Ken’s Blog

This evening I attended a small social gathering at my sister’s house. I was surprised to find that the five year old daughter of one of one of my sister’s friends knew that a Googol is 10¹⁰⁰, and that she was wondering how long it would take to count up to a Googol. I told her it would take way too long, so she suggested maybe counting by hundreds or thousands to speed things up.

I then suggested it might work better if she counted by double each time — one, then two, then four, and so on. She quickly saw the logic of this and started working it out. “Let’s see,” she said, “one, then two, then four, then eight, then sixteen, then …” she thought a moment, “thirty two!”

Soon the topic shifted to parallel universes. I mentioned having read recently that scientists think there might be an infinite number of parallel universes, so it’s possible that we exist in many different worlds, only we could be different versions of ourselves in each one.

After thinking about this for a bit, she pointed out that there might be a universe where there are still dinosaurs. “Yes,” I said sadly, “but we could never see them, because you can’t get from one universe to another.”

“But maybe,” she said, “we could invent robots that could travel between worlds. We could send them to take pictures of the dinosaurs for us.” I was doubtful, but I had to admit it was an intriguing thought.

Our conversation then broadened. Since parallel universes can contain anything, we conjectured, there could be universes where dragons are real. Then we realized that there might be a universe where dragons are having this very conversation. “Imagine,” we wondered, “one dragon talking to another dragon about some other universe where people are real, and not just imaginary creatures.” We both thought this was very funny.

It was one of the more interesting conversations I’ve had recently.

My post yesterday asked what it might be like if we actually had the instant knowledge upload capability from “The Matrix”, In response, J. Peterson commented:

“Your Google Glass frames could handle this. Start face recognition on the person your talking to. Listen for voice and context cues (”…I write for the New York times”, GPS coordinates in the city). Then it’s just a matter of managing the awkward stare as you try to skim the articles floating just above her head.”

It’s an insightful comment, but one could argue that what Google Glass is, in a sense, the antithesis of Trinity’s skill upload. The former provides a tantalizing glimpse into a world of knowledge, whereas the latter actually delivers that world.

Imagine, for the sake of argument, a future society where everyone is “wearing”. In such a world, my conversant would expect me to know, mere seconds into our conversation, the titles of her articles in the NY Times — they would be showing on my heads-up display. But I would still know none of the substance.

In reality, I spent more time reading those articles after the party than we had spent conversing. Google Glass and similar devices, such as the Vuzix M100, cannot replicate that experience. Whereas an actual brain upload (which is most likely decades away), might indeed provide true in-depth knowledge in real time.

In a way it’s like the difference between a spyglass and a jetpack. The spyglass will let you see the contours of a distant mountain that remains tantalizingly out of reach. The jetpack will take you there.

 
When I woke up this morning, the above sequence came to me. Apparently I was thinking about this in my sleep. It’s so cool that you can form 2013 as a countdown using only simple arithmetic of 10 separate numbers. I’m starting to suspect there are many solutions for any given year. Maybe I’m just a nerd. 🙂

Speaking of which, a recent encounter reminded me of the following snatch of conversation from the film “The Matrix”:

	Neo:		“Can you fly that thing?”
	Trinity:		“Not yet.”

 

This is the scene in which Trinity, the female lead, instantly downloads to her mind the ability to pilot a helicopter, and the entire audience thinks (to quote Keanu) “Whoa!”

I attended a holiday party the other week at which I was introduced to a clearly very interesting and intelligent woman whom, I was told, wrote for the New York Times. I found out only later, when I did a Google search, that she had written a number of features about research topics I have worked on, which I would have loved to discuss with her.

I might have figured that out at the party, but pumping people for questions about their work while they are holding a drink can be socially awkward. If it had come up in the flow of conversation, that would have been ok.

If we really had the capability posited in “The Matrix” — if I could have simply stood there and acquired, from one moment to the next, the knowledge I later looked up, I might have been able to start that conversation in a fun and interesting way. But would that have been better?

In a way, this is like asking whether a world with cars and trains and airplanes is better than a world where people just walk. Of course such a capability would be enormously empowering, but would it be better?

In other words, would you prefer to live in a world where any body of information could be acquired instantly, even during the flow of conversation? Or would the disadvantages of such a universal ability outweigh the advantages?

 
Yesterday’s post was inspired by Peter Norvig’s new year’s greeting, which was:

Happy 10/9!*8!*7!-6!*5!/4!+3!*2!+1!
 

I thought his greeting was wonderful, but it bothered me that it relied so heavily on factorials, which many people don’t understand. I wondered whether it would be possible to use only add, subtract and multiply, plus concatenation (eg: 1 and 2 can become 12), so that more people would be able to read the message. For variety, I decided to put the digits in forward order.

My strategy for finding a solution was to start with 2013 and work backwards, trying to whittle things down to zero. First I tried 2013 – 1234, but that gave 779, and I couldn’t see how to get from 779 down to zero using just the remaining digits 5,6,7,8,9.

So I then backtracked and tried 2013 – 123. That gave me 1890, and I knew I was in luck, since 1890 is a multiple of 90, so it must also be a multiple of 45. That gave (2013 – 123) / 45 = 42, which is just 7 × 6 — two more digits down.

At this point it was done, except for incorporating 8 and 9. Fortunately (8 – 9) is -1, which is easy to slip in, giving the final result: 0 + 123 – 45 × 6 × 7 × (8 – 9) = 2013.

Still, there was something very cool about the fact that Peter Norvig’s sequence was an actual countdown from 10 to 1 — just like the countdown to midnight at Times Square on New Years Eve. So this morning I figured I’d try such a countdown, again using only “easy to read” arithmetic.

Since 2013 = 61 × 33, this time I took a different approach:

61  →  10 + 56 – 5  →  10 + (98 – 42) – 5  →  10 + 98 – 7 × 6 – 5

33  →  12 + 21  →  4 × 3 + 21

 
And there you have it — the title of today’s post.

 
Happy New Year everyone!! Today marks the fifth anniversary of this daily blog.

Or, to put it another way, this is my one thousand eight hundred and twenty eighth consecutive post. Whew!

I’m not sure what it all means, except perhaps that 2013 is an auspicious year.

Hence today’s title. 🙂

Years are complicated things, with funny shapes and odd bits that stick out here and there. The only thing you can be sure of about a year is that it won’t turn out the way you thought.

I’ve come to realize that I do not measure my years by accomplishments or grand events, but rather by the state of my friendships — my connections with the people I care about. I have been reminded this past year that such matters are wildly out of my control. Wonderful friendships have entered my life seemingly out of nowhere, whilst others have sunk beneath the waves, never to be seen again.

This whole business of letting ourselves become close to others while bracing for the consequences of our inherent separateness — for the possibility of loss — is something I may never fully get used to. How do you love people properly, knowing they may be gone from your life a year hence?

If I have only one resolution for the new year, it is this: To accept this odd coming and going of human souls, both into and out of my life, as simply the way of the universe.

You can love others — even with all of your heart — but the hard truth of it is, you cannot be responsible for any soul but your own.

For the last week or two I’ve been working on a software project that I am very happy about. It’s an ambitious undertaking, arguably too ambitious to be tackled by one person, but the challenge is part of the fun.

I’ve been observing how I’ve been wrapping my life around this project and vice versa. Whether or not I go into work, hang out with friends, see a movie, each day I make sure to put in several hours of work on the project. It’s astonishing how much you can get done over the course of time if you devote several hours each day to something.

Of course not all hours are the same. Sometimes I feel tired and distracted, at other times full of energy and focus. So I’ve come up with strategies. When I’m at my best and most clear headed, I tackle the harder parts. But at other times I have a list of “clean up jobs”. These are tasks that really just require putting one foot in front of the other — nothing spectacular, but necessary for getting the job done. In this way there’s always something useful I can do, no matter what my mental state.

And if all else fails, I go to NetFlix and watch a few episodes of some stupid TV show or other. This strategy is always successful in the long run, because sooner or later I realize that I’d really rather be programming. 🙂

In feminist theory there is a clear distinction between first wave feminism — the original movement that led to women’s suffrage and other rights, and second wave feminism — the more recent movement from the 1960s through 1980s that focused more on rejection of pornography and other cultural manifestations of pervasive domination of women by the patriarchy.

We are now in the era of third wave feminism — a backlash against the reductionism of the second wave. The third wave acknowledges the great diversity among women in ethnicity, in culture, and in religious norms, and seeks equality within this more nuanced and expanded context.

I just started watching the TV series “Lost Girl”, in which the heroine is a succubus, and I realize that our culture is in a third wave of what might be called “supernaturalism”.

The first wave was exemplified by the supernatural as monster, exemplified by Dracula, the Mummy, the Wolfman, the Thing and Frankenstein’s creation. These beings could be sympathetic, but they were always, in essence, the Other — our fears and nightmares manifested as a creature from beyond.

Beginning more or less in the 1960s, our society began to embrace what might be called a second wave of supernaturalism: The recognition that the supernatural creature might have its own normative existence — that from its perspective, it was “self”, and we were “other”. And so we saw such pop culture creations as Bewitched, the Addams Family, the Munsters.

The second wave acknowledged that supernatural beings, like any beings, would see themselves as real, even ordinary, not merely as a creation of our own projections. Seen in this light, Tolkien’s Hobbits were an early pioneer of second wave supernaturalism.

But now, in the era of Buffy, Harry Potter, Twilight, True Blood, Lost Girl and other pop culture creations, we have moved beyond even the duality of human / non-human. We are in the age of third wave supernaturalism, where there it may no longer suffice to label fictional beings in such reductive terms.

Newer fictional universes have moved far beyond mere battles of good versus evil (except as a strawman) toward a more humanist view, in which characters may simply manifest aspects of what could be called “supernatural spectrum disorder”.

Our understanding of the supernatural as metaphor for the human condition has become so sophisticated, so integral to our ongoing cultural narrative, that we now invoke it simply as a useful way to illuminate our own infinite complexity.

A friend sent me a link to a video excerpt of this year’s Kennedy Center Honors — in particular to the 22 minute long tribute to Led Zeppelin, who were among this year’s winners.

In attendance were Barack and Michelle Obama and a roster of contributors to our nation’s diverse culture, such as Yo Yo Ma, David Letterman (another winner this year), Tina Fey, Bonnie Raitt and Alec Baldwin.

Watching this video, I was struck by how timeless and universal are such events. Sitting in their box seats, President and Mrs. Obama essentially functioned as the Royal Presence, lending gravitas to the affair. Caroline Kennedy, as the evening’s host, effectively tied the event to an even earlier regal lineage.

Of course the U.S. does not have a monarchy. But the rhetorical framing is effectively the same as in days of old. The State, in the person of its highest representative, presides over and blesses the awarding of high cultural honors.

Watching how tremendously the Obamas were enjoying the tribute to Led Zeppelin, I realized that our President and First Lady represent a generation that grew up in the shadow of this music, a generation whose very soul was shaped by rock and roll.

And I wondered, how different would the scene have been had it been Mitt and Ann Romney in that box? Would everyone have felt the same air of ecstatic celebration when Ann Wilson sang “Stairway to Heaven” so beautifully that Robert Plant wept?

Or would the cultural clash between the Romneys and these children of the ’60s simply have been too strange, too weird?

I guess we’ll never know.

An unplanned evening
With mathemusician friends.
God, I love New York!