Axiomatize This !

“Analyze This”, is a very funny 1999 sendup of the Mafia and psychiatry with Robert DeNiro and Billy Crystal.  For some reason the diagram on p. 7 of Barrett O’Neill’s book “Elementary Differential Geometry” revised 2nd edition 2006 made me think of it.

O’Neill’s  book was highly recommended by the wonderful “Visual Differential Geometry and Forms” by Tristan Needham — as “the single most clear-eyed, elegant and (ironically) modern treatment of the subject available — present company excpted !”

So O’Neill starts by defining a point  as an ordered triple of real numbers.  Then he defines R^3 as a set of such points along with the ability to add them and multiply them by another real number.

O’Neill then defines tangent vector (written v_p) as two points (p and v) in R^3 where p is the point of application (aka the tail of the tangent vector) and v as its vector part (the tip of the tangent vector).

All terribly abstract but at least clear and unambiguous until he says — “We shall always picture v_p as the arrow from point p t0 the point p + v”.

The picture is a huge leap and impossible to axiomatize (e.g. “Axiomatize This”).   Actually the (mental) picture came first and gave rise to all these definitions and axioms.

The picture is figure 1.1 on p. 7 — it’s a stick figure of a box shaped like an orange crate sitting in a drawing of R^3 with 3 orthogonal axes (none of which is or can be axiomatized).  p sits at one vertex of the box, and p + v at another.  An arrow is drawn from p to p + v (with a barb at p + v) which is then labeled v_p.  Notice also, that point v appears nowhere in the diagram.

What the definitions and axioms are trying to capture is our intuition of what a (tangent) vector really is.

So on p. 7 what are we actually doing?  We’re looking at a plane in visual R^3 with a bunch of ‘straight’ lines on it.  Photons from that plane go to our (nearly) spherical eye which clearly is no longer a plane.  My late good friend Peter Dodwell, psychology professor at Queen’s University in Ontario, told me that the retinal image actually preserves angles of the image (e.g. it’s conformal). 1,000,000 nerve fibers from each eye go back to our brain (don’t try to axiomatize them).   The information each fiber carries is far more processed than that of a single pixel (retinal photoreceptor) but that’s another story, and perhaps one that could be axiomatized with a lot of work.

100 years ago Wilder Penfield noted that blood flowing through a part of the brain which was active looked red rather than blue (because it contained more oxygen).  That’s the way the brain appears to work.  Any part of the brain doing something gets more blood flow than it needs, so it can’t possibly suck out all the oxygen the blood carries.  Decades of work and zillions researchers have studied the mechanisms by which this happens.  We know a lot more, but still not enough.

Today we don’t have to open the skull as Penfield did, but just do a special type of Magnetic Resonance Imaging (MRI) called functional MRI (fMRI) to watch changes in vessel oxygenation (or lack of it) as conscious people perform various tasks.

When we look at that simple stick figure on p. 7, roughly half of our brain lights up on fMRI, to give us the perception that that stick figure really is something in 3 dimensional space (even though it isn’t).  Axiomatizing that would require us to know what consciousness is (which we don’t) and trace it down to the activity of billions of neurons and trillions of synapses between them.

So what O’Neill is trying to do, is tie down the magnificent Gulliver which is our perception of space with Lilliputian strands of logic.

You’ve got to admire mathematicians for trying.

Why me, O Lord, Why me?

It was very hard for my multiple sclerosis (MS) patients to understand why they were singled out for MS, given the publicity given to theories of viral causation, popular at least since I started getting seriously interested in neurology as a 3rd year medical student in 1964.  Herpes simplex (fever blisters) was a popular culprit, but we all know lots of people who’ve had them without coming down with MS.

The best explanation I could give them was of my med school classmate Marty, a Jewish kid from Pittsburgh.  Graduating in 1966 at the height of American involvement in Vietnam, all my classmates entered the service within a few years.  Marty was sent to Vietnam  as a GMO (General Medical Officer).  He was quickly sent back stateside as he developed a severe anemia.  Why?

Well malaria was endemic in Vietnam, and anyone going over received an antiMalarial as prophylaxis.  The malarial parasite does its damage by infecting red blood cells.  The antiMalarial drug he received inhibited a red cell enzyme Glucose 6 Phosphate Dehydrogenase (G6PD), essentially starving the parasites.  Marty had a partial deficiency of this enzyme.  Such deficiencies are relatively common in areas endemic for Malaria, as it is protective, just as the sickle cell trait is protective against Malaria in Africa.  A variety of other mutations in different red cell proteins arising in endemic areas are also protective (example Thalassemia in Greece, etc. etc.)

So if Marty had never been sent to Vietnam he would never have become anemic.  I’d tell my patients that they had some biochemical difference (totally unknown back then) that made them susceptible to complications of infection with a common organism.  Not very satisfying, but it was the best I could do.

In the case of another virus Epstein Barr Virus (EBV) which causes infectious mononucleosis, this explanation (50+ years later) turned out to be exactly correct.    Not only that it shows the extreme subtlety of what ‘causation’ in medicine actually means.

Not only must the unlucky people getting MS after EBV infection be different biochemically, they must be infected with a particular variant of EBV (not all EBV is the same, just as not all people or SARS-CoV-2 are the same).

That’s the view from 30,000 feet.  You can stop here but the full explanation is unsparingly technical.  It is to be found in Cell vol. 186 pp. 5675 – 5676, 5708 – 5718 ’23 ]

Here goes.

Long term control of Epstein Barr Virus is mediated by cytotoxic T lymphocytes which recognize parts of EBV proteins.  One such protein is EBNA1, and antibodies to amino acids #386 – #405 of EBNA1 cross react with amino acids #370 – #389 of a human protein called GlialCAM (for Glial Cell Adhesion Molecule) which is important in maintaining the myelin sheath around axons in the brain (MS is basically a destructive immune attack on myelin).

Such an antibody is called autoreactive, in the sense that it is reacting to a normal human protein.  Cells producing autoreactive antibodies (autoreactive cells) are normally eliminated by cytotoxic natural killer cells.  In the case of EBV specific T cells they are eliminated by natural killer cells expressing proteins NKG2C and NKG2D.  They target the autoreactive GlialCAM specific autoreactive B cells.  Some people have deletion of the gene coding for NKG2C rendering them more susceptible to MS after EBV infection.

But wait, there’s more. There are many EBV variants and some of them upregulate another human protein HLA-E by containing another protein (LMP1) which stabilizes HLA-E.  HLA-E blunts the natural killer cell attack on autoreactive GlialCAM cells.

So it’s a delicate dance of unfortunate events ‘causing’ MS.  A mild genetic defect in the human, and a genetic variant in the virus, both of which must occur for causation.

Who knew that medical causation could be so subtle.

The higher drivel revisited

Only 3 potentates of the academy could have said opprobrium of genocide depends on context. The exchange between the 3 and Congresswoman Stefanik has been viewed over a billion times and it’s only been a few days.  For most viewers it was like turning over a rock and seeing what crawls out.

So it’s time to republish an old post on the higher drivel and its happy home in the higher reaches of academe.  Not much has changed since 2011

The higher drivel – II

From the obituary of a leading philosopher at an Ivy League institution. He proposed the following thought experiment to resolve the question of whether objects and relationship exist in the world independently of how we perceive them. This is what bothered Einstein about quantum mechanics, and he is said to have asked Bohr (I think) ” do you think the moon is not there if we don’t look at it”. The thought experiment is a brain placed in a vat by a mad scientist (I’m not making this up). So the brain in the vat — call him Oscar –could not formulate the sentence of “I am a brain in vat” because Oscar has no experience of a real brain or a real vat.

For this they’re currently paying 60K+ a year? It’s the higher drivel. (note this was written in 2011)

I read a book by another philosopher (Nozick) with similar impossible situations he worried about after a rave review in the New York Times book review a few years ago. It had questions of the order ‘would bubblegum taste the same on the surface of the sun’.

“The predicament of any tropological analysis of narrative always lies in its own effaced and circuitous recourse to a metaphoric mode of apprehending its object; the rigidity and insistence of its taxonomies and the facility with which it relegates each vagabond utterance to a strict regimen of possible enunciative formations testifies to a constitutive faith that its own interpretive meta-language will approximate or comply with the linguistic form it examines.”

From p. 35 of the NYTimes book review 16 October’11

You could actually major in this stuff (Semiotics) at an Ivy League university (Brown) in the 80’s. According to the article, Semiotics was the third most popular humanities major there at the time.  One son got in in ’86, but (fortunately) didn’t go there.  Nonetheless he was quite interested in Semiotics, hence the name of this blog.  Fortunately the author of the above quote recovered and notes “I now spend more time learning from the insights of science than deconstructing its truth claims.”

What a gigantic waste of time.  Think what Brown could have done by abolishing the department and using the funds for chemistry or mathematics.  The writer tries to salvage something from the experience noting that ‘a striking number of semiotics students have gone on to influential careers in the media and the creative arts.’  Unfortunately this explains a lot about the current media and ‘the creative arts’.

Students were being conned then, and they’re being conned now.  It might not have mattered what you majored in 50+ years ago at an Ivy League university, the world seemed to want us regardless.   A friend majored in Near Eastern studies, was hired by a bank, never saw the MidEast and did quite well.  Not so today.  The waitress serving us last Wednesday at a local bar was a graduate of one of the seven sisters in 2010.  She majored in Sociology and Psychology, is in debt for > 20K for the experience and is unable to find better work.   It isn’t clear what such a major prepares you for other than what she’s doing.  Finding out the distribution of majors of the jobless 20 somethings participating in occupy Wall Street would be interesting

For a taste of the semiotics world of the 80’s, Google Alan Sokal and read about the fun he had with such a journal — “Social Text”.  Should you  still have the stomach for such things read “The Higher Superstition” by Gross and Levitt, which goes into more detail about Derrida, Foucault and a host of (mostly French) philosophes and what they tried to pull off.

Tags: Alan Sokal, brain in a vat, Higher drivel, Semiotics, The Higher Superstition.

Book Review — On the Origin of Time

I got to “On the Origin of Time” rather late as the review in Nature (vol. 616 pp. 243 – 244) last April by a philosopher rather than a physicist turned me off to the book.  I bought it on a trip to Iceland published by a branch of the Penguin press I’d never heard of (Torva) and had plenty of time to read it.

The book has been reviewed to a fare thee well — Amazon has 407 reviews and counting.  So what follows are a few asides which might be of interest, because of my relationship to three of the protagonists.

First Stephen Hawking.  I followed his career closely because I ran a muscular dystrophy clinic in 1972 – 1987 and I made sure that all my patients with amyotrophic lateral sclerosis (ALS) knew about his prolonged survival.  Unfortunately none did nearly as well, showing that the median survival is far more useful clinically than the average, as outliers such as Hawking with decades of survival distort the average, particularly in studies which have under 100 participants which was typical of studies back then.

Second John Wheeler.  He taught me Freshman physics at Princeton in 1957 – 1958.  He was a very unassuming individual, and the book has a picture of him exactly as I remember him on p. 191.  I thought he looked like a shoe salesman until he brought in Neils Bohr to talk to us.

Third Jim Hartle.  Probably the smartest guy in my Princeton class.  Although intelligence and educational attainment appear to offer some protection against Alzheimer’s, it didn’t help Jim.  For much more about Jim Hartle please see — https://luysii.wordpress.com/2023/05/31/james-hartle-r-i-p/

I knew that Hartle had worked with Hawking, and closely enough to speak at his funeral, but I had no idea of just what he did until this book.  Hartle is all over it.  He and Hawking originated the idea of the wave function of the universe, something I used to disparage, because I couldn’t see what it could be written down on.   The book will explain that.  In fact the book explains a lot of physics and cosmology very well and is worth reading for that alone.

Hawking’s theories of the big bang and the origin of physical law underwent significant modification over the years, and the book details its twists and turns.  Unlike quantum mechanics they really don’t make any testable predictions.

The book describes one of Wheeler’s insights extremely well, namely his delayed choice thought experimental variant of the double slit.  As aficionados know, if you don’t know which of the two slits the beam of photons goes through, you get an interference pattern.  If you do know which slit, the interference pattern disappears and you get a single blob on the screen directly behind the slit.

Well saying knowing ‘which slit’ elides a lot.  What that means actually is experimentally setting things up so the experiment tells you which slit the photon goes through. Well that’s one experiment.  Another is just doing the classic double slit experiment where you don’t know.

Wheeler’s idea was to be able to select between the two experiment types after the photon had left its source and gone through the double slit, but before it reached the screen behind the double slit.  So the photon had to know what to do (act as a wave producing an interference pattern, or a particle producing a blob) when it was emitted from the source.

The experiment that made Einstein world famous was the bending of light by a large mass (such as the sun) predicted by special relativity in 1919.  Well time has marched on, and we can measure the same thing by gravitational lensing of the light emitted by a quasar by a galaxy in our line of sight to the quasar.  What should have been a dot becomes the arc of a circle.  Each point in that circle is a different path taken by the photon from the quasar to us lightYears away on earth.  The galaxy acted as the screen with the double slit (actually multiple slits).  Depending on our choice of experiment on earth long after it passed by the galaxy we determined what the photon did.

So photons emitted in the far distant past somehow knew what they had to do — act as a particle or a wave. Somehow the measurement on earth now determined the past.  Enter consciousness which no one understands.

Yet another way to come to grips with the essential wierdness of quantum mechanics.

This is only a small part of the book which is well worth reading.

Book review: The Theoretical Minimum (volume 1)

Volume I of the Theoretical Minimum by Leonard Susskind is a book I wish I had 61 years ago, although I doubt that I’ve would have had the time for it that I do now.  My educational and social background would have uniquely suited me for it.

Start even earlier in the fall of 1957, Freshman Physics for premeds and engineers at Princeton taught by none other than John Wheeler, typical of the way Princeton didn’t reserve its star faculty for graduate students (unlike Harvard).  As an 18 year old from a small high school  terrified of calculus and worried that I wasn’t smart enough, I turned down an offer to move up to the advanced physics and math classes having done fairly well on the first physics test.  We studied Newton’s laws, some thermodynamics, electricity and magnetism (but I don’t recall the Maxwell equations). What I do remember is Wheeler bringing in Neils Bohr to talk to the class (actually he appeared to mumble in Danish).

Fast forward to the spring 1961 and grad school in Chemistry at Harvard and the quantum mechanics course, given not to teach us much physics , but to give us a solid introduction to the quantum numbers describing atomic orbitals by solving the Schrodinger equation.

What follows is a long detour through how we did it.  Feel free to skip to the **** for the main thread of this post.

Recursion relations are no stranger to the differential equations course, where you learn to (tediously) find them for a polynomial series solution for the differential equation at hand. I never really understood them, but I could use them (like far too much math that I took back then).

So it wasn’t a shock when the QM instructor back then got to them in the course of solving the hydrogen atom (with it’s radially symmetric potential). First the equation had to be expressed in spherical coordinates (r, theta and phi) which made the Laplacian look rather fierce. Then the equation was split into 3, each involving one of r, theta or phi. The easiest to solve was the one involving phi which involved only a complex exponential. But periodic nature of the solution made the magnetic quantum number fall out. Pretty good, but nothing earthshaking.

Recursion relations made their appearance with the series solution of the radial and the theta equations. So it was plug and chug time with series solutions and recursion relations so things wouldn’t blow up (or as Dr. Gouterman put it, the electron has to be somewhere, so the wavefunction must be zero at infinity). MEGO (My Eyes Glazed Over) until all of a sudden there were the main quantum number (n) and the azimuthal quantum number (l) coming directly out of the recursions.

When I first realized what was going on, it really hit me. I can still see the room and the people in it (just as people can remember exactly where they were and what they were doing when they heard about 9/11 or (for the oldsters among you) when Kennedy was shot — I was cutting a physiology class in med school). The realization that what I had considered mathematical diddle, in some way was giving us the quantum numbers and the periodic table, and the shape of orbitals, was a glimpse of incredible and unseen power. For me it was like seeing the face of God and the closest thing to a religious experience I’ve ever had.

*****

So in the quantum mechanics course it was Lagrangians and Hamiltonians. Stuff I’d never been exposed to.  My upbringing had trained me long before college to mouth incantations in a language I didn’t understand and convince people (but not myself) that I did, and I felt this way about a lot of math, so H = T +V and L = T – V was no problem at all.  I decided to audit a mechanics course being given to understand what H and L were all about but the (intentionally nameless) prof was an obnoxious  example of a Harvard professor showing how smart he was and how dumb you were.  So I quit and remained ignorant of what H and L were really all about until Susskind’s book.

I read it on a 16 day trip to Iceland, about 1 chapter a day, thinking about the contents as we drove the 800 mile ring road, then going back and reading the chapters again and again.  Obviously, this was not something I had the time for as a grad student.

The book is marvelous, and clear.  Although informal and full of jokes, it was “not written for airheads” as the authors say.  At the end you will understand why the Lagrangian and Hamiltonian were invented (to make solution of Newton’s equation of motions easier).  You will see the action explained (but not it’s origin which will be saved for another volume on quantum mechanics) and the Euler-Lagrange equation derived.  Poisson brackets appear, and are explained, and look very much like the commutator of quantum mechanics.  Failure of commutation is widespread throughout math and physics, and failure of two infinitesimal paths to commute when applied sequentially is what curvature is all about.

Now with a better understanding of the Action and the Lagrangian under my belt, I’ll have to reread a lot of stuff, particularly Tony Zee’s book on Quantum Field Theory as simply as possible.

The following might be skipped unless you’re interested in how I became expert in mouthing incantations in a language I didn’t understand, and later used it in college and grad school.

The Chinese room argument was first published in a 1980 article by American philosopher John Searle. He imagines himself alone in a room following a computer program for responding to Chinese characters slipped under the door. Searle understands nothing of Chinese, and yet, by following the program for manipulating symbols and numerals just as a computer does, he sends appropriate strings of Chinese characters back out under the door, and this leads those outside to mistakenly suppose there is a Chinese speaker in the room.

So it was with me and math as an undergraduate due to a history dating back to age 10.  I hit college being very good at manipulating symbols whose meaning I was never given to understand.  I grew up 45 miles from the nearest synagogue.  My fanatically religious grandfather thought it was better not to attend services at all than to drive up there on the Sabbath.  My father was a young lawyer building a practice, and couldn’t close his office on Friday.   So my he taught me how  to read Hebrew letters and reproduce how they sound, so I could read from the Torah at my Bar Mitzvah (which I did comprehending nothing).  Since I’m musical, learning the cantillations under the letters wasn’t a problem.

Thanks to Susskind I no longer feel that way about Hamiltonians, Lagrangians and Action.

Bookmarking mechanisms during mitosis

When you think of what happens to our DNA during mitosis, it’s remarkable that the two daughter cells produced look anything like their mother.  Our 3.2 billion positions in DNA when stretched out (as they are in cells not in mitosis { in interphase for those who like terminology } ) are about 1 meter long.  You can’t see them with a light microscope as they’re only 2 nanoMeters wide, and the shortest wavelength of visible light is 400 nanoMeters.  To scrunch our chromosomes  down so they are visible and more importantly, so they don’t get tangled up with each other as they migrate to the daughter cells,  they are compacted 100,000 fold.  Unsurprisingly, DNA transcription into mRNA and protein synthesis pretty much stops during mitosis [ Cell vol. 150 pp. 725 – 737 ’12 ], as the transcription machinery can’t get into compacted DNA, and even if it did couldn’t unwind the DNA of a gene enough to transcribe it.

Well, we’ve got 20,000 protein genes, and what distinguishes the wildly different cell types in our body is the collection of proteins they make, and the way they organize the membranes of the cell.  Each cell type has a different collection of proteins.  After mitosis how do they make the correct collection.  What keeps a blood cell from turning into a neuron (or vice versa).  The answer is bookmarking, some sort of way to distinguish an interphase gene making mRNA (e.g. an active gene) from an inactive one, so that only the previously active genes start up again.

We’re just beginning to find out what those bookmarks are.  One mechanism has long been known, keep the DNA of an active gene from being compacted [ Science vol. 307 pp. 421 – 423 ’05 ] and is particularly true for heat shock proteins.

TATA binding protein (TBP) is an essential component of transcription factor complexes which remains bound to promoters of active genes during mitosis [ Nature Cell Biology vol. 10 pp. 1318 –> ’08 ] forming yet another bookmark.

The latest bookmark found is the chromatin remodeler SWI/SNF which moves nucleosomes around so the transcription machinery can get to DNA.  Some of its core subunits remain bound to gene promoters during mitosis [ Nature vol. 618 pp. 180 – 187 ’23 ]

I’m sure more bookmarks will be found

I think we’ve become far too blase about mitosis and our DNA and how it sits in out cells. So I’m going to republish a series of posts, that puts the goings on in the nucleus on a humanly comprehensible scale — a (US) football field and enclosing stadium.

So relax and enjoy (and hopefully be amazed).  Here’s the first post — more will be coming or you can follow the link at the bottom

The cell nucleus and its DNA on a human scale – I

The nucleus is a very crowded place, filled with DNA, proteins packing up DNA, proteins patching up DNA, proteins opening up DNA to transcribe it etc. Statements like this produce no physical intuition of the sizes of the various players (to me at least).  How do you go from the 1 Angstrom hydrogen atom, the 3.4 Angstrom thickness per nucleotide (base) of DNA, the roughly 20 Angstrom diameter of the DNA double helix, to any intuition of what it’s like inside a spherical nucleus with a diameter of 10 microns?

How many bases are in the human genome?  It depends on who you read — but 3 billion (3 * 10^9) is a lowball estimate — Wikipedia has 3.08, some sources have 3.4 billion.  3 billion is a nice round number.  How physically long is the genome?  Put the DNA into the form seen in most textbooks — e.g. the double helix.  Well, an Angstrom is one ten billionth (10^-10) of a meter, and multiplying it out we get

3 * 10^9 (bases/genome) * 3.4 * 10^-10 (meters/base) = 1 (meter).

The diameter of a typical nucleus is 10 microns (10 one millionths of a meter == 10 * 10^-6 = 10^-5 meter.   So we’ve got fit the textbook picture of our genome into something 1/100,000 smaller. We’ll definitely have to bend it like Beckham.

As a chemist I think in Angstroms, as a biologist in microns and millimeters, but as an American I think in feet and inches.  To make this stuff comprehensible, think of driving from New York City to Seattle.  It’s 2840 miles or 14,995,200 feet (according to one source on the internet). Now we’re getting somewhere.  I know what a foot is, and I’ve driven most of those miles at one time or other.  Call it 15 million feet, and pack this length down by a factor of 100,000.  It’s 150 feet, half the size of a (US) football field.

Next, consider how thick DNA is relative to its length.  20 Angstroms is 20 * 10^-10 meters or 2 nanoMeters (2 * 10^-9 meters), so our DNA is 500 million times longer than it is thick.  What is 1/500,000,000 of 15,000,000 feet?  Well, it’s 3% of a foot which is .36  of an inch, very close to 3/8 of an inch.   At least in my refrigerator that’s a pair of cooked linguini twisted around each other (the double helix in edible form).  The twisting is pretty tight, a complete turn of the two strands every 35.36 angstroms, or about 1 complete turn every 1.5 thicknesses, more reminiscent of fusilli than linguini, but fusilli is too thick.  Well, no analogy is perfect.  If it were, it would be a description.   One more thing before moving on.

How thinly should the linguini be sliced to split it apart into the constituent bases?  There are roughly 6 bases/thickness, and since the thickness is 3/8 of an inch, about 1/16 of an inch.  So relative to driving from NYC to Seattle, just throw a base out the window every 1/16th of an inch, and you’ll be up to 3 billion before you know it.

You’ve been so good following to this point that you get tickets for 50 yardline seats in the superdome.  You’re sitting far enough back so that you’re 75 feet above the field, placing you right at the equator of our 150 foot sphere. The north and south poles of the sphere are over the 50 yard line. halfway between the two sides.  You are about to the watch the grounds crew pump 15,000,000 feet of linguini into the sphere. Will it burst?  We know it won’t (or we wouldn’t exist).  But how much of the sphere will the linguini take up?

The volume of any sphere is 4/3 * pi * radius^3.  So the volume of our sphere of 10 microns diameter is 4/3 * 3.14 * 5 * 5 * 5 *  = 523 cubic microns. There are 10^18 cubic microns in a meter.  So our spherical nucleus has a volume of 523 * 10^-18 cubic meters.  What is the volume of the DNA cylinder? Its radius is 10 Angstroms or 1 nanoMeter.  So its volume is 1 meter (length of the stretched out DNA) * pi * 10^-9 * 10^-9 meters 3.14 * 10^-18 cubic meters (or 3.14 cubic microns == 3.14 * 10^-6 * 10^-6 * 10^-6

Even though it’s 15,000,000 feet long, the volume of the linguini is only 3.14/523 of the sphere.  Plenty of room for the grounds crew who begin reeling it in at 60 miles an hour.  Since they have 2840 miles of the stuff to reel in, we’ll have to come back in a few days to watch the show.  While we’re waiting, we might think of how anything can be accurately located in 2840 miles of linguini in a 150 foot sphere.

What makes us human (genetically at least) take 1

We are now able to watch natural selection mold and shape our recent ancestors.  The genomes of 1,500 ancient humans have now been sequenced.  They range in age from 1,000 years ago to 45,000 years ago (based on the geology of where they were found and optically stimulated luminescence).  Multiple genomes from the same site in space and time have been sequenced, so we have multiple sequences of the same protein gene allowing us to look for coding variants (alleles).  You can read all about it in Proc. Natl. Acad. Sci. vol. 120 e2213061120 pp. 1 –> 12 ’23.  Be warned, a lot of terms are undefined assuming that you are experts in genetics, so I’ll try to provide some background.

They estimate that the genomes are from 18 different populations spread across space (many in the Arabian Peninsula) and time. Most of them are from 5,000 to 10,000 years old.

The paper talks about ‘anatomically modern humans’ (AMHs e.g. us), excluding Denisovans and Neanderthals.

We know that primates have been migrating out of Africa for millions of years. However sometime between 30,000 and 1o0,000 years ago AMHs migrated out of Africa, interbreeding with close relatives (Neanderthals, Denisovans) who then died out.  Their DNA has been sequenced and now constitutes a small part of our own (1 – 5%) a process called introgression.

The 1,500 genomes were compared to the Yorubas of Nigeria.  So for each of their proteins we know how many variants (alleles) are present and at what frequency.

Suppose one allele of protein X (present at 5% in the Yorubas) was unhelpful in a cold climate.  If it disappeared in one of the 18 populations, we can say this was due to natural selection against it (negative selection).  The authors call this a selective sweep.

Another possibility for a selective sweep  would be a mutation in protein X not seen in the Yorubas appearing in nearly every member of one of the 18 populations.  This would be evidence for positive selection.

A technique to scan ancient genomes called SweepFinder2 (SF2) detected some 57 selective sweeps in the ancient population (none were found in the Yorubas)  Many of the genes in the sweeps were involved in fat metabolism (something likely important in cold adaptation).   Other selected genes were involved in skin pigmentation (another adaptation to strong sunlight or the lack of it).   The paper gives specific examples of these genes, but that would be too technical.   The cognoscenti should jump right in.  There’s tons more in the paper.

Our first evidence for evolution were fossils separated in time by millions of years.  The record remains sparse and fragmentary, and led to the idea the evolution and natural selection were very slow, slower in fact than glaciation.

The idea that we could actually witness natural selection was proved by the Grants, studying Darwin’s Finches in the Galapagos.  I seriously recommend “The Beak of the Finch” by Jonathan Weiner, if you’ve not heard of the Grants and their excellent work.

But here we are actually observing natural selection in action.  Clarence Darrow would have hated it.

How far we’ve come from the McCulloch Pitts neuron

The McCulloch Pitts neuron was described in 1943.  It consists of a bunch of inputs (dendrites) some excitatory, some inhibitory, which are just summed (integrated) the results determining the output (whether the  axon of the neuron fired or didn’t).  Hooking them together could instantiate a variety of boolean functions and ultimately a Turing machine.

The McCulloch Pitts neuron really isn’t that far from the ‘neurons’ in neural nets which underlie the spectacular achievements of artificial intelligence (ChatGTP etc. etc.)   The neuron of the neural net is nothing more than a set of inputs, a set of weights, and an activation function. The neuron translates these inputs into a single output, which can then be picked up as input for another layer of neurons later on.

The major difference between the computation a linked bunch of neurons in the two models (McCulloch Pitts and neural net) is that given the same set of inputs in McCulloch Pitts you always get the same output, while in neural nets you don’t.  The difference is that the set of weights on the inputs to each neuron in the net which can be and are adjusted which depends on how close the output of the net is to the target (which in the case of ChatGTP is how accurately it predicts the next word in a sample of text).

There is a huge debate going on as to whether ChatGTP and similar neural nets understand what they are doing and whether they are/will become conscious.

So does ChatGTP explain how our brains do what they do?  Not at all.  Our neurons are doing far more than integrating input and firing.  This was brought home in a paper focused on something entirely different, the gamma oscillations of brain electrical activity (Neuron vol. 111 pp. 936 – 953 ’23).  People have been studying brain rhythms since Hans Berger discovered alpha rhythm just shy of a century ago.  The electroencephalogram (EEG) measures the various rhythms as they occur over the brain.  Back in the day when I was starting out in neurology (1967), it was one of the few diagnostic tools we had.  It wasn’t very good, and a cynical attending described it as useless but not worthless (because you could charge for it).

The gray matter of the surface of our brains (cerebral cortex) is gray because it is packed with the cell bodies of neurons — some 100,000 under each square millimeter of cortex.  Somehow they are wired together so that they can produce coherent rhythmic electrical activity as they fire.

The best place to study how a bunch neurons produce rhythms is the hippocampus, an area crucial in forming memories and one of the earliest places the senile plaques of Alzheimer’s disease show up.

Unlike the jumble of neurons in the cortex, the large neurons of the hippocampus are all lined up and oriented the same way like trees in a forest.  All the cell bodies lie in roughly the same layer, with the major dendrite (apical dendrite) going up like the trunk of a tree, and the ones near the cell body spreading out like the roots of a tree.

Technology has marched on, and it is now possible to fashion electrodes, which can measure neuronal electrical activity along the trunk, and watch it in real time.

Figure 2b p. 941 shows that different parts of the trunk of the hippocampal  neurons show rhythmic activity at different frequencies at any given time.  Not only that, but as time passes each area of the trunk (apical dendrite) changes the frequency of its rhythmic activity.  This is light years away from the integrate and fire model of McCulloch Pitts, or the adjustment of weights on the inputs to the neurons of the neuronal net.

It shows that each of these neurons is a complex processor of information (a computer if you will).  Even though artificial intelligence has made great strides, it really isn’t telling us how the brain does what it does.

Finally if you want to see what genius looks like, check out the life of Walter Pitts — https://en.wikipedia.org/wiki/Walter_Pitts  — corresponding with Bertrand Russell about Principia Mathematica at age 12, studying with Carnap at the University of Chicago at 15, all while he was homeless.

 

When does a description of something become an explanation ?

“It’s just evolution”. I found this explanation of the molecular biology underlying our brain’s threefold expansion relative to the chimp extremely unsatisfying.  The molecular biology of part of the expansion is fascinating and beautifully worked out. For details see a copy of the previous post below the ***.

To say that these effects are ‘just evolution’ is using the name we’ve put on the process to explain the process itself, e.g.  being satisfied with the description of something as an explanation  of it.

Newton certainly wanted more than that for his description of gravity (the inverse square law, action at a distance etc. etc.) brilliant and transformative though it was.  Here he is in a letter to Richard Bentley

“That gravity should be innate inherent & {essential} to matter so that one body may act upon another at a distance through a vacuum without the mediation of any thing else by & through which their action or force {may} be conveyed from one to another is to me so great an absurdity that I believe no man who has in philosophical matters any competent faculty of thinking can ever fall into it. ”

But the form of the force law for gravity combined with Newton’s three laws of motion (1687) became something much more powerful, a set of predictions of phenomena as yet unseen.

The Lagrange points are one example.  They are points of equilibrium for small-mass objects under the influence of two massive bodies orbiting their common center of gravity.  The first Lagrange points were found by Euler in 1750, Lagrange coming in 10 years later.  One of the Lagrange points of the Earth Sun  system is where the James Webb telescope sits today remaining stable without expending much energy to keep it there.  In a rather satisfying sense the gravitational force law explains their existence (along with Newton’s laws of motion and a lot of math).  So here is where a description (the force law) is actually an explanation of something else.

But Newton wanted more, much more than his description of the gravitational force (the inverse square law).  It took Einstein centuries later to come up with General Relativity — the theory of the gravitational force.  Just as a ball rolls down an incline here under the force of gravity, planets roll down the shape of Einstein’s spacetime, which is put there by the massive bodies it contains.  By shaping space everywhere, masses give the illusion of force, no action at a distance is needed at all.

It is exactly in that sense that I find the explanation for the 8 million year scuplting of our brain as evolution unsatisfying.  It is essential a description trying to pass itself off as an explanation.  Perhaps there is no deeper explanation of what we’re finding out.  Supernatural explanations have been with us in every culture.

Hopefully if such an explanation exists, we won’t have to wait over two centuries for it as did Newton.

*****

The evolutionary construction and magnification of the human brain

Our brains are 3 times the size of the chimp and more complex.  Now that we have the complete genome sequences of both (and other monkeys) it is possible to look for the protein coding genes which separate us.

First some terminology.  Not every species found since the divergence of man and chimp is our direct ancestor.  Many banches are extinct.  The whole group of species are called hominins [Nature vol. 422 pp. 849 – 857 ‘ 03 ].  Hominids are species in the path between us and the chimp — sort of a direct line of descent.  However the terminology is in flux and confusing and I’m not sure this is right.   But we do need some terminology to proceed.

Hominid Specific genes (HS genes) result which result from recent gene duplications in hominid/human genomes.  Gene duplication is a great way for evolution to work quickly.  Even if one gene is essential, messing with the other copy won’t be fatal.  HS genes include >20 gene families that are dynamically expressed during the formation of the human brain.  It was hard for me to find out just how many HS genes there are.

Here are some examples. The human-specific NOTCH2NL genes increase the self-renewal potential of human cortical progenitors (meaning more brain cell can result from them).  TBC1D3and ARGHAP11B, are involved in basal progenitor amplification (ditto).

A recent paper [ Neuron vol. 111 pp. 65 – 80 ’23 ] discusses CROCCP2 (you don’t want to know what the acronym stands for) which is one of several genes in this family with at least 6 copies in various hominid genomes.  However, CROCCP2 is a duplicate unique to man.   It is highly expressed during brain development and enhances outer Radial Glial Cell progenitor proliferation.

The mechanism by which this happens is detailed in the paper and involves the cilium found on every neuron, mTOR, IFT20 and others.

But that’s not the point here, fascinating although these mechanisms are.   We’re watching a series of at least 20 gene duplications with subsequent modifications build the brain that is unique to us over relatively rapid evolutionary times.  The split between man and chimp is thought to have happened only 8 million years ago.

What should we call this process?  Evolution?  The Creator in action? The Blind Watchmaker?   It is certainly is eerie to think about.  There are 17 more HS genes to go involving in building our brains remaining to be worked out.  Stay tuned

 

The evolutionary construction and magnification of the human brain

Our brains are 3 times the size of the chimp and more complex.  Now that we have the complete genome sequences of both (and other monkeys) it is possible to look for the protein coding genes which separate us.

First some terminology.  Not every species found since the divergence of man and chimp is our direct ancestor.  Many banches are extinct.  The whole group of species are called hominins [Nature vol. 422 pp. 849 – 857 ‘ 03 ].  Hominids are species in the path between us and the chimp — sort of a direct line of descent.  However the terminology is in flux and confusing and I’m not sure this is right.   But we do need some terminology to proceed.

Hominid Specific genes (HS genes) result which result from recent gene duplications in hominid/human genomes.  Gene duplication is a great way for evolution to work quickly.  Even if one gene is essential, messing with the other copy won’t be fatal.  HS genes include >20 gene families that are dynamically expressed during the formation of the human brain.  It was hard for me to find out just how many HS genes there are.

Here are some examples. The human-specific NOTCH2NL genes increase the self-renewal potential of human cortical progenitors (meaning more brain cell can result from them).  TBC1D3and ARGHAP11B, are involved in basal progenitor amplification (ditto).

A recent paper [ Neuron vol. 111 pp. 65 – 80 ’23 ] discusses CROCCP2 (you don’t want to know what the acronym stands for) which is one of several genes in this family with at least 6 copies in various hominid genomes.  However, CROCCP2 is a duplicate unique to man.   It is highly expressed during brain development and enhances outer Radial Glial Cell progenitor proliferation.

The mechanism by which this happens is detailed in the paper and involves the cilium found on every neuron, mTOR, IFT20 and others.

But that’s not the point here, fascinating although these mechanisms are.   We’re watching a series of at least 20 gene duplications with subsequent modifications build the brain that is unique to us over relatively rapid evolutionary times.  The split between man and chimp is thought to have happened only 8 million years ago.

What should we call this process?  Evolution?  The Creator in action? The Blind Watchmaker?   It is certainly is eerie to think about.  There are 17 more HS genes to go involving in building our brains remaining to be worked out.  Stay tuned