Abstract Mathematics is Real


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Zero, negative numbers, and the square roots of negative numbers were all taken to be mathematical abstractions with no real meaning. The last are still called "imaginery numbers." Leonhard Euler found a neat little expresion using opened the door to the reality of imaginary numbers. It is hard to express here because of the limits of the text processor. 9e9a547076c6820b95e439dd1a5d6a32.png

This is known as Euler's Identity. (Identity is important to Objectivists,)

Euler's Formula is c9f2055dadfb49853eff822a453d9ceb.png In fact, alternating current electricity is engineered with this. In both cases it is clear that the base of "imaginary" numbers has very real meaning. Mathematicians may construct airy or ephemeral glissandos of their own amusement. But, as reality is real, these must have some practical application, even if the technology has not yet been invented.

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Zero, negative numbers, and the square roots of negative numbers were all taken to be mathematical abstractions with no real meaning. The last are still called "imaginery numbers." Leonhard Euler found a neat little expresion using opened the door to the reality of imaginary numbers. It is hard to express here because of the limits of the text processor. 9e9a547076c6820b95e439dd1a5d6a32.png

This is known as Euler's Identity. (Identity is important to Objectivists,)

Euler's Formula is c9f2055dadfb49853eff822a453d9ceb.png In fact, alternating current electricity is engineered with this. In both cases it is clear that the base of "imaginary" numbers has very real meaning. Mathematicians may construct airy or ephemeral glissandos of their own amusement. But, as reality is real, these must have some practical application, even if the technology has not yet been invented.

After over 200 years this is still considered the most amazing equation in mathematics. If you substitute pi for x you get

e ^ (i*pi) = - 1 or e^(i * pi) + 1 = 0. This connects the busiest numbers in mathematics ; 1, 0, i, e and pi.

The sin and the cos functions are periodic and basic to the physical harmonies: light and time. Pendulums rock themselves to sleep to the tune of sin and cos. And the waves of light are described by these. In addition, the sin and cos functions are the basis of Fourier series and integrals which are basic to all of the mathematics used in physics. It is a remarkable equation.

Ba'al Chatzaf

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Zero, negative numbers, and the square roots of negative numbers were all taken to be mathematical abstractions with no real meaning. The last are still called "imaginery numbers." Leonhard Euler found a neat little expresion using opened the door to the reality of imaginary numbers. It is hard to express here because of the limits of the text processor. 9e9a547076c6820b95e439dd1a5d6a32.png

This is known as Euler's Identity. (Identity is important to Objectivists,)

Euler's Formula is c9f2055dadfb49853eff822a453d9ceb.png In fact, alternating current electricity is engineered with this. In both cases it is clear that the base of "imaginary" numbers has very real meaning. Mathematicians may construct airy or ephemeral glissandos of their own amusement. But, as reality is real, these must have some practical application, even if the technology has not yet been invented.

Isn't the zero the greatest single advance in mathematics?

--Brant

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Zero, negative numbers, and the square roots of negative numbers were all taken to be mathematical abstractions with no real meaning. The last are still called "imaginery numbers." Leonhard Euler found a neat little expresion using opened the door to the reality of imaginary numbers. It is hard to express here because of the limits of the text processor. 9e9a547076c6820b95e439dd1a5d6a32.png

This is known as Euler's Identity. (Identity is important to Objectivists,)

Euler's Formula is c9f2055dadfb49853eff822a453d9ceb.png In fact, alternating current electricity is engineered with this. In both cases it is clear that the base of "imaginary" numbers has very real meaning. Mathematicians may construct airy or ephemeral glissandos of their own amusement. But, as reality is real, these must have some practical application, even if the technology has not yet been invented.

Isn't the zero the greatest single advance in mathematics?

--Brant

One of the most important. There are others.

Ba'al Chatzaf

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Zero, negative numbers, and the square roots of negative numbers were all taken to be mathematical abstractions with no real meaning. The last are still called "imaginery numbers." Leonhard Euler found a neat little expresion using opened the door to the reality of imaginary numbers. It is hard to express here because of the limits of the text processor. 9e9a547076c6820b95e439dd1a5d6a32.png

This is known as Euler's Identity. (Identity is important to Objectivists,)

Euler's Formula is c9f2055dadfb49853eff822a453d9ceb.png In fact, alternating current electricity is engineered with this. In both cases it is clear that the base of "imaginary" numbers has very real meaning. Mathematicians may construct airy or ephemeral glissandos of their own amusement. But, as reality is real, these must have some practical application, even if the technology has not yet been invented.

Isn't the zero the greatest single advance in mathematics?

--Brant

One of the most important. There are others.

For example, the limit concept. Archimedes using the limit concept figured out the area of a circle and the constant pi without the zero.

Ba'al Chatzaf

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