Huh? You are saying that given a T/2i, then that equals T/(2(sqrt(-1))) , and if the T is “a positive real number” as you’ve stated, then T/((2(sqrt(-1))) is not a negative number.
I thought there is no such thing as an “imaginary negative number” —except in Patrick’s imagination???
It is moments like this everyone needs to stop and learn how to use the latex markup with $ delimiters, just so we can all follow and figure out who really made the math error.
In my day Latex notation was so obscure that it was relatively useless as a mathematical lingua franca. Meanwhile, even Google still uses the standard programming language notation [e.g., (sqrt(-1)) ]
Hmmm, I wonder if my first edition Latex manual is now a collector’s item. I should have had Don Knuth sign it while I had the chance. (Of course, technically speaking, somebody else wrote Latex but LaTeX was a special version of Knuth’s TeX.)
Don Knuth was the only Christian I ever met who attributed his first interest in investigating the Gospel of Jesus to a “John 3:16” sign he saw on TV during a football game.
P.S. I don’t think I’ve heard anyone make mention of Latex in 30 years—but that shows how out of touch I’ve become.
I know BioLogis has a vibrant collection of articles pointing out Bruno’s flaws and the erroneous nature of his martyrdom.
But I’m not quite clear on how the errors of interpretation change things by very much. Sure… we can all agree that Bruno was BURNED ALIVE for heresy… not for Science.
But for goodness sake… this is NOT much of a mitigation! If not for the Protestant Reformation… will we ever know how much longer heresy infernos might have continued!!!
The Cosmos treatment on Bruno could have been more precise… But the jist of it was still an important component of Western religious history.
Where Cosmos failed, I believe, was in not pointing out how far the Roman Catholic institution has come in acknowledging science and it’s methods!
And that as the Catholics stepped forward into the light of knowledge… it is a loose affiliation of mysticizing protestants who every day seek to tear down the edifice of scientific discipline and trust in the motives of poorly compensated academics who seek wisdom from nature… more than they seek to make Christmas a useless vanity.
Irrelevant but fascinating: a friend of mine, on leave from Kuwait, became a Christian through reading John 3:16 daubed on a bridge on the M1 motorway.
“The heart has its reasons of which reason does not know.”
http://www.lifeissues.net/writers/mcm/mcm_239hearthasreason.html
sorry forgot how to use Latex. Dividing a positive real number T by 2i does result in a negative imaginary number. T/2i = -iT/2
My son mentioned Latex to me recently as he was publishing a paper in a cybersecurity journal. I was surprised as I used Latex about 35 years ago doing all of the equations in my PhD thesis. I have forgotten most of it but figured out enough to write a few negative imaginary numbers. 
I didn’t realize that this forum software has a Latex command prompt built right in until I clicked on your formula. Very cool!
(And, yes, my number joke was very lame. However, I still don’t get how that equation’s equivalence came about. Too many years ago for me, I guess. It’s a fun but off-topic issue so I won’t ask for a tutorial. Meanwhile, I think it is quite amazing that Latex is so easily accessible within this forum software. Not so in my day.)
I have a T-shirt from FFRF that says God = \sqrt(-1) that I run in occasionally. Mostly I get stares but once in a while someone will come up to me and argue about the math but not the theology.
Is there another bug in the forum software? If I quote your post, the Latex portion goes awry in the right-side of the screen real-display window.
P.S. I see it is wrong in the above final display also.
Meanwhile, according to many classic debates about it, “i” has plenty of theological implications in terms of taking “i” on faith after seeing how it explains the real world in so many physics equations. The entire history of “i” and its “imaginary nature” (and the debates among mathematicians about it) is a very fascinating topic.
You couldn’t do electrical power line transmission without i.
I’m just a little puzzled by the expression “negative imaginary number”, because I don’t think it means anything.
Seems to be. I quoted Patrick, and had to do some fixing up for it to work.
It does not mean anything. It is just a mathematical fact.
Curious but true!
First of all, a “negative imaginary number” is not an imaginary number with a smug and cynical attitude. (That one was a lame joke on my part.)
Secondly, I find that it is very hard to grasp a negative imaginary number without contextualizing it in some real world application of physics, such as the electrical power transmission situation which @Patrick mentioned. For example: an “i” in a mathematical expression which is related to power losses can be viewed as a negative.
Also, it often helps to conceptualize even imaginary numbers on a traditional “number line”, just like the one that is sometimes used in elementary school arithmetic classes. Yes, trying to put “i” and complex number multiples of it onto that number line is challenging but at the very least we can think of such numbers as positioned to the left of zero and therefore negative.
I remember the first time I learned about imaginary numbers. I thought they were the coolest numbers I’d ever encountered. (Even more so than primes.) The fact that they “don’t mean anything” on their own and yet they arise when working out the algebraic equations of various physical processes—and then tend to “disappear” when one gets to the last step and the “real world” solution of a problem----seemed absolutely glorious to me!
As a young person learning about imaginary numbers, I ended up simply accepting “i” by faith because it was so useful in making sense of the real world. It is an almost “magical” thing which one can’t see and yet must be there for physics to make sense. I don’t know any other way to describe it.
I realize that “transcendental” in terms of transcendental numbers is yet another category of numbers (which can involve “i”) but I’ve always felt that “i” and imaginary numbers are in a traditional religious studies academic sense almost (but not really) “transcendent” in how they relate to the real world: somehow “in” the real world but existing independently in some grand way. They are just plain cool. And imaginary numbers tend to pop up just about everywhere in physics.
You mean something like the 2d imaginary plane?
no, the negative i doesn’t mean power loss. It actually is a measurable parameter of the transverse electric field (wave) propagating through the wire. A negative imaginary parameter measurement would mean that there is a 180 degree phase lag (a time delay) between the wave and ground.
Yes, complex numbers (the sum of real numbers and imaginary numbers) are beautiful and very useful.
The most beautiful equation in mathematics that I have ever encountered is:
e ^ {i \pi} = -1
I didn’t say that negative “i” means power loss. I said (or meant to say) that “i” is associated with some of the equations associated with and related to power loss. (Yes, I probably worded it very poorly.)
That one came to mind because I noticed “i” in some equations appearing in a paper I read concerning long-distance power transmission lines and how they contribute to global warming/climate change.
I agree! It is very beautiful. I have often referred to that one over the years.
I often re-write it as:
e^(i*pi)+1 = 0
…so that I can make the point that that single equation expresses five important constants in terms of nothing but one another: 0, 1, e, i, pi
What could be more elegant than that?
Wasn’t it Bertrand Russell, an atheist, of course, who made the statement: “If there were such a thing as a mathematical proof of God, that equation would be it.” ???