A Recurring Dream

I have a few different recurring dreams, the dreams are not exactly the same each time but simply share their essential character. Last night I dreamed (re-dreamed?) one of these dreams and before I forget it again for years or months I am going to write it down. In the dream I am an elevator operator, that may not seem remarkable but in the dream the vast majority of mankind lives in the rotting remains of huge ancient sky scrapers. These would have been buildings with bases as large as entire large cities and tens of thousands of floors. But especially as you go closer to the surface the more decayed and empty are the buildings, just huge metal supports miles tall and hundreds of feet thick.
I was born in the mid levels and was lucky enough to live in a region isolated from the general barbarism enough to have retained some semblance of civil society and engineering knowledge (isolated by way of broken connecting elevator shafts and collapsed bits of building). Those living in these mid levels have access to enough sunlight breaking through the upper levels and sides of the buildings that they can grow crops of a sort. From these mid levels you can see to the shadowy lower levels and even just adjacent levels where perfectly good sun exposed floor goes un-cultivated and warring bands fight each other over what food is available (don't ask me how they have had enough food to survive for hundreds of years, I've no idea). The people in the upper floors can be seen to have very advanced technology and lavish lifestyles, they will send troops out to stop people from destroying necessary support structures etc.
I discover an ancient disused elevator on an elevator track/shaft which is still connected to floors above. I manage to repair the elevator and am thus in this world elevated to something akin to a starship captain, I am an elevator operator! I zoom up through hundreds of floors to the nearest section, the ascent is really actually sort of nightmarish, think something akin to first person pinball, the elevator "shafts" are not really shafts in the normal sense but instead can go horizontal and vertical at a whim and thanks to your regular dream logic they like to do terrifying loopty loops. The shafts are really just 4 rails with no support of their own (funny that). To travel them you connect to them with non-sensical electric arcs which allow you to both be levitating while also being chained to the elevator rails. The dream then mostly consists of zooming around on these rails in terrifying first person, never knowing when a break in the elevator line might show up and throw me off into space, but the rails become more complete as you ascend but then there are routinely security measures which one has to avoid, outrun etc etc. I wish I could communicate more easily what the dream looks like because it is really a very visual dream and I love the images.
november is coming up, perhaps I could write a novel about a rugged elevator operator...

I've worn this necklace for a decade continuously

This necklace was given to me by my sister Jenelle and her husband Andy when they came back from a dancing trip to new zealand. Originally it was carved into a stylized fish hook as a symbol of protection especially while traveling over water. The day the necklace was given to me I put it on and I just left it on. Approximately 1 decade later on Monday of this week I took it off for the first time since. Understandably no necklaces are allowed to be worn while getting a chest x-ray. (The pneumonia is getting better thank you for asking)

Mind reading SQUIDs

I have long been a fan of electroencephalogram's (EEG) a.k.a. brainwaves. An EEG monitors cranial voltage fluctuations through the skin. These voltage fluctuations are caused at least partially by the activity of neurons in the cerebral cortex (the wrinkled outer layer of the brain). Despite the mind reading power of "brain waves" in countless sci-fi incarnations there is really very little information there to be gleaned. If I may make a comparison I would say that looking at brain waves is more or less equivalent to watching the clock rate of a computer. Our brains are massively parallel computing devices and different regions of our brain ramp up their activity for different tasks. Brain waves somehow correspond to large scale activity of the cortex and while this information can certainly be valuable it ultimately carries far too little information trying to read minds using brain waves would be like trying to index the content of the internet using only character frequencies.

That is not to say that brain waves can't be used to garner some interesting information and do interesting tasks. Brainwaves can be used to determine level of focus and people can be trained to control their brainwaves to a certain extent. This has been used for some interesting devices (the emotiv device is probably the closest to having any sort of real usefulness. here is a nifty if a bit long video which includes a demonstration of the device done with none other than AI legend Marvin Minsky)

But ultimately such devices are far too limited in their information collecting ability to carry out tasks of real utility like say typing at a reasonable rate with low error. The first most obvious way to get better information is to have direct brain implants but although this might turn out to be the best way to go many decades from now since such an interface has the bonus that we can send information in as well as extract information. Such direct neural interfaces are being developed now for control of artificial prostheses complete with tactile feedback thanks to DARPA. But, even after we solve all the problems of direct neural interfaces (like decreasing sensitivity due to the slow build up of scar tissue) not everyone will want to have brain surgery so that they can check facebook by thinking.

The most elegant to get at the information locked up in our skulls depends on the use of SQUIDs. A SQUID is a Superconducting Quantum Interference Device and it enables unimaginably sensitive measurements of magnetic fields. Squids have already been used to measure magnetic fields caused by neuronal activity. In order to even detect such fields one needs femto tesla range sensitivity. It is wonderful that SQUIDs can deliver this sort of sensitivity but highly unfortunate that SQUIDs currently require cryogenic temperatures and low fields in order to operate. Let us imagine for a moment however a world in which room temperature super conductivity had been discovered and furthermore this room temperature superconducting material can be printed on silicon in the manner of current integrated circuits. In short what if one could print SQUIDs on silicon just like we can make CCD detectors for cameras. Thousands or millions of magnetic field detectors each powerful enough to detect the firing of single neurons all wrapped around our brains picking up the signal sent out from each individual neuron firing.

Admittedly such a technology is at the very least 20 years distant to be naively optimistic or the technology may even be fundamentally impossible since there is no evidence to support that room temperature superconductivity is achievable. But here at least is a scientifically plausible route to totally non-invasive and incredibly powerful brain monitoring device. This is my prediction for the "killer app" of a high temperature super conductor if one is ever found.

Today I am a man

Today for the first time in my life I am a man... at least according to the social security administration. Apparently ever since I have had a social security number it has been attached to the gender code "F". It was never the slightest problem until a few days ago when new laws went into effect that made the people in human resources at the University have to make sure that everybody's information matches with the SSA info. Today I went to the SSA and had my information changed to reflect what my birth certificate and anatomy seem to suggest. Before the day is out I wanted to make a little remembrance of the day I became a man.

Bizarre things that have cut me.

I was preparing dinner just now and somehow managed to cut myself. But I didn't cut myself with a knife as you might have imagined I would. I cut myself on the dried salsa on the salsa bottle as I opened it. Now I can add that to the list of bizarre things that have cut me.

1. buttered toast


2. a mattress (note not the mattress springs but the material itself)


3. dried salsa

It should be noted that I require at least a little bit of blood to be drawn in order to count it a cut, if no blood is drawn then it is considered a scratch. In the case of the mattress whether or not it was a cut is moot since it was really an abrasion, a particularly nasty "rug burn" if you will. But it goes on the list anyway since it bled.

bizzarre but fun

admittedly I spent way too much time playing this game. The preponderance of "media monsters" named QQQ with perfect stats makes me think that perhaps that particular name is some sort of cheat to get balanced stats.

Pollard Strassen Polynomial Evaluation Method of Factoring, and a Variation

I admit I was reading Prime Numbers by Pomerance again and I have taken a fancy to one of the factorization methods described in the book. The book only gives a single paragraph on the method and I thought it would be fun to talk about it here. The idea is essentially this, to factor a number n pick chop the numbers less than n up into equal sized blocks and multiply all the numbers in these blocks together mod n and then take the greatest common divisor of the product of these blocks of numbers with n. Once we hit a block of numbers which has a gcd > 1 then if the gcd < n then we have a proper factor of n or if not then we can just search through the numbers in that block one at a time, checking to find the first number with a gcd with n greater than 1, and wallah!

Since we are guaranteed at least one factor in the numbers less than n^1/2 we only need to worry about breaking up the numbers less than that up into blocks. Rather intuitively the best division of work would be to make the blocks all sized equally and so you naturally come to the decision to make the blocks of size B = n^1/4. In order to make the calculation of the products of these numbers as quick as possible we take the time to construct the polynomial p(x) = x * (x-1) * (x-2) * (x-3) * ... * (x - B + 1) and reduce its terms mod n. Once we have that polynomial we just have to check gcd(p(B*i), n) to see if there is a factor of n in the block of numbers [B*i, B(i-1)] until we find an i that it works for.

I rather like the algorithm it isn't quite as cool as the rho method of factorization but it is surprisingly elegant and effective and has the additional advantage that it is clearly guaranteed to work. Just for fun I want to propose an idea that is almost certain to be worthless as an effective means of factorization but nonetheless appeals to my sense of aesthetics.

These polynomials which we are using to quickly evaluate the product of chunks of numbers are using the fact that factorials are nice smooth numbers with a lot of factors. In Pomerance's book he motivates the polynomial evaluation method by talking about how if one could evaluate factorials easily then factorization could be achieved by a simple binary search since gcd(k!, n) > 1 if k is greater than the smallest prime factor of n and equal to 1 otherwise.

Being a physicist I rarely have to care about the exact integer value of a factorial and instead am perfectly alright with using Stirlings approximation to the factorial as though it were exact since for any numbers for which it would be arduous to calculate the factorial exactly the error in its approximation is the most minuscule fraction, far below the error that one could hope to measure in a physical experiment.

But of course if we are interested in the factorization of n! then if we are off by even 1 the factorization will be completely different. Clearly trying to directly apply the binary search idea utilizing Stirling series is useless. The fractional error may drop dramatically with size but the absolute error still grows exponentially. So trying to keep enough terms in the approximation to get within 1 of the value of the actual exponential is a losing game. We could simply try all the numbers "close" to the estimated number but besides the fact that we might have to try an uncomfortably large number of candidate numbers in order to be certain of having tried the actual factorial there is a more serious problem. If we were trying to factor a 10 digit number the size of the factorials involved would be millions of digits long which is just a tad bit of overkill for factoring a 10 digit number. So if we want to keep the operations manageable we should really properly evaluate the factorial mod n. But because the factorials are so much larger than n even a tiny difference percentage wise in the value of the factorial would correspond to many times n and so give answers which are well mixed on n.

From all of these considerations it would appear that we would be much much better off simply doing trial division or for that matter actually using the Pollard Strassen polynomial evaluation method to factor our number. But still one might potentially be able to use Stirlings approximation or something like it (perhaps an appropriate adaptation to keep coherence mod n) might work out in the end.... perhaps even make for an actually useful factorization algorithm... I doubt it though. Still it is fun to think about and I would consider it something of a triumph to design a factorization algorithm that used the stirling approximation that just wasn't worse than the sieve of Eratosthenes.

Listening to bubbles to find dark matter

The departmental colloquium this last week was given by Peter Cooper who is part of the COUPP search for dark matter. Just like all the other dark matter searches the idea is to make your detector have as much material in it as possible and try to shield it as much as possible from any known interactions, cosmic rays, background radiation, etc. What you don't shield away you want to be able to discriminate anything we know about and then what you are left with must be dark matter.

In the case of the COUPP experiment they are using bubble chambers deep underground with several tons of scintilator oil on top. A bubble chamber works by keeping the fluid inside it at a temperature which is just above its boiling point. But because a bubble of gas takes more space than the liquid it takes a little bit of extra energy to make a bubble form. When a cosmic ray or other particle comes through the liquid it deposits energy and this extra little kick can make bubbles form in the liquid.

Usually in a bubble chamber you would be interested in the track that a particle leaves in the detector. But anything that leaves a track of bubbles interacts way too strongly to be dark matter. So the question is how do you discriminate between dark matter single bubble events and more boring single bubble events? The answer is you listen to the noise the bubbles make when they are made! alpha events in the chamber caused by trace amounts of radioactive materials in the device will show up as louder bubbles!

I can't help but think of a picture of a physicist carefully listening to the vibrations of tiny bubble floating deep in the dark and hoping to hear snatches of unknown harmonies of nature.

I got the most AMAZING seats to see Hamlet. (and for $5!)

Thursday last week I went to see Hamlet at the pioneer memorial theater. The performance was quite good and I think so was the editing of the play. I have long been quite the fan of the play Hamlet. I have read the play more than once and gave serious effort to memorizing it at one point (I actually managed to memorize the first scene in the first act before I gave up). Until a week ago I had only seen it performed via recordings. But Last Thursday I got to see it live and much to my good fortune not only did I get to see it live but I got to see it from an EXCELLENT seat. Jenna went to the theater ahead of me and purchased the tickets a little less than 30 minutes before the show started and then when I arrived she nonchalantly led me to the best seats in the house. Two seats on the very front row and at the dead center of the very front row! The theater has a program where U students can buy tickets to get the best seats still available 30 minutes before the performance for $5 a seat. Apparently the people with the season tickets who normally would have occupied that space had canceled. For any play this would have made me happy but that this happened for HAMLET!! it is just so amazing. The last time Hamlet was performed at the PMT was in the 80's and no doubt will not be performed again for a decade or two more. To give a perspective on how difficult such seats are to obtain a conversation with our neighbors revealed that they had season tickets and had been sitting in the same seats for 30 years! Furthermore the people who normally sat in the seats we were occupying had also been sitting there for many years (though how many years exactly I alas did not ask).

Is Hinchliffes Rule True?

This paper actually got published in 1995 and Title, Author Name, and Abstract make up the entire paper. I must say I thoroughly approve.