This is a curated list of books that I recommend to people coming from computer science, engineering or other quantitative backgrounds and looking to deepen their understanding of some important themes of knowledge.
I’ve organized the list using a bottom-up approach, starting with what I consider are building blocks (Themes 1-5) for thinking about more complex questions (Themes 6-10).
Under each theme I’ve used a double asterisk (**) to mark books which I think are absolute must-reads. Items marked with a single asterisk (*) I thought were interesting and/or important and those unmarked I thought were less important and therefore only recommend as supplementary (this is all very subjective, naturally).
I’ve found that many weak positions and widespread misconceptions about some of the big questions (Themes 6-10) are deeply rooted in a poor understanding of some fundamentals (Themes 1-5). I therefore recommend getting on top of the first half of these themes before venturing to the second.
The acute reader, having read the previous two posts in this series, must now be cautious about applying intuitive reasoning when thinking about the universe. I have given two examples of how intuition might fool us into treating the universe as a physical system and assuming that it has a beginning or that there could be something outside it.
In this post, I will attempt to crack another intuitive nut.
There are probably no concepts that we find easier to grasp than causality. An infant does not need to understand what causality is or be told that the universe is causal before crying for its mother’s attention. The assumption of a causal universe is made apriori, not just by human infants or by conscious beings but by all physical systems in existence.
Causality can be informally described as an implication relationship between two events in time. If the cause happens at a point in time then the effect happens at a later point. For example, if I press a light switch then the light bulb connected to it will turn on in a non-zero amount of time later. In this case, pressing the switch can be called the cause and the turning on of the light bulb the associated effect.
I will now bring back the snapshot notation that I used to examine the nature of time in the previous post. Here, I will use it to describe what causation really means.
For my light bulb example, I can capture the two universe state snapshots that contain pressing the switch (the cause event) and the turning on of the light bulb (the effect event). Causation can be described by saying that if the cause event happens at a snapshot k1 then the laws of physics mandate the occurrence of the effect event in a subsequent snapshot k2. The timing relationships between k1 and k2 and other specifics including whether the universe is truly deterministic or inherently stochastic do not concern us here. What is important to understand is that causality is a relationship between two universe state snapshots where the one containing the cause predates the one containing the effect.
You may already be seeing where am going with this. I am now going to spell out the argument starting with the conclusion of the previous post as a premise. There are no universe state snapshots that predate the big bang. In consequence, the big bang is not the effect of any cause!
But surely all events have causes and if you follow events back in time there are always “initial causes” that predate all chains of cause and effect, can’t it be the same for the universe?
If you’ve read the previous two posts then you may have a hunch at what the answer to this question might be. Perhaps the following figure will be of help …
This question commits the same intuitive mistake of treating the universe as a physical object within a universe. We have defined causation as a relationship between the contents of two universe state snapshots. To ask what causes snapshots themselves (the universe) to come into existence is to assume the existence of a container space-time in a master universe in which this form of hyper-causation can be defined. As I’ve already explained in the previous post, this gets us nowhere because it doesn’t solve the problem but shifts it elsewhere.
In conclusion, the phrase “the cause of the big bang” is actually no different from the phrases “before the big bang” and “outside the universe”. All three are meaningless concoctions that confuse the universe for a physical object that occupies a region of space-time and whose existence is attributed to other events in prior moments of its parent universe.6 Comments
In the previous part of this series I have argued that since the universe is, by definition, the entirety of space and time then phrases like “outside the universe” carry no useful meaning. In this post I will examine a similar question that is also brought up during ontological discussions.
Our daily lives are filled with processes that have temporal beginnings and ends. My morning journey to work, for instance, starts and ends at specific times which can be measured by specialized equipment such as clocks. If I leave to work at 8:00 AM and arrive at 8:30 AM then the temporal progression of my journey can be represented as a series of universe state “snapshots” that are taken at intermediate times between my departure to work and my arrival there.
Each snapshot of the universe state contains the states of all the physical systems in the universe at that moment. Any interesting state of a given system (for example, me walking though the door of my workplace) can be called an “event” and can be “timed”. What we really mean by “timing” an event is that we specify the state of another physical system, typically a clock, in the same snapshot to which the event belongs. In other words, if I say that I enter work at 8:30 AM then this is really saying “the event of me entering work is contained within the same universe snapshot in which my watch points to 8:30 AM”.
Events, therefore, can be timed only by referring to other events within the same universe state. It is tempting to consider whether there are alternative ways of timing events that do not involve referring to the state of other physical systems within the universe. This temptation is perhaps driven by the intuitive notion that time “keeps going” whether you’re looking at your watch or not. What this intuitive thought portrays is something like the following:
Here, our intuition is leading us to believe that our universe exists within a snapshot of a master universe which has its own time frame. Looks familiar? this is actually the same mistaken notion we encountered in the previous post where our space was depicted as expanding into a container space. In this case, we’re supposing a “container time” to which we can tie events in our universe. This container time is encoded within a snapshot of the master universe in which our universe supposedly exists.
Of course it is logically possible that such is indeed the case. For example, assume that I run a simulation of a hypothetical universe in which a single universe state is represented by 1KB of memory. I can pick an initial state, formulate a set of physical laws of my choosing and compute the first 10^6 states of this universe. Putting aside the fact that phenomena like life and intelligence will probably require much more memory to encode, lets assume that intelligent beings emerge during this simulation and start pondering about the nature of time in their universe. They may postulate that their entire timeline is part of a snapshot of a master universe in which their own universe is realized. In this case their assumption will be correct; their entire timeline is indeed represented by 1GB of RAM in one snapshot of a master universe … ours!
This is a very amusing scenario which virtual reality enthusiasts might find particularly appealing. Alas it doesn’t actually help us in establishing an external time reference for our universe because it only shifts the problem to finding an external time reference for the master universe (see Begging the Question).
We are now in a position where we are ready to answer the question “what happened before the big bang?”. To do this we can use our universe-slicing-into-snapshots technique to look at the snapshots predating the big bang and examine their contents. As soon as we slice up the timeline of our universe, a complex problem comes to our attention …
The big bang snapshot is the first in the series!
How can this be? Well, the big bang is defined as the first moment in our timeline and so prior snapshots cannot exist by definition.
If your intuition is still trying to push you to speculate prior-bang moments then this is a good time to take a break. Speculating the existence of prior-bang universe snapshots requires the existence of an external time reference in a master universe which, as we explained previously, doesn’t solve the problem but moves it to another location.
But what if the first snapshot was “hanging there” for sometime before the big bang occurred? For example if the first snapshot was t=0, the second t=1 seconds and so on then couldn’t the first snapshot (the initial state of the universe) have existed from t=-infinity up to t=0 at which time the big bang occurred? If you think about this line of reasoning carefully then you may notice that it falls victim to the same mistake of assuming an external time reference according to which these snapshots are timed. In reality, time measurement, beginnings and ends are notions that exist only within the snapshots and not outside them.
We can now state our conclusion. The phrase “before the big bang” does not refer to anything meaningful and is devoid of meaning just as its sister “outside the universe” and other similar intuition traps.
When we say “everything has a beginning” we should pay careful attention not to include time as a “thing”. The statement is better stated as “the beginning of every physical process can be specified by stating the corresponding state of a clocking device in the same universe state snapshot”. Time, however, is not a physical process and has no beginning.No Comments
The universe is not just the entirety of matter and energy. It is also the entirety of space and time themselves. In this post series I will try to examine some conclusions that follow from this simple definition and point out few intuitive but mistaken notions that are often used in discussions involving the nature of existence (Ontology).
According to the big bang theory, the universe started as an infinitesimal and unimaginably-dense collection of hot matter. This collection (the matter content of the universe) has since been expanding, cooling down and forming all the familiar objects we see in existence today. This includes all galaxies, stars, planets, buildings, cars and humans. When we first learned about the big bang, and perhaps even today when we think about it, we probably picture it as an expanding object, much like a balloon being inflated by blowing air into it.
This is a useful analogy as it allows us to make sense of why things in the universe get further apart with time. Galaxies can be pictured as dots lying on the surface of the balloon and moving away from each other as the balloon gets bigger. However, there is a hidden intuitive pitfall within this analogy; the balloon is a physical object which is expanding to occupy more space while, in the case of the universe, it is space itself which is expanding!
Confusing the two leads to several interesting reasoning errors, most notably asking the question: what lies outside the universe? Here the question assumes the existence of a “container space” inside which the space of our universe exists.
This assumption contradicts our definition of the universe as the entirety of space and is therefore invalid. The universe is all of space and no more space exists “outside” or “elsewhere”.
The question “what lies outside the universe?” is a loaded question (see Complex Question Fallacy) in which the assumption of a container space is implicitly made. To answer this with “something”, “nothing”, “possibly something or nothing”, or “I don’t know” is to be wrong in all cases. The correct answer is that the phrase “outside the universe” does not refer to anything meaningful. Such is the case with all phrases that attempt to apply spatial adjectives and relationships to the universe as a whole (including “inside the universe”, “bigger than the universe” and the more common “beyond the universe”).
This makes sense logically but is very counter-intuitive. For instance, what happens if I travel to the boundary of the universe and try to stick my hand “out”? Will the atoms of my hand “be lost into the void” or will they hit an invisible wall onto which is inscribed “Boundary of the Universe – No matter shall pass”?
Several theoretical models of space give answers to the above, none of which makes intuitive sense. For example, one model predicts that travelling long enough in any direction will get you back to the same point (making the universe one big pac-man game!). The fact that our intuition fails to grasp explanations of this sort (even after being proven by formal reasoning) is no wonder: our brains did not evolve in environments in which solving problems concerning the nature of space was necessary for our survival.
In the following parts of this series I will describe two more intuitive traps that await the unwary when reasoning informally about the universe.5 Comments