July 23

[Zeke]

<p>So yeah, that sucked, sorry. However, I did get <i>one</i> thing on my list done. Forumgoers will find that a beloved feature -- custom titles -- has returned. Not just that, but I've finally got a handle on vBulletin (you would not <i>believe</i> the complexity of this thing -- it's like phpBB cubed). So I've fixed the avatar permissions problem, and when I have a little more time I'll work on the visuals.
<p>Anyway, I'm now off to Ottawa for the second math camp. I'll see what I can arrange in the way of filler. Worst comes to worst, I'll just tell you to reread Cliffhanger Week... that's at <i>least</i> a week right there if you don't skip meals.

[Hotaru]

Yay for custom titles!

[MaverickZer0]

...Woo!
I hereby take back most things I muttered about the crappiness of vBulletin.
...What? It's me. Don't expect a miracle overnight.

[Gatac]

Three cheers!

Gatac

[mark726]

Ok, so for the longest time I thought that the users were able to set custom titles...and I kept searching in vain for where I could change mine. I think I finally figured out that it's not set by me.... But, hooray!

[danieldoof]

congratulations on that zeke

I love those member titles, great job again :)
and I think that this will get a lot of posters out of the dark...only to present their member titles ;)

[PointyHairedJedi]

I think I finally figured out that it's not set by me.... But, hooray!
There's a tradition that Zeke sets them, though he is open to suggestions if you've got something particularly hilarious in mind.

[evay]

yay! thanks Zeke!

[Chancellor Valium]

May the benificent cheeses of undead Roman Emperors be always upon you!

Err, I mean, thank you, kind sir Zeke...

[Celeste]

Woohoo! Member titles! Yay Zeke I love you again! :P

[Alexia]

It's amazing how much member titles makes me happy xD

I love Losty's the best :D (Yes, I did read them all) Shortly followed by ualleverybody (who I don't think I've ever seen post... but the member title is funny anyway ;) )

[Derek]

Excellent. Member titles are always fun.

[mudshark]

Yes, they are. http://i57.photobucket.com/albums/g223/mudshark58/smilies/bigass_grin.gif

[Sa'ar Chasm]

I concur.

Deep, man.

[admiral sab]

I'm loving mine. :) Of course that pic is way old, she's 6 months now and that's two months. Perhaps an update is in order...

[e of pi]

What kind of editing was done to that image, btw. It's always looked a little odd. Anywho, thanks Zeke. But, as a student of Algebra II, heading into discrete math by way of testing out of Geometry, what does the new part of mine mean? I'm not sure if I should be offended or not.

[evay]

But, as a student of Algebra II, heading into discrete math by way of testing out of Geometry, what does the new part of mine mean? I'm not sure if I should be offended or not.
the english major takes a stab at it: that "e of pi" is considered an "irrational" number, and proving said number irrational is an exercise left to the student. Sort of like how many angels can sit on the head of a pin: calculate area of pin P, calculate area of angels' arses A, divide. the actual math is left as an exercise for the student. (roughly paraphrased from Heinlein's Friday)

[Zeke]

Yeah, I'm being a little sneaky here. A classic trick of math professors is to leave proving some theorem as an exercise -- thus saving the class time it would take to show the proof. Typically this is done when the proof in question is obvious, tedious, or repetitive of one already shown. But occasionally a prof will forget how a proof is done, and leaving it as an exercise is one way to weasel out of it.

Now, the natural way to read "e of pi" is either e times pi or e over pi. And we know that e and pi are transcendental, but combinations are another story. For example, we don't even know for sure that e+pi and pi^e are irrational, let alone transcendental. (It would be very strange if they were rational, of course.) So, rather than just give him the member title "Irrational" without proof, I decided to acknowledge there was something to prove... while not, of course, proving it myself.

Which is not to say I couldn't, of course. As a matter of fact, I have discovered a truly marvelous proof, which this post is too narrow to contain.

[evay]

I know pi is used in measuring circles, and i is the square root of -1 (so the square root of -4 is 2i), but what's "e" in mathematical terms?

[Celeste]

math makes my head hurt.

[Scooter]

I know pi is used in measuring circles, and i is the square root of -1 (so the square root of -4 is 2i), but what's "e" in mathematical terms?
It's a constant roughly equal to 2.7 and has to do with natural logarithms. If I remember correctly e is the limit as n approaches infinity of (1 +1/n)^n. Right, math-heads?

Not very applicable to my chosen field of ancient history. But if anyone asks I can always say Caesar invented it. People usually believe that. (He did invent military cryptography, which has as mathematical basis, so we're not too far afield...)

[Asky]

you could always look it up on Wikipedia or something and use your newfound knowledge to pretend to be smarter than you really are...

[Scooter]

you could always look it up on Wikipedia or something and use your newfound knowledge to pretend to be smarter than you really are...
A little unfair. I did (much to my surprise) remember the concept and the formula, but I cop to double-checking it before posting. Figures I get called on it anyway.

As for pretending to be smart: I'm a college professor, it's a marketable skill.

[PointyHairedJedi]

math makes my head hurt.
And dentistry makes my mouth hurt.

:p

[admiral sab]

wow. I have no idea what anyone has just said. Except about the head hurting. I get that. ;)

And e of pi were you talking about my pic? It's edited with Photofiltre, and not really edited. I'm no iconic genius, I just cropped her pic over the 5mv logo and 50/50'd the opacity. Apparently making it transparent. Have no idea how to do anything else with it. ;)

[e of pi]

Ah. Okay. I might recommend a new one, as the current one kinda looks like she has antenna.

[admiral sab]

lol she has a bow in her hair... ;) I actually have Photoshop but I have NO idea what I'm doing with it. I could read the help files, but I don't really have the time right now.

[Zeke]

I know pi is used in measuring circles, and i is the square root of -1 (so the square root of -4 is 2i), but what's "e" in mathematical terms?

Scooter's correct, except about Caesar. (And he is right about Caesar where cryptography is concerned. Caesar devised the Caesar shift, rot-3 in modern parlance, which is why I had the <a href="../enterprise/fiver.php?ep=minefield">Romulans</a> use it.)

Anyway, e is as deeply embedded in calculus as pi is in geometry. y = C &times; e^x is the only function which is its own derivative. As such, it's the best base for logarithms (just as pi is the best basis for angle measurement), so logs to the base e are called natural. Common logs, i.e. to base 10, are strictly for engineers and the occasional number theorist.

e also arises in accounting. If you have $1 in the bank at 100% simple interest, your balance will be $2 in a year. If the interest is compounded semiannually, that rises to $2.25. Compound it monthly and you'll end up with $2.61. It turns out that there's a limit to this process, representing a sort of continuous compounding of interest, and that limit is e dollars.

A third way e can be found is through infinite series. e is the sum of the series 1/0! + 1/1! + 1/2! + 1/3! + ..., where the exclamation point is a factorial sign. (4! = 4 x 3 x 2 x 1, and so on. Before you ask, there is a double factorial sign, and it's the only kind of double exclamation point I can stand.) Any of these three properties of e can be, and has been, used as its definition; you can derive the other properties from the one you start with.

As you can see, it's easy to get me talking about this stuff. I did some quality math-related ranting in this LJ post (http://commodore-zeke.livejournal.com/15611.html), for anyone interested.

[Scooter]

Anyway, e is as deeply embedded in calculus as pi is in geometry. y = C &times; e^x is the only function which is its own derivative. As such, it's the best base for logarithms (just as pi is the best basis for angle measurement), so logs to the base e are called natural. Common logs, i.e. to base 10, are strictly for engineers and the occasional number theorist.

Wow, that is the most lucid explanation of a mathematical concept I've seen in ages. Cool.

I bet if we'd been born with 2.7 fingers, then base 10 would never have even been invented. Except that base 10 would be base e, since our numbering system would have developed using an e-based place value...

[mark726]

Actually, I heard somewhere that mathematics would have developed a lot faster if we had 4 fingers on each hand. We would have realized the base 2 system a lot quicker and all sorts of fun stuff like that.

Also, Zeke, what the devil is up with how e^(-i*pi) = -1? My calc teacher explained it to me once...but I was lost. It had something to do with infinite series, I think, but I was really confused.

[Hotaru]

I am so confused.

Math is the devil in numerical form.

[NeoMatrix]

I am so confused.

Math is the devil in numerical form.

So math tempts you to sin by partying too hard at math camp?

[danieldoof]

well at least he doesnt have to sit in the sun..cos if he would go out he would tan

(OMG no .. I am hiding now for those cheap puns)

[Kristina]

Is that a <i>sine</i>?
*hides, too*

On another note, my new title gave me a good laugh - thanks, Zeke!

[Nate the Great]

I may as well bring up the Mathematicians Rouser:

e to the x, dy dx
e to the x, dx
secant, cosine, tangent, sine
three point one four one five nine
integral, integral
rah rah rah!

[Derek]

Actually, I went to Georgia Tech, and that's pretty close to one of our cheers.

E to the X dy dx,
E to the X dx,
Tangent Secant Cosine Sine,
3.14159,
Square roots, Cube roots, Poisson brackets,
Dis-integrate ‘em Yellow Jackets!

[Nate the Great]

I suppose as one math professor tells it to a class, who teaches it to the students they TA later, and so forth, it will mutate. Or maybe it's a byproduct of Hodgekin's (or however the heck you spell that name) Law of Parallel Planet Development. In any event, I related the version I was taught.

[Chancellor Valium]

Brek-ek-ex, Bro-ax, Bro-ax!
Brek-ek-ex, Bro-ax, Bro-ax!

[Nate the Great]

Zizzy Zuzzy Zik!

[Sa'ar Chasm]

Brek-ek-ex, Bro-ax, Bro-ax!

Somebody croak that chorus.

[Nate the Great]

By the way, "zizzy zuzzy zik" is the final incantation the wearer of the Golden Cap uses to summon the Winged Monkeys in the Wizard of Oz.