Ken’s Blog

I was reading a review today of a new book about the mathematical career of Charles Dodgson – also known as Lewis Carroll for his “Alice in Wonderland” stories. I hadn’t known until today that the wonderful brandy/water math puzzle was invented by Mr. Dodgson. It goes something like this:

There are two glasses, one containing brandy, and the other containing an equal amount of water. Take a teaspoon of the brandy from the first glass and pour it into the second glass. Mix thoroughly. Now take a teaspoon of the mixture and pour it back into the first glass.

Question: Is there more water in the first glass than brandy in the second glass, or less, or the same?

What struck me upon reading this was that I found myself less interested in just solving the puzzle than in coming up with a way of looking at it that would make the solution obvious to anybody. Maybe it’s the teacher in me.

The first thing I tried was to replace the liquid with objects – it’s much easier for people to think about counting things than to think about measuring stuff. So here is a slightly different version of the problem. Suppose there are two bags – one containing toy frogs and the other containing rubber ducks:

 

Take a frog out of the first bag and put it in the second bag. Now there’s one less frog in the first bag, and there’s one frog in the second bag, hanging out with the ducks:

 

But here is where things get problematic. If you want to put an equal amount of duck and frog from the right-side bag back into the left-side bag, you need to remove one quarter of each of the ducks, as well as one quarter of that travelling frog (in order to make one whole toy to put back into the first bag). Unfortunately that means carving up your toys. I happen to be against wanton cruelty to plastic toy animals – especially if they have big eyes and smile a lot.

The problem is that we don’t have small enough pieces to work with. Instead of cutting each toy into four parts, maybe we should use something that already is in four parts.

The solution to this problem, as to so many problems, is jellybeans. Let’s replace each toy animal with four jellybeans – each frog becomes four blueberry jellybeans, and each duck becomes four bubblegum jellybeans.

Place all the blueberry jellybeans in the left bag, and all the bubblegum jellybeans in the right bag:

Notice that we have asserted the following scientific equivalence:

Four jellybeans = one toy animal = 1 teaspoon of brandy
 

One group of four jellybeans is removed from the first bag and placed in the second bag:

Now the rest is easy. From the right bag we remove one jellybean from each of the four groups, and place it in the left bag:

Lo and behold, there are exactly as many bubblegum jellybeans in the first bag as there are blueberry jellybeans in the second bag.

And so we have found it – the answer to Mr. Dodgson’s little puzzle: There is exactly as much water in the first glass as there is brandy in the second glass.

“When I find a thing,” said the Duck: “it’s generally a frog, or a worm.” – From Alice’s Adventures in Wonderland, by Lewis Carroll

Wondrous are the ways of on-line branding. Today is the fifth anniversary of the founding of Facebook. But if you go to your Facebook page, there is virtually no indication of this red letter day in the company’s history. Oh, you can find it if you look really hard, but you have to really look.

Contrast this with Google. Everybody’s favorite search engine would be all over something like this. One of the things we are used to seeing on Google is the headline-level acknowledgement of milestones, from Martin Luther King’s birthday to the anniversary of the first Moon landing. Being a kind of historical recordkeeper is part of the way Google inserts itself into our collective lives and consciousness – which is consistent with its role of being the place you go to find out about stuff. It’s all branding of course, but still it’s rather nice.

Facebook is nothing like that. It’s more of a place where people socialize, share personal interests, talk about something of note that happened in their day. The “branding” of Facebook is now all about trying to disappear itself – to create the illusion that it isn’t even there – just us Facebook friends hanging out together, all snug in our virtual dormroom.

And so Facebook cannot even tell us: “Hey guys, we made it. Isn’t that cool? Five years and we’re still here.” Because we don’t want them to be here. They learned that lesson the hard way – after various attempts to insert themselves into the conversation backfired quite badly. We only want us to be here, in our cozy illusion of shared personal space.

It’s the ultimate Antibranding. By refusing to celebrate its own existence, Facebook has made a perfect statement of self-identity.

The last few days our news outlets have been filled with the shocking revelation that Michael Phelps, American sports hero, winner of an unprecedented 14 Olympic gold medals, has used marijuana. What I find fascinating is the sense of outrage, uproar, collective gasp of public horror, at the revelation that this young man was found to like smoking a bong from time to time.

If I were a Martian tuning in on our Earth broadcasts, trying to understand our culture only from its news sources, I would have to conclude that Michael Phelps is almost unique in his use of the dread weed. My Martian mind would logically assume that normal humans have no knowledge at all of this substance, have likely never seen it first-hand, have never been in a social situation where it was used, and almost certainly don’t know anyone who has ever used it.

But of course this is not the case. Just about everyone you know has used it, many people you know have used it far more times than they could ever count, and good friends and relatives of yours are using it right now. Our president has not only publicly acknowledged using it, but in fact has made a point of shrugging it off. When asked whether he had ever inhaled, his delightfully witty response was: “I inhaled frequently. That was the point.”

When called upon to take a position, the official reply of the International Olympics Committee was a collective shrug. The IOC pointed out that marijuana is not a performance-enhancing drug, merely a recreational drug. They couldn’t care less what Michael Phelps does on his own time.

But here it is being held up as an example of contemptible moral terpitude, a source of national shame and disgrace. A young man has been found to enjoy a little pot! How can we all continue to live in the face of such horror?

I wonder whether we are really all that far from the Islamic fundamentalists in other parts of the world whose narrow minded control of their own citizens’ lives we hold up for self-riteous condemnation. Is the vilification of Michael Phelps, a well-adjusted twenty three year old man, for doing something at a party that is being done by almost everybody, all that different from laws in other parts of the world that require the wearing of a burqa in public?

I don’t even smoke pot. And yet when I see something like this embarrassing news circus, the predominant thought that runs through my mind is: “What the hell is wrong with us?”

I had an odd thought today. We all know that riding a bicycle is a relatively “green” form of transportation. Getting your body from point A to point B by bike clearly takes far less energy than, say, transporting yourself the same distance together with a 1.5 ton automobile.

But has anybody actually calculated how much it costs in energy to feed a bike rider? Humans are notoriously inefficient converters of solar energy into useful work, given how high we are on the food chain. If you are a vegetarian it might not be so bad. But once you start talking about eating a meal that contains, say, farm raised beef, the actual energy cost of bicycling those ten miles might not be so small after all.

Does anybody happen to know how to calculate this cost?

Both comments on yesterdays’ post were in support of some current pop-cultural phenomenon centered around vampire/human romance. What is it about love between humans and vampires that excites so much interest? I suspect there is something deep going on here.

It can’t be just the whole Byronic-hero sublimated-passion thing. That might explain “Twilight” but not the new HBO series. There is nothing either Byronic or thwarted about the latter.

Any ideas?

I’ve noticed a recent trend in films – “boy meets girl” stories where the boy isn’t really a boy, or the girl isn’t really a girl, and there is no real possibility of a sexual relationship. I’m thinking in particular of “Twilight”, “Wall-E”, and “Let the Right One In”. In each case you have the classic pairing off of two characters – the “boy” and the “girl” – who meet and gradually realize, in spite of their enormous differences, they are meant for each other.

Except that in these stories, the boy isn’t really a boy, or else the girl isn’t really a girl, or neither. The boy might be a vampire, or the girl, or the girl might be a vampire who isn’t even a girl vampire, or both of them might be robots. Not really either a boy or a girl – just a robot.

And yet they assume these clear and unambiguous gender roles in their relationship with each other, they circle around each other, go through the elaborate dance of romance and seduction, and finally pair off.

But in each case, in spite of the happily ever after, there’s no sex between them. Lots of sexual tension, but no sex. I wonder whether there is some pattern here. Perhaps it is a sign of the times.

I realized today, in a conversation about prejudice, that it naturally structures itself as a fractal. In some societies, white people discriminate against black people, while lighter skinned blacks look down upon darker skinned blacks.

Religions descriminate against each other, while within each religion people divide themselves into denominations and subdenominations, each believing that theirs is the one true way to connect metaphysics with ethical guidance.

It would be interesting to plot the fractal nature of this strange structure. Patterns might emerge. Perhaps if we could teach these patterns to children, they would learn to see the absurd humor in such behavior, and this nonsense would no longer continue to repeat itself in generation after generation.

Much ink has been spilled lately over the question of illusory memories. Studies continue to show that memories that have been cleverly implanted by a resourceful researcher seem to be indistinguishable in our minds from the real thing.

When I think of this, my mind goes back to the masterful moment in Ridley Scott’s “Blade Runner” when Deckard pores lovingly over old photos, a drink in his hand, while sad theme music by Vangelis plays on the soundtrack. The audience suspects what Deckard does not – that his entire past might be only a clever fake, and the people in his treasured photos merely hired help from a casting agency.

And such musings lead to an odd question: To the man who truly believes he is the Emperor Napolean wrongly locked up in a sanitarium, does it make any difference at all whether his beliefs are true or false? And if Deckard is indeed merely a replicant with falsely implanted memories, does this fact even matter to the reality of his own experience? To him the resulting emotions are just as real and vivid in both cases – the joys as high, and the sorrows as devastating.

Perhaps we live in a world of illusory memory far more than we are comfortable admitting – and maybe that’s ok. Perhaps that teddy bear from our childhood really was blue, not brown, no matter what everyone else says.

Have you ever wondered, as you have thought back fondly on a particular day in the park, or a favorite conversation with a childhood friend, that you might have conjured it all up out of your own head, because that’s the way it was supposed to happen?

I know I have. But how could we ever know?

There was an editorial in the “New York Times” today saying that as newspapers move from paper to on-line, their revenue stream is becoming woefully too small to support proper news-gathering. The editorial proposed that in order to survive, news sources will need to move from a for-profit model to a non-profit endowment model (like museums).

So here we have an actual example of an important real-world activity – sources for trusted news gathered by trained and seasoned professionals – that is clearly of benefit to society, and yet for which (it is claimed) there is no way to survive on-line in a free market economy.

I am struck by the magnitude of the issues suggested by this possibility. Are we really entering an age, thanks to changes wrought by the culture and distribution model of the web, in which the gathering and reporting of expert knowledge is not economically sustainable?

And if so, should we be panicking?

After Manooh suggested looking at http://www.papermint.com, I spent some time on the site. It’s a fascinating experiment, and I think it brings into focus a number of the questions I was raising the other day.

You can create characters there, go shopping, meet other people, play various games. Very impressive. And its very impressiveness raises questions about the limitations of such experiences, and whether those limitations are intrinsic.

We as individuals are not the movies we see, the books we read, or the sum total of the entertainment we consume. Each of us – each individual – contains a complex assortment of competing values and desires, and our own particular kind of yearning for transcendence. As Walt Whitman said: “I am large. I contain multitudes.”

When we get together in person we have heated discussions about things we care about. Not just aesthetic questions and discussions of books and movies, but also social issues – income disparity, prejudice in all its dizzying array of forms, reproductive issues, the relationship between a society and its recent immigrants.

We try to work through, in our discussions, why we like or have faith in certain people or collective movements, while distrusting others.

An on-line world like Papermint is, by design, a place to get away from such discussions, and therefore to get away from ourselves in all of our messy completeness.

There are text forums that touch on the hard issues, but existing embodied on-line experiences seem to go for the opposite – for fun and fantasy, for the “magic circle” of play, where actions do not require consequences.

Is this simply the way it has to be? Is quasi-physical on-line embodiment necessarily limited to ways of escaping from the difficult issues of real life?