Posted on 10/25/2004 1:46:25 AM PDT by accipter
CONSIDER a verbal description of the effect of gravity: drop a ball, and it will fall.
That is a true enough fact, but fuzzy in the way that frustrates scientists. How fast does the ball fall? Does it fall at constant rate, or accelerate? Would a heavier ball fall faster? More words, more sentences could provide details, swelling into an unwieldy yet still incomplete paragraph.
The wonder of mathematics is that it captures precisely in a few symbols what can only be described clumsily with many words. Those symbols, strung together in meaningful order, make equations - which in turn constitute the world's most concise and reliable body of knowledge. And so it is that physics offers a very simple equation for calculating the speed of a falling ball.
Readers of Physics World magazine recently were asked an interesting question: Which equations are the greatest?
Dr. Robert P. Crease, a professor of philosophy at the State University of New York at Stony Brook and a historian at Brookhaven National Laboratory, posed the question in his Critical Point column and received 120 responses, nominating 50 different equations. Some were nominated for the sheer beauty of their simplicity, some for the breadth of knowledge they capture, others for historical importance. In general, Dr. Crease said, a great equation "reshapes perception of the universe."
(Excerpt) Read more at nytimes.com ...
Could you give an example of a logically consistent alternative to "A is A"?
Aaaauugghhh..... You got me, doc.... Good clarification.
While on the subject of polling, what's your take on the difference between polls and voting? Is there any way to predict turnout? If so, you can get rich.
That's a good one. Another one of my favorites is that the sum of 1/n2 as n goes from 1 to infinity is pi2/6. You don't expect to see pi in a series involving squares.
I cannot go into the detail you want, but I do remember it was in the Work-Energy Theorem. Yes--it was that many blackboards at Syracuse University. Believe me. He would fill one up and shift it to the ceiling, and fill up another. The auditorium full of students would write in their notebooks like hell--trying to keep up--understanding next to nothing. This was before PalmPilots, Laptops, and Ipods.
It was the early 80's, and at the time I was taking 24 credit hours, including Thermal Dynamics, Statics, Differential equations, Heat Transfer, and Structures.
00000001 + 000000001 = ?
Voting is self selected. Polling is only partially self selected.
I haven't tried to model voter turnout; I may sometime though. Here's a link: (left explicit so you can see the .pdf.) http://bbs.vcsnet.com/malchow.pdf
x = wife shopping. y = actual savings. z = money saved without wife hitting sales. z>x+y
Misleading question...you need to re-index your zero in essence. 28 and 29 are the 29'th and 30'th dollars
So what happened to the other dollar?
It was spent on welfare and food stamps?
First off, let's grant "A is A" as an axiom according to Webster's second definition. That said, what is important about "A?" Do we care only about the current state of "A," or is the fact that A is mutable or immutable what really matters?
Rand used "A is A" as a means of defining absolutes, which makes no sense unless we assume that A is immutable -- i.e., that "A(t-dt) is A(t) is A(t+dt)." Suppose I have fallen from a tall building, and am just an instant prior to a "sudden stop." Clearly my current state (not dead) is not the only thing that matters here -- my future state (splattered) is also important. Thus, even though "A is A is 'Not Dead'" happens to hold for the moment, it's not going to help me define an absolute.
Now to your challenge.
Suppose I say that "A is a sphere with exactly six sides." Clearly "A is A" is logically true in this case, even though it is an obvious nonsense statement.
Likewise, one might state (as Rand did) that "A is the only logically consistent moral position;" however, if one can demonstrate the existence of other "logically consistent moral positions" then Rand's particular version of "A is A" is logically incorrect.
Which is to say, it's not enough to just say "A is A" and think you've done something swell. It's quite clear that not all "A's" are created equal -- your "A" has to make sense in the first place, or else "A is A" has no logical merit.
Wikipedia has an interesting article on Axiomatic Systems.
I see you already went over this with PH. It's a self evedent truth. If it is not true, then anything is not equal to, or is itself. It's totally illogical. Liberals love a != a, because they can then claim what something is, is not, and it's what they tell you. The 'toon sat in court and attempted to get away with that very thing. He questioned the meaning of is. His purpose of course, was to toss out real meaning and present his own.
"the reason I picked on that one, is that it's possible to demonstrate that there was a time (i.e., before the Big Bang) when it is very likely that "A != A." E.g., consider the conditions ascribed by physicists to initial moments following the Big Bang. "
Any aprticular a can cease to be a and a(s) can be created. Those concepts are independant of a = a.
"Does it make sense to state that the full set of possible "A's" is invariant under transformation during the Big Bang?
The members of that set are identically 1. There are no alternative a's. Each one of those is equal to itself and no others.
Invariance refers to observables and coordinate tranformations. So if a is an observable and can be observed now, it is an invariant. The total energy of the universe is an invariant and is zero. It's conceptually the same as it was before the big bang, but you can't observe it. Big bangs are not coordinate transforms, they are events.
No it's not "self evedent" unless we're talking about the capital first letter of our alphabet, then I suppose it's true. But if I point out that "A" is also the first letter of the Greek alphabet, then "A is A" is obviously not true, as there is more than one possible definition for "A".
Yeah, that's sophistry centered on the shape of a particular symbol, but it demonstrates that the identity of the "A" in question has to be established before "A is A" can be taken as true.
The point being that "A is A" (or A != A) is dependent on what "A" happens to be. Molecularly speaking, you and I are literally what we eat. Thus, "You are You," but at the same time "You are a Cow (along with special sauce, lettuce, cheese, pickles, onions, and a sesame seed bun)."
Any aprticular a can cease to be a and a(s) can be created. Those concepts are independant of a = a.
Not really. What you're doing here is defining "a" in the sense of one of Plato's "forms" (see link above). That's a metaphysical position that depends on an assumption that the archetypal "a" is static and eternal. Essentially, in the case of physical things, "a=a" requires a particle-by-partical equivalence between "any particular a" and other a's that can be created.
Each one of those is equal to itself and no others.
Which contradicts your statement above, that a's can be created and destroyed.
The definition of a shpere precludes it having more than 2 sides(inside and outside). The A you described is logically incorrect with contradictions of meaning. Any logical operations you do with this a will propagate illogic and contradiction. That's what liberal judges do.
" Rand used "A is A" as a means of defining absolutes,"
She did not. She used it in the meaning I gave.
"... which makes no sense unless we assume that A is immutable -- i.e., that "A(t-dt) is A(t) is A(t+dt).""
Immutable is an independent property. Things may, or may not be immutable.
ping
Don't be ridiculous; a is a varible that represents quantitative aspects of truth regarding the object. It is a representation of the object. The equation states that what is, is, and is not something, anything else.
You're assuming a 3-d universe.... ;-) At any rate, I already know it's a "wrong definition," although I'll note that we're relying on the conventional definition of "sphere" to make that claim. Be that as it may, I can still say "A is a six-sided sphere," even if I know it to be nonsense. I did that on purpose, for reasons repeated below.
The A you described is logically incorrect with contradictions of meaning.
Yes it is.
Any logical operations you do with this a will propagate illogic and contradiction. That's what liberal judges do.
Yes indeed.
But note: you've stated that "A is A" is a "self-evident" statement, which means that it's logically correct no matter what I put in for A. The question is whether "A is A" has any general axiomatic meaning, and in the example of the six-sided sphere we see that it has no meaning. IOW, whether "A is A" has meaning outside of an abstract concept, depends entirely on what we choose to plug into "A."
She did not. She used it in the meaning I gave.
I was unfortunately making a short-hand statement. Rand used "A is A" as an example of an "objective truth," of the sorts she claimed as the basis of her objectivist philosophy. The problem, as noted above, is that while "A is A" is fine in the abstract, it is the choice of "A" that determines whether the statement has any real meaning. Rand's version of "A" doesn't work, but that's a matter for a different thread.
Immutable is an independent property. Things may, or may not be immutable.
I don't understand this statement. If a thing "A" is "immutable," is that not an intrinsic property of the "A" in question? Likewise, is not "mutable" also an intrinsic property?
See above. This is fun, but I gotta go now.... Perhaps we can take it up again later.
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