Sunday, June 17, 2007

Doc Martyn gets the boots (with box model)

This is Eli's humble contribution to our first mob post. Tamino at Open Mind is posting on the latest trends in atmospheric CO2 concentrations (buy, they are going up) and Simon Donner at Maribo wants to tell you about where all the carbon goes.

To get back to the shoe store, for those of you who don't know, Doc Martins are steel toed boots favored by the British version of football hooligans who want to get up close and personal. It is also the name of a climate hooligan on Real Climate who pretends he knows something about the carbon cycle and flims the flam. Eli ran into this character when he proposed to calculate the atmospheric lifetime of CO2

To do this I needed an estimate of the amount of CO2 released by Humans per year. . . I also used the Hawaiian data from 1959 to 2003 (averaging May and November).

The steady state equation for atmospheric [CO2] ppm is as follows:-

[CO2] ppm = (NCO2 + ACO2)/K(efflux)

NCO2 is the release of CO2 into the atmosphere from non-human sources
ACO2 is man-made CO2 released from all activities
and K(efflux) is the rate the CO2 is removed from the atmosphere by all mechanisms.

You can calculate that NCO2 is 21 GT per year, ACO2 in 2003 was 7.303 GT and K(efflux) is 0.076 per year. This last figure gives a half-life for a molecule of CO2 in the atmosphere of 9.12 years.

The Rabett's reply was
Flow of carbon (in the form of CO2, plant and soils, etc) into and out of the atmosphere is treated in what are called box models. There are three boxes which can rapidly (5-10 years) interchange carbon, the atmosphere, the upper oceans, and the land. The annual cycle seen in the Mauna Loa record (and elsewhere) is a flow of CO2 into the land (plants) in the summer and out of the atmosphere as the Northern Hemisphere blooms (the South is pretty much green all year long) and in reverse in the winter as plants decay. Think of it as tossing the carbon ball back and forth, but not dropping it into the drain. Thus Doc Martyn's model says nothing about how long it would take for an increase in CO2 in the atmosphere to be reduced to its original value.

To find that, we have to have a place to "hide" the carbon for long times, e.g. boxes where there is a much slower interchange of carbon with the first three. The first is the deep ocean. Carbon is carried into the deep ocean by the sinking of dead animals and plants from the upper ocean (the biological pump). This deep ocean reservoir exchanges carbon with the surface on time scales of hundreds of years. Moreover the amount of carbon in the deep ocean is more than ten times greater than that of the three surface reservoirs.

The second is the incorporation of carbonates (from shells and such) into the lithosphere at deep ocean ridges. That carbon is REALLY lost for a long long time.

A good picture of the process can be found at

A simple discussions of box models can be found at

And David Archer has provided a box model that can be run online at

and here is a homework assignment

There ensued a great deal of posing on Doc's part and confusion ensued about rather simple kinetics and similar things. Thus this post and some which will follow.

Eli has created a spreadsheet, called Box for Doc's boots, and the anonymice are free to play with it and improve thereon. You can download it at Rabett Labs, a new Google Group. The file walks you through a number of simple models. Eli does not have the space and you the patience to go through this in detail, but we can start with the simple stuff which will give you an idea how to roll your own. There are lots of better ways to do this. Symbolic algebra (and more) packages such as Mathematica, Maple and Mathcad spring to mind, as do such things as Origin and Igor on the spreadsheet/graphing side, but lots of people have Excel, and the folks that have the other packages, probably don't need this.

On the first sheet called first order decay, you get to play with a simple, first order decay where the rate of change of [A] at any time t is simply proportional to the the amount of A. The rate equation for this is

d[A]/dt = -k[A]

and if you don't speak calculus you can just read that as the rate of change of the concentration of A with time is equal to some number (the rate constant, ka) times the concentration of A. You can change the rate constant, and the initial concentrations. Eli, being a simple Rabett used Excel, and a simple differential equation solver called the Euler method. You can Google it, but the idea is that if you measure A at some time (t), and then later at (t+dt) then
[A(t+dt)] = [A(t) ]- k[A(t)]dt
This works if dt is small. In this case there is an exact solution A(t) = A(0) exp(-kt). Eli set the spreadsheet up so that you enter negative numbers (-k) for the rate constants.

This, basically is the idea that DocMartyn was pushing. The problem, of course, is that you move the carbon from the fossil fuel deposit into the atmosphere, and from there it goes into the land (soils/vegetation/rabetts) and the upper ocean, but it does not get lost, it comes right back into the atmosphere in a few years.

To model this, we have a simple two box model called "Opposing Reactions" You have box A and box B. And not only can you move carbon from box A to box B, but also from box B to box A. That looks like this

The rate constants are kab and kba respectively. After some time, the system will come to equilibrium. The rate equations are

d[A]/dt = - kab [A] + kba [B] and d[B]/dt = - kba [B] + kab [A]
if you add the two you find that d([A]+ [B])/dt = 0 , in other words the total amount of carbon just moves between the two boxes. There is an exact solution of the system of equation, but here we simply use Euler integration. The ratio of the equilibrium values of [A] and [B] are simply given by

kab / kba = [B]eq/[A]eq

You can play with this by changing the initial amounts of [A] and [B] or the rate constants at the top of the spreadsheet. Remember this is a toy you can play with to get some feel for the system. If things start oscillating wildly or diverge in strange ways you probably have to decrease either the step size or the rate constants. There are a couple of other simple spreadsheets. The next, CO2 pulse, shows what happens if you push a pulse of CO2 into the atmosphere. This is followed by "fossil fuel, where a constant amount of CO2 enters the two box system each time step.

We are now in position to put a more realistic carbon box model together. We can use the figure up towards the top to estimate how many Gt of carbon there are in each reservoir. We will for now exclude the geological reservoirs. Carbon moves very, very slowly into and out of rocks and sediments and we can treat them as being roughly constant. The first thing that one observes is that the deep ocean, with ~38,000 Gt C is MUCH bigger than the Atmosphere ( ~750) and the upper or surface ocean (~ 1000) and the land (~2000). The land includes both C in soils and in biosystems.

Us bunnies like to keep things simple and Mom Nature has helped us out. To a first approximation there is no flow of carbon between the land and the upper or deep ocean and between the atmosphere and the deep ocean for sure. Think about that for a moment, they really don't touch much. But Mom ain't that nice. We have been using first order rates to describe the flows between the various boxes. What that means is the change per unit time is equal to -kxy Mx where Mx is the mass of carbon in an box and kxy is the rate constant. You can see what happens when everything is linear in the spreadsheet called linear box model. One of the things you have to do in this model and the more realistic one below is adjust the rates so that with no fossil carbon flowing into the system they balance each other and the flow into each reservoir equals the flow out. Eli has done this in the spreadsheet called equilibria.

The linear model does not work because two of the flows are actually highly non-linear, the flow from the surface of the (upper) ocean into the atmosphere, and the one from the atmosphere into the land/soils. The former is governed by a series of chemical equilibria between CO2, H2CO3, and the negative ions HCO3(-1) and CO3(2-) as well as other ionic species dissolved in sea water. Roger Revelle's major contribution was giving us an understanding of these complex equilibria. The bottom line is that the flow from the upper ocean to the atmosphere is proportional to the ninth power of the mass of carbon in the upper ocean (Mu^9).

The rate at which CO2 flows from the atmosphere into the land is controlled by photosynthesis. This is much slower than linear, proportional to Ma^0.2. This flow depends more on biological and solar factors than the amount of CO2 in the atmosphere.

Rabett Labs created the final two worksheets which include the correct functionality for the fluxes, between the land, air, and upper and deep oceans. In the first, the emission of CO2 from fossil fuel is constant over time. That is called "Constant Fossil". In the last one, called "Stop Emitting" you can enter your own scenerio and see what the effects are. In the example shown below Eli let emissions of CO2 from fossil fuel continue for 200 years at a bit more than today's rate and then cut it off. Notice that the decay takes hundreds of years. The

Anyhow, have fun with the new toy. David Archer has a more realistic model, Shodor has one,

the Maryland Virtual High School has one, here is yet another and there are more out there. The purpose of the Rabett Lab model is to simplify things as much as possible for the mice to play.


Anonymous said...

Oh, but Eli, why did you leave out the best part of DocMartyn's comment on RealClimate? The first two sentences:

"Hi Bruce Tabor, than [sic] you for the equation for calculating the levels of Atmospheric CO2 vs. Man made carbon release.

It was a little too complicated for me so I devised my own." [Emphasis added]

Now, I'm no scientist or mathematician -- far from it -- but even I can only shake my head at the sheer naive arrogance of this statement. It's what you'd get if you threw Tony Robbins in the path of actuaral mathematics. It's almost touching.

And it reminded me of reading The Man Died, Wole Soyinka's account of his 22-month incarceration for speaking out against the Nigerian government in the late 60s. He was subjected to treatment tantamount to torture (temperature extremes, deprivation) and went on a hunger strike to protest. After a while, he became delusional and started scribbling equations in the margins of books. Even though, like me, he was a poor maths student at school, he became convinced that he had solved Einstein's Theory of Whatever. Time and space were related, he realised. Since he was confined to the space of a small prison cell, all he had to do to break out was manipulate the time axis through time travel. A small matter!

The difference between Soyinka and DocMartyn, of course, is that Soyinka read over his notes long after his eventual release, and recoiled in horror at the mad scratchings.

Oh, and he won a Nobel.

Anonymous said...

Edit: I meant "actuarial mathematics"

Anonymous said...

I don't see "wild-fire" anywhere on your Rube Goldberg contraption (unless that is included in "deforestation")

As NASA has found, it can be very significant. For example,NASA has some interesting findings related to CO2 increase during El Niño

"Many scientists thought the increases in greenhouse gases during El Niño years were likely due to a changing balance of plant growth and death. However, new research is providing a different diagnosis to the source of the Earth's heartburn.

El Niño Gives Wildfires a License to Burn

Wildfires seem to ignite the geological version of the big belch. During El Niño, vast areas of the tropic regions dry out and become vulnerable to fire. During the 1997/1998 El Niño, wildfires ravaged huge areas in Latin America and Southeast Asia, belching large quantities of carbon dioxide (CO2) and methane into the air.

"We found that a large part of the [carbon dioxide] increases [were] the result of increased fire activity," said Guido R. van der Werf, of NASA's Goddard Space Flight Center.

Horatio Algeranon

Simon Donner said...

Based on the diagram for the simple box model, all carbon emissions from land in the flux "kla". That'd include deforestation, fire/biomass burning, etc. A more complicated model would break that down... however, as far as i know, explicitly representing fire is proving to be one of the biggest challenges for carbon cycle models.

Anonymous said...

Some people (eg, physicist Freeman Dyson) think that we can take care of our CO2 problems simply through land use changes (eg, growing more plants).

How feasible is that?

How much additional vegetation (as a fraction of what is there now) is required to take up the yearly CO2 increase?

Given that the CO2 taken up by plants (and built into their tissues) eventually gets recycled. will that "solution" even work over the long term?

Wouldn't you have to have a very large ongoing planting effort in place for it to have a chance of working?

Also, because of their dark color, don't plants tend to absorb more energy in the visible than soil and re-radiate it in the IR? Isn't that how they find marijuana from above?

Marion Delgado said...

anonymous 11:53 :

one thing for sure, you don't get much benefit unless you both increase the planted area and KEEP it planted.
Also, technical genius though he may be, the fact is Dyson is at the far end of the Bell Curve of "believers in easy techno-fixes to complex problems." Not to the point of crank science, but just as a matter of personal bent.

He thinks if there is much intelligent life out there there shouldn't be any visible stars - they should all have long ago been completely surrounded with "Dyson spheres" made from pulverized planets, comets and asteroids (and dwarf stars). I think "why are there STARS?" might be an actual quote.

Marion Delgado said...

also, i suppose if you turn under plants and use various other measures for sequestering the carbon from the dead plants, you do help the C02 balance. But we have a happy-bunny view of this. In the real world, far from fixing our problem with carbon sinks, we're deforesting like crazy (and converting some land to tree-farming but also adding proposed forested land to our total of actually forested land because anti-conservationists run the world economy), and even exacerbating it, for instance, by increasing laterization .

Anonymous said...

I have read some of Dyson's books and not all of his ideas are far out. In fact, in general, he comes across as a pretty thoughtful, well-grounded guy.

Given, he's not a climate scientist so I'm not sure what the extent of his knowledge is of the whole issue of climate change.

But I guess that's really beside the point.

What I am curious about is how much planting would be required to soak up the additional CO2 each year?

How much of the yearly CO2 emissions are currently being taken up by plants and incorporated into plant tissues?

How long (on average) is this CO2 kept "locked up" in the plants before it is returned to the atmosphere?

I have not been able to find estimates for these anywhere, but it would certainly seem to me that such estimates would be critical in deciding whether the "grow more plants" solution has any chance of working.

By the way, I have read that the much touted idea of fertilizing the ocean with iron has not panned out the way some had hoped, based on preliminary experiments.

Anonymous said...

"Box model" - not just a way of formatting HTML.

Thanks to all three of you for the fascinating posts. I'll look forward to more.

Marion Delgado said...

anonymous 7:48 there is no one, simple answer:

Is it reforestation and leave alone? then it would depend on the average lifespan of the various plants, including long-lived trees, in the forest, and their average mass of carbon. Is it some other biomass where you can plow some of it under? Also, have you looked into "biochar" which is almost like plowing under the carbon?

Look at this, for instance: Sequestration: How much CO2 does a tree take up?

You have to follow the carbon. This simplifies things - one thing you can say for sure is that if you have an area that was barren and now it has plant cover containing a million tons of carbon, you have taken at least a million tons of of C02-forming carbon out of the system. And if it's mostly growing trees, then every year they'll absorb a little more carbon until they die, at which point most of it goes back (either into the air or as a carbon source so that other plants won't need to draw C02 from the environment).

Marion Delgado said...

anonymous 7:48, I might have saved keystrokes if I simply said, read all three bloggy posts and the references therein. Better than the seat-of-the-pants analysis we mere commenters can come up with on the spot.

Anonymous said...

Thanks for the link to the sequestration stuff.

But that's a little too specific and does not answer my much more general questions:

How much of the yearly CO2 emissions are currently being taken up by plants and incorporated into plant tissues?

How much planting would be required to soak up the additional CO2 each year?

I realize my questions are much harder than the ones answered in the link, since they require one to look at the big picture and attempt to take into account the variability among plants with regard to type, age, life-span, and the rest.

I am presuming that someone must have already done this and thought someone here might be aware of that "ballpark" answer.

Perhaps I should write to Freeman Dyson to see if he has made the estimates.

Anonymous said...

For terrestrial plants, integrated across the lifespans of annuals through perennials--net negligible.

"How much of the yearly CO2 emissions are currently being taken up by plants and incorporated into plant tissues?"

Marion Delgado said...

re "net negligible" - I think not. I saw a commenter on realclimate say a net of 30 gigatons a year, and this site makes it clear it's non-negligible while this site emphasizes the difference between farmland (negligible) and forest (significant).

EliRabett said...

One of the mice muttered "I have read some of Dyson's books and not all of his ideas are far out. In fact, in general, he comes across as a pretty thoughtful, well-grounded guy."

Dyson is the guy who came up with the Dyson Sphere and Orion, the spaceship that you flew by setting off small A-bombs underneath. That, in Eli's humble opinion is crazy enough for a small marching band.

Anonymous said...

..and Dyson also did statistical work that was important to winning air battles during WWII AND he explained (mathematically) how the QED theories of Feynman, Schwinger and Tomonaga were equivalent.

Th Dyson sphere is a fanciful idea, to be sure, and rocket ships propelled by A-bombs might not be a popular idea today, but in the days when he was proposing the idea, the US was still doing above ground atmospheric testing.

The idea of spaceship propelled by nuclear bombs being dropped out the back may not be quite so fanciful as some might believe.

Dyson has also been involved with quite down-to-earth projects like a prototype air conditioning system built and tested at Princeton that collected snow in a big hole in the winter, buried it and then ran th water pipes through it.

Very creative people like Dyson often have a lot of far out ideas for every idea that works. Sometimes their far out ideas are just way ahead of their time and sometimes they are just fantasy. Breakthroughs are usually the result of such imaginative thinking, at any rate.

Anonymous said...

I should have said "ran the water through it". The pipes were put in before the snow was collected.

To put them in afterward would have been crazy!

Anonymous said...

Dyson also had some ideas about genetically engineered "factory trees" to produce chemical products. (I'd bet this idea will one day come to pass)

He also was the head of a team who designed (in 1958) an inherently safe nuclear reactor (TRIGA) that is physically incapable of a core melt down. many of these reactors were built and used at universities for research purposes.

Many of us can only dream of being so crazy.

Anonymous said...

Incidentally, I found the answer to one of my above questions: How much of the yearly CO2 emissions are currently being taken up by plants and incorporated into plant tissues?

It's on the NASA carbon cycle graphic above.

It's about 25%.

121.3 - (60+60) + .5 = 1.8Gt net absorbed by vegetation.

This is out of the 7Gt yearly emissions (including deforestation)

1.8Gt/7Gt = .257

According to the graphic, the oceans absorb another 2Gt (28.5%)

The combined absorption (ocean plus vegetation) is therefore about 54% of the total yearly emissions.

That is consistent with what i have read elsewhere: that roughly half the yearly emissions end up in the atmosphere.

CapitalistImperialistPig said...

IIRC, what Dyson really proposed was carbon sequestration in topsoil. He claimed that an extra millimeter or so of topsoil (everywhere) would suck up a lot of carbon.

Dyson is a genuine genius who was one of the key inventors of quantum electrodynamics. The ideas Prof. R. makes fun of are mostly good ones, which illuminate important ideas.

He is also well into his ninth decade, and might well be nuts about the benefits of topsoil creation - but I doubt it.

Anonymous said...

He claimed that an extra millimeter or so of topsoil (everywhere) would suck up a lot of carbon."

I think you have it backwards. He proposed that increased plant growth -- eg, due to CO2 fertilization -- would increase the amount of topsoil by virtue of the increased amount of decaying plant matter. This decaying plant matter would contain a lot of carbon that had been taken out of the air.

Also, Dyson didn't invent QED. What he did was show that the different versions of it that had been proposed by others were consistent.

EliRabett said...

Dyson is certainly well out of the box that most people are delivered in. That is close enough to crazy, clever crazy maybe. Orion and the Dyson sphere are two good examples, demanding things that are beyond reach, shielding materials for the Orion for example and for building the Sphere. A typical theoretical physicists solution postulating that all engineering challenges are minor issues (Hmmmm...Lubos anyone??)

Anyhow, at what garden center are you going to get 1mm of topsoil to cover everything. It ain;t even 1 mm of topsoil, because there are lots of places where there is no topsoil because the earth, like the elephant ain't a sphere.

Do the calculation and see how much you are going to have to pick up in your SUV.

Anonymous said...

"at what garden center are you going to get 1mm of topsoil to cover everything. "

Dyson did not suggest that people go out and cover everything in sight with topsoil.

He suggested that additional plant growth would produce the additional topsoil, which would be made up of the carbon that was taken out of the air.

With regard to shielding for Orion, ever heard of lead?
Since the rocket is being propelled by nukes being jettisoned out the back, the weight of the spacecraft itself (including the shielding) become much less of an issue than they are with chemical (or other) propulsion methods.

Dyson is certainly no dummy.

Also, I suspect that Dyson may have proposed the Dyson Spehere as a flight of fancy more than anything else. futurism is by its very nature speculative. :)

I would certainly not put Dyson in the same category (or even mention him in the ssame sentence) as Motl (or vice versa).

EliRabett said...

Lead is about the worst thing you could think of. It is very heavy, with a very low melting point and ablates like crazy. The shielding has to be a. light, b. strong c. high melting point and d. radiation resistant. Lead meets condition d.

One does not simply order up 1mm of topsoil. While it is true that increased CO2 increases plant growth, it also increases decay. The CO2 fertilization effect appears to be hitting a barrier for lots of reasons anyhow. This again is a good example of Dyson's magesterial wave of the hand.

On the other hand, there is a fair amount of fancy here abouts, and the Ringworld IS unstable.

Anonymous said...

You are assuming that the lead is the first thing in the line of fire -- ie, that the shield is not layered, as it is with the space shuttle (ie, heat shielding tile first, supported by a strong metal structure underneath)

But depleted uranium would meet the conditions of strength, density and high melting point (1132.2 °C).

It need not be light because with nuclear propulsion, the amount of weight associated with fuel is greatly reduced and the amount of energy produced is certainly enough to propel even a relatively heavy spacecraft.

But whether Dysons iOrion or Shere ideas are feasible is really irrelevant to his arguments about sequestering carbon, at any rate.

CapitalistImperialistPig said...

The Dyson sphere is a theoretical concept designed to compute the maximum amount of energy potentially available to a civilization. Orion is maybe not such a great idea, but once again, it illustrates the potential limits of propulsion using known science.

Anon is correct, of course, in saying that Dyson's role in QED was not invention, but theoretical reconcilliation. I was imprecise.

Creating more topsoil is not a matter of just planting stuff. If you are going to create topsoil in, say, a desert region, land management, hydrological engineering, and bioengineering of suitable plants are all required. Don't dismiss this kind of an idea without bothering to understand it. It makes a heck of a lot more sense to me than pumping CO2 into the ground.

Anonymous said...

a link to a Book review Dyson did in which he mentions his thoughts about CO2 and top soil.

I honestly don't know whether Dyson is talking out his wazoo on this one, but I think his thoughts deserve a hearing because there may be something to what he is saying. It seems to make some sense, at least.

Even if we could sequester part of the CO2 emissions in the soil and keep it there by increasing and maintaining a greater amount of vegetation throughout the world (by planting and irrigating desert areas, for example), it might be worth pursuing, since it would have other benefits in addion to the carbon sequestration ones.

I didn't bring up the issue of Dyson because I don't think anything should be done about climate change -- though I'm sure there are some using Dyson's words to argue just that.

I just happen to believe that the solution to the problem may be many faceted. With something like increasing the amount of vegetation, there is little or no downside, at any rate.

Marion Delgado said...

I have great respect for Freeman Dyson most of the time. His Orion ship would have also been a way of usefully disposing of a-bombs, part of its conceptual purpose. I also agree that solutions will come in many parts.

Also, in fairness to Dyson, Orion is no madder than a Mars mission - neoliberals - which most denialists are - have a "dispose-a-planet" attitude to the Earth that needs to be fought tooth and nail as long as it takes. A good example of that is pointing out just how badly cosmic rays will savage anyone going to Mars and back. It's not impossible to shield people (one idea is to have hydrogen fuel be part of the shielding, though i dunno what you do when it runs down. If we sent people to mars no better protected than they were going to the moon, they'd probably be dead or dying when they got back. Outside the shadow of Earth, space is completely inhospitable. That and the gravity well and the limit to the speed of light are three good boring science reasons we have to save THIS planet, not count on shipping our surplus population to space colonies.

BTW didnt Dyson sign that ill-advised global warming denial petition thing out of the crank institute here in oregon? If i have to get my information from someone out of the fields involved, I might prefer Frank Herbert. He wrote Dune after working with and observing pioneering switch grass and sand reclamation work here in Oregon.

Anonymous said...

These models are much appreciated.

Are there any around that include pH models in a similar framework? I.e., generating pH charts over time under different assumptions?

Unless I've gotten confused:
a) As long as the ocean keeps absorbing CO2 at a high rate, the pH will keep dropping, but at least it keeps some of the CO2 out of the atmosphere.

b) If the oceans get "warm enough", they absorb less CO2 (or start emitting), in which case the pH stabilizes, but of course more CO2 goes into the air, which makes it warmer.

Anyway, I've rummaged around, but I haven't been able to frame a query that gets me to a concise description, with a few good simple graphs [presumably based on scenarios] to try to understand where the (upper ocean, at least) pH is likely to go.

Any pointers?

Anonymous said...

BTW didnt Dyson sign that ill-advised global warming denial petition thing out of the crank institute here in oregon?

I don' think you can fault him for that. The petition came out in 1999 and a lot of well respected scientists did sign it. It is possible to have been opposed to Kyoto without being a global warming denialist.

What is reprehensible is not the petition itself or the people who signed it, but that the results were (according to
) misrepresented:

"We urge the United States government to reject the global warming agreement that was written in Kyoto, Japan in December, 1997, and any other similar proposals. The proposed limits on greenhouse gases would harm the environment, hinder the advance of science and technology, and damage the health and welfare of mankind.

"There is no convincing scientific evidence that human release of carbon dioxide, methane, or other greenhouse gasses is causing or will, in the foreseeable future, cause catastrophic heating of the Earth's atmosphere and disruption of the Earth's climate. Moreover, there is substantial scientific evidence that increases in atmospheric carbon dioxide produce many beneficial effects upon the natural plant and animal environments of the Earth.

"The text of the petition is often misrepresented: for example, the petition's website states that "scientists declare that global warming is a lie with no scientific basis."[2]
The people who signed the petition are in a different category than the ones who originated it, as far as I am concerned.

Anonymous said...

And are you interested in business incorporation?

Anonymous said...

Fred M. Mouse says if you use atomic bombs to power a spaceship, can't you just make the ship out of cockroaches?

Anonymous said...

Hi Eli. This is a great post which I find myself revisiting every so often. Unfortunately some of the figures are missing. Not such a big deal though, I can make sense out of it even without the figures.