Against Against Theory

I’ve been getting a lot of hits on my critical theory posts and the ones on Hirsch’s Validity in Interpretation. I thought I’d do some more on famous papers on related issues. Probably the most important and influential is Steven Knapp and Walter Benn Michaels’ Against Theory. It appeared in the Summer 1982 issue of Critical Inquiry.

My initial goal was to provide a synopsis of this paper in a similar way I did to Hirsch’s book. Unfortunately, I’m either so confused by what they are trying to argue, or their argument is fundamentally flawed. So I’m going argue against its main point.

The entire second section of the paper is based around debunking Hirsch’s defense of intentionalism. If you’ll recall, Hirsch’s book is centered on the idea that the only valid interpretation of a work is the one the author intended. Then he spends the book constructing a theoretical framework for reconstructing the author’s intended meaning.

For some reason, Knapp and Michaels think they will succeed in their argument against theory if they prove there is no such thing as intentionless meaning, i.e. a text cannot have meaning if there is no authorial intent.

I think everyone on the authorial intent side of things (including Hirsch) is in agreement here. It is quite a bizarre thing to focus on. The crux of the paper ought to be an argument for why there is no need for theory if authorial intent is the only thing that matters. They just assert, without argument, the truth of this claim. But it’s the only claim in the paper that seems to need justification!

I’ll try to lay out my case for why theory still matters. First, Knapp and Michaels seem to believe that theory is the attempt to relate authorial intent to meaning. I’m not sure where this comes from, but it takes a narrow view of theory that actually excludes Hirsch’s book. So I’m not sure why they even talk about that book if this is their view (I know they separate the ontological and epistemological parts of theory; more on that later).

Theory, as seen in practice, is almost always an attempt to relate authorial intent to interpretation. This creates no conflict with equating authorial intent and meaning. It doesn’t posit a need for intentionless meaning.

It is a fact that language is inherently ambiguous. So even though there is only one valid interpretation, a reader may not know what that is. This makes interpretation necessary. This means there must be tools for the reader to discover the meaning of the text. The grounding of these tools in a theoretical framework is what is usually meant by “theory.” Thus theory is needed.

One way I could see arguing against theory is to claim that Hirsch provides all the theoretical framework we need, and so there is no point to continue the enterprise. I’d almost be able to get on board with that. Unfortunately, they seem to be arguing against Hirsch, and so they are creating a hole that needs to be filled with more theory!

Here’s an example to illustrate the point. Suppose you have a math problem. It has one right answer. This doesn’t eliminate the usefulness of a theoretical framework for arriving at the correct answer. Once you have a way to get to the correct answer, more theory can be created to get to the correct answer more accurately or more quickly. You never have to posit “other answers” for this to be true. There is only ever one correct answer through the whole process, but it is still possible for someone to make a mistake and get a “wrong answer.”

Hopefully you see where this is going. Knapp and Michaels claim that theory is not needed if a text’s meaning only ever has the correct interpretation of the author’s intent. But the above example shows this not to be the case. A person can look at a math problem and not immediately see the answer, but after some derivation come to the correct answer. Similarly, a person can read a sentence and not immediately ascertain the author’s intention, but after some interpretation can come to the meaning. It is in that interpretation step that theory still has a function.

I’m actually still extraordinarily confused at how Knapp and Michaels didn’t think of this or how they could read Hirsch’s book and think it was about an intention/meaning distinction rather than a book about how to interpret correctly. It is called Validity in Interpretation for goodness sake, not “Validity in Meaning.”

I’ll just reiterate how bizarre it is that they want to assume theory is only about an intention/meaning distinction and then engage Hirsch’s book which clearly is not about this at all. You can’t insist his book is theory and hold to the idea that theory is only about intention/meaning.

They must be aware of this, because in section 3 they say, “For Hirsch and Juhl, the goal of theory is to provide an objectively valid method of literary interpretation.” So far, so good. They continue, “To make method possible, both are forced to imagine intentionless meanings or, in more general terms, to imagine a separation between language and speech acts.”

That’s where they lose me. It may be the case that Hirsch and Juhl abstractly talk about this in their works (though I don’t recall because of how minor it is to their theory), but as I pointed out above, it isn’t a necessary component. You never have to imagine intentionless meanings for Hirsch. The only thing you have to imagine is that the reader doesn’t immediately know the author’s intention, which is almost a tautology of how reading works. If you don’t believe this, think of the math problem. We never had to imagine wrong answers to still have to do work to get to the right one.

Sorry for harping on this point over and over, but it is exactly what the paper does. This makes no sense to me, because this “problem” (which I don’t see to be a problem at all; please make an argument!) is tangential to the question of theory at best and a non-issue at worst. How this paper became so important is beyond me when they seem to have offered a long-winded, purely semantic strawman.

I have the book Against Theory: Literary Studies and the New Pragmatism on its way, so hopefully that will provide some more answers and clarification.

Examining Pro’s Prose Part 7

Today we’ll examine something I think Ethan Canin does well: description. Description is one of those things that is very hard to get right. I think this is because it is difficult to notice when someone has done a good job. Bad description jumps out; good description goes unnoticed.

Everyone notices an overwrought passage that contains strange similes and metaphors and goes on forever trying to paint as explicit a picture as possible. The story breaks to set the scene. This is a case of show-don’t-tell-itis. The reader ends up skimming to find the story and gets nothing out of all the work that went into the description. Or the reader that suffers through it gets bored.

For this reason, I’ll make the first rule of description: show as little as possible without sacrificing useful information. This is counter to what most of us have been taught, but one carefully chosen detail can tell the reader more than a whole page of useless ones.

Ed wore Reebok’s to the party. Does that detail tell us anything? Probably not. Tina picked up on Ed’s Saucony Kilkenny XC5 minimal running flats as soon as he entered the party. Does that tell us something? Maybe. Ed is a runner? Tina knows enough about running shoes to identify these? We’re getting somewhere now. This example isn’t great, because most people won’t be able to visualize the shoe. But you should see the point that describing because you feel you need to or that it makes the scene “more realistic” is not a noble goal. Describe with purpose.

This brings us to the second rule: make the details serve more than one purpose. Often people think of description as the way to paint a picture in the reader’s mind. It can serve many other purposes in addition to this and often multipurpose description keeps the story moving.

Here’s an example. Take something simple like describing snow (I’m in the middle of NE Snowpocalypse 2016). Someone who has show don’t tell ingrained in them might try to give every painstaking detail as accurately as possible. But this isn’t non-fiction; it’s literature. The same exact thing can be described in multiple ways, giving different moods.

Maybe the character is falling in love, so she sees the beauty in it. The sun hit the ice crystal dangling from the pine, breaking the light into a dozen shimmering rays. The gentle snowflakes danced among the light. Blah, blah, blah. As you see, you can use words like “shimmering,” “gentle,” “dance,” “light,” “sun,” etc to emphasize the joy of the character.

The same exact scene could be described by an angry character. Harsh light glared off the frozen surfaces. The snow plunged relentlessly and suffocated everything like an infinite, oppressive mask. Okay, so maybe that got a little depressive or melodramatic with words like “harsh,” “glare,” “plunge,” “suffocate,” “oppressive,” etc. But I merely wanted to illustrate a point. There isn’t one objectively accurate way to describe anything.

Now you see why good description is hard to spot. You don’t have alternate versions to compare it to, so you’ll read right over it and not realize the carefully chosen details. The details will evoke the right feeling, but you didn’t read a version that didn’t evoke those feelings to see how well it was done.

Obviously this can be taken too far, and you’ll start to produce abstract, experimental prose poetry. Striking the right balance is hard, so let’s examine how a pro handles it. Here’s a passage from For Kings and Planets by Ethan Canin. The main character was kissed by his best friend’s sister. Note how the description doesn’t come as a block. Details are woven in and out of thoughts and actions so that the story doesn’t stop.

He would leave Marshall reading a book on the porch and then set off rambling along the shoreline, not sharp in his thinking until he had passed two or three curves on the great spits of sand and the house had long ago vanished behind the dunes and the low stands of trees. She lived constantly in the center of his thoughts. He would try to think about his plans for the rest of the summer, but his eyes would conjure up her forthright gaze; he would try to listen to the clap and rumble of the surf, but would instead recall their conversation together on the porch, and then the kiss, and then in return her enigmatic scolding.

Note how the use of “clap” and “rumble” suggests a rough ocean, which imitates the turbulent emotions he feels. The curves of the shoreline mimics the winding thoughts in his head. The girl lives in the the center of his thoughts, and he stands in the center of a vast nothing.

Canin could have spent a page writing a description of the beach, and then continued with the story. We would have gotten a much more vivid picture in our minds, but that would have been boring. Instead, he chose a few sparse details of description that added to the mood, and then wove them into the action.

Here’s an early passage (pg 17) from Carry Me Across the Water. Many writers describe a ton of physical traits of their characters. Here we see a hyperfocus on one tiny detail that draws out characterization.

Walking up the front path to Jimmy’s building, Kleinman took a yarmulke from his back pocket and set it on his head. It wouldn’t stay in place: maybe God knew. Since boyhood, yarmulkes had never stayed—something about the shape of his cranium: an irreligious skull. He still had plenty of hair, though—thank his mother’s father for that. He laughed and pushed the yarmulke down on the crown again. He was trying to start off on the right foot with Claudine.

In that amount of space, we could have gotten a description of his size, hair color, age, body type, clothing, etc. But that would have given us much less information than focusing on the action of putting a yarmulke on.

First, it was in his pocket. He is putting it on to make an impression. This tells us he cares much more about what Claudine will think of him than wearing it. We see that he was raised Jewish, because he’s had the problem of keeping it on since boyhood. We see that he’s basically always been irreligious. He’s well-educated enough to know that hair genetics is passed through your mother’s father. He has the ability to laugh at himself as he fumbles with the yarmulke. Etc.

If you want to read more, I’d highly recommend Canin. His subtle use of description to create moods and characterization is excellent.

That vs Which: examples that compare apples to apples, which will help you out.

Many people take the loose view that grammar and language evolves over time, and therefore you should go with whatever sounds right. Others argue the that/which distinction has basically disappeared. I want to do a comparison to prove once and for all the distinction is necessary. It isn’t preference. They aren’t interchangeable. The meaning of the sentence gets changed by swapping one for the other.

Let me be clear. I am not some obsessive grammar person. I kind of suck at it. But the way people dismiss this point as unimportant and a matter of personal taste (including professional editors!) drives me crazy. It isn’t taste. It’s important.

Many great sources fail miserably in describing the difference between that and which. I’m looking at you Grammar Girl (I love you for everything else) and you Chicago Manual of Style (an excellent doorstop as well). I’m not sure I’ve ever seen a source that gives you the same sentence with “that” and “which” swapped to show the distinction. Everyone has one sentence with “that” to show the use and then a different sentence with “which” to show the use. How is that helpful? It’s like comparing apples to oranges.

Let’s start simple.

Example 1: I played with the marbles, which were blue.

When you use which, you imply that every single marble was blue. This is what is meant by “which is nonrestrictive.” You aren’t restricting your attention to just the blue ones out of a bunch of colors. You’re saying they were all blue. This implication matters. Consider what happens with a simple substitute of “that.”

Example 2: I played with the marbles that were blue.

This sentence has a totally different meaning! “That” implies you have a bunch of marbles of all sorts of different colors in front of you, but you’ve decided to only play with the ones that were blue. This is what is meant by “that is restrictive” or “that is essential.”

Example 3: The puppies, which were cute, ran across the yard.
Example 4: The puppies that were cute ran across the yard.

In example 3, all the puppies ran across the yard. It just so happens they were also all cute. In example 4, only some of the puppies were cute, and only those few puppies ran across the yard. Read these over and over until it makes sense.

Now be horrified at all the times you used these incorrectly and probably implied something you didn’t mean to (did you seriously just imply there are non-cute puppies? Are you sure?). Now look what you’ve done. He’s self-conscious:

Some people argue it’s the comma causing this change in meaning and not that/which. Walk away from that argument. You’ve found someone wrong on the internet, and it isn’t worth your time to engage them. They’re probably a troll anyway. What’s more probable: the distinction made for hundreds of years in a rigorous way still retains some meaning or the words have no meaning anymore and the meaning has magically shifted to comma usage even though the words are still there? Think about it.

I’ve seen a bunch of rules for trying to distinguish between that and which. To me, they’re all pretty terrible. Here’s the easiest rule, which will work 99% of the time.

Step 1: What noun comes before that/which?
Step 2: Does the thing after that/which apply to all of [insert Step 1 answer] or just the ones you’ve described?
Step 3: If Step 2 answer is “all,” use which. If Step 2 answer is “only those described,” use that.

Officially, I wanted to end the post here, but I just know that someone is going to complain I’ve only told you how to tell the difference between that/which when they distinguish between restrictive/nonrestrictive clauses. Not only is the other type of distinction easier, I’m much less concerned with it. Here things can be a bit more stylistic, because the use (often) doesn’t change the meaning of the sentence.

Rule: If you can delete the stuff after that/which without causing confusion, use which. Otherwise, use that.

These examples are slightly harder to give, because they often require context to know if the information is needed.

Example 5: I went to the store, which had roast beef.
Example 6: I went to the store that had roast beef.

If you’re writing a story and there’s only one store. You can delete “which had roast beef” without confusion. The clause “which had roast beef” is inessential. The store just happens to have it. No big deal.

If the story is about a person who must get a serial killer roast beef or they will kill again, and they find out that three of the four stores in their area are out, then “that had roast beef” specifies which of the four stores you went to. It’s essential information, because if you delete it, the reader will think: which store? Are they wasting time picking up some quinoa pasta at the Whole Foods when they need to be getting to the roast beef store?

As you can see, the meaning doesn’t change all that much if you use the wrong one here, but there’s still a correct choice between the two words. If you play fast and loose with this distinction, puppies aren’t going to start hiding their faces, so the stakes aren’t as high.

And there you have it. Some comparisons that actually make sense. I hope that helped.

Year of Giant Novels Part 2: Don Quixote

I’ve made it into Part 2 of Don Quixote. I’ll fully admit upfront that it has become a bit of a slog. I find it difficult to get motivated to keep reading. The book is indeed episodic, and many of those episodes involve a random character telling a story. This makes it hard to care about the story when you know the character is only there for 20 pages or so.

In any event, let’s continue to point out ways in which the book was way ahead of its time. If you’ve studied classic philosophy, you’ll probably be familiar with Descartes’ First Meditation. This was published in 1641, and it has a thought experiment so famous that people refer to it as Descartes’ evil demon.

The idea is that there might be some powerful evil demon out there that makes us believe reality is a certain way, but in fact, it is completely different. How do we know such a thing isn’t deceiving us? This lead Descartes to doubt all of reality as the starting point for his philosophy.

Now that I’m reading Don Quixote, I’m confused by why we attribute this to Descartes. Thirty years before Descartes wrote this thought experiment down, Cervantes perfectly articulated the same idea. Unfortunately, I didn’t mark the page, or I would quote it directly.

This was probably one of my favorite moments in Part 1, because it so brilliantly illustrated the whole point of the book. Some people see Don Quixote and try to convince him he is crazy; what he sees is not reality. But in a great twist Don Quixote argues back that they are the ones being enchanted by an evil sorcerer. It is he, Don Quixote, that sees reality and everyone else is being fooled. As Descartes found out, it is quite difficult to argue back against that.

Part 2 is where things get really heavy on the meta-fiction. Cervantes’ novel Don Quixote has made it into the fictional universe of Part 2. Early on, he even has a character make the same criticism I made above. There are too many digressions in which Don Quixote (the person) isn’t a character. Don Quixote and Sancho go off on new adventures and keep meeting people that know all about him because of reading Part 1.

You have to know a bit of real life history to be in on some of the more complicated jokes. Someone under the pseudonym Alonso Fernández de Avellaneda wrote a fake Part 2 to Don Quixote (sort of like fan fiction). In real life, this fake version actually got Cervantes motivated to finish the real Part 2.

But that’s not all. He actually uses the fake Part 2 for plot points in the real Part 2. This fake Part 2 has been read by the people in Cervantes’ real Part 2. Don Quixote (the character) is unaware of this fake version of himself for some time, and some great silliness happens when he finally realizes this impostor version of himself exists.

He gets upset when he encounters people who have read the fake version in which he is no longer in love with Dulcinea. To spite the fake version, he decides to change what he was planning on doing (which actually corresponded with something that happened in the fake version!). These meta-fictional episodes play right into the novel’s main concept of blurred lines between fiction and reality, because the fictional version of Don Quixote overlaps with the “real” Don Quixote in places.

These jokes get quite complicated, and really nothing like it existed for hundreds of years afterward.

Year of Giant Novels, Part 1: Don Quixote

Back in my youth, I used to love reading giant novels: Infinite Jest, Underworld, Gravity’s Rainbow, The Brothers Karamazov, Anna Karenina, Les Misérables, etc. There are still quite a few left on my list that I haven’t gotten around to.

In the past few years, I’ve mostly read short novels. I even find myself getting annoyed when a 350-pager has gone on too long. The most common complaint I have these days is a lack of focus that leads to too long of novels.

I hereby declare this The Year of Giant Novels, where I will attempt to get through all the giant novels I own but haven’t read. I may even get some more if it goes well. I will, of course, blog about them as I read them. My list so far is: Don Quixote, Moby-Dick, and Ulysses. Let me know if I should do any others (Warning: I might veto War and Peace). I would like to add something from the past 50 years (maybe 2666?).

Anyway, on to Part I of Don Quixote. This novel is quite a strange beast. Say the name Don Quixote to anyone, and they will probably think they know all about it without having read it. They’ll have images of pure silliness.

They probably won’t be able to tell you why he fought the windmills, but they will know it happened. Some might even predict that the novel is episodic and monotonous going through his crazy and delusional adventures. Pretty much everything anyone knows about the book happens in the first 5%.

What most people don’t realize is that this novel was published in 1604 (according to the Penguin Classics edition). 1604! They also don’t realize how far ahead of its time it was; we’re talking about being hundreds of years ahead of its time. This thing is a tome of post-modernism 200 years before modernism happened.

First off, the narrator wants you to believe this really happened. Cervantes goes so far with this idea that in an early chapter, he has the narrator interrupt the story mid-action to say that he doesn’t have the proper citations to continue the story.

The narrator goes off on his own story. He visits a library where he accidentally comes across an Arabic text that contains the end of the story about Don Quixote he interrupted. This qualifies as Borges-level mind games (which is probably why Borges chose Don Quixote for the backdrop of his famous “Pierre Menard” story). When Barth used this technique in the 1960’s, it was considered a mind-boggling innovation. But here it is in something published in 1604.

Another example of these postmodern techniques is in Chapter 6, where a barber and a priest are trying to destroy the books that Don Quixote read that led him to his delusions (already a clever premise examining the interaction between fiction and reality, author and reader). The two come across another of Cervantes’ novels.

This nearly killed me. Cervantes’ character, Don Quixote, has been so enamored by one of Cervantes’ other novels, which somehow exists in this fictional universe, that he goes mad. That’s not all. Then the barber claims to know Cervantes in real life. This means the author wrote himself into his fictional universe! Then the barber goes on to criticize the novel. This is brilliant. A fictional character speaks a critique of the author who wrote him.

I’m starting to see why Don Quixote went crazy.

Thoughts on Björk’s Vulnicura

Björk has been quite a polarizing figure throughout the years. I used to absolutely love her music in the early 2000’s. I thought Vespertine was a brilliant culmination in all the ideas she had been exploring.

It was an album with palpable emotional output. It pushed the boundaries of accompaniment with grandiose and experimental orchestration combined with electronica. The chord progressions were otherworldly in their strangeness. The melodies wound around in huge, tangled phrases.

Iceland is known for its musical creative geniuses, but this was something special even for Björk. Then came Medúlla. That album terrified me. It not only marked a change in direction to a more aggressive and wild sound, but the album only used voice. It was a wildly successful experiment in just what a human voice could achieve.

Björk basically fell off my radar at that point. I’d periodically notice something new come out, but it felt safe and sterile. I couldn’t get too excited about it. Sure it was more interesting and original than most of the other things released by mainstream artists, but she had also turned to a more pop sound. Her collaborations were still pretty great through these years (especially the one with The Dirty Projectors).

It just came to my attention, nearly a year after its release, that she came out with her ninth album Vulnicura. I decided to give it a chance, because I can’t quite shake how much her earlier stuff influenced me.

I’m glad I did. This album returns to the Vespertine sound in many of the aspects I listed above. The emotional content is back. This is essentially a break-up album, but not like any you’ve heard before. This goes right to heart with its poetic lyrics and winding, understated melodies.

There are a few standout tracks. “Black Lake” occurs as roughly the half-way point, and it really focuses the other songs on how painful the experience was. It is only string and voice for over 4 minutes. It then ramps up with sparse but hard hitting electronica to bring depth to the song:

The other highlight is “Atom Dance” where Antony Hegarty from Antony and the Johnsons makes an appearance. Their two voices create a huge mass of agony.

My one complaint is that some of the earlier songs use repetition effectively on the first few listens, but once you’ve heard it five or so times, it feels like too much.

Overall, this is an excellent album by Björk, and if you’ve been turned off by her lately, you might still want to give this one a try.

Silly Calculations Related to Driving

A few weeks ago I mentioned that I had a long car trip. Whenever I have to drive a lot, I find myself thinking of the same silly questions, but I never care enough when I stop driving to do the calculation. Here they are:

Motivation: If you’re driving 69 mph on the highway (65 mph speed limit), you will probably never get pulled over. I’m not advocating breaking the law. I’m just stating a pretty well-known fact. If you go 71 mph, you’re flirting with getting a ticket. I always wonder just how much time I would save by going those 2 mph faster.

I warned you this would be silly. You can probably even do this one in your head. Suppose my trip is about 500 miles long. Going 69 mph would take a little less than 7 hours 15 minutes. Going 71 mph would take a little over 7 hours. So you’d only save about 10 minutes on a trip that is over 7 hours. Considering the significant increased risk for a ticket, this doesn’t seem worth it to me. On short trips of an hour or less, the difference in time can’t even be detected.

Motivation: No one drives perfectly straight. You always have to make little adjustments back and forth to stay in the lane. You also probably change lanes on the highway. I always wonder just how much distance those little adjustments add. Do they add up over a long trip, or does it remain insignificant?

Wikipedia tells us a highway lane is 12 feet wide. Let’s do an underestimate that doesn’t factor in lane changes and say you swerve from one end to the other of the lane twice every mile:

Now use the Pythagorean theorem, and you’ll find that the diagonal line isn’t even a full foot longer than if you didn’t swerve. In fact, the 4 diagonal lines don’t even add up to an extra foot over that mile. That means this swerving estimate produced less than 500 feet extra travel distance over 500 miles. It’s not even a quarter of a mile!

Even if you try to modify the estimate to be way over, factoring in lane changes and everything, as long as you keep the numbers realistic, you probably can’t even get it to be more than a mile or two. This means that these little adjustments do not add up, even over a very long drive. So swerve away!

Do We Perceive Reality As It Is?

Recently I had to do a ten hour drive, so I was listening to a whole bunch of stuff. One of the weirder ones was a conversation with Donald Hoffman at UC Irvine. The discussion revolved around what reality is and whether we can know it.

This is a well-known, old philosophical question. I’ve also discussed it in several forms on the blog before (see embodied mind and cognitive biases). What interested me was how clear of a metaphor Hoffman described to get this idea across.

Consider the computer (or phone or whatever) on which you are reading this. There are probably icons that help you run programs. This interface with the computer is basically never confused with the reality of what the computer is doing.

If you have a folder icon, you secretly know that the information of that folder is a bunch of 0’s and 1’s encoded by low/high voltage transistors, etc. But it would be paralyzing to think like this all the time. This interface we use completely alters our perception of the reality of the computer in a way that makes it functional.

So that’s the analogy. We basically have no idea what reality is. All we get is the way our brain presents reality to us. And like the computer, it is almost certainly presenting us with something that makes the world a functional place for us rather than presenting every detail of reality “as it is” (whatever that means).

This is abundantly clear when you think about our visual spectrum. We cannot see in the infrared part of the light spectrum. That information is out there and part of reality, but it isn’t functionally necessary for us to see it. The bigger jump is that maybe it isn’t only our body filtering out excess information, but that our perceptions are some sort of interface that has nothing to do with reality.

The evolutionary explanation for this is painfully obvious with a little thought. If a mutation occurs that causes us to perceive the world in some “false” way, but that false perception increases our chance of surviving, it will stay.

He went into some suspicious sounding math, claiming he had a theorem that there is a probability 0 chance that our perception of reality is true. The specifics don’t matter, because anyone with a basic understanding of evolution should immediately admit that it is exceedingly unlikely that every trait conducive to survival also gives us a true perception of reality.

On another note, this topic actually came up in one of my first posts ever on the blog. I used to debate whether or not aliens would have the same math as us. It seems the further you go in math, the most offensive people find the view that aliens may have a different math. For some reason, people are really tied to the idea that math is some universal that exists out in a mysterious Platonic universe.

In light of the above description, doesn’t it seem very likely that an alien species with a different evolved brain would vastly deviate in their perception of the world? We are so trapped in our bodies as humans, we find it hard to even entertain what a different experience would be.

If you know about the foundations of math, then you know everything is built from a set of axioms. Our choice of these axioms is based on how we experience the world. Therefore, it is reasonable to assume their mathematics would be different.

Status of ABC Conjecture

I rarely do this, but I’m going to direct you to a different blog this week. I’m in the middle of two big projects, and I didn’t feel like blogging today. The abc Conjecture is one of the most important unsolved problems in math. It is also relatively simple to state. Go read about it at that link if you haven’t heard of it.

A few years (?!) ago someone claimed to have solved it. Unfortunately, the proof was one of the longest and most complicated things the math world had ever seen. Ever since, the status of the conjecture has been up in the air. Some people have attempted to understand it to try to verify if the proof holds up.

A few days ago, we got a massive status update. You can read about it here.