Sex, violence, and meaning · 11:12pm Dec 5th, 2013
Yesterday I made a borderline-nihilistic blog post saying that calling a sex scene "gratuitous" is really making a value judgement that sex is not worthy of being written about and can only play a structural, supporting role in literature. And that is, even more sneakily, a pathetic attempt to pretend that whatever non-sexy thing we're writing about has deep meaning.
I think I learned something from the comments that followed, so I'm going to try another approach: Stories are morals. I might even say stories are the real thing, and morals are just a muddled abstraction of the stories that we like.
(This is probably all in Nietzsche somewhere.)
I can think of 3 things you can praise in a story:
1. Values
2. Ideas
3. Technique
Raw terminal values / preferences / tastes are the sort you find in the Iliad or Conan the Barbarian: "What is best in life? To crush your enemies, to see them driven before you, and to hear the lamentations of their women." Entertainment is anything that pushes our pleasure buttons over and over. Sex and violence entertain because people want to have sex and want to be victorious.
I'm counting feelings as values. When we say "OH THE FEELS" after reading a story, we enjoyed having that feeling, so it's a value. A feeling you want to avoid is also a value (with a negative sign before it).
I can imagine 3 different types of values: Personal values, social values, & objectively true values (which may or may not exist). Values are “correct” if they’re objectively true values. They’re “right” if they’re in your set of social values. If they're in your set of personal values, they just feel good. If what mesmerizes you most is pictures of naked women, then that's your highest personal value. It isn't incorrect, but somebody else who finds something else more fascinating will still say it's wrong.
Ideas are the sort of meaning you find in a science fiction story published in Analog. You can speculate about the possibility that people in the future will take their employer's last name rather than their father's without making a value judgement about it.
The values of the Iliad, Beowulf, and Conan are taken as given. If heroes asked "Why is it good to rape these women, but good to die protecting these other women?", everything would have fallen apart. They'd have been unable to really throw themselves into slaughtering and enslaving their neighbors, and would have been slaughtered and enslaved themselves.
Eventually somebody, maybe Zoroaster, maybe Greeks in the 5th century BC, created a new thing: Morals. Morals are values derived from other values via thinking and feeling. They make it possible to build new social structures never encountered in evolutionary history that don't rely entirely on brute force to prop them up. (Not coincidentally, Greeks in the 5th century BC also invented tragedy.)
I objected to calling sex gratuitous because it's applying a value judgement to literature. But if I try to write stories without making arbitrary value judgements, I'm left with ideas, feelings, and technique. In other words, post-modernist fiction.
I was trying to find meaning without choosing an arbitrary set of values. Maybe you can't do that. Maybe meaning is just a story that feels worthwhile. We search for meaning by finding stories that mesmerize us. We try to figure out what's important in the stories that do, and call that mix of values, feelings, and ideas our morality. And while the stories, values, and morals we develop can never be correct, we can argue with each other about which ones are best, and build enough of a consensus to build a better life for us all.
There's still the possibility that you can find some objectively true values--and in fact I think I may have found some--and write stories with meaning based on those values. But most humans don't respond much to stories about such abstract ideas. The closest things I can even think of are some Borges stories such as "The God's Script".
This leaves me in the uncomfortable business of writing stories to discover morals that aren't correct. This feels bizarre to anyone with a scientific mindset. Why devote oneself to disclosing things that are not in fact true, when you can be a scientist and uncover actual truths?
Stories and social morals are correct on a meta-level: You need them to build a society. It's like running a business: You'll never find the single best business strategy, but you'd better pick one, or you'll be out of business.
ADDED:
But stories are a private thing nowadays. Shouldn't they then be searching for personal morals? Which, I implied, are not so changeable? I'm still confused on this topic.
I like putting different morals up against each other in a big morals-fight, in my books.
Almost always, readers will take sides and develop intense hatreds in one direction or another. In some ways, I look to have it balance out. If I've done things right, each extreme will feel validated and understood.
I'd like to think I understand them all, but it seems that's a tall order for readers.
I did pretty well in bio and chem, and the impression I always got was that scientists spend a lot of time finding things that don't work in the pursuit of eliminating them until they find something that does. I even recall one of my teachers clarifying that it is indeed the case, and very frustrating sometimes (although rewarding other times, particularly in the case of accidental discoveries.)
Maybe I'm seeing it wrong, or missing your point, or something else -- but to me, Gil Grissom's words have, at least in spirit, always been my guiding principle:
I'm not really sure what to say to this, other than I think it's fun to create character and stories whose values and morals don't necessarily align with my own. Keeps me on my toes.
I think you've nailed the reason that science and art rarely mix well. (ETA: Thematically. Science, of course, advances art technologically very well.)
Good art is rarely about truth in the sense of showing people something true. It's about showing them something false in a way that makes them think about whether it's true or not, or should be true.
In science, the scientist is reporting something true to people who will either agree or be looking for more proof. In art, the artist is only half the equation. You have to formulate your truths so that you're not simply reporting them to people, no matter how beautifully, but you're making people discover them for themselves.
(ETA2: And the problem with art as a medium for this sort of dissemination of truth is that it's exactly as easy to use it to to make people discover a lie, and the context often offers no hint as to which is which.)
1575917 The point is that in science there are facts, things to get correct or incorrect. To be crude and not entirely correct, if P is not correct, then not P is correct. A discovery that something doesn't work is thus still a new truth.
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I feel like there's a useful response I could provide, but I haven't the mental energy for it at the moment. (I am a mare of little brain.)
Huh. And here I just saw "life is gratuitous" on my dashboard, smirked a little, and moved on. Clearly someone had a disproportionate reaction here, but I'm not sure who it is.
Because it is a fun mental exercise.
I've found that scientists seem to really adore doing stuff like this - most people I know with scientific mindsets love imagining stuff, love thinking about various situations, love running simulations in their head, love asking weird questions, love designing things, and indeed, often love storytelling - I mean, scientists are classic nerdy folk. If you think of "what do nerdy people do for a living", science, engineering, and computer programming come to the top of the list, I think.
To a scientist, doing this sort of thing is fun. But there are right and wrong answers (or rather, wrong and less wrong answers). Many people have trouble with the idea that they might be wrong - even scientists do, but scientists are trained specifically to recognize that you aren't always right and that being wrong an be helpful in making you less wrong in the future. But most ordinary people get very upset when they are wrong, especially about something they think they're good at or knowledgeable about.
People often think of art as being a purely abstract thing where there aren't right and wrong answers, but in actuality, there are right and wrong ways of doing things in art - that's why people get better at making art over time, and why different things have different stylization. That's why the universal engagement curve exists. It may explain why the four chord song is so prevalent, and why some of Eminem's songs work so well. It is why the Golden Ratio exists, why people perceive certain facial anatomy as beautiful or ugly, why big eyes make things look cute to us... the underlying nature of how people perceive and interpret reality allows us to manipulate our audiences, provide us with tools and guidance on how to effectively impact our audience, the works. But if there is a "right answer", then that feels like it takes away from the craft of being an artist, even though these are skills as much as anything and understanding how to use these tools properly can make you much stronger or weaker as a writer.
There's a reason why the various stories about people going to visit graves work well on audiences even though they are all essentially the exact same story written thousands of times, and why certain other aspects of stories exist - the first kiss, the first night together, the admission of feelings, marriage... there are stories which lead up to all of these things, and they are very common and no less powerful for it, even though we've all seen them dozens of times. The hero's journey is another example of a story which exists all over the place, from Star Wars to Harry Potter to The Lord of the Rings.
Actually analyzing things in this manner from a more engineering-based standpoint is threatening to many people who write stories because it implies that there might be some "right" story that they are just failing to hit. I think this comes partially from a misunderstanding of how and why people read stories, but there is some basis to the fear - there really are certain structures which we've found which have a very strong inherent value to them. Whoever wrote the first "walking to a grave" story, whenever that was, stumbled across a really powerful story structure which still can punch people in the gut, even when they know what the story is. Is that the only story worth telling? No, obviously not. But the fact that that story works so well, even though it is everywhere and I'm sure every one of us has read it five times on this site alone, says something - and I think most people, even the cynical, feel something for those stories when they are at least reasonably well written.
You can only read the same story so many times before it starts to become trite, at least for a while, but there's a reason that many of these stories are so popular - the hero's journey is omnipresent because it works very well from a structural and engagement point of view.
I think in the end there are many reasons to read and write stories, and there is value in variation. Sure, writing the best "Walking to the Grave" story might be compelling, but everyone writes those stories, while writing something which everyone doesn't write allows you to engage via originality and the unexpected - and maybe you can find something else interesting off in the weeds that we haven't seen before.
I read to know and to enjoy.
All stories are knowledge and made of knowledge and impart knowledge. When I read it is all about what I want to know. I want to know about the characters, the world, the who, what, when, where, why, and how. And the way the story presents this, combined with the nature of this information, filtered through how I personally relate to it, determines my enjoyment.
From the perspective of a story being packets of knowledge, filtered through a personal screen into emotion, I detetmine what knowledge imparted by the story, whether via narration, action, or plot, benefits the experience and results in my enjoyment. This determination is also aided by weighing the experience of similar knowlege (scenes) that I have experienced and enjoyed or not in the past.
A huge amount of the knowlege I acquire via fiction, in any medium, incorporates sex and sexuality. I have read and seen and learned and felt along with so much sexual content in so many contexts that I genuinely feel I have a pretty good idea of both how it functions well as knowlege and what it needs to do to make me enjoy it. You can also interchange this sentiment with violent content. Or any content.
That said, you imply there is no correct criteria. I believe there is no incorrect criteria. There is only knowlege and whether it matters and how it is presented.
This is silly.
You should realize that you're effectively saying that every perception is a value. Every single thing perceived is perceived by qualia, and the only way to show this false is to find something you don't perceive and consider to be a value. But as soon as you find that thing, you can say that it's perceived, and therefore a value. So any story about absolutely anything is considered a story about values, and any judgement whatsoever can be considered a value judgement. By getting rid of the qualia, you're not left with "post-modernist fiction". You're left with absolutely nothing. I think the word you're looking for is "emotion", not "qualia". It's still not right, but it's closer.
You have no way of separating "objectively true" from "subjective true". Any time you disagree with something, you can just call it subjective. Since you can disagree with anything, you can restrict the set of "objectively true" things to only things you consider true. You're going to have to drop this point since you believe that everything known to be true must be verified, that all verification must be solely the result of experiences, and that all experiences are subjective.
I think I see where you're trying to go with this. I would put it to words, but it's interesting watching you climb that hill.
1576325 You're right. Very sloppy of me. I'm counting pleasurable feelings as values. Plenty of qualia have no valence. I think I do mean emotions.
>You have no way of separating "objectively true" from "subjective true". ... You're going to have to drop this point since you believe that everything known to be true must be verified, that all verification must be solely the result of experiences, and that all experiences are subjective.
If your argument were correct, it would also apply to mathematics. I don't believe it does.
I wish you could favorite blog posts. Oh well, Cmd+D then.
1576173 I'm talking about "meaning" in story, and arguing that for a story to have a meaning, the author has to commit to some value judgements that are arbitrary, neither correct nor incorrect. That's a different issue than whether there's a correct or incorrect way to tell a particular story.
Thank God I'm not the only one who regards that stuff with derision.
As for writing a story with meaning, one should have it that one could, from the content of the story, derive those values.
@re: central point of the essay
Interesting.
@re: 'values'
I understand what you are trying to say, but I think that the term 'values' may have been poorly chosen.
@re: objective correctness of morals
Well, consider also that morals operate in a context and change the context as they operate. Determining correctness in those circumstances is a bit dicey. Consider that the circumstances--context dependent/modifying--occur in evolution, too, and that's notoriously difficult to value-judge. What's a good change, in evolution, and what's a bad one? Well, it depends on when, doesn't it?
You could say that the job of writers--and artists and philosophers, too--is to build little hillocks in the possibility space, so we can climb up there and see the peaks and valleys around us and maybe move a little less blindly. A worthy goal, that, even to a scientific mindset.
Also fiction is fun. There's that, too, to consider.
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Whoa there, you'll end up deep in epistemology if you follow that route, and there's nothing but madness down that road, yea, madness and the bones of scores of philosophers.
But just to stoke the fires a little bit, the idea that there's a special way of knowing mathematics as opposed to the way we know the experiential is very Kant, but there's really no particular reason to be sure of it. After all, qualia apply to such things as 'experience of consciousness' and so they apply, too, to things like 'experience of the mathematical abstraction of equality.' The question becomes if that qualia is catalyzed in your mind by (a) some abstract realm of mathematics you can briefly commune with (b) the continuous experience of the Universe impressing upon your consciousness certain implicit rules or (c) the continuous experience of being a monkey-brain with certain information-processing quirks[1] that, in time, become the rules of reasoning/mathematics.
[1] Which are put there by evolution to help deal with the material universe--if you'll forgive the teleological writing there for a moment--and so make sure our abstractions are oddly applicable.
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You are correct, and I'm surprised you saw that. The argument does apply to mathematics, and I'll explain how it could be that math is subjective.
I think the easiest way to start explaining this is to demonstrate that the sum of one and one is not necessarily two under algebra and real-world units.
1 + 1 = 2
(1 + 1) * meters = 2 * meters
(1 + 1) * meters/second = 2 * meters/second
(1 * meters/second) + (1 * meters/second) = 2 * meters/second
I started with something true under mathematics and used operations valid under algebra. I concluded something that's true under algebra but blatantly false under special relativity. The problem is that equality under arithmetic operations does not apply to "meters/second". Addition is not a function that can be generally applied to all units.
The problem is that math doesn't provide a way to verify its applications. Since math is general enough to describe anything, it can literally be used to describe anything, even things that are not true, like Newtonian physics.
Since the application of math is subjective, its verifications are necessarily subjective unless verification can be done independently of its applications. To do this, we're left messing with symbols and nothing else. Now we have two options for this: either mathematics has to verify its own proofs, or some other system has to verify mathematical proofs. Both options have been demonstrated to be flawed.
The first case has been shown to be impossible under any interpretation of mathematics that is consistent: http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems#Second_incompleteness_theorem
You can use Godel's second incompleteness theorem again on whatever math-verifying theory you come up with. No matter how far you go, you'll necessarily end up using a flawed system.
You can argue that mathematics may be objectively true, just unprovably so, but you have to wonder what it means for math to be objectively true if none of its applications can be objectively correct, and if it cannot be demonstrated to be objectively true. If math is objectively consistent, but not with anything observable, then what is it consistent with?
The answer is obvious if you recognize that there is no math without a language of math. Unlike universal observations, "addition" is not a thing that exists independent of its understanding. If all things forget and never rediscover the operation, then it no longer exists. The consistency of math depends on the consistency of the understanding of its language. You can actually see this in action every time a mathematical concept is "generalized". Euclid believed that a triangle formed whenever one line intersected two to create two angles with a sum less than 180 degrees. That was true until people realized that using only flat surfaces was too limiting.
This post is getting long, so I'm going to cut to the end since I think you can find the rest of the path yourself. At best, math is a means of communicating analogies in a way that most humans accept as logical.
1575917 I've heard science defined as "truth by process of elimination," and I'm pretty sure that was paraphrasing a Sherlock Holmes quote. Remember that in science everything is called a theory because it's always possible to have more proof. Gravity is merely the best explanation we have for why things fall down. And by best I mean "the only one that works."
The idea of 'political science' is to discover, through rigorous examination, the best possible way to organize people. (Incidentally, it would be fascism if microeconomics weren't such a crock. Oh well, back to the drawing board.)
Can't remember why I was reminded of this, but Robert Heinlein, in Starship Troopers (the book, not the movie) talked about an idea of scientific morals: he didn't give details, but he posited there may be a way to "prove," based on repeatable measures, that one value is more correct than another. It's not much more than a throwaway line or two, but it's one of the deepest ideas in the book.
Lastly: 1576658 I prefer Shakyamuni's answer.
You're comparing storytelling to the scientific process, but I think it's closer to a philosophical or mathematical argument. When evaluating an argument, there are two separate operations. You have to check if each claim would be true given its premises; if so, the argument is logically sound. You also have to check whether the premises are actually correct. If the premises are correct and the argument is sound, then the conclusion is true.
A story can build on a few values to reach a moral. A story can be persuasive if the reader shares the relevant values, and if the story is good. (A bad story based on shared values might seem trite or muddled or boring. A good story based on values the reader doesn't share won't be persuasive.)
Because in the case of values and morals, "correct" isn't a relevant concept. (Can't derive "ought" from "is," and all that.) Still, like a sound argument can explore how topology changes with or without the parallel postulate, a good story can explore how morality changes with or without certain values. Given that I think crushing my enemies &c &c is bad, what should I do when I have enemies?
1576927 he posited there may be a way to "prove," based on repeatable measures, that one value is more correct than another
That would be statistically correct if there were a way to prove that each measure were truly random, or that the set of all measures were truly representative. I believe that this is unprovable.
1576927 I prefer Shakyamuni's answer.
One of the core ideas of Buddhism is that its teachings should not be blindly accepted, and that they should be judged by the experiences of those we trust. As I understand it, the idea that all truths are subjective is implied.
In some ways, you've captured my exact objections to the practice of storytelling. "Stories aren't bad. Stories aren't good, either."
I was trying to find meaning without choosing an arbitrary set of values. Maybe you can't do that. Maybe meaning is just a story that feels worthwhile.
The idea that we can 'find' meaning seems to be a common problem. As far as I can see (and as a chronic meaning-seeker), you can't find meaning, only make meaning (by structuring your life and thoughts along consistent principles).
When I look at people who really seem to find life quite meaningful, they seem to orbit around only one or two central ideas in their life, which they allow to dominate them utterly. When I decide I'm gonna do 30 drawings in the next 30 minutes, and do so, I get a sense of meaning out of that because I had set up that expectation -- it's meaningful because I set up that property in myself, not because I had some preexisting preference for speedrunning stuff.
My experience is that's the only reliable way to get more meaning in life: understand exactly what you are committing to, precommit to it, act as if, and it becomes true in retrospect.
Human minds are strange critters.
(there's more about the construction of meaning in any Dorothy Rowe book, FYI. They're all amazing.)
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The exact reason I read your stories is because you are that kind of person.. Such a person is quite rare to find.
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I wrote that for Bad Horse, and the language and argument I used there were heavily tailored for him. The main difference (I believe) between you and him is that he conflates mathematics and other logics, and you don't.
You're right that I'm conflating "objectively true" and "real". The word "objective" to me means things that are constant for all subjects, and the set of these things is equal to the set of "real" things. You seem to have a definition of the phrase that I don't understand.
What do you mean when you say "objectively true"? More specifically, what does it mean for a logic to be objectively true, but unprovably so, and what does it mean for that logic to be objectively true if none of its applications can be objectively correct, and if it cannot be demonstrated to be objectively true?
"I don't know" is a perfectly valid answer, and a common one, but keep in mind that this answer opens the possibility that "objectively true" means something different to different people, and may therefore be subjective.
If you don't have an answer, examples of things that you believe to be objectively true would also help. Keep in mind that I can't accept human mathematics as support of any answer since there are numerous examples of mathematical proofs that have been accepted and later proven false (see http://mathoverflow.net/questions/35468/widely-accepted-mathematical-results-that-were-later-shown-wrong for a short list).
Since mathematics as understood by humans is not an acceptable answer, answers supported by statistics are also under question. I'm particularly biased against these since a lack of understanding in statistics is at the heart of many problems in a field closely related to mine.
Saying that objective truth is relative to a theory is an answer I can understand without additional support, so long as you don't say that the theories are objectively describable. Equivalently, saying that truth can be objective relative to a subjective theory is something I can understand and believe.
As a side note, I don't think there was a problem with my application of the incompleteness proof since any system capable of proving mathematics is necessarily capable of performing mathematics. If X is able to reason about Y, and if Y is able to reason about Z, then X is able to reason about Z. The intuitive explanation is that X must be able to describe Y exactly to be able to exactly reason about Y, and so X must be able to describe all things describable by Y.
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The number of noncomputable functions (example: http://en.wikipedia.org/wiki/Busy_beaver) is uncountably infinite. Mathematics has a finite set of symbols, and there cannot be more than countably infinite finite combination of these symbols. Most functions cannot be described by mathematics, no matter how far mathematics evolves. (Starting point: http://en.wikipedia.org/wiki/Aleph_number.)
I think the easiest way to understand why math seems to be able to describe everything is to start with the fabrication of the language. Whenever something is found that doesn't fit into the theory of mathematics, and when people want to use it or try to reason about it, it just gets added to the language as a new symbol. "My theory doesn't have a way to represent itself, so I'll add this Σ symbol that represents just that." Of course the original theory may not be able to deal with that, so exactly how it integrates with the rest is left to human intuition and experimentation (often with things outside of the theory).
There exists a one-to-one mapping from all infinite countable sets to all other infinite countable sets. The language of math can describe countably infinite many things, as can any other human language that can be broken down into a finite number of symbols. No matter what you think, if it can be described in any human language, then it can be translated or fabricated in mathematics. That does not mean that mathematics can describe everything.
None of this has anything to do with whether or not math can be objective, but maybe it'll give you an idea of just how large the error bound can be when translating concepts from one person to another.
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Example of difficulty translating concepts between people: http://en.wikipedia.org/wiki/Pirah%C3%A3_people
Even something as seemingly basic as natural numbers is a cultural thing.
Yes, I'm that guy who comments on week-old blogs.
1577130 Because in the case of values and morals, "correct" isn't a relevant concept.
That's the question.
> (Can't derive "ought" from "is," and all that.)
Semi-tangential rant of mine: "Can't derive ought from is" is properly addressed toward conservative moralists who argue that homosexuality is immoral because it is uncommon. It should rather say "Is is not ought": You "shouldn't" choose values simply by enumerating what is (or value would be a redundant concept). It doesn't mean that "ought" and "is" are non-overlapping magisterium, and the statement "can't derive ought from is", interpreted literally, is unfounded.
> Still, like a sound argument can explore how topology changes with or without the parallel postulate, a good story can explore how morality changes with or without certain values.
And perhaps I can be happy with that, although humans are nearly incapable of reasoning with hypotheticals, especially in stories. Ghost said something similar:
1576639 You could say that the job of writers--and artists and philosophers, too--is to build little hillocks in the possibility space, so we can climb up there and see the peaks and valleys around us and maybe move a little less blindly. A worthy goal, that, even to a scientific mindset.
1576658 1577740
Math, and all consistent logics, are objectively "true", but their applications to the real world are not.
However, the existence of subjectivity does not preclude finding objective truth. equestrian.sen speaks as if everything were either completely objective or completely subjective. Newtonian physics is "incorrect" in that it is imprecise, particularly at certain speeds or masses. It is correct in that it dramatically decreases uncertainty. Given a starting situation and Newtonian mechanics, you can provide a much tighter probability distribution over the set of outcomes. Speaking more strictly, acting based on the predictions of Newtonian mechanics will provide more favorable outcomes than acting on the predictions of Aristotelian mechanics.
At the least, it's possible to identify sets of values that are incoherent because they contain undefined terms, or are inconsistent because they name something as a root value whose value can already be computed from other values.
1579476 Even something as seemingly basic as natural numbers is a cultural thing.
I disagree. No culture has the number 462, but not the number 461. And if (as is the case) you study 10,000 cultures around the world, and you find a single one that does not have natural numbers, you don't conclude from that that natural numbers are a cultural artifact. You conclude there's something odd about that one culture.
I've spent over 10 hours on this blog post now.
1593105 Math, and all consistent logics, are objectively "true"
That falls back on the "consistent with what" problem. You can say that math is "consistent with itself, and therefore objectively true", but I can create two theories, both consistent with mathematics and themselves, and both inconsistent with each other. Would that make both of them "objectively true", even though they are mutually incompatible theories?
Theory 1: Same as mathematics, but include the axiom of choice as a premise.
Theory 2: Same as mathematics, but include the negation of the axiom of choice as a premise.
To know that something is objectively true, and not just subjectively true, you would need apriori knowledge of that since all other knowledge comes from subjective experience and subjective understanding. I don't know how to refute that idea that you have apriori knowledge of this, except to show you a case where your apriori knowledge can be proven false. I have no doubt that I can find some example of this if I knew enough about what you knew about mathematics.
Newtonian physics doesn't provide error bounds, by the way. I also didn't mean to imply that I thought Newtonian physics was incorrect. Just that it's not "true" in the same sense that you believe math is "true". The same would go to all theories of physics once you believe that application of models is subjective. Error bounds and statistics don't help there since you have to decide which distribution is the proper one to assume for your data. Not even maximum entropy models provide a method of determining how correct your model is without making assumptions about the data you're processing.
I realize that to most people, my position of rejecting statistical arguments seems stupid. For all I know, those people are completely correct, and my optimism relating to what can be done to a person given sufficient understanding of the brain may be a deceptive artifact of me spending too much time making computers construct a completely artificial view of what's going on. As I understand it, it's all physics in the end, and physical processes can be manipulated.
--
The interesting part of that page is the following:
There is something odd about that culture, relative to our understanding of humans and of numbers. There's room for error in at least three places which would lead us to recognize that.
1593105
By the way, I'm glad you responded to the "can't derive an ought from an is" and the "correct isn't morally relevant" responses. I wanted to refute those, but I didn't want to get into complicated parallel discussions here.
1593658
That falls back on the "consistent with what" problem. You can say that math is "consistent with itself, and therefore objectively true", but I can create two theories, both consistent with mathematics and themselves, and both inconsistent with each other. Would that make both of them "objectively true", even though they are mutually incompatible theories?
As I meant to use the term, yes. A logic system (and we now know math is a logic system, at least over the rationals--I'm not sure what the status is of real-valued math) sets its own rules. All I meant is that if you set up the system and it's consistent, derivations within it are true. I didn't mean true in an external world. The axiom of choice is a perfect example, as would be Euclid's fifth postulate.
>Error bounds and statistics don't help there since you have to decide which distribution is the proper one to assume for your data. Not even maximum entropy models provide a method of determining how correct your model is without making assumptions about the data you're processing.
I don't know what you mean by that, but empirically, physics is useful, and you seem to be trying to convince me that theoretically, it can't be. I think I'm using a statistical model of "truth" and you are not.
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Your idea of "X is objectively true" seems to be the same as my idea of "X is true relative to theory Y", so I believe we agree on this, and on mathematics as it relates to your understanding of "objectively true".
>> physics is useful, and you seem to be trying to convince me that theoretically, it can't be
Nonono, I haven't said anything about usefulness. I'm going to be more precise with the next paragraph to explain this.
The fact that human understanding seems to have some sort of consistency to it relative to the way we perceive the universe interacting with us makes formalization (relative to common human understanding) very useful. But all of this is heavily dependent on the observer doing some perceiving, the observer doing some reacting, the observer doing some understanding, and the observer doing some communicating. That does not mean that theories based on human understanding are useless. It does mean that these theories are very, very dependent on the observer.
Even if our entire lives existed in some sort of matrix, our matrix understanding of matrix physics would still be useful. This is because understanding physics lets us take actions that seem to benefit us. Whether or not this happens by chance is irrelevant, and whether or not a similar action taken outside the matrix would lead to the same results is irrelevant. Perceived understanding -> perceived action -> expected perceived consequence. That's all that matters as far as physics is concerned. It doesn't matter if what we're perceiving is accurate for all subjects or for just one. Physics and math lend themselves to inducing the "perceived understanding" part, and so they are useful.
Internal consistency and external accuracy aren't actually necessary for math/physics to be useful. This could take a while to explain though...
As a side note, and on the statistics blob you quoted, statistics works so long as you understand the uncertainty that you're dealing with, and so long as the numbers you have are representative of the actual data. If I assume my data is poisson-distributed, and it's really gamma-distributed, then my error bounds are going to lie to me. If my browser tells me that I have $x in my bank account, that doesn't mean I have $x in my bank account (my browser could be lying to me, eg. due to malware, as could anything else between my monitor and my bank). There may be more conditions for your statistics to hold up, but I can't think of them at the moment.
1594334 That does not mean that theories based on human understanding are useless. It does mean that these theories are very, very dependent on the observer.
They depend on the observer in that an observer is necessary to state the theory. They do not depend on the observer in that any culture, species, or alien intelligence progressing through human-level intelligence would at one point develop Newtonian mechanics. Maybe there's some way they would develop a different theory if they were, say, perceiving the Fourier transform of the unverse as we know it, but I wouldn't bet on it.
1595693
How about this:
There's no reason to believe that an alien species would make use of infinities when none exist in the perceivable universe. Because of this, there's no reason to believe that an alien species would develop a theory of infinitesimal calculus. Because of this, there's no reason to believe that an alien species would develop Newtonian mechanics.
You say "human-level intelligence", but very few humans are capable of deriving calculus even when they know that infinities exist as a concept, and that they're useful.
They would probably think that our use of infinities, and the conclusions we draw from them, are insane until we can show experimentally that they lead to valid conclusions.
1595693
You say you doubt that an alien species would perceive the Fourier transform of the universe, but that's exactly what humans do. When you see light, you're effectively seeing its frequency and intensity. Same for sound. That's exactly what a Fourier transform is composed of.
1595952 I'm not persuaded that a sufficient intelligence wouldn't eventually develop calculus, as it is such a simple and powerful tool for information compression. But it is a clever response. It hadn't occurred to me that you must understand derivatives to define the right sorts of variables.
Any sufficient intelligence would develop a geometry in which Euclid's first 4 postulates were all true. (Unless they perceive space quite differently.)
1595961 Yesss.... now I've forgotten what I meant by that. Something along the lines of perceiving shapes by perceiving the amplitude of a set of sine waves that could be added up to draw curves around their outlines.
1597134 (Unless they perceive space quite differently.)
Which they easily could if they're large enough. And anyone that requires the existence of "black holes" in their definition of space would reject at least the first postulate.
Take a look at our formulation of arithmetic: http://en.wikipedia.org/wiki/Peano_axioms
Under these axioms, S(n), the "successor" function that's supposed to determine the natural number following n, is not well specified. Any bijective mapping from the non-negative integers to the positive integers works as a definition of S. (Any injective mapping satisfies the axioms, but addition and multiplication require a bijective mapping.)
Axioms 1-5 are unchanged.
All positive integers are natural numbers, so axiom 6 holds.
0 is not in the set of positive integers, so axiom 7 holds.
Bijections are injections, and S is a bijection by construction, so axiom 8 holds.
Axiom 9 holds for any S since it defines K relative to the natural numbers and S.
For example:
S(0) = 3
S(1) = 2
S(2) = 1
S(3) = 6
S(4) = 5
S(5) = 4
S(6) = 9
S(7) = 8
S(8) = 7
and so on (read it backwards to see the pattern).
The formulations for addition and multiplication make no assumptions about S or N, except that S(x) is in N for all x and that all positive integers have a unique inverse under S, so the generalized definition for S will always apply. Of course, addition and multiplication could now mean completely different things, and our understanding of them would be impossible for formulate for most formulations of S without depending on higher mathematics, some of which cannot exist under certain formulations of S (because not all natural numbers will have a pair of inverses under the new additions/multiplications).
1597134
The subjectivity is in choice of S. There are uncountably infinite possible choices of S.
1597294 No, you're imagining that the natural numbers exist before hand, and that S maps natural numbers to natural numbers. S is defined over a domain of sets, not of numbers. The sequence it generates is then labelled with the integers.
1597667
That's not how arithmetic defines natural numbers. S^k(0) is only required to define a subset of the naturals over k. Even if X isn't in the set defined by S^k(0), it can be considered a natural number so long as S(X) exists and is considered a natural number.
1597721 No, sorry. I used to teach this stuff. The Wikipedia page is misleading because it's about Peano arithmetic rather than about defining the natural numbers. S is not defined over numbers. The whole point of the exercise is to generate the naturals from set theory, reducing arithmetic and mathematics to logic. 0 is a label assigned to a starting set, typically the empty set. S(0) is a set generated from that set by a logical operation, typically the power-set operation, and it is given the label "1". But what is really happening under the hood is
S({}) = { {} }, and we will call this "1".
S({ {} }) = { {}, { {} } }, and we will call this "2".
etc.
1597768
It's the set theoretical definition of natural numbers that the naturals are recursively generated by S from the empty set. That's one way to start defining the numbers. Peano arithmetic can be seen as working on an entirely different idea of numbers that's more general than the set theory idea.
I feel like it says something that we have completely different ideas of numbers.
1597768
This has been fun, and I've learned a lot here. Unfortunately, I have to get back to work for the next few days and wrap things up for the semester. If you respond, I'll get back to you early next week.
1605294 Right; that's what I was trying to say.
The larger, more broadly-applicable point (from before we departed into math) is still that we shouldn't try to classify things outside math as being one of either "completly, objectively true" or "subjective and every possible interpretation is equally valid".
1605294
You're right that S(0)=3 is the new "1", but there are also now naturals (under Peano's axioms) where
1. S^k(a) can equal a
2. The set of S^k(a) can be mutually exclusive of the set of S^k(b)
I think I've been arguing this point incorrectly up until now. Suppose statements about pure mathematics are equivalently interpreted by all subjects (ie. they are objective). I am a subject, you are a subject, and the above two statements are about pure mathematics. Therefore they should be interpreted equivalently by the two of us.
By my interpretation of the above two statements, the numbers as definable by Peano arithmetic and the numbers as definable by set theory are not equal. Moreover, this is a direct, one-step consequence of my interpretations of (1) and (2).
I'll tell you my interpretations of them in my next post, and you can decide whether or not they are valid interpretations of statements (1) and (2), and whether or not your interpretations of (1) and (2) are equivalent. You can also decide whether or not you would have come to the same conclusion as me if you interpreted them in the same way as me.
For your next post, I want you to try to explain your interpretation of (1) and (2), and any consequences of the two.
Bad Horse: I'm hoping you do this too, since I know you believe the two sets to be equal.
1605732
Agreed, there are more useful ways to classify things when trying to do most things. This is only important when trying to understand miscommunication and differences in understanding.
Parts of this are in spoiler tags because Bad Horse hasn't had the chance to respond, and it would take too long for him to recover and type up a response. You can highlight the whole post to read it easily.
1607211
We only need an additional restriction on N if we're trying to make Peano arithmetic equal to set theory arithmetic. The circles provide a useful and intuitive way to label infinities, which is something set theory's generation of numbers cannot do. Infinity can be a natural number in Peano arithmetic, but not in set theory arithmetic.
Let S(a)=a, and let a be a representation of infinity.
a+3 = a+S(0) = S(a+0) = S(a) = a
You can do this for any S^k(0), so a+k=a for all k, which makes intuitive sense if a represents infinity.
Multiplication comes up with unsurprising results, but it's consistent with the way infinities are handled in limits. 2*a ends up reducing to a+a, 3*a to a+a+a, and so on.
So, does it make sense? Is the interpretation equivalent to yours? Does the inequivalence of set theory arithmetic and Peano arithmetic obviously follow from my interpretation?
1609788
I am using the earlier definition where S(0)=3, S(3)=6, etc. It was a weird decision that I should have made clear.
For Sᵏ(a)=a, k!=1, it seems to reduce to something similar to modular arithmetic base k, except any Sᵏ(a) can be the relative 0. It's a very strange case where every Sˣ(a) can be treated equally, but can't be proven equal by any method I've found. I believe you're right, this is same as your interpretation.
1609788
>>You can also decide whether or not you would have come to the same conclusion as me if you interpreted them in the same way as me.
If you have a response to this, I'm hoping you'll post it so we can bring that part of the discussion to a close.Nevermind, we answered the original question with
>>Your interpretation is not equivalent to mine
And the fact that both of our interpretations lead to different valid conclusions.
Warning: the second page of this comment section contains untagged spoilers.
I'm going to stop spoiler-tagging because it's annoying to read, and we're on a separate page from the question now. I put a note on my last comment saying as much.
1610828
You're right about having a different interpretation because you missed a case, but that's the original point I was trying to make. The subjectivity comes into play because of communication problems that are inherent in everything, including math. The fact that you missed a case means that the language we use to describe mathematical statements isn't sufficient to exactly translate mathematical concepts between the two of us. This leads to the problem of verifying that we're actually thinking about the same thing when we say any mathematical statement, and yada yada subjectivity.
>>The consistency of math depends on the consistency of the understanding of its language.
I actually saw the k≠1 case when I tried to apply my "a is infinity" idea to my original table with length-2 cycles, and saw that I couldn't prove a=S(a), so I had to make that a given.
Yes, I would be interested in a math group, but I really need to get back to work for a little while. I'll get back to the rest of your comment later because it's a little hard to parse.
Keep in mind that addition is not necessarily commutative between rings, and that your final answer will share the same unit as the left operand's ring.
I don't think you'll be able to prove that a+S(a)=a because, for a=infinity, this is not true in the limit. In the limit, a+S(a)=a+a. If you could prove that, then my understanding of S(a)=a would be wrong, and we can't have that.
1611456
Quick note (refusing to read anything above just yet): We misunderstood that ninth axiom. It doesn't define K relative to S and N, it declares a property of all sets. That axiom does rule out cycles in the natural numbers.
It would still be fun to see where things would go without that axiom.
1611456
I have some more time now.
I created a group called "My Discalculic Pony: Math is Hard". We should move the discussion there so we stop flooding Bad Horse's blog. Feel free to suggest another name or create your own group, which I'll join. I've never created or run a group here before, and I'm more than okay with you running it.
http://www.fimfiction.net/group/201562/my-discalculic-pony-math-is-hard
I'll create a topic summarizing things here soon.
Edit: Yes, this is very similar to affine spaces. The only quirks are that these are discrete (not an issue) and finite (maybe not an issue). I'll look more into it tonight.
1636062
http://www.fimfiction.net/group/201616/my-discalculic-pony-math-is-hard
I'll post a response there once I understand what a "modular group of a prime" is. I'm reading the wikipedia article on modular groups, and my mind has already been blown twice.
It's kind of idiotic for me to look at these blog posts without taking time to dredge through all the comments. I know what comments on your blog posts are like. That said, I'm still going to skip them because I have writing to do, but I wanted to share a thought.
You're contending that the point of a story, on some level, is to share values, be they personal, social, or absolute—and you sound uncomfortable with the idea that we may not actually have absolute values which can be understood and shared.
In that case, doesn't it make some sense to just try to tell stories that are as true as possible, whatever values they may contain? Even if something muddles the value you want to communicate, if it feels like a true depiction, would it not make sense to let that value get muddled for the sake of providing a story that might more closely match an absolute value, if one were to exist? It sort of goes hand in hand with the idea that stories should challenge the reader, I think—and I'm not sure I think that's entirely true (and likewise I'm not sure it's not, I just haven't really thought about it), but if one were to adopt it as a perspective, it seems like it's perfectly sensible to allow stories to be inconsistent in a way that requires the reader to sift values and look for what truth they may be able to find, if there is such a thing.