Sometimes an invention is so profound and significant yet apparently obvious in retrospect that it is difficult to imagine how people around the world struggled over millennia to discover it, and how slowly it was to diffuse from its points of origin into general use. Such is the case for our modern decimal system of positional notation for numbers and the notation for algebra and other fields of mathematics which permits rapid calculation and transformation of expressions. This book, written with the extensive source citations of a scholarly work yet accessible to any reader familiar with arithmetic and basic algebra, traces the often murky origins of this essential part of our intellectual heritage.
From prehistoric times humans have had the need to count things, for example, the number of sheep in a field. This could be done by establishing a one-to-one correspondence between the sheep and something else more portable such as one’s fingers (for a small flock), or pebbles kept in a sack. To determine whether a sheep was missing, just remove a pebble for each sheep and if any remained in the sack, that indicates how many are absent. At a slightly more abstract level, one could make tally marks on a piece of bark or clay tablet, one for each sheep. But all of this does not imply number as an abstraction independent of individual items of some kind or another. Ancestral humans don’t seem to have required more than the simplest notion of numbers: until the middle of the 20th century several tribes of Australian aborigines had no words for numbers in their languages at all, but counted things by making marks in the sand. Anthropologists discovered tribes in remote areas of the Americas, Pacific Islands, and Australia whose languages had no words for numbers greater than four.... [Read More]
Is there any other holiday that fills the world with song? I live in Japan but that does not stop the BGM elves from taking control of the speakers. The songs are so varied from Santa to silly and even sacred but isn’t Christmas all those things.
Pick one and let us know in the comments.... [Read More]
The GitHub repository for the Ratburger Code Base is now on-line and accessible to anybody. The code base is a live mirror of the software and documents which run the site, less its content (the posts, comments, uploaded images, etc.) Here is the README file for the repository.
Ratburger.org is an online community where a wide variety of topics are discussed in a civil manner among an international membership whose only common denominator is their distaste for the sewer that so many Internet fora and comment sections have become.... [Read More]
Lost amid all the other news recently, is that VA still hasn’t certified all of the Commonwealth’s state races due to a number of races requiring recounts. The 94th district was closest. David Yancey (R) initially led by 10 votes after election night. After the recount, Shelly Simonds (D) led by one vote. Now a three-judge panel has declared the contest a tie after one additional contested vote was determined to have been uncounted for Yancey. Control of the House of Delegates rests on this contest (either 51-49 [R] or 50-50), and under VA law, the winner is decided by lot in the event of a tie. The loser can then demand a second recount. I’ve never seen an election so crazy.
There is still a wild card in the 28th district where Democrats are petitioning for a new election when it was realized around over 100 voters were registered in the wrong district by the registrar in a race that was only 82 votes apart. The twist? The registrar has since died so no one has an explanation why she registered people incorrectly, but the Department of Elections conclusions were developed by manually checking addresses of voters, which identified at least 384 registered voters wrongly assigned to either the 28th or 88th district, then comparing those names against voter rolls from Nov. 7. Of the 384 voters, 110 were wrongly assigned to the 88th District but should be in the 28th; 207 were wrongly assigned to the 28th but should be in the 88th; and 67 were wrongly assigned to the 28th but should be in a third neighboring district, the 2nd. The analysis concludes 125 voters incorrectly voted in the 28th District, where the State Board of Elections was due to certify results that show Republican Bob Thomas leading Democrat Joshua Cole by 82 votes. It finds 22 voters wrongly cast ballots in the 88th House of Delegates District, where Republican Mark Cole won re-election by 4,104 votes. There is no way for elections officials to know which candidate any of these voters cast ballots for.... [Read More]
Ratburger.org supports MathJax, which permits including beautifully typeset mathematics in posts and comments (but not, at present, in group posts or comments). For example, here is Einstein’s gravitational field equation:
About 15 years ago I had lunch with an environmental journalist, writer for LA Weekly among other publications. She wrote a book about Earth First!, the radical enviro-terrorists. That should tell you all you need to know about her political leanings. Besides writing for leftist publications, she also freelanced for outdoorsy mags like Field & Stream and Outdoor Life. Typically, these were run by more conservative or libertarian types.
The ratification of the Eighteenth Amendment to the U.S. Constitution in 1919, prohibiting the “manufacture, sale, or transportation of intoxicating liquors” marked the transition of the U.S. Federal government into a nanny state, which occupied itself with the individual behaviour of its citizens. Now, certainly, attempts to legislate morality and regulate individual behaviour were commonplace in North America long before the United States came into being, but these were enacted at the state, county, or municipality level. When the U.S. Constitution was ratified, it exclusively constrained the actions of government, not of individual citizens, and with the sole exception of the Thirteenth Amendment, which abridged the “freedom” to hold people in slavery and involuntary servitude, this remained the case into the twentieth century. While bans on liquor were adopted in various jurisdictions as early as 1840, it simply never occurred to many champions of prohibition that a nationwide ban, written into the federal constitution, was either appropriate or feasible, especially since taxes on alcoholic beverages accounted for as much as forty percent of federal tax revenue in the years prior to the introduction of the income tax, and imposition of total prohibition would zero out the second largest source of federal income after the tariff.
As the Progressive movement gained power, with its ambitions of continental scale government and imposition of uniform standards by a strong, centralised regime, it found itself allied with an improbable coalition including the Woman’s Christian Temperance Union; the Methodist, Baptist and Presbyterian churches; advocates of women’s suffrage; the Anti-Saloon League; Henry Ford; and the Ku Klux Klan. Encouraged by the apparent success of “war socialism” during World War I and empowered by enactment of the Income Tax via the Sixteenth Amendment, providing another source of revenue to replace that of excise taxes on liquor, these players were motivated in the latter years of the 1910s to impose their agenda upon the entire country in as permanent a way as possible: by a constitutional amendment. Although the supermajorities required were daunting (two thirds in the House and Senate to submit, three quarters of state legislatures to ratify), if a prohibition amendment could be pushed over the bar (if you’ll excuse the term), opponents would face what was considered an insuperable task to reverse it, as it would only take 13 dry states to block repeal.... [Read More]
As some of you know, my Dad designed the Vanguard TV-3 satellite (and its sister, the oldest satellite still in orbit the Vanguard 1). When TV-3 blew up on national TV. https://www.youtube.com/watch?v=JK6a6Hkp94o After it cooled down, Dad put in its wooden box and carried it on board a commercial flight back to DC. It sat in our house and is now in the National Air and Space Museum (see above).... [Read More]
Progressives around the world are bound and determined to destroy the family as the core of society. What they haven’t factored into their plans is that the future belongs to those who show up, and that means families.
This photo from July includes my daughter-in-law, who was carrying my grandson at the time. And recently arrived:... [Read More]