Pearls ...

Renee' referred the Frog Leap Brainteaser to me, to which she was referred by her sister.



I didn't time myself; but it took me something like 15 minutes and 4 or 5 tries to solve it the first time. Then it took me about 4 more tries to catalog all the moves.

Now, I know it's not that interesting and I'm sure Chinese school children solve it way faster than I did. But what is interesting (to me) is the heuristic I arrived at and that (I think) helped me solve it the first time. The idea is that for every move you make, you need to increase or preserve the number of face to face pairings of the frogs. If you have a frog facing the back of another frog, except for the final state, you'll get stuck with no moves.

Anyway, there are 2 solutions, depending on which color frog you move first. Here's one of them. First number the frog's rocks from 1 to 7, left to right. Then make the following jumps:

1. 3 - 4
2. 5 - 3
3. 6 - 5
4. 4 - 6
5. 2 - 4
6. 1 - 2
7. 3 - 1
8. 5 - 3
9. 7 - 5
10. 6 - 7
11. 4 - 6
12. 2 - 4
13. 3 - 2
14. 5 - 3
15. 4 - 5

I got my Vibram 5 Fingers KSOs yesterday, courtesy of FootZone. I "ran" with them this morning. I put "ran" in quotes because I really don't run. I'm too fat and slow. I really jog, which plays into what I'm about to write.

First a little back story. When I was a kid, my dad used to bitch at me for "walking like a girl". I've always tended to walk on the balls of my feet. I think I learned to do it because we had a 2 story house and I didn't ever want my dad, downstairs, to know when I walked from room to room. So, I learned to walk on the balls of my feet. That's just conjecture, though. I really have no idea why I did it because I've always done it. If that makes me effeminate, so be it. However, Ireally don't think it does. It came as a great boon when I started martial arts training in middle school.

Similarly, I joined the band in middle school and played cornet. So, naturally, when I went to high school, I was in the band (for 1 year [grin]). It was a marching band. I don't know how many people realize this; but it's pretty damned hard to play the trumpet while marching. Mind you, this is military style, not the smoother "corps" style. So, if you march so that your feet land on your heels, your lips bang pretty hard against your horn, not only making you a sucky trumpet player (which I most definitely was); but putting you at the constant risk of a fat lip. So, I remember this very vividly. Our "first chair" trumpet player, who was also the most talented musician we had at the time, used to say "You have to walk like a fag." (Sorry, if that's offensive. I don't think it is; but what do I know? This was Houston, Texas in the early '80s.) He would constantly say that. Well, anyway, because I already "walked like a fag", as so thoroughly pointed out by my dad, it was pretty easy for me.

OK. One more story from high school. After they realized I sucked as a trumpet player, they wanted me to be the "drum major" because I marched very well. I quit the band and joined the cross country team. Here, my tendency to walk (and run) on the balls of my feet worked against me. My coach and the other people on the team would constantly tell me that my stride was too short and I should stick my legs out further in front of me. That never made much sense to me; but being new to the whole thing, I figured I just sucked at running, too, which I do, pretty much. So, I tried to increase my stride; but it never worked. Whenever I wanted to go fast, my stride shortened up so that I could land on the balls of my feet, sort of. This is very difficult when you're wearing shoes with humongous sponges glued to the heels. Everyone then bitched about me "plodding", i.e. making a loud thumping noise every time my feet landed because I was landing on the flat of the sole. But, again, I didn't know any different. After about 1.5 years running, I quit that, due mostly to a knee injury, and stuck with martial arts. I continued to run by myself; but without other yahoos telling me how to do it, I settled into my own pace.

So, a few weeks (months perhaps?) ago, a friend of mine tweeted about barefoot running and some data that showed that many of the very fast runners land mid-foot. It turns out that if you learn to run as an adult in the West, you tend to land mid-foot. If you learn to run as a child, guided by the shoes they convince you to wear, you land on your heel. And in places where they run barefoot, they land mid-foot, as well. (Side note, why are kids' feet "cute" and adult feet "ugly"? Hmmm.)

This friend pointed me to a web log entry about a guy who was re-learning to run in the Vibram 5 Fingers. Sorry I don't have the link anymore. I thought PERFECT! So, I bought some and today was my first run in them.

It went FANTASTIC! For the first 2 miles, I thought: "This is how the gods intended us to run". But then my calves started tightening up. Running down hill is a bit of a lesson. While on a flat surface or going up hill, I'm running naturally, with little effort. In fact, it seemed like I went much slower on this run. I only got out of breath once. But my actual speed was the same as it was Monday. So, while I felt like I was going slower, I wasn't. It was just plain easier ...

Except for the down hill parts. Having run in regular shoes my whole life, I suppose I land on my heel when running down hill. So, I had to make an extra effort this morning to land mid-foot when going down hill. That really put a strain on my calves. I foresee a few night time charlie horses in my immediate future.

A few other notes are in order. 1) You can feel the surface you're running on! I happen to live in Portland, where the sidewalks are kinda broken up from the trees. I don't run in the street, even though the asphalt is softer, because the roads slant for water run-off, which puts a damaging, constant, lean on you. Plus, the broken up sidewalk reminds me of running in the forest where you have to jump over things like roots and rocks and such, anyway. It's better for all those tiny control muscles. But it feels so decadent being able to feel every stick or mid-sized stone you step on. And having the water splash over your feet when you run through a puddle is fantastic!

2) Despite it being a bit chilly (45 deg F this morning), my feet didn't get cold even once. In my Asics, which have a mesh top, but otherwise complete coverage, my feet often get cold. I attribute this to the idea that the muscles in my feet are actually working in these shoes, unlike the others. Your toes are moving, gripping the pavement, wrapping themselves around every bump in the road. At several points, it felt like I was going to pull a muscle on the bottom of my foot as it flexed with every step. Anyway, for whatever reason, my feet weren't cold.

3) My right foot is much wider than my left, and my left is pretty damn wide. I have duck feet. I have to wear shoes that are about 1.5 US sizes too large in order to get shoes that are wide enough for my right foot. And even then, my right shoe always fails by poping open at the ball where the upper meets the sole. It's no different with these, except, since the uppers are very stretchy and there's a velcro strap that goes over the top, the mount for the velcro strap is rubbing seriously hard on the inside left of my right foot. That soft skin there will either have to toughen up, or I'll have to use band-aids or something to interfere.

So far, it's a great success! And I highly recommend these shoes. We'll see how I feel in a month or two, though.

I really like it when things seem to converge. For example, in December, 3 things converged together around light sensitivity: 1) We watched a rather silly sci-fi movie where people's pineal gland grew and poked out of their heads like a little tentacle, 2) we had a long discussion over Christmas about my S.O.'s and her sisters' inability to sleep if there's the slightest bit of light in the room, and 3) I learned that some animals have a well developed "third eye" that is related to their pineal gland. It's like the gods were telling me to learn a little more about melatonin and the pineal gland! As usual, I only did about 1/3 of my homework.

Anyway, it's happened again. Three tidbits my mind has assembled into a pattern. (Make no mistake, convergence like this is a figment of your imagination. It is NOT your God talking to you.)

Anyway, so I'm reading this "Evolution without Selection" book by Lima-de-Faria (LdF) and finally arrive at the following paragraphs:

Population control in mammals by chemical interaction

Several species of mammals regulate the size of their population. The fluctuations in number of progeny are controlled by means of chemical communication between the different individuals of the community.

The rabbit shows autocontrol of its fecundity. If the community is small the females produce as many as 30 animals per year, but if the population is large this number diminishes appreciably. The same behaviour pattern is displayed by the squirrel Sciurus carolinensis, the black rat Rattus rattus and the mouse Mus musculus (Reichholf 1984).

This autocontrol of the population occurs by the transmission of chemical information. Male rats are able to distinguish between the pheromones originating from the urine of females which are in oestrus or in dioestrus. In the mouse a pheromone is produced by the males which is received by the olfactory organs of the females. This influences the production of the pituitary gonadotropin in the females and results in a shortening of the oestrus cycle and leads to a synchronization of the oestrus and copulation periods (Carr and Caul 1962). The boar accumulates in its saliva the hormone androsterone. A chemical precursor is carried by the blood stream into the submaxillary gland where it is transformed into androsterone. The courtship and copulation are directed by the male saliva which is injected into the mouth of the female. If the female is in oestrus she becomes receptive and copulation takes place.

OK. So far so good. A bunch of biological gobbledy-gook that, if you think too much about it, starts to sound kinda gross. But combine that with my belief that 99.99% of the earth's problems are caused by over-population by humans, I hear a tiny resonant humm. I wonder how/if humans control their own population?

One conjecture might be war. LdF talks about war just a few paragraphs later, but with no explicit connection with autoregulation of the human population. He points out that war is a relatively modern invention (8,000 years relative to the million-year existence of our genus), roughly corresponding to the move to agrarian society.

The relation between the over-population of the earth and permanently squatting on a plot of land seems pretty clear to me. It's OK to permanently squat on a plot of land when there's plenty of land and very few humans. But as the population grows, it becomes easier to remove the squatter than to find an empty plot of land. Hence, WAR. ... Oh, and hence banks and foreclosure, too.

So, the first element in this convergence was running across the population autoregulation text in LdF's book. The second element was my commitment to the Global Population Speakout, which was scheduled for this month, February. (BTW, I've only done a little speaking out on twitter and 1 mailing list so far. So, this web log entry is my actual speak out attempt.)

The third is the following article: Cost of raising child breaks �200,000.

It suddenly hit me that money, the universal unit of measure for the transmission of goods, might well be our (human) population autocontrol pheromone! Granted, it's not a chemical. But, as biologists seem to think, a chemical is just a mediator for information and control. And money is the mediator, at least for western society, for information and control. (Yes, yes, I know that most people tend to think things like language, books, the internet, etc. are the media for information. But a few good long conversations with some CFOs and, perhaps, the few classical liberals left in the world, will convince you that it's money that makes the decisions in this world, not thought or votes.)

Perhaps money has become our pheromone for population autoregulation?

Here are a few provocative paragraphs from Chapter 26 of Lima-de-Faria's "Evolution without Selection":

The physico-chemical basis of ethics

"Not only is a physico-chemical concept of life compatible with ethics, but it seems to be the only approach to life that will allow us to understand the origins of ethical principles". This statement comes from Loeb (1912), who emphasized that most if not all of our instincts have such a basis.

He points out that we eat, drink and reproduce not because humanity has decided by general consensus that such behaviour is desirable to the species, but simply beause we are forced to do so by our construction. A woman loves and cares for her children not because of the fact that the psychologists think that such behaviour is desirable, but because she is obliged to do so due to the physico-chemical processes going on in her own body.

Our fight for justice and truth also has no other source.

The point Lima-de-Faria is raising is merely the old problem of determinism and free will, of course. But he's doing it in the context of "autoevolution". It's unfortunate that if you search for the phrases "autoevolution" and "autoevolutionism" on the internet, you get references to intelligent design. Let me be very clear about this:

Lima-de-Faria's concept of autoevolution is NOT intelligent design.

It is simply the concept that biological form and function is a natural, self-organizing, extension of mineral, chemical, and physical form and function. Plants and animals are constructed in precisely the same way that the elementary particles, chemicals, and minerals are constructed. In simple terms, a human grows and lives in the same way a crystal or a hunk of rock grows and lives.

Although this is difficult to swallow in these simple terms, he makes his case working backwards from he current neo-Darwinist concept of evolution to this point simply by considering evolution without selection. All the same concrete mechanisms of the modern theory of evolution are present in autoevolution. He just attempts to remove the abstract and problematic concept of selection. And in that context, although autoevolution won't be popular until we either falsify selectionism or identify concrete mechanisms for selection, it's a perfectly reasonable alterative to neo-Darwinism WITHOUT resorting to nonsense like intelligent design.

Indeed, I believe we have found some concrete mechanisms for some forms of selection; but I am largely ignorant of biology and can't build strong rhetoric for it. However, it does seem to me that Lima-de-Faria is, in this book, arguing from a dual position to that taken by the selectionists. I imagine the actual system working analogous to any complementary system, like a hand to a glove or Lagrangian to Eulerian perspectives. Autoevolution examines the system solely from the perspective of the construct. Selectionism examines the system solely from the perspective of the environment that surrounds the construct.

Hence, selectionists think in terms of constraints and degrees of freedom. Autoevolutionists think in terms of composition and construction (for lack of better terms).

In this sense, I think that Lima-de-Faria's conception of neo-Darwinism is outdated. I think there are some few concrete selection mechanisms (constraints) that are the precise duals of the self-organizing mechanisms that give rise to biological diversity. Again, I am too ignorant in biology to build the rhetoric to show that.

All this smacks to me of the age old question of determinism versus free will. It's almost like the selectionists are simply those of us who are agnostic enough to allow for free will, whereas the determinists are those of us who see life as a series of straightforward actions to be taken. In autoevolution, an organism takes the next best action where "best" depends on whether it needs food, has an chemical urge to mate, or whatever. There is no free will required, only a canalized most efficient next action. In selectionism, there is plenty of wiggle room surrounding any next action. At any point, there are sets of actions to be chosen from. The environment circumscribes the set of actions the organism can take. It then takes the action it WANTS to take, where "want" would be determined by some random (inexplicable and/or unpredictable) process.

Of course, both of these are over-simplifications because selectionists allow for selection at multiple scales and autoevolution would, presumably, posit composition at multiple scales.

Scientifically, what we really need is a particular concrete multi-scale situation that's determined at the lower scale and indeterminate at the higher scale. The trouble is that our best and smallest scale theory (quantum mechanics) also alows the dual. In some ways, it's deterministic and in other ways it simply circumscribes the wiggle room for the mysterious mechanisms underneath.

Anyway, as you can see if you're still reading, I'm just muddling through all this as best I can. There's no point, no moral to the story. Sorry.



Loeb, J. (1912) La Conception M�canique de La Vie. Librairie F�lix Alea, Paris.

Below are my notes as taken by me in the Android AK Notepad tool and shared with that tool. Note that this is exactly how they came out when I typed them, including the stupid "smart" capitalization.

Maude talk @galois, joe hendrix 2010.02.02
Kind & sorts, typechecking only on kinds
Only combine powerlists of same length
Cond membership needs powerlists


? Len(illformed powerlist)?
    -- len() won't be applied


Head(N List) -> head(3) -> head(3 nil) -> 3


Termination: maude is indeterminate but any term has a normal form


Maude termination tool (mtt) reduces it to unsorted spec preserving non-termination


Reasoning assumes theory is confluent
   Ie order of simplif preserves normal form
   Confluence checker (crc)


Parameterized theories (from OBL lang)
   Fth Loose semantic fmod
   Need param fmod
To use param theories, need view


Meta-level is reflection module


Inductive theorem prover (itp) for reasoning over the term algebra
   Uses reflection


Rewriting logic
    Ops not symmetric mod not fmod


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