Binary Arithmetic
Along with his enormous contributions to the development of Calculus, Leibniz was also the single largest investigator of the system of numeration used by all digital technologies in the modern era: the base two, or binary, number system.
Number systems are organized by base. The system most widely used by humans is the decimal, or base ten system. Ten from the Hindu-Arabic numerals we use to represent abstract numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. We can represent any number using these digits and a place value for each. Base certainly has its drawbacks as well as it's benefits, and several other bases have been proposed by mathematicians, philosophers as well as more practical minds whose interest was in a number system better suited to commerce. Any benefit to be gained was far outweighed by the cost of switching, partially because of the evolutionary heritage of the base ten system. We've got ten fingers and ten toes. Ten is an inescapable biological reality for all humans. The word "digit" pays homage to this relationship between our biology and our historic number system, having the meaning of both a finger or toe or a Hindu-Arabic numeral. Ten is part of our physical reality.
Electronic systems are composed of components that are either on or off. Like the transistors in a computer, or the neurons in a biological brain, which either fire and propagate a signal, or do not.
Leibniz's contributions to the not-yet-established field of computing machinery and science is celebrated in an article in the Guardian newspaper, entitled "My Hero Leibniz", where the author argues that there is evidence that he anticipated Einstein's notion space and time as one, intertwined dimension.
"He not only invented the relational conception of time and space that best fits our world, he was a pioneer of the digital universe, as he greatly advanced mechanical calculators beyond while developing the binary numbers that underlie modern computers. He went beyond others of his time in his speculations about the formal logical operations that could be automated on a machine. He could be called the first digerati."
http://www.theguardian.com/books/2013/may/10/my-hero-leibniz-lee-smolin
Along with his enormous contributions to the development of Calculus, Leibniz was also the single largest investigator of the system of numeration used by all digital technologies in the modern era: the base two, or binary, number system.
Number systems are organized by base. The system most widely used by humans is the decimal, or base ten system. Ten from the Hindu-Arabic numerals we use to represent abstract numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. We can represent any number using these digits and a place value for each. Base certainly has its drawbacks as well as it's benefits, and several other bases have been proposed by mathematicians, philosophers as well as more practical minds whose interest was in a number system better suited to commerce. Any benefit to be gained was far outweighed by the cost of switching, partially because of the evolutionary heritage of the base ten system. We've got ten fingers and ten toes. Ten is an inescapable biological reality for all humans. The word "digit" pays homage to this relationship between our biology and our historic number system, having the meaning of both a finger or toe or a Hindu-Arabic numeral. Ten is part of our physical reality.
Electronic systems are composed of components that are either on or off. Like the transistors in a computer, or the neurons in a biological brain, which either fire and propagate a signal, or do not.
Leibniz's contributions to the not-yet-established field of computing machinery and science is celebrated in an article in the Guardian newspaper, entitled "My Hero Leibniz", where the author argues that there is evidence that he anticipated Einstein's notion space and time as one, intertwined dimension.
"He not only invented the relational conception of time and space that best fits our world, he was a pioneer of the digital universe, as he greatly advanced mechanical calculators beyond while developing the binary numbers that underlie modern computers. He went beyond others of his time in his speculations about the formal logical operations that could be automated on a machine. He could be called the first digerati."
http://www.theguardian.com/books/2013/may/10/my-hero-leibniz-lee-smolin