Upside down E was Re: Mathematical Symbols

[Baker, John]

        After writing the previous message, I realized that I'm uncertain which axis is considered "vertical."  I was referring, perhaps wrongly, to the z-axis, not the y-axis.

        For the less mathematically inclined:  Suppose you have a cut-out of the letter F.  You want to turn it upside down.  There are two ways you can do this.  First, you can rotate it on the desktop.  After doing so, you are still looking at the front of the letter F and the bars are at the bottom but pointing to the left.  Second, you can lift the letter off the desktop and flip it in the air.  After doing so, you are looking at the back of the letter F and the bars are at the bottom and still pointing to the right.  Neither approach is necessarily preferable to the other, but I intuitively think of the second way when I think of something being turned upside down.

John Baker


-----Original Message-----
From: nee1 at MIDWAY.UCHICAGO.EDU [mailto:nee1 at MIDWAY.UCHICAGO.EDU]
Sent: Thursday, February 20, 2003 10:47 AM
To: ADS-L at LISTSERV.UGA.EDU
Subject: Re: Upside down E was Re: Mathematical Symbols


Quoting "Baker, John" <JMB at STRADLEY.COM>:

>         It's easier to understand what Barbara Need is saying if you imagine
> a capital F instead of a capital E.  The right-side-up F has bars in the
> middle and top of the letter, pointing to the right.  What would an upside
> down F look like?  If the paper is simply rotated on a vertical axis (i.e.,
> the paper remains flat on the desk and is turned around, or the viewer walks
> to the other side of the desk), the two bars of the F, now at the middle and
> bottom of the letter, will point to the left.  But I think of an upside-down
> F as having bars that point to the right, just as they do when the letter is
> right-side-up.

> John Baker

That certainly helps. But for me, a rotation on the vertical axis would involve
lifting one edge of the paper and turning the paper over! In such a scenario,
the previously top bar of the F is still at the top but pointing left (in
scenario described above, which is also Larry's) the "top" bar is now at the
bottom and pointing left. For me turning the E or the F upside down results in
the bars still pointing right, but, in the case of the F, the top bar is at the
bottom.

Barbara

>
>
> -----Original Message-----
> From: Laurence Horn [mailto:laurence.horn at YALE.EDU]
> Sent: Thursday, February 20, 2003 12:03 AM
> To: ADS-L at LISTSERV.UGA.EDU
> Subject: Re: Upside down E was Re: Mathematical Symbols
>
>
> At 9:42 PM -0600 2/19/03, Barbara Need wrote:
> >
> >My first thought was: wouldn't an upside down E be identical to a
> >right-side up E? But then I thought, when you look at someone's
> >writing "upside down" it is the reversed E, because the writing is
> >also right to left FROM YOUR PERSPECTIVE. But when I turn something
> >upside down, I usually only rotate on a horizontal axis, not also on
> >the vertical one. Is this the usual sense of turn something upside
> >down?
> >
> I don't know; this is too complicated for me.  I write a
> right-side-up E on a piece of paper and I turn the paper upside down
> and I get an existential quantifier, not the E that I started with.
> (Works with computer monitors too.)  Don't know from perspectives and
> axes, but that's how I do it.
>
> L
> ht-side up E? But then I thought, when you look at someone's
> >writing "upside down" it is the reversed E, because the writing is
> >also right to left FROM YOUR PERSPECTIVE. But when I turn something
> >upside down, I usually only rotate on a horizontal axis, not also on
> >the vertical one. Is this the usual sense of turn something upside
> >down?
> >
> I don't know; this is too complicated for me.  I write a
> right-side-up E on a piece of paper and I turn the paper upside down
> and I get an existential quantifier, not the E that I started with.
> (Works with computer monitors too.)  Don't know from perspectives and
> axes, but that's how I do it.
>
> L