# Interstellar: The Greatest Movie That Never Was

For the first time since 2014, I watched Christopher Nolan’s Interstellar. I liked this film the first time I saw it. The visuals are breathtaking, the science is accurate, and the acting is exceptional. I would expect nothing less of a Nolan film, but I was left somewhat underwhelmed, and it seems I was not the only one. Before its release, one could not help but hope Interstellar might make a run for the title of best space film ever made, knocking Stanley Kubrick’s 1968 masterpiece 2001: A Space Oddysey off its throne. The comparison was an obvious one to make, even if the two films differ in significant ways. For instance, Kubrick prefers the long shot, whereas Nolan rarely lets the viewer ponder something for more than a minute. Instead, I was all but fuming when confronted by a poorly contrived theme that the power of love is a physical thing, which transcends all else.

It is hard to argue Nolan is not one of the best directors working today. I think he may be one of the best of all time. While Interstellar is by no means a bad film, it falls short of Nolan’s seminal works: Memento, The Prestige, The Dark Knight, and Inception. I wanted, perhaps even expected, Nolan to continue to innovate, pushing the limits of film in new and unexpected ways. The real disappointment is that Nolan did innovate with Interstellar, and it still fell short. I enjoyed watching Interstellar more the second time around than the first. I have also come to think not only that Interstellar should have taken 2001‘s throne. More than that, I think Interstellar should have taken aim at best film of all time, or at least the best of an era.

To make myself clear, let me say that Interstellar really is a good film. (The ratings of 7/10 to 9/10 seem fair to me; I would probably give it an 8/10 or 8.5/10.) The beauty of the work cannot be understated. Hans Zimmer’s score is predictably exceptional, and van Hoytema’s masterful use of 70 mm film combines with the natural wonder of nature as understood by Kip Thorne for astounding cinematography, including some of the best visual effects ever rendered on the big screen. The film’s primary conflict is based in reality, but it manages to feel fresh, because Michael Caine’s character correctly sees the situation on Earth as hopeless. Instead of saving the planet, we leave it. Nolan’s classic style is evident, and the production value is high. There is no shortage of rich idea even if they are more scientific and less philosophical than those found in The Prestige or Inception. The science is even relatively well explained, and most of the time the viewer is treated as a reasonably intelligent adult. The problem is really the script. The rest of the film is exceedingly well, near perfect in some parts. Some rewriting of the love story and the Dr. Mann episode would do wonders for this film. Even if the rewrite was nothing extraordinary – included no twists, no heady ideas, just made sense – it would be blatantly superior to the original. Slight dialogue changes would also be nice. Given slightly better lines, McConaughey could have really shined and Hathaway could have avoided her laughable moments.

Many people seem to think critics’ complaints about the connection between Cooper and Murph miss the point or disregard the power of emotion. Emotion certainly has a place in Interstellar, as does Cooper and Murph’s relationship. The problem is in the execution. Anything love might have added to the film was lost when it was decided that emotional connection would physically manifest itself. That’s just cheesy. Love could have played a key role in the plot while avoiding this problem. But when love guides you through a five dimensional tesseract to save your planet by connecting with your child, you are a lazy writer.

I really like Interstellar. I absolutely love what it could have been.

# A Circle is an O is a 0

Recently, I was speaking with my brother while he played a video game. At some point, he wanted me to do something, and eventually I asked him for the button combination to perform a task. In the middle of this sequence, he called the circle button “zero,” to which I invariably pointed out that the button was not zero but circle. Clearly, I meant nothing of this and was simply poking fun at him, but, much to my surprise, he claimed the two were one in the same. Moreover, he claimed a circle is a zero is an o.

To this I quickly responded with “Can you add a circle and an o? Do they represent quantities?” At this point, I am quite sure my brother realized his fault and simply sought some banter. So, he replied saying you could, because if you write that down, you see it is just 0+0=0. We continued for a while in this manner. I defined the three entities: a circle being the curve formed by connecting the locus of all points equidistant from a center, a 0 being the magnitude of the empty set, and an o being the 15th letter in the English alphabet which has certain properties. Moreover, I said that based on these definitions it is clear that the three are distinct, despite the fact that their symbolic representations are similar if not the same. Then my brother surprised me again by asking somewhat incredulously “Aren’t those [the representation and the object] the same thing?”

I am not the first person to be amazed by how important representations can be, nor am I the first person to realize many mistakenly conflate an entity with its representation. In René Magritte’s famous La trahison des images (The Treachery of Images), one sees a depiction of what could hardly be argued to be anything but a pipe, but below that are the words “Ceci n’est pas une pipe.” (For the anglophones out there, this reads “This is not a pipe.”)

Magritte’s own explanation is perhaps the most satisfying and succinct. He is quoted as having said the following:

The famous pipe. How people reproached me for it! And yet, could you stuff my pipe? No, it’s just a representation, is it not? So if I had written on my picture ‘This is a pipe’, I’d have been lying!

The distinction between a symbol and the thing it symbolizes is a relatively nuanced one. It requires abstract thinking, and it is often difficult to make when one is not actively considering this duality. Of course the discussion about this is much older than Magritte’s work. One can get quite technical with this in several ways; you can write long philosophical monographs, or you can rephrase this in terms of mathematics, and so forth, but I will not do that here.

In 1931, Alfred Korzybski used the phrase “the map is not the territory,” which was inspired by Eric Temple Bell’s epigram on the subject. And, this is the best way I know to summarize the matter, which is often referred to as the “map-territory relation.” While the map may be similar or dissimilar in many ways with the territory it seeks to represent, it will never, can never, and should never become synonymous with that territory. I can properly experience Marseille, France only by visiting, only then can I touch the monuments, interact with the people, and do all sorts of other things. No representation, no matter how elegant or seemingly perfect, could ever do that.

We should care about this because representations shape our worldview in more ways than we usually recognize. As an example, you may have heard something about different map projections and how cartographers need to make certain choices in making maps, choices which inevitably distort. It is impossible to make a map which preserves all features one would likely care about: relative size, distance, angles, shape, et cetera.

Here is another example: popularity is not an accurate representation of significance. This and related matters are something I have pondered a bit in the last few days after having re-read John Green’s wonderful The Fault in Our Stars. Many wish to die in heroic fashion, with hundreds of mourners, because this would give meaning to their life. They feel people must be extravagant to be important, but this is not the case, and John Green makes the argument in his novel far better than I ever could here, or anywhere else for that matter. Interestingly, this is not the only example of this in John Green’s work either, or even The Fault in Our Stars. A theme in that book that too few notice but that is incredibly important is that fiction is important. Green argues this point using meta-fiction, his author’s note, and other means.

These philosophical matters seem pointless to many, but I hope that the above has demonstrated that they are not.

# The Best Unlimited Free Cloud Storage Solution

Hive (the storage site) is actually pretty good, but there are some issues. Still, combining it with Mega for secure files and Drive for common use and quick access is a good free set up.

Hive provides free unlimited storage with a 50GB daily limit and up to 20GB file size, which should be sufficient. The ability for Hive to, if they wanted, screen or delete everything of your’s is less than ideal, as is its HQ being somewhat sketchy. But, it’s free of malware or anything else, so it’s still a good option for things you deem less sensitive, and it works nicely to share files with friend.

Hive also lacks folder uploads and desktop syncing, which is a huge bummer. It’s a bit of a clunky design all around.

Mega is one of the most secure free options around and still provides a solid 50GB of storage, which should be enough for anything you really don’t want to be seen by others. Drive is likely to always have your files and is a nice platform, which makes it nice for some things you either (a) could not lose or (b) use often. This is in contrast to Hive, where they could theoretically delete all your stuff at will; you should also avoid uploading illegal documents of any kind, as they could be screened and deleted. Drive should also have enough space for this sort of thing with 15GB free.

Now, it is true that getting, say, Mega Pro (I, II, or III) for up to 4TB of secure storage would be better, as would getting how ever much you need from Drive, which is still pretty secure and can be made more secure with good practices. However, you will be paying a premium for this, and not the nice kind where you give them your money and they shut up – no – this is the kind where you have to dish out the cash monthly, which can get uber-expensive.

# The Decline of Extensive Reading and Why It’s Worrying

Reading, long-form reading that goes beyond small articles or Facebook posts, is of incredible importance, and reading is in decline (see, among other studies and articles, Sharp Decline in Children Reading for Pleasure, Survey Finds).

Reading of the aforementioned kind allows for one to juggle many things in one’s head at the same time, analyze a text, learn substantial new things, and more. A good example of an advantage of reading is that of learning languages. Professor Dr. Alexander Arguelles discusses the current status of reading today as well as its relation to polyglottery and polyliteracy in this video.

The hard truth is that we as a society must continue reading books of substantial size, and children and adults alike are beginning not to read as such, for pleasure or otherwise. In fact, even when instructed to in school, children often do not read, commonly opting out for notes or some other alternative. Clearly, with the fairly recent introduction of other options – audio, video, the internet – reading is expected to decline, but with so many reading virtually nothing at all, we clearly have a problem, one we should probably address.

# What If Other Sports Adopted the WWE Strategy?

Many sports (oddly enough, sumo comes to mind) have within their leagues corruption and cheating, but unlike in sports such as football where throwing a game would be shocking, in popular wrestling – WWE and its predecessors, TNA, et cetera – such behavior is commonplace and fairly well known. Now, what if other sports were to adopt the WWE business plan, optimizing for entertainment value rather than actual sport?

Certainly, there are isolated examples of this, for instance the Harlem Globetrotters, but there are not – at least not to my knowledge as a sports fan(atic) – leagues of football, soccer, basketball, or baseball teams where the winner is decided a priori, where drama (i.e. performance, acting) plays a major role, or where play is maximized for “wow” moments.

Imagine now for an instant that such a thing were not purely hypothetical. What if we did have, say, World Baseball Entertainment (WBE)? What would it look like? How successful would it be? Would it be effective even if spectators knew it was all “fake”?*

In the case of baseball, I suppose pitching would be more or less gone from the game, unless the balls were not true baseballs, so that pitchers could throw with freakish action on their breaking ball and/or more speed. Moreover, home-runs, steals, inside the park home-runs, and diving catches (although, I am not sure how they would set up these) would feature prominently. But, for the game of baseball, would this not ruin everything?

At least for me, part of the fun of a perfect game or a steal or a home-run is that they are rare occurrences. One might even argue that a hit is rare, and in some games the same could be said of a strike.

But, then what makes this form of entertainment so specific to wrestling? I think it has to do with the lack of popularity of “real wrestling” among laypeople, particularly outside of the Olympics and local competition. It takes great amounts of popularity and time to have a game be such that one would actually care if “cheating” were introduced, and wrestling simply never gained the popularity, at least not in, for one, the United States.

Furthermore, it takes time and popularity to have a game reach the point where fans no longer accept change. Look at basketball or football or most other popular sports and you will notice that they have remained largely unchanged, at least in their basic premise, since they gained mass popularity. So, even if someone were to find a way to make the WBE a reality, it is unlikely to happen. People simply do not like change.

*Note: This is something I wonder even with wrestling. Is it more or less entertaining if you know it is fake? Having some actual experience in wrestling and martial arts as well as just plain old fighting, I could, as I think anyone should be able to, see through the WWE from a very young age. (My older brothers were fans.) Even the dramatic aspects seem blown out of proportion. I can’t see how anyone watches it most of the time; it seems to be the worst of the acting world mixed with the best of the wrestling world, just being done very poorly as to remove any reality.

# An Accessible Introduction to Sheaves

Below is reproduced a post that will be featured on the blog cozilikethinking at https://cozilikethinking.wordpress.com/ as a part of a series of posts on introductory algebraic geometry. This reproduction is partly for the sake of ensuring there are no $\LaTeX$ errors and partly because I would like to soon begin blogging again, for the first time here. The aforementioned blog, cozilikethinking, is run by Ayush Khaitan, who I have had great pleasure communicating with and who writes exceptionally about a wide variety of mathematical topics, which are typically within the realm of undergraduate interest. Without further ado, below is the post.

Let me just preface this by saying that I look forward to writing, in an accessible way, about the realm of algebraic geometry with Ayush on this blog.

In the study of algebraic geometry, one often hopes to delve into abstract notions, research tools, and topics such as those of cohomology, schemes, orbifolds, and stacks (or maybe you just want to prove that there are 27 lines on a cubic surface). But, all of these things probably seem very far away, because algebraic geometry is a very rich, very technical field. It is also one that was inaccessible to most until recently, despite often being concerned with rather simple ideas and objects. Luckily, today we all need not read the SGA and EGA. While I think it unwise to jump ahead to something as modern as schemes just yet, it should be possible to study one of algebraic geometry’s most important and deceivingly intuitive tools: sheaves.

In not-so-technical terms, a sheaf is a device used to track locally defined information attached to the open sets of some (topological) space. Basically, this is a nice tool to organize information. To get a bit more formal, we’ll need to first define what a presheaf is.

Presheaf: A presheaf $F$ on a topological space $X$ is a functor with values in some category $\mathbf{C}$ defined as follows:

• For each open set $U \subset X$, there is a corresponding object $F(U)$ in $\mathbf{C}$
• For each inclusion of sets $S \subseteq U$ there exists a corresponding morphism, called the restriction morphism, $\mathrm{res}_{S, U}: F(U) \to F(S)$ in $\mathbf{C}$
• $\mathrm{res}_{S, U}$ must satisfy the following:
• For all $U \subset X$, $\mathrm{res}_{U,U}:F(U) \to F(U)$ is the identity morphism on $F(U)$
• For open sets $S \subseteq T \subseteq U$, $\mathrm{res}_{S,T} \circ \mathrm{res}_{T,U} = \mathrm{res}_{S,U}$, i.e. restriction can be done all at once or in steps.

Presheaves are certainly important, but I will stay focused on our goal to understand sheaves instead of dealing with details about presheaves. With that having been said, recall the property of locality from our loose definition of a sheaf, as it is also our first axiom for sheaves, with the other being concatenation or gluing. These two axioms may also be thought of as ensuring existence and uniqueness.

Sheaf: A presheaf satisfying the following:

• (Locality) If $\{U_i\}$ is an open covering of the open $U$, and if $x,y \in F(U)$ such that $\mathrm{res}_{U_i,U}(x)=\mathrm{res}_{U_i,U}(y)$ for each $U_i$, then $x=y$.
• (Gluing) Suppose $\{ U_i \}$ is an open cover of $U$. Further suppose that if for all $i$ a section $s_i \in F(U_i)$ is given such that for each pairing $U_i, U_k$ of the covering sets $\mathrm{res}_{U_i \cap U_k, U}(s_i)=\mathrm{res}_{U_i \cap U_k, U}(s_j)$, then there exists $s \in F(U)$ where $\mathrm{res}_{U_i,U}(s)=s_i \; \forall i$.

In other words, a sheaf is a presheaf if we can uniquely “glue” pieces together.

For the sake of brevity and simplicity, we will ignore some technical details henceforth. We will also focus on functions and let the reader work out the details for the same reason.

For our first example, consider topological spaces $X$ and $Y$ with a “rule” $\mathscr{F}$ such that open $U \subset X$ is associated with

$\mathscr{F}(U)=\{f: U \to Y : f \; \mathrm{is \; continuous} \}$

This is a sheaf. It is actually a pretty well-known example too. (Hint: In justifying that this is a sheaf, it may be a good strategy to begin by considering restriction maps.)

For our second and final example, we shall consider the sheaf of infinitely differentiable ($\mathbb{C}^{\infty}$ smooth) functions. The sheaf of infinitely differentiable functions of a differential manifold $M$ has two properties:

• For all open sets $U$ the ring of $C^{\infty}$ functions is associated from $U$ to $\mathbb{R}$
• The restriction map is a function restriction

Again, it’s worth playing around with this sheaf a bit.

So, to review a sheaf is a tool used in algebraic geometry and other fields, and it serves as a sort of data collection method such that the data is all put in one place, i.e. a point.

Notes

• It’s worth noting that there are tons of different definitions of presheaves and sheaves, but I think the provided one is most intuitive and works well for many instances.
• An alternate notation for $\mathrm{res}_{V,U}(s)$ is $s|_{V}$; keep this in mind if you plan to read more on this topic.
• Be sure to keep functions in mind while you’re developing an understanding of sheaves. Another example to consider is the sheaf of regular functions.