Reflections on past teachers
May. 7th, 2026 03:14 pmInspired by my high school math teacher, whose own memoirs describe HIS teachers, I thought I'd write some portraits of interesting and influential teachers I've had.
Let me start with Bob Young. Mathematics professor at Oberlin College.
I think it's shameful that he only gets 3.8 out of 5 stars on ratemyprofessors! I get 4.6 stars at Clayton State and 4.4 stars at U of South Carolina.
https://www.ratemyprofessors.com/professor/236410
Only 29% of students say they would take him again.
Although 20 of 45 students rate him a 5 for "awesome".
I had him for Multivariate Calculus my first semester at Oberlin. This is a course usually taken in the second year, but thanks to Unified Math VI in high school and scoring a 5 on the Calculus BC exam, I jumped in easily. I scored a perfect 100 on the first exam. Gradients, Lagrange multipliers, divergence, curl, line and surface integrals, Green's theorem, Stokes's theorem, I'd already learned those in high school.
I later took Young for Linear Algebra, Complex Analysis, and Real Analysis.
He was a friendly and urbane fellow, although very private. Some teachers let you know a lot about themselves and lead students by giving a window into their inner lives, they share a vulnerable side. Not so much Bob Young. We knew he sponsored a walrus in the zoo, named Olga, and he sometimes drew pictures of her on exams. That was it.
Young's lectures were extremely polished. A common student complaint was that he made everything blindingly clear while he was lecturing but as soon as you left the classroom it all fell apart in your mind and you couldn't reproduce it. Being at a liberal arts college, Oberlin, instead of a university, led me to have this teacher who was a true artist of teaching, and not someone who was primarily a researcher.
After graduating, I did ask him about his research interests, and he mentioned something about spectral theory, and I think a book by someone named Berbarian?
I see the whole book is available as a PDF online:
https://web.ma.utexas.edu/mp_arc/c/09/09-32.pdf
Anyway. He was noted for his use of color chalk. Everything on the board was beautiful, elegant, colorful. And he was hilarious. I'd laugh as hard in his class as watching Monty Python. He'd get super enthusiastic. In describing how you define integration starting with adding up slabs and then taking the limit of Riemann sums: "What happens when you replace the DESPAIR of slabs with the JOY of Riemann sums???"
I remember several classes where some promising line of mathematics seemed to fail and he'd say: "And now, I leave you on a note of despair..."
Sometimes he'd give a class an unusual framing structure. Like a menu for a meal: This bit of mathematics, a proof maybe, or a lemma, would be labelled "Appetizer", and there would be a main course, side dishes, dessert, etc.
Students complain about his hard tests and optional homework. That was perfect for me though! I'm one of those lazy students who because he was labelled gifted, thought he didn't have to grind at hard work so much. Homework optional, but some of his tests were... week-long, take-home and open book! How could all the students consider those too hard? (Maybe in the LLM / AI era that wouldn't work!) Because the problems often involved some super clever trick. Young made me a fan of the elegant trick. One exam in particular had a problem you had to prove by induction. It kept not working though. I wrote it out on the whiteboard in my room and lived with the problem a bit. I slept on it. Finally I realized you had to prove something slightly STRONGER, making different assumptions, and then it all fell out!
Young was a Platonist. He thought math was REAL, which I never did. Oh, I should be leaving this cafe soon! Cathy will be coming over before too long.
So for example, I asked him about those unprovable math claims, like the Continuum Hypothesis. Couldn't we just make up different math with different "truths" depending on which alternative possibility we assumed? He said: we'll always be able to build our intuition and see a larger picture in which one answer will be obvious.
Ok, a very different math teacher at Oberlin. Actually mathematical methods for physics. Robert Weinstock. He taught Applied Analysis I and II. In some ways he wasn't such a great teacher, and his approach seemed to me outdated. But he had an admirable personality, and a few things he's said have stuck with me.
He was noted for a common introductory text he wrote on "The Calculus of Variations". The calculus of variations was in a sense invented by Newton, in solving the "brachristochrone" problem. The story behind that is very impressive. In this "calculus", you extremize integrals with respect to functions within them. For example, what path of a particle over time minimizes a certain quantity, when integrated over a path? That's used a LOT in physics, and in fact is often used as the foundation for all physics. You define an "action" or "Lagrangian" and then the Euler-Lagrange equations let you solve for the function that will extremize the integral.
https://engineerine.com/newton-vs-bernoulli-the-legendary-brachistochrone-challenge/
He was also on a crusade to show that one of Newton's greatest claimed achievements was in fact a fraud. Newton allegedly proved that conic section orbits are possible if and only if you have an inverse square force law. But Weinstock claimed that Newton only had a one way proof, that his proof was flawed, papered over with circular handwaving. Only later did someone else prove the "only if" side I think, maybe one of the Bernoulli brothers.
Weinstock didn't have a fancy coddled upbringing. He worked in the boiler room of a ship in World War II. But he was very widely read and educated. He bragged to me the first time we met that he went to a concert where his son was playing all 3 of Beethoven's late piano sonatas. I believe he and his wife read each other classics, like Don Quioxte (his wife also helped him grade our papers--unlike Young Weinstock assigned homework that was graded).
These classes were hard. In fact class met also on Saturday mornings at 10 am. At least he brought donuts.
Why did I think his teaching was so flawed and outdated?
For one a lot of the work was done within particular coordinate systems, where we were buried in detail. In math department courses things like tensors were treated abstractly in a coordinate free way. You'd talk about tangent spaces, and things like d/dx and dx would be co and contra vectors, acting on each other to give delta functions. (Delta functions were hard for me to accept as a physicist as they don't make sense to high school level math and can only be defined in a weird way rigorously that's not intuitive.) You'd talk about functionals, wedge products, etc.
But in Weinstock's class we'd look at the forms for gradient, curl, divergence, etc., in various curvilinear coordinates, spherical, cylindrical, etc.
We spent a lot of time solving the "secular equation", finding eigenvalues and eigenvectors. That does have deep applications to quantum physics.
Later I'll write about my thesis advisor Dick McCray. When first getting to know McCray, he asked me about my college math education. He was incredulous when I told him that Weinstock spent class after class proving something called the "Implicit Function Theorem". McCray had never heard of it, but it was a central part of our course.
https://en.wikipedia.org/wiki/Implicit_function_theorem
The point of view of an astrophysicist is very different from that of a mathematician!
One student collected "Weinstockisms", favorite sayings of Weinstock. He'd quip things like: "is the derivative of a product the product of the derivatives? NO, that's a political slogan."
The one though that has really stayed with me is succinct: "Gather, don't strew"
There's a temptation to EXPAND every expression you have factored. You want to see what your equation is made of, each little bit. But, particularly because his problems were all within coordinate systems and involved a lot of complicated terms, it's easy to lose track of some terms when you expand them all out.
Given that Weinstock's Saturday morning 10 am classes followed so soon after night in the Friday Disco on campus (open until 2 am), I sometimes got in to class a little late. My sneakers had this tell-tale squeak to them, probably from dancing on them so hard, so that when I came in Weinstock still facing the board would quip, "Here comes Bram with his squeaky sneakers!"
I didn't do super-well in Weinstick's classes, as I did in Young's, and his lectures weren't as entertaining and sometimes got bogged down in detail, but we all respected his knowledge and personal values.
Sue Colley. Notable as a female teacher / mentor. I also had You-Hua Chu as an astronomy mentor, but that was for only one month of January and then over a summer. And then Saku, now my most common research collaborator, who came to astronomy from a very different point of view from me. I'm more theoretical minded, and Saku very observational, leading her to be highly skeptical of ideas that weren't grounded in observation.
Colley taught my differential equations class and my Linear Algebra 2 class, and sponsored my honors math project in self-taught differential geometry and dynamic systems.
At times when Colley was mentoring me, I was distracted by the start of my attempted relationship with J. Once Colley said to me something like: if I had your talent I'd take it a lot further, you're in danger of squandering it... And once in our 8 am Linear Algebra II class, she found we weren't paying sufficient attention (I think there were only 2 or 3 of us in the class) and cancelled it.
Now on to my thesis advisor, Dick McCray.
He was really a kind of superlative person. He had all sorts of gifts, but it didn't go to his head and make him arrogant. He was extremely broad-minded and broadly educated. He championed students from diverse backgrounds, but was also fascinated by China, learning Chinese, visiting China, and finding most of his graduate students in China (one postdoc had been through the Cultural Revolution.) He said if a student could find their way out of China, where there was so much hidden talent, they had to be very good!
While McCray was my advisor, his wife had serious medical problems, and I often had to fend for myself. She was on dialysis for a while, needed hip replacement surgery, etc.
He was very charismatic, with Clark Gable movie star looks. He was an amateur airplane pilot, and in fact I found out at the birthday party celebrating his 70th, he sometimes flew his students to other universities for talks! He won some kind of award for swimming in the over-40 age category.
Before getting a PhD himself (he studied with Peter Goldreich, who did important work on Saturn's rings and many other fields, and who himself studied with Thomas Gold), McCray taught private high school science, I believe, specializing in optics, I think.
As I mentioned previously, he wasn't so grounded in abstract mathematics (like the Implicit Function Theorem), but knew tricks about applying math and computers to astrophysics models. When we found differential equations that were hard to integrate numerically, he'd point out a class of "stiff" differential equations.
Sometimes he'd surprise me with finding an alternate way to view something in astrophysics we took for granted. One of his research specialities was Supernova 1987a, the supernova closest to us in modern times when we had telescopes that could see across the electromagnetic spectrum. He worked on these mysterious "rings" surrounding the supernova. The spectrum showed some gas was coming towards us and some away, a sign of expansion--but he said: maybe it's contraction? That would also have some coming towards us and some away. It turned out it was expanding, not contracting, but still it impressed me on the need to think outside the box.
When I was a postdoc I developed this really clever mathematical and geometrical method for figuring out what was going on in a stellar wind with a neutron star inside it. The shadow of the X-rays moved through the wind, "slicing" it, and logical and geometric arguments showed how you could infer what was going on in the wind through these slices.
https://iopscience.iop.org/article/10.1086/307336/pdf
I showed it to McCray and he was not only very enthusiastic, but right then and there one-upped the clever geometry! I included both my method and his extension in the paper we wrote. He pointed out that the X-ray shadow of the star would be a cone, and then the nearly planar "isovelocity surface" would intersect the cone, so the region causing emission at a given velocity would be a conic section--simplifying a complex problem!
Now, this paper and its result haven't been all that important scientifically, but it was a neat situation where I could use clever math and logic to learn something real.
I got started with McCray when, floundering in grad school at first, I had to do a research project as part of our "comprehensive exams". Revising a telescope proposal he had written, I came up with this fascinating scenario.
A pulsar beam could reflect off a surrounding accretion disk. And the reflection could appear to move faster than light! That's a problem I sometimes suggest to my intro astronomy students: can the Bat-Signal on the clouds move faster than light? And yes, it can because it's not a physical thing. If you think the Bat-Signal is really moving across the sky, you're like my cat who thinks the red dot is really doing the moving.
So I used the old standby, proof by induction, which I used in my high school Westinghouse project, and then to answer Bob Young's devilishly tricky exam problem, to prove exactly how many points you could see at once from the disk, even though only 1 was lit up at a time, because of these "effectively faster than light" effects.
I also briefly did some freelance training of "AI"s in math, and was able to stump and then correct the AI with this problem.
Here's McCray with... none other than 10 year old Kanye West, in China!
https://www.reddit.com/r/Kanye/comments/zfb6jd/a_young_kanye_west_living_in_china_he_spent_his/
(Third photo)
Ed Bostonian:
Going back in time now a bit, I want to mention (or re-mention) another formative teacher, Ed Bostonian, my 10th grade physics teacher (actually this was 11th grade physics, but I took the class in 10th grade).
There are contrasts and similarities at the same time with my thesis advisor McCray. McCray was universally admired (though some said he was a better researcher and mentor than teacher), a charismatic pilot, world traveler, medal winning swimmer.
And I feel kind of bad that the other entry I wrote about Mr. Bostonian, written the day after 9/11/2001, when you can see I was being flippant in reaction to the grim mood that I felt as a stultifying enforced unity, emphasized too much that he was very UNPOPULAR (unjustly!) with the mass of students in our time:
https://bram.dreamwidth.org/2001/09/12/
Later his daughter found that entry and angrily came to his defense, though saw later that I also had respect for him. She let me know about other difficulties in his life. The outward impressiveness of McCray wasn't the essence (his modesty and empathy were), a teacher can also be struggling in life and inspire.
I think I impressed Mr. Bostonian explaining to him a similar issue to the one that let me become McCray's research assistant: astrophysical illusions of faster than light travel. At the time a "superluminal" jet from a star system had been discovered, which puzzled Mr. Bostonian. I explained to him that the jet moving MOSTLY towards us with a little sideways motion had the sideways motion fast-forwarded from our perspective, as the jet started to catch up with the image it gave off.
Let me start with Bob Young. Mathematics professor at Oberlin College.
I think it's shameful that he only gets 3.8 out of 5 stars on ratemyprofessors! I get 4.6 stars at Clayton State and 4.4 stars at U of South Carolina.
https://www.ratemyprofessors.com/professor/236410
Only 29% of students say they would take him again.
Although 20 of 45 students rate him a 5 for "awesome".
I had him for Multivariate Calculus my first semester at Oberlin. This is a course usually taken in the second year, but thanks to Unified Math VI in high school and scoring a 5 on the Calculus BC exam, I jumped in easily. I scored a perfect 100 on the first exam. Gradients, Lagrange multipliers, divergence, curl, line and surface integrals, Green's theorem, Stokes's theorem, I'd already learned those in high school.
I later took Young for Linear Algebra, Complex Analysis, and Real Analysis.
He was a friendly and urbane fellow, although very private. Some teachers let you know a lot about themselves and lead students by giving a window into their inner lives, they share a vulnerable side. Not so much Bob Young. We knew he sponsored a walrus in the zoo, named Olga, and he sometimes drew pictures of her on exams. That was it.
Young's lectures were extremely polished. A common student complaint was that he made everything blindingly clear while he was lecturing but as soon as you left the classroom it all fell apart in your mind and you couldn't reproduce it. Being at a liberal arts college, Oberlin, instead of a university, led me to have this teacher who was a true artist of teaching, and not someone who was primarily a researcher.
After graduating, I did ask him about his research interests, and he mentioned something about spectral theory, and I think a book by someone named Berbarian?
I see the whole book is available as a PDF online:
https://web.ma.utexas.edu/mp_arc/c/09/09-32.pdf
Anyway. He was noted for his use of color chalk. Everything on the board was beautiful, elegant, colorful. And he was hilarious. I'd laugh as hard in his class as watching Monty Python. He'd get super enthusiastic. In describing how you define integration starting with adding up slabs and then taking the limit of Riemann sums: "What happens when you replace the DESPAIR of slabs with the JOY of Riemann sums???"
I remember several classes where some promising line of mathematics seemed to fail and he'd say: "And now, I leave you on a note of despair..."
Sometimes he'd give a class an unusual framing structure. Like a menu for a meal: This bit of mathematics, a proof maybe, or a lemma, would be labelled "Appetizer", and there would be a main course, side dishes, dessert, etc.
Students complain about his hard tests and optional homework. That was perfect for me though! I'm one of those lazy students who because he was labelled gifted, thought he didn't have to grind at hard work so much. Homework optional, but some of his tests were... week-long, take-home and open book! How could all the students consider those too hard? (Maybe in the LLM / AI era that wouldn't work!) Because the problems often involved some super clever trick. Young made me a fan of the elegant trick. One exam in particular had a problem you had to prove by induction. It kept not working though. I wrote it out on the whiteboard in my room and lived with the problem a bit. I slept on it. Finally I realized you had to prove something slightly STRONGER, making different assumptions, and then it all fell out!
Young was a Platonist. He thought math was REAL, which I never did. Oh, I should be leaving this cafe soon! Cathy will be coming over before too long.
So for example, I asked him about those unprovable math claims, like the Continuum Hypothesis. Couldn't we just make up different math with different "truths" depending on which alternative possibility we assumed? He said: we'll always be able to build our intuition and see a larger picture in which one answer will be obvious.
Ok, a very different math teacher at Oberlin. Actually mathematical methods for physics. Robert Weinstock. He taught Applied Analysis I and II. In some ways he wasn't such a great teacher, and his approach seemed to me outdated. But he had an admirable personality, and a few things he's said have stuck with me.
He was noted for a common introductory text he wrote on "The Calculus of Variations". The calculus of variations was in a sense invented by Newton, in solving the "brachristochrone" problem. The story behind that is very impressive. In this "calculus", you extremize integrals with respect to functions within them. For example, what path of a particle over time minimizes a certain quantity, when integrated over a path? That's used a LOT in physics, and in fact is often used as the foundation for all physics. You define an "action" or "Lagrangian" and then the Euler-Lagrange equations let you solve for the function that will extremize the integral.
https://engineerine.com/newton-vs-bernoulli-the-legendary-brachistochrone-challenge/
He was also on a crusade to show that one of Newton's greatest claimed achievements was in fact a fraud. Newton allegedly proved that conic section orbits are possible if and only if you have an inverse square force law. But Weinstock claimed that Newton only had a one way proof, that his proof was flawed, papered over with circular handwaving. Only later did someone else prove the "only if" side I think, maybe one of the Bernoulli brothers.
Weinstock didn't have a fancy coddled upbringing. He worked in the boiler room of a ship in World War II. But he was very widely read and educated. He bragged to me the first time we met that he went to a concert where his son was playing all 3 of Beethoven's late piano sonatas. I believe he and his wife read each other classics, like Don Quioxte (his wife also helped him grade our papers--unlike Young Weinstock assigned homework that was graded).
These classes were hard. In fact class met also on Saturday mornings at 10 am. At least he brought donuts.
Why did I think his teaching was so flawed and outdated?
For one a lot of the work was done within particular coordinate systems, where we were buried in detail. In math department courses things like tensors were treated abstractly in a coordinate free way. You'd talk about tangent spaces, and things like d/dx and dx would be co and contra vectors, acting on each other to give delta functions. (Delta functions were hard for me to accept as a physicist as they don't make sense to high school level math and can only be defined in a weird way rigorously that's not intuitive.) You'd talk about functionals, wedge products, etc.
But in Weinstock's class we'd look at the forms for gradient, curl, divergence, etc., in various curvilinear coordinates, spherical, cylindrical, etc.
We spent a lot of time solving the "secular equation", finding eigenvalues and eigenvectors. That does have deep applications to quantum physics.
Later I'll write about my thesis advisor Dick McCray. When first getting to know McCray, he asked me about my college math education. He was incredulous when I told him that Weinstock spent class after class proving something called the "Implicit Function Theorem". McCray had never heard of it, but it was a central part of our course.
https://en.wikipedia.org/wiki/Implicit_function_theorem
The point of view of an astrophysicist is very different from that of a mathematician!
One student collected "Weinstockisms", favorite sayings of Weinstock. He'd quip things like: "is the derivative of a product the product of the derivatives? NO, that's a political slogan."
The one though that has really stayed with me is succinct: "Gather, don't strew"
There's a temptation to EXPAND every expression you have factored. You want to see what your equation is made of, each little bit. But, particularly because his problems were all within coordinate systems and involved a lot of complicated terms, it's easy to lose track of some terms when you expand them all out.
Given that Weinstock's Saturday morning 10 am classes followed so soon after night in the Friday Disco on campus (open until 2 am), I sometimes got in to class a little late. My sneakers had this tell-tale squeak to them, probably from dancing on them so hard, so that when I came in Weinstock still facing the board would quip, "Here comes Bram with his squeaky sneakers!"
I didn't do super-well in Weinstick's classes, as I did in Young's, and his lectures weren't as entertaining and sometimes got bogged down in detail, but we all respected his knowledge and personal values.
Sue Colley. Notable as a female teacher / mentor. I also had You-Hua Chu as an astronomy mentor, but that was for only one month of January and then over a summer. And then Saku, now my most common research collaborator, who came to astronomy from a very different point of view from me. I'm more theoretical minded, and Saku very observational, leading her to be highly skeptical of ideas that weren't grounded in observation.
Colley taught my differential equations class and my Linear Algebra 2 class, and sponsored my honors math project in self-taught differential geometry and dynamic systems.
At times when Colley was mentoring me, I was distracted by the start of my attempted relationship with J. Once Colley said to me something like: if I had your talent I'd take it a lot further, you're in danger of squandering it... And once in our 8 am Linear Algebra II class, she found we weren't paying sufficient attention (I think there were only 2 or 3 of us in the class) and cancelled it.
Now on to my thesis advisor, Dick McCray.
He was really a kind of superlative person. He had all sorts of gifts, but it didn't go to his head and make him arrogant. He was extremely broad-minded and broadly educated. He championed students from diverse backgrounds, but was also fascinated by China, learning Chinese, visiting China, and finding most of his graduate students in China (one postdoc had been through the Cultural Revolution.) He said if a student could find their way out of China, where there was so much hidden talent, they had to be very good!
While McCray was my advisor, his wife had serious medical problems, and I often had to fend for myself. She was on dialysis for a while, needed hip replacement surgery, etc.
He was very charismatic, with Clark Gable movie star looks. He was an amateur airplane pilot, and in fact I found out at the birthday party celebrating his 70th, he sometimes flew his students to other universities for talks! He won some kind of award for swimming in the over-40 age category.
Before getting a PhD himself (he studied with Peter Goldreich, who did important work on Saturn's rings and many other fields, and who himself studied with Thomas Gold), McCray taught private high school science, I believe, specializing in optics, I think.
As I mentioned previously, he wasn't so grounded in abstract mathematics (like the Implicit Function Theorem), but knew tricks about applying math and computers to astrophysics models. When we found differential equations that were hard to integrate numerically, he'd point out a class of "stiff" differential equations.
Sometimes he'd surprise me with finding an alternate way to view something in astrophysics we took for granted. One of his research specialities was Supernova 1987a, the supernova closest to us in modern times when we had telescopes that could see across the electromagnetic spectrum. He worked on these mysterious "rings" surrounding the supernova. The spectrum showed some gas was coming towards us and some away, a sign of expansion--but he said: maybe it's contraction? That would also have some coming towards us and some away. It turned out it was expanding, not contracting, but still it impressed me on the need to think outside the box.
When I was a postdoc I developed this really clever mathematical and geometrical method for figuring out what was going on in a stellar wind with a neutron star inside it. The shadow of the X-rays moved through the wind, "slicing" it, and logical and geometric arguments showed how you could infer what was going on in the wind through these slices.
https://iopscience.iop.org/article/10.1086/307336/pdf
I showed it to McCray and he was not only very enthusiastic, but right then and there one-upped the clever geometry! I included both my method and his extension in the paper we wrote. He pointed out that the X-ray shadow of the star would be a cone, and then the nearly planar "isovelocity surface" would intersect the cone, so the region causing emission at a given velocity would be a conic section--simplifying a complex problem!
Now, this paper and its result haven't been all that important scientifically, but it was a neat situation where I could use clever math and logic to learn something real.
I got started with McCray when, floundering in grad school at first, I had to do a research project as part of our "comprehensive exams". Revising a telescope proposal he had written, I came up with this fascinating scenario.
A pulsar beam could reflect off a surrounding accretion disk. And the reflection could appear to move faster than light! That's a problem I sometimes suggest to my intro astronomy students: can the Bat-Signal on the clouds move faster than light? And yes, it can because it's not a physical thing. If you think the Bat-Signal is really moving across the sky, you're like my cat who thinks the red dot is really doing the moving.
So I used the old standby, proof by induction, which I used in my high school Westinghouse project, and then to answer Bob Young's devilishly tricky exam problem, to prove exactly how many points you could see at once from the disk, even though only 1 was lit up at a time, because of these "effectively faster than light" effects.
I also briefly did some freelance training of "AI"s in math, and was able to stump and then correct the AI with this problem.
Here's McCray with... none other than 10 year old Kanye West, in China!
https://www.reddit.com/r/Kanye/comments/zfb6jd/a_young_kanye_west_living_in_china_he_spent_his/
(Third photo)
Ed Bostonian:
Going back in time now a bit, I want to mention (or re-mention) another formative teacher, Ed Bostonian, my 10th grade physics teacher (actually this was 11th grade physics, but I took the class in 10th grade).
There are contrasts and similarities at the same time with my thesis advisor McCray. McCray was universally admired (though some said he was a better researcher and mentor than teacher), a charismatic pilot, world traveler, medal winning swimmer.
And I feel kind of bad that the other entry I wrote about Mr. Bostonian, written the day after 9/11/2001, when you can see I was being flippant in reaction to the grim mood that I felt as a stultifying enforced unity, emphasized too much that he was very UNPOPULAR (unjustly!) with the mass of students in our time:
https://bram.dreamwidth.org/2001/09/12/
Later his daughter found that entry and angrily came to his defense, though saw later that I also had respect for him. She let me know about other difficulties in his life. The outward impressiveness of McCray wasn't the essence (his modesty and empathy were), a teacher can also be struggling in life and inspire.
I think I impressed Mr. Bostonian explaining to him a similar issue to the one that let me become McCray's research assistant: astrophysical illusions of faster than light travel. At the time a "superluminal" jet from a star system had been discovered, which puzzled Mr. Bostonian. I explained to him that the jet moving MOSTLY towards us with a little sideways motion had the sideways motion fast-forwarded from our perspective, as the jet started to catch up with the image it gave off.

