Epistemologists Don’t Surf

Silver Surfer and The Enemy WithinThe day conference in Pasadena passed symmetrically, and at dusk I cruised west on the 10 to Santa Monica. I hit Magdelene’s for the only real Mexican food in West L.A, then turned north on PCH.

There was a shabby bar with jukebox I knew, right on the beach, where I could ponder the floating silver coins of moonlight on ocean, and think of that one girl so far away.

If you spend time in surfer hangouts, eventually you’ll find yourself in some kind of confrontation.

The argument started over best Baja breaks. Pounding the bar, I tried to put words to the catch in my heart I felt in every moment at Todos Santos. My buddy droned on about some mush beach I’d never heard of, where he’d “shredded” five or six waves in one storm back in December. He’d met a Reef model there. And oh yeah, the fish tacos were “killer”.

It was all downhill from there. We started arguing about “proof” and the “scientific method” and other gibberish, on and on, inevitably, to number theory.

The bar got perceptibly quieter.

I offered up Euclid’s proof of the infinity of primes -

Pick a prime, any prime greater than 2. Call it the largest possible prime. Multiply together all the primes less than or equal to that largest prime, and add 1 to the product. Now, this new number can’t be factored by the largest possible prime or any lesser primes (because we added 1 to the product). So it is either a larger prime itself, or it has a prime factor larger than what we started out calling the largest possible prime. No matter what prime number you pick, we find one larger.

It was nothing but white-noise-surf-hiss to my friend. I fetched the laptop from the truck and saw the low clouds drifting before the moon. When I walked back in, the jukebox was playing Toulouse Street, and bang….there was that catch in my heart once more.

I asked him to pick a prime, any prime. Madre de Dios, the only one he could think of was 19. Mas cerveza, por favor.

:load Primes.hs
:load Factoring.hs

*Factoring> let primes = find_p [ 2.. ] where find_p (p:x) = p : find_p [ n | n <- x, n `mod` p > 0 ]
*Factoring> let p = take 100 primes
*Factoring> [n | n<-p, n<100]
[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97] *Factoring> foldr (*) 1 [n | n<-p, n<20] + 1 9699691 *Factoring> isPrime 9699691 False *Factoring> factors 9699691 [347,27953] *Factoring>

“So our new number is 9699691,” I said. “It ain’t a prime, and when we factor it, we get two numbers, 347 and 27953 – both larger than 19.”

The barkeep served. My friend sieved. In a minute he came up with another prime: 97.

*Factoring> foldr (*) 1 [n | n<-p, n<98] + 1
*Factoring> isPrime 2305567963945518424753102147331756071
*Factoring> factors 2305567963945518424753102147331756071

Before we could begin exploring the nether-regions of factoring efficiency he grew sullen, but bought me another Corona.

I left him there at 2:00 AM. He was humming “Flight of the Valkyries” under his breath, and muttering phrases like “Epistemologists don’t surf.”

I drove north into the night, hoping for a new day of green rooms.

Journeys of the Spirit

Blue mountains on a far horizon

Some will sleep, but all shall be changed.

One of my 23 great-great-grandfathers was Samuel Mulliner: immigrant from Edinborough in the early 1800s, polygamous husband of at least five wives, pioneer into some of the wilds of Southern Utah, and participant in an early experiment in social equality called “The United Order”.

He helped lead an emigrant wagon train which started out from Council Bluffs, Iowa in June, 1850, and arrived in Salt Lake City, Utah, on September 26. He wrote on the journey -

The company was organized on the 12th of June by Elder Orson Hyde on the camping ground 2 miles from the ferry above Bethlehem….On the 17th, our whole company camped on a creek about 3 miles West from the ferry where the officers met and passed the following resolution for the intended benefit of the company while journeying to the valley of the Salt Lake:

  • Resolved that the company will arise in the morning when the horn shall blow at 4 o’clock and after the necessary preparation for starting the horn shall blow for prayers, also the horn shall blow for prayer every evening at 1/2 past 8.
  • Resolved that if any of the company who is in the habit of profane swearing and after being reproved by their captain shall still persist they shall be published from the stand.
  • No cattle shall be taken out of the carrel till after prayer in the morning.

20 June. We traveled 10 miles, had 2 delays in crossing creeks, met a number of gold diggers returning home, saw 2 graves of our people, several cases of cholera in camp tonight, the case of Alfred Brown serious, one wagon tongue broke and replaced.

22 June. More of Brother Spafford’s children dead, making 3 in one day in the 2nd division.

24 June. Still wet – our 2nd division near us. Several more deaths in 2nd division. Captain Foote called a meeting for prayer of the whole company, also a council of all the captains. There was a good spirit manifested by all the captains…

28 June. A severe storm of rain and thunder in the night…not much water for cattle. A part of our camp not able to come to the camping ground tonight – the 3rd and 5th ten absent. The absentees came up late and for the first time we saw the power of death in our camp. One boy had fallen in a few hours and this morning.

7 July. This morning we had to bury Mrs. Hart. This being Sabbath we would fain have rested, but we had no wood nor water…Three new cases of cholera this morning…

9 July. We are camping on Plumb Creek for the purpose of washing, etc. Captain Maughan’s ten of their division fell behind some days but have come up and camped by us tonight. This captain was very dissatisfied at their slow movement, as he called it of our our camp, but some of his cattle have given out, and he couldn’t keep up. So much for go ahead folks.

11 July. We had a severe storm of rain and wind last night but the Lord preserved us all from danger. Camp in good health. One violent attack of cholera this morning, but means promptly used with the blessing of God it was an instant cure. The medicine used was 2 doses of pain killer in 15 minutes…This day we passed 25 graves….

14 July. In the afternoon when our folks had got along with their cleaning up we went to the river and I baptized and rebaptized some 30 or 40 of our camp. In the evening we had a good meeting, several of our brethren spoke well, a good spirit prevailed and we parted rejoicing.

18 July. Our camp in good health, – feed very scanty. We have passed a great many graves in the last few days mostly buried from the 5th to the 15th of June and mostly from Missouri and scarcely a grave but has been robbed of its contents by the wolves.

1 August. We traveled 12 miles today – had to stop, for an axel tree broke. A number of the Sioux Indians about us – they appear quiet. Smallpox is among them, we hope the Lord will preserve us from that plague.

7 August. We started this morning from 1/2 mile east of the Bend in the road Dead Dry Timber Creek and as the first ten reached near the deep ravine a stampede took place in the 5th ten as they were coming into line on the road. The teams that were running were providentially stopped or who can tell the awful scene that would have taken place in that deep ravine for every wagon would have been found at the bottom of it. Poor Brother Clements lost his life in endeavoring to stop the wagons. William McDonald at the risk of his life, and his horses rode in before the teams and stopped them before they got far enought to scare the front teams. Brother Clements was knocked down by the oxen, who trode on his body, and a heavy wagon passed over his bowels. He lived till toward evening.

19 August. Still in camp – 1 mile from the ford in a heavy cold rain storm, our cattle suffering with cold and hunger.

20 August. This day we saw the Sweet Water Mountains capped with snow.

3 September. We traveled 10 miles today, all well except Sister Blodgett who has been confined. She had a fine Boy – doing well.

26 September. Arrived at our long wished for homes, the City of the Great Salt Lake, making in all 101 days since we started from the Missouri River opposite Bethlehem.

At the foot of the last mountain, where we camped for the last time before we entered the valley, the first fifty were called together for the purpose of settling all difficulties, if any existed, and ask each others forgiveness, so that we could enter the Valley free from any hard feelings towards any of our brothers and sisters.

A good spirit prevailed, and all expressed a desire to forgive, and to be forgiven.

Single Cell Intelligence?

Writing in a recent issue of Physical Review Letters1, researchers in Japan believe they’ve seen behavior complex enough to suggest intelligence in single cell organisms, ie organisms without neurons.

I gave a talk recently in part on the idea that consciousness might arise algorithmically, or from other simple mechanisms. Conventionally, however, we tend to explain intelligence and consciousness as phenomeon rising from aggregations of highly specialized cells, neurons.

The organism is the amoeba Physarum polycephalum, and what you see above is a plot of its speed and acceleration over time.  It is confronted with environment changes (cooler, drier air) at points S1, S2, and S3, at which times it slows.  Notice, however, that significant periodic velocity changes continue at regular intervals in the absence of further environmental changes, at C1, C2, and C3. Note the periodicity matches the original environmental change timing. These velocity changes then appear to subside, until reinforced by a single change at S4, which reinstates the previous behavior.

The researchers speculate that simple nonlinear dynamics explain the behavior. The journal Nature comments, “Like all living organisms, slime moulds have built-in biochemical oscillators, like the human body clock…The team’s calculations show that such a group of oscillators can pick up and ‘learn’ any imposed rhythmic beat, although the knowledge decays quickly once stimulus ceases.”

The study authors note

It is not common to encounter recurrent environmental changes with periods of 0.5–1.5 h in nature. Thus, some might consider the capacity to learn a periodicity of this kind to be meaningless. However, the opposite conclusion could also be drawn, namely, that the organism is able to remember periodic changes that it has not experiencedbefore. This indicates that the organism has a generalized capacity for learning, independent of the details of the periodicity.

Discerning a periodicity is not easy, even for humans. According to history textbooks, when the ancient Egyptians recognized the regular periodicity of the flooding of the river Nile and succeeded in anticipating the next flood, this breakthrough triggered the invention of the calendar and was a symbol of the dawn of civilization. It is thus remarkable that a single-celled organism can perform such a function.

Others have tried to explain the seemingly intelligent behavior of single cell organisms in terms of relatively simple chemotaxis, and even via quantum mechanical phenomenon in microtubules. Ironically, much work proceeds in trying to understand the collective intelligence (if you can call it that) of phenomenon like financial markets (and other pyramid building), in terms of nonlinear dynamics.

1. Saigusa, T., Tero, A., Nakagaki, T. Kuramoto, Y. Phys. Rev. Lett. 100, 18101 (2008).

Feynman, before the sea

I was like a boy playing on the sea-shore, and diverting myself now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me - Isaac Newton.

Richard Feynman, in his 1965 Nobel Prize Lecture, said, “Theories of the known, which are described by different physical ideas may be equivalent in all their predictions and are hence scientifically indistinguishable. However, they are not psychologically identical when trying to move from that base into the unknown….If every individual student follows the same current fashion in expressing and thinking about electrodynamics or field theory, then the variety of hypotheses being generated to understand strong interactions, say, is limited. Perhaps rightly so, for possibly the chance is high that the truth lies in the fashionable direction. But, on the off-chance that it is in another direction – a direction obvious from an unfashionable view of field theory – who will find it?”