From zzpol w adjani.astro.uni.torun.pl Thu Feb 1 16:24:15 2007 From: zzpol w adjani.astro.uni.torun.pl (Zbigniew Bulinski) Date: Thu, 1 Feb 2007 16:24:15 +0100 (CET) Subject: [Shape-univ] circles-0.1.62 In-Reply-To: References: <45b0c9e16ae8b@wp.pl> Message-ID: Niestety zadna z podanych rozwiazan nie zadzialalo. 2a i 2b nie bylem w stanie wykonac, a 1 i 3a,3b nie przynioslo efektu. w zalaczniku jest plik log. pozdr zbyszek On Tue, 30 Jan 2007, Boud Roukema wrote: > Cze?? Zbyszek, > > On Fri, 19 Jan 2007, ZBIGNIEW BULI?SKI wrote: > >> Wiam! >> >> plkik pxalloc.c dzia?a teraz poprawnie lecz niestety s? nowe b??dy w >> rdWMAP_.f oraz rdCOBE.f w których jest niezdefiniowane odo?anie do funcji: >> ftopen_ >> ftmahd_ >> ftgtbb_ >> ftclos_ >> W za??czniku wysy?am raport > > ANALIZA: > > Brakuj?cy funkcji s? w bibliotece cfitsio, tzn plik libcfitsio.a je?li jest > wersja staticzna (te? istnieje wersja "shared" - podzielona). > > W zasadzie, ,,-lcfitsio" w komendzie kompilacja, ?e cytowa?e?, jest > interpretowany > automatyczny jako ,,libcfitsio.a" i jest szukany w niektórych katalogach > standardowych i w katalogach np /usr/lib/gcc/i586-mandriva-linux-gnu/4.1.1 > /usr/lib/gcc/i586-mandriva-linux-gnu/4.1.1/../../.. (tz. /usr/lib) > > Tu jest twój komend: > > f95 -g -O2 -Lcosmdist/lib -Lisolat/lib -Lastromisc/lib -o circles circles.o > xmalloc.o circles_f77.o lib/libcircles.a -lcosmdist -lisolat -lastromisc > -L/usr/local/pgplot -lpgplot -lpng -L/usr/X11R6/lib -lX11 -lm -llapack > -lblas -L/usr/lib/gcc/i586-mandriva-linux-gnu/4.1.1 > -L/usr/lib/gcc/i586-mandriva-linux-gnu/4.1.1/../../.. -lgfortranbegin > -lgfortran -lm -lgcc_s -L/usr/lib/gcc/i586-mandriva-linux-gnu/4.1.1 > -L/usr/lib/gcc/i586-mandriva-linux-gnu/4.1.1/../../.. -lgfortranbegin > -lgfortran -lm -lgcc_s -lcfitsio -lgsl -lgslcblas -lm -lgcc -lX11 -lm > > > Wydaje mi si?, ?e albo twoja instalacja mandriva jest troch? nie-standardowy, > albo skrypt configure nie dobrze dodawa? ca?ych katalogów -L/tu/katalog w > komendzie kompilacji. > > Czy mog?by? zrobi?: > > ./configure --prefix=$HOME > /tmp/log 2>&1 > > i nas wysy?a? /tmp/log ? (Je?li kto? nie lubi to czyta? na > shape-univ, niech go wyja?ni? gdzie jest b??d lub to poprawi? :P. > Albo si? wypisywa? z listy lub zmieni? jego paramety w li?cie. Na > http://cosmo.torun.pl/mailman/listinfo/shape-univ mo?esz prosi? robot > mailman > o wysy?aniu Ci twój has?o.) > > > EWENTUALNE ROZWI?ZANIA: > > W mandrivie, szukaj pakiet typu cfitsio-dev lub cfitsio3-dev lub > libcfitsio-dev lub libcfitsio3-dev lub co? podobny i to instalowa? - w > debian to jest dodatkowy pakiet dla osoby, ch?cie do > u?ycie pakiet jako bibliotek?. > > Wtedy ./configure && make && make install > > > BIBLIOTEKI OD ?RÓD?A: > > 1. Kompilowa? cfitsio od ?ród?a, tworz? bibliotek? staticzn?: libcfitsio.a > > albo 2a+3a: > > 2a. Umieszczy? go np $HOME/mylib/ jako zwykly u?ytkownik. > 3a. LDFLAGS=$HOME/mylib/ ./configure --prefix=$HOME > > albo 2b+3b: > > 2b. Umieszczy? go w /usr/local/lib/ jako root > 3b. ./configure --prefix=$HOME > > > Idealnie, 2a + 3a powinna dzia?a? tzn bez prawa root'a. W debian unstable, > dzia?a. > > > BUG: ANNOYING: W piernix-0.0.4, 2a+3a nie dzia?a? dla mnie - configure nie > mog? znale?? kompilator gcc ! Mo?e bo zale?y od pusty warto?ci LDFLAGS aby > sam dodawa? ,,standardowy katalogów" do LDFLAGS. > > > Wi?c je?li nie mo?esz to zrobi? jako u?ytkownik, spróbuj 2b jako rootem i 3b > jako u?ytkownikiem. > > To testowa?em tak?e dla liblapack.a w piernix-0.0.4 i dzia?a. > > > pozdr > boud -------------- nast?pna cz??? --------- checking for a BSD-compatible install... /usr/bin/install -c checking whether build environment is sane... yes checking whether make sets $(MAKE)... yes checking for working aclocal-1.4... missing checking for working autoconf... found checking for working automake-1.4... missing checking for working autoheader... found checking for working makeinfo... found checking whether to enable maintainer-specific portions of Makefiles... no checking build system type... i686-pc-linux-gnu checking host system type... i686-pc-linux-gnu checking for a BSD-compatible install... /usr/bin/install -c checking for gcc... gcc checking for C compiler default output file name... a.out checking whether the C compiler works... yes checking whether we are cross compiling... no checking for suffix of executables... checking for suffix of object files... o checking whether we are using the GNU C compiler... yes checking whether gcc accepts -g... yes checking for gcc option to accept ANSI C... none needed checking for g77... no checking for f77... no checking for xlf... no checking for frt... no checking for pgf77... no checking for fort77... no checking for fl32... no checking for af77... no checking for f90... no checking for xlf90... no checking for pgf90... no checking for epcf90... no checking for f95... f95 checking whether we are using the GNU Fortran 77 compiler... yes checking whether f95 accepts -g... yes checking how to get verbose linking output from f95... -v checking for Fortran libraries of f95... -L/usr/lib/gcc/i586-mandriva-linux-gnu/4.1.1 -L/usr/lib/gcc/i586-mandriva-linux-gnu/4.1.1/../../.. -lgfortranbegin -lgfortran -lm -lgcc_s checking for dummy main to link with Fortran libraries... none checking for Fortran name-mangling scheme... lower case, underscore, no extra underscore checking how to get verbose linking output from f95... 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(cached) yes checking sys/param.h usability... yes checking sys/param.h presence... yes checking for sys/param.h... yes checking sys/time.h usability... yes checking sys/time.h presence... yes checking for sys/time.h... yes checking time.h usability... yes checking time.h presence... yes checking for time.h... yes checking sys/mkdev.h usability... no checking sys/mkdev.h presence... no checking for sys/mkdev.h... no checking sys/sysmacros.h usability... yes checking sys/sysmacros.h presence... yes checking for sys/sysmacros.h... yes checking for string.h... (cached) yes checking for memory.h... (cached) yes checking fcntl.h usability... yes checking fcntl.h presence... yes checking for fcntl.h... yes checking dirent.h usability... yes checking dirent.h presence... yes checking for dirent.h... yes checking sys/ndir.h usability... no checking sys/ndir.h presence... no checking for sys/ndir.h... no checking ndir.h usability... no checking ndir.h presence... no checking for ndir.h... no checking alloca.h usability... yes checking alloca.h presence... yes checking for alloca.h... yes checking locale.h usability... yes checking locale.h presence... yes checking for locale.h... yes checking whether time.h and sys/time.h may both be included... yes checking utime.h usability... yes checking utime.h presence... yes checking for utime.h... yes checking for struct utimbuf... yes checking whether sys/types.h defines makedev... yes checking for working alloca.h... yes checking for alloca... yes checking whether struct tm is in sys/time.h or time.h... time.h checking for struct stat.st_blocks... yes checking for dirent.h that defines DIR... yes checking for library containing opendir... none required checking whether closedir returns void... no checking for mkfifo... yes checking for mknod... yes checking argp.h usability... yes checking argp.h presence... yes checking for argp.h... yes checking getopt.h usability... yes checking getopt.h presence... yes checking for getopt.h... yes checking whether make sets $(MAKE)... (cached) yes checking for ranlib... ranlib configure: creating ./config.status config.status: creating Makefile config.status: creating astromisc.lsm config.status: creating astromisc.spec config.status: creating lib/Makefile config.status: creating config.h config.status: config.h is unchanged config.status: executing default-1 commands From boud w astro.uni.torun.pl Mon Feb 5 15:26:59 2007 From: boud w astro.uni.torun.pl (Boud Roukema) Date: Mon, 5 Feb 2007 15:26:59 +0100 (CET) Subject: [Shape-univ] circles-0.1.62 In-Reply-To: References: <45b0c9e16ae8b@wp.pl> Message-ID: Cześć Zbyszek, On Thu, 1 Feb 2007, Zbigniew Bulinski wrote: > Niestety zadna z podanych rozwiazan nie zadzialalo. 2a i 2b nie bylem w > stanie wykonac, a 1 i 3a,3b nie przynioslo efektu. w zalaczniku jest plik > log. Nie rozumiem dlatego nie mogłeś zrobić 2a. Musi pierwszy tworzyć katalog $HOME/mylib/ , inaczej będzie błęd - nie możesz umieszczyć coś w katalogu, który nie ma. :) 1 sam nie może mieć efekt - kompilować bibliotekę jest tylko pierwszy krok; potem w kroku linkowanie, kompilator musi wiedzieć, gdzie jest biblioteka ta. Proponuję, wszystko jako użytkownik zwykly. # 1. Kompilować cfitsio od źródła, tworzą bibliotekę staticzną: ls -l libcfitsio.a # Jeśli ma problem tutaj, kolejny kroki nie będą mieć sens. Ostatnio raz, # kiedy kompilowałem fitsio od źródła, było bardzo prosty. Wolno (10-20 minuty?) # ale prosty. Na końce, jest plik (biblioteka) libcfitsio.a . # Jeśli OK, chodź do 2. # 2a. umiesczyć w miejsce praktycznym mkdir $HOME/mylib/ cp -p libcfitsio.a $HOME/mylib/ ls -l $HOME/mylib/ # Jeśli OK, chodź do 3. # 3a. konfiguracja cd circles-0.1.62 LDFLAGS=$HOME/mylib/ ./configure --prefix=$HOME # Jeśli ma błęd, wtedy: ./configure --prefix=$HOME # Jeśli OK, chodź do 4. # 4. kompilacja - # Próbuj: make # Jeśli masz błęd w make wtedy próbuj: emacs Makefile # Znajdź linię np LDFLAGS = -Lcosmdist/lib -Lisolat/lib -Lastromisc/lib # Zmienuj do: LDFLAGS = -Lcosmdist/lib -Lisolat/lib -Lastromisc/lib -L/home//mylib # gdzie /home/ jest wartość $HOME # Teraz próbuj make Dla logów tym raz, lepiej nas dać *całości* logów. Jeden prosty sposób mieć całości logów: script # teraz zrób wiele rzecze exit Teraz masz plik tekstowy "typescript" z całości co napisałeś i co było napisany w ekranie. Możesz to wysyłać jako log. pozdr boud >> BIBLIOTEKI OD ?RÓD?A: >> >> 1. Kompilowa? cfitsio od ?ród?a, tworz? bibliotek? staticzn?: >> libcfitsio.a >> >> albo 2a+3a: >> >> 2a. Umieszczy? go np $HOME/mylib/ jako zwykly u?ytkownik. >> 3a. LDFLAGS=$HOME/mylib/ ./configure --prefix=$HOME >> >> albo 2b+3b: >> >> 2b. Umieszczy? go w /usr/local/lib/ jako root >> 3b. ./configure --prefix=$HOME >> >> >> Idealnie, 2a + 3a powinna dzia?a? tzn bez prawa root'a. W debian unstable, >> dzia?a. >> >> >> BUG: ANNOYING: W piernix-0.0.4, 2a+3a nie dzia?a? dla mnie - configure nie >> mog? znale?? kompilator gcc ! Mo?e bo zale?y od pusty warto?ci LDFLAGS aby >> sam dodawa? ,,standardowy katalogów" do LDFLAGS. >> >> >> Wi?c je?li nie mo?esz to zrobi? jako u?ytkownik, spróbuj 2b jako rootem i >> 3b jako u?ytkownikiem. >> >> To testowa?em tak?e dla liblapack.a w piernix-0.0.4 i dzia?a. >> >> >> pozdr >> boud From blew w th.nao.ac.jp Fri Feb 9 04:13:33 2007 From: blew w th.nao.ac.jp (Bartosz Lew) Date: Fri, 9 Feb 2007 12:13:33 +0900 Subject: [Shape-univ] just a note and a small caveat Message-ID: <200702091213.34011.blew@th.nao.ac.jp> hi shape-univ, I see there's a debate going on on the shape-univ about the circles stuff. I see that Zbyszek has problems with compilations stuff /configuring/making/compiling/including dynamical, static libraries/ setting pathes/ environ variables etc or whatever first thing: I've been trough this too and I consider this as a serious hole in the programming course in the studies at UMK !!! this should be changed as soon as possible at the undergrad. level programming is not only writting one's own code but also (or maybe primarily) including smbodys others code/ objects/ libraries and it SHOULD be taught ! IMHO. and it isn't also writting makefiles, making configuration scripts etc. second thing - not quite my bussines but: Boud (,Zbyszek), unless Zbyszek deals with the circles packege only for learning how to handle with the software things, you should stop him from doing that ! It's a WASTE OF TIME since I hear his subject is not topology, but grav. lensing and cosmic strings. ! I see it now how little time there is to do anything on the PHD course, and there's NO time for looking around. :( pozdr. Bartek From boud w astro.uni.torun.pl Fri Feb 9 16:26:04 2007 From: boud w astro.uni.torun.pl (Boud Roukema) Date: Fri, 9 Feb 2007 16:26:04 +0100 (CET) Subject: [Shape-univ] just a note and a small caveat In-Reply-To: <200702091213.34011.blew@th.nao.ac.jp> References: <200702091213.34011.blew@th.nao.ac.jp> Message-ID: hi Zbyszek, Bartek, all, On Fri, 9 Feb 2007, Bartosz Lew wrote: > hi shape-univ, > > I see there's a debate going on on the shape-univ about the circles stuff. > > I see that Zbyszek has problems with compilations stuff > /configuring/making/compiling/including dynamical, static libraries/ setting > pathes/ environ variables etc or whatever > > first thing: > I've been trough this too and I consider this as a serious hole in the > programming course in the studies at UMK !!! this should be changed as soon > as possible at the undergrad. level > > programming is not only writting one's own code but also (or maybe primarily) > including smbodys others code/ objects/ libraries and it SHOULD be taught ! > IMHO. and it isn't also writting makefiles, making configuration scripts etc. As a matter of principle, i totally agree. In practice, adding more coursework for undergraduates means removing some other coursework, unless we want them to have even less time free for thiking and organising their own learning. So that's a political thing requiring wide discussion and/or something flexible like we tend to do in astronomy. E.g. piernix was a single lecture for 2nd year students this year, in the hope to get them to use gnu/linux much faster. The second difficulty is how to teach this and be able to make some reasonably objective measurement of the students' success in learning/understanding the material. IMHO it's a highly non-linear and complex process - since part of it is things like grep but it's also RTFM, finding good introductory texts on different programming languages, and also automake+autoconf which i am still only at an elementary level of understanding using. One idea i had (if i get to teach a course on this) would be to use wims (http://cosmo.torun.pl/wims) to put random errors in code and or config files etc. and then the student has to sufficiently well understand the code and/or config files etc. in order to get them to compile and/or work. Since the random error is known to wims, it can objectively check if the student correctly found the error, and more importantly, each student has code with an (essentially) unique error, so that students can freely discuss with each other the errors in their individual versions of the code, but copying verbatim without understanding fails. In other words, if the students discuss with each other (or even on forums, mailing lists, etc.) they'll have to explain and understand, not just memorise answers. Anyway, that would be a lot of work to prepare... > second thing - not quite my bussines but: > Boud (,Zbyszek), > unless Zbyszek deals with the circles packege only for learning how to handle > with the software things, you should stop him from doing that ! > It's a WASTE OF TIME since I hear his subject is not topology, but grav. > lensing and cosmic strings. ! > I see it now how little time there is to do anything on the PHD course, and > there's NO time for looking around. :( Again, i more or less agree here, though i prefer the word used in India - "guide" - rather than supervisor. i cannot "stop" Zbyszek or any PhD student working with me from working in a particular direction. Well, i guess i could make threats of not signing official documents or writing a bad report, but that's not my style and it's not going to help anyone. Rather, i think i can make recommendations, which may or may not be worth listening to, and be something of a guide. And i think it's good that PhD students who work with me can make recommendations/suggestions to each other as well, especially at this meta-level. :) AFAIK, Zbyszek *is* dealing with the circles package mainly as a learning exercise, not just for him, but also for us as a group. There's only a small number of people who use the circles package, but general software skills, including sending in bug reports and knowing what information you need to send and where to send it, and especially learning to send it to *public* bug reporting websites or forums or mailing lists, is something useful. For the most popular cosmology software (circles is not (yet ;)) so highly popular, the software forum on http://www.cosmocoffee.info is probably one of the best places to start. Also i would probably not use the expression "WASTE OF TIME" - i think the real question is efficiency in use of time - anything we spend time learning from gives us some useful learning experience. Deciding in advance what things are more or less likely to be useful is difficult. Probably a power law mix of a small number of things learnt in depth and a large number things studied less deeply during short periods of time is what most of us do and/or should do. The question then is what the slope of the power law should be and how to be sure that the total time required has a finite integral. Since we know that \int_1^\infty x^{-n} dx is infinite when n=1, it's probably obvious that either the index should be greater than 1, or we should cut off the integral to \int_1^\x_{max} x^{-n} dx . Clearly then, a small change in n or x_{max} can potentially give more time for relaxing. :) OK, enough meta-science for now... :) pozdr boud From blew w th.nao.ac.jp Mon Feb 26 12:46:15 2007 From: blew w th.nao.ac.jp (Bartosz Lew) Date: Mon, 26 Feb 2007 20:46:15 +0900 Subject: [Shape-univ] the dodec paper Message-ID: <200702262046.16179.blew@th.nao.ac.jp> Hi Boud, I put these comments also on shape-univ to stimulate discussion 1) if I understand correctly these functions have nothing to do with the circles on sky right ? Me :: 17:16:36 2) these corr. fn. should measure the cross-talk between different angular scales pesent in the multiply connected univ, but absent in the simply connected univ. is that right ? Me :: 17:18:23 3) the fig 1. is still not clear to me. what is the choice of the points you selected ? seems to me that you focus on scale x1x2 but e.g x1,g14 defines a different scale is that true ? Me :: 17:19:30 ad2) absent under GRF (gaussian random field) hypothesis Me :: 18:57:42 do I understand right that the correction to the corr. fn. due to topology comes only from the extra correlations from various ang. scales only when at least one point is fixed at a circle ? then the extra correlation signal comes from the matched pixel in the matched circle seen at totally different angle relative to the second direction in the corr. fn. is that right ? in that case you're looking for an extremly small signal Me :: 19:00:21 because in case of all other correlations in a corr. fn. calculated for the hypothesized PDS model, when none of the directions is fixed at some matched circle any possible images are currently not accessible in the SLS. Me :: 19:01:17 if this is the case then I don't userstand why you get such a huge discrepancy between the SCU model and the PDS model Me :: 19:05:22 ----------------------- above was from gg. cont. below. to be honest the paper is rather unclear. I'd propose make lots of wording changes regarding statistics of CMB field, and regarding maps details. but this isn't very important at the moment except that it makes for me things harder to understand. the paper focus on 3 quite independent points: 1)putting error bars and CLs onto S statistics of the RLCMB04 2) shows again the phase relation 3) does the corr. fn. test as for (1) I see you haven't change the analysis at since our last talk on this, so I have the same objections to it as the last time. If you want corrected GRF simulations of WMAP 3 yr I'm happy to contribute this way. (these however will not be suitable for Tegmark's map) (I can easily generate also WMAP1 maps if you like) basically one simulation should be enough and then you could get your distributions by calculating S on maps rotated by an 3 random Euler angles, but for the same orientation of the PDS model. I disagree (mostly) with the analysis given in sec. amplitude ;( If you can find "anything" your results is meaningless, and you need change the approach. btw. do you know that there are the Steven Hawking's initials in the WMAP data ? does it mean anything ? (sort of close to the galactic plane and at around l = 50 or so :)) the assessment of the CLs on the fig.2 is not very clear or convincing and transparent. btw. I'd like to see also -1, -2, -3 sigma contours. I understand that you get the CDF error function for S stat. but in that case you should plot S stat. of the WMAP data, not S for individual pairs. I'd like to see this one too. if you resolve 3 sigma contour, this means that you need to probe at least something like 1000 random circles for each alpha, is that right ? as for (2) IMHO the phase analysis is very relevant to the amplitude analysis. However it's already included into S analysis. S has all the info. about the model that is need. if you'd calculate the S err. fn. from RGF sim. rotated 1000 or 10000 times randomly for the same PDS you'd have it all right IMHO. In fact showing the S vs phase does not carry any additional information about the likelihood of the RLCMB04 result. (of course the best thing to do would be to have 10^4 sims. to assess the errors but probably it'd be enough to use only Nsim= #of rot./ effective number of pixels in the 2deg FWHM smoothed maps or so) as for (3) the corr. fn. part I'm not sure If full understand so will wait for your comments and explanations. pozdr. Bartek From boud w astro.uni.torun.pl Wed Feb 28 14:54:31 2007 From: boud w astro.uni.torun.pl (Boud Roukema) Date: Wed, 28 Feb 2007 14:54:31 +0100 (CET) Subject: [Shape-univ] semestr zimowy 2006/2007 - 5ego punkt... Message-ID: Witam shape-univ, Wydaje mi się, że dla semestr zimowy, dwa osoby zrobili 5ego punktu, jeszcze trzy mają (mogą) to zrobić. Zawsze myślę, że zrobić coś kreatywny, związany z tematem, ale zrobić to w sposób publiczny - tzn, że masz intelektualną odpowiedzialnością dla co zrobić, czy jest coś prosty czy komplikowany - jest ważna część badania naukowa. To nie tylko ważny dla badania, też jest dla znaleźć pracę w np informatyce. Cytuję od toruńskiej grupy użytkowników linuksa: http://www.man.torun.pl/cgi-bin/wa?A2=ind0702&L=tlug-l&F=&S=&P=859 > > I chyba dlatego osoby z własnymi projektami są tak cenione - wiadomo, że > > potrafią radzić sobie z problemami i wiadomo, że znają się na rzeczy a > > nie polegają tylko na tym, co im pokazano na ćwiczeniach. > > > Na osobny temat zasługuje wychowanie i nawyki - znaczna część młodych > ludzi przejawia postawę roszczeniową wyniesioną jeszcze z domu. W takim > wypadku trudno o podejmowanie wyzwań, kreatywność, uczestnictwo w > projektach czy zwykła ciekawość świata - liczy się bryka, kasa i nowa > komóra osiągnięte po linii najmniejszego oporu. Skłamałbym, gdybym > powiedział, że kiedyś tak nie było. Było, ale teraz zjawisko się > niepokojąco nasiliło. W przypadku naszego wykładu monograficznego, zrobić całego projektu dla jednego punktu nie jest wymagany, ale kreatywność zaczyna od pierwszych małych kroków. Więc, moim skromnym zdaniem, warto zrobić coś kreatywny (i użyteczny). W każdym bądź razie, dodawałem nowy przykład punktu do: http://cosmo.torun.pl/Cosmo/MonographCosmo punkt, na czymś ktoś (ewentualnie dwa studenci z IIIego roku) mogłby pracować: Hasła http://pl.wikipedia.org/wiki/Prawdopodobie%C5%84stwo_obiektywne i/lub http://pl.wikipedia.org/wiki/Prawdopodobie%C5%84stwo_subiektywne są względnie zły z porównanie do http://en.wikipedia.org/wiki/Frequency_probability i http://en.wikipedia.org/wiki/Bayesian_probability - to prawda, że "frequentist" interpretacja prawdopodobieństwa jest więcej konserwatywna niż interpretacja bayesowska, ale ten druga nie jest całkowicie subiektywna. W każdym bądź razie, interpretacja bayesowska jest dużo używana w kosmologii nowoczesnym (np ,,Czy Wszechświat jest płaski 'jak Ziemia'? lub nawet więcej płaski?"), więc warto wiedzieć, co to jest, ale też wiedzieć, co to jest interpretacja więcej konserwatywna, tzn. frequentist. (,,częstotliwościowa" ?) pozdr boud