Category Archives: Uncategorized

The pleasures of reading Feynman on Physics – V

Feynman finally gets around to discussing tensors 376 pages into volume II in “The Feynman Lectures on Physics” and a magnificent help it is (to me at least).  Tensors must be understood to have a prayer of following the math of General Relativity (a 10 year goal, since meeting classmate Jim Hartle who wrote a book “Gravity” on the subject).

There are so many ways to describe what a tensor is (particularly by mathematicians and physicists) that it isn’t obvious that they are talking about the same thing.   I’ve written many posts about tensors, as the best way to learn something it to try to explain it to someone else (a set of links to the posts will be found at the end).

So why is Feynman so helpful to me?  After plowing through 370 pages of Callahan’s excellent book we get to something called the ‘energy-momentum tensor’, aka the stress-energy tensor.  This floored me as it appeared to have little to do with gravity, talking about flows of energy and momentum. However it is only 5 pages away from the relativistic field equations so it must be understood.

Back in the day, I started reading books about tensors such as the tensor of inertia, the stress tensor etc.  These were usually presented as if you knew why they were developed, and just given in a mathematical form which left my intuition about them empty.

Tensors were developed years before Einstein came up with special relativity (1905) or general relativity (1915).

This is where Feynman is so good.  He starts with the problem of electrical polarizability (which is familiar if you’ve plowed this far through volume II) and shows exactly why a tensor is needed to describe it, e.g. he derives  the tensor from known facts about electromagnetism.  Then on to the tensor of inertia (another derivation).  This allows you to see where all that notation comes from. That’s all very nice, but you are dealing with just matrices.  Then on to tensors over 4 vector spaces (a rank 4 tensor) not the same thing as a 4 tensor which is over a 4 dimensional vector space.

Then finally we get to the 4 tensor (a tensor over a 4 dimensional vector space) of electromagnetic momentum.  Here are the 16 components of Callahan’s energy momentum tensor, clearly explained.  The circle is finally closed.

He briefly goes into the way tensors transform under a change of coordinates, which for many authors is the most important thing about them.   So his discussion doesn’t contain the usual blizzard of superscripts and subscript.  Covariant and contravariant are blessedly absent. Here the best explanation of how they transform is in Jeevanjee “An introduction to Tensors and Group Theory for Physicists”  chapter 3 pp. 51 – 74.

Here are a few of the posts I’ve written about tensors trying to explain them to myself (and hopefully you)

Death rates from coronavirus drop in half 2 months after Georgia loosens lockdown restrictions

There were apocalyptic predictions of doom when Georgia loosened its lockdown restrictions against the pandemic coronavirus SARS-CoV-2 on 25 April.  Here they are

From The Atlantic — “Georgia’s Experiment in Human Sacrifice — The state is about to find out how many people need to lose their lives to shore up the economy.” —

A month later (25 May) not much had happened —

7 day moving average of new cases of COVID19 ending 25 April — 740

7 day moving average of new cases of COVID19 ending 13 May — 525 (the state allows 14 days for all the data to roll in, so the last date they regard as having secure numbers is the 7th of May and here the number is 539)

7 day moving averages of deaths from COVID19 ending 25 April — 35

7 day moving average of deaths from COVID19 ending 13 May — 24 (the state allows 14 days for all the data to roll in, so the last date they regard as having secure numbers is the 7th of May and here the number is 27).

Back on 25 May I wrote “People who assumed (on purely correlative evidence) that lockdowns prevented new cases, and that lifting them would cause a marked increase in new cases and deaths, are clearly wrong.  It’s possible that cases will spike in the future proving them right, but pretty unlikely.  It’s only fair to give the doomsayers a sporting chance and followup is planned in a month.”

So here’s the followup.   The 7 day moving average of daily deaths had dropped to 17 as of 11 June.  Remember Georgia waits 14 days as data filters in to regard the numbers as definitive.  Here’s the link —

So the death rate from COVID-19 dropped in half 2 months after Georgia loosened some of the lockdown restrictions.

There are only two useful statistics in all of this.  The moving average of the daily death rate and the number of COVID19 cases in the hospital.  I no longer follow the number of new cases, because they include people with a positive antibody test (all of whom have recovered).  We know that most cases are asymptomatic.  It’s very hard to get the second number of people sick in the hospital with COVID19 (I’ve tried with no luck).  COVID19 used to mean that you were sick — no longer, it now counts positive antibody tests, rendering the number relatively useless.  By choosing who to test, numbers can be easily inflated —

Daily death rates are great for cherry picking scare headlines — it’s worth looking at this article from Tampa —

It contains a great figure with the number of deaths each day from March onward on which is superimposed the moving average — the range is from 10 to 100.  Even more impressive is the fall on weekends and the rise during the week.

Fortunately, every Friday  Florida releases the weekly results for antibody testing, so we’ll be able to see how many of these new cases of COVID19 are people who have recovered from it.

Here’s another link — well worth looking at — with the number of new cases in Florida in one graph (with the marked increase in the past week) and the number of death from the disease just below.  The deaths in the past week are the lowest they’ve been in a month —


These are grim times.  I was going to write yet another post on the virus, but it can wait.  We all need a joke, so here goes.

This guy has been going to a psychiatrist for years. She’d been very supportive.

On a recent session he said, I had a strange dream last night.

Psychiatrist’s ears perk up.

Tell me about it.

Well, I dreamed that you were my mother.

Psychiatrist sits bolt upright in her chair.

That’s fascinating what did you do?

Well I was so upset I couldn’t get back to sleep, so I got up, had a cup of coffee and went in to the office

That’s a breakfast?

Covid19 could be coming for you

A friend and his wife are getting 3 days of meals delivered to their room in their retirement home.  Clearly a great way to socially isolate themselves.  This will help ‘flatten the curve’.  What that means is that the peak won’t be as high, so we won’t run out of beds and respirators.

But look at the curve in this article —

Now integrate the area under the curve.  Looks like the number of cases is comparable (more actually under the flattened curve).

Add this to the extreme likelihood that covid19 will become endemic in the population (given the number of cases out there).  This means that absent a vaccine or a treatment, you will meet it sooner or later with whatever biologic resources you have.

On the positive side, the amount of research into the way virus kills is only matched by the number of therapeutic trials underway (both enormous).  The way the journals have opened up so results are widely available gratis and freely shared is impressive.

Do glia think?

Do glia think Dr. Gonatas?  This was part of an exchange between G. Milton Shy, head of neurology at Penn, and Nick Gonatas a brilliant neuropathologist who worked with Shy as the two of them described new disease after new disease in the 60s ( myotubular (centronuclear) myopathy, nemaline myopathy, mitochondrial myopathy and oculopharyngeal muscular dystrophy).

Gonatas was claiming that a small glial tumor caused a marked behavioral disturbance, and Shy was demurring.  Just after I graduated, the Texas Tower shooting brought the question back up in force —

A recent paper [ Neuron vol. 105 pp. 954 – 956, 1036 – 1047 ’20] gives good evidence that glia are more than the janitors and the maintenance crew of the brain.

Glia cover most synapses (so neurotransmitter there doesn’t leak out, I thought) giving rise to the term tripartite synapse (presynaptic terminal + postsynaptic membrane + glial covering).

Here’s what they studied.  The cerebral cortex projects some of its axons (which use glutamic acid as a neurotransmitter) to a much studied nucleus in animals (the nucleus accumbens).  This is synapse #1. The same nucleus gets a projection of axons from the brainstem ventral tegmental area (VTA) which uses dopamine as a neurotransmitter.  However, the astrocytes (a type of glia) covering synapse #1 have the D1 dopamine receptor (there are 5 different dopamine receptors) on them.  It isn’t clear if the dopamine neurons actually synapse (synapse #2) on the astrocytes, or whether the dopamine  just leaks out of the synaptic cleft to the covering glia.

Optogenetic stimulation of the VTA dopamine neurons results in an elevation of calcium in the astrocytes (a sign of stimulation). Chemogenetic activation of these astrocytes depresses the presynaptic  terminals of the neurons projecting the nucleus accumbens  from the cerebral cortex .  How does this work?  Stimulated astrocytes release ATP or its produce adenosine.  This binds to the A1 purinergic receptor on the presynaptic terminal of the cortical projection.

So what?

The following sure sounds like the astrocyte here is critical to brain function.  Activation of the astrocyte D1 receptor contributes to the locomotor hyperactivity seen after an injection of amphetamine.

Dopamine is intimately involved in reward, psychosis, learning and other processes (antipsychotics and drugs for hyperactivity manipulate it).  That the humble astrocyte is involved in dopamine action takes it out of the maintenance crew and puts it in to management.

A final note about Dr. Shy.  He was a brilliant and compelling teacher, and instead of the usual 1% of a medical school class going into neurology, some 5% of ours did.  In 1967 he ascended to the chair of the pinnacle of American Neurology at the time, Columbia University.  Sadly, he died the month he assumed the chair.  Scuttlebut has it that he misdiagnosed his own heart attack as ‘indigestion’ and was found dead in his chair.

Riemann curvature tensor

Hideous isn’t it ? — this will be fleshed out tomorrow night, with a comprehensible explanation of what the Riemann curvature tensor is all about.  Just wanted to see if I could get these formulas to print out in my blog

Book idea proposal

While up in Nova Scotia (where the people are as friendly as midwesterners) on vacation reading Feynman I got an idea for a book.  Unfortunately, I don’t think anyone has the breadth of knowledge of physics that Feynman did, so no single person can write it.

Remember that the Feynman lectures were delivered in 1963 – 4.  The authors of the Millennium edition noted that > 1,000 errors were corrected in the various editions (which is a good reason to buy it, if you’re studying it on your own).  But almost none of them were conceptual.

So the lectures are  true as of 1964 and brilliant to boot.  As Kip Thorne notes in “Modern Classical Physics”  — “The three-volume Feynman Lectures on Physics had a big influence on several generations of physicists and even more so on their teachers.Both of us (Blandford and Thorne) are immensely indebted to Richard Feynman for shaping our own approaches to physics”.

The idea for the book came as early as p. 2-7 in Volume I, where Feynman says “no phenomenon directly involving a frequency has yet been detected above approximately 10^12 cycles per second”.  Well we’re up to 10^18 presently and shooting higher.

p 3-5 “all enzymes are proteins.”  Not so and a Nobel was won for the first RNA enzyme to be discovered.

p. 7 – 7  What is holding galaxies together — a mention of dark matter would be interesting.

p. 9 – 9 “A very good computing machine may take 1 microsecond to do an addition”  — we’re up to 10^18 exaFlops (of floating point calculations) not addition.

Well you get the idea.  I have no idea what the size of the market would be, but I’d love to see something like this.

Something similar was actually done with the Origin of Species.  Darwin’s Ghost by Steve Jones (published in 1999) updates Darwin’s book, the Origin of Species (published 1999)  to contemporary thinking (and knowledge) chapter by chapter.   It is fascinating to go through both together.

The book would be one of the few things better done by a committee

Off to Nova Scotia

No posts for a week or two.  If you’re ever up that way, the Hopewell Rocks in New Brunswick are not to be missed.  Our friends say Cape Breton is magnificent.  We hope to see it.   Taking Feynman vol. I along.  I can’t say enough good about it, but I doubt that it’s the way to learn physics the first time, but if you’ve had undergraduate physics, it will explain what is really going on.

Feynman and Darwin

What do Richard Feynman and Charles Darwin have in common?  Both have written books which show a brilliant mind at work.  I’ve started reading the New Millennium Edition of Feynman’s Lectures on Physics (which is the edition you should get as all 1165 errata found over the years have been corrected), and like Darwin his thought processes and their power are laid out for all to see.  Feynman’s books are far from F = ma.  They are basically polished versions of lectures, so it reads as if Feynman is directly talking to you.  Example: “We have already discussed the difference between knowing the rules of the game of chess and being able to play.”  Another: talking about Zeno  “The Greeks were somewhat confused by such problems, being helped, of course, by some very confusing Greeks.”

He’s always thinking about the larger implications of what we know.  Example: “Newton’s law has the peculiar property that if it is right on a certain small scale, then it will be right on a larger scale”

He then takes this idea and runs with it.  “Newton’s laws are the ‘tail end’ of the atomic laws extrapolated to a very large size”  The fact that they are extrapolatable and the fact that way down below are the atoms producing them means, that extrapolatable laws are the only type of physical law which could be discovered by us (until we could get down to the atomic level).  Marvelous.  Then he notes that the fundamental atomic laws (e.g. quantum mechanics) are NOTHING like what we see in the large scale environment in which we live.

If you like this sort of thing, you’ll love the books.  I don’t think they would be a good way to learn physics for the first time however.  No problems, etc. etc.  But once you’ve had exposure to some physics “it is good to sit at the feet of the master” — Bill Gates.

Most of the readership is probably fully engaged with work, family career and doesn’t have time to actually read “The Origin of Species”. In retirement, I did,and the power of Darwin’s mind is simply staggering. He did so much with what little information he had. There was no clear idea of how heredity worked and at several points he’s a Lamarckian — inheritance of acquired characteristics. If you do have the time I suggest that you read the 1859 book chapter by chapter along with a very interesting book — Darwin’s Ghost by Steve Jones (published in 1999) which update’s Darwin’s book to contemporary thinking chapter by chapter.  Despite the advances in knowledge in 140 years, Darwin’s thinking beats Jones hands down chapter by chapter.

‘Happy Fourth of July to the world’s worst economist — Paul Krugman

Stocks closed at record highs Wednesday as traders bet on a potential rate cut from the Federal Reserve later this month after the release of weaker-than-expected economic data.The Dow gained 179 points, notching intraday and closing all-time highs. The Nasdaq advanced 0.75%.The S&P 500 also rose 0.75% as the real estate and consumer sectors powered the broad index to record levels. Tech boosted the index, rising 0.7% to a record high. The S&P 500 closed just 0.1% below 3,000.







Here is Paul Krugman Nobel Laureate in Economics writing in the New York Times 9 November 2016, the day after Trump was elected

“It really does now look like President Donald J. Trump, and markets are plunging. When might we expect them to recover?

Frankly, I find it hard to care much, even though this is my specialty. The disaster for America and the world has so many aspects that the economic ramifications are way down my list of things to fear.

Still, I guess people want an answer: If the question is when markets will recover, a first-pass answer is never.

Under any circumstances, putting an irresponsible, ignorant man who takes his advice from all the wrong people in charge of the nation with the world’s most important economy would be very bad news. What makes it especially bad right now, however, is the fundamentally fragile state much of the world is still in, eight years after the great financial crisis.

It’s true that we’ve been adding jobs at a pretty good pace and are quite close to full employment. But we’ve been doing O.K. only thanks to extremely low interest rates. There’s nothing wrong with that per se. But what if something bad happens and the economy needs a boost? The Fed and its counterparts abroad basically have very little room for further rate cuts, and therefore very little ability to respond to adverse events.

Now comes the mother of all adverse effects — and what it brings with it is a regime that will be ignorant of economic policy (Luysii — praise be to God) and hostile to any effort to make it work. Effective fiscal support for the Fed? Not a chance. In fact, you can bet that the Fed will lose its independence, and be bullied by cranks.

So we are very probably looking at a global recession, with no end in sight. I suppose we could get lucky somehow. But on economics, as on everything else, a terrible thing has just happened.”

If that wasn’t enough here’s Krugman in 2010 writing about ‘peak oil

“Oil is back above $90 a barrel. Copper and cotton have hit record highs. Wheat and corn prices are way up. Over all, world commodity prices have risen by a quarter in the past six months.

So what’s the meaning of this surge?

Is it speculation run amok? Is it the result of excessive money creation, a harbinger of runaway inflation just around the corner? No and no.

What the commodity markets are telling us is that we’re living in a finite world, in which the rapid growth of emerging economies is placing pressure on limited supplies of raw materials, pushing up their prices. And America is, for the most part, just a bystander in this story.

Some background: The last time the prices of oil and other commodities were this high, two and a half years ago, many commentators dismissed the price spike as an aberration driven by speculators. And they claimed vindication when commodity prices plunged in the second half of 2008.

But that price collapse coincided with a severe global recession, which led to a sharp fall in demand for raw materials. The big test would come when the world economy recovered. Would raw materials once again become expensive?

Well, it still feels like a recession in America. But thanks to growth in developing nations, world industrial production recently passed its previous peak — and, sure enough, commodity prices are surging again.

This doesn’t necessarily mean that speculation played no role in 2007-2008. Nor should we reject the notion that speculation is playing some role in current prices; for example, who is that mystery investor who has bought up much of the world’s copper supply? But the fact that world economic recovery has also brought a recovery in commodity prices strongly suggests that recent price fluctuations mainly reflect fundamental factors.

What about commodity prices as a harbinger of inflation? Many commentators on the right have been predicting for years that the Federal Reserve, by printing lots of money — it’s not actually doing that, but that’s the accusation — is setting us up for severe inflation. Stagflation is coming, declared Representative Paul Ryan in February 2009; Glenn Beck has been warning about imminent hyperinflation since 2008.

Yet inflation has remained low. What’s an inflation worrier to do?

One response has been a proliferation of conspiracy theories, of claims that the government is suppressing the truth about rising prices. But lately many on the right have seized on rising commodity prices as proof that they were right all along, as a sign of high overall inflation just around the corner.

You do have to wonder what these people were thinking two years ago, when raw material prices were plunging. If the commodity-price rise of the past six months heralds runaway inflation, why didn’t the 50 percent decline in the second half of 2008 herald runaway deflation?

Inconsistency aside, however, the big problem with those blaming the Fed for rising commodity prices is that they’re suffering from delusions of U.S. economic grandeur. For commodity prices are set globally, and what America does just isn’t that important a factor.

In particular, today, as in 2007-2008, the primary driving force behind rising commodity prices isn’t demand from the United States. It’s demand from China and other emerging economies. As more and more people in formerly poor nations are entering the global middle class, they’re beginning to drive cars and eat meat, placing growing pressure on world oil and food supplies.

And those supplies aren’t keeping pace. Conventional oil production has been flat for four years; in that sense, at least, peak oil has arrived. True, alternative sources, like oil from Canada’s tar sands, have continued to grow. But these alternative sources come at relatively high cost, both monetary and environmental.

Also, over the past year, extreme weather — especially severe heat and drought in some important agricultural regions — played an important role in driving up food prices. And, yes, there’s every reason to believe that climate change is making such weather episodes more common.

So what are the implications of the recent rise in commodity prices? It is, as I said, a sign that we’re living in a finite world, one in which resource constraints are becoming increasingly binding. This won’t bring an end to economic growth, let alone a descent into Mad Max-style collapse. It will require that we gradually change the way we live, adapting our economy and our lifestyles to the reality of more expensive resources.

But that’s for the future. Right now, rising commodity prices are basically the result of global recovery. They have no bearing, one way or another, on U.S. monetary policy. For this is a global story; at a fundamental level, it’s not about us.  ”

Nonetheless Krugman can currently be found on the editorial pages of the New York Times authoritatively pronouncing on matters political

For the world’s second worse economist please see