I was so impressed and sometimes confused to articulate past, present, and future tense in English. This maybe one reason why I feel so bad in English. Another reason maybe because of “unlucky” of letter A and E for the notation of “Universal quantifier” and “Existential quantifier” in Mathematical logic :
I was also impressed with the use of such symbols that lead naturally to the Russell’s paradox.
In Arabic grammar, which I learned from classic books of Islamic scholastic literatures, the present and future tenses are very complex and unified in one class of syntax but with many rules of instantiation more sharpened, namely fi’il mudhori, and the past tenses in Arabic grammar is same as in English and named fi’il madhi.
John F. McGowan on Math-blog.com has an interesting article on audio pitch shifting by manipulating the Fourier transform of the voice and some additional mathematical acrobatics. This produced a recognizable pitch shifted voice and a relatively smooth pitch shifted voice similar to the output of the analog processing.
Traditional pitch shifting algorithms give artificial qualities to the pitch-shifted voice. The improved algorithms can create more natural sounding pitch-shifted voices. These voices can be used for humor, entertainment, or emphasis in movies, television, video games, video advertisements for small businesses, personal and home video, and in many other applications.
This video is President Obama’s original introduction from his April 2, 2011 speech on the energy crisis.
This video is President Obama speaking with his pitch doubled by shifting the Fourier components but without the mathematical acrobatics to compensate for un-centered frequency components:
This video is President Obama speaking with a chipmunked voice; his pitch has been doubled.
This video is President Obama speaking with a deep voice; his pitch has been reduced to seventy percent of normal.
This video is President Obama speaking with a voice similar to the voice of Mickey Mouse:
© 2011 John F. McGowan, Source : math-blog.com
Often we have question about something (question) where the answer is already contained in it. It may be called analytic questions, that is the relation between them is the relation of identity. The question is just like the answer that is already contained in it. Or it’s like an ordered pair, the first member of the pair is the best possible question we could ask, and the second member of the pair is the answer to that question. But the intelligent robots in the following video have the wisdom and consideration about the type of question.
These intelligent robots ponder deep philosophical questions of life : “What is the best possible question, and what’s the best answer to it?” By Teja Krasek and Cliff Pickover, at Youtube.