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interesting monotony

First of all, 5OSME is here in Singapore! (Registration is over, but I think there are some portions of this convention for Origami in Science, Math and Education which are open to the public.)

Which explains why Erik Demaine and Robert Lang are here in Singapore!

Erik Demaine gave a talk today at NUS, and among the many amazing things he displayed, he demonstrated a “trick” that makes use of something called monotonous Boolean functions.

Before proceeding, I shall state the problem.

First, suppose we have a picture frame hanging from a nail by a piece of string like so:

If we remove the nail, the frame will fall.

Now suppose we have two nails instead of one. We can hang the frame from both nails in a few ways:

In the leftmost example, the frame will still remain suspended if we remove either nail; only by removing both nails can we cause it to fall. In the middle example, removing the red peg will cause the frame to remain suspended, while removing the green one will cause it to fall. The problem is this:

Is it possible to loop our string around the two pegs in such a way that removing either nail will cause the frame to fall?

This should be relatively simple to solve. (A version of the answer is here. There is no picture frame in the answer, so you have to imagine it hanging from the bottom of the loop, and convince yourself that removing either nail will cause the frame to fall)

Erik demonstrated the above in his talk today. He then asked: can we generalize this to more nails? Can we hang a picture from n nails such that removing any nail causes the picture to fall?

I’ll post about the solution, and its relation to monotone Boolean functions, in subsequent posts.

.

(Picture Credits:

Pictures of curved origami sculptures in glass

Picture frame)

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big red riding hood

“Grandma! What big feet you have!”

“All the better to cover you with, my child!”

And with that, the Big Bad Weather jumped out of his grandma-clothes and consumed Big Red Riding Hood with the largest foot of snow she’d ever seen!

But a huntsman in the woods nearby heard Big Red Riding Hood’s cries for help, and rushed up the hill. There lay the Big Bad Weather, fast asleep. Hastily, he took his shovel, and began to shovel the snow off Big Red Riding Hood.

All through the night he shoveled, but the snow was so thick that when day came, it seemed he’d only dusted some snow off her head.

But Big Red Riding Hood knew that being devoured by the Big Bad Weather was no excuse to skip school. And so, after hibernating in the snow for an additional hour in the morning just for good measure, she thanked the huntsman, mustered all her strength, and dragged her reluctant student body to class.

And they all lived happily ever after. The End.

yes

love is a place
& through this place of
love move
(with brightness of peace)
all places

yes is a world
& in this world of
yes live
(skilfully curled)
all worlds

e e cummings

castles in the sand

We’ve found each other.
Half surprised, bashful,
We stand together alone,
Then bend to build a sanctuary
Around us,
Defining this, projecting that,
Like children on the beach
Building castles in the sand,
“To protect us from the sea,”
We say.
“This is our cove, our love,
Us two, you, me, we…”
When beyond our walls we hear a voice,
Then see our Father’s face,
An intrusion,
Coarse, like the sands beneath our tender feet.
“Playtime’s over, kids,” and we kick, sulk,
We do not want to leave, to give
Up what we have so recently
Received.
We frown, displeasure in our brows,
As the Father gently sweeps our castles
Off their feet, then,
Eyes widening,
Watch
As from beneath the sands He raises blocks of stone
Where once our shaky spires stood, piling
One atop the other, beautiful
Temple around the
Cornerstone.
“Thus shall you love, thus shall you live,
Not as the world, but as the Word.
For I have given once, and shall I not once more,
If you would but give in, shall I not
Give?”

salut d’amour

salut /saly/ masculine noun

1. greeting;
~! hello!, hi!;
bye!;
~ de la tête nod;

2. salute;

3. salvation.

– from wordreference.com

Thus, salut d’amour: not just love’s greeting, but the salvation that comes from love.

one-and-twenty

When I was one-and-twenty
I heard a wise man say,
“Give crowns and pounds and guineas
But not your heart away;
Give pearls away and rubies
But keep your fancy free.” Continue Reading »

connu sous le nom de (a.k.a.):
Les rêveries du promeneur solitaire sur le bord du printemps

What follows is not so much a translation as a transposition

***

It’s the end of Winter Break. Tomorrow, Spring Term begins even though spring time has not yet come. But it is the beginning of something new, nonetheless, and coming down from Minnesota to Ithaca, it does feel as if, not that spring has come, but that I have come to spring.

On the way back from the Commons after a serendipitous purchase, I forget I’m on a different bus, and end up in a corner of the school I have never seen before. And since I’m in no hurry, it being an hour before dinner, I decide to take a walk.

Continue Reading »