In the fall of 2022 it was my great pleasure to see and hear the orcas of J pod at Lime Kiln State Park with David Neiwert (see bibliography) and his son Devin.

Einstein's visit with Henry Ford is entirely a product of my imagination. Had Ford asked Einstein in 1935 for a simple thought experiment to convey the meaning and essence of relativity, Einstein would have been more likely to have taken Ford to look down from the top of the university's highest building and then to have explained that the happiest thought of his career was that a man falling from a rooftop does not feel any of the effects of gravity (until he strikes ground, of course). We will analyze and criticize Einstein's "happiest thought" in Chapter Twenty-Nine.

It has been said that imitation is the sincerest form of flattery, and
you will find much of that here. This vignette is in equal parts a
shameless imitation of, an adoring homage to, and an unfair satire of,
Douglas Hofstadter's famous tome *G** ödel, Escher,
Bach*. It is therefore equally self-referential, and any facetious
criticism of his work implicit in what I have written here is at least as
applicable to my own. Anyone even passingly familiar with Hofstadter's
book is likely to notice at several points in this one where I have taken
cues and inspiration from

The use of the word "fit" to title subdivisions of a longer work
originates with Lewis Carroll's poem *The Hunting of the Snark *
("An Agony in Eight Fits") This convention was imitated by the radio
series *The Hitchhiker's Guide to the Galaxy*. Speaking of the *Guide*,
the tablet the tortoise reads from is in some respects similar. Douglas
Adams anticipated Wikipedia in some ways, but allowed the entire
enterprise to fall under the control of the Vogons ("a horde of
bureaucrats who'd be perfectly happy to destroy this planet and everyone
on it"). The tortoise having found the tablet discarded by the roadside
stems from my memory of Arthur Dent having thrown his copy of the Guide
into a river on prehistoric Earth. Achilles asking the tortoise what she
is reading is intended as an imitation to Hamlet's dialogue with Polonius,
which I re-imagine later in this book.

*Recommended resource*s:

- This video by the Khan Academy on Cartestian coordinates.
- Ferris'
*Coming of Age in the Milky Way*(see bibliography), particularly for its discussion of how mankind's understanding of space has evolved over time.

Long before Magellan's time and hundreds of years before the implementation of the International Date Line, the Arab geographer Abulfeda (1273–1331) made the earliest known prediction that those who circumnavigated the globe would accumulate a one-day offset in their reckoning of time, depending on which direction they traveled. Alas, Magellan and Mr. Fogg were not aware.

Figure 2-2 is described as showing the earth's rotation "at equinox" because it is only during these two times of year that the north and south poles would be on the line between day and night, or more precisely, between sunlight and shadow. Due to the tilt of the earth relative to its orbit around the sun, the poles remain in the earth's shadow for six months at a time.

In the early 1930s, Einstein did come to Oxford as a guest lecturer and
stayed in the rooms once occupied by Lewis Carroll, whose other
professional identity was the mathematician Charles Dodgson (see
Robinson's *Einstein On The Run*, p. 173).

Does anyone here remember usenet?

"*Even now, physicists occasionally stumble when relating projectile
motion below to planetary orbits above.*" See, for instance, Lee
Smolin's *Time Reborn* (page 21): "Ellipses trace the planetary
orbits and parabolas trace the paths of falling bodies on Earth." This
fallacy is discussed at length in Chapter Sixteen.

*Recommended resource*s:

I wanted to mention Benjamin Franklin in connection with my comments on static electricity, but I didn't see a place where it wouldn't have interrupted the flow. Franklin is so well-remembered as a statesman, even I had started to forget his work as a scientist.

"*Calculus is thought to have been an invention of necessity for
Newton, though Gottfried Leibniz arrived at many of the same ideas
independently around the same time.*" For further information on the
history of the development of calculus, see https://www.quora.com/Is-it-true-that-calculus-was-invented-before-Leibniz-and-Newton-in-India

"*the answer involves calculus (which really isn't that difficult once
you throw away the tedious first third of your textbook dealing with
limits and the fundamental theorem of calculus)*" I think it's poor
practice that a typical calculus course subjects students to this material
before getting to the practical applications of calculus. Yes, show us *why
*calculus works, but only if we care after having been shown *how*.

One of the many ideas that caught my eye but didn't make it into the main
text was something in Wolfon and Pasachoff's Physics for Scientists and
Engineers (their Figure 18-32b). A ball with angular speed **ω**
and velocity **v** through a mass of air experiences a force
**ω**x**v** which is analogous to q**v**
x **B**. I wouldn't have expected aerodynamics and
electromagnetism to have that math in common, but there we are.

Here is the relevant excerpt from Carroll's *Sylvie and Bruno
Concluded *(1893):

"They run their railway-trains without any engines nothing is needed but machinery to stop them with. Is that wonderful enough,Miladi?"

"But where does the force come from ? " I ventured to ask.

Mein Herr turned quickly round, to look at the new speaker. Then he took off his spectacles, and polished them, and looked at me again, in evident bewilderment. I could see he was thinking - as indeed I was also - that we must have met before.

"They use the force of

gravity" he said. "It is a force known also inyourcountry, I believe?""But that would need a railway going

down-hill," the Earl remarked. " You ca'n't haveallyour railways going down-hill?""They

alldo," said Mein Herr."Not from

bothends?""From

bothends.""Then I give it up!" said the Earl.

"Can you explain the process?" said Lady Muriel. "Without using that language, that I ca'n't speak fluently?"

"Easily," said Mein Herr. "Each railway is in a long tunnel, perfectly straight: so of course the

middleof it is nearer the centre of the globe than the two ends: so every train runs half-waydown-hill, and that gives it force enough to run theotherhalfup-hill.""Thank you. I understand that perfectly," said Lady Muriel." But the velocity, in the

middleof the tunnel, must be somethingfearful!"

See also https://en.wikipedia.org/wiki/Gravity_train#Origin_of_the_concept.

As an amusing aside, the opposite points of the earth which such a train
might connect are called *antipodes*. In a much earlier novel,
Carroll's Alice mispronounces the word as "antipathies."

*Recommended resource*s:

- https://www.3blue1brown.com/lessons/differential-equations A great presentation on phase space and phase flow.

- The Stanford Encyclopedia of Philosophy on Zeno's paradoxes: https://plato.stanford.edu/
entries/paradox-zeno/

"Potentially losing some information is a fundamental consequence of differentiation." The initial values are lost; the indefinite integral suggests that you can just make one up when you go in reverse, because any starting value would be valid.

Thanks to "Mark44" in Washington state for setting me straight when I couldn't figure out how I was not getting a calculation right (I started with the wrong formula). https://www.physicsforums.com/threads/differentiating-euler-formula-vs-multiplying-by-i.1048002/

*Recommended resources:*

- https://www.3blue1brown.com/lessons/eulers-formula-via-group-theory This is a must-see visualization of how addition and multiplication work on the real number line and in the complex plane.
- Penrose,
*The Road to Reality*, chapter four. The history of complex numbers, including cubic solutions. - https://www.3blue1brown.com/lessons/groups-and-monsters The cubic formula is discussed at about five minutes in.
- Veritasium on how imaginary numbers were invented (including the cubic formula): https://www.youtube.com/watch?v=cUzklzVXJwo
- On Lewis Carroll's supposed satire of 19th-century mathematics: https://www.newscientist.com/article/mg20427391-600-alices-adventures-in-algebra-wonderland-solved/
- https://www.intmath.com/complex-numbers/9-impedance-phase-angle.php Finding the phase angle in an AC circuit. See also https://www.intmath.com/complex-numbers/6-products-quotients.php
- https://en.wikipedia.org/wiki/Electrical_impedance#Complex_voltage_and_current Complex voltage calculations
- https://en.wikipedia.org/wiki/Phasor

Poincaré's description of a world where changes in size are driven by temperature calls to mind Alice's ability in Wonderland to shrink by fanning herself. When Alice is told to "keep her temper," the more archaic second meaning is that she must take care that her changes in size all happen in proportion rather than, for instance, growing a serpent-like neck.

I had originally intended to show the metric tensor and the calculation of distance with covariant vector components, but after realizing I had gotten it wrong on my first attempt I decided that the whole affair was better suited for the end notes. What I had forgotten to do was to include the dot products of the dual bases with themselves.

Since the angle θ between the *covariant *components **v**_{1}
and **v**_{2} (and between the dual basis vectors *
* **e**^{1} and **e**^{2})
is π (180 degrees) minus the angle φ (Figure 17-32)
between the two basis vectors **e**_{1}
and **e**_{2}, we could rewrite this as :

v^{2}=(v_{1})^{2}+ (v_{2})^{2}- 2(v_{1}v_{2}cos(π- φ )) = = 1v_{1}v_{1}- 1v_{1}v_{2}cos(π- φ ) - 1v_{2}v_{1}cos(π- φ ) + 1v_{2}v_{2}

Equation 17-3.The length of a vector in terms of its covariant components and the angle between them and between the dual basis vectors.

where π- φ is the angle between the two covariant components of **v**.

In terms of a metric tensor, this would be as follows in Figure 17-35, remembering that the elements of this tensor are indexed as shown in Figure 17-36:

Figure 17-35. A metric tensor for use with contravariant (dual) basis vectors and covariant vector components in a system with non-orthogonal coordinate axes.. The index key for the metric tensor in Figure 17-35.

Figure 17-36

*Recommended resources:*

- More on hyperbolic geometry in Penrose,
*The Road to Reality*, chapter two. Also O'Shea's detailed history in*The Poincaré Conjecture*. - "The meaning of the metric tensor" https://www.youtube.com/watch?v=Dn0ZZRVuJcU The most visual and thorough presentation I have yet seen on the subject.

*Recommended resources:*

- The life cycles of stars: https://imagine.gsfc.nasa.gov/educators/lifecycles/LC_main3.html

*Recommended resources:*

- https://www.3blue1brown.com/lessons/span
- https://www.3blue1brown.com/lessons/linear-transformations
Linear transformations
- https://www.3blue1brown.com/lessons/determinant See the determinant diagram around 8:43.
- https://www.3blue1brown.com/lessons/inverse-matrices
Systems of linear equations and solving them; invertibility

To those readers wondering what on earth this chapter was all about, I
thank you for indulging me in a bit of fun. This** **was the
first chapter of the book written largely — if not solely — for the
purpose of entertainment (preferably, yours as well as mine); others
followed, eventually to become this book's "fits." It all began with the
idea of Hamlet's tribute to Einstein. Several other aspects of this scene
seemed to develop together, and I decided to lean into the obvious
anachronism of its premise; it presented itself as a humorous way to
precede a more serious discussion of time (and a certain loss of
sequentiality) in the next chapter. I decided to name the inn the Non
Sequitur (Latin for "it does not follow"), and to play with the comedic *non
sequitur *in the tradition of two of the great plays whose
characters I have borrowed and placed in this setting.

Alice's tutor would presumably have been Lewis Carroll himself, who
taught mathematics at Oxford under his real name, Charles Dodgson. I have
cast the former Oxford-area furniture dealer Theophilus Carter (a.k.a. the
Mad Hatter) as the owner of this restaurant. See page 69 of *The
Annotated Alice* for more amusing background on the historical and
fictional Mad Hatters.

The inn's relationship with time is not unlike that of the Hatter's Mad
Tea-Party, but perhaps more like the concept of Douglas Adams' Milliways,
*The Restaurant at the End of the Universe* where people "of all
ages" might mingle, and where it is always the same time. Adams borrowed
from Carroll many times; compare his "If you've done 6 impossible things
this morning, why not round it off with breakfast at Milliways" with this
snippet of dialogue from *Through the Looking-Glass*:

Alice laughed. “There’s no use trying,” she said: “one can’t believe impossible things.”

“I daresay you haven’t had much practice,” said the Queen. “When I was your age, I always did it for half-an-hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast.”

I only wrote the dialogue around the reception desk in order to smooth the way for my Edgar Allan Poe reference (which also pointed to the strange cyclical time of Milliways and the Tea Party); but having done that, I decided that the hostess ought to give her responses subtly out of sequence in her dialogue with Alice. Perhaps she is related to the White Queen?

The philosophers song was written by Eric Idle of Monty Python (https://www.youtube.com/watch?v=l9SqQNgDrgg). In regards to the posters on the wall, my non-exhaustive survey of time travel in cinema finds that the stand-alone movies (those not having sequels or prequels to speak of) often feature strange loops (which I note with a nod in the direction of Douglas Hofstadter).

Some of the humor just wrote itself. I didn't have his paradoxes in mind when I wrote Zeno's comment about not yet having managed to get to the Restaurant at the End of the Universe; I hope that line strikes others as funny as it did me.

Alas, something instructive did find its way into this chapter, but I only allowed it because I found it too amusing. Rosencrantz's retort to Guildenstern reflects a key concept in this book, indeed one that relates to its title: that we are not always justified in asserting that something has or has not yet taken place somewhere else. This idea is developed further in the following chapter, in a subsequent chapter again featuring these characters, and finally in the concluding chapter, "Einstein's Cat."

The quotation that ends this chapter is an "aside" from Polonius in the
play *Hamlet*, taken from a scene that I have parodied in a
subsequent "fit." It seems fitting both for that reason and as my excuse
for what I have written as this "fit."

*Recommended resources:*

See Robinson's *Einstein on the Run* regarding Einstein
discussing Poincaré with his mates Habicht and Solovine. The trio
"...argued in detail about a recently published book, *Science and
Hypothesis* . . ."

"As early as 1898, Poincaré questioned the meaning of simultaneity over
large distances and wrote that there may not be a meaningful, universally
applicable time." See Orzel, *Timekeeping, *pp. 199-202 regarding
Poincaré's 1898 "The Measure of Time."

This bonus figure shows how various proper distances (on the *y*
axis) become infinite at various speeds (as a percentage of the speed of
light):

In his second relativity paper in 1905–06 Henri Poincaré showed how, by taking time to be an imaginary fourth spacetime coordinateict, wherecis the speed of light andiis the imaginary unit, Lorentz transformations can be visualized as ordinary rotations of the four dimensional Euclidean spherex^{2}+y^{2}+z^{2}+ (ict)^{2}= const . Poincaré setc= 1 for convenience. . ...

The analogy with Euclidean rotations is only partial since the radius of the sphere is actually imaginary which turns rotations into rotations in hyperbolic space (see hyperbolic rotation). This idea, which was mentioned only briefly by Poincaré, was elaborated by Minkowski in a paper in German published in 1908 called "The Fundamental Equations for Electromagnetic Processes in Moving Bodies". Minkowski, using this formulation, restated the then-recent theory of relativity of Einstein. In particular, by restating the Maxwell equations as a symmetrical set of equations in the four variables(x, y, z, ict) combined with redefined vector variables for electromagnetic quantities, he was able to show directly and very simply their invariance under Lorentz transformation. He also made other important contributions and used matrix notation for the first time in this context. From his reformulation he concluded that time and space should be treated equally, and so arose his concept of events taking place in a unified four-dimensional spacetime continuum.

Einstein used both systems of notation in his 1916 general-audience book
*Relativity*.

*Recommended resources:*

- https://www.youtube.com/watch?v=rB83DpBJQsE Divergence and curl: The language of Maxwell's equations, fluid flow, and more

I found https://www.geometrygames.org/CurvedSpaces/ very amusing. This is NOT the idea of curved spaces that I will be presenting here, but an idea of this type was entertained by Einstein: that the universe might be unbounded yet finite. That the three-dimensional universe could loop back on itself in all directions is an idea that seems too slippery for my mind to grasp very tightly.

The rows and columns of books of maps is a metaphor for the phase space
explained by Grant Sanderson (https://www.3blue1brown.com/lessons/differential-equations,
cited above) and Sean Carroll (*Biggest Ideas*, p. 76-80) On
Carroll's page 80: "The entire trajectory is fixed by knowing what point
to start at;" page 99: "According to the Laplacian paradigm, specifying
one point in phase space at one moment in time is enough to determine the
entire trajectory of a system."

- https://www.3blue1brown.com/lessons/uncertainty-principle "The more general uncertainty principle, regarding Fourier transforms"
- The Science Asylum: The True Meaning of Schrödinger's Equation
- The Science Asylum: Photons, Entanglement, and the Quantum Eraser
- The Stanford Encyclopedia of Philosophy: Philosophical Issues in Quantum Theory

"I am he as you are he . . ." In* Rosencrantz and Guildenstern
Are Dead*, the confusion of one character with the other is a
running joke which apparently extends a long-standing thespian tradition:
https://en.wikipedia.org/wiki/Rosencrantz_and_Guildenstern.
I'll leave it to you to puzzle out the thematic references I make to
Carroll's poem here.

Scene one is a satire of the gravediggers scene in *Hamlet* which
takes aim at certain celebrity scientists who shall remain unnamed in this
context. "Eric Geller" is a mashup of names of two sensationalists of a
bygone generation.

Scene two is parody of another scene in *Hamlet *(Act II, Scene
2). The comedic non sequitur was integral to the original. Some of the
dialogue still fits my story but with a new meaning that touches directly
on the "Einstein's Cat" question (Introduction and Conclusion).

The limerick Rosencrantz has written on the wall is my adaptation of an
original by A. H. Reginald Buller, published in a 1923 issue of *Punch
*(see
https://www.nationalreview.com/corner/a-young-lady-named-bright-etc/).
This is also a bawdy allusion to Hamlet's mother, who in her "haste"
"wandered" in a "relative way" in allowing herself to be wooed by her
deceased husband's brother "the previous knight", setting the "time" "out
of joint" in a different sense than how the reverse time travel of the
limerick would cause a paradox.

*Recommended resources:*

- "Circuit Energy doesn't FLOW the way you THINK!" This video by Nick Lucid on "The Science Asylum" YouTube channel discusses the principle mentioned at the beginning of the chapter.

In this chapter, the "Alice" we have come to know from the previous
"fits" turns out to be a story-within-a-story; she is the creation of an
early-mid-90s cyberpunk by the name of Alice who shares an affection for
Lewis Carroll with one of her favorite authors, Douglas Adams. Unlike
Carroll's Alice, this one writes her own story. Inspired in part by the *Hitchhiker's
Guide to the Galaxy*, she has envisioned a future in which
information is more free, not tethered to university enrollment or to a
9600-baud telephone connection. In the words of the Sex Pistols song she
parodied, she is a "dog's body" with a "council tenancy." In that she has
anticipated such things ahead of her time, she is like Thomasina in
Stoppard's *Arcadia*.

How can you write Alice without parody verse? You have to include it, and it's best to aim it at something that is taken too seriously. Lewis Carroll was a brilliant satirist, subverting overly-sober popular poems and replacing their moral lessons with absurdities ("You Are Old, Father William"). This was in the same grand tradition as Warner Brothers studios' take on "Ride of the Valkyries" starring Bugs Bunny and Elmer Fudd ("What's Opera, Doc?"), and "Weird Al" Yankovic's "Theme From Rocky XIII."

Chapter one of *Through the Looking Glass* has one of Alice's two
kittens playing with a ball of yarn and making a mess "all knots and
tangles." Later Tweedledee and Tweedledum spar over a "spoiled" rattle.

*Recommended resources:*

- Arianrhod, Robyn.
*Einstein's Heroes: Imagining the World Through the Language of Mathematics.*New York: Oxford University Press, 2005. - Ball, Philip.
*Beyond Weird: Why Everything You Thought You Knew About Quantum Physics is Different.*Chicago: The University of Chicago Press, 2018*.*

- Barnett, Lincoln.
*The Universe and Dr. Einstein*(second edition). New York: Mentor Books, 1957. - Bertschinger, Edmund; with Edwin F. Taylor, and John Archibald
Wheeler.
*Exploring Black Holes*. 2008 draft for 2nd edition, downloaded July 2009 from exploringblackholes.com. - Brockman, John.
*My Einstein: Essays by the World's Leading Thinkers on the Man, His Work, and His Legacy*. New York: Pantheon, 2006. - Brockman, John.
*Know This: Today's Most Interesting and Important Scientific Ideas, Discoveries, and Developments.*Harper Perennial, 2017. - Carroll, Sean M.
*From Eternity to Here: The Quest for the Ultimate Theory of Time.*New York: Plume, 2010. - Carroll, Sean M.
*Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime.*Boston: Dutton, 2019*.* - Carroll, Sean M.
*Spacetime and Geometry: An Introduction to General Relativity.*San Francisco: Addison-Wesley, 2004. - Carroll, Sean M.
*The Biggest Ideas In The Universe: Space, Time and Motion*. New York: Dutton, 2022. - Cole, K. C.
*First You Build a Cloud: And Other Reflections on Physics as a Way of Life.*San Diego: Harcourt Brace & Co. 1999.

- Einstein, Albert.
*Relativity: The Special and General Theory*. 1916 (2006 edition with foreword by Roger Penrose). - Ferris, Timothy.
*Coming of Age in the Milky Way.*New York: Anchor Books, 1989. - Fleisch, Dan.
*A Student's Guide to Maxwell's Equations.*New York: Cambridge University Press, 2008. - Fleisch, Dan.
*A Student's Guide to the Schrödinger Equation.*New York: Cambridge University Press, 2020. - Fleisch, Dan.
*A Student's Guide to Vectors and Tensors.*New York: Cambridge University Press, 2012. - Galison, Peter.
*Einstein's Clocks, Poincaré's Maps: Empires of Time.*New York: W. W. Norton, 2003. - Gardner, Martin.
*The Annotated Alice.*New York: Norton, 2000. - Gilder, Louisa.
*The Age of Entanglement: When Quantum Physics Was Reborn.*New York: Alfred A. Knopf, 2009.

- Gleick, James.
*Time Travel: A History.*New York: Pantheon, 2016. - Gribbin, John.
*In Search of Sch**rödinger's Cat: Quantun Physics and Reality.*New York: Bantam, 1984. - Griffiths, David J.; and Darrell F. Schroeter.
*Introduction to Quantum Mechanics*(third edition). New Delhi: Cambridge University Press, 2018. - Halpern, Paul.
*The Quantum Labyrinth*:*How Richard Feynman and John Wheeler Revolutionized Time and Reality*. New York: Basic Books, 2017 - Hartle, James B. Gravity:
*An Introduction to Einstein's General Relativity.*San Francisco: Addison-Wesley, 2003. - Hawking, Stephen.
*A Brief History of Time.*New York: Bantam, 1988. - Hofstadter, Douglas R.
*G*(20th anniversary edition). New York: Basic Books, 1999.*ö*del, Escher, Bach: An Eternal Golden Braid - Kaku, Michio.
*Hyperspace*. New York: Doubleday, 1994. - Krauss, Lawrence M.
*Hiding in the Mirror:The Mysterious Allure of Extra Dimensions, from Plato to String Theory and Beyond*(Viking Penguin, 2005) - Lang, Kenneth R.
*The Cambridge Guide to the Solar System*(Cambridge University Press, 2011). - Lawden, D. F.
*Introduction to Tensor Calculus, Relativity and Cosmology.* - Lay, David C.
*Linear Algebra and its Applications*, third edition. Boston: Pearson Education, 2006. - Lindley, David.
*Uncertainty: Einstein, Heisenberg, Bohr, and the Struggle for the Soul of Science.*New York: Doubleday, 2007. - Lewin, Walter.
*For the Love of Physics: From the End of the Rainbow to the Edge of Time - A Journey Through the Wonders of Physics.*Free Press, 2012*.*

- Mazur, Joseph.
*The Motion Paradox.*New York: Dutton, 2007. - Mermin, N. David.
*It's About Time: Understanding Einstein's Relativity*. Princeton: Princeton University Press, 2005. - Musser, George.
*Spooky Action at a Distance.*New York: Scientific American, 2015. - Neiwert, David.
*Of Orcas and Men*. New York: Overlook Press, 2015. - Ohanian, Hans.
*Einstein's Mistakes.*New York: W. W. Norton, 2008. - Orzel, Chad.
*A Brief History of Time-keeping.*Dallas: BenBella Books, 2022. - Orzel, Chad.
*Breakfast With Einstein*:*The Exotic Physics of Everyday Objects*. Dallas: BenBella Books, 2018. - Orzel, Chad.
*How to Teach Physics to Your Dog.*New York: Scribner, 2009. - Orzel, Chad.
*How to Teach Relativity to Your Dog.*New York: Basic Books, 2012. - O'Shea, Donal.
*The Poincare Conjecture: In Search of the Shape of the Universe*. New York: Walker & Company, 2007 - Penna, Michael A.; and Richard R. Patterson.
*Projective Geometry and its Applications to Computer Graphics.*Englewood Cliffs, NJ: Prentice-Hall, 1986. - Penrose, Roger.
*Cycles of Time: An Extraordinary New View of the Universe.*London: Vintage, 2011. - Penrose, Roger.
*The Road to Reality: A Complete Guide to the Laws of the Universe.*New York: Alfred A. Knopf, 2005. - Raymer, Michael G.
*Quantum Physics: What Everyone Needs to Know*.New York: Oxford University Press, 2017 - Resnick, Robert; and David Halliday.
*Basic Concepts in Relativity and Early Quantum Theory*(second edition). New York: John Wiley & Sons, 1985. - Robinson, Andrew. Einstein On The Run: How Britain Saved the World's Greatest Scientist. (Yale University Press, 2019)
- Rovelli, Carlo.
*The Order of Time.*New York: Riverhead Books, 2018.

- Schey, H. M.,
*Div grad curl and all that*(fourth edition). New York: W. W. Norton, 2005. - Schutz, Bernard.
*Gravity From the Ground Up.*New York: Cambridge University Press, 2003. - Seife, Charles.
*Decoding the Universe.*New York: Penguin Books, 2006.

- Smolin, Lee.
*Einstein's Unfinished Revolution: The Search for What Lies Beyond The Quantum*. New York: Penguin Press, 2019. - Smolin, Lee.
*The Trouble With Physics*. New York: Houghton Mifflin, 2006. - Smolin, Lee.
*Three Roads to Quantum Gravity.*New York: Basic Books, 2001. - Smolin, Lee.
*Time Reborn: From the Crisis in Physics to the Future of the Universe.*New York: Houghton Mifflin Harcourt, 2013. - Steane, Andrew M.
*Relativity Made Relatively Easy.*Oxford: Oxford University Press, 2012. - Stoppard, Tom.
*Arcadia.*Faber and Faber, 1993. - Stoppard, Tom.
*Rosencrantz and Guildenstern Are Dead.*Grove Press, 2007.

- Susskind, Leonard and George Hrabovsky.
*The Theoretical Minimum: What You Need to Know to Start Doing Physics.*New York: Basic Books, 2013. - Susskind, Leonard; and Art Friedman.
*Quantum Mechanics: The Theoretical Minimum.*New York: Basic Books, 2014. - Von Baeyer, Hans Christian.
*Maxwell's Demon: Why Warmth Disperses and Time Passes.*Random House, 1999.

- Wheeler, John Archibald.
*A Journey Into Gravity and Spacetime.*New York: Scientific American Library, 1990. - Woit, Peter.
*Not Even Wrong: the Failure of String Theory and the Search for Unity in Physical Law*New York: Basic Books, 2006. - Wolfram, Stephen.
*A New Kind of Science.*Wolfram Media, 2002. - Wolfson, Richard.
*Simply Einstein: Relativity Demystified*. W. W. Norton, 2003. - Wolfson, Richard; and Jay M. Pasachoff.
*Physics for Scientists and Engineers*(third edition). Reading, MA: Addison-Wesley, 1999.

- de Broglie, Louis-Victor. "On the Theory of Quanta." 1924. https://fondationlouisdebroglie.org/LDB-oeuvres/De_Broglie_Kracklauer.pdf
- Einstein, Albert. "On the Electrodynamics of Moving Bodies." 1905. https://www.physics.umd.edu/courses/Phys606/spring_2011/einstein_electrodynamics_of_moving_bodies.pdf
- Riemann, Bernhard. "On the Hypotheses Which Lie at the Bases of Geometry." https://www.emis.de/classics/Riemann/WKCGeom.pdf

- Bayley, Melanie. "Alice's adventures in algebra: Wonderland solved" https://www.newscientist.com/article/mg20427391-600-alices-adventures-in-algebra-wonderland-solved/
- Garret, Ron. "Quantum Mysteries Disentangled" https://flownet.com/ron/QM.pdf See also https://www.youtube.com/watch?v=dEaecUuEqfc
- Honner, Patrick. "The (Imaginary) Numbers at the Edge of Reality" https://www.quantamagazine.org/the-imaginary-numbers-at-the-edge-of-reality-20181025/
- Orzel, Chad. "How Do You Create Quantum Entanglement?" https://www.forbes.com/sites/chadorzel/2017/02/28/how-do-you-create-quantum-entanglement/
- Russ, Kelley. "The Ontology and Cosmology of Non-Euclidean Geometry" http://www.friesian.com/curved-1.htm
- Siegel, Ethan. "Are we approaching gravity all wrong?" https://bigthink.com/starts-with-a-bang/are-we-approaching-quantum-gravity-all-wrong/
- Siegel, Ethan. "Does Time Really Exist?" https://bigthink.com/starts-with-a-bang/does-time-exist-182965/
- Thomson, Jonny. "A brief history of (linear) time" https://bigthink.com/thinking/a-brief-history-of-linear-time/
- Wood, Charlie. "The Strange Numbers That Birthed Modern Algebra" https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/
- Wolchover, Natalie. "The Peculiar Math That Could Underlie the Laws of Nature" https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/

- 3blue1brown: Abstract vector spaces
- 3blue1brown: The determinant
- 3blue1brown: Differential equations, studying the unsolvable
- 3blue1brown: Divergence and curl: The language of Maxwell's equations, fluid flow, and more
- 3blue1brown: Dot products
- 3blue1brown: Euler's formula with introductory group theory
- 3blue1brown: Group theory, abstraction, and the 196,883-dimensional monster
- 3blue1brown: Inverse matrices, column space and null space
- 3blue1brown: Linear combinations, span, and basis vectors
- 3blue1brown: Linear transformations and matrices
- 3blue1brown: The more general uncertainty principle, regarding Fourier transforms
- Arvin Ash: Everything - Yes, Everything - is a SPRING! (Pretty much)
- Dialect: The meaning of the metric tensor
- DrPhysicsA: Special and General Relativity playlist
- DrPhysicsA: Quantum Mechanics playlist
- eigenchris: Tensors for Beginners playlist
- eigenchris: Tensor Calculus playlist
- eigenchris: Relativity playlist
- MinutePhysics: Bell's Theorem: The Quantum Venn Diagram Paradox
- MIT OpenCourseWare Physics 8.01 (Physics I): Classical Mechanics
- MIT OpenCourseWare Physics 8.02 (Physics II): Electricity and Magnetism
- MIT OpenCourseWare Physics 8.03 (Physics III): Vibrations and Waves
- MIT OpenCourseWare Physics 8.04 (Quantum Physics I)
- MIT OpenCourseWare Physics 8.05 (Quantum Physics II)
- MIT OpenCourseWare: Physics 8.224 Exploring Black Holes
- Physics with Elliot: To Understand the Fourier Transform, Start From Quantum Mechanics
- The Science Asylum: Circuit Energy doesn't FLOW the way you THINK!
- The Science Asylum: Photons, Entanglement, and the Quantum Eraser

- The Science Asylum: The True Meaning of Schrödinger's Equation
- Veritasium: The Big Misconception About Electricity
- Veritasium: How Imaginary Numbers Were Invented

Kent Heiner lives in northwest Washington state. He studied math, physics
and computer science at Western Washington University and has an
undergraduate degree in international relations from Brigham Young
University. He is also the author of *Without Smoking Gun:
Investigating the Death of LCDR William B. Pitzer *(TrineDay,
2004). He recently concluded a twenty-year career as a database
administrator in the insurance and telecommunications industries and will
be looking for something different after the completion of this book. Kent
maintains a website at www.monstro.us
and welcomes your feedback. If you find some value in this book, you can
make a donation at ko-fi.com/heiner.

"The long-awaited completion of the *Hamlet *trilogy which also
manages somehow to incorporate a natural completion of the story arc begun
in *Alice's Adventure in Wonderland*. A must-read for lovers of
any kind of book whatsoever." — No one, ever. Or Henri Poincaré,
eventually?

"Pundits and gurus outgrowing their britches? Reductive satire that keeps
you in stitches." — Maria von T.