in heaven we will drink liquid helium

Reflections on A Course in Miracles

I first became aware of A Course in Miracles (ACIM) via Wikipedia1.

While I have not read the work, I am aware of its general nature. It was “scribed” by Helen Schucman between 1965 and 1972. Due to what I can only assume is divine inspiration, the book was initially published in such a way that the work was subject to a legal dispute regarding copyright; as a result it entered the public domain in 2004.

This is a course in miracles. It is a required course. Only the time you take it is voluntary. Free will does not mean that you can establish the curriculum. It means only that you can elect what you want to take at a given time. The course does not aim at teaching the meaning of love, for that is beyond what can be taught. It does aim, however, at removing the blocks to the awareness of love's presence, which is your natural inheritance. The opposite of love is fear, but what is all-encompassing can have no opposite.

This course can therefore be summed up very simply in this way:
* Nothing real can be threatened.
* Nothing unreal exists.
Herein lies the peace of God (full text)

The most prominent practitioner of ACIM today is Marianne Williamson. Williamson wrote the book A Return to Love, which was featured on the Oprah Winfrey show in 1992. Its most famous quote is "Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure.” While Williamson’s presidential campaign explicitly avoided talk of ACIM, Williamson is once again preaching at her Substack.

What is a Miracle?

The terms “miracle” and “love” both have non-standard definitions in ACIM. In general, the use of religious metaphors is both confusing and disconcerting to many potential readers.

I would try to translate “love” as “mana” (or, if you want to go down the rabbit-hole, Independence Compensation), and “miracle” as “synchronicity”.

A longer, slightly different (and more accurate) definition of “miracle” as “achieving that which you thought was impossible”. You thought was impossible. Miracles do not accomplish impossible things. The things they accomplish may seem impossible even after they are done, but they were not.

And synchronicities do seem impossible. Carl Jung talked extensively about synchronicities, but it is difficult to come up with any definition that fits within traditional space-time.

A History of Space-Time

The ancients had a simple model of the world: it is “flat” and things fall down. Even dogs and horses understand this basic model.

Later it was discovered that the Earth is not flat, but a sphere. Things still fall down. The heavens are either a fixed sphere surrounding the Earth, or are made of objects in orbit. I am not sure if Archimedes or Ptolemy knew about orbits, but they surely could have figured it out with the right questions.

Today, that basic model still holds. The Earth orbits the Sun, and the Sun orbits Sagitarrius A*, and the various galaxies are flying away from each other for reasons that even scientists struggle to explain2. Of course the orbits are approximations; with there being so many bodies involved even a closed-form solution would be impractical to calculate.

Yet this model does not explain Special Relativity, General Relativity, or Quantum Mechanics.

Relativity is fairly easy to add to the basic model. Just as the surface of the earth isn’t flat in 2 dimensions, the universe isn’t flat in 3+1 dimensions. You have to travel faster to notice. If we could all fly as fast as Superman, nobody could pretend the earth is flat. And if we all had 1-g acceleration spaceships, nobody could pretend the universe is flat. As it is, you will have to trust the scientists3 (and the fact that GPS works).

Quantum Mechanics is the set of disturbing conclusions of the fact that the universe is quantized. The word “quantum”, formally, means, “the minimum amount of an entity”. Light is quantized into photons. Matter is quantized into atoms. Atoms are made of nuclei and electrons; those electrons are extremely useful for providing electricity. Nuclei are made of protons and neutrons; each different type of atom has a different nucleus.

Those protons and neutrons emit radiation when they collide with each other. If you study quarks, you can get an excellent model of what radiation will be detected when they collide. Even helium (alpha particles) demonstrates some of this behavior. Some of you will be familiar with the strange properties of liquid helium. And, because of the uncertainty principle4, collisions between alpha particles work differently than collisions between larger atoms.


It is said that William Rowan Hamilton discovered quaternions “in a stroke of genius” while crossing Broom Bridge in Dublin. Much like Archimedes screaming “Eureka” in a bathtub, I suspect the tale has been embellished in some ways.

There are (at least) two ways of defining the quaternions. One way is to use the Cayley-Dickson construction. The other is more explicit, and defines i, j, k via i^2 = j^2 = k^2 = ijk = -1 . Multiplication is not commutative; ij = k but ji = -k.

To a certain extent, quaternions are an extension of the complex numbers. In other words, it may be difficult to distinguish between a system on the complex numbers, and a system on the quaternions restricted to the complex numbers “almost everywhere”.

To a certain extent, complex numbers are an extension of the real numbers. In other words, it may be difficult to distinguish between a system on the real numbers, and a system on the complex numbers restricted to the real numbers “almost everywhere”.

To a certain extent, real numbers are an extension of the positive rationals. In other words, it may be difficult to distinguish between a system on the positive rationals, and a system on the real numbers restricted to the positive rationals “almost everywhere”.

And, in quantum mechanics, we do see probabilities that are negative or imaginary. We generally do not see quaternions. My speculation is to hand-wave and blame the uncertainty principle. Quaternions allow too much; the convenient properties of single-variable complex functions do not hold. So they only exist in limited areas, mostly hidden behind the uncertainty principle. This is, roughly, a hidden variable + FTL communication theory of the Bell test5.

Indistinguishable from Magic

I must assume the average reader is completely befuddled at this point; presented with walls of text about maths and physics ta does not understand, and confused about what this has to do with miracles or anything else.

Well, our initial goal must still to be to “define” miracle as used in ACIM. Or to “translate” it into common English. And to do so without changing the meaning; what does [{Hamiltonian}] refer to? What does “awareness” mean?

If one does not understand the fundamental nature of reality, “miracles” are indistinguishable from magic.


In particular, the third and fourth Articles for Deletion discussions regarding Gary Renard, author of a book related to ACIM called The Disappearance of the Universe.


A conversation from a cocktail party:

S: I’m an astro-physicist.

R: I’m a biologist. What type of research are you doing?

S: I’m studying the development of galaxies. First, do you know what dark matter is?

R: Do you know what dark matter is?


For details, check the history at International Atomic Time. The first definition of TAI did not account for differing gravitational time dilation at different altitudes.


It is a gross simplification to say it is specifically “because of the uncertainty principle”. If you know enough quantum mechanics to understand why, you can probably skip this blog post entirely.


For details on the Bell test, read Scott Aaronson's blog and not Wikipedia.