by Rasmus & Jim
Who would think that Internet, ideas, disease, money, birds, and climate literacy have anything in common? Recent progress on complex systems and network theory suggests that they all can be described in terms of a ‘Levy flight‘. A recent and lengthy paper with the title ‘A study on interconnections between climate related ideas in complex networks’ (Ann. Trans. ICCPRS Soc. 52(3):1647-71; subscription required) by John McVenus argues that new ideas can be traced over the Internet just like dollar bills are traced at Wheresgeorge. Our take on this is that this study muddles things more than clarifying the facts – probably because McVenus tries to explain almost everything.
Random walks (RW) may have a much wider applicability than just describing climatic processes (see ‘Naturally trendy?‘). Recent progress on complex systems and nonlinear network information theory suggests that many information transfer and evolution processes exhibit characteristics that are effectively modeled by RW or its variants. These concepts can help us to understand the transmission and evolution of ideas in science, particularly when an extensive communication network (i.e. the internet) is a dominant communication medium, as it very much is today, and probably will be for some time.
There is, in particular, one type of random walk known as a “Levy flight“, which is simply a walk in which a highly skewed distribution of step distances leads to a small percentage of steps that are much larger than average (“jumps” or “flights”), altering the system state rather abruptly. Such behaviour can be studied with methods such as the agent-based approach for describing the spread of disease and meta-population models, but are used in McVenus to describe how information travels. Similar “agent-based” approaches are also used for example, in ecology for the modeling of metapopulation dynamics and the spread of diseases and wildfires.
After briefly laying out some conceptual and mathematical bases for Levy flight behavior and analysis, McVenus gets quickly to details. He begins a long litany of interesting examples with the recently proposed idea that orbital patterns in Jupiter and Saturn can in fact affect the solar center of mass, which in turn influences the level of solar activity, and hence the climate.
The McVenus paper also cites a small group in Norway which argues that changes in the moon’s orbit affects the climate through changes in ocean circulation, sea-ice cover, and hence the climate. This group coordinates a project called ‘Luna-Ticks’, and is interested in the idea of Jupiter and Saturn. But nobody has ever seen a Jupiter-tide or Saturn-tide here on Earth, and hence, they fear that critics convincingly will argue that the effect of the planets is pretty weak. But they really do like the idea, and instead proposed that the general principle could be translated to the moon and its measurable effect here on Earth. Everything but greenhouse gases, they argue, affects our climate.
Some bloggers have dubbed the process through which such arguments spread as ‘dispersion of confusion‘, which does not follow a simple diffusion law, but exhibits strange characteristics in addition to distant leaps in space. In addition to spreading, the ideas also change over time, morphing into new concepts, according to the McVenus paper.
While much more investigation into this topic is needed to get any sort of reasonable estimate of when and exactly how such conditions might be important, from an information flow analysis perspective, it is a fairly easy trace from there to the recent proclamation that astronomical alignments (astrology) can cause the climate to change, however strangely misguided such a pronouncement may be. Fair and straightforward enough; a good choice of examples with which to illustrate McVenus’ overall approach. But from here things start to get more complex–and highly interesting–pretty quickly.
McVenus further proposes that there is also a wealth of information to derive from all the “gates” and network analysis, because their number is rather limited and their identification is easy. Usually, a “gate” is a label telling the media to start a hype, being proposed by someone with limited imagination. But there are exceptions to this rule, such as “Colgate”. This notion also exists in plural form, such as “Billgates”.
The recent “Cowgate” appears to be a highly noteworthy Levy flight example. However, the gender of this gate turned out to be wrong – it later turned out really to be a “Bullgate”. It was traced by McVenus back to its press source via a principal system node in the propagation and evolution (usually via catastrophic mutation) of multiple climate science ideas at a web site called ‘the Gate Depot’.
It could have been no small task for McVenus to accurately trace these ideas as they went through the conceptual sausage grinder, rarely resembling anything remotely like their original form, much less some aspect of external reality as we know it. But perhaps this is just the typical warmist nitpicking about evidence, discernment, truth, reality and larger scale meaning.
This node represents what McVenus calls (using the slanderous invective of scientists, which has generated 99% of the bad blood in public discussions) “a mad man with an affinity for black listing”. The language here is unfortunate, even if the idea sleuthing is still first rate. And speaking of bloodsucking and bad blood, we apparently now have a ´Draculagate‘, fresh from the Gate Depot. But here we note that McVenus may have misinterpreted things slightly. Is that really the blood bank Dracula is in charge of, or is he rather just caught up fang-deep in ketchup? Where’s the photographic, or even metaphoric, evidence? What’s up with that? Caution is urged; the analysis is good but not without errors.
It is in illuminating such otherwise opaque connections that we simply would not otherwise make, that McVenus is at his best. For example, he tracks down how the longer term surface temperature increases are based exclusively on the completely untrustworthy HadCRUT data, which are contaminated by siting issues and more generally by the impossibility of calculating a global mean temperature. These issues also affect the regional to local scales that really affect the man in the street, where urban heat island effects are exceedingly extreme, notwithstanding all the snow this winter.
But the temperatures are still not a problem to humans in the summer because of manifest human adaptability exemplified by air conditioned buildings and vehicles, even in the third world where they are just not as obvious because of there being fewer of them. And even if we jump back to the first world, the European heat wave of 2003 that killed a lot of people in urban areas cannot be due to AGW because for the umpteenhundredth time weather is not climate, and thus the hyperbolic and incendiary alarmist exaggerations based entirely on the now utterly discredited computer modeling of Pachauri’s IPCC in Himalayanglaciermeltrategate need to stop forthwith. One does not often run across comprehensive arguments of this magnitude in one place. McVenus shines like the morning star.
But an even stranger change is seen in the disperion of confusion process in terms of a combination of the the Jupiter-Saturn hypothesis with the intelligent design (ID) concept. This aspect is not really fully acknowledged in the McVenus paper. To give some quick and concise background on this vast subject, it is important to note that Richard Bawkin, the author of “The Evil Particle” is critical to ID, and has argued that due to symmetry, everything has opposites in the universe. The particles have anti-particles, there are opposite spins in quantum physics (e.g. top spin and bottom spin), and so on. If there is intelligent design, there has to be stupid design too if symmetry holds. A quote from Oscar Wilde puts it nicely into perspective: “Where the devil is the Devil in intelligent design?”.
In logical terms, idiotic designs just proves natural selection, because over time, idiotic design doesn’t survive. A new research project proposed by John Spence had an objective to try to prove the existence of the anti-intelligent design. Colleagues have informally and jokingly threatened to nominate him for the igNobel prize. Anyway the project proposal had changed when it was submitted to the Norwegian Research Foundation: Instead of looking into evil issues, the project proposed to look for stupid designs. In particular it aims to look into stock markets, Icelandic banks, Greek economy, and accelerator pedals in hybrid cars.
However, the McVenus paper turns into a more tangled mess when it at great length discusses the propagation of ideas based on the church of ‘The Flying Spaghetti monster‘ (FSM) and almost neglects ID. The paper should have noted that FSM is an anti-thesis to the ID. Nevertheless, FSM has a say on global warming and hence influences the dispersion of confusion. According to FSM, global warming is inversely related to the number of pirates in the world. In November 2003, ‘Pirate Bay‘ was founded in Sweden, correctly acknowledged in McVenus, and the Swedes managed to elect representatives from their Pirate Party into the European parliament. Since then, some FSM-climate-protagonists have argued that the recent levelling off in the global mean temperature (from CRU!) can be explained. We think that this idea is unconvincing, even though the global mean temperature from CRU hasn’t really increased much since 2003.
An interesting and somewhat related point is that John Spence also has claimed that there must be anti-blogs too, and that there exists an unrealClimate-site. It’s not so straight forward to find it, as it uses a different name, however. Bart Verheggen from wuttsupwiththat, has pointed out the site UnrealClimate’s real name may be “blogal cooling”, but others suggest that the name of the anti-site is just made up with ‘real’ and ‘climate’ in reverse order (although they would have to swap ‘.org’ with ‘ists.com’).
There are also experts and un-experts, and organizations such as the Hartland institution provides a list of known experts in the world – and they say that an ‘expert’ is a person who does not think that an increase CO2 can lead to climate change. Many of these men and women provide part of the nodes in the agent-based approach models.
Finally, one remarkable conclusion about the spread of confusion in the McVenus paper, published by the Silly Paper Publishing Inc (SPPI), is that it’s distribution has a strong resemblance to the migration of cuckoos. In addition, cuckoos do lay eggs, and hence form new generations with new characteristics, thus changing over time, just like the ideas. Hence, he concludes, it is very likely that the confusion is spread by birds.
UPDATE: Apparently the recent story regarding the global warming activist who froze to death was missed by us. We apologize for this rank oversight; fortunately numerous other highly reputable news outlets known for their thorough fact checking have been all over it, even if their original reports of this tragedy have in some cases gone missing for some reason.
UPDATE AGAIN! Apparently, there are some who deny this story about network – they claim there are disrupted networks!
wilt says
Flxible (#146) you are right. I have never claimed that the recent “expansion” of Arctic sea ice is saying much about the summer minimum this year. And even if it does, then data from one year only should not be taken out of context. That is exactly what happened in 2007 (as M. Serreze now admits) and we should not make the same mistake again. I fail to see why such a remark would be silly, as Reisman does (#147). In my view extremists on both sides are often making precisely the same mistake by completely focusing on one piece of (welcome) information and ignoring everything else.
Completely Fed Up says
Wilt, that is a rebunked issue. Which if there had been ANY research would have been seen fairly easily.
Still nothing to prove an alternate interpretation.
Please try again.
jyyh says
#124 Hunt Janin; (what Gavin said) I guess the writer in the climate issue site was referring to West Antarctic Ice Sheet, which is being monitored quite closely. And anyway the whole sheet will not come down at once, if a large break happens there (due rain or meltwater pores decreasing the integrity of the sheet) the upper rest of the glacier will stop as it is thicker and will touch the ground after the break has happened (someone please correct if that is totally out of line). (that’s why the breakup -story on my blog is Science Fiction.)
J. Bob says
#150 Hank, I don’t think wave erosion to have an effect on sea level measurement. The scales I’ve seen are set in concrete for wave action to significantly effect results.
As far as geological raising (2-10 m/1000 yrs.), that would not be the case for Juneau.
Juneau Alaska’s sea level dropped 8m since 1940, that’s a lot of earth rising, a lot of sea dropping or questionable data taking.
Comparing Victoria BC (up ~0.5m since 1910) and across the sound at Neah Bay, WA down ~1.5m since 1935. Alameda Naval Air Station flat since 1940, La Jolla (Scripps Pier) up ~1m since 1940. And that’s just along the NE Pacific coast
Looking at the data it would seem like there is to much variability and contradictions in the data, at least of what I have looked at so far, to come to any real conclusion.
J. Bob says
P.S. eric, that Juneau data was a continuous line with NO sharp breaks so as to indicate a earthquake. The Anchorage did however have a discontinuity in it’s data.
Hank Roberts says
J.Bob, you didn’t get the point. Try that animation again. Notice that sometimes it’s the sea going up or down, and other times it’s the land side going up. That’s typical on this side of the continent. The terraces mark places where the sea and land happened to line up at some time in the past for long enough to erode some of it.
The PDF file describes some of the erosion terraces along the N. Ca. coast — and points out that pieces are rotating and tipping as well as moving along the faults and being eroded, and includes mention of rates at various points. It’s not simple. All the pieces and the sea level are changing at the same time.
Yes, you’re right that after looking at this for a few minutes you won’t understand it all. Science is like that, people can spend a lifetime working on a little piece of the big puzzle. Once they do they try to explain it to people like us.
Hank Roberts says
http://www.nytimes.com/2009/05/18/science/earth/18juneau.html?_r=1
—excerpt follows—
As Alaska Glaciers Melt, It’s Land That’s Rising
By CORNELIA DEAN
Published: May 17, 2009
JUNEAU, Alaska — Global warming conjures images of rising seas that threaten coastal areas. But in Juneau, as almost nowhere else in the world, climate change is having the opposite effect: As the glaciers here melt, the land is rising, causing the sea to retreat….
…
The geology is complex, but it boils down to this: Relieved of billions of tons of glacial weight, the land has risen much as a cushion regains its shape after someone gets up from a couch. The land is ascending so fast that the rising seas — a ubiquitous byproduct of global warming — cannot keep pace. As a result, the relative sea level is falling, at a rate “among the highest ever recorded,” according to a 2007 report by a panel of experts convened by Mayor Bruce Botelho of Juneau.
Greenland and a few other places have experienced similar effects from widespread glacial melting that began more than 200 years ago, geologists say. But, they say, the effects are more noticeable in and near Juneau, where most glaciers are retreating 30 feet a year or more.
Completely Fed Up says
“The geology is complex, but it boils down to this: Relieved of billions of tons of glacial weight, the land has risen much as a cushion regains its shape after someone gets up from a couch.”
It’s a bit more like a water bed for a giant.
Rebound occurs, unlike a couch.
J. Bob says
Hank, I chose Juneau, due to the rapid change in sea level. It is much higher the then normal continental uplift, and out of the norm. But that is one big change in 60 years. Now it could be geological in nature, I will grant you that, but it started a thread, so I went down the coast and compared Victoria and Neah bay reading. Relatively close but the sea level at Victoria is essentially flat, while Neah Bay is down about 1m. All since 1940. Do you have an explanation?
As far as “terracing”, or wave action,we are not talking long term, but within the last say 60 years. Good meter stations are set on bedrock, unlikely to be effected by wave action in 40-60 years.
P.S. Did you look at the Juneau plot? The downward trend looks fairly consistent.
John P. Reisman (OSS Foundation) says
J. Bob
I noticed you have not signed the petition yet? Why?
You said in post #281 in
https://www.realclimate.org/index.php/archives/2010/03/the-guardian-responds/comment-page-6/#comment-168402
that you only needed my thoughts on the ice extent before you signed the petition. You have now heard my thoughts, but you have not yet signed the petition?
Or did you mean my other thoughts?
—
VIDEO: A Climate Minute
History of Climate Science
Arctic Ice Melt
—
Our best chance for a better future ‘Fee & Dividend’
Understand the delay and costs of Cap and Trade
http://www.climatelobby.com/fee-and-dividend/
Sign the Petition!
http://www.climatelobby.com
jyyh says
To continue my answer to Hunt Janin: When the earth warmed up because of the Milankovich Cycles at the end of the Last Glacial Period, it took quite a while ( about 5000 years see f.e. http://shef.ac.uk/aps/apsrtp/cunniff-jen/Picture2.jpg ) of sustained warming to warm up the Laurentide Glacier to form Lake Agassiz that produced the Meltwater Pulse 1A with an ocean level rise of 5m/century. The only glaciers currently on the planet that may produce such massive floods are the Greenland Ice Sheet and East Antarctic Ice Sheet and while there are some signs that the core temperature of GIS has risen they’re not yet near melting point. I’m not very good with numbers, but judging from different images this warming of 6 degrees at the end of last glacial happened in appr. 5000 years, that is 0,012 degrees/decade so the current warming of ~0,2 degrees/decade (with a possible increase in speed) is currently about 17 times faster. If the glaciers behave as they did when the glaciers last melted with speed, this would mean appr. 300 years before a meltwater pulse occurs. This very rough approximation does NOT include the gradual ocean level rise from the West Antarctic Ice Sheet (+6m) that likely happens before as is evidenced by the fluctuations of Ocean levels during the Eemian Period.
J. Bob says
#160, Hi John. My comments were about the accuracy of the sea ice data. That is, what is the error band we are working with, on the sensors and calculations. In the discussion you seemed to use accuracy and confidence level interchangeably, which they are not. I believe you were going to replay, which I have not seen yet. So you still haven’t convinced me that Arctic sea ice area, extent, much less volume has continued to decrease. One comment, I wish they would not use the term “ice mass”, as the density of the volume is not known. Kind of picky, but this is a scientific discussion, and “ice mass” could be misleading to some.
Unfortunately, we have somewhat realistic data, to the accuracy we need for evidence of AGW, only in the last few decades. and even that is sometimes questionable. It was interesting to look at sea levels, and interesting results. Getting sea levels from:
http://www.pol.ac.uk/psmsl/psmsl_individual_stations.html
some interesting sites stood out, Jeueau had a high measured decrease in seal level sincen1940 (~ 8m). Some one can attribute to geological forces. But going down the coast, a couple of sites presented a problem, Victoria and Neah Bay. Both in proximity to each other, facing the same water. Victoria mostly flat since 1910, and Neah Bay WA dropping about ~1.5m since 1940. So unless there is some significant fault line between them, something doesn’t make sense, to me anyway. Unless the data taking is that bad.
Someone suggested wave erosion, but the few measuring stations I’ve seen are set in bedrock and concrete.
Juneau: http://www.pol.ac.uk/psmsl/pubi/rlr.annual.plots/821044.gif
Victoria BC: http://www.pol.ac.uk/psmsl/pubi/rlr.annual.plots/822101.gif
Neah Bay WA: http://www.pol.ac.uk/psmsl/pubi/rlr.annual.plots/823001.gif
Any ideas? If you want you could post your reply on the thread “Making of a Sea Level Study”, it might be more appropriate.
flxible says
JBob@162 Victoria and Neah are NOT “facing the same water”, beyond it all being salty.
The relative locations, with Victoria being on the inland side of the Island in the Juan deFuca Strait and Neah [just above the “U”] on the continent, no doubt has much influence, particularly with respect to the plates. Vancouver Island was weighted down with glaciation to below sea level and is still uplifting. The area is called “the Triple Junction” in tectonics and no doubt the spreading Juan deFuca ridge [new ocean floor being created] has an influence. So yes, there may be some “significant fault between them”.
J. Bob says
#163 fixable
Neah Bay is about 55 mi west of Victoria BC, both facing the Jaun de Fuca Strait, and both on the same N. Americian plate.
http://www.mapquest.com/maps?city=Neah+Bay&state=WA
http://upload.wikimedia.org/wikipedia/commons/4/4a/Cascade_Range_related_plate_tectonics-en.svg
I added a couple more stations from the same general area, with 60+ yr records:
Victoria: http://www.pol.ac.uk/psmsl/pubi/rlr.annual.plots/822101.gif
Neah Bay: http://www.pol.ac.uk/psmsl/pubi/rlr.annual.plots/823001.gif
Friday Harbor: http://www.pol.ac.uk/psmsl/pubi/rlr.annual.plots/823006.gif
Seattle: http://www.pol.ac.uk/psmsl/pubi/rlr.annual.plots/823011.gif
Victoria and Friday Harbor Ocean Labs are closest, about 15 mi. apart. Victoria level is about flat from 1940, while Friday Harbor Ocean Lab’s level is up about 0.5 m in the same time frame. From your reference both are about the same distance from the plate face. So is the sea level difference between Victoria and Friday Harbor due to geological differences, or in measurement methods? Or just how many significant digits are valid in the sea level measurements, with the difference of two relatively close stations above?
Unfortunately most of the ocean boundaries are along fault lines, or were buried under miles of ice. Oslo’s sea level reading dropped about 2m since 1940:
http://www.pol.ac.uk/psmsl/pubi/rlr.annual.plots/040321.gif
so about the only place where the earth seems to be relatively stable, and some longer sea level records is along the east coast of S. America, which will be my next visit.
flxible says
JBob – Sorry, I live on Vancouver Island, Victoria faces [south]east [where the weather stations are] on the inside end of the strait [toward the Strait of Georgia], Neah faces [north]east and is at the mouth of the Strait much more exposed to oceanic effects [I’d expect Neah to get double the amount of rain Victoria does, which is actually one of the driest cities in Canada], also with Puget Sound nearby, that whole area is an ecology of it’s own – not to mention that much of the Victoria area is pure rock, not sure about Neah
THEN, open both windows, Victoria and Friday Harbor, if you can and compare them side by each – note that the the graphs have different start dates [and scales?] – compare about 1982/3 to the end, they definitely varying pretty well in lock step, and with Neah as well – who knows what the numerical difference means? And what happened at that giant drop after ’82? And what effect does ElNino temperature change have? And how much tidal difference is there between Vic and Neah? You’re welcome to the can of worms that regional sea level is. :)
Hank Roberts says
> Do you have an explanation?
Try Google Scholar, look for each place name and associated search terms.
Or go to a college geology department and ask if they have a graduate student who’d like to make some money tutoring you on the field, if looking the details up yourself doesn’t suffice.
Ask how long it takes to become an expert on a particular geological location, while you’re at it.
Don’t forget to insist on recent photographs of every location, in case there’s some obvious alteration that all the scientists have missed seeing.
Hank Roberts says
Remember the discussions about the difficulty of detecting a small climate trend in a noisy data set? How noisy do you think sea level data is?
This may help: http://svs.gsfc.nasa.gov/vis/a000000/a003200/a003206/index.html
Hank Roberts says
PS seriously, once you have some of the key words used in the field, you can use those and search out an education, or at least the beginnings of one, yourself. Just as an example, 30 seconds of effort:
Searched:
http://www.google.com/search?q=pacific+northwest+geology+uplift+sink+glacial+sea+level
Found: http://academic.emporia.edu/aberjame/ice/lec09/lec9.htm#complicated
Brief excerpt follows:
“… Complicated responses
Changes in relative sea level can become quite complicated in coastal regions adjacent to ice sheets. The effects of both crustal depression/rebound and eustatic sea-level changes are involved. The coastal area of western British Columbia shows the possibilities. Most of the shelf of Queen Charlotte Sound was ice covered and depressed during maximum glaciation, >15,000 years BP. When northern Vancouver Island was deglaciated by 13,000 years BP, the shelf and coastal area was submerged under the Pacific–see Fig. 9-14. Marine shorelines were locally as much as 200 m higher than today.
Crustal rebound then took place; the coastal region was uplifted, and parts of the present shelf were eventually exposed as dry land–see Fig. 9-15. Soil development and forest growth took place about 10,500 years BP. Meanwhile fjords to the east were still depressed well below sea level. Between 10,500 and 9000 years ago, most remaining glaciers on the mainland melted and eustatic sea level rose. The results were rebound of the fjord-head region (emergence) and drowning of the shelf area (submergence)….”
(the above from an ordinary Google search)
Using the exact same terms, here’s
Scholar:
http://scholar.google.com/scholar?hl=en&q=pacific+northwest+geology+uplift+sink+glacial+sea+level&as_sdt=2001&as_ylo=&as_vis=1
Images:
http://images.google.com/images?hl=en&q=pacific%20northwest%20geology%20uplift%20sink%20glacial%20sea%20level&sa=N&tab=si
J. Bob says
#165 fixible, I agree Victoria & Friday Harbor do track pretty well,they both, and Neah Bay, have many of the same peaks and valleys. My basic question is a explanation as to WHY these had their trending differences. If one is saying the rising sea level is due to AGW, and one has these unknowns in sea level readings in the same local, it would be nice to know why the differences. If it’s plastic flow under the earth’s surface so be it. When you are measuring things to mm or cm units, it’s not nice to have discrepancies in m.
#166 Hank, yes I know what is is to tutor, I had to help a student taking a geology course. Geology was also part of a course I had in Rheology.
flxible says
JBob – I wouldn’t expect to find a simple answer to an extremely complex question concerning decimal values on a chart plotted in thousands. Martin Vermeers thread about sea level demonstrates just how complex sea level is, as do the mechanisms in the study Hank points to. What counts is the anomolies at any given point and overall, not the base measured value.
The simpliest explanation of the discrepancies in the base measure is that water in a moving container tends to slosh around. :)
Hank Roberts says
> J. Bob
> rheology
Looks like you’ve got a good start.
http://www.aip.org/tip/INPHFA/vol-10/iss-2/p29.html
Instead of asserting that “one has these unknowns” why not say “I don’t know but I’m curious and I know how to look this stuff up” — and look into it?
Hank Roberts says
http://www.agu.org/pubs/crossref/2010/2010GL042947.shtml
How will sea level respond to changes in natural and anthropogenic forcings by 2100?
“… With six IPCC radiative forcing scenarios we estimate sea level rise of 0.6–1.6 m, with confidence limits of 0.59 m and 1.8 m. Projected impacts of solar and volcanic radiative forcings account only for, at maximum, 5% of total sea level rise, with anthropogenic greenhouse gasses being the dominant forcing. As alternatives to the IPCC projections, even the most intense century of volcanic forcing from the past 1000 years would result in 10–15 cm potential reduction of sea level rise. Stratospheric injections of SO2 equivalent to a Pinatubo eruption every 4 years would effectively just delay sea level rise by 12–20 years. A 21st century with the lowest level of solar irradiance over the last 9300 years results in negligible difference to sea level rise.”
jyyh says
some kitchen thermodynamics for fun (sadly one needs a very accurate scale and a micrometer to do this properly):”Make similarly sized salty ice cubes in a freezer, wrap those in kitchen paper for insulation, warm up from upside by applying a match over it. Repeat with increased amount of matches applied at the same time. Draw a graph of melt water vs. IR-radiation (in the form of matches) from the top (hint: the weight of the paper). At which point of time does the ice cube crack ion each case? Is this because of a)water seepage to inside the cube b) unequal heating of the cube c)permeability of the ice for salts d)other, what? Do the ice cubes enlarge when warmed slowly to melting point from the freezer temperature of -20C? (apply your micrometer :-( )”