Belief in torture's efficacy = Belief in witchcraft

This piece on Slate about the history of witch hysteria demonstrates to me the absolute absurdity of torture. Anyone who thinks that torture techniques such as waterboarding are effective tools of interrogation must also believe in witches. Why? Because throughout history (and into the present day) people have confessed to being witches under torture. Therefore, if you believe that torture works to "extract the truth" then all those people who confessed must really have been witches!

This demonstrates the insidious evil nature of torture. Not only can the torturer come to a false conclusion -- the one they want -- but even the tortured can come to hold the same false ideas. In other words, torture isn't merely morally reprehensible, but it doesn't even work!

Indeed, suppose you were "the Devil" and your goal was to explicitly foil legitimate interrogations because, as the devil, you had a sick desire to ensure chaos reigns throughout the world. As such, you couldn't come up with a "better" interrogation technique than torture. The questioner ends up reinforcing the ideas they started with and thereby ignores possibly valid alternative leads and the suspect may end up believing the planted ideas thereby reinforcing the incorrect assumptions of the torturer. If it weren't horrific, it would be the plot of a goofball comedy where two characters engage in a circular conversation convincing themselves of something absurd like up is down or love is hate. A "real" malevolent Devil would watch humans engaged in such cruel pointless floundering and be amused to no end. Will we stupid humans ever stop entertaining "the Devil" by engaging in this ghastly charade given the obvious pointlessness and immorality of it? Signs are not hopeful.

Shopping in the Science Supermarket

"Can you tell me where the mustard is?", I asked the nerdy looking storekeeper.

"It's next to the mayonnaise."

"Um okay....... But where is the mayonnaise?", I replied peevishly.

"Near both the ketchup and the soup."

"Again, this isn't really helping me. Maybe some sort of landmark independent of the foodstuffs themselves would be helpful?"

"Sorry."

"I mean, really? All you can give me is the location of everything in terms of other things! I want mustard and I'm standing next to radishes what am I suppose to do?!"

"Radishes are near the soup!"

"And?"

"Soups..." he directed me like I the slow child I was, "... are... near... the... mayonnaise."

And so I headed towards the soup. Turns out something called "onions" are also near the soup and the smell of these caught my attention: so pungent yet sweet. I peeled one back to see what was inside and what I found was... another onion! Onions are made of onions?! How can that be? So I tore open the onion and found onions all the way down.

That was 30 years ago. Someone just asked me where the mustard is. I don't know, I never did find it but, I told him. "the mayonnaise is near the bread."

Tree logic

The pecan in front of my house is slow. I think it might be, you know, one of the thicker trunks in the forest. The tree in the back yard tells me that it's time to blossom, flower, leaf out, spread its tree-semen with abandon. I say delicately to the front tree, "Look, I don't want to criticize, but, you know, the tree in the back..."

The front tree is having none of this; and, frankly, it resents being judged. "Look, just stop right there monkey," it says to me "I don't need to hear your thoughts on this. I was planted here 100 years ago. I didn't ask to be put here. I'm doing the best I can. I'm from Illinois, I know about snow. You ever had snow on your new leaves? No, you haven't because you're an ape. Trust me, you don't want to get caught out in that. I'm not going to get caught out in that."

"But in the 100 years you've been here has it ever snowed in April?" I queried cautiously.

"I got my ways. I've never been caught out in the snow."

"But it doesn't snow here in spring."

"And I've never been caught out in it."

"But if you don't get a move on, you're going to lose your chance to pollinate the other trees. I mean, don't you care about your legacy?"

"I'm not interested in having children that are so dumb as to leaf out too early and get caught in the snow. I don't want to breed with those premature blossomers, like your friend back there -- that's reckless risk taking. Rather not have children than have stupid children," the tree sulked.

"But it doesn't snow here in April." I repeated.

"And I've never been caught out in it."

Rugs!

The first of a few new rugs has arrived. Thanks to Amberlee for all the help in finding these. I especially like the runner in the entrance.

Molecular computers -- A historical perspective. Part 2

We left off last time discussing the precision of an analog signal.

Consider a rising analog signal that looks like the following ramp.


Notice that there's noise polluting this signal. Clearly, this analog signal is not as precise as it would be without noise. How do we quantify this precision? The answer was described in the early 20th century and is known as the Shannon-Hartly theorem. When the receiver decodes this analog variable what is heard is not just the intended signal but rather the intended signal plus the noise (S+N); this value can be compared to the level of pure noise (N). Therefore the ratio (S+N)/N describes how many discrete levels are available in the encoding.



The encoding on the left is very noisy and therefore only 4 discrete levels can be discerned without confusion; the one in the middle is less noisy and permits 8 levels; on the right, the low noise permits 16 levels. The number of discrete encodable levels is the precision of the signal and is conveniently measured in bits -- the number of binary digits it would take to encode this many discrete states. The number of binary digits need is given by the log base 2 of the number of states, so we have log2( (S+N)/N ) which is usually algebraically simplified to log2(1+S/N).

It is important to note that although Shannon and Hartley (working separately) developed this model in the context of electrical communication equipment, there is nothing in this formulation that speaks of electronics. The formula is a statement about information in the abstract -- independent of any particular implementation technology. The formula is just as useful for characterizing the information content represented by the concentration of a chemically-encoded biological signal as it is for the voltage driving an audio speaker or the precision of a gear-work device.

We're not quite done yet with this formulation. The log2(1+S/N) formula speaks of the maximum possible information content in a channel at any given moment. But signals in a channel change; channels with no variation are very dull!


(A signal with no variation is very dull. Adapted from Flickr user blinky5.)

To determine the capacity of a channel one must also consider the rate at which it can change state. If, for example, I used the 2 bit channel from above I could vary the signal at some speed as illustrated below.


(A 2-bit channel changing state 16 times in 1 second.)

This signal is thus sending 2 bits * 16 per second = 32 bits per second.

All channels -- be they transmembrane kinases, hydraulic actuators, or a telegraph wires -- have a limited ability to change state. This capacity is generically called its "bandwidth" but that term is a bit over simplified so let's look at it more carefully.

It is intuitive that real-world devices can not instantaneously change their state. Imagine, for example, inflating a balloon. Call the inflated balloon "state one". Deflate it and call this "state zero". Obviously there is a limited rate at which you can cycle the balloon from one state to the other. You can try to inflate the balloon extremely quickly by hitting it with a lot of air pressure but there's a limit -- at some point the pressure is so high that the balloon explodes during the inflation due to stress.


(A catastrophic failure of a pneumatic signalling device from over-powering it. From gdargaud.net)

Most systems are like the balloon example -- they respond well to slow changes and poorly to fast changes. Also like the balloon, most systems fail catastrophically when driven to the point where the energy flux is too high -- usually by melting.


(A device melted from overpowering it. Adapted from flickr user djuggler.)

Consider a simple experiment to measure the rate at which you can switch the state of a balloon. Connect the balloon to a bicycle pump and drive the pump with a spinning wheel. Turn the wheel slowly and write down the maximum volume the balloon obtains. Repeat this experiment for faster and faster rates of spinning the wheel. You'll get a graph as follows.


(Experimental apparatus to measure the cycling response of a pneumatic signal.)


(The results from the balloon experiment where we systematically increased the speed of cycling the inflation state.)

On the left side of the graph, the balloon responds fully to the cycling and thus has a a good signal (S). But, on the left side very few bits can be transmitted at these slow speeds so there's not a lot of information able to be sent despite the good response of the balloon. But, further to the right the balloon still has a good response and now we're sending bits much more rapidly so we're able to send a lot of infrmation at these speed. But, by the far right of the graph, when the cycling is extremely quick, the balloon response falls off and finally hits zero when it popped so that defines the frequency limit.

The total channel capacity of our balloon device is an integral along this experimentally sampled frequency axis where we multiply the number of cycles per second at that location by the log2( 1+S/N ) where S is now the measured response from our experiment which we'll call S(f) = "The signal at frequency f". We didn't bother to measure noise as a function of frequency in our thought experiment, but we'll imagine we can do that just as easily and we'll have a new graph N(f) = "The noise at frequency f". The total information capacity (C) of the channel is the integral of all these products across the frequency samples we took up to the bandwidth limit (B) where the balloon popped.



If you want to characterize the computational/communication aspects of any system you have to perform the equivilent of this balloon thought experiment. Electrical engineers all know this by heart as they've had it beaten into them since the beginning of their studies. But, unfortunately most biochemists, molecular biologists, and synthetic biologist have never even thought about it. Hopefully that will start to change. As we both learn more about biological pathways and we become more sophisticated engineers of those pathways we will have an unnecessarily shallow understanding until we come to universally appreciate the importance of these characteristics.

Next, amplifiers and digital devices. To be continued...

Molecular computers -- A historical perspective. Part 1

I've been having discussions lately with Andy regarding biological/molecular computers and these discussions have frequently turned to the history of analog and digital computers as a reference -- a history not well-known by biologists and chemists. I find writing blog entries to be a convenient way to develop bite-sized pieces of big ideas and therefore what follows is the first (of many?) entries on this topic.


In order to understand molecular computers -- be they biological or engineered -- it is valuable to understand the history of human-built computers. We begin with analog computers -- devices that are in many ways directly analogous to most biological processes.

Analog computers are ancient. The first surviving example is the astonishing Antikythera Mechanism (watch this excellent Nature video about it). Probably built by the descendants of Archimedes' school, this device is a marvel of engineering that computed astronomical values such as the phase of the moon. The device predated equivilent devices by at least a thousand years -- thus furthering Archimedies' already incredible reputation. Mechanical analog computers all work by the now familiar idea of inter-meshed gear-work -- input dials are turned and the whiring gears compute the output function by mechanical transformation.


(The Antikythera Mechanism via WikiCommons.)

Mechanical analog computers are particularly fiddly to "program", especially to "re-program". Each program -- as we would call it now -- is hard-coded into the mechanism, indeed it is the mechanism. Attempting to rearrange the gear-work to represent a new function requires retooling each gear not only to change their relative sizes but also because the wheels will tend to collide with one another if not arranged just so.

Despite these problems, mechanical analog computers advanced significantly over the centuries and by the 1930s sophisticated devices were in use. For example, shown below is the Cambridge Differential Analyzer that had eight integrators and appears to be easily programmable by nerds with appropriately bad hair and inappropriately clean desks. (See this page for more diff. analyzers including modern reconstructions).


(The Cambridge differential analyzer. Image from University of Cambridge via WikiCommons).

There's nothing special about using mechanical devices as a means of analog computation; other sorts of energy transfer are equally well suited to building such computers. For example, in 1949 MONIAC was a hydraulic analog computer that simulated an economy by moving water from container to container via carefully calibrated valves.


(MONIAC. Image by Paul Downey via WikiCommons)


By the 1930's electrical amplifiers were being used for such analog computations. An example is the 1933 Mallock machine that solved simultaneous linear equations.


(Image by University of Cambridge via WikiCommons)

Electronics have several advantages over mechanical implementation: speed, precision, and ease of arrangement. For example, unlike gear-work electrical computers can have easily re-configurable functional components. Because the interconnecting wires have small capacitance and resistance compared to the functional parts, the operational components can be conveniently rewired without having to redesign the physical aspects of mechanism, i.e. unlike gear-work wires can easily avoid collision.

Analog computers are defined by the fact that the variables are encoded by the position or energy level of something -- be it the rotation of a gear, the amount of water in a reservoir, or the charge across a capacitor. Such simple analog encoding is very intuitive: more of the "stuff" (rotation, water, charge, etc) encodes more of represented variable. For all its simplicity however, such analog encoding has serious limitations: range, precision, and serial amplification.

All real analog devices have limited range. For example, a water-encoded variable will overflow when the volume of its container is exceeded.



(An overflowing water-encoded analog variable. Image from Flickr user jordandouglas.)

In order to expand the range of variables encoded by such means all of the containers -- be they cups, gears, or electrical capacitors -- must be enlarged. Building every variable for the worst-case scenario has obvious cost and size implications. Furthermore, such simple-minded containers only encode positive numbers. To encode negative values requires a sign flag or a second complementary container; either way, encoding negative numbers significantly reduces the elegance of the such methods.

Analog variables also suffer from hard-to-control precision problems. It might seem that an analog encoding is nearly perfect -- for example, the water level in a container varies with exquisite precision, right? While it is true that the molecular resolution of the water in the cup is incredibly precise, an encoding is only as good as the decoding. For example, a water-encoded variable might use a small pipe to feed the next computational stage and as the last drop leaves the source resivoir, a meniscus will form due to water's surface tension and therefore the quantity of water passed to the next stage will differ from what was stored in the prior stage. This is but one example of many such real-world complications. For instance, electrical devices, suffer from thermal effects that limit precision due to added noise. Indeed, the faster one runs an electrical analog computer the more heat is generated and the more noise pollutes the variables.


(The meniscus of water in a container -- one example of the complications that limit the precision of real-world analog devices. Image via WikiCommons).

Owing to such effects, the precision of all analog devices is usually much less than one might intuit. The theoretical limit of the precision is given by Shannon's formula. Precision (the amount of information encoded by the variable, measured in bits) is log2( 1+S/N ). It is worth understanding this formula in detail as it applies to any sort of information storage and is therefore just as relevant to a molecular biologist studying a kinase as it is to an electrical engineering studying a telephone.

.... to be continued.

Utility yard fence

In the last few days I've finished up the fence line that separates the backyard from the utility yard. This involved staining more boards with Pinofin which is as malodorous as it is beautiful. Thanks to Jules for the help with staining! Fortunately she is hard-of-smelling so didn't notice how bad it was!