Kill Math - <AUTHOR> http://worrydream.com/KillMath/ <comment><USER2> What we have here is a failure to define our terms.

Math _is_ the manipulation of abstract symbols according to abstract rules. If you don't like symbols, you don't like math. If you are illiterate in symbols you are illiterate in math.

The word is often used imprecisely, though. Because so many real-world problems can be translated into math, there is a temptation to equate "math" with "any problem that can be expressed in math". Thus you frequently see poetic statements like "my cat is great at solving differential equations", or "music is math because it's all about harmonic series and Fourier analysis". But these things aren't literally true. You can put a bucket under a flowing faucet, and it will collect all the water, but that isn't really integration. The bucket isn't doing math.

And being ignorant of math isn't the same as being stupid. As the OP points out, you can get a lot of quantitative reasoning done without using math. A classic Fun Fact About Math is that it took thousands of years to invent the number zero. And it's true. But that doesn't mean that the ancient Egyptians used to waste hours staring into newly-emptied buckets and baskets in stunned amazement, murmuring "what on earth is that" to themselves in Coptic. People understood what "having no objects" meant long before there was a _symbol_ for "the number of objects in an empty basket". It was the _highly abstract symbol_ "zero", and the highly abstract operations involving zero, that had to be invented. [1]

It's worthwhile to recognize that interpreting the real world in terms of abstract symbols, and vice versa, is a terribly difficult skill that requires lots of practice. (In my case, I was well through grad school before many bits of physics clicked.) And it's worthwhile to recognize that you can often do without math: You can reason quantitatively without it. Birds do it! Bees do it! But don't pretend that you're doing math unless you are actually doing math. The abstractions _are_ the math.

\---

[1] Or, rather, discovered. Although we'd better stop there, because I won't be able to cope with the ensuing philosophical back-and-forth.

<comment><USER3> Completely disagree. Math _isn't_ manipulation of symbols. At all. Math is the study of mathematical objects, a practice often done using a formal language for the convenience and power it provides.

"0" is a formal symbol with particular formal behavior

"empty/missing/none" is a well-known physical concept

Zero is a precise, powerful mathematical object which can be represented by them both.

\---

This is difficult to deny. Unless you want to deny the providence of most widely recognized mathematicians throughout history, you have to accept that formal language of math is relatively new. Furthermore, it's alive and growing, inconsistant and incomplete. There is a meaningful frontier, and there you observe mathematicians are really studying something else and furiously creating the formal language to describe it.

In this light, metaphor is absolutely a useful tool in the same class as formal language for explaining and reasoning about math. You're right to point out the non-equivalence of the two, but the author's Kill Math project is in no way not math. Furthermore, I'm anecdotally a supporter of the author's belief that doing math competently requires knowing a the metaphorical side since your symbolic projects may fail or be unclear.

I'd be willing to accept that metaphor will never be as powerful as formal language, but it does discredit to the way (I'd wager) most people understand math to deny the metaphorical.

\---

At the heart of this trouble of definitions is Gödel's Incompletenesses. The practical effect of their discovery was the destruction of the dreams of formalists who had for years hope to discover the essential shape of the formal language from which all math would spring. With Incompleteness however, we are forced to admit that we can study, meaningfully, the behavior of mathematical objects for which the language of math cannot be used to reason about.

Then we extend that language, of course.

<comment><USER4> Are you sure you're accurately describing Godel's Incompleteness theorem? It's been a while, but I understood it at a technical level briefly. I'd be interested in knowing more about how you think it applies here.

<comment><USER3> No, I'm not. I'm interpreting it pretty loosely. Sorry about that. Correct me if I'm wrong here, though.

More directly, what I meant to say is that since there exist true theorems which cannot be proven within any particular choice of mathematical formalism, we need to operate with tools beyond simply symbolic manipulation. That was the death knell of Hilbert's Program and solidly separated the formal specification of math from "that thing which we're studying".

<comment><USER4> I think you are wrong - even though there are true, unprovable statements, they're unusual and to the best of my knowledge, not the subject of extensive study. More like curiosities ([http://en.wikipedia.org/wiki/List_of_statements_undecidable_...](http://en.wikipedia.org/wiki/List_of_statements_undecidable_in_ZFC)). Even if that were not the case, there is no alternate approach to studying them.

I'm not really sure that you mean about the "formal specification" for math vs. the "that thing we're studying". An informal (ie, not expressed in ZFC + 1rst order predicate calculus) proof of something non-trivial can go on for dozens, if not hundreds of dense pages of symbols. If I recall correctly, Whitehead's Principae Mathematica derived arithmetic from ZCF and predicate calculus, and it took the whole book.

I did a little reading to refresh myself on the subject, and this stood out as a good summary of the topic:

"In a sense, the crisis has not been resolved, but faded away: most mathematicians either do not work from axiomatic systems, or if they do, do not doubt the consistency of ZFC, generally their preferred axiomatic system. In most of mathematics as it is practiced, the various logical paradoxes never played a role anyway, and in those branches in which they do (such as logic and category theory), they may be avoided."

([http://en.wikipedia.org/wiki/Foundations_of_mathematics#Foun...](http://en.wikipedia.org/wiki/Foundations_of_mathematics#Foundational_crisis))

<comment><USER3> Your picture of mathematics is quite a bit more robust, so I won't deny that what you wrote here is more accurate than my "Gödel say it won't work, woe is our field!" brimstone version. So I'll explain my reasoning for invoking Gödel.

I mostly wanted to walk around the historical event I mentioned, the breaking of the Hilbert Program. At the time, it seemed that formal specification of math would provide a complete picture of what math was! Once the Program was finished then the job of mathematician would eke out into "computer" (of the abacus sort) or into other fields which interpreted the canon.

I'm not sure which death stroke was stronger, the incredible opaqueness and complexity of proof systems like ZFC or Gödel just saying what he was trying was outright impossible, but Hilbert's Program was killed before it even seriously took off, leaving the study of mathematics and the practical formalisms we use to study it pretty ad-hoc instead of grand and unified.

I'm unifying that with the fact that the way math seems to be practiced never comes from the formal language but instead first comes from imagining some kind of "mathematical object" and then taming its behavior with formalisms. You could consider them to be one and the same and argue that the difference is highly philosophical, and then this is where I'd invoke Gödel and inform you that there definitely exist things we could benefit from reasoning about that your formal language would fail to describe. This existence proof separates the classes of true things and provable things and makes their distinction more than philosophical.

Now, talking about what a "mathematical object" is gets you to the bleeding heart of the philosophy of science and epistemology. It's a tough question!

\---

As a final note, ZFC is ZF + Axiom of Choice... which, yes, most practicing mathematicians just accept AoC so that they can integrate or whatever. The formal world without AoC is very sparse, _but_ nobody has any sort of idea what the arbitrary decision means. I know that there has been some significant study of ZF-C, though it's been "impractical", I don't know if anyone is willing or capable of stating that ZF-C is in any way worse than ZFC. Impractical is a Mathematicians favorite adjective, so they're just two extant formal systems which disagree quite a lot on important things but we mostly pay attention to ZFC.

</comment></comment></comment></comment></comment></comment><comment><USER5> I appreciate that symbols can be an odd way to represent every day quantitative problems, but I have never had a problem with it. Sure, some people do, but this guy seems really royally pissed off at ordinary mathematics.

I have always been a proponent of having more than one way to teach a certain subject. Studies have shown that different people perceive and interact with information in very different ways. The current "one size fits all methodology" to teaching is lame, to say the least. So a new way of teaching people mathematics is welcome.

But that's not to say the old way didn't work for people like me. If this site kills math so that English majors can cope, I hope someday someone will kill poetry so that I can cope.

<comment><USER6> (Compacted for space. Original. Use tr '/' '\n' | sed -e 's/^ //' -e 's/ $//' to reëxpand, with a paragraph break being "\n\n". Sorry for the repeated initial edits and such; I had to try to work out the HN formatting rules.)

When humans try to learn symbolic math / How many of them struggle with the test! / The teacher thought of like a psychopath / Dishonoring the realm of human zest

"We must have our emotions!" students cry / "Or else we'll run around like apes, confused / Our brains are built for stories, not to scry / A world of numbers, strangled and abused."

The teacher sighs, "They always drag their feet / Unless they're cornered, up against the wall. / To risk _my_ job with answers incomplete! / They'll never use it later, after all."

Then, big surprise! The math is found at fault / Tear-stained by cringing memories of school / "Dispense with all the symbols, and Exalt / Thine Intuition"—that shall be the rule.

Professors' lamentations curse the air / Hung out to dry for calling any bluff / "To shun defective math must be unfair / For surely no one understands the stuff."

So woe to ye from near the world of forms / Who strain to show the populace your realms / They're immunized against your grand transforms / And explanation only overwhelms.

(Now, please don't take this poem at its word / Or treat it as authoritative fact / Exaggerated story and absurd / Polemic leave specifics inexact

The author's nearly _made_ of symbols, note— / Despite the slow decay of some to blanks / So though he doesn't mean to seem to gloat / He'd rather keep his "freakish" symbols, thanks.)

</comment></comment><comment><USER7> I'm sorry to be the one to have to bring this up. But not all mathematics can be represented visually. Maths breaks into a number of main branches, among them principally algebra, analysis and geometry.

Usually only the third can be represented visually, though often mathematicians develop diagrams which help internalise the complex notions involved in analysis and algebra too.

For example, in algebraic geometry, the more familiar notions of geometric objects such as curves and surfaces are replaced with purely algebraic notions, such as schemes. This is because of various categorical equivalences between geometric objects (on the geometric side) and various algebraic objects (on the algebraic side). But on the algebraic side, schemes are a very expansive generalisation of things that actually correspond to geometric (and visualisable) objects.

I once went to a teaching seminar on the use of a package called GeoGebra for the teaching of mathematics. None of us mathematicians could bring ourselves to put up our hands and ask how one might represent a complex of modules over a noetherian ring pictorially in GeoGebra. There's this fundamental misunderstanding amongst educators that symbolic mathematics is not essential to understanding maths.

This is an important insight when it comes to computer programs though. The same thing happens in computer science. You get splits between things that are geometric, symbolic and purely computational.

Often I get really annoyed at people showing off their latest concurrent programming paradigm by implementing a GUI or event loop for some graphical or network application. They forget that many things simply don't fit into that paradigm.

I equally get annoyed at computer scientists for forgetting that the number of integers is not about 10. Sometimes us mathematicians really want to do things with matrices of ten thousand by ten thousand entries.

</comment><comment><USER8> One of the great things about math is that it lets us surpass our own intuition. The spatial intuition we evolved in the wild doesn't work well for a number of things, which is why symbols and abstraction are so useful in the first place.

We don't need mathematics to figure out how a swinging pendulum works; we can do that intuitively. (Actually, this isn't completely true, but we can at least get the general idea.) Simple problems like that are worked out in classes so that students can get used to the mathematics. In domains where our intuition fails us - e.g. quantum mechanics, high-energy physics, statistical mechanics, not to mention 11+ dimensional formulations of string theory, infinite or fractional dimensional spaces, and more esoteric theoretical mathematics and physics - we rely on mathematical symbols and abstraction to guide us, because our finely honed physical intuition is useless (and sometimes worse than useless).

I'm interested in seeing what the author does with concepts like superposition and n-dimensional spaces. Replacing them with graphs and animations is not going to cut it.

<comment><USER9> I agree with you, not to mention the beauty of some very abstract mathematical concepts.

</comment></comment><comment><USER10> Two fairly simple improvements (to mathematics) I can think of:

1) Abandon the absolutely batty practice of representing everything with a single symbol. It's crazy. We still can't reliably represent mathematical symbols over the internet in text, we have to rely on images. I'm obviously biased, but mapping mathematical functions to _actual words_ (ala programming) would be a big win, imo.

2) Lock up all the physicists, mathematicians, engineers, logicians, you name it, and have them agree on a single unified notation. Every symbol ought to have one meaning and everyone needs to stop stealing symbols from a different field and giving it a new meaning! I'd wager that more than half of the symbols in this list (<http://en.wikipedia.org/wiki/List_of_mathematical_symbols>) have several valid interpretations. No thanks!

<comment><USER11> 1) What do you mean? It depends on field, but in most mathematical papers I read, the ideas are explained with words, not with symbols -- they only serve as helpful shortcuts. Anyway, I believe that properly used symbolism usually clarify the issue at hand, especially when word explanation is very long. For instance, what is faster to read and comprehend:

<http://mathbin.net/62276>

or

"Let V1 and V2 be a subspaces of W, such that their intersection is zero. Let f be a mapping from a direct sum of V1 and V2, such that it takes a vector, whose first component is x and second y to a difference of x and y multiplied by two."

And this was easy example, I can think of _a lot_ harder.

There is no regulating body of mathematical notation -- it can be (and usually is) created by introducing it in some paper or book by some mathematician who invented it and regards as useful. Frequently, there are more than notation introduced, but usually only one survives -- hopefully the best one. The only possibilities of encountering several different notations in use at once are either reading very old works, which is not good anyway, or the most recent ones, but I presume that people who are able to read them are also able to get over such a minor problem.

Seriously, I believe that the mathematic notation is a lot clearer, more intuitive and easier to understand than syntactic rules of many programming languages, for instance C++. Symbol overloading almost never pose a problem, since the intended meaning is usually obvious from the context. If one frequently misunderstands the intended meaning, it is a sign he does not really get the concepts involved, and the fact he is confused by notation is his smallest problem.

Even symbol overloading most often takes places only if the sign represents the same idea in all contexts. For instance, one usually uses '+' sign to represent a binary commutative operation whatever structure we all talking about, because, well, it represents similar idea. One can go even further and say that symbols like \oplus and \times in most contexts they are used in (Cartesian product of sets, direct product/sum of rings/groups/modules/vector spaces/mappings) are actually representing _exactly_ the same idea -- namely, the notion of product/coproduct in some category.

There are a lot of different symbols in use in math. If we abandoned symbol overloading, we would need to introduce _many, many_ new symbols, and this would create real confusion.

<comment><USER12> _Symbol overloading almost never pose a problem, since the intended meaning is usually obvious from the context._

Heh. Heh. Heh.

So I would have believed until I tried to learn differential geometry. The default is to eliminate all parts of the notation that are unambiguous. Proving that they are unambiguous is left as an exercise to the reader, and the exercise is often non-trivial. Furthermore widely used constants vary by factors of 2 pi depending on who is using it.

</comment></comment></comment><comment><USER13> Kind of tangentially related (no pun intended), this reminded me of an interesting article by Tom Apostol, well known calculus teacher and textbook author. Here's the opening paragraph:

        Calculus is a beautiful subject with a host of
        dazzling applications. As a teacher of calculus for
        more than 50 years and as an author of a couple of
        textbooks on the subject, I was stunned to learn that
        many standard problems in calculus can be easily solved
        by an innovative visual approach that makes no use of
        formulas. Here's a sample of three such problems:

Here's the article, in PDF format: <http://eands.caltech.edu/articles/Apostol%20Feature.pdf>

</comment><comment><USER14> Is this guy trolling? First two paragraphs sound to me similar to what some of my math untalented friends said about it in highschool. "Power to understand and predict" is not limited only to those who can manipulate abstract symbols - for some reasons it seems that such abstract manipulation is the best way to do it now.

The second paragraph is even worse. This guy have simply no idea what he is writing about. 'Assigning meaning to set of symbols' is just abstracting unnecessary details and focusing on important information in problem, 'blindly shuffling symbols according to arcane rules' - um, calling math 'arcane' is a clear indicator of person's lack of understanding. Rules are not arcane, everything has explanation (proof) and is derived from other things in logical way (and as far as we know, world acts logcailly) - some of the are axioms, which seem to be abstractios of most basic properties. Also, 'shuffling blindly' is in fact spotting patterns in things on different levels.

Sure, explainig things on more intuitive level, using e.g. graphical representations is sometimes really helpful. However sometimes intuition doesn't work, and how do you graph 3-dimensional manifold embedded in R^4? Or finite field? Also, I can't imagine of other way of doing math that would be consistent and useful other than the one we are using now.

<comment><USER15> This "guy" studied electrical engineering and computer science at Caltech and UC Berkeley, I am sure his grasp of mathematics is ok. Perhaps you should try to stop feeling offended at his proposal and try to see where he might be coming from. Also as he admits in the article, it is by no means a comprehensive set of thoughts, but rather a few hunches hinting at a bigger idea.

<comment><USER16> _This "guy" studied electrical engineering and computer science at Caltech and UC Berkeley_

I'm actually quite surprised by that. Those are both excellent schools with top notch math departments, and the example that he mentioned in the article (about not really grokking the second order ODE and what it meant re: the phase space plot, etc.) indicates that he took a _seriously_ badly taught class. I'm kind of surprised you could get through a diff eq's course at either school without having such basic stuff taught to you...makes me wonder who the teacher was, maybe it was pawned off on a grad student?

Edit: whoops...just looked back at the article, turns out he _didn't_ take that diff eq course at Caltech or Berkeley, it was at a local college. That explains a lot. I'm not going to say that there are no good teachers at mediocre schools, nor that there are no bad teachers at the good ones, but on average there's a huge discrepancy in the quality of the classes.

I had similar experiences, where I took classes at a local college while in high school, and thought I was stupid or something when I didn't "get" them, only to find that when I took them again at a better school they were, in fact, very easy topics.

I blame the textbook writers in part: for one example, Serge Lang's math books are _extremely_ difficult as a rule, and leave a lot of the scaffolding out. Scaffolding which, when he taught classes himself, he always filled in to make for an amazingly smooth and effortless learning experience, but which lesser teachers would never think to talk about (perhaps because they don't understand it themselves, or at least don't understand how important it is to explain). It's really a shame that even now, after so many centuries of teaching math to people, the effectiveness of the process is still so utterly dependent on the teacher. Hopefully things like the Khan Academy will begin to rectify these problems.

<comment><USER17> > It's really a shame that even now, after so many centuries of teaching math > to people, the effectiveness of the process is still so utterly dependent on > the teacher.

Maybe it's not a shame. Maybe it's just an indication that teaching is hard, like art, science, programming, and discovering new theorems, not easy like answering phones in a call center or being a short-order cook.

</comment></comment></comment></comment><comment><USER18> I am really in love with the sentiment/insight here- that the reason people are turned off by math (even just numerals) is because it's a complex mess of symbols that they maybe don't understand.

I am all for finding a way to explain quantitative concepts in a new way. However, it will be extremely difficult to avoid falling into the trap of "reinventing the wheel" if all we're talking about is coming up with a new set of symbols.

 _A certain recipe serves 3, but the cook is only cooking for 2, so she needs to 2/3 all of the ingredients. The recipe calls for 3/4 cup of flour. The cook measures out 3/4 cup of flour, spreads it into a circle on the counter, takes a 1/3 piece out of the circle and puts it back into the bag. That's 2/3 of 3/4._

Much easier to eyeball 1/3 when it's laid out in a rectangle as opposed to a circle. Author credibility -1

 _mindless tradition_

Did you just call the set of symbols evolved by mathematicians for thousands of years _mindless?_ Credibility -2

Finally the two animated examples given are clever but not groundbreakingly clear. -3

It's a neat project but maybe you could think a little harder about defining your problem.

<comment><USER19> "Much easier to eyeball 1/3 when it's laid out in a rectangle as opposed to a circle."

Maybe for you, but certainly not for me, and I'm guessing most bakers would agree with me. Bakers are used to circles because of pies. I can eyeball a third of a circle, but I'd have trouble eyeballing a third of a rectangle that I couldn't fold.

Further, the baker often works by feel, so an exact is not needed in these circumstances.

"Did you just call the set of symbols evolved by mathematicians for thousands of years mindless?"

Perhaps a better word would have been arbitrary, but there's no fundamental reason we pick y=mx+b. Y, M, X, and B are picked arbitrarily, and we _do_ pick them without questioning whether these are optimal for initial learning.

I grokked math as a kid, but it was precisely because I was able to make the leap that the language of math was arbitrary and substitutable while other kids were stuck not understanding the meaning.

<comment><USER18> _I grokked math as a kid, but it was precisely because I was able to make the leap that the language of math was arbitrary and substitutable while other kids were stuck not understanding the meaning._

Then we need to teach them that, not a new set of symbols. Again, I think the crucial insight here which you uncovered is that people are distracted/confused by the symbology, perhaps trying to take everything too literally.

By the way, the way to "eyeball" a third is to use your two hands (rotate them so palms facing each other) to divide into sections A B and C; since we can very accurately eyeball a 50/50 split, you simply compare A to B and B to C, then adjust your hands until A=B and B=C. Bam, you have thirds. Once you get good at this you just mentally visualize invisible dividers instead of actually using your hands.

When it comes to a circle, if you are staring at pies all day then maybe you are better than average, but many studies have shown that humans are horrible at discerning angles other than 180 and 90 degrees.

</comment></comment></comment><comment><USER20> Ugh. Math is a collection of concrete symbols for simplifying different problems. It's evolved over thousands of years to help us understand difficult things. We don't make it that way just to piss people off.

<comment><USER21> Most of the symbols are pretty recent; if you read mathematics from even 300 years ago, there's a much bigger proportion written in prose. Along the lines of, "Consider two quantities, such that the latter is at least twice the former ...".

<comment><USER22> And you will understand, why we switched from prose to symbols. But that doesn't mean we should go overboard with the symbols.

<comment><USER23> Exactly. Why do devs shout "comment your code" but academic papers have no explanation next to the equations?

"Next, calculate the fitness of the algorithm and add it to the pool if it is better than the worst of the last generation: <math here>"

<comment><USER11> _Why do devs shout "comment your code" but academic papers have no explanation next to the equations?_

That's exactly the opposite of my impression. Most papers are full of text, and symbols are not the main feature. For instance:

<http://ttic.uchicago.edu/~yury/papers/kuratowski.pdf> Graph theory, the symbolism is next to nonexistent.

<http://math.berkeley.edu/~aboocher/math/tietze.pdf> Topology, still symbolism does not take much space.

<http://www.jstor.org/stable/1989708> Classical and very highly technical, yet the ratio of text to symbolism is still in favour.

<comment><USER23> I remember trying for hours to understand Adaboost before it all clicked (it's an ingenious algorithm, by the way). The paper could certainly do with some more explanation, rather than just "this is the weight updating function, this is the evaluation step, done".

<comment><USER21> I think AI and machine learning are worse than math in that respect for some reason. Part of it might be the greater focus on 6-page conference papers, which tends to require everything to get squished.

</comment></comment></comment></comment></comment></comment></comment><comment><USER24> Sure. Speak French without learning French. Or maybe learn French by reading a picture book. I sympathize with the author because there is a great deal of room for improvement in the _language_ of math, which may let us model the world on a computer much more easily.

One example: Using Robinson infinitesimals allows you very easily to write code for forward mode exact differentiation (not symbolic, not approximate). But justifying these simplifications is hard. The question is how much math can be simplified by analogous means without wrecking the foundations.

Another example: Many really useful systems have to deal with uncertainty. I have yet to see a system that allows programmers to easily build such models. I have seen some nice ideas probability monads, Bayesian networks, etc. But how many non-specialists are prepared to use such tools? Happy to have HNers prove me wrong on this one.

<comment><USER13> > Sure. Speak French without learning French. Or maybe learn French by reading > a picture book.

That's basically the approach Rosetta Stone takes, and it works fairly well.

<comment><USER24> Rosetta Stone for math? I'd like to see it.

I have a friend who was able to buy a laxative in Italy without knowing a word of Italian. It's a funny story. I doubt the same approach would work with math.

</comment></comment></comment><comment><USER25> Math is a language. The problem is that this language is archaic, difficult to teach, and is generally taught very poorly.

I remember learning calculus in college. The professor went up to the board, scribbled down symbols, and took us through various procedures. I was absolutely, utterly lost until my father (an engineer) told me that "a derivative is a rate of change."

At that instant, I understood everything. My professor never said this.

This taught me to approach math concepts-first, and that helped, but I've always had a problem with math. To make a long story short: I hate math for the same reason that I hate Perl. My mind recoils in horror from messy, crufty languages.

At the very least, all math lessons should begin by teaching the __language __and the concepts that the various symbols, arrangements, etc. refer to. Only once the language is thoroughly grasped should they proceed to methods, procedures, and problems. Right now it's like teaching Chinese literature before teaching Chinese...

</comment><comment><USER26> When I was a child, I always found math easy. Fractions, calculus, formulas—they were always _visual._ Fractions were pizzas; equations were deformations of the plane; integration was tracing out a shape using a slope.

So I'm sympathetic to the author's desire for better visualization and teaching tools.

But when I reached college, I became frustrated with math. It just wasn't _easy_ anymore, the way programming was: I could pick up a programming book, read it in a weekend, and understand it. But when I tried to read an advanced math text, I became lost after 10 pages.

Eventually, I figured out what had happened: The information density of college-level math texts is _insane_. Even if you're bright and talented, it may take you a day to understand a single page. And there's no substitute for working carefully, finding concrete examples, and slowly building a deep understanding.

Here's an example that involves programming. Once upon a time, I needed to understand monads, in hope of finding a better way to represent Bayesian probabilities.

I started with the monad laws, a handful of equations relating _unit, map,_ and _join_. I read countless monad tutorials, and dozens of papers. I read every silly example of how monads are like containers, space suits, C++ templates, and who knows what else.

I wrote little libraries. I learned category theory. I _wrote_ a monad tutorial. I eventually wrote a paper explaining a whole family of probability monads:

[http://www.randomhacks.net/darcs/probability- monads/probabil...](http://www.randomhacks.net/darcs/probability- monads/probability-monads.pdf)

And then one day, I thought about the monad laws again. I realized, "Hey, that's it. That's _all_. Just _unit, map, join,_ and a handful of equations. Anything which quacks like a monad, _is_ a monad. How did I ever think this was complicated?"

But when I look at the monad laws today, there's this huge structure of connections in my head. All that work, just to grasp something so simple, and so easy.

So I'm all for building better visualizations, and for helping people to understand math intuitively. That's an important step along the path. But math doesn't stop at an intuitive understanding. When you really understand it, the equations will suddenly be easy, and everything will fit together.

And then you'll encounter the miracle of math: Your deep understanding will become the raw material for the next level. Counting prepares you for addition, addition prepares you for multiplication, basic arithmetic for algebra, algebra for calculus, and so on. And someday, I hope that my rudimentary understanding of category theory will prepare me to understand why adjoint functors are interesting.

<comment><USER27> I had a different problem, I found that word density increases 10 fold, but symbol density and proofs go down as you go through it.

My favorite example to use is this: Complex Variables and Applications by Brown and Churchill. This book has been in print for 70 years or something, and it's somewhere around 400 pages in the current edition I believe. My professor I did research for had a early 80s edition, and it had almost 100 less pages than the current edition. There wasn't really anything new added between the versions (chapters are only about 5-10 pages, so there's something like 65 of them) I ended up using mine for the problems and his for reading because I have ADHD, and the wordiness absolutely kills me. Symbols and relationships are _much_ more meaningful to me than words describing them. The real nightmare with the ADHD sets in because of the break in context when you have to switch between two or three pages to find the next theorem, formula or proof.

I retook that class twice.

On the other hand, I utterly and completely rocked my Advanced Electrodynamics course, outscoring even the graduate students, in a course which even made use of the stuff we were learning in Complex Variables (as well as PDEs and all that fun stuff) Why? I had a crazy russian professor who hated all the current textbooks (I'm looking at you, Griffiths) for the same reason that I hated textbooks, too much words and not enough symbols. So he wrote his own notes to every lesson and made his own homework. He said he originally wrote those notes when he first came here, and his english was worse, so there's little or no explanation, just proofs -- math and symbols. A few of these would span two pages, and very rarely three, but there wasn't the context break you get in many college level books, just beautiful math and lots of intermediate steps. The intermediate steps, almost never provided in most textbook proofs, really help the visual learners like me and provide stepping stones for the inevitable manipulation you will perform with those equations in your homework and on tests.

I still have all his notes, I want to bind them up some day when I get a chance.

<comment><USER28> I really liked Griffiths. I thought it had struck a great balance between explanations, mathematics, and examples. That book had great examples and homework questions, which I find the most useful anyway.

<comment><USER16> Griffiths' E+M book (actually, also his QM book) is a shining star to me, a perfect example of the way introductory textbooks should be written. It ends up being criticized a lot once you get to the advanced level ("Who'd you learn quantum mechanics from, _Griffiths_ lol?"), but that's _fine_. It's perfect, even - if you really need all the gory stuff, sure, go get a copy of Jackson's book, or some 800 page tome on perturbation theory and the rigorous mathematical underpinnings of quantum theory, if you're going into the field you should absolutely know more than you can get from an intro text. But an introductory textbook should be exactly that. Rigor is awesome once you have the intuition down, but it's often very difficult to go the other way (mainly because a rigorous understanding is difficult to achieve without having the intuition first).

<comment><USER29> I think Griffiths EM/QM texts are fine if your not studying physics. However if you are they just skim the surface of material and this is were I think a lot of the bashing comes in. Physics curriculum (presumably like all) are a constant stepping stone and when your senior level professors expect you to know Clebsch Gordon coefficients in detail and Griffiths QM didn't then some questioning about his texts start to rise. In my opinion I thought Sakurai's QM was excellent in delivering a solid foundation in quantum mechanics

</comment></comment></comment></comment></comment><comment><USER15> Highly recommended reading by the same author: <http://worrydream.com/#!/MagicInk>

(To pique your curiosity: read it to understand why Hipmunk is awesome - there's much more to it than just that of course)

<comment><USER30> There's some discussion on that here <http://news.ycombinator.com/item?id=600799> (from about 2 years ago)

</comment></comment><comment><USER30> I'm just really curious to know what Brett was involved with at Apple

[Edit: wow! <http://worrydream.com/cv/bret_victor_resume.pdf>]

<comment><USER31> Don't know that I've ever seen a resume that covered everything from hardware engineering all the way up to some of the most highly regarded user interface designs. He has certainly covered the entire gamut of "things you can do with a computer."

Which makes him the perfect Apple employee, as they cover the space from hardware engineering through user experience better than anyone.

<comment><USER32> Magic Ink is my single favorite statement on software design: <http://worrydream.com/#!/MagicInk>

</comment></comment></comment><comment><USER33> I also have a problem with the way mathematics is taught currently where the student is more adept at the mechanics than the philosophy of mathematics. If anybody is attempting to change that, my best wishes. I don't necessarily have a problem with the current system of notations. It is just the method of teaching that lacks.

Just started with 'What is Mathematics' by Courant and I am totally hooked on. He talks about everything from why we chose to adopt the decimal system to why pi was needed to solve certain problems.

As Hammock says, the author has to be clear about defining the problem itself. Is it mathematics as it is represented today which is lacking or the method of teaching which is lacking

</comment><comment><USER34> > This "Math" consists of assigning meaning to a set of symbols, blindly > shuffling around these symbols according to arcane rules, and then > interpreting a meaning from the shuffled result. The process is not unlike > casting lots.

> using concrete representations and intuition-guided exploration.

Is it just me, or are these two lines very much at odds with each other?

</comment><comment><USER35> This is awesome: <http://worrydream.com/SimulationAsAPracticalTool/>

</comment><comment><USER36> Pictures aid understanding. But in the vast majority of sophisticated mathematics (that I've seen), pictures would be unable to accurately represent the real assertions.

For instance, if I want to talk about 26-dimensional discontinuous space (the space of the basic alphabet), there is no visualization that can help you grasp the totality of the matter.

I believe there are a few interpretations of what math actually is (formal reasoning, interpretation, etc), philosophy of math 'junk'. I'll leave that to a more-beered time. :-)

</comment><comment><USER37> " _those with a freakish knack for manipulating abstract symbols_ "

The downside of the growing public awareness of people on the autism spectrum, some of whom are geeks, has been the slow trend towards conflating intellectualism with atypical mental function.

Some people like to call right now the "victory of the geeks". I suspect that within the next 10 years, nerdy kids will start being diagnosed as having Asperger's by school counselors and the like with about as much care, caution, and accuracy as we saw with ADHD.

</comment><comment><USER38> This post reminds me the visual explanation of pythagoras' theorem : <http://www.mathsisfun.com/pythagoras.html> Also, the math language symbols are great for communicating easily and efficiently among us, but it's not the best materials for learning. Distinguish learning (with visual) and communicating (with language symbols) activity in math should help...

</comment><comment><USER39> Can we start by killing all the Greek letters and replacing them with Mathematica-esque notation, now that computers have dramatically reduced the convenience of writing symbols rather than words?

<comment><USER40> Computers have not reduced the convenience of writing symbols on PAPER or on a BLACKBOARD, the places where math is actually done.

</comment></comment><comment><USER41> I've gone back to Bret's site for years since its so amazing. Imagine my thrill to see he is finally out of the shadows of Apple and is sharing his ideas with the world again. Awesome!

<comment><USER42> I'll second that. I was _thrilled_ to see him pop up again in my RSS reader last month, after years of radio silence.

</comment></comment><comment><USER43> I just wish that scientific publications came in Python code instead/besides of "in formula (a) the variables ... represent ..." . Just get me the code and I will just plug into the general framework for that (robotics, chemistry, politics, finance) and see if it works as stated in the article.

And ! code cannot be misinterpreted, either it runs or it does not.

So dear mathematicians please do the evolution and cast your ideas as python code.

<comment><USER44> what python code should people write for non-constructive results?

</comment></comment><comment><USER45> For quite a long time I hated Math and was horrible at it - I remember being up until 2AM in the morning with my father during 7th and 8th grade trying to do my math homework, taking tests and feeling confident about all of it then receiving my grade that said I failed. After I dropped out of high school and did some self-discovery (involved India, a commune, and a few other journeys) I began a self-study curriculum (created by me). I didn't bring math into the curriculum until about three years ago, I've been fond of logic and the methods of logic for quite some time and ended up finding "The Foundations of Arithmetic" by Gottlieb Frege - a treatise attempting to provide a purely logical framework for number (he influenced set theory) and the operations on number; but, reading it really fired me up, I was absorbed and interested, Frege showed me a completely different side if mathematics that _no one_ in my education had cared to show me or even hint at.

With that new found interest in Mathematics I set about to find a book that I could use to teach myself. I won't say how I came across it, but I ended up coming across "Practical Mathematics" by C.I Palmer - the 1919 publication, very old. The book is intended for working adults in mechanical trades; the problems in the book were often given using real-world problems in the technical trades. The author also used _much_ more technical language! It was refreshing! Even my high school math textbooks felt like the authors were trying to teach kids and regarded their audience as nothing more than insufferable immatures. This book has been immeasurably valuable to me, I now feel less "darkness" and confusion when I see a math problem, I'm finally seeing the utility in my everyday life of the things I'm learning (my gf had a wedge table and was selling it on Craigslist and needed to know the length of the arc, for example). I actually _know_ how to add and subtract fractions, it's no longer a mystical act of numbers disappearing here and showing up there.

The greatest thing about that book? Certain operations that most schools only _ever_ taught me as a mechanical process were taught to me and explained to me with the underlying fundamentals in "Practical Mathematics". In 1919 there were no calculators, it had to all be done by hand, even square roots, and you couldn't really survive without knowing _why_ or _how_ certain mechanical operations are used the way they are in Math.

I'm not sure if college or higher mathematics gets into that stuff, but, it was a revelation for me and I'm well on my way through the Algebras and Trig now - I didn't even make it out of pre-algebra in the traditional educational system. I can also see the beauty of mathematics too, something I never thought I would understand about mathematicians when I used to hate the subject.

There will never be any "killing" of math. But our educational system has a long way to go.

<comment><USER46> Free on Google Books: <http://books.google.com/books?id=EAmgAAAAMAAJ>

<comment><USER47> Thanks for this!

</comment></comment></comment><comment><USER48> Technical tangent: I opened this in a tab, intending to read it later, then came back and noticed Firefox was using 100% CPU. I thought "oh god what's happening" and tried closing other tabs to determine the cause. Eventually I discovered that a) this website was the culprit, and b) this is most likely because, a few pages down, there's some kind of (processor-intensive) simulation happening.

Lessons I draw from this:

\- In designing a website that outsiders visit, you should probably follow this rule: If your page must have a majorly resource-intensive object on it, it should either be visible and obvious at the top of the page, or have a "Start" or "Play" button and not run until the user presses it.

\- Firefox should get some (easily accessible) way to see resource usage broken down by tab. Chrome does this; it's probably made easy by the fact that Chrome makes a separate OS process for each tab (or group of tabs). I wouldn't recommend switching to that model, because it would be work and because I wouldn't like it (I don't like how it clutters up the global process list in Activity Monitor), but it would be nice if you could see CPU and memory usage broken down by tab.

\- (Optional) Browsers shouldn't run purely graphical animations if they're not visible (like if they're several pages down). This might not be perfectly achievable--e.g. if animations started when you scrolled down to them, then one animation slightly higher than another might start earlier when the designer wanted them to be synchronized. Maybe you would instead have background things keep time without actually rendering anything. This might not work for cases where the nth frame depends on the conditions of the n-1th frame, and so you'd have to run the whole simulation in the background anyway --though maybe leaving out the "draw" part would make a big difference, I don't know. But if it's a series of static frames, like a GIF, then I think this would work--when the GIF is offscreen, the browser would just keep incrementing a frame number (mod the number of frames in the GIF).

</comment><comment><USER9> Math is not a collection of symbols. It's language + reasoning.

<comment><USER9> Also math provides us with a framework to work on things that we could not visualize or even imagine ... how about visualizing an n-dimensional riemannian manifold ?

</comment></comment><comment><USER49> You can do "language" without all of those pesky symbols as well but it makes it hella hard to tell other people 100 years down the line what you were on about.

</comment><comment><USER50> I think it misses a key point of math which is to take an idea from a concrete example and expand it to demonstrate something in general.

</comment><comment><USER51> Always happy to read what is on Bret Victor's mind. Chris Knight, Mitch Taylor? Morons. Bret is the shit.

</comment><comment><USER52> I like the idea, but the headline is totally off. The author wants to make math available with less formalism and less reliance on symbols, not kill math in any way.

</comment><comment><USER53> After killing math, this site kill my browser.

<comment><USER54> Same here hotdox. It killed my machine. I had to reboot.

</comment></comment><comment><USER55> Math is about abstraction. It's OK to describe elementary maths and calculus with water-filling bottles, but it ends there, because the higher order abstract structures of mathematics have no real-world equivalent. If we start teaching people with Flash simulations, we 'll have to forget about the Standard model, relativity, electromagnetism, Symmetry, string theory etc. Sure, visual representations make some subjects more accessible, but they can also be terribly misleading and limiting. (Just imagine how much bias our 3-dimensional world experience imposes to our visual thinking). If anything, abstract (written) math allows us to escape the confines of perceived reality.

Math and language are 2 faces of the same ability we have to model the world in arbitrary symbols. Just like math, language has symbols and syntax, that have meaning to us regardless of representation (spoken, written or digital).

</comment><comment><USER56> He doesn't understand math at all, not at K-12, college, graduate school, research, applications, etc. at all.

E.g., his claim about symbol manipulation is total nonsense.

His direction is a waste of time.

If he wants to improve materials for learning math, then fine, but he should first learn some math.

He should start with the books and papers of P. Halmos, one of the best writers of math ever.

Note: My Ph.D. dissertation research was on the math of stochastic optimal control.</comment>


Why Socialists Don't Believe in Fun (1943) - <AUTHOR> http://www.orwell.ru/library/articles/socialists/english/e_fun <comment><USER2> Perhaps it used to be the case that people had trouble imagining a utopia, but here's two solid utopias (or near enough) I've encountered in fiction: the entirety of Ian M Bank's "Culture"; and the second chapter of Cory Doctorow's "Walkaway".

Also, there's the perennial example of Burning Man (and related festivals) - here's an example of people creating happiness that has little to do with the removal of scarcities, and plenty to do with the addition of abundance.

To go off @mactintyre's selection: if "nearly all creators of Utopia have resembled the man who has toothache, and therefore thinks happiness consists in not having toothache. They wanted to produce a perfect society by an endless continuation of something that had only been valuable because it was temporary", well, seems to me that's a failure of imagination and experience more than an incapacity in humans or reality.

You could also look to Asimov's "Profession" ([http://www.inf.ufpr.br/renato/profession.html](http://www.inf.ufpr.br/renato/profession.html)) - again, while not exactly a Utopia, it's decently close - and more importantly:

"It won't do to say to a man, 'You can create. Do so.' It is much safer to wait for a man to say, 'I can create, and I will do so whether you wish it or not.'"

These are the people that, when all scarcity has been eliminated, take that bland contentedness which results and turn into something _more_.

Not to say the Orwell is wrong - he's on the nose: "Happiness hitherto has been a by-product, and for all we know it may always remain so. The real objective of Socialism is human brotherhood."

<comment><USER3> > Also, there's the perennial example of Burning Man

Which is a temporary outlet for a select very affluent few Westerners (non- affluent person wouldn't even be able to afford transportation and supplies, not mentioning $500 entrance fee) who drive there for a week (increasingly accompanied by air-conditioned tents and personal chefs), frolic in costumes or negligee, burn stuff down for fun and return to their regular lives. A lot of fun, but I can't see how any sane person can see it as a model for a society.

> The real objective of Socialism is human brotherhood

Somehow in the real socialism it happens in exactly the opposite way (the famous joke is that under capitalism man exploits man, and under socialism it's the other way around). Socialism always produces the nomenklatura (note that I have to use a Russian word for it, because it is so inherent to the largest Socialist experiment in history) and the privilege networks (another Russian word, "blat") which create a complex network of inequality and privileged access to formally "equal" benefits. In a capitalist society, most inequality is monetary - through class, sex and race play its role, ultimately money usually overcomes most of it (especially in a modern society, where things like open racism are frowned upon). In a socialist one, not only money can't do much without privilege, if you are outside the privilege network, the mere attempt to make this money (or otherwise route around the privilege network) would get you imprisoned or executed. Some brotherhood it is.

<comment><USER4> Proof by example is a logical fallacy.

 _I know that x, which is a member of group X, has the property P. Therefore, membership in X causes property P._

I can play this game too.

Haiti, Ethiopia, Liberia, India, Honduras and Somalia have market economies, and they are poor. Therefore, market economies make nations poor.

There's really not much to learn from this kind of argument.

<comment><USER5> It seems that the phenomena the parent describes were or are present in all instances of fully implemented socialism to date, not just in the USSR.

Since you edited to add your counter-examples, I'll edit to point out that socialism is a system that has been deliberately implemented by its instantiators in each case I'm aware of. To compare it to capitalism, but only those capitalist countries that have suffered lawlessness or other calamity, is to compare apples to oranges.

<comment><USER4> You don't need to speak Russian to understand the nomenklatura. It's a group of privileged people who are appointed to positions of power based on their personal loyalty to the leader or to the party.

Seems like a very familiar concept ripped from today's headlines, certainly not restricted to archaic economic systems.

I usually find that apples and oranges are quite easy to compare.

<comment><USER5> You seem to have a habit of dramatically changing your comments after you've posted them, without noting that you've done so. In this case, you originally posted only what now seems to be your final sentence, the one about apples and oranges, then added everything that now precedes it. I have the sense that you are hoping for a political argument.

</comment></comment></comment></comment></comment></comment><comment><USER6> I'm always amazed at how readable and relevant Orwell remains. This essay is a good example.

 _It would seem that human beings are not able to describe, nor perhaps to imagine, happiness except in terms of contrast. ..._

I wonder if this also works in reverse: humans are incapable of describing or imagining unhappiness except in terms of contrast.

This reminds me of a line that goes something like: revolutions happen not because of poverty but through the process of a society becoming poorer.

<comment><USER7> Hmm... I guess I'm not amazed that something written less than 100 years ago seems relevant when Aristophanes is still hilarious.

<comment><USER8> Almost nothing from 50 years ago is even remembered, let alone still read, let alone as fresh as Orwell. You make the same point by giving him Aristophanes for company.

</comment></comment></comment><comment><USER9> A great anti-elitist rant.

Beautiful language: "Nearly all creators of Utopia have resembled the man who has toothache, and therefore thinks happiness consists in not having toothache. They wanted to produce a perfect society by an endless continuation of something that had only been valuable because it was temporary. ... when [Swift] tries to create a superman, [he] leaves one with the impression the very last he can have intended that the stinking Yahoos had in them more possibility of development than the enlightened Houyhnhnms."

</comment><comment><USER10> _At the dances I was one of the most untiring and gayest. One evening a cousin of Sasha [Alexander Berkman], a young boy, took me aside. With a grave face, as if he were about to announce the death of a dear comrade, he whispered to me that it did not behoove an agitator to dance. Certainly not with such reckless abandon, anyway. It was undignified for one who was on the way to become a force in the anarchist movement. My frivolity would only hurt the Cause._

 _I grew furious at the impudent interference of the boy. I told him to mind his own business, I was tired of having the Cause constantly thrown into my face. I did not believe that a Cause which stood for a beautiful ideal, for anarchism, for release and freedom from conventions and prejudice, should demand the denial of life and joy. I insisted that our Cause could not expect me to become a nun and that the movement should not be turned into a cloister. If it meant that, I did not want it. "I want freedom, the right to self- expression, everybody's right to beautiful, radiant things."_

\-- Emma Goldman, _Living My Life_ (1931) [http://www.lib.berkeley.edu/goldman/Features/danceswithfemin...](http://www.lib.berkeley.edu/goldman/Features/danceswithfeminists.html)

<comment><USER11> Goldman wasn't the kind of socialist that Orwell is describing.

Orwell was obsessively critical of Authoritarian Socialism - namely big [S] State Socialism as represented by the Soviet Union.

That is in stark contrast with Goldman's Democratic Anarcho-Socialism which shares little relation - philosophically or sentimentally - with the State Socialism that Orwell was writing about.

<comment><USER12> _Orwell was obsessively critical of Authoritarian Socialism - namely big [S] State Socialism as represented by the Soviet Union._

I don't think George Orwell would necessarily be cotton to variations of Authoritarian Socialism implemented in very large corporations.

 _That is in stark contrast with Goldman 's Democratic Anarcho-Socialism which shares little relation - philosophically or sentimentally - with the State Socialism that Orwell was writing about._

I have friends who claim to be "anarcho-" something, who at the same time espouse state socialist politics. Their action in aggregate is often authoritarian, and I don't see how any anarchic politics can prevent the oppressive rule of a majority. As such mechanisms play out in my private life, it seems that anarchy results in less diversity of thought and virulent oppression of minority viewpoints.

EDIT: My corollary -- Oppressive tribalism is just a later stage development of anarchy.

<comment><USER11> My post was a historical contextualization about the thrust and focus of Orwell's criticism of Socialism, as the parent seemed to be trying to object to the premise with an anecdote from a "socialist" with whimsical predilections. The implicit point there, being that there was a categorical error being made.

I do not claim to say anything about possible or theoretical corollaries that Orwell may or may not have drawn around hierarchical structures more broadly.

To your last point, conflicts around self-organizing groups and spontaneous formation of oppressive hierarchies is an ongoing debate within Anarchistic philosophy itself, so no new ground tread there simply by stating it.

See: Proudhoun, Bakunin, Kropotkin etc...

<comment><USER12> In that case, you really need to do something about self styled "anarchists" on social media declaring that they can do any evil to fight evil, so long as they use just a little less evil.

From what I can see, thought leadership doesn't reach the "anarchist" on the street, leaving them to wallow in a toxic tribalism which is welcoming of nihilistic violence. Have all the erudite debates you want. Others are presenting a far different face to the public. The fact that the media will then dissemble and cover for such actions and attitudes then makes it all much worse.

Or is it ok to use evil to fight evil, so long as you use a little less?

<comment><USER11> Well, Anarchism has been pretty successfully demonized, misinterpreted and put into the "evil" bin with every other -ism except for capitalism. Kind of hard to organize when you're whole philosophy is allergic to hierarchical structures. When Noam Chomsky is your most famous public personality it's hard to build a broad and passionate following.

I don't see it getting anything like mainstream traction ever, as it's a lifestyle as much as it is a philosophy. I also don't think it's how people naturally behave. People seem to like to be ruled, so long as they have just enough freedom.

<comment><USER13> I don't think anarchists have _really_ thought through their position or have noticed particular ironies within it.

At its core, it's basically everyone doing themselves. I do my thing, you do your thing, it's all good. Until the thing I want to do interferes with your thing. And yes, we _could_ come to some agreement. But there is going to be a certain segment of asshole that will just decide: Me strong, you weak, and just override you.

And that's what you really get, a rule of the weak by the strong. Unless, of course, we gather enough of us to overwhelm the asshole. But what if, in our group, we have conflicts? Well, we have _some_ rules. Yeah, not everyone will get exactly what they want all the time, but a tiny bit of compromise is still better than having the asshole take your stuff for the fifth time this week.

But that's a winning strategy. And don't think the assholes won't notice. Then they get groups. So the groups escalate further and further. And as you bring in more and more people, there are more and more rules. Eventually, what you will have done is simply to have recreated modern governmental structures. We are living in the endgame of anarchy.

So, I don't think it's so much that "people like to be ruled", as much as "people would rather there be a set of standards people are expected to follow". Someone needs to enforce the social contract.

I don't think anarchism is evil, just naive.

<comment><USER14> _> At its core, it's basically everyone doing themselves._

No, it isn't. Anarchists can cooperate; in fact, rational anarchists will certainly cooperate with each other, to reap the benefits of specialization and trade and comparative advantage.

What anarchists object to is being _forced_ to cooperate when, if left to themselves, they would choose not to.

 _> there is going to be a certain segment of asshole that will just decide: Me strong, you weak, and just override you._

These people exist whether society is an anarchy or not. The difference is, in an anarchy, they have no way to capture more resources and power by, for example, becoming politicians or regulators or lobbyists or heads of corporations getting government favors. Whereas, in the system we have now...

In other words, anarchists are basically pointing out that trying to "fix" the problem of assholes by having a government is a "cure" that is worse than the disease.

 _> Someone needs to enforce the social contract._

You enforce the social contract socially: by refusing to deal with people who do not respect it. In an anarchy, everyone has that option; and therefore people who do not respect the social contract quickly find themselves ostracized and powerless.

Whereas, in the system we have now, people can break the social contract with impunity without losing anything, if they can get themselves into certain privileged positions.

<comment><USER15> It seems to me that this argument essentially relies on everyone being an anarchist. This is not the case for systems we have observed in reality - totalitarian regimes can function even if significant parts of population don't want to be in a totalitarian regime; democracies can function (perhaps poorly, but function) even if significant parts of population don't agree with core principles of democracy; oligarchies have functioned as well without much of the society not acting in an oligarchic manner.

Does the same apply to your vision of anarchy? Is your proposed method of enforcing the social contract _stable in the face of adversity_ (a Nash equilibrium of sorts)? I.e. for a non-anarchist participant, is it _really_ in their own best selfish interest to participate in that enforcement instead of defecting, and _not_ refusing to deal with people who don't respect the anarchist social contract because it's good for them at that point of time? In an anarchy, everyone has _that_ option as well, and if the boycott isn't sufficiently strong (which IMHO requires it to be organized, monitored and _enforced_ to work in any community much larger than Dunbar's number), then people who do not respect that social contract do _not_ find themselves ostracized and powerless; especially since they'll be dealing between themselves if the anarchist community does not. Are there sufficiently strong incentives for people to actually 'keep to the plan' and fully ostracize the others? There will be some misdeeds done by well-loved, respected members of the community against someone that's not liked - will _those_ misdeeds be punished at all? It's not sufficient to _try_ to ostracize them if there's enough critical mass (which is quite small) for them to be somewhat self- sufficient; there certainly will be both individual maniacs and random gangs and extended family clans that will laugh at such ostracism, in which case you need to be able to reliably organize enough violence to physically prevent them from breaking the social contract and getting away with it; and you need to be able to get everyone to agree that this person or group _has_ broken the social contract, instead of you just wanting to remove a competitor.

My core point is probably the following:

1\. there would inevitably be certain sub-groups run by decidedly non- anarchistic principles, obtaining strong cohesion by whatever means. Cliques, family units/clans, groups of friends, etc - the concept and benefits of cooperation can't be eliminated.

2\. at least some of these groups (or their leaders) _would_ have a way to capture more resources and power by easily taking them from any disorganized groups or disjoint individuals, so either:

3a. the surrounding anarchists would be forced to cooperate in a sufficiently organized manner, to become a _larger_ and _more organized_ group than the local strongman/warlord/whatever, and enforce that social contract on them; and be prepared to do it _permanently_ , as otherwise the threat would re- appear - in which case that organizational structure and its decisionmaking process, whatever it may be, is a de-facto non-anarchistic ruler of that area.

3b. the surrounding anarchists do not manage to cooperate in a way that results in them being the largest/most organized group in the area, in which case, their communities are eventually 'eaten up' by the larger non- anarchistic groups/organizations that force their will on them, and eliminate anarchy in that area.

Can you imagine (and describe) how would an anarchistic community operate sustainably next to a miniature equivalent of North Korea, a plantation using slaves, or a religious cult that's eager to push their rules onto everybody they can? How would many village-sized anarchistic communities cooperate to unify against a common threat that one or two villages can't handle on their own? For a social system to be possible, it has to be somewhat stable, it has to be able to overcome competing systems (both from within and from outside); both dictatorships and democracies have shown themselves to be capable of resisting/suppressing at least a certain size of revolution attempts; if a system can be overthrown or overtaken by a reasonably organized band of men, then it _will_ be overthrown, and if such threats force a system to change, then the system _will_ change and the unchanged system can't exist.

All competing systems have processes to eliminate other systems (i.e. enforce their rule) within their 'zone of control' \- if anarchy has no plausible process to enforce 'rule of anarchy' i.e. prevent pockets of democracy or dictatorship or theocracy or whatever from rising, thriving and expanding within its zone of control, that's what will happen and the anarchy will cease.

<comment><USER13> Not just anarchists, but also agree to follow a certain set of rules or laws that will be enforced by no one.

Even the "ideal" he is putting forth isn't _really_ anarchy. Because anarchy means absolute freedom and the minute you don't allow someone something, freedom isn't absolute. And the minute you get two people living as some sort of unit, you have compromise.

Cooperation is good, systems of cooperation are better. Government is a solution to the problem of individual trust. In a completely anarchistic system, I can't trust you and you can't trust me. Either of us are allowed to break our bond at any time. We need an impartial third party to manage our interactions so that if one of us decides to screw the other, that person is appropriately admonished. Something to govern interactions of citizens, if you will. So whatever system you've set up to govern the interactions of your citizens is de facto a government. Even if you don't explicitly call it that.

<comment><USER14> _> anarchy means absolute freedom_

No, it doesn't. It means the absence of government. Nobody has absolute freedom; even in the absence of government, everyone has to deal with other people in some ways.

 _> In a completely anarchistic system, I can't trust you and you can't trust me._

This is simply false. Do you trust your friends? If so, would you stop trusting them if there were no government?

There are plenty of ways for people in the absence of government to build trust relationships with each other.

 _> We need an impartial third party to manage our interactions so that if one of us decides to screw the other, that person is appropriately admonished. _

And you think government, as it actually is instead of as it might be in somebody's idealized model, is such an impartial third party? Surely you jest.

<comment><USER13> Yes it does. It is the very definition.

[https://en.oxforddictionaries.com/definition/anarchy](https://en.oxforddictionaries.com/definition/anarchy)

Absolute freedom.

You do understand I'm talking about two strangers. Of course, you can build trust between people over time. But no one comes into a situation with trust. And if we can't start on a basis of trust, then we can't start. Knowing there are repercussions for breaking that trust allows us to treat.

You're the one peddling a libertarian fiction novel as the-one-true-way and not even taking half a second to consider the actual ramifications. Or if "anarchy" is what you actually want. (Hint: it isn't)

<comment><USER14> _> It is the very definition_

You can't make reality be the way you want it to be by defining words. Nobody has absolute freedom in reality.

 _> Knowing there are repercussions for breaking that trust allows us to treat._

There are repercussions for breaking trust whether there is government or not.

If your claim is that governments do better at enabling trust relationships to develop than a society without government (I'll stop saying "anarchy" since you keep quibbling about the definition of that term) would, then please show your work. From where I sit, governments have possibly done better in some respects, but those benefits, on net, are more than outweighed by the ways in which governments allow people in positions of power to abuse trust without paying any price.

<comment><USER13> No, you can't, so I suggest _you_ stop trying to do that.

I'm using the common, accepted definitions. You're trying to define "thug" to mean "can't engage in productive endeavors" and "government" to include a coercive element. Neither is commonly accepted.

I nobody has absolute freedom in reality, then by your admission, anarchy is impossible and what you want isn't anarchy.

Yeah, if we agree on something and I break that agreement, the repercussion is you don't like me. Whoop de shit. I can fleece you as hard as I want until that point.

Once you envision a body that will recover your property, you have envisioned a type of government. The problem is you have a very narrow definition of "government". You only see it as a bunch of people "in charge" in a central building making laws by fiat (even though that's pretty reductionist, but then again, you are). It's not always that.

Even an ad hoc, informal system of rules and enforcement is a government.

<comment><USER14> _> I'm using the common, accepted definitions_

I strongly disagree, but at this point I don't think further argument will help. You and I are simply speaking different languages, and I don't have the time or the inclination to try to learn yours, and I get the idea you feel the same about mine.

</comment></comment></comment></comment></comment></comment></comment></comment></comment></comment></comment></comment></comment></comment></comment><comment><USER16> Note: I am responding to comments here, haven't read the article yet.

Utopia is not possible because the desires and wants of millions of people (focusing on a country) don't overlap with everyone else's 100%, or sometimes not at all. We also don't live long enough to truly appreciate what we have today, as I'm sure people from hundreds of years ago would think today's society is a utopia: (basically) infinite potable cold and hot water, heat and air conditioning, electricity, sewage removal, relative privacy, trash removal, modern medicine, fast, cheap transportation, a wide variety of fresh food all year round, internet... I could go on.

So maybe utopia is genuine appreciation on a personal level for what one has. You can't do this without contrast, and contrast is best developed from real experiences. Maybe one could spend a couple weeks out in the woods with canned food and a stream for water (and no electronics except a flashlight), and come back with a new found understanding for the amount of convenience and comfort one has in this modern life.

<comment><USER17> That's pretty close to some schools of Buddhist philosophy.

</comment></comment><comment><USER12> _Here you have a picture of the world as Wells would like to see it or thinks he would like to see it. It is a world whose keynotes are enlightened hedonism and scientific curiosity. All the evils and miseries we now suffer from have vanished. Ignorance, war, poverty, dirt, disease, frustration, hunger, fear, overwork, superstition all vanished...But is there anyone who actually wants to live in a Wellsian Utopia? On the contrary, not to live in a world like that, not to wake up in a hygenic garden suburb infested by naked schoolmarms, has actually become a conscious political motive._

This is a neat summary of the ideological contradiction of the Bay Area and Silicon Valley. Everyone wants edginess with safety, but no one wants the Disnified, safe version of edginess. We want the hard-nosed meritocracy of innovation, technical prowess, and commerce, but we don't want to let our children risk even the failure of losing in sports.

 _All 'favourable' Utopias seem to be alike in postulating perfection while being unable to suggest happiness._

'Favorable' Utopias are like Mary Sue characters or fanfics without real conflict. There is no interest without real risk and real adversity. Even Iain M. Bank's Culture universe has imperfections, conflict, and death, even if there are untold trillions in it living idyllic lives of enlightened hedonism and curiosity.

<comment><USER18> Humans can't really tell the difference between real and simulated risk.

Online games are incredibly compelling for the people who play them, but they're a lot less risky than taking part in a real war and risking real blood and real body parts.

I don't see why we couldn't sublimate games like economics in the same way. The experience of winning would be almost identical, but simulations wouldn't have to be zero sum in the way that meatspace acquisition games usually are.

<comment><USER19> Err, I think going much further down that line of reasoning, you will discover something unpleasant: The winning, for some, isn't as important as someone else losing.

<comment><USER20> Which can still happen in a simulated way that minimizes harm but maximizes perceived harm by the inflictor. The gory death of an opponent in an FPS who respawns without incident elsewhere, for instance.

<comment><USER12> _Which can still happen in a simulated way that minimizes harm but maximizes perceived harm by the inflictor._

The old form of this is known as "sports."

</comment></comment></comment></comment></comment><comment><USER21> There's a fundamental conflict between conceptual Utopia/Heaven and the law of supply and demand. All literary conceptions of a utopia rely on abundance of some good that is scarce in the author's time. Usually ignoring that its ubiquity makes it tend toward zero value.

Here's my stab at Utopia, but it requires a belief that Knowledge is infinite:

Utopia is a state of unhindered, continual learning at your own chosen pace.

<comment><USER22> The U.S. founding fathers had another definition which is life, liberty, and the pursuit of happiness. It is very individualized. Suggests it is relevant to the one as opposed to relevant to the masses. Very anti-elitist on its own merit.

<comment><USER23> The "pursuit of happiness" is what is being discussed, given that "life" and "liberty" are already guaranteed. The question is, how exactly to pursue happiness.

<comment><USER12> Basically, keep striving until you are satisfied.

[https://www.ted.com/talks/dan_gilbert_asks_why_are_we_happy](https://www.ted.com/talks/dan_gilbert_asks_why_are_we_happy)

</comment></comment></comment></comment><comment><USER23> This article focuses on a utopia of worldy pleasures, and goes on to explain why such a place would be a pretty boring place to live. But that's just human nature: we're never permently satisfied with what we have. The only way that we feel happiness from these things is if we get more of whatever it is, and that's kind of impossible in a utopia. However, I still think there's a way to get satisfaction out of a world like this: through learning. Even if we, at some point, discover everything there is to know, I think it's still possible to find joy, since there people will be born unaware of this knowledge. Perhaps we might even mark a lifetime by the amount of time it takes to learn everything.

<comment><USER24> I would say through making. Making things gives life purpose, something to struggle against and triumph over. And you also get to learn. Learning for learning's sake doesn't give you the sense of purpose as learning in order to make something great .

<comment><USER25> Marx and others who elaborated on his work developed the notion of alienation under capital—the notion that capitalism really screws up the specific sort of pleasure you describe. The idea, if I'm not messing it up too badly, is that a worker under capitalism encounters the stuff they make as something alien to them—and in fact something that shapes and brings the worker into being rather than the other way around. I know I experienced this phenomenon all the time staring at code on a screen when I was working in tech.

</comment></comment></comment><comment><USER26> "This Christmas Day, thousands of men will be bleeding to death in the Russian snows, or drowning in icy waters, or blowing one another to pieces on swampy islands of the Pacific; homeless children will be scrabbling for food among the wreckage of German cities." \- Should be some context for how completely alien the world of the writer is to us now.

<comment><USER27> It may be alien to us, but there are millions of people for which this describes their reality.

<comment><USER28> But millions less than there were even a few decades ago. The world is making progress toward peace, health, safety, and a decent standard of living at an _extraordinary_ pace right now.

This is not to say everything is hunky-dory. But it is to say that this is no longer World War II.

edit: Where do you think all the Syrian and Lebanese restaurants in America came from? Refugees from the collapse of the Ottoman empire post-WWI. It was just as bad then as it is now. But it can get better, and I am totally convinced it will.

Every wave of immigration that made America what it is today came from people fleeing poverty and violence. Hardly anyone emigrates away from a safe, comfortable life with family and friends and familiar sights nearby. In the 19th century, 20% of the population of Sweden came to the US to escape famine. Sweden was 90% illiterate, mired in extreme poverty, with a birth rate above 5. Now, it's... Sweden. The most civilized country in the world.

If Sweden can evolve from an impoverished hellhole to being the epitome of modern civilization in a century, why can't the same thing happen to Syria? Or Sudan? Or Myanmar? I think it can, and it will.

<comment><USER29> >If Sweden can evolve from an impoverished hellhole to being the epitome of modern civilization in a century, why can't the same thing happen to Syria? Or Sudan? Or Myanmar? I think it can, and it will.

Except Sweden one hundred years ago was not an impoverished hellhole. In fact, it was one of the richest (maybe the richest) countries on earth, smack in the middle of the most developed, richest and urbanized part of Europe (the Baltic region) already enjoying a booming economy and 100 years of peace.

<comment><USER30> Sweden in the 1920s was indeed in a comparatively sweet spot, but so was much of Western world before the Great Depression and WW2 hit. However, by modern standards, Sweden was still quite poor and agrarian: life expectancy for both men and women was under 50 years until the 1890s, and it was the last nation in Europe to experience a major natural famine in 1867-9, with ~15% of the population dying.

[http://www.scb.se/en/finding-statistics/statistics-by- subjec...](http://www.scb.se/en/finding-statistics/statistics-by-subject- area/population/population-composition/population-statistics/pong/tables-and- graphs/yearly-statistics--the-whole-country/life-expectancy/)

[https://en.wikipedia.org/wiki/Swedish_famine_of_1867%E2%80%9...](https://en.wikipedia.org/wiki/Swedish_famine_of_1867%E2%80%931869)

</comment></comment></comment></comment></comment><comment><USER31> Judging by the list of _" Ignorance, war, poverty, dirt, disease, frustration, hunger, fear, overwork, superstition all vanished."_ it seems many of us are living in a utopia yet we still aren't satisfied.

<comment><USER23> Are you? Do you have no worries in the world?

<comment><USER32> Many do not. There is a theory of something called the Power Process, which states that for people to be happy, they need goals which require effort, and need to achieve at least some of those goals. The lack of meaningful goals which require effort in the first world may be responsible for much of the depression, suicide, and other issues that plague us today.

I found this Medium post which quotes the relevant parts: [https://medium.com/chris-messina/surrogate-activities-the- po...](https://medium.com/chris-messina/surrogate-activities-the-power- process-16203dda87)

<comment><USER33> > There is a theory of something called the Power Process,

This is not a theory in the scientific sense. It's an idea Ted Kaczynski, the Unabomber, wrote about in his manifesto.

<comment><USER32> Ok, not sure how that changes the point.

</comment></comment></comment></comment></comment><comment><USER34> He never really gets to the point in the title about not believing in fun

He says reasonably enough

>...not in order to establish some central-heated, air-conditioned, strip- lighted Paradise, but because they want a world in which human beings love one another instead of swindling and murdering one another.

But the fact you don't want an aircon paradise doesn't have to mean no to fun. Why not party / go surfing / whatever seems fun?

</comment><comment><USER8> Heaven is a place, a place where nothing, nothing ever happens.

[https://www.youtube.com/watch?v=9bKW7JkHKm8](https://www.youtube.com/watch?v=9bKW7JkHKm8)

</comment><comment><USER35> This site is blocked by openDNS for malware distribution :-/

<comment><USER36> umatrix tells me the site, orwell.ru, wants to load a script from yandex.ru.

When Orwell wrote the essay he may still have been feeling his combat wounds from the Spanish Civil War, where he took a bullet in the neck from one of Franco's snipers. He also spent some days manning barricades in the streets of Barcelona, futilely resisting a coup within the Republican government, instigated by a Soviet-backed faction.

Something ironic in that, with the page here coming from a .ru TLD.

</comment></comment><comment><USER37> Seems like a good counterpoint to the silly, loaded argument of "Those Who Walk Away from Omelas", which boils down to "Can you imagine a perfect, happy, society and take that seriously?"

The answer is that few people really can, even among those people who think society can be perfected.

</comment><comment><USER38> Just an opinion here.

The article says a number of things about the Christian Heaven. But fails to recognize the premise is that people who go there are changed. On the inside. There is peace, on the outside, because there is peace in the heart, on the inside. There is contentment, because it is on the inside. There isn't a lust for power and control over other people's lives. Nor any shortage of resources. And the biggest thing described as great about Heaven is being in God's presence. Not material things or power.

The problem with all other utopias is that they seem to imagine something that people create without a change on the inside. People have tried to create ideal kingdoms for millennia. The problem is that its seeds of destruction are on our insides. It is us that is the problem.

<comment><USER39> The idea of peace in the heart in Christian Heaven is an idea entirely absent in the New Testament. Peace, in the NT, is always interpersonal--and it's this very thing that causes conceptions of heaven to fail.

To describe it as peaceful, as tranquil is not the point. To describe it as peaceful, where all have been reconciled and relationships have been restored starts to capture an essence of what the purpose is.

<comment><USER40> Would it be fair to describe it as a place where nothing ever happens?

<comment><USER41> Actually, there's a lot of activity, responsibility, and work to be done once heaven arrives. A few thoughts:

In the final state, there will be new heavens and a new earth (i.e. a very physical Earth like we know it now, with mountains, trees, grass, animals) -- a sort of Eden restored, but better, since God's throne and presence will be _on_ the earth, instead of in a separate place (Revelation 22, Isaiah 11). There will be cities to rule, a lot of responsibility and work to do, many "ages to come" in which things will change (scripture references provided on request).

Imagine the grandeur of Tolkien's and Lewis's fantasy novels -- the ages upon ages of interesting history and characters. I honestly don't understand how the narrative will work without any antagonists present, because we presently understand narratives via conflict and resolution. The "they lived happily ever after" seems rather bereft of content, and is kept for the very end of stories. I suspect that's because we have yet to see what the great, true "happily ever after" looks like.

However, the boredom with eternity that Orwell alludes to will not be present, simply because of the person of God. He is full of infinite love, creativity, power, etc... and he will be the delight of all who are there -- that sort of ever-flowing fountain of life and "newness". Indeed, without God himself, everything would get incredibly dull after a while. Jesus says as much in his prayer to the Father in John 17: ".. and this is eternal life, that they may know you, the only true God, and Jesus Christ, whom you have sent." The "life" here is love, joy, and peace, not merely length of days.

<comment><USER42> >> _" I honestly don't understand how the narrative will work without any antagonists present, because we presently understand narratives via conflict and resolution. The "they lived happily ever after" seems rather bereft of content, and is kept for the very end of stories."_

There are other ways to tell a story. For example, you've probably run into kishōtenketsu without realizing it: [https://en.wikipedia.org/wiki/Kish%C5%8Dtenketsu](https://en.wikipedia.org/wiki/Kish%C5%8Dtenketsu)

</comment></comment></comment></comment></comment><comment><USER43> 1943 was the same year that Maslow first presented his hierarchy of needs. I believe that it goes much further to explain the requirements for human happiness.

</comment><comment><USER44> Lest the headline imply otherwise, Orwell was a proponent of democratic socialism: _"Every line of serious work that I have written since 1936 has been written, directly or indirectly, against totalitarianism and for democratic socialism, as I understand it."_

</comment><comment><USER45> I never liked the formulation that utopia is not worth it because people lack the creativity to imagine what could be done for fun in it. It's like we've never tried but hey here's an explanation as to why you shouldn't want it! It should really not be a surprise that imagination is lacking here because for a lot of people, happiness is just defined as having things other people don't have, because that's simply how we came out to be wired and because we continue to live in a world that follows those principles.

 _Until those principles_ have been modified, you have no idea what a utopia is and would look like. _This has never, ever, been the case_ , not in any society you can think of. You might think you live in some super nice societies but you have never escaped those principles.

Utopia isn't about making people not have toothaches or whatever anymore. That's not the point. Utopia is about letting people live in a manner that they would want, not in the manner, currently, prescribed by the law of the powerful and the powerless.

But if you really think that if suddenly your problems being solved, you'd find nothing to do, you are not thinking hard enough, and you are already too wrapped up in the thinking of having things other people don't have. It's a mindset problem of people born into a world working on that principle and it's a hard one to rewrite.

<comment><USER46> > Utopia is about letting people live in a manner that they would want

One of the lessons I learnt from Huxley's Brave New World is that this phrasing is very ambiguous and the meaning of utopia is more complicated, if the word is indeed meaningful. The people in BNW live in the manner that they desire, but not many would call it a utopia. Sure, those desires themselves are the result of genetic and environmental conditioning, but so are ours!

It seems to me that Huxley is saying that some element of struggle and overcoming of adversity is necessary for human flourishing.

<comment><USER27> Between Huxley ("Brave New World") and Orwell ("1984"), I think Huxley saw the future more accurately, although Orwell has amazing insights.

I actually thought that "Wall-E" was a good, and particularly accessible, commentary on utopia. Without the need to strive, we might all just turn into human potatoes. I'm not far from that now, which is pretty frightening.

<comment><USER47> I just want to mention here for those who haven't heard of it: Huxley's "Island" explores the complement to the ideas presented in "Brave New World", i.e. it is an imagining of utopia. I highly recommend it.

</comment></comment></comment></comment><comment><USER48> Most here can eat 3 times a day, have fresh water, warm home and go wherever they want. We are living in an utopia.

</comment><comment><USER49> Interesting that Orwell adopts Eliot as an _English writer_. He was from Saint Louis and educated at Harvard.

<comment><USER50> Eliot renounced his American passport and became a British subject. Orwell respected that decision.

</comment></comment><comment><USER51> My absolute favorite Orwell essay - it cemented my appreciation of him as an essayist and political thinker.

</comment><comment><USER52> The original 1943 title this was published under was _Can Socialists Be Happy?_ The title used here was used in a later republishing.

</comment><comment><USER53> Socialists believe in fun.

Socialists Orwell was familiar with 75 years ago may not have written much about fun (or, at least things Orwell found fun) in their utopian literature, but I suspect hat that's largely because _recreation wasn 't an area of society that they felt needed fixed_, so it wasn't the focus of it utopian literature.

In any case, I'm not sure how much relevance the observation (much less the explanation offered for it) has now, even if it had some in 1943; more recent left-wing utopian fiction _does_ address recreation (whether Orwell would find the utopias described therein to be fun is, I suppose, an open and unanswerable question), notably including Callenbach's _Ecotopia_ , which certainly is more relevant to the views of the modern American (or Western, more generally) left than the works referenced in Orwell's work.

</comment><comment><USER54> I guess the question is, "Which socialists?"

Nancy Mitford professed herself a socialist, yet wrote frivolous social comedy about the English and French upper classes. Kingsley Amis at one point was a communist, and wrote very funny novels.

</comment><comment><USER55> A perfect society requires demonetization.

</comment><comment><USER56> Socialism is like love - it does not work on a large scale.

</comment><comment><USER57> The problem, at least back then, was that fun and such "non-essential" things were considered either bourgeois or vulgar. Both of which were looked down upon because they were the opposite of work and progress and the greater good. At least to some in power.

<comment><USER58> This comment looks almost entirely unrelated to the text of the linked article.

<comment><USER33> I'd have to agree. Here's the thesis of the article:

> The inability of mankind to imagine happiness except in the form of relief, > either from effort or pain, presents Socialists with a serious problem. > Dickens can describe a poverty-stricken family tucking into a roast goose, > and can make them appear happy; on the other hand, the inhabitants of > perfect universes seem to have no spontaneous gaiety and are usually > somewhat repulsive into the bargain. But clearly we are not aiming at the > kind of world Dickens described, nor, probably, at any world he was capable > of imagining. The Socialist objective is not a society where everything > comes right in the end, because kind old gentlemen give away turkeys. What > are we aiming at, if not a society in which 'charity' would be unnecessary? > We want a world where Scrooge, with his dividends, and Tiny Tim, with his > tuberculous leg, would both be unthinkable. But does that mean we are aiming > at some painless, effortless Utopia? At the risk of saying something which > the editors of Tribune may not endorse, I suggest that the real objective of > Socialism is not happiness. Happiness hitherto has been a by-product, and > for all we know it may always remain so. The real objective of Socialism is > human brotherhood.

</comment></comment></comment><comment><USER7> Of course, "brotherhood" is as impossible as "happiness" without contrast, even more so whatever replaces it when it isn't inclusive enough.</comment>


Ask HN: TP - Google did not find - <AUTHOR>

What is the minimum possible character length of a search keyword with which Google search can return a message "Your search did not match any documents."? Of course, 1) keyword MUST use only characters and numbers 2) No special characters 3) Google shouldn't ask "Did you mean?"<p>My lowest count was 6 with "i9qew8" (until this page gets listed by Google :P) Yours? <comment><USER2> seems like a different take on <http://www.googlewhack.com/></comment>