Cosmological Koans

Cosmological Koans by Anthony Aguirre

A brief summary

Part 1

The Path Laid Out before Us

1: The Arrow

How does the arrow move? What is the relationship between time and motion? Is there such a thing as the present moment?

2: Setting Sail

All motion is relative. Being at rest is the same as moving at the same speed as one’s surroundings. What are inertia and acceleration?

3: Being Time

If motion is relative, is time also? Why is the past so different from the future? Is the future already laid out, just inaccessible to us, or can we choose our future?

4: The Tower

Gravity: the only “force” that acts on objects independently of their mass or what they are made of. How?

5: A Perfect Map

You cannot make a truly accurate map of the spherical surface of the Earth on a two-dimensional page. We can get close by dividing up the map into smaller areas, each with a different scale. What is “straight”? What is “curved”?

6: The Cosmic Now

Though it seems reasonable that there are billions of events happening right now, there can be no universal “now.”

7: Drifting Dreams of Venice

There can be no universal time because time flows differently depending on our reference frame (it is relative). Like our map divided up into small sections, each frame has its own timescale. And so on the scale of the universe, we cannot measure time among different reference frames!

8: Choose Your Path

Compex math shows that there is a way to define relations between inertial frames. One conclusion of this is that particles always take the path that maximizes its “action” (actually the longest space-time path between two events). This is like saying that you somehow always choose the most efficient path down the mountain? How?

9: Taking the Leap

What looks like a curved path (due to gravity) should actually be considered straight. Gravity curves the fabric of space-time. So a curved line relative to a flat surface may actually be a straight line in curved space! This is Einstein’s general theory of relativity.

Part 2

An Uncertain Trail through Treacherous Terrain

10: Releasing the Djinn

Early 20th c. physicists had a worldview based on just three things: space-time, particles, and fields. Knowing information about these allows you to basically predict the future, like when the next eclipse will be: scientific determinism. Scientific determinism (Newton, Einstein) claims that the future is determined, and there is no real difference between past and future.

11: Many Paths Make the Road

Enter quantum mechanics. If you follow all paths equally, you end up just following a single path: the one true path.

12: Sufficient Reason for a Roll of the Dice

We need to understand quantum states, superpositions, Schrodingers’s equation, and probabilities for measurements. The point is that even if we know the initial conditions of a system, we cannot know its future with certainty. This seems to contradict the view of classical physics. This chapter also introduces the idea of quantum mechanics as information: asking and answering questions about a system. “A question cannot be answered until it is asked, and one asked, it cannot be unasked.”

13: Through the Gates

The strangeness of the double-slit experiment. Because there is interference, particles must take more than one path simultaneously. In reality, this is the same as saying they take all possible paths. 

14: Splitting the World 

Quantum states in superposition decohere upon observation. But how does a combination of possible outcomes turn into an actual outcome? The epistemic view says that the quantum state is a mathematical description of everything an observer can know about a system. After the measurement, all the probability shifts to the observed outcome. The ontic view holds that the wavefunction is reality, and that all possible outcomes do indeed happen, splitting the world into many worlds.

15: What Cannot Be Known

In classical physics, we can know nothing outside our past light cone. In quantum physics, we cannot know some detail if we know another. In sum, everything being entangled with everything else, we can never truly isolate a system, and so some knowledge is always uncertain. “The cost of isolation is ignorance.”

16: What We Talk About When We Talk About Free Will

Relativity and quantum mechanics seem to say that we cannot know everything, and thus cannot perfectly predict the future. But can we know enough to predict most things?

17: The Mind of Ming

“The empire is wise, even if the emperor is not.” The human mind is incredibly complex. How does the objective physical system of the brain connect to our experience of the mental processes? Does the mind function as a computational device? A multi-layered collection of integrated systems? If so, can we potentially understand the reasons for all our choices?

18: A Halting Problem

Hmm. Perhaps the real question is not whether we make choices or not, but simply whether we (or anything else) can predict the outcome. Perhaps building a simulation of our thinking would always be less efficient than the thinking itself, and so always unable to perfectly predict our choices?

Part 3

Torn Apart and Reassembled

19: Instructions from the Cook

Entropy inside a closed system will always increase, giving more disorder. But entropy can decrease (temporarily) if we appeal to a larger system. 

20: Nothing Is Lost

Another definition of entropy involves probabilities. Entropy is maximized when all probabilities are equal, and minimized when all of the probability is accorded to a single state. Maybe we call this randomness instead of disorder. Less randomness equals more information. This is hard to follow, but seems to suggest that “the second law of thermodynamics points to a loss of macroscopic order, even while microscopic information is preserved by a closed system.” “Perhaps nothing is lost, but everything is hidden,”

21: Being and Knowingness

Are probabilities properties of the world, or of our understanding of the world? Objective or subjective? How important is measurement in determining knowledge? 

22: Each Morning Is the Universe

Why does order exist? Let’s define information as the difference between actual randomness and the maximal possible randomness of a system. We can then talk about information being preserved at the micro level while disorder increases at the macro level. Then how does information or order get created? We can put the system inside a larger ordered system. “Millions of terabytes of information are created in a burrito if it is put in the freezer.” We can also create order by increasing a system’s state-space (and thus its maximum randomness or disorder). Finally, we can create order by measuring a system and collapsing its probabilities (whoa). “Then are we part of the information that the universe has, or is the universe made out of the information that we have?

23: Wandering in the Desert

“Equilibrium (maximal disorder) can be a state of enormous hidden information or a state of entirely absent information, with pretty much nothing to distinguish the two.”

24: A Hundred Thousand Million Kalpas

In a closed system, over infinite time, everything will happen, over and over. How many times have you been here?

25: Mountains and Mist

How to combine classical mechanics and quantum mechanics? Something about mass? Higher mass equals more interference, equals reduced probabilities? Most paths cancel each other out, leaving just one?

26: Hazy Bifurcations in Decohered Histories

If we look to the past, can we determine how we got here? Can we see where all the possible paths decohered into the real ones?

Part 4

Lofty Peaks with Endless Views

27: Beneath the Firmament

Is the Universe fixed or expanding? Eternal or finite? Physics dictates that an eternally expanding universe (with constant creation of matter and energy) is mathematically identical to a steady state universe.

28: Celestial Spheres

We might imagine that the world we observe is created of nested spheres (successively more distant and old). So, as we look out, the spheres get bigger. But as of 9.6 billion years ago, they get smaller, because the universe is shrinking (expansion in reverse). What? This is hard to comprehend. Also, the fabric of space-time seems flat, which may be due to rapid expansion in the early universe, akin to pulling a sheet tight, suppressing any wrinkles.

29: Through the Looking Glass

We inhabit a middle ground in terms of size. Big enough for complexity, small enough to live on a planet. This is due to certain cosmic values. Any smaller and we could not be complex enough for thought. Too big and signals would take too long to travail, thus limiting thought.

30: Theodicy

Are we lucky to exist? True, the constants of nature have just the right values to allow our existence. There are really just a few options: we got really lucky; someone designed the universe this way; or the universe has begun many times, eventually landing on our lucky number.

31: The Floating Gardens

Might our universe be one of many expanding regions separated by inflationary areas? Part of a huge tapestry of an infinite variety of worlds?

32: The Painting in the Cave

If only quantum mechanics, general relativity, and inflation are true, there could be a multiverse of universes with different properties.

33: A Dialogue Concerning Infinitely Many Things

What is infinity? Can two infinite sets be of different sizes? Though each universe in the multiverse would look finite from the outside, from the inside it is infinite, because expanding (faster than light?)

34: Sickness unto Death

Buddha: Attaining a human birth is like a turtle coming up for air once every 100 years and just happening to get caught in a yoke with a single hole. Is that like us, our universe? When we awaken in this world, how can we statistically evaluate our chances of being here? How much of all this depends on us? “Does the universe make you, or do you make the universe?”

35: An Honored Guest

Though in some ways or existence is meaningless, in other ways we are quite rare and special. Do only universes with sentient life “matter”? If observers matter, are universes without observers real?

Part 5

Who Am I? Don’t Know!

36: Who Sleeps, Perchance to Dream?

What are we? If we are simply constructed out of matter, how can we be aware and free? If we are more than matter, what is it? Who is the “I” that asks these questions?

37: A Simple Arrangement of Some Bits

Could we duplicate a human, like a Star Trek transporter? The amount of information it would require (if we consider quantum states) would not fit into the observable universe.

38: What Survives

Perhaps nature duplicates us itself, every time reality splits according to a quantum observation?

39: The Ice Garden

Does the universe really evolve, or is it frozen? Block or river? Who observes the whole universe? No one. “Many parts of the Universe, ineffable in its totality, describe many other parts with as much care, detail, and understanding as they can manage…The Universe is alive at the tips (at one of which you sit, reading and considering), solid where it has grown into an ancient tree. Brimming with potential toward the future.”

40: An Unfettered Mind

Andy Clark in “The Extended Mind,” suggests that our minds extend outside ourselves, and actually encompass everything. Intelligence is a process extended in time and space.

41: The Simulation Argument

How can we be sure this is not a simulation? Well, it seems as if creating a simulation of the human brain would be nearly impossible, especially given the randomness and chaotic nature of the mind’s construction.

42: Time and Free Will

Everything we have seen so far points to a world of uncertainty and thus freedom, in particular because when you try to isolate a system, you introduce uncertainty, because its entanglements extend out into the universe. So perhaps the quantum state of the universe as a whole is determined, but a thing, history, or mind is not?

43: An Arc of Recohering Trajectories

(suggestion that various times and places — and maybe realities — are entangled)

Part 6

Form Is Emptiness; Emptiness Is Form

44: What Is It Your Sail In?

Form (or information) is much more meaningful than the matter that embodies it. So everything is form? What about quarks or electrons? What are they made of? Even the electron is really a pattern, an answer to our questions, a form. Things are forms of forms of forms of…order? Defined by us?

45: The Clear Blue Sky

How might we think of some knowledge as invented, other knowledge as discovered? What actually exists? This is a more difficult question than it would seem. In some sense, both an atom and a theorem are made of information. Does anything exist fundamentally, for sure, eternally? Matter? Rules? Math?

46: At the Foundation

What is the foundation of the world? Atoms? Basic constants? But even they depend in some way on other conditions.

47: The Great Inheritance

We know more about the world around us than we think. This implicit information allows us to estimate probabilities with a high degree of accuracy. This information exists thanks to the high energy conditions of the early universe. And the growth of disorder provides the arrow of time. And these conditions have allowed our intellectual and emotional awareness to develop, which is our most precious gift.

48: A Long Hidden Game

Is the world made up of answers to questions? Anything can “ask” a question by interacting with another system, thereby getting an answer but also co-creating that answer. “We can thus imagine a sort of hierarchical structure in which things ask questions of smaller/more quantum things and, in doing so, create information and also shape the world via the choice of questions asked.” Through this, information and order are generated. So perhaps complex systems like us can best be defined as infinite loops of questions and answers. Perhaps the best we can do is craft ever more complex and accurate predictions about the world, while never being able to know for sure the underlying foundation truths (if they exist). 

49: The Mind-Only School

For is emptiness (nothing is real without a mind to know it). But emptiness is also form (we create very real things out of ideas). Objectivity is real to a degree, but not fully. Subjectivity is also problematic, as the “I” is quite illusory. Perhaps these are ends of a continuum, with most of reality existing in between, in a matrix of relativity. 

50: East and West

We have worked through many unresolved dichotomies in this book. The lesson is that there are no easy answers, and many questions. We can relish in the delight at being able to contemplate them.

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