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Text of the page (random words):
e cold that is expected to affect today s inauguration would be less of a problem then so the two have coincided on monday january 20 1997 clinton s second inauguration and monday january 21 2013 obama s second given the 28 year cycle of the calendar in the short term this continues 2025 2041 2053 2069 2081 2097 but that 28 year cycle relies on leap years coming every four years and 2100 won t be a leap year so there will be irregularities around 2100 and also 2200 and 2300 the full calendar follows a 400 year cycle in which the coincidences are in the following years blue is years when mlk day falls on january 20 red on january 21 2013 2025 2041 2053 2069 2081 2097 2109 2121 2137 2149 2165 2177 2193 2205 2217 2233 2245 2261 2273 2289 2301 2313 2329 2341 2357 2369 2385 2397 and every 400 years thereafter across century boundaries you get a recurrence after 12 or 40 years plus 2 or 9 leap years as from 2097 to 2109 so in a full 400 year cycle there are 13 occurrences of monday january 20 in the year after a leap year like today 16 occurrences of monday january 21 in the year after a leap year like in 2013 so today s coincidence happens 29 times out of 100 or very nearly two of seven also former president jimmy carter died on december 29 at age 100 after a surprisingly long period in hospice care nearly two years he wanted to make it long enough to vote for kamala harris which he did on october 16 his birthday was october 1 i like to think he did not want his funeral to take place under trump flags fly at half mast for thirty days after a president dies so has a president ever been inaugurated in this period of mourning as a quick estimate there have been 45 distinct presidents but five the younger bush clinton obama biden trump are still living so there are 40 dead presidents therefore if this has always been the law there have been forty months of such mourning presidents are inaugurated every four years so we d expect something like 40 48 of these i am of course ignoring non regularly scheduled inaugurations caused by a president s death they don t get a ceremony anyway as it turns out there was one harry truman died on december 26 1972 putting nixon s second inauguration on january 20 1973 within the period with flags at half mast flags won t be at half mast today in washington and in many states but will go back down after the inauguration this is as far as i can tell because trump is petty there are two georgians he doesn t want to share his day with michael lugo uncategorized 1 comment january 20 2025 january 20 2025 2 minutes morrie s law plus one john cook tweeted from his account analysis fact sin 6 sin 42 sin 66 sin 78 1 16 analysis fact analysisfact june 15 2023 i responded that this feels like it s in a family with sin 30 1 2 sin 18 sin 54 1 4 sin 10 sin 50 sin 70 1 8 michael lugo miclugo june 15 2023 the third of these was somewhere in my head the first one is trivial i had to play around a bit to find the second one these all have in common that the arguments are all whole numbers of degrees which isn t as arbitrary as it sounds that s from a set of rational multiples of π the product with n terms is 1 2 n so what s going on here it s probably a bit more revealing to write the identities in terms of cosines cos 60 1 2 cos 36 cos 72 1 4 cos 20 cos 40 cos 80 1 8 as now the arguments are in geometric progression each one double the previous let s prove the third one recall the double angle formula sin 2x 2 sin x cos x from this it follows that sin 40 sin 80 sin 160 2 sin 20 cos 20 2 sin 40 cos 40 2 sin 80 cos 80 and cancelling gives sin 160 8 sin 20 cos 20 cos 40 cos 80 finally sin 160 sin 20 giving the result essentially this is an octuple angle formula sin 8x 8 sin x cos x cos 2x cos 4x which is one of a family sin 2x 2 sin x cos x sin 4x 4 sin x cos x cos 2x sin 8x 8 sin x cos x cos 2x cos 4x where the formula for sin 2 k x can be derived by applying the double angle formula k times then we set x to be π 3 π 5 π 9 in order that the sines cancel since 3 5 and 9 are all factors of 180 these look nice in degrees but the next entry there is π 17 giving the identity cos π 17 cos 2 π 17 cos 4 π 17 cos 8 π 17 1 16 which i won t even bother to write in degrees but say we take x not as π 17 but as π 15 or twelve degrees which gives sin 16 x sin x then you have sin 192 16 sin 12 cos 12 cos 24 cos 48 cos 96 and the sines cancel to leave a negative sign that gives 1 16 cos 12 cos 24 cos 48 cos 96 and taking complements yields the identity cook gave so it s not exactly the next member of the family but it s not far off colin beveridge observed that i believe morrie s law is the furthest this can be taken with integer degree angles but this goes one further historical note the three factor identity is known as morrie s law after a boy named morrie jacobs known to richard feynman but apparently otherwise lost to history james gleick had it in his biography of richard feynman that if a boy named morrie jacobs told him that the cosine of 20 degrees multiplied by the cosine of 40 degrees multiplied by the cosine of 80 degrees equaled exactly one eighth he would remember that curiosity for the rest of his life and he would remember that he was standing in morrie s father s leather shop when he learned it michael lugo uncategorized 2 comments june 17 2023 2 minutes translate eleven plus two twelve plus one into spanish the spanish translation of eleven plus two twelve plus one is once mas cuatro catorce mas uno why both of these are anagrams with the same multiset of letters on the left and right sides both are mathematically true 11 2 12 1 and 11 4 14 1 or perhaps trece mas dos doce mas tres but that s not as good in mark dominus sense since it involves less rearrangement of the letters you can just swap ce and s etymologically this all makes sense eleven descends from old english enleofan literally one left and twelve from old english twelf literally two left spanish once is more straightforward it descends from latin undecim from unus one and decim ten and catorce is from latin quattuordecim from quattuor four and decim ten and latin unus quattuor give spanish uno cuatro i d known about the english anagram before i had thought the spanish ones were new but it seems to be an independent rediscovery i came to this problem through this reddit thread where the poster lucpel18 wondered if it was possible to solve a system with for example and so on this can be done up to 10 it can t be done for 12 and the obstruction is precisely the anagram above in looking through the comments to that reddit post i found a link to some previous investigations by lee sallows in which he finds the spanish anagram but it s not possible to assign the letters in english or any language with a similar numbering system a value so that the value of all number word is just the sum of its letters why not constructive argument seventy six and sixty seven have the same letters but do not have the same numerical value in german funfundvierzig and vierundfunfzig that is five and forty and four and fifty fancy argument the lengths of the words for numbers only grow logarithmically in the size of the numbers this suggests the original multiplicative formulation but we still have that pesky little obstruction at 67 and 76 michael lugo uncategorized 2 comments may 22 2023 1 minute percentage of songs with parentheses in the title agentrocket at metafilter asked a few weeks ago for modern song names with parentheses saying that it s hard to find songs after about 2000 with parentheses in the title officialcharts com explains why version control this will come up later to make songs easier to find to cut down long titles and so on and as far back as 1994 critics were commenting on this this reminded me of a segment of good job brain that i d heard which was a quiz on such songs which did in fact tend to be from pre 2000 here s a list of the songs in the podcast segment the segment goes from 31 50 to 51 00 gypsy woman she s homeless crystal waters 1991 the 59th street bridge song feelin groovy simon and garfunkel 1966 i can t get no satisfaction the rolling stones 1965 it s the end of the world as we know it and i feel fine r e m 1987 st elmo s fire man in motion john parr 1985 from the movie soundtrack i ve had the time of my life bill medley and jennifer warnes 1987 from the dirty dancing soundtrack i d do anything for love but i won t do that meat loaf 1993 sic even though it s i would do anything for love in the song escape the piña colada song rupert holmes 1979 christmas baby please come home darlene love 1963 you gotta fight for your right to party beastie boys 1986 hard knock life ghetto anthem jay z 1998 you make me feel like a natural woman aretha franklin 1967 against all odds take a look at me now phil collins 1984 norwegian wood this bird has flown the beatles 1965 nothing after 2000 is this because of what the author of the quiz knows or is it harder to find songs in this century with parentheses in the title well we ll need a list of songs fortunately sean miller has scraped the billboard hot 100 charts going back to the chart s beginning in 1958 this represents a total of 30 444 songs from 1958 08 02 to 2023 01 07 and with a dozen or so lines of r we can make a nice plot the only tricky thing is the filter time_on_chart 1 miller s file has a row every time a song appears on the chart but i wanted to only count each song once and fortunately he s included a variable that lets me do exactly that time_on_chart is the running count of weeks all time a song_id has been on the chart library tidyverse hot_100 read_csv https raw githubusercontent com hipstervizninja random data main music hot 100 hot 20100 csv hot_100 filter time_on_chart 1 mutate has_paren grepl song grepl song mutate year lubridate year chart_date group_by year summarize n n has_paren sum has_paren paren_rate has_paren n filter year 2023 ggplot geom_line aes x year y paren_rate theme_minimal ggtitle songs with parentheses in the title peaked in the nineties scale_y_continuous labels scales percent name of charting songs with parentheses in title but what s going on in 2021 let s drill down hot_100 filter time_on_chart 1 mutate has_paren grepl song grepl song mutate year lubridate year chart_date filter year 2021 has_paren select chart_date song performer this returns 53 songs of which the first 10 alphabetically are 2021 11 27 22 taylor s version taylor swift 2021 01 02 adderall corvette corvette popp hunna 2021 12 04 all night parking interlude adele with erroll garner 2021 11 27 all too well taylor s version taylor swift 2021 11 27 babe taylor s version from the vault taylor swift 2021 11 27 bad man smooth criminal polo g 2021 11 27 begin again taylor s version taylor swift 2021 11 27 better man taylor s version from the vault taylor swift 2021 04 10 big purr prrdd coi leray pooh shiesty 2021 12 11 christmas tree farm old timey version taylor swift taylor swift has been re recording her first six albums which she doesn t own the masters to in april she released her first re recording fearless and in november red in 2021 53 of 652 charting songs had parentheses in the title including 36 of 37 charting songs where the artist name included the string taylor swift the exception is a song that only featured her renegade by big red machine so let s redo the chart hot_100 filter time_on_chart 1 mutate has_paren grepl song grepl song mutate taylor grepl taylor swift performer mutate year lubridate year chart_date group_by year summarize n n paren_total sum has_paren paren_rate paren_total n paren_no_taylor_total sum has_paren taylor no_taylor_total sum taylor paren_no_taylor_rate paren_no_taylor_total no_taylor_total filter year 2023 ggplot geom_line aes x year y paren_no_taylor_rate color red geom_line aes x year y paren_rate color black theme_minimal ggtitle songs with parentheses in the title peaked in the nineties nand in 2021 with taylor swift rerecordings scale_y_continuous labels scales percent name of charting songs with parentheses in title essentially the entire 2021 spike like so many things in the music industry now was due to taylor swift michael lugo uncategorized leave a comment january 10 2023 january 9 2023 4 minutes is hanukkah s new moon always the darkest one my second child was born on the day of the new moon closest to the winter solstice in the darkest year in recent memory that is 2020 i remember there was a new moon because there was a solar eclipse that day in the year of her birth her birthday fell during hanukkah maybe the new moon that falls during hanukkah rosh chodesh tevet is always the new moon closest to the winter solstice basic information about the hebrew calendar that s relevant for this post a year in the hebrew calendar consists of 12 or 13 months 12 in common years and 13 in leap years leap years are 7 years out of 19 following the metonic cycle in theory these months start at the new moon but the beginning of the year can be postponed not preponed so that for example yom kippur the tenth day of the year doesn t fall on a friday or sunday the exact circumstances under which those adjustments are made are beyond the scope of this post the months alternate between 29 and 30 days with the odd months having 30 and the even months having 29 summing to 59 x 6 354 except that if things work out so that the year should be lengthened by a day then the second month cheshvan is 30 days and if they work out so that the year should be shortened by a day then the third month kislev is 29 days so hanukkah starts on the 25th of the third month kislev and ends on the 2nd or 3rd of the fourth month tevet rosh chodesh tevet the first day of the fourth month is either the sixth night of hanukkah if kislev is short or the seventh if kislev is long to answer the original question no this post follows betteridge s law thinking through the theory passover is always the first full moon after the spring equinox so between 0 and 1 lunar months after the equinox from passover 15 nisan year n to the following rosh chodesh tevet 1 tevet year n 1 is 8 5 lunar months so from the spring equinox to rosh chodesh tevet is 8 5 to 9 5 lunar months but from the spring equinox to the following winter solstice is 9 solar months that is three quarters of a year or about 9 x 235 228 9 28 lunar months the 235 comes from the metonic cycle embedded in the calendar in which there are seven leap years out of 19 so the new moon closest to the winter solstice is between 8 78 and 9 78 lunar months after the winter solstice so it s usually rosh chodesh tevet i e the new moon during hanukkah but not always alternately it was a big deal when thanksgivukkah happened in 2013 when the first day of hanukkah fell on thanksgiving november 28 2013 the first night of hanukkah was the night before that proves that rosh chodesh tevet can be at least as early as december 4 if kislev is long which is about 17...