Geometry of Biological Time, Chapt 2.

Co-tidal map from NASA via Wikicommons. The points of intersection are the "phase singularities" where the tidal phase is undefined.

Slowly making my way through this book. Chapter 2 is about phase singularities -- places where the phase of some oscillation is undefined. The coolest example is the earth's tides. The surface of the earth is a sphere ("S2" in topology speak) and the tides are defined by a phase (S1). So for each point on earth at any given moment there's a tidal phase. But S2->S1 mappings (with certain continuity assumptions) must contain phase singularities -- there must be places where you can't define the phase. Above is a map from NASA showing these places as the intersections of the co-tidal lines. You can think of the tides as sloshing around those points where the sea level doesn't change.

The chapter is mostly about biological versions of such phase singularities. Detailed examples are given from fruit fly circadian rhythms, but the technical details of the experiments were overwhelming so I didn't fully follow and decided, perhaps unwisely, to plod forward without complete understanding.

BSTQ - Bull Shit Tolerability Quotient

There are many traits that determine someone's performance in various social settings such as school, work, military, etc. A popular metric for correlation to "success" in such social system is the "Intelligence Quotient" which purports to measure elements of abstract intelligence. Another metric that has gained popularity is the "Emotional Intelligence Quotient" which purports to measure the ability to perceive and mange emotions in oneself and others. Both of these metrics claim a high correlation to success in aforementioned social institutions.

I submit that success in roles within said social systems -- student, factory worker, warrior, etc. -- requires a high tolerance of activities such as: implementing poorly articulated tasks, engaging in inane conversations, attending pointless engagements, and other time-wasting activities known informally as "Bull Shit" (BS). The ability to tolerate such BS is a very important trait that is not normally rigorously evaluated.

I propose a simple test to measure an individual's tolerance for BS: a list of increasingly inane questions and pointless tasks is given to the test taker. For example, the test might begin with questions like: "Fill in the blank: Apples are __ed" and end with stupendously pointless tasks such as "Sort these numbers from least to greatest" followed by several hundred ~20 digit numbers and then having the next task say: "Now randomize those same numbers". The Bull Shit Tolerability Quotient (BSTQ) would just ignore the given answers and simply count the number of questions that test taker was willing to consider before handing the test back in frustration and declaring: "This Bull Shit!"

If a formal BSTQ test is not available, most standardized academic tests can be used as a reasonable substitute. However, the dynamic range of such generic academic tests to measure BSTQ is low. In other words, only extreme low-scorers of a proper BSTQ test will be measurable via the number of unanswered questions on a standard academic test used as a BSTQ surrogate. Extreme caution must be used when interpreting an academic test as a BSTQ analog -- the test giver may misinterpret the number of unanswered questions as the result of the test taker's low knowledge of the test's subject matter instead of as a spectacularly low BSTQ score.

BSTQ tests can easily be made age independent. For pre-verbal children the test would involve increasingly inane tasks such as matching sets of colored blocks to colored holes and so forth. The test would simply measure how many of these tasks the pre-verbal child could engage in before he or she became irritated or upset with the examiner.

Like the IQ and EIQ I suspect that the BSTQ will be correlated to the degree of success within many social endeavors, in particular: school; however, I also suspect that there is a substantial fraction of the population that has an inverse correlation between their IQ and their BSTQ scores. Of these, of particular interest are those with high IQ with low BSTQ. I would not be surprised if the population of people rated by their co-workers as "indispensable" is significantly enriched for individuals with a high IQ / low BSTQ score. Finally, I submit that these individuals are severely under-served by the educational system which demands -- indeed glorifies -- extremely high BSTQ, especially among those with high IQ.

Adding a BSTQ evaluation to pre-academic children might suggest that the student would excel in a non-traditional educational environment where the student is allowed to select their own agendas and tasks. A very low BSTQ coupled with a very high IQ would seem to almost guarantee rebellion if a traditional educational approach is applied. Identifying individuals with exceptionally high IQ scores and exceptionally low BSTQ scores may be a valuable tool to prevent the mis-classification of such students as "trouble makers" and instead correctly classify them as "potential indispensable iconoclasts".


(This idea evolved from lunch discussion with Marvin today, so thanks Marvin!)

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...