One form of arguing to be avoided at all costs is a "declaration of the obvious" from a position of ignorance. This shows up all the time—from a misguided creationist wandering onto Panda's Thumb and asking "Evolution is bollocks, after all what good is half an eye?" to those refuting Calvinism by proclaiming "If that's true, we should all just do whatever we want." A satisfactory education should instill in people a sense of restraint and caution. Think before you declare victory. *You know, all these biology Ph.Ds probably have an answer to that half-and-eye criticism. Surely I'm not the first person to bring that up. Maybe I should ask, could someone explain to me how the eye could evolve? *Or *a lot of smart theologians are Calvinists. Maybe I should ask, can you explain why Calvinism doesn't naturally lead to antinomianism?*

That came to mind when reading the comments on an interesting UD article on imaginary numbers. I have no problem with the UD post, which is really an extended link to another article, the gist of which is that the history imaginary numbers reminds us that some ideas in math and science that meet fierce resistance occasionally prevail. It doesn't take Fellini to figure out the subtext: the same thing could/will happen with ID. Fair enough.

It's the comments that are noteworthy.

The extent to which people are willing to expose their shortcomings with total confidence is surprising. Perhaps there is something admirable about someone saying, in effect, *I have no clue what I'm talking about, but I'm certain I'm right, and the elitist experts can kiss my hiney.*

For those of you who don't know, imaginary numbers extend the ordinary number line—that wrap-around poster on the walls of kindergartens, at least kindergartens of yesteryear, into two dimensions. Instead of a number living only on the traditional line, which is now the x axis in this two dimensional system, it can also have a y coordinate—called its imaginary component. One step in the y direction is noted by the symbol *i*, which is formally defined as the square root of negative one.

Imaginary numbers are enormously useful in mathematics and physics. Physics, of course, describes the real world and when you measure something you don't get an imaginary result. So in physics we sometimes use imaginary numbers to simplify the math. (In many cases the simpler algebra of exponentials will then replace the more complicated algebra of polynomials) and at the end just take the non-imaginary part of the answer.

It seems clear to me that imaginary numbers are no less real, or just as abstract, as their ordinary counterparts. I can compute with them, and when I'm done I know how big something is, or how fast it is, etc. If you go beyond that level of considering the reality of complex numbers (or ordinary numbers) then you enter a place—call it the philosophy of mathematics, that holds no interest for me.

Back to the UD post. The second comment was this:

Hah! I say, and balderdash! Imaginary numbers, my eye (

i)! Math was originally made as a convenient symbology to describe the universe. Now, arrogant mathematicians and mathematical physicists, thinking that math is an absolute, and indeed, defines the universe rather than describing it, think that because if it didn't, their precious disciplines would be asymmetrical, that the universe must incorporate such nonsense as the square roots of negative numbers, when negative numbers themselves are only symbols of convenience from arbitrary zero points!

Maybe that's a joke—the *my eye* part was clever enough. I'm willing to give this commenter the benefit of the doubt. But not for long. For after several attempts to explain the utility of imaginary numbers, the same commenter responds:

So, what you're saying is, it's like some modern art. Ultimately meaningless, but pretty. By the way, how the Hell do you find anything to the power of

i? Clearly, I'm no mathemagician, but I'm not a slouching mouth-breather either.

At this point the author of the post is graciously holding out hope that our commenter is joking—in fact he throws him a lifeline. A simple *of course I'm just joking* would save face. Out commenter sniffs the lifeline and swims away, unimpressed. He then lectures:

Mathematics have been used to "prove" that time is illusiory, that space is curved, and indeed, stretched like a balloon over… um. Math has been used to justify the idea that a universe, expanding from a single point, could have neither center nor boundaries. So much hokum and nonsense comes from people who think far too much of math believing that the universe must submit to it, that because it is something we can understand, that it defines, rather than describes, the universe.

And a bit later:

I hold reason in the highest regard, but, as with scientists, mathematcians need to realize that their disciplines are merely offshoots and subordinates to philosophy. You extrapolate bizarre ideas from mathematics, based on an assumption which has not been proven, that mathematics has any meaning separate from that which it references.

Science subordinate to philosophy! *I've been Ayn Randed and nearly branded*… Oh well.

Our commenter moves on to the subject of modern physics. Following an *in for a dime, in for a dollar* strategy he comments, apropos nothing as far as I can tell:

I have some problem with empirical tests in advanced physics. Looking through the web, I have been able to find many statements of test results consistent with mathematical predictions, but never how those tests were conducted, how the data was gathered. Besides this, physics papers tend to be so cluttered with Greek letters and other Expertese that they are incomprehensible to the layman, and we are expected to just take their word for it. Well, screw them. Until I see how the tests were conducted, I cannot know if there is a more plausible solution that nonetheless does not match the experimenter's prejudice.

He takes special aim at the paradigm for quantum mechanics, the double slit experiment:

For instance, in the double-slit experiment so famous in quantum physics, what exactly is going on? They fire an electron, but in what direction? Right between the slits? Is the whole environment, except the receiver, resistant to electrons? How do they detect it on the other side? How do they know it's the same one? See, I'm of the belief, and I know it's not a valid argument, that I'm under no obligation to believe something that sounds like BS until you can demonstrate that it's true in terms I can understand. If there are no terms, no analogies even, to it, than I propose that if ANY simpler explanation could exist, Occam's Razor at the very least demands it. This is rather pertinent here, given that ID basically says, "Stuff looks designed. You say it wasn't. Prove it."

It is a fascinating position he takes. He admits his argument is not valid, but stands by it anyway. And he asserts his natural right to treat any science as BS if it cannot be reduced to terms he can grasp. Later he explains how all this QM crap is little more than an insider's joke, a method of obfuscation used to milk additional grant money from Joe Taxpayer:

If you say to me that a particle travels in two places at once, I call you a liar unless you can show it to be true, and unless that proof is forthcoming, I witdraw my money. Or I would if I could. To those that must make decisions about funding, even in private institutions, most will not understand even as well as someone like me with a degree in biology would. I could go in and establish a program and make ridiculous claims and if there are only three people in my field, I have the support of at least a third, and if we surrounded ourselves with enough jargon and Expertese, none from outside could say us nay.

I would be impolite, I suppose, to point out that the components of computer with which he composes his rants were developed using that fraudulent quantum mechanics. I'll leave you with this commenter's pièce de résistance:

If any here would hold, as I do, that the burden of proof lies with the Darwinists who defy what the common conclusion of our senses would be by saying that machines of great intricacy came about without design, than I think you will be hard-pressed, looking at this issue honestly, to argue that that same burden does not lie on those who propound such ideas as multiple states in quantum physics or curved space (whatever the Hell that means).

Whatever the hell that means. Indeed.

**Math Puzzle:**

Some discussion on UD concerned the famous formula e^{ip} = -1. This is a special case of the more general

e^{iq} = cos q + *i* sin q

Thus, not only is e^{ip} = -1, but e^{i2p} = +1.

Let's evaluate the following: (e^{i2p})^{p}. That is, the quantity e^{i2p} raised to the p power. On the one hand, since e^{i2p} is equal to 1, this is just 1 raised to the p power, which is still just one.

On the other hand, using simple algebra (power times exponent) we can write (e^{i2p})^{p}= e^{i2p2}. Now using the formula given above, this quantity is cos(2p^{2}) + *i* sin(2p^{2}), which is not equal to one.

What gives?

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