## Thursday, December 23, 2004

### Prime multiplication table

```Prime multiplication table to 1000 (or slightly over...)
7	11	13	17	19	23	29	317	49	-	-	-	-	-	-	-11	77	121	-	-	-	-	-	-13	91	143	169	-	-	-	-	-17	119	187	221	289	-	-	-	-19	133	209	247	323	361	-	-	-23	161	253	299	391	437	529	-	-29	203	319	377	493	551	667	841	-31	217	341	403	527	589	713	899	96139	259	407	481	629	703	851	107341	287	451	533	697	779	94343	301	473	559	731	817	98947	329	517	611	799	893	108153	371	583	689	901	100759	413	649	767	100361	427	671	79367	469	737	87171	497	781	92373	511	803	94979	553	869	102783	581	91389	623	97997	679	1067101	707	1111103	721107	749109	763113	791127	889131	917137	959139	973149 	1043151 	1057

Any three-digit number not divisible by 2, 3, or 5
must either be one of the above numbers, or it must be

343 = 7 × 7 × 7
539 = 7 × 7 × 11
637 = 7 × 7 × 13
833 = 7 × 7 × 17
931 = 7 × 7 × 19

...the next smallest combination is 7 × 11 × 13 = 1001.
```

### Prime tableaux

Tableau encodings to 2100:

(ON bits are composite)

0000: 00.04.08.81.92.24.43

0210: 60.54.0D.87.30.A8.9A

0420: 48.86.98.CF.34.34.23

0630: 44.65.5A.A9.19.B6.42

0840: E1.87.9A.95.95.38.4A

1050: 4B.84.AB.CD.55.64.3A

1260: F0.06.3F.D5.7A.E0.8B

1470: 40.DD.68.99.90.37.A3

1680: E2.CD.2B.A3.5D.77.02

1890: D5.CE.7C.A1.32.EC.C2

[4-bit must be ON 8-bit must be ON 1-bit must be ON 2-bit must be ON]

Each tableau of length 30 is encoded by two decimal digits, where an on bit in each digit means that the associated number is composite:

```
First digit: 30n+1   30n+7   30n+11  30n+13
Second digit: 30n+17  30n+19  30n+23  30n+29```

The colored digits above are characters where one of the bits is pre-determined due to a multiple of 7

## Monday, October 18, 2004

### Ishmael draft essay [Posted for Sarah Averill]

Sarah Averill
Biology 110
Draft Essay on Ishmael

Only recently have I come to terms with being alive at this time in human history. Starting when I became conscious of environmental issues in high school, I spent the better part of a decade feeling guilty for being here, when I knew there were too many of us on the planet.

And yet I didn’t really want to leave any time soon, just to fix the problem! Life really is rather interesting, in all its perplexing detail. In my decade of guilt, I kept feeling trapped -- no matter what my individual actions were, it seemed that larger institutions with much greater momentum would keep doing damage on my behalf.

I could recycle paper, or even go paperless, but the health insurance company would still send me reams of paper with the same annoying and useless information a hundred times before sending me the bill I was supposed to pay. I could divorce my car, but my life would be circumscribed relative to my peers until the place I lived in was built for people who didn’t have cars. I was being carried along in a mental and physical juggernaut, without a clue as to on how to live without contributing to the destruction of the biosphere. I was part and parcel of the system.

I voted, but you can’t vote 5 billion people out of existence, not very quickly anyhow; and if George W. has his way, we won’t even be able to plan them out of existence through measured slow population decline. I went to all sorts of public meetings, volunteered for a handful of organizations, and voted. I still vote and recycle and hope that the economics will come into line for more dramatic change.

So what happened at the ten-year mark? What happened was that I wanted to have children (oh shit, not more people!) And I planned my family -- to the great shock of my healthcare providers. From their response, I guess that most people still don’t do much in the way of family planning -- in Iowa, anyway. I was in graduate school at the University of Iowa at the time, and taking a biogeography course. That class was my first deep exposure to the theory of evolution, and the history of life on Earth. For the class we read E.O. Wilson’s The Diversity of Life, which is an eloquent plea for conservation of biodiversity as one could find.

A combination of reading that book and reflecting on the amazing process of bringing a baby into the world shifted my guilt feelings about my part in destroying the planet. I realized that the changes we as humans were making were unlikely to snuff out all of life. And I began to imagine great radiations of squirrels and raccoons and crows, and many other broadly adapted species, into new and unimaginable communities of plants, animals, or even new kingdoms of life. I was able to breathe a sign of relief: it wasn’t *life*, all of life, all the potential for life, that was on my shoulders. Life would go on.

So what would really happen, I thought, if we drove 90% of all species into extinction? Who will care? Who will be impacted? Will Nature care? She/he/it’s seen it all before -- extinction is a regular feature of geologic time, and mass extinctions are rare events but they have happened before. We may manage to produce the worst mass extinction of all time, by some measurements -- but to whom will it really matter?

E.O. Wilson addresses this issue by placing things in a time frame that is human, saying simply that what is lost now, is lost essentially for all of human time, because the evolutionary time frame that gave us the current biodiversity is much greater than a timeframe that humans are likely to see. What is lost now, will essentially be lost to us forever. Biodiversity matters to us. What I took from his book was that, at least from the point of view of pragmatic conservation politics, the best possible argument for protecting as much biodiversity as we could was that it was for our own good.

Profesor Hirsch, I wish I had more time to develop this essay, and I’d love to talk to you more about my responses to Ishmael, but I simply don’t have time right now except to point out the things that really disturbed me about his book.

1) Quinn suggests that we can learn from observing the animals to live a leaver Life-style. Sure, we can look at the systems which are more or less in balance and see that we are not in balance, we are taking more than we need in many cases, but every animal does what is within its means to promote the survival of its “family/group”. I agree that we, especially in the West have gone well beyond that, but I think that part of what drives us is our animal nature. What we need to do now is to go further, not to turn back. From my point of view, we have taken a half step and now we need to go the rest of the way. We need to step outside our little system and take responsibility for the whole planet. We happen to have evolved skills that are well adapted to short-term survival, but which are poorly adapted for a long time span. It will be critical for our own survival that we learn to take the long view in planetary management -- but giving up the job of manager altogether doesn’t seem like the best option.

2) Quinn places humans in a double bind. On the one hand he criticizes us for elevating ourselves outside of nature, and then he criticizes us for not limiting our reproduction and so forth. Either we are supposed to be like the other animals or we are not. He can’t have it both ways.

3) While Quinn asks us to get out of our skin and look at things from the perspective of other animals almost as highly evolved as we are. Why did he choose an ape if the story is equally valid from the perspective of a jellyfish? Presumably he knows that we care more about species that are closer to us—the charismatic species, as they are known in the conservation world. Fundamentally, the issues of conservation biology have to matter to us for any program to be successful. While I don’t have a very developed philosophy on animal rights, I don’t think we need to go down that road to argue for conservation and biodiversity preservation. It matters to humans (and I haven’t gone far enough with why), and that’s enough of an argument. I think it gets too confusing when we try to argue from the perspective of other animals. At least, when I feel sad about the loss of a species, I have to ask why. And I think its because I won’t get to see it, and my children won’t and their children won’t. I am sad because they are lost to humans. It seems to me that this is an argument that has much broader appeal than the animal-rights perspective, which is bound to remain deeply controversial: a large fraction of humanity may never accept it.

_Points_of_agreement:_

We need a new story and a new way to live and we need to get there quickly -- for our own good. There is a better way to live on the planet that will keep more species alive and which is healthier for people and other living things.

And I began to wonder if we were really destroying the planet and if so in what time frame. Time. I started thinking a lot about time, perhaps as part of stepping up to the parental plate. It was now going to be my turn to pass on culture to a new member of the species. In part this was driven by an underlying sense of responsibility for all of life in its many forms. I felt that as a member of the human species, I was contributing, by the very fact of being alive, to the annihilation of life. Yet, here I was, doing what I was designed to do by the very forces that made all of the rest of living matter.

Like the rest of my fellow humans, I am too damned good at it for my own good and the good of the planet. Sit still? Do nothing? Not me. I have a lot in common with the beavers. I hear that water trickling through the dam of my life, and I want to contain it. I grow a garden and I fertilize it to make things grow, I work, I move around, I get the most of every minute traveling and meeting others of my kind, making plans for what's next. I'm on the go every minute. Deep inside, while I despair at the part I'm playing in this destructodrama, I also celebrate, knowing that this energy I have for life and living, is at its best what kept my ancestors alive, and theirs before them. It can't be bad in any absolute sense. Troubles ahead? Bring them on!

Is man fatally flawed? Ishmael spends a lot of time getting his student to question that assumption of Western civilization. Being flawed is only the other side of our strength. We have evolved to become master manipulators of our environment. That is our strength. And, it is our weakness too.

Studying evolution changed how I felt about my role in the current environmental crisis. I started thinking about time, and how vast the evolutionary timeframe was. And beyond the evolutionary time frame there was the celestial time frame. The sun and the planets would someday change and it would be all over for everything, even the lowly bacteria. I spent more time dwelling on the evolutionary time frame.

It was a great sense of relief to learn that there had been great radiations of life and great extinctions before ours. It made me realize that it wasn't all of life for all time that was at stake. I could see the crows, squirrels, raccoons, and the cockroaches radiating into every environmental niche. Surely, there would be a new and fantastic world after we'd come and gone. This thought focused my attention differently on environmental concerns.

Now, before going forward, I have to make clear that I do think of people as fundamentally different from other animals. While we do share some traits, I think humans have one unique feature: we can look much farther into the future than any other species (when we choose to do so) and we can take responsibility, at least in a limited way, for that future. We can’t manage everything on the planet, but we can choose to take responsibility where we need to, and manage as well as we know how.

Ishmael is perfectly correct in saying that we need to learn to leave well enough alone, instead of taking over everything we see; but we need also to learn how to keep an careful eye on things, just to make sure that all will really be well (in human terms) if it’s left alone. Mother Nature makes no promises on that score.

Once you enter adult life, and all of the responsibilities that come with it and with running a household fall on your shoulders, paying bills, taking children to the doctor, buying appliances and cars and so forth. The whole messiness of life becomes more overwhelming. In some sense I felt even less able to change things, more complicit in the destruction of the biosphere. At heart, I kept thinking that ending one's life was the responsible thing to do where the environment stood. (Don't read into this -- never had a suicidal day in my life!). This did not seem, however, to be what was asked for by my life. I wondered why more staunch environmentalists weren't quietly taking cyanide pills. There had to be another "story" (as Ishmael puts it) that we could tell ourselves. A story for our time.

What is our time? Is it the time of the stars, the time of the rocks, the time of evolution, the time of history, the time of our lifespan? Which of these time frames belongs to me, I wondered. The stars move too slowly, and when the sun goes out, my worries and the worries of man will be long since put to rest. The time of the rocks, likewise, is too vast. And so too for the evolutionary timescale: there will be new radiations and extinctions many as the continents shift around. My time, then, is historical time, human time, and the time of my lifespan. Since beyond this time frame life will be renewed in unimaginably wonderful and new ways, it is only from the perspective of my time frame that the extinctions of life forms and degradations of the planet matter.

For reasons that I find difficult to articulate, this feels much better to me and it makes the problem at hand more manageable from a moral and personal point of view. I was liberated from the dark side of what is happening to the environment. Each extinction, in the long run beyond my time and the time of people, was simply an opportunity for a new life form to evolve. Surely Mother Nature will take a philosophical view of extinctions in human time, having given birth to each of the previous sets of life forms, and watched them come and go.

I don't mean to suggest that the problem is any less great for people, simply that it is a human problem. The "tragedy" of the current mass extinction is taking place on a human time frame, and it therefore matters most on a human time scale. Really, my argument is simply that the perspective from which to argue for preservation/conservation/restoration is the human one. The reason that campaigns for charismatic species are successful is that people care about those species. The problem lies in whether they care about the rest of what the ecosystems provide to them. And the model for that is not going to be found in nature, no matter what Ishmael says.

Nature just doesn't think ahead, it doesn’t manage things -- it only works on finding new temporarily stable structures in response to new situations. If the new state of equilibrium doesn’t contain Species A, or Species B through Z, that’s just the way it goes. Other animals don't care either, no matter what Ishmael purports to tell us by giving us his Ape perspective: a mongoose will happily drive fifty other species to extinction on a tropical island, in its quest to make more of its own species.

Humans are and aren't different.

I agree with Ishmael that we are not outside of Nature. We are very much inside of it. I disagree with his analysis that our actions are the result of our trying to elevate ourselves above Nature.

I think we are simply an accident of evolution. We happen to have been too good at the struggle for survival. Mother Nature, in this case, outdid herself.

Whether you agree with this simplification or human bias probably rests on whether you think humans are just another animal or if you think that are somehow "special" with all the good and bad that goes with being special. One of the things that troubled me about Ishmael was the way he criticized maggot-faced people on the one hand for "elevating" themselves from the rest of nature, while also criticizing them for not controlling themselves in ways that no other species is expected to.

It seemed like he didn’t want people to have a higher status, but he expected them to be responsible in ways that were not typical of other animals or "natural systems." (I’d need to read the book several more times to tease this out or we could talk about it more.) Sex/birth control is probably the most obvious example of these types of problems.

## Friday, October 08, 2004

### Pacific vs. Atlantic, round 3

Following my old memories, I have since dug up some references to the effects of Coriolis forces on ocean water -- there's a phenomenon called "Ekman transport" that can result in elevation differences up to a meter: see, for example,

www.mhhe.com/earthsci/geology/duxoceans/student/studyguide/chapter8.doc

Related or supporting concepts:
- As the prevailing winds drive the large surface gyres, water is
directed inward to the center of the gyres by Ekman transport.
- Ekman transport creates an elevated sea surface due to the piling
up of the water. The difference in elevation is as much as 1 m (3 ft) > or more.
- Gravity causes water to flow down the slopes of this elevated mound.
The water will be deflected by the Coriolis effect and when
everything is in balance there will be a circular rotation of water
around the mound.

Unfortunately, this doesn't seem to have *anything* to do with the (relatively minor) difference between Atlantic and Pacific average levels. And the only Coriolis-related effect on ocean basins that I can find (on the same Web site) says that currents are stronger, and water piles up a bit, on the _western_ sides of ocean basins. Which could only tend to counteract the observed difference in levels between the eastern side of Pacific and the Western side of the Atlantic...

Oh, well. So much for trusting my memories of old half-learned facts. -- Though of course the fact that my explanation was wrong _still_ doesn't mean that the density explanation is all there is to it -- I'd love to see an extra few sentences explaining how the water that tries to flow down the 20-centimeter average gradient from the Pacific evaporates along the way, and/or mixes with the higher-salt Atlantic and ends up obeying the same gravitational rules as the rest of the water, or whatever is happening.

But unfortunately I don't have nearly enough knowledge or credentials to supply those extra sentences... (No, I'm nothing like an oceanographer -- not even a competent physicist, which might help in evaluating the density explanation. I just know an incomplete story when I see one...)

However, I will venture to add a few facts to my previous amateur speculations: I live 200 km up the Hudson River from the ocean. The Hudson is six feet above sea level here, but its level still goes up and down with the tides (while maintaining that six-foot difference in levels!) So obviously there's nothing strange about a small gradient in water that's apparently flat and unobstructed -- as long as there's a current flow to maintain it, and somewhere for the water to go when it reaches the lowest level.

In the Pacific/Atlantic case, the only place the water could possibly disappear to would be into the air, by evaporation -- which would make sense, since the Atlantic is rumored to be warmer. Unless Coriolis-inspired currents have something to do with the matter after all!

[Now I just need to find a real oceanographer to straighten this all out for me.]

### Pacific vs. Atlantic, round 3

Ran into this quote about the 20-centimeter average difference between Pacific and Atlantic water levels:

http://css.sfu.ca/sites/water-web/

The Pacific ocean is higher than the Atlantic ocean because the Atlantic ocean is warmer, hence saltier, hence more dense, and being so heavy, it is lower. Water flows from the Pacific to the Atlantic in the Panama canal. This was actually an environmental concern when the canal was built and a series of locks prevents too much flora and fauna from going through.

-- and it surprised me considerably. I thought I had read somewhere that the difference had something to do with the rotation of the Earth: water piling up on the western shelves of continents, or some such. I wouldn't be surprised if that were a silly superstition, but then again I still wouldn't be surprised if it were true, either.

In any case, I didn't like the density explanation very much. If the Atlantic were full of molten lead, it would theoretically be a heck of a lot lower, "being so heavy" -- but that wouldn't prevent the water in the Pacific from flowing right in over the top of it.

It would make sense to me if the difference were due to the Atlantic being warmer and thus evaporating more quickly -- and apparently it is warmer, as the quote above says. Certainly 20 centimeters' difference in height over half a world wouldn't do a whole lot to create a raging current to correct the situation; so maybe the discrepancy is just the equilibrium point between the extra evaporation and the water that comes in from other oceans to replace it. That picture would also account for the Atlantic being saltier, of course -- but this reverses the cause and the effect given in the explanation above!

## Thursday, October 07, 2004

### Pacific vs. Atlantic, round 2

Ran into this quote about the 20-centimeter average difference between Pacific and Atlantic water levels:

http://css.sfu.ca/sites/water-web/

-------------------------------------

The Pacific ocean is higher than the Atlantic ocean because the Atlantic ocean is warmer, hence saltier, hence more dense, and being so heavy, it is lower. Water flows from the Pacific to the Atlantic in the Panama canal. This was actually an environmental concern when the canal was built and a series of locks prevents too much flora and fauna from going through.

-------------------------------------

-- and it surprised me considerably. I thought I had read somewhere that the difference had something to do with the rotation of the Earth: water piling up on the western shelves of continents, or some such. I wouldn't be surprised if that were a silly superstition, but then again I still wouldn't be surprised if it were true, either.

In any case, I didn't like the density explanation very much. If the Atlantic were full of molten lead, it would theoretically be a heck of a lot lower, "being so heavy" -- but that wouldn't prevent the water in the Pacific from flowing right in over the top of it.

It would make sense to me if the difference were due to the Atlantic being warmer and thus evaporating more quickly -- and apparently it is warmer, as the quote above says. Certainly 20 centimeters' difference in height over half a world wouldn't do a whole lot to create a raging current to correct the situation; so maybe the discrepancy is just the equilibrium point between the extra evaporation and the water that comes in from other oceans to replace it. That picture would also account for the Atlantic being saltier, of course -- but this reverses the cause and the effect given in the explanation above!

### Earth vs. Billiard Ball, round 2

I ran into the following quote on Wikipedia (http://en.wikipedia.org/wiki/Flat_earth, final paragraph):

The Earth is very smooth, which is to say, locally flat. By comparison, if a well-polished billiard ball were enlarged to the size of the Earth, it would have mountains about 50 miles high.

After a bit of research, I can't find a source for the 50-mile figure anywhere, and I think it's probably off by something like an order of magnitude. Here are my own calculations:

First, here's a quote from http://mentock.home.mindspring.com/ifaq.htm :

----------------------------------------------
IFAQ007 Is the Earth really as smooth as a billiard ball?

We contacted an engineer at Brunswick, and he gave us their specifications for their better billiard balls. Each ball is rolled and measured and an average diameter is computed. The average diameter must be no greater than 2.258 inches, and no less than 2.245 inches. Deviation from the average diameter must be no more than .002 inches. So, if you only consider such minor outcrops as Mt. Everest (6 miles high), the Earth, if reduced to the size of a billiard ball, would pass the smoothness test. Unfortunately, because of the Earth's rotation, the Earth's equatorial diameter is 24 miles more than its polar diameter. The Earth is smooth, but it is out of round. No cosmic corner pocket shots for us.
----------------------------------------------

From memory, the Earth is about 8000 miles in diameter. Some Brunswick balls apparently have radial tolerances of .003, or as low as .001, but .002 seems like a good number to go with. Now we can check some ratios --

height of highest mountain : diameter of sphere
----------------------------------------------
billiard ball: .002 inches : ~2.25 inches; ratio = .000889

yet another Internet source (minimum BCA standards from http://www.bca-pool.com/play/tournaments/rules/equip.shtml -- not "better billiard balls", apparently):

worst possible billiard ball: .005 inches : 2.25 inches; ratio = .00222

Earth: 6 miles / 8000 miles = .00075 (Everest), and
7 miles / 8000 miles = .000875 (Marianas Trench), but
24 miles / 8000 miles = .003 for equatorial bulge
26 miles / 8000 miles = .00325 (another Internet source for Earth's deviation from round)

Earth-sized billiard ball --
multiply by factor of 3555 miles per inch-of-billiard-ball:
7.11 miles / 8000 miles (Brunswick "better billiard balls")
17.775 miles / 8000 miles (worst possible BCA-standard billiard ball)

But because the Brunswick engineer is actually talking about deviations from the *average diameter*, the above assumes that both Everest and the Marianas Trench have land at about sea level on the other side of the Earth. Haven't checked that yet, but that's probably close enough for this calculation (certainly there are no other Everests or Marianas Trenches over there...)

Doesn't really matter anyway. In any case Earth does _not_ pass the billiard ball test, due to the equatorial bulge, by a factor of three or so. Also, even with the above simplistic analysis, the mountains on a "better billiard ball" the size of the Earth would be just slightly higher than Everest -- assuming the 7-mile-high lump was all on one side of the sphere. A worst-possible standard billiard ball might just possibly have 18-mile-high mountains -- but not mountains "about 50 miles high".

More importantly, that's the _maximum tolerable_ deviation we're talking about; the *average* "better billiard ball" probably doesn't have such high deviations in the diameter. Half of that might be a good bet (but I personally don't go around measuring deviant billiard balls, so obviously I don't have exact figures). In other words, the odds seem to be good that the average "better billiard ball", fresh from the factory, is just as smooth as, or smoother than, the Earth -- in terms of the distance between its ideal surface and its actual surface, relative to its diameter.

And MOST importantly, the billiard ball has been polished, so there aren't necessarily any local spikes or dents in it that look anything like Everest or the Marianas Trench! Any "mountains" on an Earth-sized billiard ball are likely to be smooth bulges without any well-defined top -- there would be many places where a marble would roll in one direction or another, but there might not be any vertical cliffs bigger than a few feet high -- very different from Earth.

In point of fact, the above billiard ball test is entirely a test of roundness, not of smoothness! And it may not even be a very good test of roundness -- you can make significantly non-circular shapes that have the same diameter everywhere, and it seems possible that this could be extended to three dimensions (?). Let's have a quick look at the smoothness of a few sample things:

CAMI 100-grit sandpaper has an average grit particle size of .0055 inches, which is way too big; let's find something smaller. The CAMI scale appears to go down to 1000-grit or so on the table I found,

with an average grit size of .00042 inches. So if you stuck 1000-grit sandpaper on a billiard ball, the sand grains would be about twice as high as Everest (not counting the thickness of the paper, which would add a few more Everests to that).

So I suspect that an accurate billiard-ball scale copy of the Earth (minus the oceans, of course) might still feel very slightly sandpapery. Certainly there are things out there that "feel smoother" -- probably including nearly all billiard balls, unless they've been treated badly.

As an upper limit, the Hubble Space Telescope was at one point the "smoothest optical mirror ever polished", with a surface tolerance of one millionth of an inch. IANALLP (I am not a licensed lens-polisher), but assuming I understand what "surface tolerance" means... if a billiard-ball-sized Earth were machined to *that* tolerance, I think the tallest mountains would be less than ten feet high:

Billiard ball machined to Hubble Space Telescope tolerances:
.000001 inches : 2.25 inches; ratio = .00000045

Multiplying by 3555, we get a maximum deviation on an Earth-sized Hubbilliard-ball of .00158 miles, or 8.34 feet.

Conclusion:
The Earth is definitely not quite as round as a billiard ball, and it probably isn't nearly as smooth as a billiard ball, either -- but I must admit that I don't have absolutely conclusive data available...