about the leakage at Tricastin
July 16th, 2008An update to my comment to this randform post. In their latest publication the french authority for nuclear safety ASN is declaring that concerning the accident at the Tricastin nuclear power centre:
Les dernières mesures réalisées dans l’environnement semblent indiquer un retour à la normale pour la quasi-totalité des points surveillés dans les eaux superficielles et les eaux de nappe. Deux points de mesure des eaux de nappe qui ont montré ou qui montrent des valeurs plus élevées que la valeur guide préconisée par l’OMS pour les eaux destinées à la consommation humaine retiennent l’attention des experts.
So “retour à la normale” sounds as if everything is OK again – after the leakage. Unfortunately this is not the case. Besides some doubts about the official versions (for example an independent investigation of the organisation CRIIRAD found atoms with a mass of 236 which is probably Uran 236 and thus contradicting the statement that only natural uranium had been spilled (info via Schockwellenreiter)) one should note that the latency time for cancer due to incorporated radioactivity (the radiotoxicity of uranium as well as plutonium is is mainly due to alpha radiation and such it is mainly dangerous if incorporated) for bone, liver and kidney cancer approximately 20-30 years for Leukemia it is about 2-10 years. So higher cancer rates will probably be visible only after that times (if they are monitored at all?)
Still it seems that things could have been much much worse. I dont know what exactly is processed at Tricastin, but the fact that France’s fast breeder the Phenix is much closer to the Tricastin site than to the site of the reprocessing plant at La Hague and the fact that it seems that it was already discussed to built an EPR at Tricastin, which as I explained here and here may burn MOX fuels (and thus also Plutonium) could mean that people were lucky that it was “just (unenriched) uranium” and not plutonium, which was spilled. Why? Because plutonium 239 has a specific activity which is about 180.000 times bigger than uranium, as can be seen in this table by the University of Oldenburg. Roughly means: If you incorporate the same amount of uranium 238 or plutonium 239 then plutonium is about 180.000 times more dangerous.
Who is Fr. Ed. Mueller?
July 10th, 2008The above scientific visualization (which displays the wave pattern of a little droplet dropped into mercury in one focus of the ellipse) can be found in a book by Wilhelm Weber and his brothers Ernst Heinrich Weber. It can be found in principle on p.582 in the html version or on p. 619 of the pdf version at a google books scan of the book: “Wellenlehre auf Experimente gegründet, oder, über die Wellen tropfbarer Flüssigkeiten mit Anwendungen auf die Schall und Lichtwellen” (The theory of waves based on experiments or about waves of drippable liquids with applications to sound and lightwaves). The book is from 1825. Unfortunately the google scan has not such a nice quality as e.g. a scan of galileos works mentioned in this randform post. In particular in the google scan one can’t read that the drawing was made by:
Is Fr. Ed. Mueller the secret pioneer of Op Art?
Tenjin
July 9th, 2008I got some hints that my last posts were a bit too technical. So here some pictures from Tenjin in Hakata. It is not easy to summarize all the impressions one gets from this part of Fukuoka. It is a strange mixture of decent shops and restaurants on one hand and on the other hand bars, which look more as if they belong to some red light district. There were quite some women on the roads which didnt look too happy.
Fukuoka graffiti
July 8th, 2008nuclear future-part II
July 3rd, 2008I hereby post the answer to new comments by a reader called Ken concerning the previous discussion about the future use of nuclear energy (please see the preceding posts). Again I think that they give a fairly good overview about the current stage of the discussion.
Ken’s comments are again in light grey blockquotes.
You again misunderstand the concept of a resource peak. It is when the supply and demand curves deviate. Not when the resource runs out.
Hi Ken, thanks for the comments, here my answers:
In the blogpost I wrote: “with the nowadays conventional commercial use of nuclear energy the Uran sources will be finished in about 60 years.”
In my answer to your last comment I wrote:
“..you can put it also like this: it seems to be cheaper to built breeders than to employ more costly exploitation methods.”
So maybe I expressed myself unclear. With “nowadays use sources will be finished” I meant that uranium wont be available anymore for the nowadays use and prices. So this is in particular the case when supply and demand curves deviate. Means: instead of the nowadays use of nuclear energy one will make more and more use of other technology in order to compensate for the higher and higher prices for uranium exploitation. It is clear that there will be in principle still Uranium on earth in 80 years, but it will be harder and harder to exploit it, so one will increasingly built breeders.
U233 is the desired product of the Thorium cycle, not a waste product.
First even if you would use U233 in a closed cycle, I believe that there will always be rests in the reprocessed spent fuel. Secondly to my knowledge up to now there exist only research plants, which are capable of burning U233.
According to world nuclear
India thinks about burning U233 in a three stage process:
* Pressurised Heavy Water Reactors (PHWRs, elsewhere known as CANDUs) fuelled by natural uranium, plus light water reactors, produce plutonium.
* Fast Breeder Reactors (FBRs) use this plutonium-based fuel to breed U-233 from thorium. The blanket around the core will have uranium as well as thorium, so that further plutonium (ideally high-fissile Pu) is produced as well as the U-233. Then
* Advanced Heavy Water Reactors burn the U-233 and this plutonium with thorium, getting about 75% of their power from the thorium.
So according to this plan, next to the uranium-233, plutonium will be produced in a fast breeder. Given that Russia has already problems to burn all of its plutonium from old weapons (half life of Plutonium 239: 24,110 years), it is clear that this creates a plutonium market which wants to feed itself. And just think about the high proliferation risk of plutonium.
I can give the British Jounal of Cancer Research article that shows the inverse correlation between proximity of children to nuclear power plants and the incidence of cancer.
Yes thanks I would like to have a look at it.
When I spoke of cancer causing chemical agents I was not referring to those leaching from nuclear power plants, I was speaking for those from the hundreds of vastly less regulated industries that are in the same areas nuclear power plants are located as well as distrubuted through out the country.
These industries could be a reason for cancer, so it would be important to include the local industries in a study which investigates the causes for a higher cancer risk near a nuclear power plant.
You vastly underestimate the difficulty in containing the witches brew of heavy metals that come form coal burning power plants and claim falsely that it is easier to contain mercury from coal plants, which accounts for up to 40% of all environmental mercury and will stay with us for a very long time. Mercury is only one toxin emmited and rarely contained from coal plants. The waste from nuclear plants is contained. Very little ever makes its way into the environment.
I didnt claim that it is possible to fully contain mercury from coal plants, I just said that there exist mercury filters, which one could think about employing in existing coal plants as a fast measure against blasting all this mercury into the air.
As a matter of fact it seems that also burning forests contribute to the mercury in the air, in this article in a (rather conservative) german newspaper it is claimed that this contribution is far higher than by coal plants.
But again: I am not in favour for coal. In particular if we speak about conventional green house gas emmitting power plants then there is a variety of alternative power plant types, which seem to be less environmentally harmful than coal plants.
And again: in principle one should try to do everything possible to employ renewable energies sources and not greenhouse gas emitting sources.
Although I should feel honored by the attention, your analysis is more polymical than analytical and so I really am just frustrated by your response.
Would I spent all this time answering carefully to your comment if I wanted to be polemical? I surely take your comments serious, last not least one can only test back ones own hypothesis’ in a discussion.
Second comment by Ken:
Here is the problem,
“In short: if mankind is unable to deal with this rapid expansion it probably doesnt matter how we blow up our planet.”
Why do you think this is even possible with commercial nuclear reactors.
The question was how to deal with a rapid population and industrial growth/expansion. The problem is that with or without commercial nuclear reactors at some point the problems regarding the distribution of ressources, let it be food, place, energy etc. will accumulate. And it is very suggestive that there will be wars about scarce ressources. Thats what I basically meant with “blowing up the planet”. Nuclear reactors do not help in solving these substantial problems. On the contrary due to a high proliferation risk, due to a hardly controllable waste problem etc. they just postpone and make the problems worse and rather irreversible. Like if a soil is radioactively polluted then it is lost for a long long time.
Also your argument for “renewables” is not founded on physics. No matter how efficient you think that wind mills will become, they will not provide the power needed. You can debate this, but you will lose. Solar is the same. The cost of these technologies are also (meaning in addition) prohibitive.
I consider solar energy to be a renewable energy. Regarding the costs one has to take into account a lot of things.
Look at the example of photovoltaic solar cells (it is the example I know about best, thats why I prefer to use this example over windmills, hydropower, thermosolar energy, geothermal energy or other renewable energies, but there are similar arguments for these energies). So just as an example: Solar cells used in spain produce electricity which costs roughly as much as electricity produced in conventional power plants. In Germany this looks different, because there is just not so much sun. So one has to look carefully at the local circumstances. The price e.g. for photovoltaic solar cells depends currently highly on the price of high pure silicon which is currently rather high due to the demand for high pure silicon in the semiconductor industry. But first this price is declining and secondly there are now slowly emerging companies who specialize on producing silicon for solar cells (which needs not always be that highly pure). Moreover there is a lot of research going on with other materials for photovoltaic solar cells. So there exists prognosis’ that the price for electricity produced with photovoltaic solar cells will be even in Germany down to conventional energy prices within a few decades. I wrote a bit about solar cells here in this and this post.
We have here also the question of where the money for research went and goes. I still think there should be some money go into research in nuclear energies, however the bulk money should be put into renewable energies and energy saving technologies. There is now a project of a whole city to be built in Abu Dhabi, which will be “fueled” only by renewable energies.
So my argument for “renewables” is definitely founded on physics and even on economical considerations.
Spent fuel rods are DANGEROUS. Stand within a score of meters of one after it has been pulled from a reactor and it will kill you with an absolute certainty. So will standing inside a blast furnace. I do not suggest that you do either. So what? Nearly every home in the Western world, by law, has trace amounts of Americium. It is classic reactor waste. It is probably in your hall way, keeping you safe. Millions of smoke detectors are thrown away in land fills every year. This is the same stuff that the famous radioactive boyscout used to drive his back yard nuclear reactor. I do not advocate being caviler about this, but you definately have expressed a favoritism towards coal over against a technology that is vastly less polluting, not just in terms of heavy metals but CO2 and acid rain.
I again like to point out that I am not in favour of coal.
It is safe and efficient and you would prefer that we put up windmills that are inefficient.
What means safe? With any technology you may have problems and sometimes life-endagering problems. The question is just, where do we expect more problems and where is a higher likelyhood of problems. windmills are definitely less dangerous than nuclear power plants, especially on a long term basis. About the efficiency of renewable energies I wrote already above.
Reactor and fuel designs are evolving very rapidly as well. You are using statistics to swat at gnats when there are vultures circling. Compared to the heterocyclic hydrocarbons, heavy metals and other toxins produced by a variety of industrial activities, the trace amounts of radiation that might leak into the environment from nuclear power plants is not harmful.
If a nuclear power plant works as planned then you are right, the traces of radiation should be OK with the given scientific knowledge. But firstly this scientific knowledge may change, like for example the recommended values for an absorbed dose are largely based on scientific studies done in relation to the events in Hiroshima and Nagasaki, so under quite a bit different conditions than the one one has in the case of a longterm dose of a nuclear power plant. Secondly I think the problems due to nuclear waste, accidents (think also of transport) and proliferation are much more important than the radiation of a normal working power plant.
We live in a cocktail of chemicals, how do you so easily single out radiation as the source in any epidemiological study, it seems like it would be very hard.
Where did someone single out radiation as a source?
The childhood cancer study gave no reason or cause for the higher incidence of Leukemia they ust stated that there is a higher risk.
The researchers said (but that was not part of the study) that given the
allowed radiation from a power plant and given the current scientific knowledge of a harmful absorbed dose one shouldnt get a higher Leukemia risk by living near a power plant. But the study says that there is a higher risk. So in short: There s a higher risk, but nobody knows why.
A good indication wether radiation is the source for that higher Leukemia risk would be to look wether the occurences of Leukemia are spatially homogenously distributed, but maybe they do not have not enough samples for that. I dont know.
People get worried about harmful isotopes within fuel rods but drink organo-mercurial compounds without a second thought. They fret about radiation causing the leukemia around Sullifield, even after it is demonstrated that the real culprit was munitions manufacturing during WW II.
I didnt look into that case.
Is it better to figure out a way to clean up the chemicals or get rid of the reprocessing plant. I’ll bet if you did the later it wouldn’t affect out comes that much. but would cost resources that may be better spent attempting the former, I’m just guessing.
You won’t get rid of the reprocessing plants. Reprocessing plants are used in order to reuse parts of the spent fuel, you could e.g. use reprocessed uranium in a fast breeder or plutonium in MOX fuel.
If you shuttered the nuclear plants you would replace them with coal fired ones. Would that be a step in the right direction? You believe that you are doing the right thing in your opposition to nuclear power, are you?
The share of nuclear energy is currently about 6% of the total worldwide energy consumption. Alone better energy saving would reduce the energy comsuption by far more than 6%, so you wouldnt need to replace them with coal plants. On average. What do I mean by on average? This means that also if you have to built a coal plant, because you couldnt provide renewable energies fast enough to substitute the need of electric currency at a particular location (a location where you switched off a nuclear power plant) and because you dont have the money for a cleaner conventional green house as emmitting power plant (one could see this as an international task to help developping countries in avoiding to employ coal plants) then there should be a coal plant saved somewhere else, where energy saving and renewable energies were already efficiently employed.
Yes at the moment I think I am doing the right thing in opposing commercial nuclear power, but I am also very concerned about the global warming (see eg here, so in particular i see keeping up nuclear research as a fall back option in case global warming would lead to a series of survival-of-mankind-threatening effects. But currently this is not the case. So as I already wrote at the moment I think nuclear energy is rather counter productive in solving the problems and I am not suggesting good old coal as the preferred substitute.
nuclear future
July 1st, 2008I decided to post hereby my answer to a comment on the last nuclear energy post (please see below), because people usually do not read the comment section and because I think this small discussion with a reader called Ken gives a good overview about the current situation. I included Ken’s comments in blockquotes (letters in light grey):
Hi Ken thanks for the comment. Please let me comment on it:
Is the untested technology you speak of the use of the Thorium cycle instead of the Uranium cycle? It’s safer.
I spoke of both. In this elder randform post (which I linked above) I agreed with you that the Thorium cycle seems to be safer than the U-238 – that doesnt make it safe though.
With current methods of uranium mining it is expected to peak in 50 years. This does not mean it will run out. Uranium is freely soluble and the Japanese have developed a method of extracting it from sea water. It will cost a lot more than the current spot price but it will be inexhaustible.
My source about the limits of Uran was the website of the World Nuclear Association – a PRO nuclear organisation, which is fairly matter of fact. At the time when I wrote the post they listed 60 years, they currently have the opinion that it may be 80 years. I cite:
“Thus the world’s present measured resources of uranium (5.5 Mt) in the cost category somewhat below present spot prices and used only in conventional reactors, are enough to last for over 80 years.”
On the seawater option they say:
“…seawater (up to 4000 Mt), which would be uneconomic to extract in the foreseeable future.”
So of course in principle it is possible to extract more Uranium. However given the current use and exploitation methods the ressources will be done in about 60-80 years. Given the current development of breeder technology and what is written on their webpages you can put it also like this: it seems to be cheaper to built breeders than to employ more costly exploitation methods. Please take also into account that nuclear energy is on the rise. So the ressources may be faster finished than assumed.
In addition, Thorium is the fuel cycle of the future and uranium will be used primarily to drive this, although plutonium is also a good source of neutrons from the reaction creating a market for reactor produced and weapons grade plutonium leading to its destruction.
You are right that breeders may create a new market for plutonium, something I actually mentioned in another post, where it seems that the US is going to built a reactor type, which can burn MOX fuel. Why do you think this is good?
Childhood cancer in France is lower than in the rest of Europe.
I may believe you, but that doesnt say much.
If childhood cancer in France is lower than in the rest of Europe, – and if nuclear power plants are a source for cancer- then this could mean that the density of nuclear power plants in France is still low enough for being recognizable as a risk factor on a national level.
As a matter of fact the reactors in France are probably also fairly well maintained.
Your statistics do not link radiation from nuclear power plants to cancer.
Well yes, the childhood cancer study doesnt link radiation from plants to cancer. BUT – that was not the point of investigation of the study!
The study says that a child is clearly more likely to get Leukemia if it lives in the vicinity of a nuclear power plant. The study doesnt say anything on the cause for this higher likelyhood! In fact I could imagine that the cause may actually be more due to radioactive ground water or radioactive particles in the air than to radiation.
There are many cancer causing chemicals that have not been excluded which are likely to >co-exist with any isotopes which you have given no evidence for actual exposure to.
yes the non-radioactive chemicals used in a nuclear power plant can also be a cause for a higher cancer rate. I didnt exclude this. But that would be bad enough. Wouldnt it?
If these is a cause for any increased up tick in cancer rates (and not, for example increased life >span, which is also a risk factor), then by supporting the quasi-religious view that nuclear power is evil you could in fact be diverting attention from a true danger that could be removed or dealt with.
I said in that above mentioned elder randform post that I actually would support research in nuclear technology, so I definitively have no quasi-religious view on nuclear power. I am just very concerned about the future commercial use of nuclear energy -especially with regard to worldwide future energy consumption. Last but not least it is the scale which makes a real difference.
And i think especially the waste is a big, big problem.
The example of this that pops to mind is the much touted Navajo Neuropathy story from NM. This is caused by a point mutant originating in a single individual and is recessive. The anti-nuclear people claim that it was cased by uranium mining, which started in the 1950’s. No one explains how in 50 years time this amount of inbreeding could happen to account for scores of families being affected, but that didn’t stop the LA times from linking it to uranium. I think that the people in NM would be better served by access to genetic testing and consulting, but I’m an advocate for nuclear power, so I must just be nuts and not know what I’m talking about. There was mining for uranium and there are people in poor health and they both exist in the same place, ergo…
I dont know about this case.
The burning of coal is vastly more dangerous than the small amounts of radioactive waste produced at nuclear power plants. These include tens of thousands of tons of mercury, chromium, arsenic, lead, uranium, and thorium. This is spewed into the air along with carbon dioxide, nitric and sulfuric acid and silicate particulates. This is your true alternative that you are promoting to radioactive isotopes contained within zirconium ceramic fuel pellets in intact fuel assemblies in overly engineered fuel.
I am fully aware that burning carbon causes tremendous environmental problems.
However I think one can easier deal with them than with the ones from nuclear energy, like for example with filters etc. At the moment I think that it is easier to deal with a rapid global warming due to too slow development of renewable energies than with a rapid expansion of nuclear energy.
In particular I am not in favour for coal. I think the question is more how to deal with overpopulation and a rapid industrialization. As I wrote above -even breeders will provide energy for only a relatively short time period (looking at the time of existence of mankind). In short: if mankind is unable to deal with this rapid expansion it probably doesnt matter how we blow up our planet.
The ressources let it be energy, food or place are limited. period.
Enforcing nuclear power seems to me rather a way how to postpone and enlarge the real problems.
If one would get a hold of this rapid expansion then by employing measures like energy-saving architecture etc. renewable energies will be fully sufficient in my opinion.
In around 500 years, most of the biologically dangerous isotopes are decayed to natural levels.
No. As an example: Uran 233 (produced in the Thorium cycle) has a half-life of 160000 years.
They pulled intact wooden furniture from King Tut’s tomb, I think that we can safely sequester the small amount of waste produced from nuclear power plants until it poises no threat.
I dont understand this argument.
The Mercury from the coal plants that you are advocating will be circulating around the environment for eons.
There are already pretty good mercury filters, they are just not everywhere installed.
Sorry dude, the future is looking to be nuclear, not your precious coal.
As I already pointed out, I am not in favour for coal. Concerning the nuclear power: I fear you may be right.
special functions special
June 27th, 2008The US National Institute of Standards and Technology has released a beta version of some chapters of a Digital Library of Special Functions. The final atlas is expected 2009 and shall be available in print as well. The figures showing graphs are in 3D as well and here good old VRML comes back again. If I had been asked I kwould have opted for either a more recent file formar or a simpler one.
just waste
June 26th, 2008
“Die Toteninsel im Nebel”, artwork by Justin Hoffmann
This is an update post to a previous post about a nuclear dump site near San Francisco. I will discuss in this post here a possible relation to an increased risk of cancer near San Francisco.
Due to the alarming results of the IPCC study concerning the world climate the discussions about using nuclear energy got a new boost. An often heard argument is that nuclear energy is relatively safe and that nuclear fission is a fairly well tested technology.
This is not true.
First the old technology is not as safe as assumed, as pointed out e.g. in this study. And secondly and more important: future use of fissile techology would make rather new and untested (and on average more dangerous) techologies necessary, namely the technologies of BREEDER REACTORS. (please see this randform post (and the therein cited other randform posts) for details)
Why? – because with the nowadays conventional commercial use of nuclear energy the Uran sources will be finished in about 60 years.
In this post I also gave a rough outlook on how an increased demand of nuclear energy (which accounts nowadays for about 6 percent of the total worldwide energy consumption) by a factor of ten would change the world.
– One may infer that a factor ten is too big since it would mean that 60 % of nowadays worldwide energy consumption would be covered by nuclear energy, however given the general increase of energy consumption this portion will shrink very fast and will still leave us with about 4000 new nuclear power plants (instead of nowadays about 450).
And these are nuclear power plants in a rather untested technology as pointed out above.
Likewise the nuclear waste problem is accumulating over the years- means if the waste per year is ten times more than before it will be in ten years 100 times more than in the initial year.
And nuclear waste is longterm problem.
An example:
In this randform post a considerably small nuclear waste problem (an old nuclear dump site near San Francisco) was mentioned which may have affected the lives of people.
I looked into this example a bit more.
If there is an environmental cause for an increased cancer mortality rate it is not far fetched to assume that there should probably be also an increased childhood Leukemia mortality rate (especially given the above mentioned study about childhood leukemia). So I looked wether I could find something there. However there is a study carried out mainly by the Center for Occupational and Environmental Health which says:
A simple and direct analysis of the spatial distribution of childhood leukemia was performed using geographic data from a large case/control study. The data consists of cases of childhood leukemia and their corresponding birth cohort controls located in seven San Francisco Bay Area counties. Both parametric and randomization analyses show no evidence of a non-random spatial pattern of childhood leukemia among six of these counties….
So the study found no spatial pecularities, i.e. no increased risk of childhood Leukemia in Marin County. Based on geographical data using GPS:
…the latitude and longitude coordinates were mathematically transformed so that
distance is measured in kilometers; that is, a new Cartesian
coordinate system was established in kilometers relative to
the latitude and longitude point (37.5, ± 122.5). Nearest
neighbor distances were then calculated to compare
statistically the spatial patterns of cases and controls.
So with statistical methods nearest neighbour mean distances between living locations of sick children (case/case pairs) and sick/nonsick children (non-case/case) where compared where
When no spatial pattern exists, the mean nearest
neighbor distances calculated from case/case and non-
case/case pairs are expected to be equal and the frequency
of the case/case pairs is expected to be equal to a known
value that depends only on the number of cases and
controls sampled.
If I understood correctly the statistical techniques used in the study are based to a great extend to techniques listed in this article.
I currently do not have the time to look into all the details but what I find important to mention is that the study (if I understood correctly) compared a total number of 12 (case+non-case/control) observations in Marin county. (In all the counties 333 observations).
The Northern California Cancer Center has a quite well documented archive of cancer statistics, which is publicly available to some extend and I looked briefly into it. Unfortunately spatial differences in cancer occurence are only listed since the year 2000.
But to my worry: on a first glance (which is just a suspect and NO statistical analysis!) one CAN actually observe spatial pecularities for Marin county, i.e. the five year death counts of cancer for Marin county seem to be increased for : skin cancer, the already mentioned breast cancer and Leukemia (where no difference between adult/non-adult had been made). (I looked only at death counts in order to avoid errors from over-diagnostization).
This means on the other hand: If this first glance would turn out to be of statistical significance than an environmental cause is rather likely.
Looking at the statistics it is clear that the local pecularities of cancer mortality rates for e.g. liver cancer (probably due to too much drinking) or Karpozy Sarkoma (due to Aids) in San Francisco look much more dramatic than the local pecularities of Marin County – just already by the sheer size of death cases. However for the individual case this is no consolation.
Concluding: this “small” waste problem (if I understood correctly the authorities see NO problem) MAY have had already quite dramatic consequences.
This tells us what?
IF it would turn out that there is a nuclear waste problem in Marin County (I again emphasize, what I found are only loose suspects) then just extrapolate this for the to be expected nuclear waste problems (see above) and how authorities would deal with them.
But apart from this – lets put it that way: I wouldnt necessarily swim in Marin county waters anymore until this question hadn’t been thoroughly examined.
La done butterfly
June 19th, 2008The above image displays a visualization of the socalled blancmange curve at various iteration steps and with a slightly randomized sawtooth function. The blancmange curve -not to confuse with the blancmange pudding– is -like e.g. also the devils staircase a socalled pathological function, i.e. a function which displays a counterintuitive behaviour. In order to obtain the blancmangecurve one sums up little sawteet h which get smaller and smaller. However also if the sawteeth are getting in the end infinitely small this particular curve will never be smooth.
mathematical subleties after the more