not that anyone actually cares, but - Lograh — LiveJournal
Thursday, 12.Feb.2004
7:42 - not that anyone actually cares, but
here's the correct answer to the pop-quiz about π+e.
It is as yet unproven what kind of number π+e is. We are fairly certian that it's not a whole number (that much can be seen by adding decimal aproximations of them, 3.14+2.71 is not whole), but beyond that we don't know anything for certain. π+e could actually be a fraction, no one knows.
Go here (opens in new window) for more information on Transcendental numbers, fun stuff!
"Because the number (pi) is transcendental, the construction cannot be done according to the Greek rules."
And at the bottom:
"At least one of (pi * e) and (pi + e) (and probably both) are transcendental, but transcendence has not been proven for either number on its own."
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I know mathematics is a different language, but when "on its own" is used in English, it tends to refer to the specific elements separately. Either the author is in error because that statement is false (because he meant it the way I read it) or that he made a gross miscommunication (because he meant it the way you read it, and chose very poor phrasing).
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I figured you took it to mean π and e on their own, but it took me about 2 or 3 minutes of re-reading to see that. I've been doing mathspeak for so long, when I read that sentance it parsed like:
at least one of [elementA] or [elementB] has [property], but it is unknown which (or if both).
where [elementA] was (πe) and [elementB] was (π+e). I didn't even see π or e on their own in that statement at all.
It's a classic problem of mathematicians talking to non-mathematicians. Like when the words "or" or "if" come up in conversation. These words have drastically different meanings in math than they do in english, and they are used *all the time* in math, so their mathematical meanings tend to get reinforced in our heads more than the english meanings. I'm sure you can appreciate the problem, being that CS uses the mathematical definitions of them as well.
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for those reading along and wondering "what's so big about 'or' and 'if'?", an explaination:
"or", when used in an English statement such as "dude, it's this or that!" is often meant to mean that both options cannot be true. In mathspeak, however, a statement such as "this or that" carries with it the understanding that both could very well be true at the same time.
"if", when used in an English statment like "if this than that" carries with it the implication that "not this" would imply "not that". "if" in mathspeak makes no such claim. "if this than that" in math implies that we are making no claims about "that" should "this" not hold.
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(b) "on its own" is not a logical statement. Please tell me if it is a mathematical one. If not, then the author was using English, rather than math or logic speak, and chose poorly. I can say he chose poorly because there is an inconsistency between our viewpoints that isn't reconciled by your appeal to miscommunication via jargon (which until you can prove to be that that is the case, I seriously doubt).
"Either one" would have been a far better choice of words. I stand by my claim that there is an inconsistency in the article. It doesn't make the author a bad person, it just means that there is some errata that needs addressing.
It's strange, but I've never heard eπ referred to as Gelfond's Constant--I guess it's just a physics thing, since we weren't really required to take number theory beyond the basics. It makes me want to learn more now--I feel so ignorant!
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Yer welcome. I found it kinda creepy that we have yet to figure out what happens when you multiply or add π and e with eachother. I mean, we've known of those two numbers for so long, you'd think by now we'd know what happens when they are combined!