Friday, December 21, 2012

Why I am sad it is not a re-collapsing universe

Why I am soooooo sorry that we are apparently (meaning according to the latest astronomical data and relativistic cosmologies) no longer in a closed (re-collapsing) universe. According to the latest, the expansion of the universe is decelerating, but at an ever lower deceleration which will cumulatively not be enough to turn the expansion around. 

How terribly sad! Suppose that there were to have been enough mass density in the universe to cause the universe to stop expanding and then to contract. Then there are theorems in GR which state that within a finite time everything will recollapse to a final singularity. 

Now, listen closely: We would then already be INSIDE the event horizon of the final singularity. Yes, you, me, the earth the sun the solar system the galaxy the local cluster the supercluster etc. You don't notice anything different do you? No "the earth shook" nor nothing, nada? 

Being inside the event horizon of a sufficiently large, isolated Black Hole would feel exactly the same.

"But if I was inside the event horizon of a Black Hole wouldn't I be able to see the Black Hole I was falling towards!?"

Nope! A Black Hole, like any final singularity, is like next Monday. You can't see "next Monday" can you?

End of the World

In case you missed it, the world did end, exactly according to prophecy. The end of the world started at the barycentre of the pyramid of the magician in the Yucatan and radiated out at the speed of light.

But the idiots who translated the prophecy forgot to translate the second page, which also prophesied that a new world would start with exactly the same initial data as was present on the outgoing lightcone of the end-of-the-world event. You didn't notice anything did you?

But what I really don't get is the self-hating "Westernized" Hindoos who fall all over each other to believe in the "new-age misinterpretation of Mayan calendar - the Maya Y2K" end of the world prophecy. Don't we have enough of our own revered and ancient crackpot astroboogers to believe in? Why do you have to outsource your insanity and take away domestic jobs from our own jyotishis and jadi-booti vendors?

Physics Phriday - It is a Time Machine

From Jack van Ryswyck:
You know it's funny you should mention that. The other day I suddenly saw Mike vanish before my very eyes, desk chair and all. Left in his place was a box shaped area of seemingly totally empty space, filled with absolutely nothing but some strange looking radiation.

Two seconds later Mike suddenly reappeared, looking very normal. In fact, looking rather exactly like he had at the moment he vanished. He then looked at me as if I had done something totally strange.

He told me that he had not seen anything vanish at all, but to him it looked like I instantaneously had shifted position and facial expression, as if I were an old time movie that had skipped a few frames. We then noticed that the atomic clocks that we had coincidentally been carrying were inexplicably off by 2 seconds. We had just synchronized them earlier that morning, but now his was 2 seconds behind mine.

Some time later a very similar thing happened, but this time a part of his desk chair stayed behind when Mike and the rest of his chair vanished. The remaining part of his chair just got cut clean off and fell to the floor. Mike and the rest of the chair reappeared two seconds later, though the chair did not reassemble. He said that he saw part of his chair suddenly teleported to the floor instantly.

Then the other day Josh and I were passing juggling balls when the same thing happened again. Suddenly everything in the box shaped area vanished, and many copies of a juggle ball appeared, all moving in a parallel direction. I then found myself tossing a juggle ball into the box. Oddly enough it happened to have the same colour as all the copies, and by some mysterious coincidence it was moving in just the same direction. Two seconds later all but one of the balls disappeared, and everything else reappeared. At the far side of the box, one juggle ball flew off. The net effect was just as if I had thrown the ball across the box incredibly fast. Impossibly fast really.

The next time it happened I saw the empty box appear filled with many copies of about one-third of a juggle ball. All but one of them were moving in a parallel direction away from me, but the nearest copy seemed to be moving towards me. In self defense I grabbed the juggle ball nearest to me, which happened to be the same colour, and as a makeshift missile defense system I threw it against the partial juggle ball that was moving menacingly towards me. They collided. The partial ball got knocked into a trajectory parallel to all the others. My defense missile ball got nudged back towards me. Then all the partial balls disappeared, except one that flew off at the far side. My defense missile ball was suddenly missing about a third of it. The remainder fell to the floor. The part that fell to the floor on the other side of the box seemed to fit it exactly.


Friday, December 14, 2012

Physics Phriday

Take your time on this one, as many times as you wish.

The first image is a model of a 1+1 dimensional spacetime, the time axis is vertical, the x axis is horizontal, the speed of light is 1, the orange cone is the light cone and the blue line is the world line of any physical object. At any point on it the world line is confined to the future (+) and past (-) of the light cone at that point, and the point always moves forward in time.

In the second image, I've done some "manifold surgery": I've made a cut each at t = -1 and t = +1 each of which extends from x=1 to x=3. Now I restitch them, but stitch the bottom edge of the lower cut to the top edge of the upper cut, and also the top edge of the lower cut is stitched to the bottom edge of the upper cut.

What have I built?

Friday, December 7, 2012

Mirror Mirror

Sex advice to the young (25 year-olds)

Not to the “young at heart”, just “young”.

If you expect to have a long and satisfying sex life, or just a long sex life, you should now start fucking a 30-year old, a 40-year old, a 50-year old, a 60-year old, a 70-year old … because if you expect to have a long sex life and hence a satisfying one, at some point you will be fucking a 30-year old, a 40-year old, a 50-year old, a 60-year old, a 70-year old …

… or you will be fucking somebody who is at that moment fucking a 30-year old, a 40-year old, a 50-year old, a 60-year old or a 70-year old …

… so you might as well start getting accustomed to it now.

Friday Night Epiphany

Most Private Thing I'm Willing to Admit Dept.

No matter how explosive the sex, no matter how available they were tonight and might be in the future, no matter how horny you were nor that you had just wanted to fuck and had imagined a long night of mutual pleasure, no matter that for a day or two it might help you avoid pining over someone or something unattainable - sex with someone who seems not to like you is just deeply unsatisfying.

Ask yourself, did you want to fuck them a second time?

Wednesday, November 28, 2012

Loud and Clear!

I love you sweetheart, I look forward to have the life I want with you. (I would never admit this to anyone, but know I think of you often, all the time!). I Love you :)))) and miss you and can't wait for our chats. When I come back I cannot wait to see you. :). You will come to the airport to pick me up, won't you, and take me back home? It will have been weeks, I can't imagine what it will feel like to be in your arms again  xoxo! Make that XOXO... :))

(Send the above to a real or imaginary actual loved one (for present purposes it doesn't matter which) and “accidentally on purpose” CC the one who doesn't seem to understand “N,O!”. Based on personal experience, I guarantee that it works like a charm. 

... Ouch!)

Monday, November 19, 2012

New Relics

We'd cleaned up the kitchen together after putting the girls and the baby to bed and I sat down at the table, wanting to be by myself before going upstairs. I telethought my spouse that I would come up in a bit. I felt the reassurance come back, and then turned the telepath off. My sister was asleep in one of the girls' rooms and Jess was downstairs in the study.

At the final moments of the atomization, I'd cried, my sister had cried, even Jess – his intimate from the last few years – had cried, and I'd found it strange that my mom hadn't. If there had been nothing else there, there was that bond through me, but perhaps she'd hardened herself long ago to potential loss.

I walked up to check on the girls. I never do that, but today, I just felt the need, to see them, with whom he'd spent more time lately than I'd been able to … neither with them nor with him. Some nights, if he was here visiting us when the girls got home with their father from swimming lessons or cello practice, he'd drop whatever we were talking about (math) or arguing about (math) to go be their toy. Surprisingly, he never once tried to teach them math, leaving that work to me and keeping his questions and inquisitiveness about my work for when the girls weren't around.

I'd wiped the tear stains off both the girls, but they were still a little puffy eyed. I am sure other parents, as the girls' aunt certainly did, would think me cruel for having taken them with us to the atomization. Now I found the younger one had crawled into her older sister's bed, pulled the blanket off her and cocooned herself. Just like my sister used to do to me. I spread the blanket out and covered them both up again - once they were sound asleep they would be fine, all the tussling took place early at night.

It struck me that as a child I'd never woken up cold. Did Dad cover me up at night when sis and I were asleep?

I suddenly wanted to hold him again, to feel his physical presence, to clutch him to myself - protection, protectiveness all jumbled together in this tangible vacuum that sat across from me as if forever. Milk seeped from my breasts and I realised I hadn't yet fed the “sleeps-through-the-night” baby but my body still felt too wracked to go up and do so immediately. I rebraided my hair, a single short braid I've worn since 5th grade, this time using generators of B_5, for which I'd had a soft spot ever since my discovery of their relation to conformal matrices had caused a small resurgence of interest in Strings.

On a sudden recollection I pulled open the wall behind me and there beneath the tabletop controller I found the only remaining physical vestiges I had of him. I lifted out the little plastic canister, the less-than-an-inch wide black body about the length of my pinky, the grey top with faded “IMLI SEEDS” written on it. Dad had had a few of those when I was a child - film-roll containers (from his childhood?) that he'd managed to hold on to through multiple international moves. I flipped open the top with my thumb and spilled the contents out on the kitchen table.

Nails. His nails. Both he and I had laughed when my sister had insisted on collecting these, “People collect hair and nails. Dad collected mine!”, she'd protested. “Only baby hair and nails, when they are soft!”, I'd sniggered. But she collected them anyway, that one time, and borrowed one of Dad's canisters which he used for taking spice mixtures on camping trips. She'd cried then because I'd made fun of her, but a few years ago she divided the contents with me, for safe-keeping. I opened the telepath and sent her a thank you, for morning delivery, and recalled her tying my half of his hair with a rubber band. I stuck my finger in the canister and sure enough there was a tuft of hair, with brittle pieces of broken rubber band sticking to it. The hair was a couple of inches long, grey. I sniffed it, painted my face with it, rubbed it between my fingers, desperately wanting to believe in re-incarnation, in a higher power, anything that would bring him back to me.

I carefully put the hair back in and looked at the nails. He'd been cutting his nails, we the three of us had all been cutting our nails before he took us climbing that day, and I remember that day because it was when I first climbed a 5.9, and then tried a 10a and he'd smiled and hugged me and said, “You already out-run and out-swim me, is there nothing you will leave me, not even climbing?”


What have you left me, Dad?

Friday, November 16, 2012

Review - The Wind-up Bird Chronicles

Review of “The Wind-up Bird Chronicles”, by Haruki Murakami

Murakami seems to be a very popular author with women on the dating websites, at least with the women who interest me. As preparation for the battle between the sexes, I wanted to read what they are reading. I could have armed myself by reading “Think like a man, act like a woman”, but while the movie was funny, I don't know if it was particularly edifying and none of the other BASPs with whom I watched it found it worth commenting on afterwards. Besides, having been a full-time male mom for 8 years, I'd already thought like a man and acted like a woman, and well, here I am.

So Murakami it is. Now, if you want a regular old book review, look for one on the web.

A few lines I wish I would have written: “Which is not to say that I didn't have any distinguishing characteristics. I owned a signed copy of Miles Davis' Sketches of Spain. I had a slow resting pulse rate: forty-seven normally and no higher than seventy with a high fever. I was out of work. I knew the names of all the brothers Karamazov. But none of these distinguishing characteristics was external.”

Now for the feelings the book aroused in me: mostly it left me very disturbed, there is palpable occult-like evil, but it is so unexplained and unmotivated, and only tangentially personified, that I could never really grasp what it was. This is mostly carried out against women, and the violations are mostly more mental than physical. There is gristly, bloody, gruesome, slow, pit of the stomach violence and detailed empathetic pain. This is mostly against men. The scenes seem gratuitous, except as mysterious and near mythical events in the past that explain future senses of deep connection. The women survive, the men don't.

I suspect that one of the reasons women like this book is because it is a singular example of a book with anticipated, prolonged, detailed descriptions of infernal physical violence on men and of violations of males bodies on a mass scale. Does it make women who like this book man-haters? Perhaps, but only in the sense that men who like Paul Auster's “The Book of Illusions” (in which 8 women are gratuitously and violently killed off) or indeed who like any of the numerous books and movies in which gratuitous or non-gratuitous violence against women is lovingly portrayed, are woman-haters.

As the accompanying diagram shows, the book has numerous loose ends, vestigial characters with no development that play a repeating, non-minor role but remain completely disconnected from any other character other than the protagonist. I was never even able to understand whether they were the shades of some other characters. These are the dangling characters in the diagram. They seem superfluous in the sense that the book would not have been essentially different without them.

Now for the diagram. It is a map of the main characters, a few key non-human objects and their interconnectedness. I had hoped that drawing it would show me the center, and was motivated to draw it when the protagonist sketches out some of the interconnections (as a circle) and wonders what is at the center. However, circles needn't have centers in the space they belong to: while the rim of a flat dish has a center, what is the center of the rim of your coffee cup? Or the center of a circular orbit around a black hole? And indeed, I haven't found any obvious center in the Wind-Up bird network.

In the diagram, green characters are founts of positive energy, red characters of evil. Green arrows indicate positive, life-enhancing acts, passive or active. Red arrows indicate life-draining actions. Light blue characters are carriers of energy of undefined sign. However, almost all the characters are in some way contaminated by this “energy”, whether positive or negative, except for May, who in the end seems the most real of all the characters.

Other comments or unanswered questions:
  1. Nutmeg's father has a blue stain of the same shape and color on his cheek that Mr. Wind-Up Bird acquires and loses. But there is no other connection: the former is a birthmark and brings no special powers or heat, the latter is acquired on a parallel world excursion, is connected with and is a source of this mysterious energy and is lost towards the end of the narrative.
  2. What happens to Noboru Wataya the cat, and what is his connection to Malta Kano, if any? What is the significance of his tail and whether it has the same bend or not as before?
  3. Why is the wind-up bird audible only to males? Is there any associated mythology with this ill-omen?
  4. WTF with the connection between Lt. Mamiya and Creta? This is an instance of the author getting tired of writing the book towards the end, and puts these two unrelated characters together to tie up two ends.

Sunday, November 4, 2012

Answers for "Man from the South" probability questions

Links to Dahl's  "Man from the South"

The questions are repeated in this post.

Preliminary answers

Q1. What does American Boy think is the probability of his lighter lighting during any single attempt?

Most people accept a bet when they think the odds are at least 50-50. Since Man from the South and American Boy have had time to negotiate the terms and think about it, both think they can win it. So as neutral observers we can consider the probability that the American Boy will win the bet to be 0.5.

So what does this tell us about what he thinks is the probability of the lighter lighting on any one attempt? Let this probability be p. The probability that he will win the bet, i.e. that it will light N times out of N trials, is pN. We just decided that this is ½, for N=10. So,
p10 = ½
I was driving and couldn't very well use my laptop (my phone is not a very smart phone), leave alone the log tables, slide rule or abacus in my back seat. And I can't do powers of 1/10 in my head, not in general. But I can calculate powers of numbers near 1! So let's calculate q=1-p instead, which is bound to be small since the boy is so sure of success.
½ = (1-q)N ~ 1-qN, so for N= 10, q=0.5/10 = 0.05.
Which gives us our first answer: p = 95%, which we know is a bit of an overestimate. (The exact answer is 93.3%.)

But this is like focusing on conversion ratio and not on cost-per-action.

Q4. Were there to have been a 9th attempt, and were American Boy to have failed in it, what would he have lost?

A: His left pinky, those were the terms of the bet. So American Boy is staking his pinky every time! All but the last time, if he wins, all he wins is the right to stay in the game, if he loses, chop-chop (and the right to play!)

So this is kinda sorta like conversion attribution: every bid-request we (RFI) win and then every impression we serve only gives us the right to stay in the game, in the sense that if we don't serve the impression we certainly won't get attribution credit.

Q2. How many fingers to a Cadillac?

On the face of it, it would seem to be one finger to a Cadillac, C = F, since if he loses, he loses a finger, and if he wins, he wins a Cadillac. But as we saw above, the American Boy stakes his one finger 10 times and thus faces 10 opportunities to lose his finger vs. one opportunity to win the Cadillac. So,
10F = C

After the eighth successful attempt, 

Man from the South's wife surprises them and ends the game. She sends American Boy away empty handed.

Q3. How should he have been compensated, if at all?

Aha! “How to distribute the spoils in an interrupted game?” The very question that my colleague Jack pointed out was the leading cause of the rise of probability theory!
The way I think of this is in terms of “vesting”. Each time they play and American Boy wins, he wins a 10th of a Caddy, but, BUT, he only gets to keep his winnings (the entire Cadillac) if he keeps his head (figuratively) and finger (literally) for 10 trials. American Boy can't get cold feet and walk out after say 5 trials and demand half a Cadillac – so really he can get cold feet and walk out but he can't drive off. So there are two possibilities. Under one, the Man from the South gets cold feet and decides not to play anymore. In this case he forfeits his Cadillac, which was held in escrow by the narrator. Under the other possibility, the “authorities” intervene. Since neither party has broken their terms, in this case I think American Boy gets to keep his “unvested” winnings, which would be 8/10 of a Cadillac. Now since the Cadillac wasn't the possession of the Man to begin with, but belonged to the “authorities”, … this isn't a math problem anymore. (By the way, who intervened and broke up Cardano and Pascal's poker game?)

Legal opinions? Aji, Joanne?

Q1 (Re-evaluated). What does American Boy think is the probability of his lighter lighting during any single attempt?

Most people accept a bet when they think it is a game with at least a zero sum in their favor. Since Man from the South and American Boy have had time to negotiate the terms and think about it, both think they can win it. So as neutral observers we can consider the game to be a zero-sum game.

What does it mean for this to be a zero-sum game? Winnings * probability of winning – losses * probability of losing = 0! Which yields:
p = 1/(W/L + 1). (Check: if W are high, p is low; if W are nearly 0, p is nearly 1 and if W=L, p =1/2.)

In our case the winnings are the Cadillac C, the losses are the finger F and the probability P of winning the entire game is P = pN, where p is the probability of the lighter lighting in a single trial. Combining things we have
C*P – F*(1-P) = 1, or P = 1/(C/F + 1)
Putting in C/F = 10,
p10 = 1/11

1/11 = (1-q)N ~ 1-qN, so for N= 10, q=1/11 = 0.1.
Which gives us 78.7%.

Really? Would you play that game with a lighter which only lights less than 80% of the time? I think that the Man from the South has fuddled the American Boy into undervaluing his finger, by making him think he is wagering a finger vs. a Cadillac, whereas really he is wagering a finger against a 10th of a Cadillac.

Some preliminaries

If you aren't interested in the nuts and bolts, skip them, but this is so anyone can check my work.
Notation: Sum[i, 0, Infinity] f(i) is to be interpreted as the sum of the function or series f(i) over the index i from i=0 to i= Infinity. Then,
Sum[n,0,Infinity] pn = 1/(1-p)
Sum[n,0,N] pn = (1-pN+1)/(1-p)
Sum[n,1,N] pn = (1-pN)*p/(1-p)

Look at the following table of outcomes of consecutive tosses and the overall probabilities
W ← 1 → L
1: p (1-p) (End)
2: p2 p(1-p) (End)
3: p3 p2(1-p) (End)
So after n trials, the probability of winning all is pn and the probability of losing any is
(1-p)* Sum[i,0,n-1] pi = (1-p) * (1-pn)/(1-p) = 1-pn = 1- prob(Winning). Which is good since it indicates I can still sum correctly.

Back to the problem, to get a handle on 

what if anything AB deserves when the game is stopped.

From making the last, Nth, trial a zero-sum game, we know that
pN = 1/(C/F + 1). We've assumed that AB wins 1/N th of a Cadillac (virtually) when his lighter lights. So assuming the first trial is also a 0-sum game, we have:
p*C/N = (1-p) *F, which resolves as
p = (C/NF + 1) ^(-1).

Can these two equations be solved simultaneously for both C/F and p?
Yes, but the solution is i) independent of N and ii) meaningless:
We have (1+C/NF)^N = (1 + C/F), but the RHS is simply the first two terms in the binomial expansion for the LHS, so the equality holds only when C/F = 0 and p =1.

So one of our assumptions above is wrong. 

Let's try another tack. 

Assume that at the nth trial, AB wins some unknown portion of the Cadillac a(n)*C. (When Ari and I were talking about this last week, Ari guessed, “Wouldn't it be some quadratic or increasing portion that he wins?” Ari's motivation was to take into account the wearing out of the flint, the gas running out, the thumb getting tired, AB getting nervous etc. Dahl, spends an entire paragraph describing the care and attention to detail taken by AB, after each light, he blows on the lighter, closes the lighter, waits a few seconds perhaps for gas pressure to build up again, re-opens it and then flicks it once. ) What we know is that
Sum[n,1,N] a(n) = 1, over the course of the entire game, if he survives, he wins the entire Cadillac. So at every trial, AB stands to lose not just his finger and the right to play, but also the “won but not vested” portion of the Cadillac, and he stands to win some portion of the remaining.

At the last, Nth trial: W : L
p : (1-p)
a(N)C : F + (1-a(N))C
Using the 0-sum equation, we get:
a(N) = (1 +F/C)(1-p).
Great, so now we have ONE equation and 3 unknowns: a(N), F/C and p. But we also know that if the game is 0-Sum over all: p^N * C = F*(1-p^N),
which yields:
0 < p = (1+C/F)^(-1/N) < 1. So now at least we have two equations for three unknowns, and the solution for p is valid. This doesn't guarantee that 0

If we knew C/F, we could solve the problem. However, clearly, C=F is no longer valid. C = 10F could be used for AB's assumption. We also have another source of information: The Man from the South's wife explains that he has lost eleven cars and taken forty-seven fingers. Assuming that he considers these equivalent, we have 11C = 47F

The fraction C/F is the ratio of the value of one Cadillac to the value of one Finger.

But all this hasn't answered the question of 
what AB deserves when the game is interrupted. 
Also, we've assumed that the entire game is 0-sum and that the last trial is 0-sum. Can't we make use of the assumption that 

every trial is also 0 sum 

to see if we can figure out the intermediate non-vested winnings?

Recall that at the nth trial, AB stakes his previous winnings and his finger for a chance to win a(n)*C portion of the Cadillac. So the 0-Sum equation for the nth trial is:
a(n)*C = (1/p -1) *(F + C* Sum[i, 0, n-1] a(i)). The resulting recursion relation is for a geometric series!
a(n+1) = (1/p)* a(n),
whose solution is
a(n) = a(0)/p^n.
Note immediately that a(0) != 0, so AB has to stake (even if only virtually) something more than just his finger. 

We find a(0) 

by using the fact that the total portion of the Cadillac gained over 10 trials is 1:
1 = Sum[i,1,N] a(i) = a(0) * Sum[i,1,N] (1/p)^i = a(0) * (1/p^N -1)/(1-p), or

a(0) = (1-p)/(1/p^N – 1)

For the first trial (note that this is independent information since so far we have used the recursion relation and established a(0) using the “normalization”, but we haven't yet used any 

“initial conditions”):

a(1)*C = (1/p – 1) * ( F + a(0)*C), which yields
C/F = ((1/p)N -1)/p, which is a different relationship between C/F, N and p than we had previously. I am not sure I can invert this to yield p(C/F), but it can certainly be numerically solved.

Let us also calculate the virtual winnings after each trial:

W(n) = C*Sum[i,1,n]a(i) = C*a(0)*(1/p^n -1)/(1-p), which simplifies to
W(n) = ((1/p)n - 1)/((1/p)N - 1)

So given p we could calculate C/F (or vice versa), a(0), a(n) and W(n)

Working on the “wife's numbers”, we see that the American Boy should be compensated with 66% of the Cadillac when the wife interrupts the game after the 8th trial.

How do the winnings increase as the trials proceed:

Winnings in units of "Cadillacs"
which look like
Levenfeld curve

Conclusion and final answers:

Q1. What does American Boy think is the probability of his lighter lighting during any single attempt?
About 80%.

Q2. How many fingers to a Cadillac?
In American Boy's valuation based on his behaviour, 10 fingers to a Cadillac.

After the eighth successful attempt, Man from the South's wife surprises them and ends the game. She sends American Boy away empty handed.

Q3. How should he have been compensated, if at all?
With 60 or 66% of a Cadillac. I would go with 66%, which is based on the Man from the South's experienced equivalence between Cadillacs and fingers.

Q4. Were there to have been a 9th attempt, and were American Boy to have failed in it, what would he have lost?
Ah, his finger, of course, and, his virtual stake, which is 3.9 % of a Cadillac. How could he have lost something he never had to begin with? Well, for the bet to proceed, AB would have had to ask the narrator to spot him 4% of a Cadillac, or its cash equivalent, or its (OUCH) finger equivalent, which is 17% (3.9% * 4.3 F/C).
If AB's lighter fails during the game, he loses 1.17 fingers since he would have to sell 0.17 fingers to the Man from the South to pay off the debt to the narrator. If AB's lighter doesn't fail during the game, he simply returns the cash or Cadillac equivalent from whoever he borrowed it, and is ahead one Cadillac. 

Why did I ever think of approaching the problem this way, with a “virtual stake”? In particle physics, one can borrow virtual particles from the vaccuum in order to simplify calculations. It is all halal as long as the virtual particles don't violate any conservation laws for quantum numbers and the mass-energy of the particles exists for a short enough duration of time that Heisenberg's Uncertainty principle is not violated. The really interesting thing is that these virtual particles have real effects: A pair of uncharged conducting plates will attract each other because a virtual charged particle – anti-particle pair will come into existence from the vacuum for a brief time, and the effective dipole and its images will cause the plates to experience an attractive force. Don't believe me, look up the Casimir Effect.

What happens if you grab those particles and forcibly separate them from each other and prevent them from annihilating each other as any decent particle-anti-particle pair should do? You end up creating a Black Hole-White Hole pair, which you can then use for superluminal transportation and as a time-machine! (Okay, I just made that up, but is it really any crappier than “The Secret” or Deepak Chopra?)

Back to reality: The Man from the South's wife explains that he has lost eleven cars and taken forty-seven fingers.

Q5. What does Man from the South think is the probability that American Boy's lighter will light during a single attempt?

Q6. How many fingers to a Cadillac does Man from the South figure?
Th ratio of the values is C/F = 47/11.

Q7. Do your answers to Q3 and Q4 change?

Added on 16th Nov. 2012
What was Fermat and Pascal's approach? Instead of looking backwards, they looked forward and calculated the probability (on the condition of the current circumstances) of winning or losing the game and divided the spoils accordingly. So if AB has a probability of p of lighting the lighter and has already done so 8 times, the probability that he will then do so 10 times is simply p^2 and the probability that he will lose is (1-p^2). According to this approach, AB wins p^2 of the Cadillac and loses 1- p^2 of his pinky. I think this is close to Jon's suggestion, who strongly felt that since the game hadn't finished AB would have to lose part of his finger in exchange for part of the Cadillac.

Thursday, November 1, 2012

Probability questions from "Man from the South"

The Man from the South (see earlier post) and the American Boy negotiate terms and make a bet: If the American Boy lights his lighter 10 times in a row he gets Man from the South's Cadillac. If the lighter fails to light during one of those 10 attempts Man from the South immediately cuts off American Boy's left pinky, and keeps it.

Think about the following questions in any order. You can make any assumptions, come up with an approximation, an estimate, a minimum or maximum.

Q1. What does American Boy think is the probability of his lighter lighting during any single attempt?

Q2. How many fingers to a Cadillac?

After the eighth successful attempt, Man from the South's wife surprises them and ends the game. She sends American Boy away empty handed.

Q3. How should he have been compensated, if at all?

Q4. Were there to have been a 9th attempt, and were American Boy to have failed in it, what would he have lost?

The Man from the South's wife explains that he has lost eleven cars and taken forty-seven fingers.

Q5. What does Man from the South think is the probability that American Boy's lighter will light during a single attempt?

Q6. How many fingers to a Cadillac does Man from the South figure?

Q7. Do your answers to Q3 and Q4 change?

I don't necessarily have answers to all the questions, but here they are.

Wednesday, October 31, 2012

Probability and "Man from the South"

A few nights ago I read Roald Dahl's "Man from the South", which brings to mind Dahl (surely no relation of Borges' Dahlmann) as a combination of Poe, Borges and O. Henry, and surely no writer of children's books. A RocketFuel colleague, Ari, pointed out a Hitchcock movie based on the story, which I might get around to watching some nice and bright sunny Saturday morning. To tranquilize myself after reading the rather macabre tale at night, I fell to thinking about some rather interesting probability questions based on the events described.

I want to give you the chance to read the story first, and I really hope, post your own questions, before I raise my questions in a blog in a couple of days. Then, a few days later, I'll give my solutions, which, because of possible differing assumptions, may be different from yours. I'll also add the takes of people who talk to me about it.

Yet another RFI colleague, Jack, referred me to a wikipedia article and pointed out that I was not the first to start thinking about probability motivated by games of chance. Late by a whisker again, Jeeves, dash it all!

Sunday, September 16, 2012

Oakland Police Brutality Ends!

... and I have a bright orange single suspension bridge I can sell you cheap.

Now that I have your attention ... whether you are a parent or not, if you think it is okay for police to go around killing teenage children with impunity, perhaps you should listen to Jeralynn Blueford speak about the cold-blooded murder of her son Alan Blueford:
addressing the Oakland City Council
speaking in Chicago about her son

Better yet, go see her in person

There are numerous and continuing rallies and events attempting to bring to justice the criminal who cold-bloodedly shot Alan (first while he was running away, the second and third time while he was lying on his back), then shot himself in the foot in order to claim self-defense. You can find about future events at

The event at Sunnyside Park in West Oakland (above) was supported by Occupy Oakland. I had initially thought I would just drive down, drop off the food and return, but ended up staying to serve food and then to listen to the speakers and talk to attendees there, many of whom were family, friends or neighbours, and many of whom came to the event for various places around the Bay Area.

There were many friends there I hadn't seen in months, and it was heartening to see their continuing involvement with Occupy Oakland, and Occupy Oakland's successful outreach to communities in Oakland.

Vangibhath with sesame seeds (no vangi, just mixed veggies)

Leila, the kitchen coordinator for Occupy Oakland

The food service

Food service during a lull

Donated food, which will be used either in the community or prepared and served at the next assembly or community event.

One of the BBQ cooks

"Fuck Masso!", refers to Miguel Masso, the OPD officer (I wonder how many times he has been referred to as "brave"?) who murdered Blueford

The cooks taking a break.

A pastor speaking out.

Jesse, Isabella and Dana - I was thrilled to see that other parents had brought their children to this community event. 

Sunday, July 8, 2012


I was wondering if I could convince you to bring some of your amazing cuisine to this Sunday's GA.  I can help you cover your costs if you don't receive enough on spot donations to cover everything.  We are trying to get quorum so we can have an important group vote.  So, hopefully a lot of folks will come out.  Let me know your thoughts.
Thank you,
Maya helped me deliver the food.

Pasta with sauce: sauteed onions, garlic with "Shaan" vegetable curry mix, zucchini, a couple of hot banana peppers and then chopped tomatoes cooked for 3 minutes.

Sunday, June 24, 2012

Un relativista cuenta El Sur

Un relativista cuenta El Sur de Jorge Luis Borges

Pido perdon a los lectores que vienen del mundo de literatura o estudios culturales, no soy un relativista cultural de la tela de Franz Boas sino que estudié la relatividad general de Albert Einstein;.

Juan Dahlmann (c. 1905 -19:05 PM), o, La distorsión del tiempo y posible influencia de la Física Moderna en El Sur, de Jorge Luis Borges

Leen el texto antes de leer el ensayo.

La obra del escritor Jorge Luis Borges ha sido analizada de diversos puntos, entre ellos el matemático. Su cuento mágico-realista El Sur es un texto asignado muy frecuentemente a los estudiantes de la literatura en Español. Borges escribió el cuento antes del año 1944, para cuando la física moderna (la relatividad de Einstein y la mecánica cuántica de Schrödinger, Heisenberg, Bohr, Einstein, Dirac y otros) ya estaba en pleno aflorecimiento y se habían metido las ideas (sobre todo la de la relatividad del tiempo y la de la evolución probabilística) en las mentes de los artistas y del pueblo vulgar. (Claro, puede que Foucault lo vea como una violación de la causalidad.)

Ya que “uno de los elementos primordiales del realismo mágico es la distorsión del tiempo”, una cuestión muy examinada es “el método que emplea Borges para lograr esta distorsión” en El Sur.

Como científicos, antes de empezar a dar explicaciones y crear teorias para algun hecho, debemos convencernos que haya un fenomeno. Al leer el cuento, se siente y se ve la distorsión del tiempo. Luego, dada la existencia del fenomeno, lo tenemos que medir. En este ensayo me voy a enfocar en medir (y atraves de la medida, demostrar) la distorsión del tiempo, y examinar un poco las calidades de la distorsión.

Lo que vamos a ver es que hay cuatro etapas distintas en el texto. Cada etapa se distingue por el promedio (tomado sobre el largo de la etapa) de la medida del ritmo a que pasa el tiempo verdadero con respeto al tiempo que experimenta el lector. Al leer el texto (lo cual Ud.s deberian haber hecho antes de leer este análisis), se notan estas roturas, estas descolocaciones temporales. Al ver los datos, y mas claramente al ver los dibujos, los gráficos confirman y miden nuestros sentimientos al pasar de una etapa a la siguiente. Ademas, el flujo del tiempo tampoco es constante dentro de cada etapa. Esta es una distorsion especialmente fuertemente explotada por Borges y experimentada por el lector en las dos últimas etapas.


Vamos a seguir el siguiente camino: Primero, una definición generalmente aceptada de “tiempo”, segundo la búsqueda de una variable que cumple los requisitos de la definición, tercero medir y dibujar la evolución de la narativa como función de éste y solo después se puede buscar las distorsiones, es decir las nolinealidades, y empezar a analizarlas.

La fibra de tiempo debe ser una variedad unidimensional, continua (sin ni saltos ni cambios bruscos de rumbo o ritmo) y Hausdorff (sin bifurcaciones). La coordenada natural que se nos ocurre es el numero de lineas escritas, que es obviamente unidimensional y Hausdorff, y, en una version publicada sin notas narativas a pie de página, comentarios parentéticos, cambios de tamaño de tipo o ilustraciones en el medio del texto, es continuo. Eligimos la version publicada en Abriendo Puertas .

Con el número de lineas como la variable independiente medimos el transpiro del tiempo cronológico (el tiempo que experimenta Juan Dahlmann, o el tiempo propio del mundo verdadero que inhabita) dentro de la narativa. Para eso primero utilizamos las numerosas pistas que nos da Borges, como fechas, horas del día, horas o días entre acontecimientos, referencias al sol etc. Tambien tenemos que inferir el tiempo cronológico razonable basado en algunos acontecimientos, en esos hay mas incertidumbre. Hay, pero pocos, ciertos tiempos completamente inventados, los cuales aumentan la estética de nuestro análisis sin dar lugar a duda sobre sus conclusiones.

Para hacerlo independiente del formato del texto, se puede elegir el numero de orden de las palabras escritas en vez de el de las lineas, pero la coordenada palabras es demasiado finamente granificada para nuestros fines.

En la tabla que sigue, tenemos las medidas hechas:
En la primera columna, los acontecimientos descritos pos Borges.
En la segunda columna, el numero de orden de la linea en el texto, el tiempo de coordenada o tiempo fiducial, experimentado por el lector.
Luego, en tres columnas distintas, el año, el dia o la hora del acontecimiento, el tiempo experimentado por Dahlmann o el tiempo verdadero del mundo que ha creado Borges. Hay tres columnas porque los acontecimientos toman lugar a ritmo de años, dias, horas o minutos segun la etapa en que estamos.
En la siguiente columna tenemos el “lapso” calculado: el tiempo verdaderamente pasado dividido por el tiempo de coordenada del lector, es decir, el numero de lineas traspasado.
En la columna final, la etapa a que he asignado el acontecimiento.

Las etapas quedan obvias en la tabla si se fija en el lapso, y para ver las variaciones dentro de cada etapa vamos a dibujar el tiempo verdadero contra el número de linea, separando los dibujos según etapa.

Cómo entender los dibujos: Cada punto representa un momento cronológico en la narrativa del texto y el numero de la linea en que aparece. Una pendiente alta entre dos puntos indica que ha pasado mucho tiempo en pocas lineas. Por ejemplo: En la primera linea, el abuelo alemán desembarca en Buenos Aires en el año 1871, y tan solo 26 lineas despues, empiezan los acontecimientos del año 1939 y han pasado 68 años muy rapidamente para el lector.

En contraste, una pendiente baja entre dos puntos indica poco paso de tiempo, a lo mejor es un dialogo, el ritmo de escribir el cual es casi igual que el ritmo que lleva la conversacion. O tal vez es una seccion descriptiva como al principio de la cuarta etapa, entre que Dahlmann entra en la cantina y se seinta a cenar, traspasan probablemente cinco minutos pero Borges toma 24 lineas para describir el local, la reaccion de Dahlmann al proprietario de la cantina, y para describir los otros huespedes desde el punto de vista de Dahlmann.

Una pendiente negativa hubiera indicado una vuelta hacia el pasado, quizas una escena de memoria o un viaje en el tiempo. Hay pequeños momentos de recuerdos, pero son demasiado cortos para que nos molesteos en contarlos. Asi que la narrativa de El Sur sigue monotona en tiempo.

En el primer grafico, he dibujado el lapso, el ritmo del flujo del tiempo (bueno, el logaritmo de ello) contra el numero de linea en el texto. El lapso se puede entender como la derivada del tiempo cronologico con respeto al numero de linea. Aqui, se ven las cuatro etapas claramente. (Para decidir la frontera entre las etapas 3a y 4a, he usado acontecimientos significativos del texto.)


Primera etapa:

Aqui vemos por primera vez un truco que emplea Borges para distorsionar el tiempo dentro de cada etapa: despues del comienzo de la etapa, el tiempo verdadero fluye cada vez mas lentamente, mas que simplemente contar los hechos, Borges empieza a contar la historia.

Segunda Etapa “En Buenos Aires”:

El efecto de la distorsión en esta epoca es mas sutil. Primero, ocho días pasan en tan solo 6 lineas (#39-#45), relativamente rapidamente. Sin embargo, Borges dice que Dahlmann los sintio pasar muy lentamente: Ocho días pasaron, como ocho siglos.”. Extraña que en ocho siglos haya pasado tan poco. Se debe decir mejor que ocho días pasaron como ocho segundos: no pasó nada, y ocho segundos es del orden del tiempo que se tarda en leer 6 lineas. Luego, el tiempo que Dahlmann pasa en la cama en el sanatorio sí que pasa muy lentamente, Borges utiliza ocho lineas (47-55) para describir los pensamientos y sentimientos de Dahlmann y lo que le hacen en el sanatorio, es una pausa introspectiva y descriptiva. Al final, pasamos otra vez a una fase narativa donde los hechos y el tiempo pasan a cierto ritmo seguido.

Tercera (“El Viaje al Sur”) y Cuarta etapas:

Entre las primeras tres etapas hay dos transiciones, y los dos son descontinuos; el lapso, o visualmente la pendiente del gráfico, da un salto. (Eso indica, matemáticamente, que el tiempo coordenada es mala.) Sin embargo, entre la tercera y la cuarta etapa la transición es mucho mas suave, como se ve en el dibujo de arriba. Otra vez, al final de la etapa tercera, se baja la velocidad del cuento, analogo a la bajada de la velocidad del tren en que viajaba Dahlmann a la velocidad de su caminata hacia la cantina.

El patrón en las dos últimas etapas es el mismo. Hay tres fases, en la primera fase el tiempo pasa muy lentamente, hay mucho que describir o contar, o a lo mejor Borges relata un dialogo. En la segunda fase el tiempo pasa muy rapidamente, por ejemplo, en la tercera etapa, Dahlmann come, toma una siesta y se despierta ya con el tren casi en el destino. Es casi como si Borges tuviera impaciencia de llevarnos a la ultima fase, donde otra vez, muchas cosas pasan, y hacen falta muchas lineas para un periodo corto de tiempo.

(El análisis de las pistas que da Borges sobre la “verdadera” realidad, de lo que realmente pasaba a Dahlmann, lo dejé a los alumnos de Literatura Española 5 AP Honors de la Sra. Montague de Nichols Academy en Buffalo, NY. A cambio, les presenté este análisis.)

Cuarta etapa “La Cantina”:

El salto en tiempo en medio de esta etapa es entre el momento en que decide cenar y el momento en que acaba de cenar y empieza a absorber el local, y se pasan en muy pocas lineas. Depsues de esto, pasan muy lentamentes las cosas, a mi me dio la sensación de movimientos muy viscosos, como si tomaran lugar en miel. Los últimos segundos y muchas lineas, los pasamos en la cabeza de Dahlmann.

Borges utiliza muchos círculos: el taxi que aparece dos veces, el patron de la cantina que se parece al hombre del sanatorio, la clavada de la aguja. Es justo entonces, que la vida de Dahlmann acaba a las 19:05, que corresponde al probable año de su nacimiento, 1905, y tambien es el año en que Einstein publicó la Teoría Especial de la Relatividad.

Y por fin, lean “Pincher Martin” de William Golding.

A Mechanic Does The South

A mechanic does Borges' The South (Translated from my Spanish, so take your chances with the English.)

I apologize to readers who come by car, I'm a mechanic not of cars but of the quanta.

The influence of quantum mechanics in The South, by Jorge Luis Borges

Read the text before reading the essay.
The South in English

The work of writer Jorge Luis Borges has been analyzed from various points, including the mathematical. His magical-realist tale The South is a very frequently assigned text for students of literature in Spanish. Borges wrote the story before the year 1944, by the time modern physics (Einstein's relativity and quantum mechanics of Schrödinger, Heisenberg, Bohr, Einstein, Dirac and others) and was in full flower and its ideas (especially those of the relativity of time and probabilistic evolution) had come to form part of the minds of artists and common people. (Of course Foucault may view this as causality violation.)

What is it that comes to mind when you mention quantum mechanics? Emotionally, fascination and fear, and then thoughts about the Schrödinger cat in a box, the separation between the observer and the observed, the effect of interaction between them (an "experiment"), the probabilities and the uncertainty principle of Heisenberg. You see these themes in the text.

The cat in the cafe in the train station, "the magical animal." Its presence in the text serves to underline the unreality of the situation of Dahlmann, that he is no longer part of the world ("this contact was illusory") and as a subtle reminder of Schrödinger's cat.

A quantum system can be a combination of states that are distinguishable: for example the system of a radioactive atom can be in a mixed state of pure intact and pure decayed,
for example: | atom> = (0.87) | intact> + (0.71 + i 0.71) (0.5) | decayed>
with complex amplitudes whose magnitudes are the probabilities of finding the atom intact or decayed atom when we do an experiment. (In the above case when we make the experiment on an identical set of atoms on the average 75% will intact and 25% will have decayed.)
However, an animal, a macroscopic system, can only be alive or dead, we are disturbed about the state of cat as a complex combination of live and dead states, for example, what would our representation of the cat state as:
 | Cat> = (0.87) | alive> + (0.71 + i 0.71) (0.5) | dead> mean?
Normally we do not have to take issue with this since we can not put a cat in such a mixed state.

The trick is to couple the macroscopic state of the cat with the quantum state of a system. In the Schrödinger gedankenexperiment, we put a cat inside a closed box with a fissible atom and a radioactivity detector which opens a bottle of poison gas when it detects the splitting of the atom, which yields the coupling of corresponding states of the atom and the cat.
When we start the experiment the atom is in a pure state of not having fissioned. Based on the dynamics of the nucleus, it immediately begins to evolve into a mixed state of pure intact and pure decayed over time, and the amplitude of the decayed state increases to 1 with an exponential decay. The cat begins alive and in a live state. After a while, both the atom and the cat will be in states similar to those above.

Analogously, after being injected in the hospital, to us Dahlmann is a mixed state of living or dead / dreaming feverishly. Our doubts about Dahlmann's state evolve towards certainty of his death. But at an intermediate point, is he alive or dead?

The separation between observer and observed: Dahlmann feels "like they were separated by glass." If there are two beings, either can be the observer and the other the observed. The cat may be there to test the state of Dahlmann. As meta-observers, we do not know if the cat has felt the caresses of Dahlmann, and we continue with questions about the state of Dahlmann.

The effect of experiment: In classical mechanics, if we know the dynamics of a system, the observations after an experiment to measure, for example, the position and velocity of a thrown ball, allow us to know both the past and the future state of the system. In quantum mechanics, to the comtrary, unless we know the previous state the experiment only allows us to know the future state and generally only probabilistically predict the outcome of a future experiment. (Using Bayesian analysis on an ensemble one may deduce something of the previous state.) In contrast, in The South, in the hospital, "a masked man stuck him with a needle." We knew the prior state Dahlmann - wounded and sick. But for readers, the injection causes the start of the uncertainties, the bifurcation of the state between dead and alive. Furthermore, the dynamics of the story cause more and more separation between the two directions and more uncertainty.

Uncertainty: There is uncertainty about the state of Dahlmann until the end of the story, but I don't see that is shaped according to the Heisenberg principle.

Probabilities: We can argue, and the students did so very much, the chances of this dead or alive Dahlmann during the second part of the story. But what distinguishes quantum mechanics is not classical stochasticity and the probability distribution of the state - such as the classical mechanics we have in the statistics - rather the quantum state is a distribution of complex amplitudes, whose absolute value is the probability distribution, and interference between the amplitudes leads to the more dramatic effects of quantum mechanics (eg Young's experiment with ultra-low intensities of light).

I remind you also that Borges, like physicists, is very fond of symmetries. Borges and reality like slight anachronisms, and Borges anticipates that the issue of possible violation of causality in quantum mechanics: the Einstein-Podolsky-Rosen paradox and corresponding gedankenexperiment were described only in the 1950s.

Un Mecanico Cuenta Borges

Un mecánico cuenta El Sur de Jorge Luis Borges

Pido perdon a los lectores que vienen en coche, no soy un mecánico del coche sino del quantum.

La influencia de la Mecánica Cuántica en El Sur, de Jorge Luis Borges

Leen el texto antes de leer el ensayo.

La obra del escritor Jorge Luis Borges ha sido analizada de diversos puntos, entre ellos el matemático. Su cuento mágico-realista El Sur es un texto asignado muy frecuentemente a los estudiantes de la literatura en Español. Borges escribió el cuento antes del año 1944, para cuando la física moderna (la relatividad de Einstein y la mecánica cuántica de Schrödinger, Heisenberg, Bohr, Einstein, Dirac y otros) ya estaba en pleno aflorecimiento y se habían metido las ideas (sobre todo la de la relatividad del tiempo y la de la evolución probabilística) en las mentes de los artistas y del pueblo vulgar. (Claro, puede que Foucault lo vea como una violación de la causalidad.)

¿Que es lo que viene a la mente vulgar cuando se menciona la Mecánica Cuántica? Emocionalmente, fascinación y miedo, y luego los pensamientos sobre el gato de la caja de Schrödinger, la separación entre el observador y lo observado, el efecto de una interacción entre ambos (un “experimento”), las probabilidades y el principio de incertidumbre de Heisenberg. Se ven estos lemas en el texto.

El gato del café de la estación del tren, “el mágico animal”. Su presencia en el texto sirve para subrayar la irrealidad de la situación de Dahlmann, que el ya no forma parte del mundo (“aquel contacto era ilusorio”) y como un sutil recordatorio del gato de Schrödinger.

Un sistema cuántico puede estar en una combinación de estados que son distinguibles: por ejemplo el sistema de un átomo radioactivo puede estar en un estado mixto de puro intacto y puro fisionado, (pero no puro fumado)
por ejemplo: |átomo> = (0,87)|intacto> + (0,71 +i 0,71)(0,5)|fisionado>
con amplitudes complejas cuyas magnitudes son las probabilidades de encontrar el átomo o intacto o fisionado cuando hagamos una prueba. (En el caso de arriba cuando hagamos el experimento sobre un conjunto de átomos idénticos en el promedio saldrán 75% intactos y 25% ya fisionados.)
Sin embargo, un animal, un sistema macroscópico, solo puede estar o vivo o muerto, nos perturba hablar del estado de gato como una combinación compleja de estado vivo y estado muerto, por ejemplo, ¿que significaría nuestra representación del estado de gato como:
|gato> = (0.87)|vivo> + (0.71 +i 0.71)(0.5)|muerto> ?
Normalmente no nos tiene que dar dolor de cabeza este tema puesto que no podemos poner un gato en tal estado mixto.

El truco consiste en acoplar el estado macroscópico del gato con el estado cuántico de algun sistema. En el gedankenexperimento de Schrödinger, metemos un gato dentro de una caja cerrada con un átomo fisíl y un detector de radioactividad que abre una botellita de gas venenoso cuando detecta la fisión del átomo, lo cual consigue el acomplamiento de los estados correspondientes del átomo y del gato.
Cuando empezamos el experimento el átomo está en un estado puro de no haber fisionado. Por la dinámica del núcleo, inmediatamente empieza a evolucionar al estado mixto de puro intacto y puro fisionado y a lo largo del tiempo la amplitud de la parte fisionada aumenta con un decaimiento exponencial hacía uno. El gato empieza vivo y en un estado vivo. Después de un rato, tanto el átomo como el gato van a estar en estados parecidos a los de arriba.

Analógicamente, después de que le pinchan con la aguja en el sanatorio, en nuestra representación Dahlmann está en un estado mixto de vivo o muerto/soñando febrilmente. Su estado y nuestra certidumbre sobre ello evolucionan hacía su muerte segura. Pero en algún momento dado, está vivo o muerto?

r”, o la separación entre observado y observador: Dahlmann siente “que estaban como separados por un cristal”. Si hay dos seres conscientes, cualquier puede ser observador y el otro observado. El gato puede estar allí para probar el estado de Dahlmann. Como meta-observadores, nosotros no sabemos si el gato ha sentido las acaricias de Dahlmann, y seguimos con dudas sobre el estado de Dahlmann.

El experimento: En la mecánica clásica, si sabemos la dinámica de un sistema, las observaciones después de un experimento de medir, por ejemplo, la posición y velocidad de una pelota tirada, nos permiten saber tanto el pasado como el futuro estado del sistema. En la mecánica cuántica, a cambio, si no sabemos el estado anterior ya, el experimento solo nos permite saber su futuro estado y en general predecir solo probabilísticamente el resultado de un futuro experimento. (Usando analysis de Bayes sobre un conjunto de experimentos se puede saber algo del estado anterior.) Al contrario, en El Sur, en el sanatorio, “un hombre enmascarado le clavó una aguja”. Sabiamos el estado de Dahlmann anterior – herido y enfermo. Pero la clavada causa en los lectores el comienzo de las incertidumbres, la bifurcación de su estado entre muerto y vivo. Además, la dinámica del cuento causa cada vez mas separación entre los dos rumbos y mas incertidumbre.

La incertidumbre: Hay incertidumbre sobre el estado de Dahlmann hasta el fin del cuento, pero no veo que tenga la forma segun el principio de Heisenberg.

Las probabilidades: Podemos discutir, y los alumnos lo hicieron mucho, las probabilidades de que este muerto o vivo Dahlmann durante la segunda parte del cuento. Pero lo que distingue a la mecánica cuántica de la clásica no es la estocacidad y la distribución probabilística del estado – esas ya la tenemos en la mecánica clásica estadística – sino que que el estado es una distribución de amplitudes complejas, cuyo valor absoluto es la distribución de probabilidades, y la interferencia entre las amplitudes da lugar a los efectos mas espectaculares de la mecánica cuántica (por ejemplo el experimento de Young con intensidades ultra-bajas de luz).

-->Les recuerdo tambien que a Borges como a los físicos les gustan mucho las simétrias. A Borges como a la realidad, le gustan las leves anacronísmos, y en eso Borges anticipa la cuestión de la posible violación de causalidad por la Mecánica Cuántica: la paradoja de Einstein, Podolsky y Rosen y el corespondiente gedankenexperimento se describió solo en los 1950s.