<div>By the same token, any number times itself is non-negative. i breaks existing rules too. (lol)</div>
<div><br>You know, I could just have said, oh, since you're multiplying i times i the result is negative, by definition, and accepted that it works. I could just be the kid who writes down what the teacher says and memorizes it for the test, instead of asking questions. I suspect there is something else at work for the result to be correct, because the only reason given for using i was to represent the vertical axis. At no point was there actually a quantity of -1, for which we found the root before multiplying by the second part of the complex number.
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<div>-Chuckk</div>
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<div><span class="gmail_quote">On 11/11/05, <b class="gmail_sendername">Martin Peach</b> <<a href="mailto:martinrp@vax2.concordia.ca">martinrp@vax2.concordia.ca</a>> wrote:</span>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">Chuckk Hubbard wrote:<br><br>> What I'm getting at is that expressing rotation as complex numbers is<br>
> no different than using cartesian coordinates. Why, when you multiply<br>> two points, would one of the multiples turn negative?<br>> I see no reason you couldn't say i = 1/0. Then 4*0*i=4. That makes<br>> as much sense.
<br><br><OT lecture_and_rant><br>Not really. Any number multiplied by zero becomes zero. You can't break<br>the existing rules. There is a philosophical need for i because<br>intuitively every number ought to have a square root, even negative
<br>numbers. The other philosophical need comes from the idea that the<br>energy of an oscillator should be constant if the oscillator is at a<br>constant amplitude and frequency, but the observable output of the<br>oscillator passes through zero, which implies there is no energy there.
<br>Where is the energy? In an imaginary dimension...imaginary just means<br>unobservable. This is basically how in quantum mechanics one decides<br>what is actually observable versus just virtual, so there is some<br>connection with reality here, but it's probably hard to grasp since
<br>humans have never used such concepts until about a hundred years ago<br>simply because there was no practical use for them.<br>It also took a long time for people in Europe to accept the concept of<br>zero after it had been invented in North Africa and Central America and
<br>elsewhere...in Roman numbers (I, II, III, IV...) there is no zero but in<br>Arabic numbers (0,1,2,3,) there is. The Maya used a shell glyph for zero<br>and dots and bars for the other numbers. I wouldn't get hung up on the
<br>use of i, it's like using an empty shell for zero, a kind of handle on a<br>concept. Some people think that concepts cannot be expressed in a<br>language that doesn't already have words for them, but they are wrong.<br>
The concepts are just expressed in a crooked, crooked way.<br></OT lecture_and_rant><br><br>Martin<br><br></blockquote></div><br><br clear="all"><br>-- <br>"It is not when truth is dirty, but when it is shallow, that the lover of knowledge is reluctant to step into its waters."
<br>-Friedrich Nietzsche, "Thus Spoke Zarathustra"