\nu} - \frac{1}{2}\, g^{\mu\nu} R + \Lambda g^{\mu\nu} = \frac{8 \pi G}{c^4}\, T^{\mu\nu} \tag{2} $$ where \(T^{\mu\nu}\) is the energy-momentum (or stress-energy) tensor, which accounts for the presence of matter and radiation (which in turn affects the geometry). Einstein viewed the left-hand side (which is pure geometry) as being made of fine marble, whereas the right-hand side is cheap plastic (but matter and radiation have to be tacked on somehow, he reasoned). If \(S_M\) is the action for matter and radiation, then $$ T^{\mu\nu} = -2 \frac{1}{\sqrt{-g}}\, \frac{\delta (\sqrt{-g}\, S_M)}{\delta g_{\mu\nu}} $$ where the \(\delta\) operator means "variation." It is easily seen that both sides of (2) have the dimensions of length\(^{-2}\). But the Lagrangian in (1) is dimensionless, meaning that the proportionality term \(8 \pi G/c^4 \) would be unnecessary for a stress-energy that is also dimensionless. Go figure that out!

* This is Equation (15) in the paper, which is the key identity in the reseachers' argument. I've been unable to derive it, and I wonder if it's correct.

Changes? We Don't Need No Stinking Changes! — Posted Wednesday March 24 2021
You've by now heard about the Ruger AR-556 "pistol," the weapon that was used to murder 10 people in Colorado two days ago. It's classified as a pistol because previous mass killings motivated the National Rifle Association to request minor changes to the weapon, which was originally classified as an assault rifle. Pistol or rifle, it shoots NATO 5.56-mm jacketed ammo, whose diameter is a little less than a quarter inch. This seemingly small bullet belies the huge cartridge and powder charge in the round, which can push the bullet up to about 2,800 feet per second. The energy delivered is sufficient to cut a person in half—there are no flesh wounds with these things, as you're lucky to come away as a paraplegic or quadraplegic.

[It always bugs me when I watch a World War II movie in which a soldier gets hit with a machine gun or aircraft round, invariably clutching his chest or stomach while heroically uttering "They got me, Joe!" This is nonsense, and perhaps it's time to start airing autopsy photos of the children who were slaughtered by such weapons in places like Sandy Hook, Columbine, Parkland and Rancho Tehama.]

The Ruger pistol (on the left) has roughly the same killing power as the Vietnam-era M16 assault rifle (on the right), including a 30-round magazine that also holds the 5.56-mm round. The major difference is that the M16 can be fired in either semi-automatic or fully-automatic mode, while the Ruger is semi-automatic only. Clever gun enthusiasts have found ways to illegally modify the trigger and housing to fire the weapon like a machine gun, although all fully-automatic weapons are banned in America (even in Red States).

But search the Ruger website and you'll find that the AR-556 is listed as a pistol, thanks to the NRA. The NRA probably patted itself on the back getting it listed as such, but deep down you know they hated doing it. Conservatives hate change, which is why they will never allow a ban on assault rifles or any other deadly firearm that can be easily concealed, then whipped out to mow down dozens of victims. Republican lawmakers have even bragged that if President Biden proceeds with any related gun control measure, they'll see to it that the required 60% Senate majority is never achieved. Their tried-and-true argument is that some 50,000 Americans die in auto accidents every year, but no one calls for a ban on cars and trucks.

It's the same with the COVID-19 vaccines—Republicans weren't getting vaccinated last year, so why change now? Add to that the fact that 47% of Republicans say they will not get vaccinated, thanks to Trump's persistent effect on their tiny, pathetic minds. Consequently, America will likely not achieve herd immunity, guaranteeing that the virus and it variants will go on killing many thousands more.

Freedom! Liberty! Second Amendment! Huzzah!

"You Mean I've Been Eating Hamburger From 1960?!" — Posted Monday March 22 2021
My high school's cafeteria had an outdoor lunch service window that I often frequented, and I'd always buy their hamburger for 25 cents. It had a sauce that was heavy on mustard, but I loved it. I'd sit at one of the outdoor tables having lunch with Dan E. and John Z., talking about what we would do when we left high school. Dan planned on becoming an entomologist, but ended up with a PhD in Art History. Years later I'd often see John tooling around in his yellow VW Thing, a rather bizarre-looking auto that enjoyed a brief popularity in the late 1960s. I don't know what became of John, but I went on to study chemistry.

I still remember the taste of those hamburgers, and I was reminded of those days while binge-watching 11.22.63, the 2016 eight-episode mini-series based on Stephen King's 2011 science fiction novel of the same name (which I've also read).

The book and series tell the story pf a man (Jake Epping) who travels back in time to stop the assassination of President John F. Kennedy. Unsure of Lee Harvey Oswald's guilt, he first has to determine if Oswald had first tried to assassinate General Edwin Walker in April 1963. Walker was a real-life anti-communist zealot whom Oswald deemed a fascist threat (Oswald's involvement in the assassination attempt of Walker was later corroborated by Oswald's wife, Marina). Assured of Oswald's guilt, Epping then proceeds to track down Oswald and prevent JFK's assassination.

I distinctly recall the early afternoon of Friday, November 11, 1963, when my high school French teacher (Mrs. Eleanor Farrell) was interrupted by a student from the hallway who handed her a note. In emotionless tones, Farrell recited "President Kennedy was assassinated at 1:00 pm today in Dallas, Texas. Vice President Johnson is now the President of the United States." She then returned to the blackboard without further comment, which I thought was odd at the time.

Since then I've read about a dozen books on the assassination. None have revealed the true story, which will probably never be known. The best I've seen to date is Jeremy Bojczuk's 2014 book A Brief Guide to the JFK Assassination, but it too falls short of what probably really happened, or of those who were actually responsible.

But "Since then, 'tis centuries" as Emily Dickenson once wrote (although only 57 years have passed since Kennedy's murder). Who knows what might be revealed in the coming decades (or centuries). The remains of Kennedy's brain (which record the true path of the backward- or forward-tracking bullet) are under lock and key by the Kennedy family, and may never be revealed for definitive forensic analysis.

At any rate, 11.22.63 is a great series, and to me it's also tops as a time-travel adventure. You'll have to watch it to understand the hamburger connection.

Racism and Our Gang — Posted Thursday March 18 2021
In the early 1970s, Munira and I would would regularly go for lunch with our lab co-workers to El Tepeyac, a Mexican restaurant in East Los Angeles. The restaurant featured Manuel's Special, a pillow-sized burrito of rice, beans and beef that was on the house if you could eat the whole thing. Munira and I would invariably split one, joking about the lack of neighborhood stray dogs and cats and the possible nature of the restaurant's meat given its low prices.

We'd also frequent another local restaurant called Sambo's, whose wall paintings depicted the eponymous little black child being chased by a tiger. Thank God the restaurant either went out of business or changed its name to something less offensive.

I recalled this last memory while reading Our Gang - A Racial History of the Little Rascals by Julia Lee, a Chinese-American associate professor of English at Loyola University in Los Angeles.

I have most of the Our Gang films, which were produced by Hal Roach Studios as silents (1922-1929) and early sound films (and later produced by MGM until 1944). I also have every extant Laurel and Hardy film that Roach produced from 1927 to 1940. In 1990 Munira and I attended a memorable night with Hal Roach at the Raymond Theatre here in Pasadena, where several Laurel and Hardy films were presented along with personal reminiscences of early Hollywood by Roach and Joe Cobb, a child actor and early member of Our Gang.

Lee's book was a revelation, told from the perspective of American racist attitudes that existed in early Hollywood. But I was also struck by its purely historical information on Roach, his studio and the directors and child actors who starred in and produced the Our Gang films. Surprisingly, the inclusion of black child actors in the films was a natural outcrop of the relative innocence of the times, as the white and black members of Our Gang showed no innate racism in the episodes, although "Sunshine Sammy," "Farina" and'"Stymie" (my favorite) were often stereotypically shown as ignorant, spook-fearing, watermelon-loving pickaninnies.

The fact that the book was written by a Chinese-American also resonated with me, especially in view of the recent horrific attacks on Asian Americans, spurred on by former President Trump's racist remarks regarding the "Chinese virus" and "Kung Flu."

If you have the slightest interest in the racism of early Hollywood films and the sorry state of our country's politics today, please buy and read Prof. Lee's book.

PS: In 1927, Hal Roach (1890-1990) put two of his film comedians together to form the team of Laurel & Hardy. They quickly became a favorite of young and old alike, and to this day are considered the best comedic film duo of all time. In 1983 I took my four-year-old son Kris to see a Laurel & Hardy retrospective viewing of five of their silent films, all of which had been remastered and restored. Kris enjoyed the movies, but I was dumbfounded by the superb quality of the films, which looked as if they had been shot yesterday. Since then, L&H films have been released in countless collections, but to this day they still await definitive video and audio restoration. The best I've seeen to date is the fantastic 10-volume set The Lost Films of Laurel and Hardy, of which all DVDs are sold separately (and expensively). The nearest thing in terms of quality is Laurel and Hardy - The Essential Collection, which I purchased and gave to several family members and friends, all of whom are devoted L&H fans.

The Economic Elephant in the Room — Posted Sumday March 14 2021
President Reagan proved that deficits don't matter. — Former Bush Vice President Dick Cheney

Tax cuts always pay for themselves. — The Perpetual Delusionary Mantra of the Republican Party
I watched Fareed Zakaria's GPS cable program this morning, in which economists Larry Summers and Paul Krugman talked about the pros, cons and likely consequences of President Biden's recently enacted $1.9-trillion American Recovery Act (ARA). A former president of Harvard University, Summers was a Treasury Secretary and economic advisor to presidents Clinton and Obama, while Krugman is a political writer, economic advisor and columnist who was awarded the 2008 Nobel Prize in Economics.

Summers and Krugman are friends and colleagues, but they disagree on the costs, benefits and outcome of the ARA. In a nutshell, Summers feels that the ARA does not have sufficient long-term monetary resources to pay for itself, and he worries about its inflationary potential and the deficits that are likely to result. Krugman likened the ARA to a war-times act that—like the New Deal and the 2008 financial collapse—was necessary to pull the country out of the health and economic disasters caused by the COVID-19 pandemic that has so far killed over 530,000 Americans. Krugman also noted that while the ARA is costly, is is not likely to result in runaway inflation.

I think Summers made a good point about the lack of any obvious financial resources to pay for the ARA (such as public investments like bonds), much less for Biden's plans for infrastructure improvement and climate change mitigation. Krugman's response was that similar cash outlays and fiscal borrowing occurred during the Korean and Vietnam wars, which led to manageable inflationary problems and deficits.

During the discussion, neither economist brought up the topics of taxes, America's ongoing committment to its expansive foreign military presence or to the booming stock market, which has inexplicably soared throughout nearly all of the 2020-21 pandemic year. I can understand why most politicians today won't touch the issues of raising taxes or cutting back on America's military, but the trillions of dollars now being amassed by corporations and their stockholders represents a hugely significant source of funds needed to pay for public programs, infrastructure improvements and climate change mitigation. Roughly 55% of Americans are currently invested in the stock market one way or another (through actual stock ownership, pension plans or other indirect investments), and they are now seeing rates of return far in excess of what banks are paying on savings accounts. Furthermore, the tax rate on capital gains is still only 15%, far below what most middle-class American are paying on their combined federal and state income taxes.

To me, this is the elephant in the room: if America wants a responsible pay-as-you go economy, reliable infrastructure and climate mitigation, it had better tap into the corporations and their stock holders, and this means raising taxes on those who are benefiting the most. The market is now poised for an even bigger boom as we get COVID-19 under control, and if we don't want dangerous bridges, unreliable public utilities and a ruined climate while giving a free pass to Bahamas-bound wealthy freeloaders, stock market-specific taxation is the way to go.

Why Most Women Don't Marry Scientists — Posted Thursday March 11 2021
By the way, Gary Larson is back!


Dark Matter Detection Fails Again — Posted Thursday March 11 2021
The great philosopher of science Karl Popper famously assigned a critical element to what he defined as "science", which is that it must be falsifiable. That is, every scientific theory must not only stand the test of ongoing experimental validation, but it must also be subject to being proved wrong. For example, while Einstein's general theory of relativity (gravitation) has perfectly passed every test thrown at it for over 100 years, a single confirmed observation that disagrees with the theory would disprove it, requiring that the theory be either modified or discarded in favor of something better. Consequently, there are no true laws of Nature, only theories awaiting revision or refutation. Popper's falsification idea has not always been popular, but it's a good start.

Related to this is the notion of reproducibility, which involves applying the same or similar experimental techniques, methods and materials used to establish a theory in the first place. If you conduct a experiment (or series of identical experiments) that appears to uphold a theory you've proposed, but someone else cannot reproduce the same results, then your theory remains either a hypothesis or a conjecture (or it's simply pure bunk).

A case in point is the set of experiments performed by a research team in Italy called DAMA/LIBRA, which uses a mass of thallium-doped sodium iodide to detect dark matter particles. But rather than detect these hypothetical particles themselves, its approach has been to look at whatever detection events occur over time, the idea being that as the Earth is swept along with the Milky Way's rotation, it must encounter a varying biannual number of particle events depending on whether Earth's orbit is moving with or against the galaxy's rotation. In a sense, the exact nature of the detection event doesn't matter, only the sinusoidal pattern of detected events matters. This approach would then rule out any human, systematic or random experimental errors and noise in the detection apparatus. The DAMA/LIBRA team has indeed reported such a semiannual pattern in its data, appearing to confirm the presence of something akin to dark matter.

You might recall that the famous Michelson-Morley experiment of the late 1880s tried the exact same approach in an attempt to detect the luminiferous aether, a universal substance that was assumed to exist to provide a means for light waves to travel in space (the rationale was that since sound waves need air to move through and water waves need water, then light must also have something to "wave" against in order to propagate in space). The experiment famously failed, demonstrating that light can indeed move through the vacuum of space.

However, the DAMA/LIBRA team did detect something, and until now it provided at least indirect evidence for dark matter. But more recently a series of identical experiments conducted by the ANAIS dark matter team at Spain's Saragossa University have consistently failed to reproduce the DAMA/LIBRA results to 99% confidence. The disagreement is detailed in today's Medium article by astrophysicist Ethan Siegel.

While any limited series of disagreeing experiments is not sufficient to conclusively disprove the existence of dark matter, I'm still hoping that a satisfactory answer for dark matter's presumed effects on galaxies and galactic clusters will be explained by modified Einsteinian gravity. (Only time will tell, but at 72 my remaining years are dwindling away, and I'm getting impatient.)

The Very Definition of Spin — Posted Thursday March 11 2021
And I'm not referring to quantum-mechanical spin.

The phrase "It's not a flaw, it's a feature" once applied to bug-ridden computer programs, but the Republican Party has turned it into a political term, what we currently know as spin. Mississippi Republican Senator Roger Wicker, who joined every single one of his fellow Republican senators and congressional representatives in vehemently opposing President Biden's $1.9 trillion COVID-19 relief legislation, is now trying to take credit for the benefits the legislation will provide to his constituents and Mississippi businesses. In defense of Wicker's comments, prominent GOP members are using Wicker's words as proof of Republican bipartisan support for Biden's efforts, which they have uniformly opposed ever since Biden took office.

I only wish that Sen. Wicker, an avowed devout Christian, would more carefully read the Gospel of Matthew, in which Jesus admonishes hypocrites and hypocrisy no fewer than 15 times. Since when did hypocritical spin become a treasured feature of Republican politics?

Coordinated Guessing — Posted Tuesday March 9 2021
The following is intended mainly for budding structural design engineers and nerds, but it has wide application to Newtonian and relativistic gravitational physics, electronic circuit design, fluid flow and similar computationally intense problems.


Let's say you want to build a 100-story office building. You start by designing the basic structure from scratch, using a 3-dimensional grid of steel beams, girders and columns. You also know the various loads that the structure will have to safely support, including gravity, wind, snow, earthquake and occupancy loads. The basic structure will consist of thousands of nodes (where the beams come together) and links (the horizontal and vertical beams that connect the nodes). Your design will have to take all these things into account, including a safety factor. Where do you begin?

In olden days you'd rely on rules of thumb, experience and slide rules. Nowadays the computer does most of the work, checking that your design is not only safe but can be built at the lowest possible material and labor cost. Given a few input parameters, the computer may also do the basic design as well.

Trust me that your 100-story office building will involve thousands of nodes, and these are the basic elements that the computer uses to check for allowable beam stress, strain and deflection. Also trust me that for a structure involving \( N \) nodes, the computer will need to construct an \( N \times N \) matrix (almost always symmetric), and that it will have to solve a system of \( N \) simultaneous linear equations of the form \( A X = Y \), where \( A \) is the matrix, \( X \) is the \(N-\)dimensional vector of unknowns (say, beam stresses) and \( Y \) is the vector expressing all the known constraints on the structure. The computer must somehow solve the system via \( X = A^{-1}\,Y \), where \( A^{-1} \) is the the inverse of the matrix \( A\). Lastly, trust me that calculating inverse matrices is computationally a total bitch. For a system of thousands of nodes, no computer can do it directly, and a time-consuming process known as iteration must be used, where each iteration essentially involves an increasingly more accurate guess of the unknowns.

Designing a safe and cost effective office building is thus very complicated, but the number of elements is still finite. What if you need to design a continuous structure, say an aircraft wing? Such a structure is not described by a finite number of elements like beams and girders, but the wing's stresses, strains and deflections must be calculated using a seemingly infinite number of design elements. What do you do now? Of course, you discretize the structure using a finite grid of nodes and links, an approach known as finite-element design. The computations become more accurate the more nodes and links you use, but the calculation is essentially the same as the office building example.

The importance of solving large-scale linear (or linearized) simultaneous equations cannot be overemphasized, and as noted earlier the problem spans many technological applications now essential to modern life. It is therefore not surprising that an enormous amount of effort has been expended on finding efficient computational solution methods. The number of computer interations or steps required to achieve a solution is then key, since it largely defines the effort required to solve the problem. For some problems, that number can be enormous, which, due to cumulative floating-point errors and time constraints, may result in erroneous solutions.

The latest Quanta magazine spells out the problem in more detail, and it also describes a new technique called "coordinated randomness" that has proved (at least marginally) useful. While solution guesses are helpful, it's often difficult to know just how to arrive at them. The Quanta article describes such an approach based on random guesses, and it implies that in some cases even random guessing can be useful (unlike the SAT and GRE exams you took).

The article interested me for a number of reasons, as I used to do large-scale numerical analysis of both linear and nonlinear systems and because I still think there might be some validity to the simulation hypothesis, which is the idea that something or someone (God, a post-human computer programmer or even intelligent Nature itself) is simulating our universe using an unimaginably complex computer program. Our entire observable universe is composed of roughly \( 10^{90} \) particles and fields, which is mind-bogglingly huge but still finite, and therefore subject to computer simulation.

Sorry for this overly long and nerdy post, but it underlies a fascinating and important mathematical problem.

Stanley Tucci — Posted Sunday March 7 2021
I first became aware of American actor Stanley Tucci in the excellent 1993 action thriller The Pelican Brief starring Julia Roberts, Denzel Washington and Sam Shepard (didja know that Shepard was also a 1961 graduate of Duarte High School, my alma mater?) In the film Tucci plays a cold-blooded assassin, a far cry from his comedic turn in the hilarious 1998 film The Impostors with Oliver Platt, which regularly had my wife, me and our kids literally in stitches. Don't miss the annoying German ship steward's immortal line "It has made me also \(\ldots\) moist" or Billy Connolly's "Powerful enough to snap the neck of a small beast, and yet sensitive enough to caress the tender throat of a young castrato — coax a song out of him!"

Now Tucci is starring in the popular CNN reality show Searching for Italy, in which Tucci travels to various Italian cities visiting that country's historical treasures and sites, all while stuffing his face on the local cuisine. My family members love it, but I see it as just another "food porn" show, and I can't get into it. I did like the PBS series Rick Steves' Europe, which is far more educational and entertaining (but still has Steves stuffing his face much of the time).

Perhaps my dislike of food shows stems from the food I'm eating now as an aging widower: basic stuff like fruit, vegetables, bread and the wonderful "Beyond Meat" plant products that have made me almost a vegetarian. Like the bumper stickers say, "Eat Right, Exercise, Die Anyway."

Dirac on the Constancy of the Gravitational Constant — Posted Saturday March 6 2021
Although I dearly love the work of Isaac Newton, Albert Einstein and Hermann Weyl, my favorite physicist just has to be "Father of Moden Physics" Paul Adrien Maurice Dirac (1902-1984), whose foundational contributions to physics spanned everything from quantum mechanics to general relativity. In a far saner and less ignorant world, Dirac's name would be as recognized as those of Newton and Einstein.

In the early 1930s Dirac began to question the nature of large dimensionless numbers, such as the ratio of the electric force to the gravitational force (roughly \( 10^{39} \)) and the relatively small value of the fine structure constant \( \alpha \), which is about 1/137. He went so far as to wonder if these figures were true constants of Nature, or if they might vary over geological or cosmological spans of time. For example, the Newtonian gravitational constant \( G \) is about \( 6.67 \times 10^{-11} \) in the kg-m-s unit system, but humans have only known about it for some 400 years. It's entirely possible that it might be slowly but measurably changing over periods of thousands or millions of years. We just don't know.

This situation reminds me of the story of the ephemeral fly, which I recounted long ago on this site. It's a small insect that lives for only a few hours after its hatching, and as it flits around desperately seeking a suitable mate during its brief life span it might consider the trees and flowers of its world as everlasting and permanent. We humans live far longer, but we might also find ourselves fooled into thinking that the things we observe and measure are similarly truly constant.

On the basis of what we know about modern cosmology today, the universe is doomed to perpetual and accelerating expansion, with all matter eventually being transformed into low-energy radiation, a view that is predicated upon the constancy of dark energy. But if the density of dark energy is not constant but decreasing, then the universe might halt its expansion and begin contracting, perhaps transforming itself again into a primordial mass-point and reinstigating a new Big Bang.

Here is Dirac in 1979, talking about the constancy of \( G \). He died in 1984, sadly having never learned about recent discoveries of the accelerating expansion of the universe:

PS: Dirac's eccentricities are nearly as famous as his physics. Forced to speak only French in his home while growing up, he became extremely taciturn in his adult life (his students coined the term Dirac unit, meaning one word per hour). He was notoriously aloof but not unfriendly, preferring long stretches of solitude and daily walks to social interaction. At a party on board an ocean liner with fellow Nobel Laureate Wolfgang Pauli, he was asked to dance. "Come on, there are lots of nice women here, Dirac!" said Pauli, to which Dirac responded "How do you know they're nice?"

While discovering quantum field theory, antimatter, the Dirac relativistic electron equation (the greatest equation of all time, in my opinion), the Dirac delta function and many other fundamental discoveries, Dirac managed to marry and have two daughters with the sister of fellow Nobel Laureate Eugene Wigner (Dirac's friends and colleagues were stunned that Dirac had not only a romantic side to his personality but a sex drive as well). He invariably introduced his wife Margit to others as "Wigner's sister."

Weary of the cold weather in England, Dirac took an emeritus position at Florida State University in 1972. I equate this event as akin to Einstein arriving at a community college and asking for a teaching job.

These and many other stories are recounted in Graham Farmelo's great 2011 Dirac biography The Strangest Man: The Hidden life of Paul Dirac.

Physics Leads the Way — Posted Wednesday March 3 2021
Good news: the American Physical Society will not hold any future physics meetings or conferences in American cities that tolerate social injustice. I believe this will apply to many Red State cities, whose ignorant denizens don't believe in science anyway.

Geek Tuesday — Posted Tuesday March 2 2021
I occasionally get emails asking what programs I use to write and post mathematical text. For online math, I use MathJax, which is free and requires only a basic familiarity with the LaTeX typesetting system. For documents, over the years I've used numerous computer programs, going all the way back to PCTeX, Scientific Workplace, MathType, LyX and most recently TexStudio, the latter two of which are free. In 1986 I induced my office to spend $300 for Lotus Manuscript, which had rudimentary math tyepsetting ability. It was okay as a word processor, but took hours to render readable math. Today there are more free and not-free math programs than I can name. I still use the amazingly powerful Mathematica on occasion (I still have the 1992 DOS version), but only to do calculations I'm either too lazy or too stupid to do myself.

Retired Stanford University math professor Donald Knuth is considered the father of modern mathematical typesetting, whose many books include The TeXBook, from which I learned the TeX programming language many years ago. Written in a highly amusing style, the book's illustrations by Duane Libby are both clever and hilarious:


Dirty Tricks!


A New Media Technology — Posted Monday March 1 2021
Older folks like me will recall the "colorization craze" that took place in the 1980s, which attempted to make old movies look more realistic (or at least more interesting). It failed (the phrase "putting lipstick on a pig" comes to mind), mainly because it predated the ensuing "remastering" technology that removed scratches and other defects in the original films. Even later (in the 2000s), remastering techniques had progressed to the point where frame-by-frame toning consistency, interpolation, frame speed correction and similar repair techniques made the films look almost new. Perhaps the best example of this is the remarkable 2018 film They Shall Not Grow Old, which stunningly presents a series of World War I films that appear to have been shot yesterday.

As amazing as this technology is, it's still far from perfect. Depending on the condition of the original material, facial features like hair, teeth and skin complexion cannot be rendered accurately. This is quite apparent in the above-mentioned film when the subjects smile, revealing dental features that look pretty awful (although the subject's teeth were often bad in real life).

There's an interesting recent video on YouTube describing a new technology for not only repairing and remastering old photos and films but enhancing them to near-lifelike quality using neural network learning techniques. While it relies in part on the use of existing models and morphing, the results are nothing short of amazing:

The video cites a paper that describes the technology in more detail, although I had some trouble understanding it (I have a friend with a Caltech PhD in computer recognition who might want to explain it to me).

As a fan of old silent and classic films, I'd love to see the day when they can be rendered using this or an even better technology. However, at the same time I fear its misuse in Deepfake applications that can generate phony photos and videos that are indistinguishable from real life. I can easily imagine Fox News airing a Deepfake video showing a progressive political candidate having sex with a young child, which would quickly go viral among Republicans. Even if such videos were quickly reported as fakes, the images would persist in the minds of gullible conservative voters, destroying the candidate.

Only time will tell where things will go from here. I'm hopeful (imagine watching crystal-clear Laurel & Hardy films), but I'm still realistic when it comes to the current state of the world.

PS: Some years ago I regularly exchanged emails with Dr. John Sotos, M.D., whose book The Physical Lincoln, which examined Abraham Lincoln the way a physician would, revealed physical and medical aspects of our 16th president in fascinating detail (for example, a country dentist, while pulling an infected molar from Lincoln, inadvertantly took out a piece of his lower jaw bone as well). Based on his examinations of Lincoln's features, behavior and medical history, Sotos believes that Lincoln suffered from a genetic malady that would have imminently killed him even if Booth's bullet had missed. I highly recommend the book.

My note on a recent YouTube post:


The Misinformation Pandemic — Posted Sunday February 28 2021
I caught CNN's Fareed Zakaria on his popular GPS show this morning, and as usual he addressed a number of important issues of the day.

He had multi-billionaire Bill Gates on hand to talk about climate change (again), and although the Bill and Melinda Gates Foundation is doing some worthy things to benefit the poor and disadvantaged in Third World countries, I strongly suspect that as a highly intelligent and educated man he knows full well that the human race is probably permanently screwed. One of the reasons I feel this is the case is that Gates also talked about the country's (and world's) misinformation problem, which is largely responsible for our unwillingness to seriously address many existential problems, of which climate change is just one.

Prior to the Gates segment, Zakaria talked about the incredibly brutal 2018 assassination of CNN journalist Jamal Khashoggi by Saudi agents acting under the direction of Saudi Arabia's Crown Prince Mohammed bin Salman. In particular, Zakaria addressed then-presidential candidate Joe Biden's promise to hold bin Salman responsible for Khashoggi's horrific murder and dismemberment, which now-President Biden hypocritally walked back due to supposed Real Politik realities. As Zakaria notes, Biden has decided not to punish bin Salman because ever-expanding American empire-building ambitions need to preserve the good graces of Saudi Arabia for both economic and military purposes.

Biden's decision to let bin Salman walk and Biden's recent decision to hit Iranian-supported facilities in Syria are just two reminders to me that while Biden may be a far better presidential choice than Donald Trump, America's global military ambitions far outweigh any morally admirable intentions that the U.S. tries to promote around the world.

And on that note I'll point out that the real purpose of misinformation is to promote evil while hypocritally posing it as good. When Khashoggi was murdered, dismembered and the pieces carried out of his hotel in suitcases by his Saudi killers, the world was shocked that then-President Trump chose to believe in bin Salman's innocence. But the Republican Party expressed little shock, since its members viewed journalist Khashoggi as just another dirty brown Arab. Misinformation feeds on a combination of fear, ignorance and arrogance—traits that perfectly define the Republican Party—and it is anyone's guess if President Biden will be able to escape its lure or consequences.

Geek Extra: In a straw poll taken today, former president Donald Trump got the support of 68% of CPAC attendees, or one standard  deviant  deviation.

What the Hell is Quantum Holonomy Theory? — Posted Sunday February 28 2021
Technophile Arvin Ash has an interesting series of science videos on his YouTube website, with an emphasis on modern physics. Of particular interest to me is that Ash has addressed the dark matter and dark energy problems numerous times, always citing current research and progress in these areas.

His latest video addresses something called quantum holonomy theory, a subject I admittedly never heard of before. But it sounds interesting—Ash notes that it's a theory of quantum gravity that's focused on the fundamental simplicity of Nature, an asset sadly missing from superstring theory, loop quantum gravity, supersymmetry and even the Standard Model of physics itself. Its sole distraction, at least from what I've managed to glean from the lengthy 2015 paper Ash cites in his video, is that it involves non-commutative geometry. While non-commutative algebra presents no problems in other areas of physics (rotations, matrix multiplication, differential operators, elementary quantum mechanics, etc.), its application to pure geometry is highly non-intuitive (at least for me).

Still, quantum holonomy assumes that we live in just the three space dimensions we've come to know and love, and it focuses on the properties that physical objects exhibit when they're moved from one point to another. Conceptually this is very appealing, as you can't get much simpler than that.

The video is about 16 minutes long, including the usual plug for Magellan TV (which you can skip over):


Shame on America's Conservative Republican Christians — Posted Saturday February 27 2021
The GOP's Conservative Political Action Conference is being held in Orlando, Florida this weekend. It will prominently feature a full-size golden idol of former President Donald Trump, seemingly in violation of the Second Commandment, which states that "You shall not make nor bow down to any graven image or idol."

The Republican Party is no longer a political party, but a Trump cult.


Nerd Saturday — Posted Saturday February 27 2021
First, some history. Nearly the same time that Einstein published his theory of general relativity in November 1915, the famous German mathematician David Hilbert found a simple way to express the same gravitational physics by extremalizing the action quantity $$ S = \int \!\! \sqrt{-g}\, R\, d^4x \tag{1} $$ where \( g\) is the determinant of the metric tensor \( g_{\mu\nu} \) and \( R \) is the Ricci scalar. If we vary the metric tensor of this action, we arrive at the Einstein gravitational field equations for free space, $$ R^{\mu\nu} - \frac{1}{2}\, g^{\mu\nu} R = 0 $$ where \(R^{\mu\nu} \) is the Ricci tensor (any one bothering to read this will know what I'm talking about).

Einstein also realized that the free-space equations could be extended to acount for the presence of matter by setting the equations equal to a quantity known as the energy-momentum or stress-energy tensor \( T^{\mu\nu} \), or $$ R^{\mu\nu} - \frac{1}{2}\, g^{\mu\nu} R = \frac{8 \pi G}{c^4}\, T^{\mu\nu} $$ where \( G \) is Newton's gravitational constant (the proportionality constant is chosen so that the field equations are consistent with the classical Newtonian gravitational result; it is also dimensionally consistent with that of the action).

Einstein's solution was complicated and drawn out, but his field equations matched those of Hilbert's vastly simpler approach, which must have really pissed off Einstein. Although Einstein got credit for the discovery, the action \( S \) is now referred to as the Einstein-Hilbert action.

In 1918, the noted German mathematical physicist Hermann Weyl proposed that a better action was the quadratic quantity $$ S = \int \!\! \sqrt{-g}\, R^2\, d^4x \tag{1} $$ whose equations of motion are $$ R \left( R^{\mu\nu} - \frac{1}{4}\, g^{\mu\nu} R \right) + \nabla^\mu \nabla^\nu R - g^{\mu\nu} g^{\alpha\beta} \nabla_\alpha \nabla_\beta R = k T^{\mu\nu} $$ where \(\nabla\) is the covariant derivative and \( k \) is some constant. Although the action in (1) is equivalent to that of Hilbert's (subject to a simple constraint on \(R\)), the action is of dimension zero, complicating the inclusion of the energy-momentum tensor (which is of dimension inverse length squared, so that \( k\) must be dimensionless). As it is then, we have no way of connecting Weyl's action with the energy-momentum tensor.

A few solutions have been proposed, including the division or multiplication of \(R^2\) by an appropriate scalar quantity, like the energy-momentum scalar \(T\) or some scalar quantity \( \phi(x)\) that fixes the dimensionality problem. Such fixes are called \( f(R, T, \phi)) \) theories, all of which have been examined extensively by researchers with little or no progress.

Further complicating the situation is the fact the the Bianchi identities $$ \nabla_\nu \left( R^{\mu\nu} - \frac{1}{2}\, g^{\mu\nu} R \right) = 0 $$ are inviolate and cannot be avoided, and so must somehow play a role in whatever equations of motion result from the choice of \( f(R, T, \phi)\).

As readers of this site will know, I've long been fascinated by modifications of Einstein's gravity theory that might explain the problems of dark energy and dark matter, and I hope that the answer will be found someday.

Them Thar Soshalists Had Best Listen Up — Posted Saturday February 27 2021
Here's another timely comic by Ruben Bolling, drawn again in the style of famed Disney cartoonist Carl Barks. I see Bolling's Hollingworth Hound as the modern counterpart of one of the Beagle Boys (The Beagle Boys! The Dreaded Beagle Boys!)

And it's true—Texas' power grid is completely free-market, with prices driven solely by supply and customer demand. When the Big Freeze hit Texas last week, customers saw their electricity bills going into the thousands of dollars for only a few days' worth of demand. And gosh-durn it all, they're just gonna have to pay up one way or another, despite calls for energy regulation by them-there danged progressive types.


Still Coping — Posted Thursday February 25 2021
As a food bank volunteer, I deliver food to the homebound in Pasadena, Arcadia, Monrovia and Duarte, and my route takes me right past my wife's grave. I can see our joint headstone as I drive by, and I always whisper Sabahelkhayr, ya hayati, ana behebik! (Good morning, my dear, I love you!) With 19 months now gone since her passing, my eyes still invariably fill with tears. Although I'm tapering off my antidepressant medication and my grief therapy sessions, I'm now convinced that I will never recover from the loss of my wife. Other than my family members, my only consolation is that with global climate disruption, ongoing COVID-19 isolation, the virus variants and the insane anti-truth, anti-science authoritarian crap still running rampant in this country, she's not here to suffer through it. That's a hell of a consolation.

Life on Mars? — Posted Thursday February 18 2021
NASA's Perseverance probe has landed successfully on the surface of Mars!!

Part of its mission is to detect evidence of life, and I can only wonder what sociological and religious impact it will have on the human race if it finds it.

And It's Gonna Be A Long, Long Time — Posted Thursday February 18 2021
I've been going to the gym for forty years, but in February 2020 my gym closed down due to COVID-19. It then underwent bankruptcy and restructuring and only recently reopened in Arcadia. I've hardly exercised since my wife passed away in July 2019, but I tried it again this Tuesday, barely lasting 15 minutes. I went again this morning and lasted 22 minutes, so I guess I'm on my way. But it's a far cry from the 90 minutes I used to work out.

I could only lift about half the weight I used to, and the number of reps I can do is very limited. My body was saying "Hey, I remember this, but I just can't do it any more!" so out of respect for my now-frail 72-year-old frame I'm not gonna push it.

I hope your day is going better than mine.

Laying the Blame Where It Belongs — Posted Thursday February 18 2021
Schadenfreude is a German word that means taking joy or pleasure in the misfortune of others. I would be taking Schadenfreude over the self-inflicted misery that Texas is experiencing right now over the millions of people going without power and water during a record-setting cold snap, but I know that millions of children and progressive adults are also suffering.

Texas Governor Greg Abbott and Senator Ted Cruz are blaming renewable-energy utilities for the problem, despite the fact that less than 10% of Texas' power is generated by wind turbines and solar cells. Texas experienced a similar event in 2011, but conservative hatred of regulation and "green" energy blocked progressive efforts to winterize the state's power infrastructure. The blame is laid bare in today's New York Times article.

Before flying off to Cancun to escape the cold while his constituents suffered, Sen. Cruz went so far as to point the finger at California, which he described as a dystopia with constant power blackouts and water shortages due to overregulation.

You may recall that under the Obama administration Texas expressed a strong desire to secede from the Union. With the persistent and apparently entrenched animosity of Texas and other Red States against President Biden and the progressive Democratic agenda, I think secession of these states might be a very good idea indeed. I suggest they move to Antarctica.

PS: Speaking of Schadenfreude, is it okay to start celebrating Rush Limbaugh's death? I'm not celebrating, but in truth I couldn't care less. However,
No man is an island entire of itself; every man
is a piece of the continent, a part of the main;
if a clod be washed away by the sea, Europe
is the less, as well as if a promontory were, as
well as any manner of thy friends or of thine
own were; any man's death diminishes me,
because I am involved in mankind.
And therefore never send to know for whom
the bell tolls; it tolls for thee. — John Donne
But still,


Hegemony, the Great Storm and Boltzmann Brains — Posted Monday February 15 2021
Sorry for abridging Bolling's latest comic, I just didn't find all of it that funny:


On American Christianity in the Age of Trump — Posted Monday February 15 2021
As a Christian, I've often wondered how Donald Trump took hold of (and still holds) his American Christian evangelical base with a vise-like grip, despite the obvious anti-Christian views that he has demonstrably espoused throughout his life.

Here is an article written by Isaac Bailey of Davidson College who poses the same question that I have.

My response is "They're not true Christians," but it still raises the question of how so many supposed Christians could be so misled.

Hossenfelder on the Simulation Hypothesis — Posted Saturday February 13 2021
Many practicing hydraulic engineers deal solely with one-dimensional flow regimes (especially those involving open-channel flow), while researchers will get involved in more complicated two- and three-dimensional situations, where the Navier-Stokes equations are utilized. These are highly non-linear equations whose full solutions still elude even computerized analysis. Did you ever wonder how the turbulent flow of a waterfall might be completely described by a Navier-Stokes analysis? Yet Nature does it instantaneously and seemingly without effort.

This had led me to wonder exactly how Nature pulls off such things, and if there's some complicated calculation being conducted somewhere behind the scenes. I've even thought that maybe this is why time itself exists, which might be necessary for Nature to do her stuff.

The idea that there's some calculation going on in Nature is not a new one, and it's just one simple example of why Bostrom's simulation hypothesis is embraced by many scientists. Yet, as the noted German physicist Sabine Hossenfelder points out in her latest video, there is zero empirical evidence for the simulation hypothesis, so it must be relegated to the realm of religious faith, not science.

I responded to Hossenfelder's post, where I noted that if the notions of a creator God or the simulation hypothesis are wrong, then there is really only one remaining explanation for the profound and consistent physical laws of Nature we observe in our world: that we live one of a possible multiverse of worlds (or that we live in one of a many-worlds universe). As a Christian I believe the answer is God (which if you think about it is pretty much the same as an omniscient simulator), but if I'm wrong then I prefer the many-worlds interpretation, which does not violate the laws of quantum mechanics. Whichever is true belies the inescapable fact that there is a curtain of ignorance that separates us from the actual reality of our universe. It is my fervent hope that when we die we'll find out just what the heck it is.

Here is Hossenfelder's video, which runs about 10 minutes:

PS: The Navier-Stokes problem is one of seven mathematical problems featured in the Clay Mathematical Institute's Millennium Prize offering. The prize is $1 million dollars, not an inconsiderate sum for what amounts to an idle pastime for a true geek.

Declare War, President Biden — Posted Friday February 12 2021
Today's news includes reports that President Biden is "anxiously awaiting" the Senate conviction vote against Donald Trump, but I'm sure he has no doubt what the result will be—acquittal, which Trump will view as "exoneration." My own guess is that no more than six or seven Republican senators will vote to convict, leaving Trump in the clear to run for election again or incite another insurrection.

If I were Biden and all the other Democrats, I'd see the Senate's acquittal as proof positive that the GOP has no intention of working with the Biden administration, just as it had no intention of working with President Obama's. Biden should therefore announce that he has no faith in the GOP in anything, and proceed to issue as many executive orders as he can get away with. Biden should also make public Trump's taxes and all the information he has on Trump's four-year occupation of the White House, including every scrap of data he has on Trump's dealings with Russia, Stormy Daniels and every other trollop that Trump has bedded since election.

Fifty Years Ago — Posted Tuesday February 9 2021
Fifty years ago exactly (it was also a Tuesday), I woke up on the floor of my studio apartment in Long Beach sometime just after 6 am. The place was rocking violently, and I realized it was an earthquake. I was in my pajamas, and I rushed out through the door onto the second floor balcony. Right away I noticed two things: the water in the swimming pool below was sloshing crazily back and forth, and two attractive girls in the apartment next to mine had come out wearing only their panties and bras. My first thought was: Why hadn't I noticed these girls before? And my second thought was: Yeah, this just had to happen on the second day of my last semester at California State College at Long Beach!

I later learned that the earthquake's epicenter was forty miles away in Sylmar, with a Richter magnitude of only 6.5, and I was surprised that it was felt so strong in Long Beach. But there was very lttle damage where I was, although the aftershocks kept me awake for several days after.

We had several other moderate earthquakes years later, but on January 17, 1994 (my older son's 15th birthday and on the MLK holiday), we experienced the 6.7-magnitude Northridge earthquake, which shook our Pasadena house with a violence hard to describe. My wife and I checked on our sons, and we called on other family members, but thank God everyone was alright. Our house underwent moderate damage, but those of my co-workers were far worse. The next few days at work were interesting. The afterquakes shook my 14th-floor workplace pretty good, and one unnerved long-term employee took early retirement as a result.

We're long overdue for another major earthquake in Southern California, if not the "Big One," the predicted 7.6-Richter San Andreas event that's sure to come someday. God save us all.

Why History Repeats Itself — Posted Friday February 5 2021
BTW, Entschuldigen Sie means "Excuse me," and meine Dame would be much more polite than Fräulein. Otherwise, Ruben Bolling's got the Hitler-Trump analogy spot on.

PS: It's obvious that some of Bolling's characterizations intentionally mimic the work of other comic artists (notably Disney's Carl Barks). In the above comic, Billy Dare is very similar to the character Tintin, an adventurous European youth created in the 1930s by the Belgian artist Georges Remi. I discovered Tintin many years ago, and my Egyptian wife Munira was also very fond of the comic strip and the many books that Remi published. Our sons grew up with Tintin books, although their school friends had no idea the character existed. In 2011, directors Steven Spielberg and Peter Jackson released the computer-animated film The Adventures of Tintin, which I highly recommend.

On the Fine Tuning Conundrum — Posted Thursday February 4 2021
I remember in early college wondering why the speed of light \(c\) in vacuum is some 2.99792458\(\times 10^8\) meters per second. I thought that maybe there was some deep law of fundamental physics that would provide the answer, perhaps as some complicated combination of \(\pi, e , \epsilon \) and other fundamental numbers that would give the speed of light. That's probably wrong—the speed of light \( c\) is likely just a pure constant of Nature.

Much more recently, I discovered that the cosmological constant \(\Lambda\), which appears in the full expression of Einstein's gravitational field equations $$ R_{\mu\nu} - \frac{1}{2}\, g_{\mu\nu} R + \Lambda g_{\mu\nu} = \frac{8 \pi G}{c^4}\, T_{\mu\nu} $$ is not only a small positive number, but that if it differed by more than one part in \(10^{123}\) then our universe would never have been possible. But it too is probably just a constant of Nature.

I'm quickly becoming addicted to neuroscientist Robert Lawrence Kuhn's long-running series of PBS and YouTube videos entitled Closer to Truth, whose 30-minute episodes delve into the basic question of why we (or anything) exists. Most of the episodes feature a blend of physics, religion, biology and the science of the human mind, but those dealing with what is known as fine tuning are particularly fascinating. Fine tuning refers to the fact that the observed magnitudes of various physical constants (electric charge, the strength of gravity, the fine structure constant, etc.) are so tightly constrained that if they were even slightly different, life (and possibly even the universe itself) could not exist.

Kuhn's most recent venture into the topic is perhaps his best to date, as he interviews the physicists Martin Rees, Leonard Susskind, Russell Stannard, Alex Valenkin and Roger Penrose regarding their views on the subject. Kuhn comes away with four basic answers to fine tuning: sheer accident; fundamental but as-yet unknown physics; God; and the multiverse. Susskind also addresses the cosmological constant, and while he is an atheist he admits that the observed tiny value of \(\Lambda\) is balanced on a knive edge of unexplainable, mind-boggling precision.

At the end of the video Kuhn notes that most physicists today believe that we live in a multiverse (or a "megaverse," as Susskind calls it) of possible universes. If that number is infinite (or finite but preposterously large), then at least a few would be nearly identical to our own, and we just happen to be in one of them.

The video is about 26 minutes, and well worth watching:


A Physicist Speaks Out on the Social Over-Dominance of the Internet — Posted Thursday February 4 2021
New York Times writer Charlie Warzel interviewed retired physicist Michael Goldhaber, a noted scientist who predicted many of the social problems we're currently dealing with, including the rise of inane reality television, website attention-seeking, political shamelessness, rampant celebrity-worship and the influence of terrorists on social media. Goldhaber is just one in a family of distinguished physicists who worked with many notable quantum physicists from the 1940s on.

Goldhaber's interest in politics and social issues goes back to his childhood. With the rise of the Internet in the 1990s he predicted what might collectively be called the "attention economy," which spans not only the Internet and information technology but trends in the entertainment industry as well. I encourage you to read the article, along with an earlier interview with Goldhaber posted by the American Institute of Physics in 1995.

I cannot help but see myself in some of the issues raised by Goldhaber in the interview, and it seems that my interest in posting articles on my own website may be nothing more than an attempt to grab attention and vent my feelings and opinions. But I also see my what I'm doing as a kind of online diary that my children, grandchildren and future progeny can look at long after I'm gone. Hopefully, I will be a positive influence on them in a scary future world that will need all the optimism it can muster.

How Times Have Changed — Posted Tuesday February 2 2021
I received my first Moderna vaccination today, and with the exception of a slightly sore left arm I feel fine.

While growing up in Duarte, California in the 1950s, I would eagerly await the ice cream truck coming down Bloomdale Street. When I heard the truck's jingle (which I still remember) I would beg my mother for a dime, which at the time would buy what was called a "Sidewalk Sundae" ice cream bar. Fortunately, outside of the ice cream truck and the occasional visit of Little Oscar's Wienermobile, I never saw this guy:

Those of you my age will remember getting polio booster shots in grade school. We'd have to bring a permission slip from our parents (with a dollar bill attached), then line up for the dreaded shot at the nurse's office. Bruce, John, Greg and I would try to look brave to impress the girls, but inside we were scared to death of those needles.

PS: One day the Wienermobile stopped in front of our house, and my mother and I went inside. I was only about four years old, but I towered over Little Oscar (a middle-aged "little person") whose face and wrinkles made him look strangely old to me. I was glad to get out of there, although I came away with a "Weenie Whistle."

Will They Ever Change? — Posted Monday February 1 2021
Shortly after the stoning of the first Christian martyr Stephen (which the future apostle Paul personally witnessed and approved of), Paul set out with his assistants to the city of Damascus, where he intended to arrest evangelical Christians and bring them back to Jerusalem to be tried for apostasy. Along the way, he encountered Jesus Christ, and was both blinded and enlightened. Paul's Road to Damascus experience is one that many Christians experience (I sure did), and in Paul's case it represented a complete reversal of his religious philosophy. He was totally and forever changed, yet he would always refer to himself as the "chief sinner" for his persecution of the early Christian church, which he always regretted.

Today we have millions of supposedly devout Christians who view former president Donald Trump as the new Messiah. They believe that he lost the 2020 election due to criminal conspiracy and fraud, that Democrats drink the blood of slaughtered babies to obtain a precious substance called adenochrome, and that the government of the United States must be violently overthrown in order to restore a proven sociopath and sexual deviant (Trump) to power.

Will they ever experience their own Road to Damascus moment? I highly doubt it.


For Geeks Only: Chameleon Gravity — Posted Monday February 1 2021
Have you ever heard of something called chameleon gravity? I just caught wind of it, but scientific and popular articles have been around on the topic for some time now. It's supposed to explain how galaxies form, as well as providing a window into dark matter and dark energy.

It turns out to be yet another \( f(R) \) gravity theory, but in this case \( f(R) \) is a kind of substitute for the cosmological constant \( \Lambda \). It also involves a scalar field \( \phi(x) \), which means it has to have a mass and a kinetic term in the Lagrangian. It's guaranteed to provide additional terms in the equations of motion, which is pretty much what \( f(R) \) theories are designed to do.

In July 2019, an article in Nature came out that caught the attention of the popular press, and for a while there was a flurry of Internet articles reporting what might be a major new discovery in cosmology. It all reminded me of how the press made a big fuss over a supposed great discovery that Einstein made in 1928. As Abraham Pais described it in his book Subtle is the Lord: The Science and Life of Albert Einstein, it was much ado about nothing.

Still, chameleon gravity is an attempt to dispense with the notion of dark matter by way of modifying Einstein's 1915 gravity theory, an attempt that I welcome since I believe dark matter does not exist.

By the way, if the Ricci scalar \( R \) is a pure constant in cosmological theory (and it almost certainly is), then it is easily shown that our universe will inexorably expand forever. And if the cosmological constant \( \Lambda \) is a true constant, then the rate of the expansion will increase without bound with time.

Q-Nuts, Featuring Good Ol' Charlie Brown — Posted Friday January 29 2021
I never realized Linus was insane.


We Cahn't See! — Posted Friday January 29 2021
I was supposed to get my first Moderna COVID-19 vaccination this morning, but it was canceled due to heavy rain, so I'm stuck indoors with little to do but surf the Internet.

Jim Backus' character from 1963's It's a Mad, Mad, Mad, Mad World can't see because his eyes are closed, but there are things we can't see even with giant optical and radio telescopes. The most important of these is dark matter, which I have my doubts even exists.

Beginning in the 1930s, astronomers noticed that there didn't seem to be enough observable matter (stars, gas and dust) in galaxies and galaxy clusters to account for their properties, notably the extreme velocities of rotating stars far from galactic centers. This gave rise to the notion of "dark matter" that would have to exist in gigantic halos surrounding galaxies and in between galactic clusters. Much more recently, detailed studies of gravitational lensing showed that there had to be more matter in galaxies than could be accounted for, thus supporting the idea that some kind of invisible matter existed in the universe besides ordinary matter.

In defiance of the dark matter concept, in the 1970s it was proposed that ordinary Newtonian physics could be modified slightly to account for the effects of these observational discrepancies. A theory called modified Newtonian dynamics (MOND) arose that gave some promise along these lines, but it was deficient in numerous areas (and being a modified classical theory, MOND was also not relativistically correct). To fix this, further theories came along that modified Einstein's general theory of relativity in order to patch up the discrepancies. But these theories were complicated and required too many arbitrary parameters to fit the observational data, although they're still a topic of current research.

Although his 1915 theory has admirably passed all tests to date, Einstein himself believed that it was only an approximation of the truth, although a very good one. Might some simple but reasonable modification of the 1915 theory be closer to the truth? This too is a topic of current reasearch, but everything I've seen to date seems too hopelessly complicated to be considered valid.

Although dark matter might actually exist and be the answer to all our observational problems, I'm still clinging to the hope that Einstein's theory might yet be modified to provide a successful theory. One approach, and one that I think deserves more attention, was originally proposed in 1989 by Mannheim and Kazanas, who laboriously worked out the calculations associated with the fully conformal gravity theory deriving from the Lagrangian $$ S = \int \!\! \sqrt{-g}\, \left( R_{\mu\nu} R^{\mu\nu} - \frac{1}{3}\, R^2 \right) d^4x $$ This Lagrangian automatically results in three parameters that not only reduce to Einstein's 1915 theory but also explain much of the data now being attributed to dark matter and dark energy.

Meanwhile, here's an interesting video posted by the University of Oxford's Rebecca Smethurst, who questions the existence of dark matter while discussing a recent study that appears to explain the effects of neighboring galaxies on galaxies exhibiting dark matter-like properties.


A Year and a Half — Posted Sunday January 24 2021
My dear wife Munira died exactly 18 months ago. I'm still taking an antidepressant and undergoing grief therapy, but things are gradually getting better. We were married 42 years, and it still doesn't seem real to me, as I vacillate between shock, grief and feeling sort of okay. Our church has been a tremendous support to me, as has been my family. Never stop appreciating those you love, as you won't have them forever.

Geek Saturday — What is a Spinor? — Posted Saturday January 23 2021
All of the ordinary matter in the universe, the "stuff" that everything is made out of, is comprised of particles called fermions. They include elementary particles like electrons, quarks and neutrinos, along with composite particles like protons and neutrons. They're all characterized by half-integral quantum spin numbers (\(\pm\)1/2, \(\pm\)3/2 \(\ldots\)), while all the other things—the force carriers like photons, gluons and the Z\(^0\) and W\(^\pm \) particles—are called bosons, having integer spins (0, 1, 2 \(\ldots\)). Bosons get along with one another, and can be found clumped together in various quantum states, while fermions are antisocial loners that tend to avoid other fermions. Being fermions, multiple electrons can be found in atoms, but every electron must have its own unique set of quantum numbers. The helium atom, for example, can have two electrons in the same orbital, but one will have a spin of 1/2 while the other's spin will be -1/2. This is a consequence of the famous Pauli exclusion principle, which everyone learns in high school.

One might guess that fermions and bosons have to be treated differently in quantum mechanics, and this is true. Unfortunately, the algebra that describes fermions (which make up all the familiar stuff) differs substantially from that of bosons, and that algebra is a tough act to follow. While the quantum-mechanical equations of bosons are fairly understandable, those of fermions are complicated and non-intuitive. They are described by something called the spinor algebra, which in practice is often referred to as a kind of "square root" of an ordinary vector in Euclidian geometry.

In his latest post, Columbia University mathematical physicist Peter Woit also asks about spinors, but being quite conversant in the subject he seems to have no problem dealing with them. Compare this attitude with just about anyone else, including the late Sir Michael Atiyah, who often expressed frustration with spinors. If you're a mathematician, spinors will take you into all kinds of arcane areas, like group theory and topology (often in higher dimensions), but physicists prefer sticking to more mundane applications, where spinors are still difficult to comprehend because much of the math cannot be avoided.

I remember one professor at USC touching on the subject of spinors, but he didn't elaborate, probably because he preferred to stay away from the subject. While learning the Dirac relativistic electron equation (which incorporates the Dirac spinor), I got hopelessly confused. It wasn't until many years later that I tried to improve my situation by writing an elementary paper on them, but even today I do not really understand the damned things. I still get a little ticked off when I think that God made the most common, ordinary stuff in the universe so difficult to comprehend.

Thank God, the Trump Nightmare is Finally Over — Posted Wednesday January 20 2021
In the dark days of the George W. Bush presidency and in the far darker days of the Donald Trump presidency, I would often think to myself that the biggest mistake that both Lincoln and General William Tecumseh Sherman made in 1864-65 was to first allow the South to be spared total annihilation, and then to welcome Southerners back into the Union, "With Malice Toward None." What we got was a century of Jim Crow, lynched and murdered African Americans and "Lost Cause" stupidity, all under the guise of "Southern gentility" mixed with the enduring battle cry of "The South Shall Rise Again." And rise again it did.

As the sentiment expressed in this article in today's USA Today makes clear, let us hope that President Biden will not repeat Lincoln's and Sherman's mistake.

Sure, let us act like true Christians and try to be understanding and kumbaya and all that, but let us always remember that the Red States still hate progressives with a passion, and they now have vengeance and destruction in mind. If they will not turn away from their collective racism, bigotry and anti-science, anti-fact retardation, the best we can do is to cut them off from the Union entirely and let them cope on their own, perhaps as a collection of seceded states. I don't really want any more of my tax dollars going there now anyway, since they have been and continue to be a net sink on federal assistance.

Is It Too Late? — Posted Tuesday January 12 2021
When was the last time you had a heated discussion with another over some ideological issue, only to come to the conclusion that she was right and you were wrong? And not only did you recognize that you were wrong, you wholeheartedly changed your mind and adopted your opponent's position?

The 2020 presidential election ended with Joe Biden winning 80 million votes against Donald Trump's 74 million votes. That 6-million vote difference was decisive, but the total vote split was uncomfortably close—52% to 48%—meaning that roughly half the country's voters went for Trump. Not only that, but nearly 80% of Trump's supporters today devoutly believe a rampant conspiracy theory that Biden stole the election through fraud, despite some 60 high-level court cases and numerous bipartisan investigations that confirmed the legitimacy of Biden's victory.

Add this to the number of crazy conspiracy theories that have sprung up following Trump's 2016 presidential win, including Hillary Clinton operating a child sex ring out of a Washington D.C. pizza parlor, that global climate disruption is a hoax designed to give China an economic edge over the U.S., that Barack Obama was born in Kenya and was thus ineligible to be President, and that the deaths attributed to COVID-19 are actually due to other causes like colds and influenza.

I don't care if people want to believe in extraterrestrials or that magnets can cure cancer, but the insane beliefs of nearly 50% of Americans are too much for me to accept. Today's conservatives seem to believe that personal opinions, emotions and feelings are more legitimate than facts and objective evidence, and the tragedy of January 6 proves that these beliefs have taken a very dangerous turn.

My son's best friend at university is now a respected medical doctor and specialist in nephrology. He's one of the most intelligent people I've ever met, but despite his education and training he's completely bought into the lies and conspiracy theories that Trump and his followers have promoted. This scares the hell out of me—if people as smart and educated as he is can be so completely and irreversibly hoodwinked by utter nonsense, then what hope can we have that this country can ever be truly sane?

Alluding to my first paragraph, can Trump supporters ever change their minds, or are they permanently stuck in anti-fact, anti-science fantasy?

Ross Douthat (pictured), a writer for the New York Times whose conservative views I have often disagreed with, wonders if the Republican Party can break away from the Trumpian insanity now threatening the country, or itself be broken permanently through its adherence to lies, paranoia and fantasy. It's well worth reading, and I hope it's not too late for the country to recover.

Fury — Posted Saturday January 9 2021
Videos clips of the shameful, violent and murderous attack by Trump right-wingers on the Capitol Building this week reminded me of the classic 1936 film Fury, starring Spencer Tracy and Silvia Sidney and directed by the noted German film maker Fritz Lang. The movie features a mob attack on a jail, filmed by news camera crews whose films are later used in court to identify and convict the attackers. I urge readers to find and watch the film (most libraries have the DVD) as a lesson for how the mob mentality of 85 years ago is strikingly similar to what we saw earlier this week.

Here's a brief YouTube clip of the final court scene, which I hope is repeated when those responsible for the Capitol attack are brought to justice:


Trump IS the Snake — Posted Saturday January 9 2021
In 2016 President Trump read a poem to adoring followers at a Florida rally. Called "The Snake," the poem talks about a tender-hearted woman who kindly nurses an injured snake back to health, only to have the snake bite her. "You knew I was a snake when you picked me up!" says the serpent. (The story has been told many times in different forms, usually a frog who gives a lift to a scorpion across a river.) Trump's retelling was intended as a warning that being kindly to immigrants was a mistake, as they would surely turn on us (becoming thieves, rapists, killers, etc.) The crowd ate it up.

I liken Trump's crowd as akin to the Israelites in Exodus 32 who, weary of waiting for Moses to come down from the mountain, fashioned the golden calf and partied. When Moses returned, things quickly went downhill for the Israelites. Now it's America's turn.

The incredible irony of Trump's story is too obvious today, but it was evident long before he ran for president. A serial womanizer and sexual molester, the thrice married Grab-'em-by-the-Pussy Chief Executive had shown his true colors from the time he was a young man.

On numerous occasions I sadly posted several links on Trump's current wife Melania, who posed for a series of sickening girl-on-girl nude photos twenty years ago here and here (Warning: graphic). "This is your new First Lady!" I raged at the time, although it seemed no one was paying attention. But no, Trump was a rich man, and his wives were all beautiful and hot, and that's all that mattered to the majority of American voters.

Now Trump has finally been exposed for the monster he is, but his sycophantic base is sticking with him, now turned violent and murderous. Worst of all, they're all self-professed conservative Christians. Meanwhile, the GOP is still the Party of Trump.

And it appears that things will only get worse for America.

I'm Moving! (Someday) — Posted Thursday January 7 2021
From Hamlet, Act V, Scene I:
Gravedigger: What is he that builds stronger than either the mason, the shipwright, or the carpenter?

Assistant: The gallows-maker, for that frame outlives a thousand tenants.

Gravedigger: I like thy wit well, in good faith. The gallows does well, but how does it well? It does well to those who do ill. Now thou dost ill to say the gallows is built stronger than the church ...

Assistant: [So] Who builds stronger than either the mason, the shipwright, or the carpenter?

Gravedigger: Cudgel thy brains no more about it, for thy dull ass will not mend his pace with beating. And when you are asked this question next, say "a grave-maker." The houses that he makes last till doomsday.


King Tut — Posted Sunday January 3 2021
I've long been captivated by ancient Egypt, and I'm planning to visit the new billion-dollar Grand Egyptian Museum this year. I went to the Valley of the Kings with my late Egyptian wife and our sons several years ago, and now I'm longing to see the shriveled Mr. Tutankhamun* in person again, along with the other tombs in the Valley (my wife didn't think it was a big deal, having already seen everything as a child and as a University of Cairo chemical engineering student). Here's a fascinating recent video of the 1922 discovery of Tut's tomb:

* He's got a condo made of stone-a

What is Consciousness? — Posted Sunday January 3 2021

The unexamined life is not worth living. — Socrates

When I was little I had numerous pets, including cats, dogs, snakes and lizards. I remember wondering what it would be like to have a dog's brain, to see how I would think and view the world around me. This is certainly the first time I pondered the notion of consciousness, although I had no idea what the concept meant.

Years later I would wonder why humans were so much different than other animals, even those considered to be intelligent in some sense. I learned that chimpanzees could make simple tools (like moistening a stick to catch termites), that killer whales used clever tactics and teamwork to catch their prey efficiently, and that porpoises could be trained to do complex tricks (which I witnessed during visits to now long-defunct Marineland in Southern California*). More interestly were studies I read about in which animals were placed before mirrors to see what reactions they might exhibit. Many animals ignored the mirrors, some felt threatened, believing they had encountered a rival or enemy, while a few exhibited interesting behaviors, as if they somehow knew the reflections were themselves but couldn't fully comprehend what was going on.

In college I was required to take a course in psychology. I had little interest in the subject but I was exposed to the concept of self-awareness, and I recall wondering why some animals like apes and porpoises might express some degree of intelligence but did little more than eat, sleep, reproduce and avoid danger. More importantly, unlike humans they did not progress over many millions of years, apparently lacking the ability to develop true thought or self-awareness. Consequently, chimpanzees, porpoises and elephants will never discover calculus or writing (or develop nuclear weapons).

But in spite of all our fantastic mental abilities, we still do not understand the biological basis behind consciousness, in spite of many decades of technological progress in the neural, physiological and cognitive fields of study. Where does self-awareness reside in the human brain, and how does it manifest itself? Indeed, what is the purpose of consciousness, if millions of years of evolution would have been sufficient to ensure our survival as a species?

It's entirely possible that self-awareness is a distinctive trait of humans alone, a subject that is addressed in this recent Aeon article, whose writer implies that it is indeed uniquely human. But better insight can be obtained from the work of the noted neuroscientist Robert Lawrence Kuhn, the brilliant creator and host of the great television and YouTube series Closer to Truth. Kuhn has pondered these questions many times, always seeking out top experts in the field to help him find the answers (Kuhn is equally passionate about other notable puzzles, especially in the fields of religion, physics and biology, and I encourage you to seek him out). His latest venture into the issue of consciousness appears in the following video:

But as is often the case with many of the questions he tries to answer, Kuhn largely comes away empty handed. Of the many mysteries of our universe and existence, consciousness may be the most unanswerable of all.

By far, my greatest regret in life (other than having been a non-Christian and total self-centered jerk until my later years) is that I wasn't really self-aware for most of my life. Descartes famously said "I think, therefore I am," but thinking alone isn't enough. The most important aspects of self-awareness are empathy, humility and the true concern for the well-being of others. This is what Christ taught, and I wish to God I had been aware of it earlier.

* I went to Marineland often as a kid, and later took my wife and children there many times. It was an occasional feature of the popular 1950s television series Sea Hunt, which I still love.

Rambling Thoughts on Quantum Immortality — Posted Saturday January 2 2021
Happy New Year, and good riddance to 2020.

Newton and many of his later contemporaries believed that if one knew the precise position and velocity of every particle in the universe, then one could rewind or fast-forward that information to know the past and future of everything perfectly. In particular, the initial conditions of the universe would mean that everything would evolve deterministically, with the result that all events in the future would be set for all time. There would therefore be no free will for humans, whose (admittedly very complex) collections of atoms and molecules would only be following a fixed set of events. Did you ever rob a bank or cheat on your wife? Don't feel too bad, you couldn't help yourself—like Calvinism, it was predetestined from the start. Or so some believe.

But it's impossible to know such information to infinite precision (you'd have to know everything out to an infinite number of decimals), and chaos theory would seem to guarantee that anything can happen randomly if such precison is not available.

So what does this have to do with anything? It means that free will really does exist (at least to some extent), that you weren't predestined to murder your mother-in-law (so it's to prison you're a-going), and more importantly the probability of any past or future event remains largely random and undecided. Indeed, probablity has everything to do with it.

Whatever happens, its probability is either zero, one, or something in between. It's illogical to think that the likelihood of an event is 150% or less than zero. This principal is behind what is known as unitarity in quantum mechanics, which was outlined in a recent PBS Spacetime episode on the nature of quantum information (which you can watch below). Host Dr. Matt O'Dowd explains that unitarity involves both the preservation of probability (never less than zero or greater than one) and the time-reversal symmetry of physics, in which the replacement \( t \rightarrow -t \) keeps fundamental physics intact.

Not so, you might think. While a film of the elastic collision of billiard balls can be run backward without anyone knowing which way the film is running, the dropping of an uncooked egg on the floor and its breaking cannot be filmed without revealing the proper sequence of the event—it's a fundamental property of entropy, right? But the collision of real billiard balls invariably involves the transfer of energy (which can be revealed by a flash of infrared light when the balls are struck or the slowing of some of the balls due to friction), and this would give away the sequence. When energy is conserved there's no change in entropy, and time-reversal symmetry is preserved.

As the PBS Spacetime episode explains, the fundamental Schrödinger equation of quantum physics preserves time-reversal symmetry, but the collapse of the wave function (according to the generally accepted Copenhagen interpretation of quantum mechanics) does not. Many physicists believe that this fact alone invalidates the Copenhagen interpretation, which has notably given rise to ideas like the many-worlds interpretation, in which wave function collapse does not occur (albeit at the expense of the branching off of other universes due to the mere act of observation). If true, this would seem to mean that the simple act of creating or transferring information by sentient minds or otherwise conscious observers somehow gives rise to multiple universes.

The connection of information with unitarity culminates with the notion of the eternal preservation of information, which when created cannot be destroyed. Exactly how information is preserved is a mystery—some believe that the universe stores everything on its boundary surface via the holographic principle. This principle (actually a conjecture) would seem to answer the so-called black hole information paradox, in which information falling into a black hole is either lost or somehow preserved when the black hole evaporates.

All this is getting pretty metaphysical if not downright religious in tone, so I'm stopping here. Meanwhile, enjoy the video: