Context and question: The ultimate substantive legacy of Principia Mathematica is mixed. It is generally accepted that Kurt Godel's incompleteness theorem of 1931 definitively demonstrated that for any set of axioms and inference rules proposed to encapsulate mathematics, there would in fact be some truths of mathematics which could not be deduced from them, and hence that Principia Mathematica could never achieve its aims. However, Godel could not have come to this conclusion without Whitehead and Russell's book. In this way, Principia Mathematica's legacy might be described as its key role in disproving the possibility of achieving its own stated goals. But beyond this somewhat ironic legacy, the book popularized modern mathematical logic and drew important connections between logic, epistemology, and metaphysics.
What is the general consensus of the axioms and inference rules declared in Principia Mathematica?
Answer: mixed
Context and question: Alpine symbolism has played an essential role in shaping the history of the country and the Swiss national identity. Nowadays some concentrated mountain areas have a strong highly energetic ski resort culture in winter, and a hiking (ger: das Wandern) or Mountain biking culture in summer. Other areas throughout the year have a recreational culture that caters to tourism, yet the quieter seasons are spring and autumn when there are fewer visitors. A traditional farmer and herder culture also predominates in many areas and small farms are omnipresent outside the cities. Folk art is kept alive in organisations all over the country. In Switzerland it is mostly expressed in music, dance, poetry, wood carving and embroidery. The alphorn, a trumpet-like musical instrument made of wood, has become alongside yodeling and the accordion an epitome of traditional Swiss music.
What is the name of the trumpet like musical instrument made of wood has become the epitome of traditional Swiss music?
Answer: alphorn
Context and question: During World War II, the development of the anti-aircraft proximity fuse required an electronic circuit that could withstand being fired from a gun, and could be produced in quantity. The Centralab Division of Globe Union submitted a proposal which met the requirements: a ceramic plate would be screenprinted with metallic paint for conductors and carbon material for resistors, with ceramic disc capacitors and subminiature vacuum tubes soldered in place. The technique proved viable, and the resulting patent on the process, which was classified by the U.S. Army, was assigned to Globe Union. It was not until 1984 that the Institute of Electrical and Electronics Engineers (IEEE) awarded Mr. Harry W. Rubinstein, the former head of Globe Union's Centralab Division, its coveted Cledo Brunetti Award for early key contributions to the development of printed components and conductors on a common insulating substrate. As well, Mr. Rubinstein was honored in 1984 by his alma mater, the University of Wisconsin-Madison, for his innovations in the technology of printed electronic circuits and the fabrication of capacitors.
What company developed the first electronic circuit that could be mass produced and was durable enough to be fired from a gun?
Answer:
Globe Union