Image Results for Chris Fellows

Of the Chris Fellowses in the world, the one with the largest web footprint is possibly the South African wildlife photographer known for his action shots of great white sharks. So if you google me you are likely to get results like this:


("So, Mrs Jones, number four is the man you say pulled your husband from his surfboard and bit his leg off above the knee?"
"*sniff* Yes, Officer... I'd know that face anywhere... *sniff*")

Best. Exam. Ever.

This is a reproduction in its entirety of my favourite exam of all time. It was for one of three coursework units we had to do in the Honours year and Dr Ken Adam had given me three books to read at the beginning of the year- one on Ab Initio Self-Consistent-Field Theory, one on Semi-Empirical SCF methods, and one on the application of computers to chemistry in general, with instructions to read them, except for one chapter in the last one. (Of course that chapter was about spectroscopy of molecules in interstellar space which was wildly exciting so I read it anyway).

In praise of Control+C

Paper 1: Important for the transfer of energy and matter across the ocean/sea air interface are some parameters called the roughness length, z₀, and the friction velocity, U_*, of the interface that can be determined by measuring the velocity of the sea air at various heights above the water and fitting an equation, like so:


In 1969 a group of scientists from the Massachusetts Institute of Technology went out and did a bunch of measurements like this. They looked at the variation in z₀ and U_* as functions of U₁₀, the air speed 10 m above the ocean surface. They took 299 separate wind speed profiles, binned by U₁₀ like so:


From which they got the following graph for U_* vs U₁₀ :


And the following graph for z₀ vs U₁₀:


Now, the values in Fig. 3 and Fig. 2 come from the slope and intercept, respectively, of equation (1) fitted to the same data. So I don't know why they didn't put error bars on this second graph or why they drew such a wacky line through the data points, since they didn't have Excel with 'draw a stupid non-physical line through the points' as a default option.

Paper 2: When they were sailing near Block Island this same group of scientists also did some more experiments where they poured oil on troubled water and took the same measurements, which they reported in another paper. This paper only has a graph for z₀ vs U₁₀:

And here they have only shown the trend line for the non-oil data because this paper was concentrating on explaining the oil data. They explained the difference between the oil data and the non-oil data using one model and not long afterward another scientist put out a paper (in Science, so no slouch of a paper) giving a different explanation for the difference.

Paper 3 (Science): The data presented in this paper (and cited as coming from Paper 2) looked like this:

Note that the data points that are from Paper 2 are exactly the same, but the data points that are not actually shown in Paper 2 (and are presumably from Paper 1) have wobbled around quite a bit. Paper 3 doesn't say so, but it is possible that all the points in these two plots that aren't the published points from Paper 2 come from the data used in Paper 2 but not shown (and hence for the no-oil curve, the same as Paper 1) Note that the positions of the open circles in the open circles in the z₀ graph are actually quite different between Paper 1 and Paper 3, which suggests to me that the author of Paper 3 got hold of the raw U(z) plots for Paper 1 and re-fit them to the first equation we thought of.

Paper 4: Now for the fun part. This is from a much more recent review paper.

Exhibit 1:
This is cited as being 'after Paper 1 and Paper 2'. Sure enough, it is the data from Paper 2. But it isn't the data from Paper 1. It's the silly fitted line shown in Paper 2 with spurious data points added in crayon! How lame is that?

Exhibit 2:

This is reported as being 'data collected by [author of Paper 3] (after Paper 3)', as if it is a totally independent experiment!

...


This sort of thing could have been avoided if people in earlier decades had the ability to scan papers they were interested in and cut and paste bits of screenshots of them, like I've been doing.

FWIW this is what I reckon the curves should look like, drawn on the figures sourced from Paper 3 as they appear in Paper 4 - suspect points flagged from having big error bars and lying way off the U* trend-line as reported in Paper 1:

"Any unauthorised use is strictly prohibited"

Here is a totally unauthorised reproduction of a seminar notice from the University of Sydney. It seems to describe a philosophical goal devoutly to be wished, with which I am in complete agreement:

SCHOOL OF PHYSICS COLLOQUIUM

http://www.physics.usyd.edu.au/local/coll

Monday 17th May, 2010 at 3:15 pm

refreshments from 3pm

Venue: Slade Lecture Theatre, School of Physics

Title: Quantum foundations research @ Sydney

Presenter: A/Prof. Stephen Bartlett

University of Sydney

Abstract:

Despite a century of development since Einstein's explanation of the photoelectric effect, the foundations of quantum physics remain mysterious and surprising. Rather than accept the strangeness of quantum physics as a necessary evil, the research group in Quantum Foundations here at the University of Sydney is attempting to uncover the meaning and interpretation of the mathematical structure of quantum physics in terms of understandable concepts based on an external reality.

In this talk, I'll provide an introduction and overview of the Quantum Foundations research group here at Sydney, which includes researchers in Physics, Philosophy and HPS as well as a large-scale collaboration - the Perimeter Institute-Australia Foundations (PIAF) project.



The email concluded: "This email plus any attachments to it are confidential. Any unauthorised use is strictly prohibited."

So come and get me, seminar programme Nazis. :(

Red Mars, p.211

On re-reading Red Mars after more than a decade, I have been struck with how strongly 'red' my sympathies are. I don't remember feeling strongly one way or another when I first read the book. Now the prevailing mood among the first hundred Martians to begin terraforming immediately seems appallingly reckless to me, and I find myself in complete agreement with Ann Claiborne:

'Here you sit in your little holes running your little experiments, making things like kids with a chemistry set in the basement, while the whole time an entire world sits outside your door. A world where the landforms are a hundred times larger than their equivalents on Earth, and a thousand times older, with evidence concerning the beginning of the solar system scattered all over, as well as the whole history of the planet, scarcely changed in the last billion years. And you're going to wreck it all. And without ever honestly admitting what you're doing, either. Because we could live here and study the planet without changing it - we could do that with very little harm or even inconvenience to ourselves. All this talk of radiation is bullshit and you know it. There's simply not a high enough level to justify this mass alteration of the environment. You want to do that because you think you can. You want to try it out and see- as if this were some big sandbox for you to build castles in. A big Mars jar! You find your justifications where you can, but it's bad faith, and its not science.'


On page 173, the explorers find it 'startling in the extreme' to run across the tongue of a glacier, looking like a big white Uluru, even though they knew it would be there. I'm afraid they won't find anything startling, because they will have Google Mars.


Dunes in the Vastitas Borealis - let's not drown them just yet!


Of course, there isn't nearly enough water to do so- only 820,000 km³ or so.



Some changes we've made to the surface of Mars already- rover tracks on the edge of Victoria Crater:

Happy Happy Joy Joy

Just thought I should say something about Peter Garrett blocking the Traveston Dam. This is a good, good, good, good thing. The Australian Lungfish is a species of global importance that we have a duty to look after. We make do at my place with the water that falls on our house and shed, and all those people in Southeast Queensland ought to do the same. Plants that won't thrive on rainwater have no place in Australian gardens.

Anyway, if Queenslanders want to be profligate, we have plenty of perfectly fine rivers in Northern New South Wales that we could dam to collect water to sell them...

Glass half full...

The system for electronic submission and return of assignments that came in this year is beset with all the usual follies and aggravations of new technology, but I have just made a jpeg to use in marking assignments that I am looking forward to using:

On trying to read Schopenhauer

Earlier this year Klaus Rohde made a number of posts about the ideas of Schopenhauer, the famous philosopher. I read one of the essays Klaus recommended on Schopenhauer’s thought and wrote a response to it.

I also read a book of extracts from Schopenhauer's ‘Parerga and Paralipomena’ in English and wrote two documents outlining some of the places where I agreed with what Schopenhauer said in the extracts, and some of the places where I disagreed with him.

But Schopenhauer wrote a magnum opus- practically the archetype of the magnum opus- outlining his mature thought, ‘The World as Will and Appearance’, which takes up three volumes in our library, and to argue about what he thought without reading it is really very lazy. So I thought I would have a go. I got out volume one, skipped the preface, and started wading in.

Unfortunately I did not get very far. And oddly enough I got hung up at the same point that a friend of mine got hung up on at the onset of ‘Mere Christianity’, by C. S. Lewis, when I lent it to him as an undergraduate. I rejected Schopenhauer’s initial argument, the foundation of the whole three volumes. The ‘oddly enough’ is because it was the identical initial argument of ‘Mere Christianity’- the assertion that consciousness is inexplicable by materialism. Lewis argues that consciousness is an irruption of the supernatural other into the natural universe, and from that goes on the derive Christianity; Schopenhauer argues that consciousness is the fundamental fact of the universe, the ultimate reality that generates the world of appearances around us, and that data from that world of appearances cannot explain consciousness.

I reject solipsism- the argument that the only data point I have is my own consciousness, therefore only I exist- because it is fruitless; you can’t do anything with it. It is an idea that leads nowhere and achieves nothing.

The idea that consciousness in general, as opposed to ‘my consciousness’ is the fundamental fact of the universe requires the existence of other minds.

How do we know these other minds exist? By observations we make of the world of appearances. So we must base our understanding of mind in general not only on the one data point we truly have access to, inside our own heads, but on how we observe mind to be manifested in space and time within this world of appearances. I think we cannot do this and fail to observe that mind is an emergent property. There is no sudden transition from things that are conscious to things that are not. We see insects displaying apparently conscious behaviour that we can model with a simple circuit. As we traverse the angora shawl of being*, more and more complex organisms display more and more complex behaviours, which we can explain more and more tentatively in terms of mechanistic inputs producing certain outputs. Eventually we get to us. Made out of the same kind of stuff, with a nervous system obviously just a more complicated version of the same nervous system the bugs have.

I think consciousness is just what a system of registering and reacting to sense impressions looks like from inside. A simple system, where we can see and understand that it is completely deterministic, might still feel like something from the inside. It might feel, to the moth, as if it chooses to dive toward the light.

It feels to me that I am composed of sense impressions and memories of sense impressions, and that there is nothing else. This no longer bothers me. (Of course you can come back and say: ‘Who is this ‘me’ who is feeling, Chris? Who is this ‘me’ who is no longer bothered?’ But this I will reject as mere semantic gymnastics, arguing about words rather than things.)

So I reject Schopenhauer’s fundamental division of the world into Mind and Matter. Solipsism is not rendered less vacuous and fruitless if Will, some fundamental thing underlying all consciousness, replaces my individual consciousness.

I went back some months later and had another go at ‘The World as Will and Appearance’. This time, I tried to do things properly and started with the preface. It reminded my strongly of the pretentious author’s note quoted in ‘Ghastly Beyond Belief’”:

Author's note: It is suggested that the reader not attempt to read this book at one sitting. The intellectual content of these stories, taken without break, may cause brain damage. This note is intended most sincerely, and not as hyperbole.

ARTHUR BYRON COVER, The Platypus of Doom and Other Nihilists

Really. Schopenhauer says that the entire book of ‘The World as Will and Appearance’ was the shortest way he could find to write what he wanted to say, that it was impossible to summarise, and that I would have to read the whole thing to grasp his idea. Now, I am not of the opinion that every idea can be squeezed into a thirty-second soundbite, but this seems to me just a teensy bit ridiculous. All the really big ideas that really are ideas can be squeezed down into something small enough for us to get our heads around. This does not mean that there are not lifetimes of work in unpacking everything that is involved with and implied by

‘It is impossible to convert heat completely into work in a cyclic process.’

Or

‘Do unto others as you would have them do unto you’

Or

‘The square on the hypotenuse is equal to the sum of the squares on the other two sides’

…but all these really big ideas can be expressed in a few little words. Claiming that your idea is bigger than all these ideas is up there on the angora shawl of pretentiousness with Mr Cover and his Platypus of Doom.

The other thing Schopenhauer told me in the preface was that ‘The World as Will and Appearance’ was intended as an extended gloss on his earlier essay, ‘On the Fourfold Root of the Principle of Sufficient Reason’, and should be read in conjunction with it, and that it was useless- Useless, I tell you! – to read his magnum opus without having first read ‘On the Fourfold Root of the Principle of Sufficient Reason’. I dutifully went back to the library to find it. But it was not there.

Right next to the works of Schopenhauer that were on the shelf was a slim book by Schrödinger, ‘My View of the World’. I took it home as a consolation prize.

Curiously, I found that it was not only next to Schopenhauer in alphabetical space, but in idea space. It contained what appeared to me to be practically the same Vedic philosophy of the primacy of mind.

He says, in a fine and honest way in his opening remarks, that there is very little about physics in his book, and that is because he came to his ideas about the nature of reality before he ever got into quantum mechanics: he was already marinated in the same ancient Hindu ideas that Schopenhauer had discovered and embraced so enthusiastically. I have taken the book back to the library already, so I can’t quote you the quote I wanted to quote you,*** but Wikipedia tells me: ‘At an early age, Schrödinger was strongly influenced by Schopenhauer. As a result of his extensive reading of Schopenhauer's works, he became deeply interested throughout his life in color theory, philosophy, perception, and eastern religion, especially Vedanta.’

Schrödinger did not ‘discover’ all the New Agey hippy-dippiness in Quantum Mechanics; he brought it with him. It was part of his worldview while he was figuring things out about the world of appearances, and he fit them in where they fit in his personal philosophy - and there we have one root of the muddle we are in now.

So I still have not read Schopenhauer’s Magnum Opus. Which is sad, since as Schrödinger says in a possibly apocryphal quote I found on the web just now: ‘If you cannot - in the long run - tell everyone what you have been doing, your doing has been worthless.’ I have not given up. But I have gathered enough, I think, to sum up my disagreement with Schopenhauer in a table contrasting him with the most useful and clear-headed philosopher since Aristotle and my personal favourite, 'the one American philosopher that could sing outdoors', Charles Sanders Peirce**:

*: This is my ad hoc replacement for the ‘chain’ or ‘ladder’ of being, which is what I really want to say, but which I am too conditioned by my reading of Stephen Jay Gould to dream of saying.

**: I have doctored this Hilaire Belloc poem to show you how to pronounce his name, in case you don't know:

***: Actually, I didn't take it back to the library, I lost it on my own bookshelves! Here is the quote: Not a word here is said of acausality, wave mechanics, indeterminacy relations, complementarity, an expanding universe, continuous creation, etc. ... On this I can cheerfully justify myself: because I do not think that these things have as much connection as is currently supposed with a philosophical view of the world. ... In 1918, when I was thirty-one, I had good reason to expect a chair of theoretical physics at Czernowitz ... I was prepared to do a good job lecturing on theoretical physics ... but for the rest, to devote myself to philosophy, being deeply imbued at the time with the writings of Spinoza, Schopenhauer, Mach, Richard Semon and Richard Avenarius.

Once more with the splendour of the historical sciences!

Last week or the week before I went to the niftiest seminar I have been to for a long time. It was by Prof Ian Metcalfe, who is a master of conodont lore- conodonts being the premier biostratigraphic animal. If you know enough about conodonts, and you are lucky enough to find enough conodonts, you can tell when a stratum of rock was laid down and what biogeographic province it belonged to, over a vast range of space and time. And the degree of detail that is possible with these little guys was enough for Prof Metcalfe to deconvolute the whole extraordinarily complex geological history of Southeast Asia, which is basically a matter of bits breaking of of Gondwanaland and different times and sailing away north and mashing into the ancient subcontinents of Siberia and Kazakhstan.

I remember one thing that struck me forcefully, long ago, in the writings of Stephen Jay Gould, was all the ancient oceans that we would never know anything about, because they were subducted away completely- all those primordial analogues of the Hawaiian islands, with their unique fauna and flora, irrevocably lost.

But not always! That was the most impressive bit of Prof Metcalfe's talk for me. I have pinched one of his figures so I can show you, as like me you are probably too lazy to follow the link.



In between the dark orange Sibumasu block that used to be part of the Cimmerian Continent and the pink bit that is the mashed remains of the ancient archipelago of Cathaysialand, there runs an ancient biogeographic divide: at the same time in prehistory, the fauna on one side was quite different from the fauna on the other side. And mashed up in between those two blocks are sediments that are the remains of the Palaeo-Tethys ocean. Not all subducted away! Some of it is still there, enough of the ocean for us to tell a lot about its history and the sort of things that lived there, in a kind of Reader's Digest condensed version squashed into a discontinuous squiggle across central Thailand. I think that is so cool...

Could be a coincidence...

There are, after all, only about 200 gazillion Facebook users, and the name might be as common in Chennai as 'Kylie Smith'. But I have deactivated my Facebook account (not in my real name, 'Wayne' and 'Nick'! :p ) anyway. Since otherwise to make that 'friend suggestion' Facebook would have had to have found out who I really am from my email address, then collected earlier email addresses belonging to me, and looked up users whose names appeared in lists with those earlier email addresses. Probably a long bow to draw. Such omnipotent data-trawling AI's probably have less frivolous things to do. More likely a coincidence. Freaky anyway.

My brother is participating in Movember, I am sure he would be pleased if you clicked the link and made a donation. I am too far gone, as you probably know, and am now only eligible for 'Look-like-the-unabomber-ovember'...

Think. Quantitatively.

Every year I tell my students something like: ‘When you finish any calculation in physical chemistry, have a look at the number you have ended up with and see if it is a reasonable number. Is it about the size you would expect? If it isn’t, go back and find the mistake. If you are in an exam and pressed for time, write: ‘I know this number is the wrong size, but I can’t find where I went wrong.’ Or, just change the order of magnitude to the order of magnitude it ought to be, and hope I don’t read your working carefully.’

Every year, I get more cautionary tales to tell my students when I tell them this- assignments I have received with chemical bonds blithely reported as longer than the distance from here to Alpha Centauri, molecules heavier than the Sun, energies for chemical reactions greater than the annual output of all the power plants in Europe.

The chapter ‘The Spur of the Moment’ of Kim Stanley Robinson's book 'Green Mars' is about a project to build a sea in Hellas Planitia in the southern hemisphere of Mars, a sea that is quoted as being ‘1000 by 300 km’. It order to give the project verisimilitude, numbers for amounts of water are quoted throughout the chapter.


p.400:

It was a running river, in an obviously riverine valley, placid in some places, agitated in others, with gravel fords, sandbars, braided sections, crumbling lemniscate islands, there a big deep lazy oxbow, frequent rapids, and far upstream, a couple of small falls. Under the tallest waterfall they could see the pink foam turn almost white, and patches of white were then carried downstream, to catch on boulders and snags sticking out from the bank.

‘Dao River,’ Diana said. ‘Also called the Ruby River by the people who live there.’

‘How many are there?’

‘A few thousand. … Upstream there are family homesteads and the like. And of course then the aquifer station at the head of the canyon, where a few hundred of them work.’

‘It’s one of the biggest aquifers?’

‘Yes. About three million cubic metres of water. So we’re pumping it out at a flow rate- well, you see it there. About a hundred thousand cubic metres a year.’

10⁵ m³ per year = 274 m³ per day = 3 litres per second

To put this number in perspective:
“Older firehoses with 2.5 inch diameter equipped with a 1.5 inch nozzle can typically deliver 20-40 litres of water per second” (Physics of Continuous Matter: Exotic and Everyday Phenomena in the Macroscopic World, Benny Lautrup)

I suppose the description of the river *could* apply to something that one could easily step over, but I do not think this was the author’s intention.


p.416

One day at the office, news came in from the Hellespontus. They had discovered a new aquifer, very deep compared to the others, very far away from the basin, and very big. Diana speculated that earlier glacial ages had run west off the Hellespontus range, and come to rest out there, underground- some twelve million cubic meters, more than any other aquifer, raising the amount of located water from 80 % to 120% of the amount needed to fill the basin to the -1-kilometer contour.


Let’s see, the Hellas Planitia basin is quoted as being 1000 by 300 km. That’s an area of 10⁶ m × 3 × 10⁵ m, or 300 billion square metres.

Twelve million cubic metres would cover 300 billion square metres to a depth of

1.2 × 10⁷ m³ / 3 × 10¹¹ m²

= 4 × 10^-5 m.

40 microns.

So if this raises the amount of located water from 80 % to 120 %, at a first approximation the Hellas Sea will be 0.12 mm deep.

I confess myself unimpressed by this feat of areological engineering.

I expect KSR made the common undergraduate mistake of assuming
1000 cubic metres = 1 cubic kilometre. I wonder if the numbers have been corrected in later printings?

Green Mars, p.346

My favourite bit so far has been the chapter 'The Scientist as Hero'. Unfortunately, from time to time poor Sax is set up as a bit of reductionist straw man. Take this exchange, from the beginning of the chapter 'Social Engineering', where Saxifrage Russell is talking to a hippy-dippy psychologist type:


There is a drive towards complexification that is directly opposed to the physical law of entropy. Why should that be?

I don’t know.

Why do you dislike it so when you can’t say why?

I don’t know.

This mystery of life is a holy thing. It is our freedom. We have shot out of physical reality, we exist in a kind of godlike freedom, and the mystery is integral to it.

No. We are still physical reality. Atoms in their rounds. Determined on most scales, random on some others.

Ah well. We disagree. But either way, the scientist’s job is to explore everything. No matter the difficulties! To stay open, to accept ambiguity…



I've written some new lines for Sax. I reckon it should go like this:

There is a drive towards complexification that is directly opposed to the physical law of entropy. Why should that be?

There isn’t a drive towards complexification. There’s a drive towards differentiation, a drive which is basically the same as the physical law of entropy. You have just selected your data to focus on the end of the bell curve where complex things are happening, ignoring the fact that the curve is getting bigger and broader all the time.

Well, you’re entitled to your opinion. But I think your view saps all the mystery out of the universe. This mystery of life is a holy thing. It is our freedom. We have shot out of physical reality, we exist in a kind of godlike freedom, and the mystery is integral to it.

Why are you so eager to call everything you don’t understand ‘a mystery’?

Its not that I’m eager, it’s just that I feel there’s more to life than can be explained by physical science.

Why don’t you stop feeling, and try thinking, instead? What if the mystery is just an artifact of your imperfect understanding? What if the mystery, and the ‘godlike freedom’ just exist in your head? And what exactly do you mean by ‘shot out of physical reality’? You should define your terms.

Ah, my friend, don’t be mean! We disagree. But either way, the scientist’s job is to explore everything…

Green Mars, pp.135, 177, 251-253

One problem with schemes for the terraforming of Mars is the need for a source of an inert gas to give an atmosphere of similar composition to Earth. A higher partial pressure of oxygen than we have here would ‘vigorously accelerate combustion’, tend to intoxicate us, and make technological civilisation impossible, while a much lower total atmospheric pressure would not be able to support Earth-like weather. The partial pressure of oxygen required to support combustion declines with declining total pressure, so even this lower total atmospheric pressure option might be dangerously combustible if it had enough oxygen present to support life. So, where is this inert gas to come from?

Getting nitrogen from Titan won’t stand up to any sort of cost-benefit analysis.

There are unlikely to be enough noble gases trapped deep underground from radioactive decay to amount to a hill of beans.

Thus, it has been suggested that molecular nitrogen could be obtained by ‘burning nitrates’, which seem to be present (or may be present) in considerable amounts in the Martian crust.

However, simply heating nitrates will not be very effective as a way to ‘dilute’ oxygen. For instance:

2Na(NO₃)₂ + heat → 2NaNO₂ + O₂

2NaNO₂ + more heat → Na₂O + NO + NO₂

2Ca(NO₃)₂ + heat → 2CaO + O₂ + 4NO₂

Thus ‘burning’ nitrates generates lots of toxic gas, and some extra oxygen.

Of course, with more energy input:

2NO₂ + much more heat → N₂ + 2O₂

So we have got some nitrogen eventually, but at a cost of 2.5 oxygen molecules per nitrogen molecule.

If we don’t want to add lots of extra oxygen to the atmosphere, we will have to add a reducing agent instead, and do something more like ‘burning’ . On Earth, if we had lots of extra nitrogen dioxide we wanted to get rid of, we would do something like:

NO₂ + 2H₂ → N₂ + 2H₂O

Or

NO₂ + C → N₂ + CO₂

Or more realistically, something like

4NO₂ + C₃H₈ → 3CO₂ + 4H₂O + 2N₂

The problem is that there is not a lot of carbon or hydrogen on Mars that is not already incorporated in carbon dioxide or water. I haven’t googled to find out how much hydrogen has been located/postulated on Mars, but a crude atom balance suggests that if we want to burn nitrates with enough hydrogen to generate one nitrogen atmosphere, we need to burn at least two whole hydrogen atmospheres. I don’t think this is available, it would surely have outgassed long ago. I have found references to methane clathrates on Mars, which may be there in similar amounts to the nitrates (perhaps) and would allow the reaction

2NO₂ + CH₄ → CO₂ + 2H₂O + N₂

The problem here is that it would be a very significant bit of geo-engineering to mine the methane and get it to the nitrates, or vice versa, and we are adding to the carbon dioxide load that we need to get rid of later.

So what other reducing agents are available? I suggest that much more cost-effective than bringing nitrogen from Titan would be to bring down some Iron-Nickel asteroids and rust them in nitrogen dioxide. The mass that would be transported would be much larger, but the distance would be much shorter, and there would be no need to do any complicated collection and packaging and transport, just provide the right nudge of energy to send the asteroid on a collision course with Mars.

The following reaction is certainly thermodynamically favourable, though I don’t have an idea of what its activation energy might be:

6NO₂ + 8Fe → 3N₂ + 4Fe₂O₃

While this uses considerably more mass of reductant to produce the same amount of nitrogen than methane would, instead of having to be painstakingly mined and collected like the methane, the asteroids could be crashed down into the nitrate deposits in one foul swoop. The reaction does not produce any extra carbon dioxide that will need to be scrubbed out later.