HUNGARY has produced many outstanding mathematicians and physicists. Perhaps there is a connection with rampant violin playing.
One of these was Paul Erdös who was the twentieth century’s most prolific mathematician, with 1475 papers to his credit. He rivals Leonhard Euler, the Swiss genius of the eighteenth century. There is a worthwhile biography of Erdös called ‘The Man Who Loved Only Numbers’, by Paul Hoffman (1998).
On a recent thread at this blog (Wise Men Excluded from Bushfire Royal Commission), I raised the issue of fuel connectivity, and suggested that it helped to explain the uncontrollable spread of bushfires over large areas of Victoria a few months ago.
The tonnage of available fuel determines the intensity, and convection column strength, and the number of flying embers, but connectivity determines ground spread. Wind is important, but large fires, of course, create their own wind. It seems to me that the application of Occam’s Razor makes climate superfluous to the argument, beyond there being weather dry enough for a fire to burn. Given dry fuel, fierce fires can occur even at mild temperatures. Surely we have all lit a pot-belly stove on a winter’s day.
Although I doubt if he had ever seen a bushfire, or a gumtree, Erdös had useful ideas on connectivity in networks. With a Hungarian colleague, he published papers about ‘giant patches’. These form when random connections are made between a set of random points (Erdös and Renyi 1959, 1960).
The idea of networks (connected graphs) originated, in Europe at any rate, with Euler, when he solved the puzzle of the seven Bridges of Königsberg. Recent applications have been in neural networks in the brain, disease epidemics, and the growth of the world wide web. ‘Six degrees of separation’ may ring a bell for some.
With regard to bushfire, as fire is excluded from a large area, formerly disconnected fuel patches join up, and this process suddenly accelerates as ‘cliques’ of patches start connecting. Some have called this phenomenon a ‘connectivity avalanche’. Once a certain threshold is passed, bushfire can spread uncontrollably. Ember showers, due to heavy fuel burning, can obviously accelerate the process by causing another level of connectivity.
I give this information for those constructive contributors who are interested in ideas about bushfire management. Probably I should publish it quickly before someone from academia claims it. Those involved in research will know the sequence: a) Rubbish, b) Well, perhaps in some cases, c) Of course, and I thought of it first.
Fuel reduction burning reduces both fuel quantity, and, importantly, connectivity. The restoration of something like Aboriginal patch burning, by both reducing fuel, and disrupting connectivity, would make large bushfires a thing of the past, no matter what the weather. The bush would be healthier, and safer for native animals, not to mention humans. Should I mention erosion and water supplies? Or the fact that mild fires sequester enormous amounts of carbon as charcoal, but very hot fires create mainly ash, and volatilize much of the nutrients?
*******************
David Ward lives in Western Australia and comments at this blog under the alias ‘Green Davey’.
The picture is of grass trees at Scott River, Western Australia, taken in January 2007, following a “mild, patchy burn”.
Previous contributions from Mr Ward include:
Nyoongars, Noolbengers and No Fires
http://jennifermarohasy.com/blog/2007/02/nyoongars-noolbengers-and-no-fires-a-note-from-david-ward/
Parachutes & Prescribed Burning
http://jennifermarohasy.com/blog/2007/01/parachutes-prescribed-burning-a-note-from-david-ward/
Noongars Knew Best (Part 2)
http://jennifermarohasy.com/blog/2005/09/noongars-knew-best-part-2/
Noongars Knew Best
http://jennifermarohasy.com/blog/2005/06/noongars-knew-best/
Jennifer Marohasy BSc PhD is a critical thinker with expertise in the scientific method.
Paul Erdös is an incredibly respected mathematician.
i really beg you, don t connect him to the false claims about the australian fires that you are about to make…
“It seems to me that the application of Occam’s Razor makes climate superfluous to the argument, beyond there being weather dry enough for a fire to burn. Given dry fuel, fierce fires can occur even at mild temperatures. Surely we have all lit a pot-belly stove on a winter’s day.”
About as unscientific a statement as you can make.
If Erdos was the respected mathematician that both Sod and Dave claim he was, then to find an association between Erdos’ theory of connectivity and an event in nature is to praise Erdos, to recognise the reach of his mathematics into natural events.
I might suggest Sod that your response is an attempt to cling to your own theory about the reasons for Victoria’s repeated cataclysmic fires events and not let the brilliance of Erdos show, not because you wish Erdos’ reputation any harm, but because you don’t want to see your preferred theories challenged by the work of Erdos.
I suspect Dave is well ahead of you on this one, and Erdos’ legacy is probably well ahead of us all.
Given dry fuel, fierce fires can occur even at mild temperatures. Surely we have all lit a pot-belly stove on a winter’s day.”
SJT summed it up nice enough above: About as unscientific a statement as you can make.
again, please leave Erdös out of this.
ps: you don t get an Erdös number, by forcing him into papers you write..
The physical nature of Eucalypt forests defies the notion that we could manipulate a physical threshold of “connectivity”.
Climate, weather and fuel (in managed or un-managed forest) all conspire against any idea that we can manage fuel “connectivity”. The way the ’09 fires jumped roads, highways, grass, stubble, bare earth and fire breaks would suggest that, regardless of Erdos’ genius, his theory is not practical or applicable in the Australian context.
We either accept that our forests have aspects that are beyond human control or we do away with forests altogether. My hunch is that common sense will result in the former view holding sway.
The only way to pin the fires on Industrial-CO2 is by suggesting that there IS no public policy and that we are all helpless baboons in the face of the knowledge of the wonderment and righteousness of the CO2 fertilisation effect.
If our policy makers are in fact such baboons they ought to relinquish their hold on policy and be true to themselves and become low-paid sex workers.
The issue is quite simple. An landowner has to make sure bad things from his own property don’t spill over to his neighbour. And this really sets the limit to unnowned land. If the government wants to own land, or to declare the land not viable for private ownership, and there are many good reasons to do this…. but if they want to do this they ought to take responsibility for disasters coming from their turf.
And in lieu of them being able to make up for their failure some resignations would be appreciated. If there are enough resignations there won’t need to be all that many prosecutions.
Good article, Davey, and most befitting your namesake. Connectivity goes to the very heart of the bushfire problem. As I said of Andrew Campbell on February 28th, 2009 in the thread below http://jennifermarohasy.com/blog/2009/02/the-humble-axe-and-chainsaw/?cp=all
“As a promoter of Landcare, Campbell has a huge emotional investment in the canopy connection fetish, as described in my post above.”
Indeed, the entire thrust of landcare, the $ 1 billion Natural Heritage Trust, and all related policies in respect of vegetation on private land for more than two decades has been to maximise the connectivity of native vegetation. In Victoria, many parts of NSW, and now Queensland, this has extended to the banning of pasture maintenance activities that involve the removal of native regrowth. And on all but the smallest rural holdings this has effectively precluded the removal of woody weeds that usually dominate sites where regrowth is also present.
So little wonder that our resident establishment apologistas are so keen to ensure that such intellectual traction as that provided by Erdos is left out of the picture.
The shere volume of government literature, in the form of policies, targets, promotional material and funding guidelines cannot be swept under the carpet. Attaching one clump of trees to another clump of trees by way of more trees has been the holy grail of the green dominated landscape policy. This has been assumed to be a “public good” in its own right without any serious regard for the species that use those forest clumps or the size of the gaps in clumps that those species routinely incorporate into their home range.
Yet, local lists of relevant threatened species almost invariably reveal few species, if any, that are not capable of taking a 200m to 1000m gap in their stride. The birds are clearly not adversely impacted, nor are the grassland mamals. The amphibians get their connectivity along creek lines, as do the aquatic species. And this leaves us with a few ground dwelling skinks who traverse the landcape under a connected canopy of bark or grasses.
Species willingness to cross gaps is heightened during mating season and it prompts reflection on the sometimes extraordinary lengths to which unattached members of our own species will go to ‘get laid’.
But no-one within the established policy clique has ever bothered to question the importance of this connectivity fetish if it is not even relevant to our most threatened species. And if the current claimed lack of connectivity is of minimal relevance to our most threatened species then it cannot possibly pose a danger to all the other species that are not threatened.
In fact, as Erdos has provided us with the tools to demonstrate, it is that very connectivity fetish, on the part of green dominated government, that has contributed so much to the very sorry state of wildlife and their habitat over vast areas of so-called ‘protected’ vegetation.
And Campbell has the gall to accuse his critics of being “ecologically illiterate” and to mutter his vague cautions against “perverse outcomes”.
Jennifer,
The two seminal references you requested are:
Erdos, P. and Renyi, A. (1959) On random graphs. Publ. Math. Debrecen 6:290-297
Erdos, P. and Renyi, A. (1960) On the evolution of random graphs. Publ. Math. Inst. Hungar. Acad. Sci. 5:17-61.
These are hard to access (for me at least), so I have relied on interpretation by one of Erdos’ colleagues, Professor Bela Bolobas (Random Graphs 2001 Cambridge Uni Press). There is ample material on the internet. If anyone knows how to get at the original papers let me know.
The rapid and ridiculous attacks by Sod, SJT and RWFOH suggest that I have rattled their cages. On another thread it was obvious that RWFOH had not heard of Erdos, and tried to bluster. That’s why I have offered some information. However, the truth is often painful.
Contrary to SJT’s gibberish, it is perfectly scientific to say that ambient temperature does not, directly, affect bushfire behaviour. A pot belly burning briskly on a frosty morning is proof of that. Temperature can, of course, affect both fuel and air moisture content, which does directly affect fire behaviour. S,S & R need to get their thinking straight on that. Oxygen is involved. As suggested before, they should all join their local fire brigade, and learn about bushfire reality.
I have some mathematical background, and have also attended, observed, and fought many bushfires. I believe Boxer has a similar practical background on bushfire, and I thank him for his support.
From my own field observation over 40 years, the ideas of Erdos and Renyi on ‘giant patch’ formation are clearly applicable to connectivity between patches of fuel in a landscape, although the matter can be short-circuited by ember blizzards.
From TV images, it appears to me that most (all?) of the houses lost in Victoria were ignited by intense ember blizzards, or burning gas clouds. Ditto for Canberra a few years before, Hobart in 1967, and Dwellingup in 1961. Major ember blizzards and burning gas balls only occur when fuel is both heavy, and dry. That is why regular, broadscale, prescribed burning, in a disconnected mosaic pattern, is essential if we want to avoid repetitions of the recent holocaust.
That’s the plain truth, and I don’t care how painful, or annoying it is to the likes of Sod, SJT, and What’s-‘is-name. Their opinions on bushfire are unqualified and irrelevant. They are like traffic wardens trying to solve a murder.
P.S. How is the ‘biodiversity’ (biota?) in Bunyip State Park after long fire exclusion, followed by a complete burnout?
There is a delightful elegance in Erdos’ work, and that is accentuated when one relates it to the real world and its problems.
The ridiculous and pompous plea from ‘sod’ marks him as a person with little appreciation or understanding of Erdos. He has undoubtedly been told to ‘sod off ‘by others, but let me add my encouragement!
David
Although I doubt if he had ever seen a bushfire, or a gumtree, Erdös had …
Actually, you’re wrong there. From an >a href=”http://www.gap-system.org/~history/Printonly/Mahler.html”>obituary of Kurt Mahler:
Erdös writes [4]:-
I visited Australia fairly often and of course always visited Mahler in Canberra. We had many mathematical discussions but he could no longer walk a great deal. I was in Australia for over two months early in 1988 and in Canberra in February. I had dinner and lunch with Mahler at University House and met him in the Department of Mathematics of the Institute for Advanced Studies. He was clearly frail but I did not expect that the end was so near.
I went to a talk that he gave on his 1988 visit.
I don’t think much of your Erdos theory, and even less of this:
It seems to me that the application of Occam’s Razor makes climate superfluous to the argument, beyond there being weather dry enough for a fire to burn.
I don’t think you’ll have much luck convincing people that climate is superfluous, when the three mega-fires of the last century in Vic occurred on three of the very hottest days.
Ian,
Obviously I agree with you that fuel connectivity is right at the heart of bushfire behaviour. Apologies that I had missed your previous post on the subject, being out of the country at the time.
A member of an original settler family (1830s) at Pinjarra (WA) once told me that, before the 1920s, fire rarely ran up the jarrah stems, because frequent burning (2-4 years) constantly removed the bark ‘whiskers’. This vertical fuel connectivity is another aspect. The role of ‘fuel ladders’ is well known to any fire-fighter. Jarrah bark is only slightly stringy, and obviously there is an even greater threat with eastern state stringybarks.
He also mentioned that the jarrah forest was much greener then. This agrees with the comments of Baron Von Mueller in 1879 (?) when he described the jarrah forest as ‘ever verdant’, despite the frequent fires at that time.
Nick,
Thanks for your comments. I know Paul Erdos visited Australia. He was at UWA in the 1980s so he probably did see a gumtree or two, although I doubt if he saw a bushfire, and certainly did not attend one in an operational mode. It does not matter whether he saw a gumtree, or a bushfire, or not. His ‘giant patch’ notion is still highly relevant to giant fuel patch formation, and I stick by that.
In eucalypt forest, as time goes on after a fire, there is an ‘avalanche’ of fuel patch connectivity, due to heavy summer leaf fall, which is not matched by decay. Jarrah forest will carry a mild fire at 2-4 years, and the litter under the marri trees on my hills block would carry a fire every year if I did not rake up. The fire at Karagullen a few years back was the result of 20 y.o. fuel, highly connected in the horizontal sense, and connected vertically by loose bark on the trees, and leaf litter suspended in the shrub layer.
So fuel connectivity is, in my humble opinion, of direct relevance, and so are Erdos’ papers on patch formation in random graphs, whether two, or three dimensional.
Also, bushfires certainly do occur in hot weather, but that is because of the dryness, not directly the heat. Attributing bushfire ferocity directly to temperature is classic false ‘post hoc, ergo propter hoc’. Very fierce fires can occur in autumn, under relatively mild conditions, because the litter is dry.
The Mt Cooke fire, south of Perth, was one of the fiercest on record in recent times. If I remember rightly, the maximum temperature on the day was quite mild. Have a look at the BushFire Front website for a photo. On the internet there may also be an article by Neil Burrows, of DEC. How many ‘old growth’ trees were killed outright? Fuel quantity, dryness, and connectivity were the central issues there, not temperature.
Green Davey,
I have no problem with prescribed burns. However I do have a peculiar hang-up. I believe that poor writing usually reflects poor analytical abilities.
Yes, I’ll take your word for it that Erdos was interested in connectivity. But is it the same kind of connectivity that you’re talking about? I haven’t the foggiest, and neither do you.
It would have been helpful to name at least one of Erdos’ theorems, and to show how it applies to prescribed burns. It’s fairly obvious that name-dropping was your primary motivation for mentioning Erdos. There was zero “connectivity” between the name-dropping and the points that you were trying to make.
This is a very important issue that you have raised, Davey. The entire green movement have embraced Erdos’ thinking in respect of the beneficial and synergistic outcomes of habitat connection but they are in complete denial of the relevance of this same concept in minimising the adverse impacts of wildfire.
And even this denial is highly selective. We have seen no shortage of references to “tipping points” to describe a critical point at which an accumulation of adverse impacts might, for example, speed up the rate of Greenland ice sheet melting. And respected ecological figures like Archer have also expressed concern that an accumulation of reductions in connectivity could also reach a point where “species collapse” could take place.
So the policy mandarins have accepted Erdos’ thinking in both the positive and negative sense for just about every single ecological phenomenon except wildfire. Indeed, the arguments put forward by Campbell et al, with his vague warnings of “perverse outcomes” from an accumulation of undefined fuel reduction burning outcomes, all include an implied application of Erdos’ accumulation of adverse connections.
These people’s minds are so twisted by murderous green ideology that they can accept this well established mathematical tool when debating the impacts of infrequent mild fire but remain in absolute denial of the same tool when analysing more intense and more frequent wildfire.
This level of inconsistency is both inexcusable and, in a policy sense, unlawful. And I have no choice but to conclude that we are not dealing with reasonable men and women here.
David,
Also, bushfires certainly do occur in hot weather, but that is because of the dryness, not directly the heat.
No, that won’t wash, at least in Victoria. It was just as dry on the days leading up to 6 Feb, and the days following, but the fires happened on 6 Feb, our hottest day ever in Melb (46.6C). The previous hottest day (45.6C), Black Friday, Jan 13 1939, possibly our worst ever bushfire. Again, it was just as dry on the 12th. And Ash Wednesday, our other whopper, 43.3C. And again, it was almost as dry on Shrove Tuesday.
Decades of fire behaviour research confirm that temperature affects “fire hazard” (an expression of the liklihood of ignition) so that it is generally more likely that bushfires will occur on hot days than on cold days. However, compared to variables such as fuel weight, fuel dryness and wind strength, temperature by itself is not a major contributor to “fire danger” (which expresses the intenisty of a bushfire, its rate of spread and suppression difficulty).
David Ward is thus quite correct in saying that you can have an intense fire under relatively cool conditions. The requirement is for dry heavy fuel and plenty of oxygen from fresh winds. I think he could have given a better example than the potbelly stove on a frosty morning (much as I love a potbelly stove on a frosty morning) and that is the clearing burns lit by early settlers. These were often lit in the evening on a falling hazard (temperature dropping), and with light winds so as to minimise spotting. But because of the mass of dry fuel, the fire would burn intensely, making subsequent pasture development easier and cheaper. I have used this principle myself in regeneration burns after timber harvesting where the objective was to produce a clean ashbed in which the regrowth forest would germinate.
I am no mathematician, but I can quite easily see the point of David’s use of mathematical principles to demonstrate fire spread. Without connected fuels, fires will not spread at all, or will only spread under conditions of really heavy fuel and high winds, when spotfires and fire whirlwinds are generated. I enjoy submissions to this website that make linkages across scientific disciplines, for example bushfire behaviour and mathematics . This challenges us to think a little more widely, to consider options and information outside our usual sphere of interest.
You make another very good point, Davey. Wildfires make very short work of old growth trees with nest hollows while mildfires rarely harm them. Nick Stokes might try all the nit picking he wants but when all is said and done temperature, too, is one element of a connection cluster.
The greens would like us to believe that temperature, man made temperature rises in particular, are the only element of connectivity in this wildfire equation. Yet, they deny the role of lower temperatures as a mitigating element of connectivity in the less frequent mildfire equation. What hypocrisy.
And Larry, you are totally out of your depth here matey. Isn’t there a porn site somewhere that is more your measure?
We used to make and see many bushfires when I was doing mineral exploration all over Australia. I’ve been to Kinglake and it is different. There are two main differences. 1. Many trees still hold leaves, 2 months after, though they are brown and crisp. 2. There are patches of green interspersed with patches of brown on a scale of hundreds of meters or sometimes less.
It seem a possible hypothesis that the progression of some fires was not through the motion of burning of grass or leaves, or even entirely by ember blowing. The hypothesis is that the radiant heat vaporised oils from the vegetation and formed a strongly radiating airborne fireball. The rate of movement of a gas fireball could be much the same as the wind velocity and thus greater than the rate of movement of burning twigs and leaves. I understand helicopter video showed some fireballs moving around 100 kph.
If this is correct, then it becomes a task to invent a way to minimise the vaporisation of the oils; or to control the direction of the fireball; or to extinguish it. I cannot yet conceive of a way to do any of these, but I do suggest that if the mechanism is correct, dropping water or conventional retardants from aerial platforms would be ineffective in preventing spread, but perhaps useful afterwards for remnant fire management.
Ian mentions the Government drives over the last two decades to maximise the connectivity of patches -“islands”- of native vegetation. This had its origin in island biogeography theory with its species area equation. Basically, the larger an island the more species it can support in equilbrium. There are several variations of the species area equation, but one prominent one is S=CAz (to the power of z) where S represents the number of species, A represents the area, and C and z are constants selected to get the model to account for the data. On ocean islands a good fit can be obtained by using a value for z in the range of 0.2-0.4. This means that an ten times the size has twice as many species. From Kellow, Science and Public Policy p31.
The theory was then extended to non-island habitats, on the assumption that an ‘island’ could be any area of habitat surrounded by areas unsuitable for the species on the island, including ‘islands’ of remnant ‘natural’ vegetation surrounded by human altered landscapes. Thus reserves and national parks were fragmented islands inside human-altered landscapes which could lose species as they deteriorated towards a new equilibrium of species. Kellow P32. Thus the drive for vegetation connectivity, establishing / preserving vegetation corridors, and for expanding national parks.
Load this formula into a computer, plus the untested assumptions, plus tweaked constants, and you get scary predictions of annual species extinctions in the tens or hundreds of thousands.
As an aside, Ian also mentioned the $1billion National Heritage Trust. I sat on a regional application assessment committee for this. It was loaded with bureacrats, so the various state govt departments got the bulk of that money, conveniently cost shifting their operating expenses and legal committments. The people on the ground saw very little of it, especially if a project, other than a demo, was on private property.
Extending island biogeography theory and the species area equation to land systems assumes that land species have find human altered landscapes as big a barrier to cross as oceans. This approach now seems to be justifying the establishment of huge marine parks. Are water environments a barrier for local water species?
A very good point, Helen. During the Qld and NSW regional vegetation management planning process it was normal procedure to work from maps that only showed so called “protected” vegetation. And in this way, identical habitat in State forests or on private land could be completely ignored on the basis that its contribution was not subject to 100% certainty of remaining. In many instances the so-called “unprotected” vegetation had superior habitat value (higher species and animal density) to the “protected” vegetation.
But the entire process was based on these maps of what appeared to be islands of habitat in what could rightly be described as the “bull$hit archipelago”. Those maps amounted to a serious misrepresentation of fact to the policy process and the reliance on them constituted an improper exercise of power by way of the exclusion of relevant elements of habitat connectivity.
When all native vegetation, including regrowth, was added to the picture, along with finer scale elements like paddock trees, fence line trees, road verges, riparian lines, weeds, orchards, house gardens and even crops that all provide ‘stepping stones’ and habitat services, the islands all disappear to reveal a substantial capital stock of connective habitat.
Furthermore, many species may not be able to cross particular barriers by themselves but they have still managed to make connections anyway. Tim Low gave a good example of the way isolated farm dams that have no water connection to other water bodies yet still end up being stocked with a number of aquatic species just a few years after they are formed. Fish and frogs eggs are designed to stick to the feet of ducks etc and hitch a ride to the new water body.
It seems clear that the only “insular” thinking in all this has been the narrow ignorance of the green movement.
Larry,
As Ian said, you seem to be rather out of your depth. I certainly don’t understand all of Paul Erdos’ work, but his paper with Alfred Renyi on giant patch formation is quite clear, and elegantly simple. As I pointed out, it has been applied in many fields, including brain research and the growth of the internet. I think it is blatantly relevant to fuel accumulation in flammable vegetation. To understand it, you will need some grounding in Graph Theory (also known as Network Theory).
I gave some seminal references at the start of this thread, and you can find a lot more information by Googling on combinations of keywords such as erdos, renyi, network, random graph, giant patch etc. You could have a go at the book by Belobas, although it is heavy going. Good luck with your mathematical studies. When you have progressed a bit, I hope you will be able to contribute some useful ideas on bushfire management.
I think network models of fuel and fire are the way to go, rather than the statistical ‘point probability’ models developed by such as Malcolm Gill of CSIRO. As far as I can see, these are of no practical use to managers or ecologists. Do you have any views on this?
Sorry, that’s Bela Bolobas. Wonderful names those Hungarians, heh? Oh, by the way, Sod, I have discussed this with an Erdos 1 and he agrees with me. Now, if I can persuade him to publish a joint paper with me, I will be an Erdos 2 – phew! Will you believe me then?
Thanks Donal,
You sound as if you know what you are talking about. Do you have an Erdos number? I think Sod’s is infinity.
Dave, your last comment confirms it. In the universe of the green zealot, you are destined to roast in hell for n years, where n approaches infinity.
On the effect of air temperature, is it a case of the heat energy contained in the hot air (>40C) is quite trivial compared to the heat generated by the combustion of the fuel?
I think the eucalyptus oil factor also tends to be a bit overstated in Australian contexts. If you heat any biomass to a high temperature in the absence of oxygen, the biomass effectively gasify’s down to mixtures of methane, carbon monoxide and hydrogen, and lots of other bits and pieces. The cellulose and other carbon-based molecules are simply broken into their constituent atoms and small molecules. My guess is that in the middle of large fires, where the temperatures are very high and oxygen is in short supply, huge columns of highly flammable very hot gases would readily form and then combust when they rise out of the fire and gain access to oxygen.
It would seem that the only time that ambient temperature would play a significant part in a combustion equation is at the initial point of ignition. That is the only time when the volume of fuel exposed to the flame is so low that background temperatures become relevant. As the fire takes hold the volume of fuel exposed to the fire increases and the relevance of ambient temperature decreases. It is why god invented kerosene.
Green Davey,
You seem to be rather out of your depth as a writer, unless the recent posting is not representative of your purple prose. I have a couple of points to make about this particular posting.
Bait and switch. A part of the title, “The Mathematics of Connectivity and Bushfires” is misleading. Did you state and prove any new theorems? Did you show HOW an existing theorem could be applied to bushfires? The answer to both questions is a resounding no. And dropping the name of a famous mathematician is not the same thing as mathematics. So, what is the mathematical content of your posting? Can you say zero? When I started reading the posting, I expected to learn something about the mathematics of connectivity and bushfires. Silly me.
The fluff factor. The first six paragraphs can be summarized as follows:
Paul Erdos is wonderful.
I dropped his name.
Therefore I’m wonderful too.
The real meat of the article is the last three paragraphs, which are essentially non-mathematical. I have no quarrel with your opinions about prescribed burns in relation to large bushfires. You obviously know more about the subject than I do.
You’re also right about another thing: I don’t know squat about Network Theory.
My background is in analytical chemistry. I also have interests in five areas of applied mathematics: game theory, data compression, Benford’s Law, writing mathematical puzzles, and the work of Mamikon Mnatsakanian.
Good luck with your studies in remedial English composition.
Despite the promise of the title, this topic seems to totally lack any actual mathematics.
Hey Larry, with your interest in the dark arts, can you decipher this for me…
“With regard to the perimeter of Melbourne, even a smattering of fractal geometry would tell you that it is scale dependent. It is infinite, if you use a small enough scale.“
I have no idea what it means.
It comes from a skirmish I had with GD here…
http://jennifermarohasy.com/blog/2009/04/wise-men-excluded-from-bushfire-royal-commission/?cp=all#comments
Comment from: Green Davey April 23rd, 2009 at 7:18 pm
You’ll find the style of debate here is a bit unusual and interesting. It seems to go something like this-
You question, refute or quiz substance and content of post.
People abuse you and tell you how good they are, how much experience they have, what they’d do if they had a chainsaw in the face of a firestorm etc…
You elaborate on previous post and ask insightful questions.
People abuse you and tell you how good they are, how much experience they have, what they’d do if they had a chainsaw in the face of a firestorm etc…
And then, at some point, they get all huffy and storm off or give you the silent treatment. Intellectual discourse doesn’t get any better than that does it?
Mathematic……Erdos…….Occam’s Razor……Bingo!
Nick Stokes,
and the ambient temperature affects fires actually set by an arsonist how???
Nick Stokes,
“I don’t think you’ll have much luck convincing people that climate is superfluous, when the three mega-fires of the last century in Vic occurred on three of the very hottest days.”
And all three of these mega-fires happened after years of neglect of reasonable fuel management. That is, we put out the small fires that we can handle until the fuel load is so high that a mega-fire erupts, or is SET, that we CAN’T put out.
Sorry if you BELIEVERS simply can not accept simple physics. In NATURE, there is no man to put out the smaller fires. They burn all the available fuel in PATCHES so that they rarely reach the mega-fire PATCH CONNECTIVITY!!! Even the Bushmen dealt with fuel loads much better than most Enviros.
Kuhnkat
“and the ambient temperature affects fires actually set by an arsonist how???”
By providing the conditions in which a manageable fire turns into a raging inferno travelling at 100 km/hr which noone can control. Many fires get started in a summer here, by arsonists, lightning etc. Most cause fairly minor damage if the weather is reasonable. One of the Feb 7 fires, at Bunyip, was apparently deliberately lit on Feb 4th. It was kept under reasonable control until Feb 7th, when it just broke out, burning many houses on the fringes of towns. What was different about Feb 7th? Hint – 46.4C.
When our Premier warned on 6 Feb of “worst day in the history of the state” he was unfortunately right. And he wasn’t basing that warning on a buildup of fuel, or reading an Erdos paper. He was basing it on the weather forecast.
RWFOH May 1st, 2009 at 10:52 pm wrote:
“Hey Larry, with your interest in the dark arts, can you decipher this for me…
“With regard to the perimeter of Melbourne, even a smattering of fractal geometry would tell you that it is scale dependent. It is infinite, if you use a small enough scale.“
I have no idea what it means.”
My short response: I don’t know what Green Davey means by that either.
My longer response:
1. Dark arts, eh? Does this mean that I have to wear a long robe, with a cone-shaped hat? How about white stars on a light blue background?
2. Psychic Larry’s crap detector says that obfuscation was the motive behind GD’s allusion to fractal geometry. Green Davey is a serious fire management wonk, and we’re fortunate to have him with us on this board. Unfortunately, he appears to have delusions of grandeur about his mathematical abilities.
3. Fractals. This is a 2-sided concept. The simplest way to visualize it is to pick a large fern branch, and take a close look. Then break off a smaller branch from the large branch, and take a gander at that. If you magnify it a bit, the small branch will look pretty much like the large branch. We call that the scale-independent aspect of fractals. We also call it self-similarity. Within reasonable limits, a fern branch is supposed to qualify as an example of a fractal.
The formal side of the fractal concept has a few wrinkles. According to one school of thought, some self similar objects–like the Sierpinski (spelling?) Triangle–are supposed to have a dimension that’s an improper fraction, rather than the 2 dimensions that we’d expect. That’s where the “fract” part of the name comes from.
Several years ago, I asked Mamikon (a friend, who’s also a leading mathematician) about fractals. His response was that the FORMAL definition does not hold up under Dimensional Analysis. You may remember DI from Chem 101. It’s what you used to make your unit conversions and routine lab calculations–like titrations–so much easier. The upshot? A large part of fractal geometry is junk science. Nevertheless self-similarity is an interesting and useful concept in its own right.
I have a strong interest in MAINSTREAM junk science, of which AGW Disasterism is an egregious example. Non-specialists have a difficult time questioning the conventional wisdom about AGWD, because they’re too hung up on the Dada-knows-best argument. Problem: Dada is human. Sometimes he’s a dim bulb, and sometimes he’s less than truthful.
If it’s OK with Jennifer, I’d like to post a few examples of MAINSTREAM junk science. It may be helpful for those blog participants with authoritarian leanings to see that sometimes the emperor has no clothes. (He must be German!)
“and the ambient temperature affects fires actually set by an arsonist how???”
The ambient temperature is what removes moisture from the soil and the plants. Hardy plants that are indigineous to our area were just wilting and dying. They could not maintain their moisture content, and became instant fire kindling. Preventative burning can’t fix that. In Victoria, it is also associated with Northerly type winds, which help move hot air from the desert parts of Australia to the more temperate parts. On that day, there was a North/Westerly which was particularly strong. Eye witnesses referred to ‘fire balls’, presumably branches of trees and bushes which were physically set on fire on blown through the air at high speed and over long distances. This wasn’t just an ember storm, this was a ‘fire ball’ storm. And preventative burning had been done around Marysville, and recently, according to a resident.
From your link Cohenite.
That person is completely ignorant of the science and it’s claims.
The models make no assumptions that CO2 causes temperature increases. They have the known phsycis of CO2 programmed in, amongst a whole lot of other information on the components of climate, and look at what comes.
Because these are models, it is quite easy to remove CO2 from the model altogether, or have it staying at a steady level. When they take out CO2, there is no temperature rise, but a slight cooling instead. It’s all in the IPCC report. Read it.
There is data and observations that CO2 causes temperature rises, the IPCC report provides plenty of that for the current climate.
The author of that article has no idea of the concept that CO2 can be a forcing or a feedback, that it has never been claimed that CO2 is the only forcing, nor that it is the strongest forcing. If the current state of the climate is analysed, CO2 is it. No doubt, that will change some time in the future.
Thanks Larry. But wait a minute…
“I have a strong interest in MAINSTREAM junk science, of which AGW Disasterism is an egregious example. Non-specialists have a difficult time questioning the conventional wisdom about AGWD, because they’re too hung up on the Dada-knows-best argument. Problem: Dada is human. Sometimes he’s a dim bulb, and sometimes he’s less than truthful.”
I may not know what you’re talking about but I’ll defend to the death my right to argue about it with you! (Isn’t that how the quote goes?) Surely neither side of the AGW debate has a monopoly on junk science!?
SJT,
Your quote from Cohenite’s link seems to be a reference to the Vostok ice core data. That is, an observation. When that data first became available it was low resolution with respect to time and seemed to show that T and CO2 went up and down together. This was hailed as the smoking gun, that nailed CO2 as the driver of T change. But then higher resolution data became available which showed that CO2 lagged T by about 800 years. That is, T changed first (either up or down) and changes in CO2 followed, just as you would expect from the T dependence of the solubility of CO2 in the oceans.
Are you sure this is in the latest IPCC report? This seems unlikely as it’s a direct refutation of their position. Which is why the alarmists don’t mention Vostok any more.
Boxer,
Disregarding, for the moment, all the piffle above from Larry, RWFOH and SJT, you raise two interesting points.
Firstly, eucalypt leaves will just burn at about 20% MC ODW (I think Luke and/or Cheney established that about forty years ago, and some of us repeated their findings in the karri forest in the early 1970s). As MC drops, the leaves burn even faster. Changing the ambient air temperature could change the MC, but not the fire behaviour at any given MC. So I agree with you that a few degrees change in air temperature, or even a change of ten degrees or more, is irrelevant when the fire temperature, due to heavy fuel, is over 1000 C.
On your second point, I have always assumed that the fire balls we see at major fires are due to eucalypt, or more generally, myrtaceous vapour. They are not a recent phenomenon unique to Victoria. I, and others, saw them in the 1960s in karri forest, and since in jarrah forest, and especially peppermint woodland. As far as I know, they only happen when fuels are heavy, due to neglect of prescribed burning.
Your idea that there may be another cause of fire balls, due to vaporisation of organic matter under low oxygen conditions is interesting, but I am out of my depth in physics and chemistry, so I hope some other reader can help on this. I certainly would not relish the idea of sampling in the convection column from a major bushfire. It would be like sampling the cloud over Hiroshima in 1945. I am sure laboratory methods could be used. Let’s hope the current Royal Commission directs more research into the fire ball phenomenon, and its relationship to a lack of prescribed burning.
Larry, SJT, and RWFOH your ridiculous smokescreen is not working. The ideas of Erdos and Renyi on connectivity in random graphs are clearly relevant to bushfire, and I have given enough references for you to pursue the mathematics, if you are really interested in the truth about bushfire, rather than your ideology.
With regard to the perimeter of Melbourne, consult Slarty Blartfast on his design for the coast of Norway. To understand his answer, you may need to read a primer on fractals first. Try Barnsley, M. (1988) Fractals Everywhere. Academic Press Inc., London. You will see why the perimeter of Melbourne (or Norway) is a variable, depending on the measurement units used. Have you noticed that the shortest distance between two (planar) points is a straight line? Think about it before you all make fools of yourselves again.
RWFOH,
“Surely neither side of the AGW debate has a monopoly on junk science!?”
Absolutely right, of course. But one side of the argument is forming the basis of government policy on an ETS, which will (depending on the details) damage our economy or just about destroy it. The onus is on the AGW promoters to establish their case beyond reasonable doubt. If someone opposed to AGW says something wrong, or stupid, or even dishonest that doesn’t mean that AGW is right and a sound basis for policy.
Green Davey, on May 2nd, 2009 at 2:39 pm, you wrote:
“Larry, SJT, and RWFOH your ridiculous smokescreen is not working. The ideas of Erdos and Renyi on connectivity in random graphs are clearly relevant to bushfire, and I have given enough references for you to pursue the mathematics, if you are really interested in the truth about bushfire, rather than your ideology.”
I’m NOT saying that ideas of Erdos and Renyi on connectivity in random graphs are NOT relevant to bushfire. What I AM saying is that you have FAILED to demonstrate that they ARE relevant. PLEASE STATE THE SINGLE MOST RELEVANT E&R THEOREM. You can even explain the terminology, if you feel that that would be helpful. Then show how the actual conditions on the ground satisfy the IF part of the theorem. (Or give a link to an article by someone who’s already done that.) If it’s not reasonable to assume that the IF part of the theorem is true, then the THEN part of the theorem does NOT apply.
I don’t think that you can. Your reluctance to provide specific MATHEMATICAL details is reminiscent of a similar reluctance from your counterparts in the climate change field. Getting raw temperature data from individual weather stations, algorithms for ‘correcting’ that raw data, and source code for the climate models is like pulling teeth.
Although you’re obviously very knowledgeable about bushfires and prescribed burns, you’re just blowing smoke about the mathematics. The lack of mathematical specificity in your comments suggests that you don’t understand the mathematics yourself. My gut reaction is that you’re simply trolling for impressive-sounding buzzwords and for famous names to drop, as packaging for your core ideas in your area of expertise. This is par for the course for academic hacks. So please do not feel that I’m singling you out.
Contrary to your innuendo, I do not have a strong ideology about bushfire. If you reread my postings in related threads, you’ll see that. You’ll see that I do have some limited, low-level experience with wildfires in the Western U.S. (mainly Northern California). You’ll also see that I’ve never been to your charming country. Without being a True Believer, I’m generally receptive to the idea of prescribed burns in my country and in yours. However if strong new evidence comes along, I reserve the right to modify my opinion.
An essential part of menschdom is being skillful in understanding what another person is saying, in the spirit that it was said. Your propensity for putting words into the mouths of others suggests that your GENERAL intellectual maturity–outside your area of expertise–is mediocre at best. While you’re working on your remedial English composition studies, you may want to upgrade your reading comprehension skills as well.
Once again we have the green goons applying a strategy of diversion and off-topic pedantry to avoid discussion of a HUGE INTELLECTUAL HOLE in their prevailing narrative. Once again they have been exposed for highly selective application of basic mathematical relationships.
Note that at no time have they sought to explain how the connectivity relationships that they clearly accept for accumulated adverse connections in infrequent mildfires give way to a total absence of connectivity relationships in frequent wildfires.
They are the classic deceptive propagandists who regard the truth, and fundamental mathematics, as some sort of drop down menu from which they can select any combination of facts, and number facts, that suits their squalid purposes.
And when we distill all their crapolla down we find that they want us to believe that a temperature of 47.0C renders all forest fire connective relationships, both positive and negative, redundant. So how come fellas?
You people are a trully loathsome stain on the human condition.
Bull$hit, Larry. Substitute the words “synergy” and “asinergy” for “connectivity” and your calls for an exact mathematical equation for the application of connectivity mathematics to bushfires is exposed for the boorish, self indulgent pedantry that it has always been.
But just for the record, try this.
IF a road is 10 metres wide with trees on either side and those trees have a trunk diameter of 20cm and a crown to stem ratio of 15 to 1 THEN the gap between trees will be 7 metres and the road will form a barrier to fire whenever the flames project less than 6 -7 metres.
IF those trees grow to 40cm diameter over the next fifteen years and crown to stem ratio remains at 15 to 1 THEN the gap between the trees will be reduced to only 4 metres and the number and intensity of fires that will be stopped by the road will be substantially reduced.
IF the trees do what they normally do and project branches into the open space over the road to produce a crown to stem ratio of 20 to 1 THEN the gap between the trees at year ten will be only 2.0 metres and the road will provide minimal barrier to the spread of any fire.
IF the road verges are cluttered with dead branches, leaf litter, woody weeds and regrowth which link the canopy with the ground cover THEN almost EVERY fire that is present on the ground will spread to the canopy and cross the road.
Erdos has merely devised a mathematical formula that is capable of applying a progressively higher weighting to these, and many more, elements of connectivity in much the same way as one does with a standard probability tree.
Or are you now contesting rudimentary probability for the sake of your sad little ego?
“You people are a trully loathsome stain on the human condition.”
This seems an intemperate response to a perfectly reasonable query about the relevance of Erdos theory. But Larry is right. No useful connection has been made. The challenge is to nominate just one theorem or result of Erdos, and say how it helps us to understand something practical about the Victorian bushfire. That isn’t contesting rudimentary probability.
So, if I’m to believe Mr Mott, the practical application of Erdos’ fuel connectivity theory will expand the canopy gap on a road from 2 to 7 meters? Whoa, hold the Royal Commission!
It’s all done and dusted thanks to the brilliant breakthrough of a Sandgroper and northern New South Welshman.
With such experience and familiarity with the dynamics of Victorian bushfires, these erudite gentlemen will no doubt be entrusted to read a report on a FRB conducted on a site with less than 5 t/Ha surface fuel and a FFDI value less than 6.
Here we are in the most dangerous fire alley on the planet, twiddling our thumbs for 180 years and waiting to get incinerated when all we needed was a 7 meter firebreak! I sure feel dumb for not having consulted these oracles earlier!
“Larry, SJT, and RWFOH your ridiculous smokescreen is not working. The ideas of Erdos and Renyi on connectivity in random graphs are clearly relevant to bushfire, and I have given enough references for you to pursue the mathematics, if you are really interested in the truth about bushfire, rather than your ideology.”
Reminds me of the old joke about the university professor, “I have an idea about “X”, I will leave to proof to you as an exercise.”
RWFOH has the intellectual penetration of a dog $hit in fresh snow.
The micro scale example of a road and its vegetation was used to demonstrate how a number of individual elements of connectivity can combine to produce what Erdos describes as a connectivity cluster THAT CLOSES THE GAP. In other words, the whole of the connectivity is greater than the sum of the connectivity elements.
We could have added wind speed, wind direction (either along the road or across it) humidity, ambient temperature or time of day which would all influence the connectivity equation on both a micro and macro scale.
And while the green movement has spent the past two decades claiming that the vegetative aspects of connectivity were entirely ecologically beneficial, the bushfire has demonstrated that the addition of the non-vegetative elements of connectivity to the equation has major adverse ecological, social and economic dimensions as well.
Yet, here we have our resident boofheads refusing to even recognise, let alone discuss, the concept of synergy and asynergy because they have not been provided with a precise mathematical formula for that synergy and asynergy.
So what next, eco-morons, refusal to discuss motherhood until you are provided with an exact mathematical formula for the condition? And only on condition that we limit discussion to the pleasent aspects of that state?
Your avoidance of the issue confirms your squalid ideals and malicious intent.
I’d like you to provide a practical example of how connectivity theory would be applied on either a micro or macro scale when you have 45+ temp, 50-80kmh winds and 6% humidity (i.e. FFDI 120-190) in a Eucalypt forest that’s been subjected to 12 years of drought.
Confusing and conflating fuel connectivity with habitat connectivity is the kind of sloppy and muddled thinking I’ve come to expect of you.
SJT and RWFOH,
You thirst for mathematics. I have already given you some references, but, from the haste of your repartee, you obviously have not read them. To plough through Bollobas might take a week or more, with pencil and paper handy to work out the twiddly bits.
I will offer you a simple exercise. Larry can join in, although he may have difficulty. But then, he can always call for help from his distinguished mathematical colleague, whose name escapes me at present. Are you all sitting comfortably? Very well, then I will begin…
Take two sheets of paper and a pencil. (I know its made out of a murdered tree corpse, SJT, but the alternative, a biro, is made of plastic, which comes from oil – aieeeee!). But I digress, which may confuse Larry still further. Blame the Celtic genes. We regard talking, and writing, as a form of dancing, with lots of ‘excuse me’.
On one sheet of paper, draw a number (N) of random dots, say ten. These will form the basis of an Eulerian graph, or network. On the other sheet, draw X and Y axes, to form the basis of a Cartesian graph. Label X as ‘number of connections’, and Y as ‘number of dots in largest patch’. (Larry’s friend might mutter about nodes, vertices, edges, and cliques).
Now start adding random connections to the Eulerian graph, and keep track of progress on the Cartesian graph. When N-1 connections have been made, a pattern will emerge.
Repeat the exercise with different N, and you can even try deliberately placed connections, which try to avoid large connected patches. The result will be the same, a sudden ‘connection avalanche’ before you reach N-1 connections. It’s unavoidable. Clever old Erdos.
If you still can’t see the relevance of the above exercise to ‘connection avalanches’ between patches of Victorian eucalypt fuels, or Californian chaparral, under attempted long fire exclusion, then I can’ t help you any more. Larry, who apparently believes in prescribed burning, could try talking to Prof. Richard Minnich, of California, who knows a thing or two about flammable fuel mosaics.
When you need a rest from mathematics, you should (especially SJT and RWFOH) read some political philosophy. Try the book ‘The True Believer’, by Eric Hoffer (1951), a self-educated US longshoremen. ‘True Believer’ does not mean what Paul Keating (or his speechwriter) thought it meant. I toyed with the idea of writing to Paul about this, but thought ‘nah…’
Finally (almost), I remember Francis Bacon saying, in one of his essays (1625?) that there are those who, when they do not understand something, will try to ridicule it, so hoping to make their ignorance seem like wisdom. Possibly Larry finds Francis Bacon difficult to understand.
There, I have dropped the names of Bollobas, Euler, Descartes, Erdos, and Bacon. Of course referring to geniuses does not mean that we share their brilliance. It does mean that our minds are open to ideas, and we are willing to read, even if it’s hard work.
That’s all very well GD, but all I wanted was one practical application of the fuel connectivity theory in the conditions described above.
All you’ve done so far is present a fallacious argument known as ‘appeal to authority’. It might make you feel superior to mere mortals but a snow job is a snow job is a snow job. Street smarts trump pretentious waffle every time.
All I ask is that Mr Ward and Mr Mott have a crack at presenting a practical example of the application of this scintillating mathematical theorem.
It’s unavoidable. Clever old Erdos.
nobody here has any doubts about the work of Paul Erdös. it is your application that I am sceptical about.
what you have written so far, has rather increased that sceptisism, started with the “pot-belly stove on a winter day”.
If you still can’t see the relevance of the above exercise to ‘connection avalanches’ between patches of Victorian eucalypt fuels, or Californian chaparral, under attempted long fire exclusion, then I can’ t help you any more.
well, obviously warm weather and drought will increase connectivity as well.
on the other hand it is quite unclear, how much patch burning would reduce it.
I will be holding my breath, till i see some serious evidence of your application of the Erdös math here (or in print)!
Connectivity, ??? What a load of nonsense!
As I have often said on these threads and elsewhere, these big bushfires merely travel in highly combustible fuel that has become airborne. Apart from the heavier stuff in ember showers there is another issue best looked at from furnace dynamics where the other essential ingredient is “draft” for sustained combustion as the fire races forward.
One bright spark here has noted the occurrence of fireballs in Victoria’s latest disaster and these things can be seen in daylight hours rising high in the smoke clouds above a major fire storm. Given gale force winds on a bad day such a furnace becomes horizontal and thus the fire is able to behave more like a blast furnace.
Inevitably unburnt fuel is travelling ahead of the ground fire and much of that can be a gaseous mix at very high temperatures. Therefore the rate of conversion in heavy fuel associated with forest fires becomes less of a issue at the height of a run than the availability of wind blow organic debris in the form of dust and of course the oils!
At around 40-50C these are ready to blow and natural turbulence from open combustion events provides both compression and scatter.
The most intense Victorian bushfires, as suggested above, occurred on some the hottest days. 1851 (47.2), 1939 (45.6), 1983 (43+) and 2009 (46.4). However, in Jan 2009, there was a 3 day heatwave of +43C (peaking at 45.1) that did not result in a fire. The difference may have been the strong southerly changes which was a feature of all the intense fires noted above but the S change in Jan 2009 was much weaker than the change on 7th Feb, 09.
In response to connectivity, etc maybe the levels of fuel should be included in the MacArthur fire index and more notice taken of impending changes.
RWFOH,
Is this the kind of thing you want? Let C(N) be the number of connections between the N nodes of a graph. Then C(N+1) = C(N)+N;also C(1)=0. So we easily get C(2)=1, C(3)=3, C(4)=6, C(5)=10, C(6)=15 and so on. (In fact, C(N)=N!/2!N!). So if the Cs stand for the firefronts that need to be fought, you can see that as things get worse they get worse quicker.
Of course Erdos refers to the probability of connections, not simply possible connections, but this might be a starting point for someone answering your questions.
Thanks davidc, but I will not be answering any more of RWFOH’s questions. I have given enough information – it just needs some pencil and paper work from RWFOH. I don’t think this will happen, because RWFOH and SJT are not looking for the truth, they are merely vexatious questioners.
I can well understand that they will be nervous when ghostly mathematicians are on the prowl, shining strong light into the dark corners of their dogma. They will try their best to shoot the light out. However, they are not very good shots.
I have learnt much from the positive contributors to this thread. For example, Boxer pointed out the need for more research into the actual cause of fire balls – eucalypt vapour or something else? Ian Mott raised the philosophical (logical) issue of some using connectivity when it suits them, but rejecting it when it doesn’t. Helen Maher chimed in with the ecological problems of ‘Island Theory’. Wasn’t our own well loved Jared Diamond one of the architects there?
Early on, poor old Sod appealed to me not to quote Erdos. It sounded like an appeal to my better nature. I am, I believe, good natured, and have shown some patience, for example, with the primary school (I’m sure they are chalkies) abusive style of RWFOH and SJT – but mathematics is neutral on that.
‘Larry’ seems to have disappeared. Perhaps he is busy on another thread under his other alias of ‘Luke’. He has been sore at me ever since I suggested, some years ago, that his statistics were dodgy, so I suppose some Erdosian huffing and puffing made him feel better. It did not alter the truth. Have another cucumber sandwich, Luke, I appreciate your sense of humour. We are still mates, well, up to a point, Lord Copper (Evelyn Waugh – Scoop?).
By the way, the number of possible planar connections between N points (no crossovers) is, I believe, (N-1)+(N-2)+(N-3)=3(N-1). It’s quite good fun to fiddle around with that sort of thing, knowing that Euler’s ghost is peering over your shoulder. Have a go at applying the Four Colour Theorem to bushfire mosaics. I wonder why the Nyoongars burnt at 2,3 or 4 years?
Drat – that should be 3(N-2) – check it out.
“Of course Erdos refers to the probability of connections, not simply possible connections, but this might be a starting point for someone answering your questions. “
Thank you David. I know what the inference is with regard to the introduction of Erdos’ theory. What I want to know is, what is the practical application (preferably with an example) under the conditions I have describe above? (As yet no-one has tried to directly address my questions but they have indulged in some interesting avoidance strategies.)
My contention is that under the conditions I have described, the dynamics of bushfire render the removal of small amounts of surface fuel inconsequential in terms of the overall fuel complex.
The point people are trying to avoid is that even forests that have had prescribed burns have fuel loads where, in extreme conditions, there is no safe threshold before “critical mass” in terms of fuel connectivity.
Rather than concede this point, the pompous goat has indicated he would rather run away. By introducing Erdos’ theory in the context of fuel connectivity, he would have us believe we will be safe by fiddling with a bit of surface fuel. If this lie gains currency, it will put lives at risk every time we experience extreme conditions like those of Feb 7 ’09.
Now, once more, how can Erdos’ theory be applied to fuel loads with a practical method that will mitigate fire in a useful way in extreme conditions?
RWFOH,
I suppose I must answer this one. Your incessant bleating suggests that you are the goat, not me. Your basic fire understanding is moth-eaten. Attempts at reducing fuel quantity and connectivity when a fire is in progress (backburning) is indeed a risky strategy, and recognised as such by experienced fire fighters. Sometimes it works, sometimes it causes more damage. It is rarely, and very carefully, used in Western Australia.
What we (with long fire experience) are saying is that reducing fuel quantity and connectivity in mild weather, before a big fire occurs, will definitely make any subsequent fire, even in extreme weather, milder, and easier to control. The historical evidence for that is overwhelming.
Fires in heavy, highly connected fuel, in extreme initial weather, make their own even more extreme weather, including strong and erratic wind, even higher temperature, lightning, and fire balls. Reducing fuel quantity and connectivity, before the event, avoids this.
Erdos and Renyi (1959,1960) give an abstract mathematical insight into the way in which connectivity increases as more litter is added over the years in unburnt areas. Beyond a certain time (the return period for running fire in that particular vegetation), there is a sudden ‘avalanche’ of connectivity. The logic is inescapable, and is supported by history. As a dogmatic, pompous goat, you seem to be trying your best to escape it.
Now get some paper and a pencil, and get to work understanding Erdos and Renyi (1959,1960). Those are references to mathematical papers. I look forward to hearing from you in a month’s time, when you have matured, mathematically, if not otherwise.
I will then introduce you to Knot Theory, which gives abstract mathematical insight into a neat and flexible way of creating rich landscape fuel mosaics, similar to those created by Aboriginal people, long before arrogant and ignorant whitefellas interfered. If Aborigines had not created such mosaics, they would not have survived, nor would Australia include botanical ‘biodiversity hotspots’, with hundreds of plant species. As a simple zoological example, think about Rick Shine’s snakes, and their need for sunny rocks, not deep litter and shady shrubs.
Your mind is attuned to European cultural views on fire. Australia ecology is different, and has long involved humans..
RWOFH,
Personally, I don’t see that it would be of much practical value. The probabilities involved would be different in different places and in practice unknown. I would rather have people doing controlled burning than attempting to estimate probabilities.
For those with a constructive interest in fire ecology in south-eastern Australia, I recommend a paper by Dr Beth Gott ( http://www.csu.edu.au/special/bushfire99/papers/gott/ ).
Dr Gott has a great knowledge of SE Aboriginal food plants, and their relationship to bushfire. It seems very similar to SW Australia. Obviously, Aborigines would not have wanted the whole landscape burnt in one go, because this would have destroyed all plant (and animal) food within walking distance initially, then there would have been a glut for a few years, followed by a famine again. The Aborigines used a more intelligent approach, burning a patchwork mosaic, at a walking scale, so that there was a constant, moderate, sustainable supply of food within walking distance. Common sense, when you think about it.
Paul Erdos’ work gives a clear insight into how fire mismanagement has caused big fires to occur (giant fuel patches), and how we can avoid them, by burning in such a way as to disrupt fuel connectivity (mosaic burning). Knot Theory can give us a practical way of safely restoring such patch mosaic burning, at walking scale. It will be hard, labour intensive work initially. Perhaps all Public Servants should be required to don overalls, and lend a hand, say one day a week. Good cure for obesity. Also all members of ‘The Greens’, and Mr Rudd’s proposed ‘Peace Corps’. There would be marvellous photo opportunities, for example, the Minister for the Environment striking the first match. Old foresters, with fire experience, and Bushfire Volunteers, could supervise, in return for a suitable fee.
GD “What we (with long fire experience) are saying is that reducing fuel quantity and connectivity in mild weather, before a big fire occurs, will definitely make any subsequent fire, even in extreme weather, milder, and easier to control. The historical evidence for that is overwhelming.“
You’re still laboring under the misapprehension that fires under extreme conditions are “controllable”. I think you’ll find historical evidence clearly refutes any claim that it is.
Using Marysville as an example, if you look on Google Earth you will see cleared land about 2-3km to the S-SW and then a forest on the edge of town that is about 1.5km across. That forest had FRBs in ’03, ’04, ’05 and ’08. Most of that forest block was burned in the last 5 years. DSE & CFA were attempting to backburn there on BS and had to flee for their lives when the wind change hit. The fire crossed paddocks and then fuel reduced forest before obliterating the town.
The physics of the fire were such that fuel reduction made no discernible difference in extreme conditions.
I think you obfuscate around this point because you know that accepting it will open a Pandora’s Box. I’m all for delving into that can of worms.
Paul Erdos’ work gives a clear insight into how fire mismanagement has caused big fires to occur (giant fuel patches), and how we can avoid them, by burning in such a way as to disrupt fuel connectivity (mosaic burning).
this is complete rubbish. the work of Paul Erdös does nothing of that sort.
you have again failed to provide any practical application.
why don t you give us a simple graph of a “connectivity” in a wood?
and on a very hot day after a drought?
and on a winter day (after a “pot-belly stove” fell over…)?
and both scenarios after some burning scheme?
RWFOH,
Let’s delve into the can of worms.
You say (correct me if I am wrong) that fires in extreme weather conditions are never controllable by humans. I say they are, if fuel is sufficiently low, and disconnected. We have a clear difference of opinion, which we can discuss, and others may, or may not, join in.
If there is no fuel, say a sandy desert, then there could be no fire, no matter what the weather. With a small amount of fuel, there can be connectivity through blown embers, but these embers would not travel far, because there would be only a weak convection column to loft them. A bit like the tumblin’ tumbleweed. Such a fire would be controllable by humans.
If there are say, 20-30 tonnes of leaves, bark, twigs and capsules dry enough to burn, then the convection column is enormously strong, and the heat release enough to ignite shrubs and trees. so compounding the energy release. There is also the matter of flammable vapour, whether it be from live eucalypts or by vaporization of dead organic matter, as suggested by Boxer. This can produce great balls of fire. Both wind and heat are intensified by the convection and combustion. This is the situation we all want to avoid.
Although jarrah forest is highly flammable, there are no major forest fires on record for Western Australia in the 1800s, only fires on farmland. This is because the forest was burnt, intentionally or by default, every 2-4 years, by trickling fires. It was bound to be, because jarrah will carry a fire that often, and there were no fire brigades, no motor vehicles, and not many roads. There are plenty of summer lightning strikes, and Nyoongars traditionally burnt mostly in summer, as soon as the litter was dry enough. From Beth Gott’s work, I suspect that Koori people did the same. Such frequent burning would favour the food plants for Aborigines, and prevent big fires (karla koombaniny). An Elder here told me that, sitting on a log in the jarrah forest. Others since (30+) have confirmed it.
Fire suppression in the jarrah forest was a new fangled notion, introduced in 1916 by our first Conservator of Forests, Charles Lane-Poole, who was trained in France, and did not know the jarrah forest. Locals tried to tell him, but his focus was on producing straight saw logs. He only stayed a few years, and our second Conservator, Stephen Kessell, reaped the whirlwind, literally, in the 1920s. His staff had increasing difficulty suppressing fires, whereas before they could put them out with green branches.
Although he wrote an article for an American journal on the evils of ‘creeping fires’, Kessell eventually had to admit that the locals were right, and broadscale prescribed fuel reduction burns were essential, both for human safety, and forest health. He emphasized the need for opportunistic burning by local residents, who knew their patch.
However, by that stage, the Forests Department had lost control, in that fuels were often too heavy to burn safely. It was only after the Dwellingup disaster in 1961 (ember showers, extreme winds and heat, just like Victoria) that prescribed burning was widely introduced. Recently it has declined, due to urban agitation against smoke, and we have seen an increase in major fires.
Perhaps you will choose to regard this as a fairytale, unsupported by ‘rigorous science’. You have asked me a few questions, which I have answered as well as I can. I have a Jewish friend, who recommends answering a question with a question. My questions to you are:
a) Do you live, or have you lived, in the bush?
b) Have you ever directed a hose at advancing flames?
c) Have you seen a fire in 2-4 year old eucalypt litter?
d) Have you sat down, with a paper and pencil, and sketched out a random set of points (fuel patches) and tried connecting them according to Erdos theorem?
Green Davey wrote:
“‘Larry’ seems to have disappeared. Perhaps he is busy on another thread under his other alias of ‘Luke’.”
About the ‘disappearance’. As Mark Twain would say, rumors of my demise are greatly exaggerated.
About the putative Luke alias. Gone off our meds, have we?
GD “You say (correct me if I am wrong) that fires in extreme weather conditions are never controllable by humans.” “I say they are, if fuel is sufficiently low, and disconnected.“
I am saying when a fire is going in a forest in extreme conditions (e.g. BS) it is not controllable by humans. The only thing that stops the runs of the fires in forest is abatement in weather. We have seen this time and again since the 2003 fires.
GD “I say they are, if fuel is sufficiently low, and disconnected.“
If fuels are sufficiently low and disconnected then you are not talking about the Victorian situation.
In the Four Corners story on the Marysville fire, the first CFA were on the scene in about 15 minutes. The guy was describing how the fire had already travelled about .5 to 1 km (hard to gauge off TV) across farmland and had entered the forest and was tearing up a forested hill (coincidently, that forest was fuel reduced in 2008). I’ll bet that given the hill was north facing with peppermints and messmate, it was already crowning. The impression I got from the CFA bloke was that the fire was already gone from a containment point of view.
The Toolangi forest block that covers most of the area between ignition point and Marysville has an extensive history of FRBs from the late seventies to mid eighties. The FRBs, with a few exceptions including the one mentioned above, seemed to stop when the logging intensified from the mid eighties onward. All this logging, or “management”, of the forest did nothing to prevent the severity of BS. It might even have made it worse.
DSE had in recent years fuel reduced a “C” around Marysville from north through west to south. I’m sure their fuel management will be vindicated.
I think it’s a good idea to base our FR on the Aboriginal model but we don’t know what it was. We need a lot of quality research based on charcoal in the trees, soil , alluvial flats and river and lake mud. Getting fire regimes wrong could compound our problems.
We can talk about rapid response, educating the public, safer buildings and various other issues but we can’t stop fires starting so there is always the risk they will get to BS proportions even with fuel reduction. Brumby might throw money at fuel reduction because it plays well in PR terms but I think the RC will expose how little it did for the people of Marysville.
RWFOH,
I think we are actually making some progress. Erdos and his connectivity can help, but so can history and anthropology. You mention Aboriginal burning, and say little is known.
In Beth Gott’s paper she mentions several short fire intervals, in the range 2-4 years, which best stimulate food plants used by Koori people. Kangaroo grass (Themeda triandra) is another strong indicator of former frequent burning. Left unburnt, it smothers under its own thatch. The same species is well known in Africa, where it is still burnt every 2-4 years to stimulate it. In fact it occurs all around the Indian Ocean, and seems to have a strong connection with human movement and burning. There is an outstanding patch on a farm near Geelong, owned by a relative of mine by marriage.
On another front, I have, in WA, cleaned off big old grasstree stems going back to 1750. They show, beyond doubt, that the dry woods and forests were mostly burnt every 2-4 years before European arrival (1829 on the Swan River). I think there is a photo of such a cleaned grasstree somewhere on this site, and I have done over 500 of them, despite the hostile comment of an early referee that the ‘method is not reproducible’. Other attempts have been made to discredit and bury this research, but have failed, partly due to naive use of statistics. The Conservation Council of WA does not like grasstree research one bit, because it contradicts what they say about fire. Politics and science make a bad mix.
You are a bit coy about answering my questions, in particular the one about fire in 2 year old fuel. Such fires, in WA, are extremely mild, even in 35C heat. That’s how Nyoongars got away with burning in January and February, and could easily swat out fires with green branches to protect spear thickets. Summer was their main fire season, and was called ‘biroc’, or ‘peeruck’.
Fires like that will often go out due simply to a shady patch, where leaf moisture is close to 20% ODW. I suspect Victorian dry woods and forest are very similar. The wetter forests are, of course, different, and would have had a longer fire cycle, much like our karri (Euc. diversicolor). Nevertheless, there are areas in the karri, such as along rivers. which were used as travel routes, and burnt frequently, to keep them open. Now they are choked with dense scrub, and burn uncontrollably when fires occur. The river gums (Euc. camaldulensis) are dying.
Bridgetown, on the Blackwood River, was a favorite Nyoongar camp site (Geegeelup). Up to the 1870s, there were, at times, more Nyoongars in Bridgetown than whites. The approach of the wandering bands was heralded, up to the First World War, by smoke approaching along the river.
The point of this long rigmarole is to show that, in WA at least, quite a lot is known about Aboriginal burning, because the history is more recent. People like Beth Gott have shown that Aboriginal fire use in Victoria is open to good research. Mathematics, such as the ideas of Erdos and Renyi, can help us to understand, whitefella style, what Aborigines were doing with fire. Knot Theory can help us restore, whitefella style, that skill. Even in the suburbs of Perth (and Melbourne?) there are reserves which could be maintained by careful mosaic burning, as could the broader landscape, for example along rivers and around swamps.
I think even the mighty Vics could learn a thing or two from research into Koori burning. If fires like the recent ones had occurred in the past, there would be no Kooris left. There is no alternative but to return, eventually, to a modified form of Aboriginal mosaic burning, to reduce fuels, recycle nutrients, and disrupt fuel connection. How long this takes depends on how stupid we are. We can do it more easily by embracing mathematical ideas, such as those of Erdos and Renyi. I have told you where the source references are. Try some pencil and paper work, and perhaps talk to some Koori Elders about fire. There could be a big fat Federal grant for you in this.
Hi there Larry,
Glad Mark Twain came to your rescue. On the subject of meds, may I suggest you (L) try the diet of coffee (C) and amphetamines (A) favoured by Paul Erdos (E). As a connoisseur of mathematics, you may enjoy delving into Davey’s Conjecture, viz:
Lemma 1: E + C + A = brilliant theorems
Lemma 2: L + C + A = further confusion
Let me know how you go. You will note that I have, as a true sportsman, offered you the opportunity for a comeback Larry’s Conjecture. Nothing spiteful now – something light and humorous.
P.S. Can’t you find a better gravatar than that?
Green Davey wrote:
“You will note that I have, as a true sportsman, offered you the opportunity for a comeback Larry’s Conjecture.”
By overwhelming popular demand, I offer the following original (to the best of my knowledge) puzzle:
LARRY’S CONJECTURE
In plane geometry, we learned a few theorems about congruent triangles: Side-Angle-Side, ASA, SSS, and AAS. Suppose that you have two cardboard n-gons (n-sided figures), that you have measured the sides of each, and that for each n-gon, you have made a list of the measurements in no particular order. Suppose further that there’s a one-for-one match-up between the two lists, but that the two n-gons are NOT congruent. Few would be surprised if I said that that could be true for kilogons. What is the SMALLEST possible value for n?
If even one person posts a reasonable stab at the minimal solution, I’ll post the correct answer plus a small hint of how I arrived at that number. Since my computer graphics skills are limited, I’ll not post a picture.
Sorry for leaving you holding the can, Davey. I have been down at farm.
And surprise, surprise, we still have RWFOH is full sleaze mode. The dopey dilbury has the gall to demand an explanation of how connectivity theory could possibly apply to “extreme conditions” like 45C, 6% humidity, 50-80kmh winds and 12 years of drought.
So lets take this nice and slowly for the laggards. The temperature, humidity, wind speed and soil moisture history and profile that you mention ARE ALL ELEMENTS OF CONNECTIVITY, along with wind direction, land form, slope, fuel volume, fuel structure (vertical or horizontal), time of day and the scale, timing and quality of human preparations for fire and responses to fire.
And the simple fact that some parts of Victoria did not burn on 7th Feb 2009 is absolute proof positive that there is a great deal more to fire behaviour than your four elements. Clearly, lesser amounts of all the other elements played a major part in ensuring that large portions of Victoria were not burned.
I forget which town it was, but the guy who stole an idle DSE bulldozer and put a fire break right around his township and saved it from burnout acted in a way that severed connectivity sufficiently to prevent both loss of life and property. And he did so in the face of your supposedly insurmountable extremes.
Yes, you can cherry pick particular instances where fires crossed open paddocks in apparent contradiction of connectivity theory but we don’t know what slope or aspect was involved and we don’t know what the pasture condition was. If the paddock had been spelled for a time and was due to be grazed again in rotation then a fire would have gone through it much faster than one where the stock had just been removed and the grass was much shorter.
And yes, we can have the Lindenmeyer’s of this world claiming that forest around Marysville had been fuel reduced in the few years previously but we don’t know anything about the fuel loads in forest areas outside the fuel reduced zones which defined the scale and intensity of the fire that entered the fuel reduced zones.
We don’t know the slope and aspect of the terrain that the fire travelled over on its way to the fuel reduced zones. And we don’t even know if the supposedly useless fuel reduced zones were anywhere near the 2km thickness that the research indicates as essential for extreme events.
Of equal importance, we cannot assume that fires burned both high fuel and low fuel areas with equal intensity and impact until we see what sort of recovery takes place. Mountain Ash forests destroyed in 1939 were completely replaced by young, uniform regrowth. But forests subjected to milder fires due to lower fuel loads or those areas burned at night when ambient temperatures are lower, tend to make a partial recovery of the original trees along with a new generation of seedlings.
So it is the height of ignorance to be drawing conclusions about the supposed ineffectiveness of fuel reduction and other connectivity variables from such limited information. The theory of connectivity is as much to do with the consequences of the fire as it is with the nature of the burning itself.
Reducing connectivity can serve a valuable purpose even when all it does is enhance the subsequent ecological recovery after the fire. And it is a damning indictment of the green movement that it cannot grasp, or refuses to accept, that this is sufficient grounds for conducting fuel reduction in its own right.
Most of the little that we do know about Aboriginal fire regimes in Vic is fairly generalised GD. Environments range from desert to alpine.
In the west around Lake Condah there are remnants of stone hut villages. These villages were established around a man-made aquaculture system that covered approximately 100km2. These villages are believed to have been permanently occupied and date back around 8,000 years which would make them the oldest and longest surviving permanent human settlements known. It’s believed they traded with nations and tribes from far and wide. I’ve heard of artifacts with stone traced to NW Oz.
In the east different nations from all over the south east converged on the high country in summer to take advantage of the concentration of Bogong moths. It was a very significant event culturally.
Fire intervals were less than 10 years in coastal heaths but up to 500 or more years in the wet and damp forests especially those at higher elevations.
I reckon Aborigines had the fire business down to a fine art. I doubt there was any aspect that wasn’t covered by law/lore.
It’s hard to know how and why they burned but thorough research would help before we start speculating too much and running off on tangents that may be just as misguided as those misconceptions held by our forebears..
I personally think they would have used fire to preserve and maintain ecological fire barriers and buffers. Between fire regimes and logging practices, we’ve just about removed all those natural fire mitigating factors.
This scale of fuel connectivity is probably where Erdos’ theory could be applied.
Well done RWFOH,
By George I think you’ve got it – well almost. As Motty says, just because FRB had been done, does not mean that it was effectively done. In the 1920s and 1930s our European trained Conservators of WA Forests (Lane-Poole and Kessell) thought that 5 chain fuel reduced breaks around long unburnt forest blocks would stop fires. These breaks were burnt at 3 year intervals, but were useless – too narrow, and the burning had to be done against old fuel, which often took off with a roar, due to connectivity (ahem). There was nearly a mutiny amongst the troops who had to do the burning. Attempts were made to exterminate grasstrees in the 5 chain breaks, because their thatch caused ember showers, so enhancing ground connectivity. Ideas of ‘strategic burning’ as a way of avoiding broadscale burning, are largely hare-brained, and show an ignorance of fire history and fire behaviour. It was tried in WA 90 years ago.
I say, RWFOH, I might be telling you too much. You’re not one of those publication hungry, academic weasels are you? You know (a) Rubbish (b) Well, maybe… (c) Actually, I thought of it first. I had better monitor the pages of Austral Ecology, if I can keep awake.
Larry,
I likes yer conjecture. I will fiddle with it tonight, in front of the TV – swine fever, economic meltdown, Somali pirates etc. etc. Thank God terrorism and global warming have passed their shelf life.
Hey, wait a minute, if I give you a solution you might publish and say you thought of it first. It’s a tricky old world … ah, coffee is in the little cupboard over the stove, now where are the amphetamines?
Pot-belly stove, that is. We are having cold mornings here, but it lights easily, because the fuel is dry.
It just so happens, Davey, that the purpose of my recent trip to the farm was to replace the pot belly in one of the rental houses with a splendid new Raywood with glass on two sides. Enough to warm the cockles of any heart.
Ian,
Sounds good. I can visualize it glowing. An experiment occurs to me. Take two dry sticks of firewood, and put one in the deep freeze overnight. In the morning, boil the other in a pot of water for, say, half an hour, until it is nearly 100C. Which stick will burn, and which won’t? Is temperature the key variable, or moisture content? Where does that leave ‘global warming’ as a cause of mega-fires?
Hey Larry, even before the evening TV news, it occurs to me that the number of ring permutations for N objects is given by N!/N. So doesn’t the smallest possible non-congruent n-gon have 4 sides? That is if we consider clockwise and anti-clockwise as congruent pairs. Or have the amphetamines messed up my mind again?
Green Davey wrote:
“So doesn’t the smallest possible non-congruent n-gon have 4 sides?”
Right you are. Give that man a cigar! (Not to be smoked while bushwalking in Victoria.) However I didn’t follow your reasoning. Here’s mine. Start with two identical quadrilaterals made from dowels, with wads of bread dough holding the ends of neighboring dowels together. Both quadrilaterals are lying on a tabletop. Now choose one of the quadrilaterals, and push one pair of opposite corners a bit closer together. Voila! But that was just the teaser puzzle. Now that you’ve taken the bait, here’s
Part B
What’s the smallest possible n for two non-congruent n-gons having identical lists of sides AND angles?
Larry,
Thanks for the cigar, but I don’t smoke. I think we are wandering far from the original topic. I found your analog model interesting, but think my ring permutations are more elegant. Rather than bread dough, may I suggest play dough, which is less likely to attract cockroaches.
I would love to engage in mathematical banter, but, as my late Aunt Gertrude said, a fool can ask more questions than a wise man (or woman) can answer. I hasten to add that this is a general proposition, and in no way implies that you are a fool, or I wise.
If you want a challenge, perhaps you can produce a dowels and dough model of the following conjecture:
Every even integer greater than 2 can be written as the sum of two primes.
Be quick, I have heard that a fellow called Goldbach is working on it.
I think this thread has run its course. RWFOH is hunched over a computer, writing a paper called ‘Some considerations on the application of Erdosian connectivity in pyrophilous vegetation in south-eastern Australia and its implications for biodiversity conservation and sustainability’. Motty is boiling firewood on his new pot-belly stove. Helen Mahar (sp?) is on an island somewhere, working for the University of Biodiversity, before the island is drowned by global warming. Old Sod is grumbling in the background, and dreaming up a ‘Society for the Prevention of Undesirable Applications of Connectivity Theory’.
As for you, Larry, you may find ample scope for your mathematical and modelling skills on one of the climate threads. You will be in more congenial company there.
P.S. Where did you say you studied mathematics?
Boxer, Roger, and Donal,
I did not hazard a guess at what you may be doing, but thanks for your insights.
Green Davey wrote:
“I think this thread has run its course.”
What? Giving up so easily? Part B can be solved with paper and crayons alone. Just draw some pictures. No specialized knowledge is necessary. As Erdos would say:
Even a baby can solve it.
On the other hand, I can see your point. Thanks to me, we finally have some mathematical content, beyond name-dropping and buzzword-dropping on this thread, and the thread’s title has partially lived up to its name.
Green Davey wrote:
“P.S. Where did you say you studied mathematics?”
I have an A.B. in mathematics from Humboldt State University, in N. California. Although my M.S. (Oregon State University) is in chemistry (analytical), my thesis was largely applied mathematics.
Larry,
You certainly did enrich this thread with your mathematical wizardry. I am left gasping in awe. Especially the dowel and bread dough analog model.
I don’t want to monopolize your attention though. I am sure Luke and SJT would welcome some mathematical help over on the climate threads. There is some appalling name dropping goes on there. Gore, Karoly and so forth.
Humboldt was, of course, a very great scientist. I am glad you mentioned him.
Green Davey wrote:
“I don’t want to monopolize your attention though. I am sure Luke and SJT would welcome some mathematical help over on the climate threads. There is some appalling name dropping goes on there. Gore, Karoly and so forth.”
Thanks for the vote of confidence. I’m very much interested in the climate threads, and do occasionally participate to the extent that I’m able. But my background isn’t sufficient to follow some of the fine details–not to mention the bloody acronyms. And for some reason, I don’t feel my creative juices flowing in the direction of climate modeling.
Back in the 1980s, my friend Mamikon started to do some computer modeling for a risk-analysis of a nuclear power plant in one of the former Soviet Republics. One glance at the blueprint told him that this particular facility was an accident waiting to happen. He couldn’t bring himself to finish the study, although he did raise a stink.
My feeling in both cases: An ounce of common sense is worth a pound of silicon.
Then we can conclude from the silence of RWFOH and SJT that connectivity theory is highly applicable, in both positive and negative dimensions, to both frequent wildfire and infrequent mildfire.
We can also conclude that the presence of unburned parts of Victoria is uncontested evidence that elements of connectivity, other than temperature, humidity and wind speed (ie fuel loads, land use, landform etc) are capable of reducing the scale and intensity of wildfires and are also capable of influencing the speed and extent of post fire recovery.
And we can also conclude from their silence that the expensive and widely extolled virtues of habitat connectivity through landcare activities etc, also have a very serious adverse dimension in the form of the character, scale, intensity and cost, in ecological, social and economic terms, of bushfires.
And we can also conclude from their silence that they do not contest the view that a negative dimension of a connectivity equation, or the over reliance on a positive one, is a “relevant consideration” within the meaning of Section 5A of the commonwealths Administrative Decisions (Judicial Review) Act. And the failure to consider same in any policy process would constitute an improper exercise of power.
Believe whatever you like, I laid down the challenge and your case was found wanting. The arguments on this page speak for themselves, any intelligent reader will see what a disorganised and illogical rabble you are.
Ian,
A good summing up, m’learned friend. I thought, at one stage, that RWFOH was getting the hang of it, and abandoning bluster. S/he did eventually admit that Erdos and Renyi (1959,1960) were relevant (in some cases m’lud) to bushfire connectivity. Alas, s/he has had a relapse, dropped his/her briefs, and his/her wig is askew. Paul Erdos would have a good laugh.
Now Knot Theory is interesting – might do a post on that. Perhaps Larry will help us with some mathematical insights, through astute analog modelling with dowels and bread dough.
No, RWFOH, you demanded the equivalent of mathematical proof of motherhood. And on 5th May at 3.06pm I gave you a very detailed post explaining how your claim, that connectivity was irrelevant in extreme conditions, was actually based on some of these very elements of connectivity. I went on to point out that the numerous individial houses, towns and bits of forest that did not burn on 7th Feb 2009 was proof positive that additional connectivity/ disconnectivity factors were at play which saved them from destruction. The extreme temperatures, low humidity and strong winds did not override the other elements of connectivity, or more accurately, disconnectivity, that were at play in all the places where no destruction took place.
I also went on to point out that the concept of connectivity in cases of fire went beyond considerations of whether burning took place or not to include issues like the speed, extent and quality of the recovery from fire.
Your post of 5th May at 4.45pm addressed none of these points. You only talked about aboriginal burning. You issued a challenge. I responded in detail. And you then left the field with your tail between your legs, only to give us one last pathetic woofing of the discredited party line from a position of safety.
And when given a final opportunity to respond to the key points of my summary, you sought refuge in denial, generalities and insult. But you are correct in one point. The readers certainly can look back over the thread to judge the arguments on their merits.
Thanks Davey, this has been a very important post and thread. Indeed, I would go so far as to suggest that you have added, significantly, to the sum of knowledge. Can I refer to you as “Dr Gam”?
“you sought refuge in denial, generalities and insult. ”
Ha! That’s funny!
Pot. Kettle. Black.
Houses amongst trees survived and houses in paddocks burned. Sum relevance of connectivity on BS? Zero. Start talking about the need to preserve landscape scale areas of old growth wet forests at higher elevations and you might be working on a scale where Erdos’s theory has any relevance. Otherwise, all the evidence is agin ya.
Ian,
Our learned friend RWFOH has stormed out of the courtroom, and may hold an impromptu press conference on the steps outside, in an attempt to gain public sympathy for a retrial.
S/he has yet to answer the questions about where s/he lives, what actual experience of putting the wet stuff on the red stuff, direct knowledge of fires in low fuel, and due diligence with paper and pencil in checking out Erdos’ ideas.
You may soon call me ‘Dr Gam’ although Davey is just as good. As a geriatric pastime, I am just completing a PhD on bushfire history, ecology, and behaviour, using Erdos’ ideas in one of the chapters. My mathematical supervisor is an Erdos 1, if you are familiar with that aspect of connectivity. Erdos himself is 0, those who have collaborated directly with him 1, and so on. That’s why I allocated Sod a connectivity of infinity.
Poor old ‘Davey Gam’ died at Agincourt 1415. Probably something to do with close connectivity with the Duc d’Alencon’s sword. But that was before Erdos’ time.
Pathetic, RWFOH, just pathetic, you are right out of your depth. And a mathematical simpleton to boot. So “houses survived minus houses burned = zero” indeed. You have just given us the mathematical formula for a closed mind that doesn’t want to learn anything. Ignorance as a lifestyle choice.
So run along now matey, all your fellow blog trolls have deserted you. And the river you thought you could sail on is now bone dry.
Yes David, I understand Davey Gam’s weapon of choice was a blob of iron with spikes on a handle, capable of penetrating the helmets of any gentlehombre, which he did with glee, be he ne’r so vile.
Post-mortem? Green Davey had asked for Larry’s Conjecture. Due to the overwhelming interest in the problem, I’ll give a better description of the general case.
Two NON-identical n-gons have the same sides and same angles, but in different orders. What’s the smallest possible value for n? Answer: n = 5. But that’s difficult to explain, without drawing a picture. And computer graphics is not my strong suit. Anyway, here’s a description of the case where n = 6.
Start with two dowels having the same length; let’s say 10 cm. Put them side by side on a tabletop. Then separate them by a reasonable distance, as if you were about to construct a rectangle.
Using a fencing tool, cut two identical-length sections from an old clothes-hanger. Bend both sections into identical ASYMMETRIC V-shapes, each of which has a right angle.
Cap each end of the open rectangle with one of the ‘Italic’ V’s, to form a hexagon. There are two ways to do this. One of the hexagons will have bilateral symmetry; the other will not. (I hope that you’ve baked the bread dough by now.)
The minimal n = 5 part is a conjecture, rather than a theorem. I know in my bones that it’s true, but I can’t prove that n can NOT be 4.
To all those angry people who write on this site defending their own personal pro-FRB dunghills.
As in the course of my profession over the last 7 weeks, I have done much walking along the waterways all around the Marysville area employed by an agency.
As an experienced fire scientist (25 years – yes there is more than one of these people on the continent), I can tell you that it was obvious which areas to the south, west and east of Marysville were fuel reduced. The simple facts are this. The coarse woody debris (logs, etc.) present prior to the fire was still there afterwards. The fine fuels at ground level had no been reduced prior to the fire. And yes, it appears as if the area burnt was more than a 2 km radius from the town at least to the south and west.
And do you know what, the fuel reduction burning in these areas appeared to make absolutely no difference to the extreme fire intensity experienced (and presumably the rate of forward spread) – it was a fast mostly canopy fire. In many areas, it was so intense that Mountain Ash fruit was combusted in the canopy (there will be no regeneration), and the radiant heat from this canopy fire has even killed the Bracken rhizomes in the soil (despite the ground fuel being reduced). It was an extreme event on an extreme weather day, and no amount of fuel reduction (burn back to the coast if you want) would not have made any difference.
So, when all of you pro-fuel reduction burn, burn the continent as the cure-all for everything, types respond to this as anticipated, I’ll then tell you the story of the negative ecological impacts that FRB has on veg. Based on scientific fact, not twisted logic.
By the way, for the record, I do believe in FRB around infrastructure to reduce the ground intensity in lesser events, but 350,000 ha across the States per annum …..
Steve,
I’m happy to state that i’m pro burning (current operational experience in WA) and i will respond, as expected, because I dont think you give a full picture of the FRB in this case before stating that it was of no value..I find this unusual if you were being objective.
As a fire scientist you would know that a prescribed burn can vary in its intensity based on the conditions under which it is done. Your reference to woody material being left after the burn suggests that it was a mild one.. I am assuming you made a mistake in mentioning that the “fine fuels were no(?) reduced” as it is the fine fuels which are most important in producing a successful fuel reduction burn ..If they weren’t reduced I would suggest that the FRB was patchy at best and not successful in reducing fuel levels prior to the fire.
You do not mention the levels of ground fuel pre burn..In one area it may need a few mild burns in heavy fuels before the “available fuel” levels are brought down to an acceptable level without causing severe canopy scorch.. So without an understanding of fuel levels prior to the FRB your comment cannot be taken at face value… one burn may not have been enough to reduce the fire hazard to a remotely manageable level.
I’m not saying that you are wrong about it being a canopy fire however, I dont think you have represented all the facts relating to the FRB prior to the fire that would give an true indication as to whether it had made a difference or not.