Thought Experiments

My friend Helen de Cruz, decided to illustrate a whole bunch of classic philosophy thought experiments.  All are her original art work and summary, but not her original ideas.  Unfortunately I can't open Facebook at the high school where I teach, so in order to show these to my High School Philosophy Club, I am simply going to post them here ...  All credit of course to Helen de Cruz, and the various philosophers who created the experiments.

December To Do List

Our nation has elected a vainglorious bastard who is willing to use racism, nationalism, xenophobia, Islamophobia and more in his effort to gain power.  His victory has emboldened the forces of hate within our nation, to be more aggressive in their strategies of intimidation.

A few weeks ago friends of a friend, a transwoman and her female partner, who live a few counties from me in rural Indiana, woke up to find this spray painted on their home.

Notice the Swastikas.  Notice the line "KKK strike here."  Notice the burning cross labelled "God save us from gay." (Yes, in the singular.  I guess it is one gay in particular they are praying for salvation from, and since two queer folks live in that house together ....).  Today my wife saw a Black swastika on a red background painted on a board and for sale at a yard sale a few blocks from our house.  On her way home from the store it was gone.  Perhaps one of our neighbor bought it.

This is our nation now.  This is my life.   In mid-November, I wrote a post about what we should be doing in the aftermath of the election, entitled "November To Do List." But, life got away from me, and I didn't finish that post.  Heck, didn't even accomplish much of my own to do list.  It would have been my first blog post for over a year, since I retreated from the national blog I was part of after accusations of being racist.  I probably am, but I try not to be.  And I sure don't hate any ethnicity, or wish ill on other ethnicities, or supremacy for my own ethnicity or any of that junk.  I truly value the contributions that many different ethnicities and kinds of folk make to food, and art, and music, and culture in general.  We are ALL stronger, and lead richer more beautiful lives because of our diversities.  This new wave of awful makes me sick.  I was trying to find more healthy and constructive outlets for some of the frustrations impoverished rural white folks feel.  My ethnicity gets to be part of this process of valuing diversity just like the others do, instead of just being seen as the oppressor.  (We are and have been that, but we are also more than that).  My grandmothers were't perfect, but their apple cakes and meatloafs are part of what makes America beautiful, along with the tacos and Alabama alchemy, and the local Jewish deli, and dozens of other things.  I was trying precisely to try to prevent something like the white backlash that appears to have happened/be happening, but it never worked and now the hate is here in force.  And plenty of innocent Muslims, and black folks, and hispanics, and LGBT folks, and in the end all of us, are going to suffer.

Our president-elect is a Nationalist, and if not a Fascist already, is in spitting distance of Fascism and eyeing it consideringly.  Based on his VP pick, his cabinet choices so far, his staff and transition team picks, he's perfectly willing to cozy up to the Nationalists and Fascists drooling to have power in government.

So what are we to do in response?  Everyone will have their own opinions, but here is mine.  I'm issuing a December To Do List, to all Americans of good heart who would like to find constructive ways to resist the creeping slide of our government into Fascism, and of our populace into hatefulness.

To Do for December

1)  Mourn - You get seven days of being miserable and useless.  You don't have to do jack during these seven days and probably shouldn't.  If you must work, work in phone-it-in mode.  If you have to work for real, don't count that toward your seven days of miserable uselessness.  But once you've spent your seven days, you can still be miserable and mourning, but you have to start working towards a better tomorrow again.  You have to get up and start trying again.  Doing your work for real.  Thinking about coping with the situation.  I've already spent my seven days of useless misery, and I'll bet most of you have too.  By December you've probably used up your allotment.  But on the off-chance you haven't gotten the chance to break down and cry and vent and be with others while also being a total wreck, well that's at the top of your to do list.

2) Get Your Paperwork In Order, (especially if you are trans, or female and want long-term birth control) - Make sure you have a passport.  And your kids do.  If you are trans, do everything you can to get your paperwork to reflect your actual name and gender, instead of just your old name and gender.  I'd been putting this off.  It didn't seem pressing.  It's pressing now.  The new administration can and will make this process much worse shortly after they get into office.  Right now, you only need a doctor's letter, (and some money) to get the gender marker on your passport changed.  But that is by executive decree.  Trump can change that whenever he or his proxies get around to it, after he is inaugurated.  If you have to leave the country, the gender marker on your passport will be one of the few pieces of evidence that other countries will accept that you are indeed trans.  Start the process on driver's licences or birth certificates, or any other paperwork you might have.  If you know trans people, ask them about their paperwork.  Help them if you can.  If someone needs a loan to apply for an updated passport give it.  A bunch of legal services are trying to do clinics for name and gender change for low-income trans folks, because it is so important to get that done ASAP now that Trump has won.  Similarly, if you are female and interested in getting an IUD for long-term birth control, schedule the doctor's appointment NOW.  Get the ball rolling.  Getting birth control is likely to be quite a bit more of a hassle after Trump is inaugurated.

3) Write about your core values - Sarah Kendizor has a brilliant essay here, that argues that a key early step in resisting creeping (or sprinting) Fascism, is simply to write about yourself.  To create a record of who you are and what you value, BEFORE the Fascist culture gets too far along.  In the coming times you will be forced to make compromises.  You will normalize things that would have horrified you a while ago.  So take the time, SOON, to write about who you are.  What you value.  What your core is like.  What is acceptable to you and not.  Ideally this will remind you.  Ideally in coming times you will be able to look back on this document and it will help you to resist taking a step too far, a compromise too far.  I've started this process, but am not done.  If I finish my, there is a good chance I'll get the courage to post it.  You know to avoid grading a little longer ...

4) Supporting businesses - When my wife told me about seeing the handpainted Nazi flag at the neighborhood yard sale, my first response was, hmm maybe we should have lunch at the neighborhood Jewish deli, the Oy Vey Bakery (I would have sworn I did a restaurant review for them for my old blog, hmm, they must not have opened before my old blog folded, well here is their own site, Oy Vey Bakery and Deli).  One easy way to show your love and appreciation for the Mexicans, and Muslims, and queer folks, and jews, and black folks, and well, the whole panoply of folks that are going to get extra static from recent events, is to say hi, and be nice.  Wear a safety pin if you want to.  Go out of your way to be nice and polite.  Or better yet, patronize their businesses and be nice while you're doing it.  December involves gift buying in many American traditions, so think about if there are ways you could buy gifts from folks like this.  And when you do be friendly.  It helps remind you how many different kinds of folks contribute to the betterment of our lives, and it reminds them that folks value them for their own talents and passions and work.

5) Celebrate the Holidays - Lots of American traditions celebrate holidays in December.  If your tradition is one of them, don't skimp on it this year.  Take a break from mourning and gloom and doom to celebrate instead.  Perhaps your tradition involves celebrating the birth of a middle eastern Jewish baby whose parents were far from home for political reasons.  Perhaps it involves gifts that are a modern re-enactment of Iranian Magi giving gifts to a poor child they didn't know. Perhaps your tradition is about keeping the light of hope burning miraculously long after it should have gone out.  Perhaps it is about valuing the unity of the community even when the community isn't so friendly to you.  In my tradition, it is about how even at the darkest times, the light returns, and the seasons turn. But however it is for you, celebrate, and use your celebration to remind you of the values you have that help you oppose creeping Fascism.

6) Thinking about and Organizing for Harder Steps - I suspect the time is coming when we are going to need to do things a lot harder than the first five I've mentioned.  I think a national strike on Inauguration Day, for example, is a very tempting possibility.  I've not seen a lot of do right now things that seem plausible to me though.  I doubt lobbying congress is going to have much effect immediately after they have just won their seats, unless you were an important backer of the winner or have a lot of money for example.  But learn who your allies and opponents are.  Begin the process of organizing.  Some direct actions may help if they are very carefully targeted.  A friend of mine and her mom are going to drive to Standing Rock in mid-December, and are hoping to take a bunch of supplies.  If you want to donate supplies to Standing Rock that makes a lot of sense.  (Try not to further the stereotype of white folks treating it like winter-Burning Man though, if you go work hard to be respectful and genuinely helpful).  Wanna donate to recounts?  I don't think that will change much, but I do think it will be good in it's own right for a variety of reasons.  In my opinion, the time for more widespread direct action is not here yet, but it is probably coming, and the time for organizing and preparing is always.  Think about what you can do.  What you are willing to do.  Who you can do it with.  Talk with others about what you can do together.  Stay healthy and save your sick days, I suspect we'll be spending some of them soon ...

Lavender Graduation Keynote Speech, Dec 2, Indiana State University

By Dr. Bree Morton

[Here is a link to the event,  here is a link to the basic idea of Lavendar graduations.  If I find pics of the event (lots were taken) I'll try to post those]

First, let me say, genuinely, that I am immensely proud of all of you graduates.  I'm gonna say that over and over today until it is funny, maybe even until it is annoying, but I'm going to keep saying it anyway.

2016 has been a weird year.  Earlier in the year, one of my close friends came out to his family as a crossdresser.  He was prepared for it to go pretty badly, but it didn't.  His 15 year old brother said to him at one point "Pff, it's 2016"  by which he meant something like, "don't sweat it, nobody is hung up about that kind of stuff anymore, we just want you to be happy."  And he meant it.  In many ways, there is more acceptance of queer folk and sexual and gender minorities now than at any other point in my life.  On the other hand, 2 weeks ago, shortly after the election, a translady and her bi partner that I dimly know, who live a few counties from here woke up to find their home covered in awful spray paint graffiti.  She's more of a friend of a friend really, but I've talked with her, and she lives close enough that it might as well be here.  The graffiti said "Fag Lives Here" and "Trump." There were a couple of swastikas, and some crosses, including a burning cross labelled "God save us from gay."  It said "cross-dress faget" and misspelled faggot.  Most chillingly it said "KKK strike here."  That is happening too, basically here, basically now.  Never in my life has there been this much acceptance of queer folks, but never in my life has there been this much vehement anti-acceptance either.  During the heights of the AIDS crisis I wasn't really a part of the queer community yet, but I had friends who were, and they were terrified.  It was a bad time, in many ways worse than now.  But I don't think it was quite as polarized of a time.  I don't think our culture has ever been quite as polarized about queer folks as it is right now.  Every queer person in this room is going to be surprised by support and acceptance from a direction they never expected it at some point in the coming years, and every queer person is going to be surprised by attacks and anti-acceptance from a direct they did not expect it in the coming years.  That is the way it is going to be for all of us.  And I'm saddened to say it, but it is going to get worse before it gets better.  I cannot give you the consolation that times are going to be easy.  They are not.  All lives have a mix of harder times and easier times, and we're gonna get plenty of hard ones in the coming years.  But I will try to give you the consolation of philosophy.  And that is that even though things are going to be often horrible in coming years, you can cope with it, and you can be happy anyway.  And for that I am so proud of you.

In a sense, it is my job as keynote speaker to give advice to all of you on how to live the rest of your lives, and that's a pretty tall order.   Decent advice has a lot of limitations.  Mostly it sounds like clichés you've heard before.  That's OK, my job today isn't to teach you wisdom, it is to remind you of the wisdom that you have already learned, and maybe put it in a slightly different way than you've heard before so that you can hold onto it better.  All the stuff I'm telling you are things you basically already know, if not in exactly these words, and that's good.  In fact, it's one of the reasons that I'm so very proud of all of you.

When I was a professor, I studied and taught philosophy and religion.  Now I teach math at high school, and lead the philosophy club.  People often ask me who my favorite philosopher is.  It's Master Zhuang (except that I can't really pronounce it right).  He was an ancient Chinese philosopher, one of the great masters of Daoism.  By his own admission he was a reformed poacher.  The other great Daoist classic the Dao De Jing, supposedly by a guy named "Old Master" is famous for being beautiful minimalist poetry. Few words, but the exact right words to evoke the mysteries.  Master Zhuang's book isn't like that at all.  He loved to tell long weird made up stories, almost always with lots of humor and jokes, and to use them to make philosophical points.  He describes his own writing style as "flowing words." He also loved to argue with his logician friend, Master Hui.  He often made fun of and criticized Master Kung, the philosopher that in English we call Confucius.  But I think Master Zhuang had a lot of respect and affection for Master Kung as well.  There is a lot I disagree with in Master Kung's thought, but I like him too, and there is a lot I DO agree with.  Sometimes Master Kung is just right.  Like now.  Master Kung says this in his book the Analects (Chapter 6 saying 27), and I'm translating a little loosely:

"The excellent person, broadened by culture or study, and brought back to essentials by the rites, can perhaps be relied upon not to turn against what they have stood for."    

The first requirement here is being "broadened by culture or study."  That is what you have been doing for the last several years.  You have learned the skills of your profession, but you have also learned sooo much more.  You have learned about art, and science, and society.  You have learned from engaging with communities.  You have learned from people very unlike yourself.  You have been challenged by ideas and worldviews and ways of thinking that are different from your own, and you've had to compromise with them and come to understand them.  This process has made you much broader of mind.  That was step one.  And I am so proud of you for accomplishing it.

Step two is "being brought back to essentials by the rites."  That's what graduation is for, and other rites of passage.  That is my job as keynote speaker.  I'm trying to help bring you back to what is essential, by reminding you of some key things.  Here are some of the things that I think are essential, based on the life I've lived, and what I think I've learned.

So what is essential and what is non-essential?  Well the first important answer to this, I think, is that YOU have to figure it out.  It is what is essential to YOU that matters.  You have to find your own center, your own core values, the things that make you you, instead of a cut-rate imposter of yourself.  It is possible to lose what you are, to deny what you are, to drift away from who you really are.  You can get caught up in how you think other people want you to be, or how you need to pretend to be to get by, or how you think you ought to be, instead of who you actually are.  Don't do that.  Be yourself.  Over and over.  Relentlessly.   Be proud of yourself.  Be someone you can be proud of, but also be yourself.  It's trite.  It's cliché.  But it's also true, and it's essential.   Go back to being yourself over and over.  Create little rituals in your life to remind yourself who you are.  Use the big rituals in your life like graduation to reflect on who you are and what is essential to being you.  It we put it into words it sounds like a cliché, but when you actually do it, it feels more like home.  Return to your center.  Be yourself.  Be Proud.  And if it helps remember that I, and probably many other people in this room are so proud of you being you.

Second. "Don't Quit your Day Dream."  When I was shopping the other day I got a new comfy t-shirt that had that as a quote on it.  "Don't quit your day dream."  I love it.  The cliché is, of course, "don't quit your day job."  And sometimes that's good advice too.  Your job can help you pay the bills and put food on your table.  For many of you, it may be part of your dream and may be much more satisfying than just a way to get enough to eat. Good for you.  But everybody, whether they have a dream job or not, needs dreams to get by.  My fantasies have saved my life many times over.  I'm a geek, and many of my dreams are about knights and dragons and faeries, or great philosophers of the past.  But other folks have other dreams and that's good.  Maybe it's a garden by the sea you hope to have some day.  Or travelling the world.  Or cheering a sports team.  I'm not a sports person myself, but when I'm around family who love sports I can't help but be joyful of their love.  Geeking out is about loving what you love and not being ashamed of that, whether it's comic books or college football.   Or a special someone.  The great Hoosier sage John Green likes to put the point this way "Don't forget to be awesome."  The things that you love, the things that you are passionate about, the things you geek about, the things that you daydream about when you can, those are what make you awesome, and those are what allow you to cope with hard times.  Leonard Cohen sings about the Future "I've seen the nations rise and fall / I've heard their stories, heard them all / but love's the only engine of survival."  It is what you love and dream about that will see you through … I am so proud of you all for being awesome and dreaming your day dreams and loving the things you love.

Third, you may wonder why I am qualified to give you any advice at all.  I have an odd qualification.  I have been wrong about lots of terribly important things.  If I have any advantage over other people my age, it is that I have made bigger mistakes than most people.  I was suicidal for years.  I was literally wrong about whether or not life is worth living.  That's a biggie.  I'm a transwoman.  I tried to live as a man for decades.  I didn't really think I was a man, but I sorta felt I didn't have any choice that I had to do my best to try to be a man, and that I sorta rounded off to being a man, and that I had try to make peace with it somehow.  It never worked.  I was literally wrong about my own gender for decades.  I can't tell you much about success.  I wrecked my first career, never really thrived at my second career, and I'm just now starting on my third career.  But material success is not essential.  As someone who has made deep mistakes, I tell you, being right is also not essential.  Trying to fix your mistakes and trying to learn from them, that is essential.  The more secure you are, and the more safety nets and back ups you have, the more you can afford to make mistakes and learn from them.  But no matter who you are, you are going to make mistakes of some kind, of some size, of some frequency, and you are going to need to try to fix them, and to learn from them.   Leonardo Da Vinci liked to say "Wisdom is the daughter of experience" which is more or less a fancy way of saying it is making mistakes that makes you wise.  Eventually.  Hopefully.  I am so proud of all of you for making mistakes and learning bits of wisdom from them.  Pass your wisdom on as best you can.

The fourth essential thing I want to try to tell you is to extend yourself outward.  You need to find your center, and who you are.  But then you need to stretch out.  To loved ones.  To family, maybe.  To chosen family.  To community.  To your profession.  To your society.  To your alma mater.  You are yourself, but you are also part of various things that are bigger than you.  You draw from culture, from the past, from community, but you also contribute to them.  That is what flourishing is.  Stretching out from yourself to various other people, and  things, and projects around you in the world and beyond.  You are not your loved ones or community, but when you are healthy and flourishing you will become tangled up with each other.  They will be part of you and you will be part of them.  Like plants with roots intermingling.  Like lights from different light sources overlapping.  It is not your job to fix society, but it is your job to try to fix it.  To contribute towards fixing it.  To making things better for future generations.  Hold close to the LGBT community.  Draw from it.  Contribute to it.  Be strengthened by it, and strength it in turn.  Teach the younger kids struggling with things you have struggled with.  Care for the elders who are becoming frailer and frailer.  Be part of things bigger than yourself, especially your communities.  You are also now firmly part of the vast University community.   We are wearing these robes to remind us that we are part of a tradition that stretches back centuries to medieval times.  My closet has several outfits of medieval clothing, but I'm betting I'm in the minority on that point.  For most of us, this clothing is odd, it’s a ritual thing, we wear only very rarely.  It is designed to link us into bigger things, the vast tradition of universities and scholarship and graduations.  Oxford University is older than the Aztec empire.  Harvard was founded only a few years after the Mayflower landed, and taught for a century and a half before the Constitution was even written.  Indiana State University was teaching before your great-grandparents were born.  These traditions are old.  And you all are now part of it.   Millions of smart men and women have studied and graduated and lived and died before you, and millions will after you.  But you are part of this vast stream through the ages.  University culture is part of you now, and you are part of it.  It is essential that you are yourself, but it is also essential that you are part of bigger projects …  You are about to be a graduate into a grand centuries long tradition, and I am so proud of you.

So to review.  It is not essential that others honor you, or that you are popular, or widely liked, but it IS essential that you are yourself and that you are proud of being yourself.  It is not essential that you are materially successful, but it is essential that you remember to be awesome, and don't give up your day dreams.  It is not essential that you are right.  It IS essential that you try to fix your mistakes, and that you try to learn from them.  It is not essential that you fix the world, or your society, or your community but it is essential that you are part of these things and try to contribute to them in some way.

Master Kung said "The excellent person, broadened by culture or study, and brought back to essentials by the rites, can perhaps be relied upon not to turn against what they have stood for."   You have been broadened by your university education over the last few years.  Hopefully you are being brought back to essentials by these rituals and by your own reflections.  The next step is to not turn against what you have stood for, over the coming years. Even when it is hard to stick by what you have stood for.  Especially when it is hard to stand fast in what you have stood for.

I'm not really trying to make a point about Daoism or Confucianism, rather I am trying to tell you things that all cultures have known, but perhaps in a slightly different ways than you've heard.  You are all going to face hard times in your futures, and you are going to face them with dignity.  You are going to face wonderful times in your futures and you are going to face them with joy.  With dignity and joy united within yourself you are going to flourish amidst all the things that life throws at you.  And I am so proud of you for it.  

Thank you so much for including me in your joyous evening.  Thank you for listening to me talk about some of the things that I think are important, that you probably already know.  And one last time, I am so proud of you all.  Thank You.

9.999... Reasons to be Skeptical about .999... equaling 1

So YouTube has a really great video entitled “9.999... reasons that .999...=1” by Vihart. It's clear, and cute, and far better than my plodding reply. (here)  But hey, I want to disagree with it in a friendly way, anyway. It's often the good stuff that is worth fighting with ...

#1) Appeal to Authority:

99.999...% of Skeptics agree you should suspend judgement on matters that are not forced upon you. When you can tell something is true, believe it. Otherwise hold you mind open and think maybe so, maybe not. I tell you “.999 = 1 is doubtful, maybe it is true, maybe not.” If “because I say so” works for you then skip the rest of my arguments. Or check out the ancient argument the “10 modes of Skepticism” see http://en.wikipedia.org/wiki/Sextus_Empiricus, for some very general reasons to be skeptical. Maybe you're like “.999... = 1 hmm, could be” great!

Otherwise, on to reason #2

#2) Numbers, Numerals and Expressions

So if 1 is the loneliest number, is .78+.22 just as lonely? Well, either way, they have the same numerical value. .78+.22 = 1. A number is a kind of abstract object, a kind heavily studied by mathematics. A numeral is a way of trying to express or say or write or pick out a particular number. 5, V, “Five,” “Cinco” and 11(base 4) are all different numerals expressing the same natural number. An expression is a mathematical “phrase” that uses multiple mathematical ideas to pick out a number. So “4.78+.22” or “the next natural number after 4” or “10 divided by 2” or “((2*3)-1)” are all expressions, and all of them pick out a single unique number, 5. Expressions often use operations like addition, or multiplication, or “the successor of.”

OK so yeah .78+.22 really does equal 1. It isn't just close; it is equivalent, or equi-valent, equi/equal and valent/valued, or equal in value. The value of the expression .78+.22 is the same as the value of the numeral 1. When I say or write “.78+.22=1” that is a claim or proposition or statement, it is the sort of thing that could be true or false. Philosophers say it is a potential bearer of truth-value. Its the moral equivalent of a complete sentence, rather than just being a phrase or expression, which is an incomplete part of a sentence. And the claim .78+.22=1 happens to be true. It expresses a judgment about the relation between two terms which are being compared, the expression “.78+.22” and the numeral “1” and judging them to be equal in value. The statement .73+.22=1 is also a claim. It makes sense syntactically and semantically. It is just wrong, or false. We know what both sides mean and relationship we are claiming between them, but the relationship claimed does not in fact hold. But things like “.78+lemon=1” or “.78+=1” or “.78+22fig=1” or “.78.34.6*6+.22===3” or “.78+.22={1.1, 1, .9}” these aren't even claims or statements, they are syntax errors, what we call “non-well-formed formulae.” We can't determine their meaning well enough to evaluate whether they are true or false. “.77 + ?? = 1” isn't a statement, rather it's a statement-schema. It is an incomplete statement that could be completed in various ways. One way of completing the statement will wind up making the claim true, and other ways of completing the statement will wind up making it false.

So what about “.999... = 1”? Well, 1 is numeral here surely, but what about “.999...”? what exactly is that supposed to be, another numeral? And expression? A partial expression that we need to fill in somehow before it is complete? So my second point isn't really a proof, or an argument yet, but some background and a reason to keep an open mind. It's not really very clear what exactly the “.999...” side of the equation is supposed to be.

#3) Decimal numbers

You might think that .999... is a decimal number. But it is not.

.999 is a decimal number. And so is .999999 and even .999999999999999999999999999 is a decimal number. But .999... is something else. It is a short decimal number followed by three periods.

Maybe it is an abbreviation for some decimal number? OK, but in that case, the claim comes out false. If .999... is an abbreviation for .99999, then it is exactly .000001 less than 1, and therefore not equal to 1. Similarly if we take .999... as an abbreviation for .9999999999999999999999 then still it is not quite equal to 1. Maybe .999... is an abbreviation for a number that is “too long” to write. If so then the difference between it and 1 will be “too small” to write, but there will still be one.

But people who think .999... =1, don't usually think of it as an abbreviation of any specific decimal number, but as an abbreviation for an “infinite” string of 9s. It's more as a summation or series. We'll talk about series and real numbers in a minute, maybe that is one of those, but what it ISN'T is a decimal number. It has the wrong syntax for a decimal number. It is too long.

#4) the Standard Proof

The usual proof that .999...=1 goes like this

Suppose .999...=X

multiply each side by 10, and supposedly you get 9.999...=10x

Then subtract the original equation from that, so

9.999... =10x

-.999... -x

9.000... = 9x

if we imagine the 9's “all” cancel out, or we have an infinite string of 0s, that might look the same as

9=9x, if so we can divide both sides by 9 and get

1=x=.999....

Voila!

OK so why do I doubt this proof? Well … try doing this on a simple calculator. What happens?

For starters, we can't even type .999... into the calculator, because … is not one of the basic symbols of algebra. It's not well-defined in basic algebra. And if you try to input an infinite string of nines your finger gets tired and the calculator overflows before you get there.

So how exactly do we know what .999... multiplied by 10 equals? I know what .999 x10 equals, but I don't know how to multiply a “…” by 10! Well it's just an abbreviation for a LOT of nines right? No if I interpret it that way things don't work as we saw earlier.

.99999 = x

9.9999 = 10x

-.99999 -x

8.99991 = 9x, and then x=.99999 not 1.

OK but what if we have an infinite number of nines? So that we never get to the last nine?

Well then I just don't know what 10 times that is. If I try to calculate it, my calculation never completes. (Indeed, if I use a device to do it, I can never even finish entering the problem into my calculation device). I get closer and closer to an answer, but I never get an answer. Indeed, if I use the standard pencil and paper decimal multiplication algorithm my kids learn in elementary school, I never finish writing the problem down. Nor do the rules of elementary algebra tell me what the answer would be. They don't have rules for dealing with infinite strings of digits at all. Forget semantics, and operations, even at the level of syntax the basic rules buckle in the face of this puppy. If we really mean .999... to be an abbreviation for an infinite string of 9s, then we are well outside of the realm of calculators and basic addition and algebra. Computers choke on infinity, and so do basic sections of math. We'll have to use something more sophisticated. As Vihart says in section 5, “elementary algebra can't deal with infinity, if you allow infinity in your elementary algebrazations you get contradictions.” All the same points apply to the subtraction step too.

This simple little proof doesn't prove what it is trying to. It assumes what is under dispute, when it assumes what happens if you multiply .999... by 10 or when you subtract .999... from 9.999..., and that means it is question-begging. We can't do either of these operations at the level of regular algebra.

More basically, what is going on is that we have two conflicting mathematical intuitions about an infinite string of nines in a decimal expansion. We think about .999, .99999, .99999999, and .99999999, and we notice 2 things: they keep getting closer to 1, and they are always just a little less than 1. So if we have an infinite number of nines, what happens then? Well one intuition says it should be infinitely close to 1, and another intuition says it should still be slightly less than 1. But without a more rigorous set of rules, we can't disambiguate whether the result is the first, the second or both.

#5) Real Numbers

So maybe instead of thinking of .999... a a string of digits in a decimal expansion, we should think of it as a real number. Real numbers aren't that much more advanced than basic algebra and even high school students routinely deal with them. There are more real numbers than can be expressed with decimal expansions of finite length. Pi and E and the square root of 2 are famous examples of real numbers that cannot be expressed precisely by any finite string of decimal digits.

The problem is that rational numbers and real numbers are both dense sets. Between any two real numbers there are an infinite number of other other real numbers. So between 3.1415 and 3.1416 there are an infinite number of real numbers, one of which is pi, and the others of which are not. Between 3.14159 and 3.14160 there are STILL an infinite number of real numbers one of which is pi, and the rest of which are not. So 3.1415... doesn't really “name” any particular real number, it picks out an infinite number of different real numbers, one of which, pi, is particularly interesting to us for various reasons.

The same is true with .999... If we construe it as referring to those real numbers which begin with .999. It isn't the proper name of any particular real number (1 or otherwise), rather it picks out a group of real numbers. That means that .999... =1 isn't exactly true or false, if we take it to be referring to real numbers, rather it is unfinished, incomplete or perhaps it is a syntactical mismatch (comparing a incomplete expression to a complete one). It is comparing a group of real numbers with different values (with at most 1 of them equal to 1) to a single number. .999... construed this way would include .9998, and that isn't what Vihart, or anyone else meant. But because the real numbers are dense, no matter how explicit we are in decimal expansions, we will ALWAYS be picking out an infinite number of nearby real numbers. There is no such thing as the largest real number less than 1. But there is also no such thing as the smallest real number larger than .99999999999. If .999... and .99999999..., and .9999999999999999... all refer to infinite sets of real numbers that are slightly less than (or perhaps equal to) 1, then the claim .999...=1 comes out false or incomplete rather than true, so long as we take it to be about real numbers.

The traditional way to define real numbers is via a set-theoretic construction called Dedekind cuts. There will always be an infinite number of real numbers between any finite number of .9's and 1. So in the Dedekind construction, the phrase “.999...” fails to refer uniquely. It is always talk about a neighborhood of real numbers rather than a single real number. There is an alternate construction of the reals called Stevin's construction. In Stevin's construction .999...=1 BY DEFINITION. But then we can give a sensical interpretation of the rest of the reals, that is in a sense equivalent to the Dedekind construction. But notice what this means, it means that .999...=1 is OPTIONAL rather than true. If we decide to make its truth an axiom, or a naming convention, we get an completely sane and workable system. But if we decide to leave its truth undetermined we still get a sane and workable system of real numbers. There are lots of workable constructions of the reals, there is probably even one (or more) where we make .999...=1 come out false by definition.

The basic problem is that there are so many reals, that .999... just doesn't pick out a definite single real number unless we rig our naming conventions somehow, and even if we do it will still be surrounded by an infinity of unnamable near neighbors, as we'll see in a bit.

#6) Hyperreals and Surreals

Ok here is another little prooflet

Suppose there is a difference between .999... and 1

1-.999... = ?

1.00000000...

-.99999999...

0.00000000... now it can be tempting to think there is some kind of final 1, “beyond infinity”

say “.00000...1”

now Vihart says “Of course, if the zero repeats infinitely you never get to the 1” so “you might as well leave it off the number … There is no difference.”

Notice that if this reasoning works, then it applies equally to the prooflet in #4. You try to multiply .999... by ten and you “never get done.” You try to subtract 9.999...- .9999... and you never get done. Infinities don't get completed, they just keep going on and on.

But suppose we have the opposite intuition, that .0000...1 is a way of trying to express something infinitesimal. And we mean by this argument that there is some infinitely small difference between .999... and 1. Well then we would need a system of numbers that can deal with such things. And we have one, the surreal numbers extend the real numbers with infinite and infinitesimal numbers of various kinds.

Now in a sense, this extension doesn't settle our question either, but it can also clarify our intuitions. In the Surreal number system, there is an infinitesimal number ε, which is larger than 0, but smaller than all positive dyadic fractions. (Conway's construction of the surreals basically uses binary rather than decimals, and has to use transfinite induction to get to the decimals, but it can). But there is a sense in which the surreal number ε, is .00000...1(base2). Now we are doing mathematical poetry here, we are trying to explain rigourously defined things in one system, via loose analogies to another system. But in the same loose analogy sense, “1-ε” (which is a well-formed surreal number) is larger than .1111...(base2), but less than 1(base 2).

Essentially what this means is that we have 3 logically distinct concepts, which are strictly value-wise distinct in the surreal number system:

9/10+9/100+9/1000+9/10000 … < infinitesimally less than 1 < 1

At the level of surreal numbers these 3 number concepts are all distinct values, (and hence .999... does not equal 1, because there is s distinct value in-between them). But at the level of real numbers, these three ideas are so close together than when we try to talk about one of them, we often can't distinguish which of them we are talking about. (Without some further convention or axiom - that is our ways of talking pick out a variety of nearby real numbers in the neighborhood of of the infinite sum and 1.).

Now the surreal numbers are cool, but also tricky, and fairly newly discovered (1974, first well explored in 1976 with plenty of discoveries about them since). In essence a lot of older mathematicians don't distinguish between “.999...”, “infinitesimally less than 1” and “1” because the surreals are pretty recent, and the distinction doesn't make a lot of sense in the real numbers, although Vihart clearly gets this distinction.

#7) Neighborhoods

Vihart argues “If .999... and 1 were distinct real numbers there would have to be a real number higher than .999... and lower than one.” And that is true. There would have to be, because real numbers are dense. Further we don't have an easily nameable distinct real number in-between the two ideas in the way that there IS such a distinct surreal number. But the problem is that .999... isn't a distinct real number at all. It is an incomplete description of a rough neighborhood of many different real numbers, many of which are distinct from 1 (which is a real number). Or if you prefer it is an infinite summation or series that converges to a neighborhood including many distinct real numbers.

In calculus we play this game of “neighborhoods.” Say how accurate you want me to be, and I'll give you a whole slew of numbers that are at least that close to the target. 1+ or - .001, no problem! 1 + or minus .0000001? no problem, lots of real numbers are that close to 1.

So when we try to figure out what the sum of the series .9+.09+.009+.0009+.00009 … = ?? we can't actually give a real number. If we try to do the addition, we never complete the task. But what we CAN do is say what it is CLOSE to.

[my textprocessor is choking on the standard notion here but]

The Sum from x=1 to infinity of 9/(10^x) “converges to” 1. What does “converges to” mean? Well roughly that if you pick any non-zero margin of error δ, I can find an even smaller positive real margin of error ε, and prove that the answer is at least that close to the target. Now “converging to” 1 isn't and can't be the same as just plain equaling 1 (if it were it would ruin it's usefulness in calculus where the whole point is it allows us to almost but not quite divide by zero). “Converging to” 1 means that we get as close as we like to 1, but can never quite say if we equal 1 or not.

So we can't say that .9+.09+.009+.0009 … =1 at the level of real numbers. Maybe it does, maybe it doesn't. We can't prove it either way. We CAN say that it gets close to 1. That it gets as close as we like to 1. That it is in a very small neighborhood that includes 1. But because the real numbers are dense, there are always also other numbers which are different from one, which are ALSO in the very small neighborhood around 1. And any of those MIGHT be the value of .9+.09+.009+.0009 … We can't give these other real numbers finite, unique names, because there are just too many real numbers to give them all names like that. Indeed, any real number we CAN give a finite definite name to other than 1, is guaranteed not to be the proper sum. But there are all these unnameable real numbers around 1, that might be the proper sum. Heck, we can't prove that .9+.09+.009... doesn't equal 1 at the level of real numbers either, it always might. But no matter how precise we get, 1 is always one of an infinite number of (mostly unnameable) real numbers that MIGHT be the proper summation of the series. And of course at the level of surreal numbers we can prove the distinctness of the 3 concepts (sum of the series of nines < number infinitesimally less than 1 < 1), so it is often hard to tell which of the concepts we were groping for when we could only use real number language and limits and neighborhoods and such to talk about them.

#8) Ok, now I'm just rebutting instead of explaining my own views ...

Here is another purported prooflet “Take .333...= 1/3, multiply both sides by 3, you get .999...=1”

As noted this one is very simple, and relies only on the idea that .333...=1/3 and that .333...*3=.999...

But we've seen we have reasons to doubt both of these claims.

.333... “converges to” 1/3, that means it is as close as you like to 1/3, but that doesn't mean that it is equal to 1/3. .333... gets so close to 1/3 that we can't give names to any of the other real numbers near enough to also be contenders, but there always will be other contenders besides 1/3.

.333... *3 is an operation that never terminates, it never finishes computing. It is not always well-defined within the reals (unless we make it equal to 1/3 by definition at which point our argument is question-begging again). Again, if we want, we can estimate the value of .333...*3, and we can prove that it will converge to .999... or that it will converge to 1, but we can't prove what it equals.

#9) Infinitely protected, but infinitely unclear ...

So you might argue that .9+.09+.009+.0009 … =1 is going to be wrong because at every step of the way the sum is less than 1. And that is true, but it is also getting closer to one. The tension here is between our competing number intuitions, that the sum is always less than one and that it is also always getting closer to one (which in the surreal case turn out both to be correct). But Vihart takes a different tack, she argues “but infinity has got your back,” “your sum is always less than one so far, but you also always haven't gotten an infinity of terms added yet.” And that is right, but it doesn't mean that if you could add an infinite number of terms you would get to 1, it just means that we always can't tell yet. Infinity protects, but it also mystifies. Can't tell yet. Still can't tell... At the level of real numbers neither side can prove their point, that the sum is 1 or that it isn't. We are in the classic skeptical position of suspending judgment.

#10) But .999...=1 WORKS!

Well, yeah, it does, but it doesn't work as WELL as some of the alternatives.

The Stevin construction of the real numbers works. If you wanna just define .999... as equal to 1, rather than trying to argue for it, nothing particularly bad happens. It can be done consistently. But the Dedekind construction of the reals works too. If you want to stay neutral on whether .999... equals 1 at the real number level, nothing bad happens either.

It is like the axiom of choice. Some mathematicians are strongly convinced of its axiomatic truth, others are suspicious. Or even better, there is something called the generalized continuum hypothesis (which is actually about the nature of infinity). It works. But the negation of it works too. So does simply staying neutral on it. In math we occasionally have options ...

It isn't very common that mathematicians fight, but it can happen, and part of what is cool about .999...=1 is that it is one of the easier cases to understand where mathematicians have legitimate cause to disagree.

If you said 5/3 is unsolvable over the whole numbers, you'd be right. That answer works. But the answer 5/3=1 2/3 is just plain a better answer most of the time. Harder, not always the best approach (if there really is a reason to be restricting yourself to whole numbers), but generally it is the better answer. Negative numbers, imaginary numbers, irrational numbers, quaterion numbers. Each of these seemed wacky when first developed, and they are harder, but they are also often BETTER answers than other also correct answers.

The surreal numbers are like that too. They work. But they also give better answers than we could before to a lot of questions about transfinite values, infinitesimals, games, and so on. And in the surreal numbers .999...=1 is just plain wrong.

“The square root of negative one has no answer (over the reals)” is correct but missing the point. To my mind “there is no provable difference between .999... and 1 (over the real numbers)” is equally correct but equally missing the point. There IS a difference over the surreal numbers, and that difference captures the conflicting intuitions that we had been trying to express all along, about .999... always being close to 1 but not quite equal to it.

Vihart say. “The rules of elementary algebra and real numbers can't tell the difference between .999... and 1” and that's true, (well truish). But that doesn't mean that there ISN'T a difference, just that the difference is too subtle to be a big deal for those systems. (Depending on how you set up the rules they might be able to tell the difference at the syntactical level of one number being a formula of finite length, and the other being a non-finite symbol string.)

But Vihart and I largely agree on the moral of the story. Math is beautiful and cool, and there is more than one way to understand it and think about it. It is so common for there to be a single right answer in math, 2+2=4, positive square root of 121 is 11, etc., that we can forget that it isn't always so. That some questions in math can be sources of legitimate disagreement by smart people that understand what is going on. The real numbers are beautiful and useful, and you can do all kinds of neat things with them. But so are the split-octonions. Or the surreal numbers. Things like “.999...” that aren't exactly expressions or phrases, that don't exactly fit into the rules, but are still so close to the rules as to be suggestive, to hint at the spirit animating the rules, to egg us on to coming up with even deeper rules ... these are fun! And bickering about them in a productive way might even help us to better understand the concepts nearby them in interesting ways, and that pleasure of sudden new understanding is what math is all about.

By Dr. B. P. R. Morton. Reach me at bprmorton@gmail.com if you'd like to reply. (I can't even claim to be a counter-example to your 99.999...% of mathematicians believe .999...=1, because I'm not really a mathematician. I used to be a mathematical logician, which is basically a philosopher trying to dress up as a mathematician and hang around with mathematicians.  When I wrote this in 2013, I was a housewife.  Now I'm a high school math teacher.)

Also see my friend Dr. Axel Barcelo's arguments on the deductivity of this here.

Palak Paneer

Ingredients
Palak/Spinach - 1 large bunch fresh (not baby spinach), or 1 bag thawed frozen chopped spinach
Paneer - I make it myself (instructions below), or 8-16oz of frozen cubes.  Also called queso fresca.
                 1 gallon of milk, preferrably raw milk
                 2-3 tsp of citric acid or a lemon
Onions - 2 large
Tomatoes - 1 jar or can, or 2 large fresh
Oil/Ghee/Clarified Butter - 3-5 Tbsp
Garlic - 2-3 cloves
Ginger - 1-2 inch piece
Chili powder - 1 tsp
Curry powder  - 1 Tbsp
Garam Masala - 1 Tbsp
(optional - another tsp of coriander powder,
         - a couple Tbsp of heavy cream)
need pots, pans, food processor, and clean cheesecloth, colander, an empty sink, and a kloodged pressing set up.
Typically served with rice and maybe naan or parathas

Process
1) Make the paneer, many hours ahead of time.  Put the milk in a large pot and bring to a near boil.  It will take awhile but you need to pay attention when it gets close because in most pots it can boil over easily and make a mess, and you'll need to turn the heat down when it gets close.  If it does boil it will still be fine, (if it doesn't make a mess), but the texture will degrade the longer it boils.  Dissolve the 2-3tsbp of citric acid in about a 1/4 cup of cold water, you just need enough that it dissolves.  When the milk is boiling well add the citric acid (or alternately squeeze all the lemon juice out of both halves of a fresh lemon of large lime.  Stir a bit, the milk should fairly quickly clump up into milk-solids on top (the curds), leaving behind a bunch of yellow-greenish (boiling) liquid (the whey).  If the liquid is still fairly milky in color/texture, you may need to curdle it a little more with a little more lemon juice/lime juice/citric acid.  A little vinegar will work too.  Turn off heat and let it cool 10 min.  Put the cheesecloth over the colander and both in the empty sink.  Pour the pot into the cheesecloth (curds and whey).  The whey should flow through the cloth, out the colander and into the sink, leaving only the curds.  Press the cheesecloth by hand to get more whey out, it will be hot.  Gather the corners of the cheesecloth, and tie them off, or use a rubberband, or sandwich bag tie, or something to close it.  Now you need several hours of long slow press to get more of the whey out.  I put a flat-bottomed metal strainer over the pot I just used, put the paneer-curds in the cheesecloth on it, put a skillet over it, and then a serious weight (say my 5lb jar of flour or sugar or something).  The idea is to use the weight to slowly press the whey out of the curds, and give it a place to run-off to without doing any damage or re-absorbing.  It takes a couple hours, say 3-5 optimally.  If you have a real cheese press, that should work too.  Or other similar kloodges.  Paneer is the easiest cheese to make at home.  The Mexican cheese queso fresco, and the Slavic cheese tvorog are basically the same thing in other cultures.  If you use milk that is a little soured, the same process yields the Indian chhena (don't press it quite as long), or the Slavic quark,
2) about an hour before the dish is done - if the spinach is frozen thaw it in the microwave for 6 min, if fresh, chop roughly and steam in a little bit of water until soft.  You can do this in the microwave or in a pot.
3) Chop garlic and ginger in food processor, remove (into a little bowl, with a good spatula) and set aside
4) Finely chop onions in the food processor (you'll probably need to cut them into chunks first).
5) Heat oil in heavy pan over medium-high heat.
6) And finely chopped onions and after 5 minutes add the garlic and ginger.  Fry a bit more.
7) Meanwhile, puree the tomatoes in the food processor
8) Add the curry powder, chili powder, (and optionally the coriander).  Fry 2 minutes.
9) Add pureed tomatoes and fry a while
10) Puree the spinach in the food processor
11) Add the pureed spinach and fry for 2-4 minuted
12) Add the garam masala
13) Unwrap the paneer, chop it into 3/4inch cubes, add to the frying mix and stir in softly (it breaks easily)
14) Turn heat down to low and cook for 20 minutes (Start the rice in the rice cooker nowish, don't forget to salt the rice)
15) Lace the Palak Paneer with a couple of tbsp of cream
16) Serve with rice and naan or parathas

Commentary:  This is a family favorite, taught to us by Hema Coleman-Ganupatti.  It's vegetarian, and stretches well.  Making your own paneer is totally worth it.    If you like making your own paneer at home and get the hang of it, you could advance to trying mozzerella, queso Oaxaca, or sana, each of which are only a little harder.

Khlodnik (A cold summer soup in the Slavic style)

Ingredients

1/2 lb of hardy greens (fresh beet greens are traditional, but I'll bet chard or kale, etc would work too)
3 cups  Chicken stock, chicken broth, or veggie stock
1.5 cups of Black Bread Kvass (or ginger ale, or Zima)
1/2 cup of sour cream
2 Tbsp  fresh snipped dill,  (or 1 teaspoon) of the dried stuff
1 Tbsp of chopped chives
2 large radishes, or 3 small ones, sliced not diced
1 dill pickle, diced
1 small cucumber, diced
1 small beet (cooked, peeled, diced)
2 teaspoons of sugar
optional (1/2lb of meat, cubed, - veal, beef stew meat, ham, diced bologna, etc)
salt, pepper, to taste
ice cubes
2 hard boiled eggs chopped

Directions
Cook beet greens in boiling salted water for 25 min. (Kale and Chard will wilt much faster like 5-8 min.)  Drain, squeeze out excess liquid, chop. (You can even use the stems, as long as you chop them).  Meanwhile cook beet until tenderish maybe 15 min, Cook meat if you are using it.
In a large bowl combine kvass or substitute, stock, and sour cream and whisk until sour cream is well incorporated.  Add, radishes, cucumber, pickle, dill, chives, and when ready beet, greens, and if using, cooked cubed meat.  Add sugar and salt and pepper to taste and stir.  Cover and chill.  Ideally at least 4 hours.  It does well overnight or next day too.

To serve, put an ice cube or 2 on the bottom of each bowl, fill with chilled soup, then top liberally with chopped boiled eggs.

Yields 6 to 8 servings

Comments
It's a lovely cold summer soup, refreshing and designed for once the cucumbers and radishes are ready for harvest. Pair it with bread, sandwiches or maybe homemade bread.  Goes well with tea, lemonade, ginger ale, cold vodka, etc.  Polish style Khlodnik typically has more beets (say 3 even 4 or 5) and fewer other veggies (and maybe even a tablespoon of tomato paste).  Poles often float halved or quartered boiled eggs on the top, instead of chopping and sprinkling.  Russian style, emphasizes other veggies and has only 1 or 0 beets.  If you make it with no beets, and maybe add some boiled potato, mustard, and sour it a bit, it starts shading toward another Russian soup called okroshka.  Traditional okroshka adds a teaspoon of mustard, horseradish to taste, and is a bit sourer than khlodnik (add some kefir, or buttermilk, or lemon juice, or vinegar, or substitute all the stock for kvass). Svekol'nik is another Russian cold summer soup in the vicinity here, but I'm inclined to believe that khlodnik, okroshka, and svekol'nik are all distinct.  Belarussian style, adds garlic, uses no beets, adds dairy and nowadays often uses shrimp instead of other meat, maybe some fennel. Some recipes will use yoghurt or kefir or buttermilk to make it creamier, and maybe a little lemon juice or vinegar (not much) if your kvass doesn't come out sour enough.  Ukrainians call it kholodnik, and I've found recipes for it that are similar to the Russian version.  But, I also found a reference to Ukrainian Jews over a century ago making kholodnik with mushrooms and blackberries to sweeten it (and presumably no meat so as not to mix meat and dairy), and eating it for breakfast.  Further south, and in the Caucuses it starts blending into the Ottoman soup cacik.  This dish works lovely vegetarian, but probably won't work right without some kind of dairy to set off the dill and kvass.  Kvass is the hard part, and the recipe for it is below, but you can substitute other things and still get a wonderful soup.  You want something vaguely carbonated, that will be light when chilled, and add a little flavor, maybe some acidity.  Ginger ale worked.  I'll bet a Zima, or a shandy, or alcoholic lemonade would too.  Beer is less traditional than kvass, but sometimes used in Okroshka.  If there is a little alcohol in the final soup, it's OK, but there shouldn't be much.  If you do use real black bread kvass it will add a richness, and yet still also be light and refreshing, and the hint of mint will pair with the cucumber well.  Don't neglect the pickle, the contrast of the fresh cucumber and the pickle is also great.  Polish style will come out pink, Russian style is ideally be a mix of white and green, with maybe some pink.

Black Bread Kvass
1.5 lb or Staled Black Bread - cubed
1.5 Tbsp of Mint
1 lemon, cut into chunks
10 cups boiling water
1/2 cup of sugar
1 tsp cream of tartar
1 package active dry yeast
8 grains of white rice (don't ask me why)

Place bread cubes on baking sheet and back at 325 for 20 min, to dry out.  Transfer to large crock (crock pots work fine, as do stoneware crocks if they are big enough and can be sealed).  Sprinkle mint, add cut up lemon.  Add 10 cups of boiling water, cover tightly and let sit for 5 to 6 hours.
Strain liquid through cheesecloth, pressing down on the back of the bread with a wooden spoon to extract as much liquid as possible, but without pressing the sediment through the cloth.  To strained liquid add yeast, cream of tartar and sugar.  Stir will. Cover.  Let stand for 8+ hours.  You can compost the bread, lemon,& mint.  Next day, strain it again through the cheese cloth, put it into a 1 quart bottle.  (A 2 liter bottle works fine too).  Add 8 grains of rice, seal.  let stand 8 more hours. Strain once more through cheesecloth into fresh bottle.  Refrigerate until use.  Yields 1 quart.

Comments
The result is somewhere between a beer and a Zima, but the alcohol level is pretty low, in line with a non-alcoholic or small beer, with a flavor that doesn't really have good analogs to my American/Western European palate.  You can drink it chilled, much as you would a beer or Zima, or you can add it to soups and sauces.  The same basic strategy works with almost any kind of staled bread, so it's a great way to use bread that is just beginning to go bad, but not yet moulded. Kvass served the role in Eastern Europe that bread pudding and French Toast served in Western Europe, productively using up bread that was about to go bad. Wheat, rye, and barley breads all work well. Whiter bread will yield less flavor and color, and taste closer to Zima.  Adding a little lemon juice, and maybe a little post-fermentation sugar, is nice if you're gonna drink it rather than use it in soups and sauces.  Berry, raisin, and other flavorings get used sometimes at the very end too.

If you add honey and the spit of two or more people of rival factions making tentative peace at the fermenting step, the result is sacred to the Norse god Kvasir, and having the factions drink the kvass that results a few days later is a classic way to cement successful peace talks, in the Norse and Slavic traditions.  If you make a triple batch in 3 separate crocks, (called  Boðn, Són and Óðrerir), mix them, add mead at the end, and maybe a drop of the blood of a scholar or poet, the result is a symbol of skáldskapar mjaðar and used in ritual work to gain knowledge, wisdom or poetic inspiration. Hmm, I seem to be drifting ... More recently, kvass is  seen as a competitor to cola in Eastern Europe, and one that symbolizes valuing Eastern tradition over Western colonization.  The big brand is called Nikola, (a name which also sounds like Not-Cola) and markets its drink as promoting "Anti Cola-nization."  Get it?


References:
My recipes here are heavily based on Darra Goldstein's 1983 book "A la Russe: A Cookbook of Russian Hospitality" which is my favorite Russian cookbook, but I've tinkered some on my own, and consulted the web for a bunch of Polish variations.  And, you know, the Prose Edda ...

Philosophical Percolations

So our new blog Philosophical Percolations is now up and live, at http://www.philpercs.com. I am one of 17 philosophers who has pledged to post almost every week there.  Our goals are to blog "All the philosophy that's not fit to print" and to "keep philosophy weird."  This means that all my philosophical stuff (which face it, is pretty much everything except recipes) will now be appearing over at that blog.  My first post over there is The Three Gates of Speech, and is about a fake Rumi quote.