![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
*sighs*
*sighs*
Reposted from my Facebook:
Imagine the following scenario (a variation on the classic dilemma known as Newcomb's Problem):
About six months ago, a crack team of psychologists came up with a brilliant new device, and decided to run a curious experiment to test it. The experiment takes the following form:
There is only one catch in this procedure: the case either contains blank bills or the million, as follows. If the psychologists predict the subject would return the envelope with the thousand dollars, the case contains the million. But if the psychologists predict that the subject will return the envelope with the blank paper, the case contains blank paper. And in each of the one hundred trials so far, the psychologists have always gotten it right. Everyone has either left with the thousand or left with the million.
(Edit: Well, not quite. A few clever people thought to randomize the envelopes so that they didn't know whether they lost the thousand or not. About half of them walked away with a thousand, the other half with nothing.)
The experiment is valid - it has been tested by dozens of experts in experimental protocol, sleight of hand, hypnotism, and every other relevant field. They neither coerce your choice nor switch out the million if you choose to keep the thousand.
You are in the room, with your two envelopes, and the attendant is before you with his case.
Do you give him the thousand dollars or the blank paper?
Imagine the following scenario (a variation on the classic dilemma known as Newcomb's Problem):
About six months ago, a crack team of psychologists came up with a brilliant new device, and decided to run a curious experiment to test it. The experiment takes the following form:
- Each subject, chosen by lottery, is provided with the money to purchase two identical plain manilla envelopes.
- They and their envelopes are given free transportation to the lab, where they (but not the envelopes) fill out a survey.
- They wait approximately one hour, and then are ushered into the experiment room.
- In that room, they are permitted to examine three stacks - one containing twenty U.S. fifty-dollar bills, one containing twenty fifty-dollar-bill-sized pieces of blank U.S. fifty-dollar-bill stock, and one containing one thousand U.S. one-thousand-dollar bills.
- An attendant removes the stack of thousand-dollar bills. They are instructed to privately place one of the remaining stacks in each of their manilla envelopes, so that they would have two apparently-identical envelopes, and then signal.
- On the signal, the attendant returns with a case, which either does or does not contain the million dollars. The subject then gives either of their two envelopes in return for the case.
There is only one catch in this procedure: the case either contains blank bills or the million, as follows. If the psychologists predict the subject would return the envelope with the thousand dollars, the case contains the million. But if the psychologists predict that the subject will return the envelope with the blank paper, the case contains blank paper. And in each of the one hundred trials so far, the psychologists have always gotten it right. Everyone has either left with the thousand or left with the million.
(Edit: Well, not quite. A few clever people thought to randomize the envelopes so that they didn't know whether they lost the thousand or not. About half of them walked away with a thousand, the other half with nothing.)
The experiment is valid - it has been tested by dozens of experts in experimental protocol, sleight of hand, hypnotism, and every other relevant field. They neither coerce your choice nor switch out the million if you choose to keep the thousand.
You are in the room, with your two envelopes, and the attendant is before you with his case.
Do you give him the thousand dollars or the blank paper?
Tags:
In honor of the ![[livejournal.com profile]](https://www.dreamwidth.org/img/external/lj-userinfo.gif)
goblinpaladin's birthday (last month...), here is a review of What Science Offers the Humanities: Integrating Body and Culture by Edward Slingerland, 2008.
There's an old Isaac Asimov essay I recall reading where he discusses the implicit social hierarchy of different fields of study. You know, where math is more prestigious than physics, which is in turn 'above' chemistry, which is 'above' biology, et cetera. Asimov then asked (I paraphrase), "What's above mathematics?"
His answer was "the humanities". And he defended the answer with a little story, whose details I've sadly forgotten, but which essentially compared the reactions of the faculty at a school to (a) a student named Cicero failing rhetoric and (b) a student named Gauss failing mathematics. Asimov pointed out that all of them would laugh at the former (being as we all know Cicero was a great orator) but that only the math and science people would be amused at the latter (being as none of the humanities scholars would ever have heard of a mere mathematician, nor cared about his extraordinary influence upon mere math and sciences).
Sociologically, Asimov was probably just about right. Ontology, however, is Professor Slingerland's game, and he proposes just the opposite. And inverting this hierarchy - making the case for humanities as a higher-order level of explanation above neuroscience, psychology, biology, et cetera, the same way chemistry is a higher-order level of explanation above quantum physics, and just as dependent on its substrate - is the purpose of his book. It is so, he explains, because humanities is in desperate need of new life - it is visibly, clearly stagnating, as many scholars have observed, and Slingerland argues that an "embodied" or "vertically integrated" view of the humanities is necessary to move forward. Thus What Sciences Offers the Humanities seeks to open a new strain of humanities studies in close collaboration with scientific knowledge.
There. Now let us discuss what it does.
What Science Offers the Humanities, between introduction and conclusion, is divided into three parts. The first is a refutation of the objectivist and postmodernist views of humanity, the second his physicalist tertium quid based on modern cognitive science, and the third a defense of his view against a few anticipated objections. It is quite enough of a task for a bookshelf of books, and indeed Slingerland makes reference to at least that many along the way. Further, it is by its very nature difficult reading in many places - Slingerland in this book writes philosophy, and a modern philosopher must blaze a path through some of the harshest terrain in our mental landscapes.
(Incidentally, delicious little metaphors like that are featured prominently in Slingerland's "vertically integrated" model of humanity, described in Part 2. More on that anon.)
First, the refutations. Objectivism (which, in this case, contains a sort of Smullyan-logician theory of the person and the correspondence theory of truth) Slingerland spends comparatively little time with - while it is certainly not unpopular (I have strong inclinations in its direction myself), strong criticisms of it are well-established in the humanities, to whose scholars Slingerland addresses the book. Thus he deals his objections out quickly and competently (though not completely enough for my satisfaction - as I said, strong inclinations) and turns his attention to the other side.
Postmodernism, he explains, is a controversial term to use for what he describes. As he explains in the introduction, "virtually every [modern] postmodernist denies being one". Thus his treatment of postmodernism ends up extended over two chapters, with one dedicated chiefly to showing that, as he defines it, the appellation "postmodernist" still applies to many of the scholars he addresses, and only afterwards establishing the self-refuting nature of postmodernist theories. Naturally, for the non-postmodernist reader, these are among the most difficult chapters in the book - possibly by its very disconnect with experiential reality, postmodernist writing is almost invariably turgid. The density of the material is leavened by Slingerland's well-executed asides and rhetorical flourishes - his discussion of the Sokal hoax particularly struck my fancy - but those with an active disinterest in postmodernism may find it tiring. However, those coming from the humanities would be likely to profit much from these chapters - both by exposure to some basic objections to certain common lines of thought in the works of their peers and, if they share said lines of thought, by exposure to problems with their theoretical frameworks that need resolution or refutation.
Having thus cleared the ground, Slingerland turns to his own theory.
I will not attempt to elaborate his theory for him. The most central element of it is the theory of conceptual blending. This theory (originating, Slingerland says, with Gilles Fauconnier and Mark Turner) maintains that most (perhaps all) of human thought involves the mixing of properties from various already-existing ideas, as illustrated in expressions like "digging your own financial grave". This sort of combination (in the example, drawing the emotional content of the grave to accent the suggestion that a given financial plan is unsound), Slingerland argues, is a fundamental, universal part of how human beings work with ideas - he demonstrates its generality to analysis of cultural artifacts (a major part of humanities) with an analysis of the fourth-century B.C.E. Chinese Confucian work Mencius by blending theory.
After introducing his theory, much of the rest of the book deals with probable objections from the humanities tradition. (As a proponent of a minority theory, Slingerland is obliged to spend the main part of his book in its defense.) It is interesting material - defenses of pragmatism, refutations of common fears of reductionism, and the like - and competently presented, but it is certainly a decline from the excitement of the various introductions - of his theory, of postmodernism's weaknesses, of objectivism's weaknesses, and of the book entire.
It is not surprising when a book is exciting at the start and less so towards the end. What struck me in this case, however, is that there is a definite sense of the precise element lacking - and, ironically, that element is science. Slingerland is a fan of science, but he is a sinologist - student of Chinese culture - not a scientist. He has a breadth of scientific reading that does him great credit, a breadth far in excess of mine own, but his lack of depth in the specific fields shows. He quotes Dawkins and Dennett excellently, but he seems to need to. It is not a fault - he isn't a scientist - but the difference does make his very real contributions seem a little grayer in contrast.
What is the bottom line?
Slingerland's What Science Offers the Humanities is an excellent epistle to a world of humanities work in need of new insight - one with the understanding of the Academy whose lack prevents the Sokals, and even the Dawkins and the Dennetts, from engaging and not antagonizing its audience. It draws from the strength of the sciences to build a vision of a better university - for, as Slingerland points out in the conclusion, the sociological and psychological studies are rapidly approaching territory which requires knowledge of the humanities, just as they are - or should be - transforming the understanding of what the humanities contain.
As a popular science book, it is not. In its path, it alludes to a spread of important discoveries to understanding of the humanities, and of humanity, but its aim is not to bring true comprehension of these to the reader. Its aim is to show that the social sciences are relevant.
It shows this. That is enough.
goblinpaladin's birthday (last month...), here is a review of What Science Offers the Humanities: Integrating Body and Culture by Edward Slingerland, 2008.There's an old Isaac Asimov essay I recall reading where he discusses the implicit social hierarchy of different fields of study. You know, where math is more prestigious than physics, which is in turn 'above' chemistry, which is 'above' biology, et cetera. Asimov then asked (I paraphrase), "What's above mathematics?"
His answer was "the humanities". And he defended the answer with a little story, whose details I've sadly forgotten, but which essentially compared the reactions of the faculty at a school to (a) a student named Cicero failing rhetoric and (b) a student named Gauss failing mathematics. Asimov pointed out that all of them would laugh at the former (being as we all know Cicero was a great orator) but that only the math and science people would be amused at the latter (being as none of the humanities scholars would ever have heard of a mere mathematician, nor cared about his extraordinary influence upon mere math and sciences).
Sociologically, Asimov was probably just about right. Ontology, however, is Professor Slingerland's game, and he proposes just the opposite. And inverting this hierarchy - making the case for humanities as a higher-order level of explanation above neuroscience, psychology, biology, et cetera, the same way chemistry is a higher-order level of explanation above quantum physics, and just as dependent on its substrate - is the purpose of his book. It is so, he explains, because humanities is in desperate need of new life - it is visibly, clearly stagnating, as many scholars have observed, and Slingerland argues that an "embodied" or "vertically integrated" view of the humanities is necessary to move forward. Thus What Sciences Offers the Humanities seeks to open a new strain of humanities studies in close collaboration with scientific knowledge.
There. Now let us discuss what it does.
What Science Offers the Humanities, between introduction and conclusion, is divided into three parts. The first is a refutation of the objectivist and postmodernist views of humanity, the second his physicalist tertium quid based on modern cognitive science, and the third a defense of his view against a few anticipated objections. It is quite enough of a task for a bookshelf of books, and indeed Slingerland makes reference to at least that many along the way. Further, it is by its very nature difficult reading in many places - Slingerland in this book writes philosophy, and a modern philosopher must blaze a path through some of the harshest terrain in our mental landscapes.
(Incidentally, delicious little metaphors like that are featured prominently in Slingerland's "vertically integrated" model of humanity, described in Part 2. More on that anon.)
First, the refutations. Objectivism (which, in this case, contains a sort of Smullyan-logician theory of the person and the correspondence theory of truth) Slingerland spends comparatively little time with - while it is certainly not unpopular (I have strong inclinations in its direction myself), strong criticisms of it are well-established in the humanities, to whose scholars Slingerland addresses the book. Thus he deals his objections out quickly and competently (though not completely enough for my satisfaction - as I said, strong inclinations) and turns his attention to the other side.
Postmodernism, he explains, is a controversial term to use for what he describes. As he explains in the introduction, "virtually every [modern] postmodernist denies being one". Thus his treatment of postmodernism ends up extended over two chapters, with one dedicated chiefly to showing that, as he defines it, the appellation "postmodernist" still applies to many of the scholars he addresses, and only afterwards establishing the self-refuting nature of postmodernist theories. Naturally, for the non-postmodernist reader, these are among the most difficult chapters in the book - possibly by its very disconnect with experiential reality, postmodernist writing is almost invariably turgid. The density of the material is leavened by Slingerland's well-executed asides and rhetorical flourishes - his discussion of the Sokal hoax particularly struck my fancy - but those with an active disinterest in postmodernism may find it tiring. However, those coming from the humanities would be likely to profit much from these chapters - both by exposure to some basic objections to certain common lines of thought in the works of their peers and, if they share said lines of thought, by exposure to problems with their theoretical frameworks that need resolution or refutation.
Having thus cleared the ground, Slingerland turns to his own theory.
I will not attempt to elaborate his theory for him. The most central element of it is the theory of conceptual blending. This theory (originating, Slingerland says, with Gilles Fauconnier and Mark Turner) maintains that most (perhaps all) of human thought involves the mixing of properties from various already-existing ideas, as illustrated in expressions like "digging your own financial grave". This sort of combination (in the example, drawing the emotional content of the grave to accent the suggestion that a given financial plan is unsound), Slingerland argues, is a fundamental, universal part of how human beings work with ideas - he demonstrates its generality to analysis of cultural artifacts (a major part of humanities) with an analysis of the fourth-century B.C.E. Chinese Confucian work Mencius by blending theory.
After introducing his theory, much of the rest of the book deals with probable objections from the humanities tradition. (As a proponent of a minority theory, Slingerland is obliged to spend the main part of his book in its defense.) It is interesting material - defenses of pragmatism, refutations of common fears of reductionism, and the like - and competently presented, but it is certainly a decline from the excitement of the various introductions - of his theory, of postmodernism's weaknesses, of objectivism's weaknesses, and of the book entire.
It is not surprising when a book is exciting at the start and less so towards the end. What struck me in this case, however, is that there is a definite sense of the precise element lacking - and, ironically, that element is science. Slingerland is a fan of science, but he is a sinologist - student of Chinese culture - not a scientist. He has a breadth of scientific reading that does him great credit, a breadth far in excess of mine own, but his lack of depth in the specific fields shows. He quotes Dawkins and Dennett excellently, but he seems to need to. It is not a fault - he isn't a scientist - but the difference does make his very real contributions seem a little grayer in contrast.
What is the bottom line?
Slingerland's What Science Offers the Humanities is an excellent epistle to a world of humanities work in need of new insight - one with the understanding of the Academy whose lack prevents the Sokals, and even the Dawkins and the Dennetts, from engaging and not antagonizing its audience. It draws from the strength of the sciences to build a vision of a better university - for, as Slingerland points out in the conclusion, the sociological and psychological studies are rapidly approaching territory which requires knowledge of the humanities, just as they are - or should be - transforming the understanding of what the humanities contain.
As a popular science book, it is not. In its path, it alludes to a spread of important discoveries to understanding of the humanities, and of humanity, but its aim is not to bring true comprehension of these to the reader. Its aim is to show that the social sciences are relevant.
It shows this. That is enough.
Tags:
So I was pounding away at the grading, and my mind started to drift, and, well...
Does anybody else find themselves writing their own personal scriptures in their head?
Raise not hypocrisy to the stature of a Great Sin! To prove hypocrisy is to prove moral failing, but to prove moral failing is nothing if it is not done to correct, and to prove hypocrisy corrects nothing. Instead treat each hypocrite as herself, and ask: which of the three hypocrites is she?
The first hypocrite is she whose professions are righteous and acts are unrighteous. To you, I say: praise her! Hard is the road of righteousness, and many will stumble from it - praise her for her noble words, and commiserate with her when she falls short of them.
The second hypocrite is she whose professions are unrighteous and acts are righteous. To you, I say: praise her! Rare is the soul whose instincts are so pure, and that she has been confused in her thoughts is no fault. Praise her for her noble deeds, and teach her to praise and take pride in them herself.
The third hypocrite is she whose professions are unrighteous and acts are unrighteous. To you, I say: take pity, for what all of us fear and strive to avoid, she suffers from, and teach her as you teach all who have lost their way.
Does anybody else find themselves writing their own personal scriptures in their head?
My mom told me this story once. She was in an English class, Lit class, something like that - high school or college - and the teacher was talking about that "How do I love thee? Let me count the ways" poem. Dreck, he said. Or didn't, probably; I don't remember Mom's words, and she might not remember his. Hers? I think his. Anyway, he went along describing in detail all the ways this poem was terrible, and finally said, Here, just listen to it! And opened the book and read it out loud.
(I'm going to invoke artistic license here, depart from my mother's account, and quote Sonnets from the Portugese: XLIII from RPO:)
And then he stopped.
Hey, that's actually pretty good, he said.
We may be tempted to laugh at the spectacle of the critic being overwhelmed by the work he tried to shred. But that is not the lesson here - he spoke his mind in the most laudable sense of the phrase, and that he had to - and did - reverse himself a moment later merely shows that he was honest.
Nor should we believe that we may not lambast any work of art. For example, Rescue from Gilligan's Island was a terrible, terrible movie (although not, fortunately, near-fatally so), and no amount of misplaced excoriation will change that.
Insead, we should say this: familiarity does not require contempt. The old "To be or not to be" soliloquy, High Noon with Gary Cooper, Vivaldi's Concerto No. 1 in E major, Op. 8, RV 269 ("Spring" from the Four Seasons), Ludwig van Beethoven's Symphony No. 5 in C minor, Op. 67, Leonardo da Vinci's Portrait of Lisa Gherardini, wife of Francesco del Giocondo, Melville's Moby Dick - these things are familiar because they are superb. Let never cynicism, misanthropy, the desire for originality, or the opinion of your companions stop you from recognizing that.
(I'm going to invoke artistic license here, depart from my mother's account, and quote Sonnets from the Portugese: XLIII from RPO:)
How do I love thee? Let me count the ways.
I love thee to the depth and breadth and height
My soul can reach, when feeling out of sight
For the ends of Being and ideal Grace.
I love thee to the level of everyday's
Most quiet need, by sun and candlelight.
I love thee freely, as men strive for Right;
I love thee purely, as they turn from Praise.
I love thee with the passion put to use
In my old griefs, and with my childhood's faith.
I love thee with a love I seemed to lose
With my lost saints,—I love thee with the breath,
Smiles, tears, of all my life!—and, if God choose,
I shall but love thee better after death.
And then he stopped.
Hey, that's actually pretty good, he said.
We may be tempted to laugh at the spectacle of the critic being overwhelmed by the work he tried to shred. But that is not the lesson here - he spoke his mind in the most laudable sense of the phrase, and that he had to - and did - reverse himself a moment later merely shows that he was honest.
Nor should we believe that we may not lambast any work of art. For example, Rescue from Gilligan's Island was a terrible, terrible movie (although not, fortunately, near-fatally so), and no amount of misplaced excoriation will change that.
Insead, we should say this: familiarity does not require contempt. The old "To be or not to be" soliloquy, High Noon with Gary Cooper, Vivaldi's Concerto No. 1 in E major, Op. 8, RV 269 ("Spring" from the Four Seasons), Ludwig van Beethoven's Symphony No. 5 in C minor, Op. 67, Leonardo da Vinci's Portrait of Lisa Gherardini, wife of Francesco del Giocondo, Melville's Moby Dick - these things are familiar because they are superb. Let never cynicism, misanthropy, the desire for originality, or the opinion of your companions stop you from recognizing that.
For anyone who feels like answering, here or in their own journals:
( My answers, below the cut. )
Consider the following fill-in-the-blank: "If someone said I wasn't _______________, I would object."
(Clarification: Imagine someone is describing you - either explicitly (e.g. "Robin isn't a guy!") or implicitly (e.g. "She likes LJ") - and they describe you inaccurately (see either of previous examples). The question is not whether you correct them - an interesting question of etiquette - whether you dislike being described thus.)
( My answers, below the cut. )
Tags:
This fall at UMD, I'm taking advantage of my 10-credit tuition remission/fourth year of the four year scholarship free registration to take another non-engineering course dear to my heart: PHIL282: Action and Responsibility. I mean, just read the catalog entry!
(Incidentally, I've started reading the book - it seems pretty good, and about as easily readable as philosophy can get.)
Now, most of you aren't taking the class. But it occurs to me it'd be interesting anyway to see. (And, after all, my stance could easily change over the semester.)
(Oh, if you're not sure, go ahead and be ambitious and say what you think. If I omitted your stance, of course, that's different.)
[Poll #1043677]
If what science tells us is true, that every event has a cause, can we still have free will? Does a horrible childhood mitigate a violent criminal's blameworthiness? Is anyone ever truly responsible for anything? This course deals with these problems in ethics, philosophy of mind, and metaphysics, covering such topics as personal agency, free will, and responsibility. The current version of the course will focus on theories of free will and responsibility, and the related phenomena of reactive emotions (like gratitude and guilt) and excuses (e.g., accidents and mistakes).
The required text for the course will be: Robert Kane, A Contemporary Introduction to Free Will (Oxford), possibly along with further readings containing highlights of contemporary debates over issues of responsibility.
Written requirements will include midterm and final exams, plus regular short writing assignments.
(Incidentally, I've started reading the book - it seems pretty good, and about as easily readable as philosophy can get.)
Now, most of you aren't taking the class. But it occurs to me it'd be interesting anyway to see. (And, after all, my stance could easily change over the semester.)
(Oh, if you're not sure, go ahead and be ambitious and say what you think. If I omitted your stance, of course, that's different.)
[Poll #1043677]
Tags:
Here, watch these two videos: Bad Day vs. Ordinary Day. Notice anything funny?
Now watch these two: Bad Day (live) vs. Ordinary Day (live). See it now?
I thought this was the twenty-first century. What is this crap doing here?
Edit: Whoa, she can dance! (Point still stands.)
Now watch these two: Bad Day (live) vs. Ordinary Day (live). See it now?
I thought this was the twenty-first century. What is this crap doing here?
Edit: Whoa, she can dance! (Point still stands.)
Tags:
1 July 1985: I am born.
7 March 1986: Richard W. Hamming gives a speech entitled "You and Your Research" that includes this part-of-a-paragraph:
circa 2000-2003: I read said speech off a printout m'dad had lying around. I am greatly impressed.
Ten minutes ago: I realize that this is relevant to my own life, to what I want to do in grad school and after.
7 March 1986: Richard W. Hamming gives a speech entitled "You and Your Research" that includes this part-of-a-paragraph:
Over on the other side of the dining hall was a chemistry table. I had worked with one of the fellows, Dave McCall; furthermore he was courting our secretary at the time. I went over and said, "Do you mind if I join you?" They can't say no, so I started eating with them for a while. And I started asking, "What are the important problems of your field?" And after a week or so, "What important problems are you working on?" And after some more time I came in one day and said, "If what you are doing is not important, and if you don't think it is going to lead to something important, why are you at Bell Labs working on it?" (emphasis added)
circa 2000-2003: I read said speech off a printout m'dad had lying around. I am greatly impressed.
Ten minutes ago: I realize that this is relevant to my own life, to what I want to do in grad school and after.
Okay, so I got two phones: the old, prepaid, cheapo Nokia phone, and the new, camera-enabled, flip-open, Verizon Singular phone. It should be obvious which one's better, right?
Except the new phone is kinda fragile (I bent the cover for the power socket yesterday), with an inferior user interface (more features, but less resolution on both battery life and reception), no decent games, a camera that keeps photographing the inside of my pocket, unintuitive call-waiting, &c., &c., &c.
The old phone? Snake II (i.e. Snake with bonus features), and, as I just discovered, an honest-to-goodness flashlight.
Great Ghu! A cell phone with a flashlight!
Except the new phone is kinda fragile (I bent the cover for the power socket yesterday), with an inferior user interface (more features, but less resolution on both battery life and reception), no decent games, a camera that keeps photographing the inside of my pocket, unintuitive call-waiting, &c., &c., &c.
The old phone? Snake II (i.e. Snake with bonus features), and, as I just discovered, an honest-to-goodness flashlight.
Great Ghu! A cell phone with a flashlight!
Too little stuff for a complete update*, but a few funny things:
Ta!
* Says the guy who just posted a one-line update consisting of a single link.§
† Which means this probably occurred Sunday afternoon.
‡ He'd actually started off asking for directions, then asked me if I could help him solve the problems. I carefully refused to sit in his car out of the cold while I looked at his stuff.
§ Which, incidentally, has both shown me a whole lot of tracks I might be interested in, and that I know nothing about electronic music at all. Neither of which surprised me. I was glad to see that "synth pop" was the correct category for Eurythmics, though.
- The guy (vaguely African-seeming, but I wouldn't really know) who said he was 'good at math', but needed help with 'translations'. 'Translations', in this case, being along the lines of:
Fill in the blank with the appropriate word phrase: "a - b" means b ______ a.
I begged off, saying I had to finish my art assignment†, and gave him directions to the mathematics building‡. - My ankles hurt so much afterwards, I could barely move.
- What does the question of whether you can know something absolutely as a truth have to do with abortion? No, I'm serious, I still can't figure that one out.
- If a bank can lend out 90% of the money deposited therein, adding $100 to the bank's lending stock adds $1000 to circulation by a simple geometric series (r = 0.9) ... if all the money in circulation is redeposited deposited in the bank. So, what is the point of this exercise, exactly? And why are the business students still being tested on it?
- "At schema yourself resemblant". There – now I've posted a nonsensical spam subject line too.
Ta!
* Says the guy who just posted a one-line update consisting of a single link.§
† Which means this probably occurred Sunday afternoon.
‡ He'd actually started off asking for directions, then asked me if I could help him solve the problems. I carefully refused to sit in his car out of the cold while I looked at his stuff.
§ Which, incidentally, has both shown me a whole lot of tracks I might be interested in, and that I know nothing about electronic music at all. Neither of which surprised me. I was glad to see that "synth pop" was the correct category for Eurythmics, though.
The incomparable active_apathy, in the grand tradition of SCIENCE, has begun a new SCIENTIFIC experiment in the spread of intermemes (with SCIENCE!) across LJ-space.
The instructions (of SCIENCE!):
Please reply only to the person you got the meme from. To do otherwise would be counter to SCIENCE!
Edit: Comments are now locked ... for SCIENCE! Discuss intermeme here.
active_apathy, in the grand tradition of SCIENCE, has begun a new SCIENTIFIC experiment in the spread of intermemes (with SCIENCE!) across LJ-space.The instructions (of SCIENCE!):
- Go here, and leave a comment replying to the LJer you got the meme from
- Copy either the reply or link URL for your comment
- Put a link to that URL in step 1
- Repost these instructions
Please reply only to the person you got the meme from. To do otherwise would be counter to SCIENCE!
Edit: Comments are now locked ... for SCIENCE! Discuss intermeme here.
Tags:
At IHOP this evening, I was filling out a comment card when I observed the following (quoted from memory, emphasis added):
...what?
[...]
Quality of food:
Flavor of food
Appearance of food
Temperature of food: Hot food Hot!
Cleanliness of restaurant:
Cleanliness of exterior
Cleanliness of dining area
Cleanliness of restrooms
[...]
...what?
I was lying in bed the other night thinking about bases of arithmetic....
You know, it's kinda odd that insomnia due to math isn't that rare, for me.
Anyway, I was thinking about bases of arithmetic, and Hal Clement's throwaway gag in Still River* about an ancient academic controversy over octal versus duodecimal at the School in his story, and the problem of factoring, and how weak the theoretic justifications for all those specific bases are.
You may be surprised at this claim. "But octal is clearly the most rational," you might be saying. "Binary is the most fundamental base of arithmetic, and octal is a logical extension of that."
Uh-huh. Logical extension how, exactly? If you've got an old 24-bit mainframe?
"That just implies hexadecimal is even better."
Yeah, okay, but that's still just one advantage – convenient relation to binary. Besides, larger bases get more and more inconvenient as you have to memorize more and more figures and (more importantly) bigger and bigger multiplication tables. So hex is great for computer scientists, and octal used to be great for computer scientists, but that doesn't translate to their being the best day-to-day radices. They've got one advantage – one huge advantage – but it's only a useful advantage in a few contexts.
And when we turn to duodecimal, base 12 (and its cousin, sexagesimal, base 60), we find a similar sole advantage: the base has many factors. Yeah, that's great if you're writing fractions – 1/3 becomes 0.4duodecimal, 4/15 becomes [00].[16]sexagesimal (each bracket is a decimal representation of one figure), etc. – but how often do you need to?
Actually, that gets to the key point: what do you need to do regularly with a number system? Really, it comes down to:
...pretty much in that order. I mention "write" because while messing with the basic principle of positional notation may be fun, standard positional notation is a pretty solid, intuitive way to write down how many books you have on the second shelf of your bookcase.** And while binary may be logically the simplest radix, 10101 takes up a lot more space than 21†. (Oh, and just coming up with symbols for a sexagesimal system is horrid, forgetting all its other disadvantages.)
So, what about these others? Well, we're only looking at standard positional systems, so whatever advantages balanced ternary systems have, we're ignoring them. Anyway, in standard positional systems, 'add' and 'subtract' pretty much make only one contribution to complexity: how many digits are in your basic addition tables. And since we humans have shown that we can handle base 10 pretty well, anything up to around that size is probably fine. Multiplication is almost the same, but there's an advantage for highly composite (and not-quite-highly composite) radices – all the rows with divisors of the base are simpler. (I guess that means duodecimal isn't quite as pointless as I thought.) Division – well, you're doing long division, so have to come up with a compromise between having fewer digits (higher radix) and fewer multiples of the denominator (lower radix). Oh, and having lots of divisors means fewer recurring 'decimals'.
This sounds like it's building up to sell duodecimal after all. No, it isn't.
I'm saying we should use senary. Base six.
The actual inspiration for this came that night, when I was comparing duodecimal and octal to decimal. Duodecimal, I had decided, had the advantage of many factors. Octal, of being a power of 2. But what about decimal?
Well, as it happens, I had already realized that decimal was unusually good at testing divisibility. As it happens, there are two types of numbers that are very easy to check divisibility of in a given base: factors of the base, and adjacent natural numbers to the base. In decimal, the first group consists of 2, 5, and 10. The latter group consists of 9 and 11. Divisibility by the first set can be checked through examining the final digit – an even digit means multiple of 2, 5 or 0 mean multiple of 5, 0 means multiple of 10. This is really easy – in big O notation, it's O(1), meaning it takes a constant length of time for any number. As for 9 and 11, it's easy to prove from modulo arithmetic that you need merely add all the digits (for 9 – 'casting out nines', basically) or alternately add and subtract (for 11) to check divisibility. These are both O(log n) – the time they take is proportional to the length of the number, written out.‡
Now, all bases get the benefits of these two effects. But because 9 is a power of 3, in base 10 this means that testing divisibility by 2, 3, 5, and 11 is easy. Four of the first five prime factors, accounting for 75.76% of all numbers. That's pretty good – only missing the seven. Duodecimal only gets 2 and 3 from its factors, and 11 and 13 from the casting-out methods, so it misses five and seven. Octal would get seven, of course (one less than the base), but it only has two as a prime factor and nine = three squared as one over the base, so it misses five.
But six doesn't. It misses eleven, but with seven it gets 77.14%, better than base 10, which beat bases 8 and 12. It's smaller than 10, which means only six symbols and 21 unique entries each on the addition and multiplication tables. (It would be 36, but since 2+3 = 3+2 and 2*3 = 3*2, a large fraction drop out.) Being smaller also makes long division easier – you need only write 5 multiples of the divisor, instead of 9. Against that, you've got longer numbers, but even when you get pretty large (e.g. the age of the universe, 13.7 billion years), it's not a big difference (13 senary figures as opposed to 11 decimal figures). Being divisible by 2 and 3 means 1/2, 1/3, and 1/4 are all easy (1/4 = 0.13senary), and adds extra simplicity to two rows of the multiplication table (which has only six to start with, including the ones row).
Add these factors together, and I think that makes 6 the perfect base.§
But hey, who cares what I think!
[Poll #924107]
* Which is actually a pretty lame book, on rereading, but I still like it.
** Not that bijective numerations are that hard to count in – I just didn't want every link to be to Wikipedia.
† I'm not counting the Adobe Photoshop manual in this count.
‡ Which, you must note, is often much less than the number itself.
§ Yes, I did in fact spent seven hours writing a long, technical discussion of the relative merits of five different systems of positional notation, combined with an a priori enumeration of the most important principles of a number system, just so I could conclude with that sentence. I regret nothing!
You know, it's kinda odd that insomnia due to math isn't that rare, for me.
Anyway, I was thinking about bases of arithmetic, and Hal Clement's throwaway gag in Still River* about an ancient academic controversy over octal versus duodecimal at the School in his story, and the problem of factoring, and how weak the theoretic justifications for all those specific bases are.
You may be surprised at this claim. "But octal is clearly the most rational," you might be saying. "Binary is the most fundamental base of arithmetic, and octal is a logical extension of that."
Uh-huh. Logical extension how, exactly? If you've got an old 24-bit mainframe?
"That just implies hexadecimal is even better."
Yeah, okay, but that's still just one advantage – convenient relation to binary. Besides, larger bases get more and more inconvenient as you have to memorize more and more figures and (more importantly) bigger and bigger multiplication tables. So hex is great for computer scientists, and octal used to be great for computer scientists, but that doesn't translate to their being the best day-to-day radices. They've got one advantage – one huge advantage – but it's only a useful advantage in a few contexts.
And when we turn to duodecimal, base 12 (and its cousin, sexagesimal, base 60), we find a similar sole advantage: the base has many factors. Yeah, that's great if you're writing fractions – 1/3 becomes 0.4duodecimal, 4/15 becomes [00].[16]sexagesimal (each bracket is a decimal representation of one figure), etc. – but how often do you need to?
Actually, that gets to the key point: what do you need to do regularly with a number system? Really, it comes down to:
- Write.
- Add.
- Subtract.
- Multiply.
- Divide.
...pretty much in that order. I mention "write" because while messing with the basic principle of positional notation may be fun, standard positional notation is a pretty solid, intuitive way to write down how many books you have on the second shelf of your bookcase.** And while binary may be logically the simplest radix, 10101 takes up a lot more space than 21†. (Oh, and just coming up with symbols for a sexagesimal system is horrid, forgetting all its other disadvantages.)
So, what about these others? Well, we're only looking at standard positional systems, so whatever advantages balanced ternary systems have, we're ignoring them. Anyway, in standard positional systems, 'add' and 'subtract' pretty much make only one contribution to complexity: how many digits are in your basic addition tables. And since we humans have shown that we can handle base 10 pretty well, anything up to around that size is probably fine. Multiplication is almost the same, but there's an advantage for highly composite (and not-quite-highly composite) radices – all the rows with divisors of the base are simpler. (I guess that means duodecimal isn't quite as pointless as I thought.) Division – well, you're doing long division, so have to come up with a compromise between having fewer digits (higher radix) and fewer multiples of the denominator (lower radix). Oh, and having lots of divisors means fewer recurring 'decimals'.
This sounds like it's building up to sell duodecimal after all. No, it isn't.
I'm saying we should use senary. Base six.
The actual inspiration for this came that night, when I was comparing duodecimal and octal to decimal. Duodecimal, I had decided, had the advantage of many factors. Octal, of being a power of 2. But what about decimal?
Well, as it happens, I had already realized that decimal was unusually good at testing divisibility. As it happens, there are two types of numbers that are very easy to check divisibility of in a given base: factors of the base, and adjacent natural numbers to the base. In decimal, the first group consists of 2, 5, and 10. The latter group consists of 9 and 11. Divisibility by the first set can be checked through examining the final digit – an even digit means multiple of 2, 5 or 0 mean multiple of 5, 0 means multiple of 10. This is really easy – in big O notation, it's O(1), meaning it takes a constant length of time for any number. As for 9 and 11, it's easy to prove from modulo arithmetic that you need merely add all the digits (for 9 – 'casting out nines', basically) or alternately add and subtract (for 11) to check divisibility. These are both O(log n) – the time they take is proportional to the length of the number, written out.‡
Now, all bases get the benefits of these two effects. But because 9 is a power of 3, in base 10 this means that testing divisibility by 2, 3, 5, and 11 is easy. Four of the first five prime factors, accounting for 75.76% of all numbers. That's pretty good – only missing the seven. Duodecimal only gets 2 and 3 from its factors, and 11 and 13 from the casting-out methods, so it misses five and seven. Octal would get seven, of course (one less than the base), but it only has two as a prime factor and nine = three squared as one over the base, so it misses five.
But six doesn't. It misses eleven, but with seven it gets 77.14%, better than base 10, which beat bases 8 and 12. It's smaller than 10, which means only six symbols and 21 unique entries each on the addition and multiplication tables. (It would be 36, but since 2+3 = 3+2 and 2*3 = 3*2, a large fraction drop out.) Being smaller also makes long division easier – you need only write 5 multiples of the divisor, instead of 9. Against that, you've got longer numbers, but even when you get pretty large (e.g. the age of the universe, 13.7 billion years), it's not a big difference (13 senary figures as opposed to 11 decimal figures). Being divisible by 2 and 3 means 1/2, 1/3, and 1/4 are all easy (1/4 = 0.13senary), and adds extra simplicity to two rows of the multiplication table (which has only six to start with, including the ones row).
Add these factors together, and I think that makes 6 the perfect base.§
But hey, who cares what I think!
[Poll #924107]
* Which is actually a pretty lame book, on rereading, but I still like it.
** Not that bijective numerations are that hard to count in – I just didn't want every link to be to Wikipedia.
† I'm not counting the Adobe Photoshop manual in this count.
‡ Which, you must note, is often much less than the number itself.
§ Yes, I did in fact spent seven hours writing a long, technical discussion of the relative merits of five different systems of positional notation, combined with an a priori enumeration of the most important principles of a number system, just so I could conclude with that sentence. I regret nothing!
Approximating the shape of a tomato as a cube is an example of another general strategy for making order-of-magnitude estimates. A similar situation would occur if you were trying to estimate how many m2 of leather could be produced from a herd of ten thousand cattle. There is no point in trying to take into account the shape of the cows' bodies. A reasonable plan of attack might be to consider a spherical cow. Probably a cow has roughly the same surface area as a sphere with a radius of about 1 m, which would be 4π (1 m)2. Using the well-known facts that pi equals three, and four times three equals about ten, we can guess that a cow has a surface area of about 10 m2, so the herd as a whole might yield 105 m2 of leather.
From the Light and Matter series of physics textbooks, Newtonian Physics, Section 1.4 – the textbook
alun_clewe plans to use for his class.I'm only at the beginning, but I must say: so far, very good.
Tags:
Okay, I can't sleep for wondering how people would answer this, so...
Which do you value more: truth or happiness?
Answer any way you please (though I reserve the right to delete anything obscene).
Which do you value more: truth or happiness?
Answer any way you please (though I reserve the right to delete anything obscene).
I finally got my question answered! It had been vexing me for some time, and finally at my appointment a couple days ago I worked up the courage to ask.
The answer is: Floss first, because the brushing will clear away the dislodged matter. However, it doesn't really matter, because you'll be rinsing out your mouth anyway.
Packbat ... out!
Edit:chanlemur reports that his dentist recommended the opposite, on the grounds that the floss may carry fluoridated residue from the brushing into the gaps between the teeth. Please, ask your dentist that we may clear up this controversy!
The answer is: Floss first, because the brushing will clear away the dislodged matter. However, it doesn't really matter, because you'll be rinsing out your mouth anyway.
Packbat ... out!
Edit:
chanlemur reports that his dentist recommended the opposite, on the grounds that the floss may carry fluoridated residue from the brushing into the gaps between the teeth. Please, ask your dentist that we may clear up this controversy!