Subject: Re: wind effects on aircraft
From: journali@sprynet.com
Date: Wed, 13 Nov 1996 00:52:54 -0600
Hi, Tim!
Yes, the airplane really travels at 125 mph toward the WNW. Its AIRSPEED
indicator will show only 100 mph, but its onboard electronic DME (distance
measuring equipment) or an air trafic controller's radar will show it to
be moving over the ground at 125 mph, on a ground track of WNW.
Some more musings on this subject:
The airplane's AIRSPEED doesn't change a bit, but its GROUNDSPEED does.
AIRSPEED is how fast the airplane is moving past the air molecules of the
mass of air in which it is travelling. In other words, an airplane capable
of 500 mph in still air has an airspeed of 500 mph, the speed at which it
is moving past the air molecules in the mass of still air. Now give that
same airplane a 200 mph tailwind -- its AIRSPEED is still 500 mph, because
it is still moving at 500 mph relative to the mass of air it is in. Now,
since that mass of air is also moving in the same direction, the
airplane's GROUNDSPEED (which is its speed relative to the ground, not the
air) is 700 mph, because it gets 500 mph from the airplane's thrust PLUS
200 mph from the moving air mass.
Here's one way to think of it. Imagine that the airplane is a
helium-filled airship, and does not need any airspeed in order to stay
aloft. Drop that non-moving airship into a 200 mph jetstream (tailwind,
let's say) and see what happens. Initially, an anemometer on the airship
will register 200 mph, because the air molecules of the jetstream will be
moving past the stationary airship at 200 mph (relative to the airship).
Now, blown by the tailwind of the jetstream, the airship begins to move
along with that jetstream, steadily picking up speed (with its rate of
accelleration dependent on its mass, friction, etc.). Eventually the
airship will be moving just as fast as the jetstream itself, and in the
same direction (just like a cork floating along in a stream), and the
anemometer will read zero mph since there will be no releative motion
between the airship and the jetstream it is floating in -- they are both
moving at the same speed and in the same direction.
Okay, now fire up this custom airship's jet engines, which are capable of
moving the airship at 500 mph in still air. Essentially, the airship is IN
still air, becuase even though it is moving at 200 mph over the ground as
it floats along in the jetstream, it has no motion relative to the
jetstream itself, therefore zero airspeed. But as those after-burning
engines kick in, the airship begins to move WITHIN the jetstream, until
finally the air molecules of the jetstream are racing past it at 500 mph.
And that's what the airship's airspeed indicator (and the anemometer) will
be registering -- 500 mph, the speed of the jetstream's air molecules
relative to the airship. Of course, the airship will actually be
travelling over the ground at 700 mph, which is its groundspeed.
Now, let's look at it from a headwind perspective. Let's drop the
stationary airship into that 200 mph jetstream, but now the wind is on the
nose. Initially, the anemometer will again register 200 mph becuase that
is how fast the air molecules of the jetstream will be racing past the
airship. In time though, the anemometer will again register zero mph, as
the airship is now moving just as fast as the jetstream it is floating in
(and no relative motion between the airship and the air molecules of the
jetstream). Of course, this time the airship is moving backwards over the
ground at 200 mph.
Crank up those jet engines again. The airship accellerates forward until
it is racing through the air molecules of the jetstream at 500 mph. The
airship's airspeed indicator and anemometer both register 500 mph, becuase
that is how fast the airship is moving relative to the air molecules of
the air mass it is in (the jetstream). At this point, the airship will
have a ground speed of 300 mph, becuase although it is moving forward
through the jetstream at 500 mph, the jetstream itself is carrying the
airship backwards at 200 mph. Subtract the backward 200 from the forward
500 and you see how the airship is only moving over the ground (its
groundspeed) at 300 mph.
In both of these cases we can see that the airspeed remains constant while
the groundspeed changes.
You didn't ask, but you might be wondering: What if, after one hour's
worth of flying, the pilot in your original question really wants to end
up at a destination 100 miles due west of where he/she started from,
instead of a point 125 miles WNW of the staritng point (not to mention
that that point is also 75 miles north of the desired destination!) Well,
he/she would have to crank in a considerable amount of in-flight
correction to offset that stiff wind blowing on the left wing. As it turns
out, the pilot would not point the nose of the airplane toward W but more
roughly SSW! Seen from the ground, that airplane would be crabbing into
the wind in an almost comical fashion, its nose pointed almost toward the
south as it tracked, very slowly, due west. The 100 mile trip would take 4
hours, becuase the groundspeed in this case would only be 25 mph!
To visualize this better, draw the vectors, using (as a previous poster
mentioned) one inch for 25 miles. First make a point which is the
starting point. Then four inches to the left (to the west) make another
point, which is the desired destination. Draw a line between them. This is
the distance (100 miles) the airplane would have flown in one hour if
there had been no wind.
Now, lets bring in that 75 mph wind. From the desired destination point,
draw a line three inches long toward the top of the page (due north). That
point is where the airplane would have ended up after that wind blew it
northward for an hour. As you can see, it is 125 miles WNW of the starting
point, and 75 miles due north of where the pilot really wanted to go.
Now, let's help the pilot get back to the desired destination point, which
is 75 miles due south. Simply turn the airplane 90 degrees to the left
until it's headed due south, and continue flying. With that 75 mph
headwind, its groundsdspeed will only be 25 mph, so it will take three
hours to fly the 75 miles to the destination. Total trip time has been
four hours, for an average groundspeed of 25 mph.
That's one way to fly the mission, but the real way the pilot would do it
is to fly the southerly correction needed to offset that north-blowing
wind all the time he/she was winging direclty toward the destination
(although in a crab angle as noted earlier). Still takes 4 hours, and the
groundspeed is still only 25 mph, but the ground track (the actual path
the airplane makes over the ground) would be a straight line between the
starting point and the desired destination point (which makes for easier
navigation, keeps the air traffic controllers a lot happier and keeps your
passengers from wondering if you really know what you are doing!)
Okay, knowing the airspeed of the airplane, and the speed and direction of
the wind aloft, the pilot can figure the correction before he/she takes
off. The pilot does the calculations and determines he/she will have to
fly with the nose of the airplane pointed just about SSW for four hours to
reach the desired destination. Chart the vectors and see how it works.
First, make a point which is the starting point. Then draw a line 16
inches long from that point in a direction that is SSW. That's the
distance (400 miles) the airplane would have flown, and the point it would
have ended up, in four hours if there had been no wind. Now, let's figure
in the wind.
From that second point you just marked, draw a vector 12 inches long (300
miles) going due north. That's the distance the wind would have pushed the
airpane back north during those same four hours. Now take a look at where
that point is -- it's four inches (100 miles) away from the starting
point, and due west of it, just where we want to be!
You can see why this particular trip, with the conditions you have given,
would not be a really great idea in an airplane that travels only 100 mph.
Truly, this would be the day to leave the Ercoupe in the hangar and buy a
seat aboard some airline's Boeing 737! (Even the airline wouldn't be too
happy with having to fight that considerable adverse wind on this trip,
but with the airliner's airspeed vector being over 500 mph, the wind
triangle looks much better -- proportionally, the wind isn't as much a
factor to the faster airplane.)
Hope this helps. (More than you proably wanted to know on the subject, huh?!)
If you have any further questions, please email me at
journali@sprynet.com and I'll see if I can help you.
Until later,
Happy Landings!
P.S.: This was written on my news reader's text program which has no spell
checker, and also it was written on-line (which I'm sure my Internet
provider hates!), therefore, please cut me some slack on typographical
errors. Thanks! :-)
> Langenburg High School wrote:
> >A friend and I have long debated a point. In physics texts there are
> >often problems which describe the motion of an aircraft in a certain
> >direction which is affected by the wind from a different direction. I
> >maintain that if an aircraft is in a pocket of air which is moving, it
> >will have its velocity affected by the air. Example) If a plane is
> >capable of flying at 350 km/h and heads N with a 10 km/h tailwind, it
> >will be able to move at 360 km/h over the land. Example 2) If a plane has
> >an airspeed of 100 mph [W] and is affected by a wind blowing to the north
> >at 75 mph, does the plane really travel at 125 mph toward the WNW?
> > If you can answer, please pack it up in email (I hope it is
> >automatically included on this thing) because I haven't the faintest idea
> >where in the net I am, and am very unlikely to be able to get back to
> >check a posting. Thanks,
> > Tim
Subject: Re: [Fwd: Re: The hard problem and QUANTUM GRAVITY.]
From: singtech@teleport.com (Charles Cagle)
Date: Wed, 13 Nov 1996 02:20:37 -0800
In article <327E5356.1FB7@well.com>, sarfatti@well.com wrote:
>Crowell describes a kind of back-action for quantum gravity -- a
>Godelian self-reference. The spacelike surface is the "beable". From my
>general postulate that anything with back-action is capable of
>felt-consciousness, the way Stapp defines it, it follows that we live in
>a "conscious universe" at the Planck scale. This answers Hawking's
>question about the "Mind of God".
What took you so long, Jack, to come up with this mind blowing revelation
which has been essentially incorporated into Hebraic religious culture for
a hundred generations? I would welcome you to the party if I didn't know
that you already think that you are the host.
>A true understanding of quantum gravity is going to involve some very keen
>insight into physics that can be expressed in geometric language.
How do you know what it is going to involve or by what means it must be
able to be expressed since by your own writings you come up fairly
clueless on the subject?
> It must
>in the limit that Planck's constant vanishes recover general relativity.
Absolute horse puckey! Since GR would be only an approximation to a
better theory which would be *without* 'fields' or an 'aether', the new
theory only has to perform better than GR. It doesn't have to recover or
subsume GR or even explain why GR seemed successful, it just has to be
better, more comprehensive and unify that which has lain about disparate.
Naturally, it will lead to new technology, and even eliminate the
serrendipitus nature of physics discoveries, and act as the foundation for
a new and logical way to develop new technolgy, and, not least, sound the
death knell for a dozen disciplines which sprang from the same corrupt
sources.
>General relativity is already a fairly mathematical subject with
>formalisms that involve Levi-Civita connection coefficients, Riemann
>curvature forms and Cartan structure formulas. It is this language that
>allows us to formulate conservation laws;
No it isn't. Quit trying to BS everyone, Jack. This (mathematics) is the
language which allows you to obfuscate the obvious. Since mathematics is
but an abstract of language itself it also can be no more than the
underlying physics which it seeks to describe; when it is, then it is a
poorly used tool at best. In fact, mathematics can't even be the
underlying theory unless you ascribe some mystical property to formulae.
Perhaps you think you can enunciate the hidden name of God in mathematics
and walk on water. Conservation laws are based upon physical facts not
upon formulations.
>and at its roots is the
>geometric idea that the boundary of a boundary vanishes. Quantum
>mechanics is also formulated in fairly mathematical terms; with bounded
>operators over Hilbert spaces.
Which is why it, too, is a ridiculous attempt at imposing a know nothing
approach to the inner workings of physics.
>Most field theories in nature can be quantized because the Green function
>or propagator is formulated on a spacetime back ground.
Which immediately destroys the possibility of emerging with a coherent
theory which is descriptive of reality if, in fact, there is no such
background.
>The peculiar
>thing about quantum gravity is that such a propagator would describe the
>evolution of a three dimensional spacelike surface that foliates
>spacetime. In effect there is not the same spacetime background upon
>which on can place a propagator.
If you think it is the propagator which foliates or layers a pre-existing
background (spacetime) then you are inserting mathematics into the 'Which
came first, the chicken or the egg controversy?' and imposing a
deterministic evolutionary development order for the universe in an
arbitrary non-realistic manner.
>It is as if the thing being propagated
>is also the thing you are propagating it on.
Congratulations, Jack, you actually are getting warm here. I am amazed
that the obvious answer keeps being missed by you. When you figure out of
what a charged particle is constructed and that it propagates on discrete
elements of that same construction material maybe then you will be able to
pause, smile, and say, "Oh, now I get it." Come on, Jack, the answer is
staring you in the face but you keep rejecting it. Care to tell us why
you pathologically avoid grappling with this? Or maybe someone could tell
you? Can you spell S-U-P-E-R-D-E-T-E-R-M-I-N-I-S-M, Dr. Sarfatti, Phd.?
> In a rough sense this has
>been at the heart of the problem. There are also problems of finding
>properly bounded operators for quantum gravity.
>
>In one sense I think that the kernel of the quantum gravity problem lies
>in some profound statement; much as Einstein's equivalence principle is
>the core of general relativity.
Which, incidently, isn't exactly or precisely true and stands central to
the issue of why it is being replaced. As for the profound statement you
are seeking: part of it is already articulated as Mach's Principle. That
which is lacking is an equivalent utterance associated with the
constitution of the unit charge. Even then, phenomenal parts, which evoke
a clear comprehension of the emission of EM quanta must be adduced to
round out the theory.
> This statement is then formulated
>mathematically and the structure of the theory then emerges.
What an approach. The whole, which you assume is greater than the sum of
its parts. somehow is deducible from the parts? You can't conceive of a
means where the 'whole theory' will just be intuitively grasped by the
diligent seeker, leaping into his mind fully formed?
> This
>statement is going to clearly state how state vectors evolve under the
>action of a generalized parallel translation. A mathematical formalism of
>this statement then should give the conservation laws associated with
>q-gravity. Without conservation laws and such you simply go not have
>physics; and conservation laws are described according to the symmetries
>of algebraic varieties and geometric spaces.
You are making it sound again like you are totally confused over what is
physics and what are mathematical attempts to describe the physics, of
which I'm now reassured is the case after having read this last paragraph.
--
C. Cagle
SingTech
Subject: Re: Sophistry 103 (was: I know that!)
From: Hardy Hulley
Date: Wed, 13 Nov 1996 12:16:46 +0200
Hardy Hulley:
>>>>>> If by relativity, you mean Einstein's theory, then Derrida's claim
>>>>>> that the Einsteinian constant "is the very concept of
>>>>>> variability" is surely false. If you are referring to some other
>>>>>> theory of relativity, then his claim is meaningless.
moggin:
>>>>> Your post ran back and forth between the claim that Derrida
>>>>> writes only nonsense and the complaint that his work contains an
>>>>> over-abundance of meaning.
Hardy:
>>>> Over-abundance of meaning is tantamount to nonsense. Consider the
>>>> number of interpretations available for the Book of Revelations.
>>>> Actually, that brings me to an interesting point - I wonder what
>>>> Nostradamus would have made of Derrida...or Derrida of Nostradamus,
>>>> for that matter. I sense fertile ground for satire here - a dialogue
>>>> wherein Derrida deconstructs Nostradamus' interpretations of
>>>> himself.
moggin:
>>> I see -- you think that anything which can receive more than
>>> a single intepretation is therefore "nonsense."
Hardy:
>> A non-sequitur - you have, without the slightest compunction, asserted
>> an equivalence between "over-abundance of meaning" and "more than a
>> single interpretation".
moggin:
> Here's the basis: "Over-abundance of meaning is tantamount
> to nonsense. Consider the number of interpretations available for
> the Book of Revelations." Of course, it could be that you allow
> multiple readings so long as their number doesn't multiply to the
> point that they become an "over-abundance." If that's the case,
> I can only wonder how many you permit (three? four? five? eleven?
> seven? twenty-three? forty-six? a hundred and sixty-two? Seven
> thousand, five hundred and thirty-eight?), and how you arrive at
> the figure.
Initially, you asserted that my position was: "Anything which can
receive more than a single interpretation is therefore nonsense". This
you did by conflating "more than a single" with "over-abundance" - a
very elementary mistake. Now, in a vain attempt to evade the inevitable
rotten eggs and tomatoes, you have stealthily changed your tack. "How
many" possible interpretations before we reach "over-abundance", you now
want to know. This is strictly pre-school stuff, and I'll respond in the
only way which does your puerility any justice. How many bees make a
swarm, and how would *you* arrive at the figure? (Or, perhaps you'd like
to assert that swarms don't exist).
moggin:
>>>>> Here, however, you don't seem to have any trouble finding an
>>>>> exclusive meaning and declaring it false.
Hardy:
>>>> I note, wryly, that you're in need of an introduction to the
>>>> conditional. Observe the leading "if" in the passage you quote - I
>>>> didn't claim to have isolated an "exclusive meaning" for anything.
moggin:
>>> And I reply, on pumpernickel, that I clearly observed the "if."
>>> Had I known you were obtuse, I would have written, "Here, however,
>>> you don't seem to have any trouble locating a premise which allows
>>> you to find an exclusive meaning and declare it false." Instead, I
>>> credited you with enough intelligence to follow along. My error.
Hardy:
>> So now "locating a premise which allows you to find an exclusive
>> meaning" is equivalent to "finding an exclusive meaning" (or, in
>> symbols, (P=>Q)<=>Q). Your error (as you put it) is in fact a trivial
>> misapprehension of elementary logic, apparently compounded by cavalier
>> dishonesty.
moggin:
> The only error here lies in your reading.
Yet more dishonesty. There is no denying that you asserted an
equivalence between "locating a premise which allows you to find an
exclusive meaning" and "finding an exclusive meaning". Think what you
will, gollum, your own words have condemned you.
Hardy:
>> Furthermore, even your modified assertion is false. I hadn't located a
>> premise, *allowing* me to find an exclusive meaning - the very
>> meaning, to which you refer, *was*, in fact, the premise of my
>> statement.
moggin:
> I'll try re-phrasing my point. Although you claimed that
> Derrida's work was nonsensical, nonetheless you were able, when
> it suited you, to make sense of one of his comments. And when
> did it suit you? When you wanted to press an attack.
Firstly, I didn't claim that Derrida's work was nonsense, I claimed that
it was *either* nonsense *or* false. So, even if you are right that I
had managed to interpret his remark, the interpretation I discovered
still rendered it false. Hence, the point you are making is of no
interest.
Secondly, in my initial statement I said: "*If* by relativity, you mean
Einstein's theory, *then* Derrida's claim [...] is surely false". That
doesn't mean that I *have* managed to "make sense of his comments", and
found them to be false. It means: "*assuming* that I interpret his
comments in a certain way, he is wrong". Your puerile attachment to
indefensible positions, aggravated by your vacuous apprehension of
elementary propositional calculus, has now reached alarming proportions.
Hardy:
>> Lastly, let me add that you were already flogging a dead horse with
>> your original claim ("you don't seem to have any trouble finding an
>> exclusive meaning and declaring it false"). My position, all along,
>> has been that Derrida's comment is either false or unintelligible.
>> Your startling discovery that I may have isolated an interpretation
>> which does, in fact, render his stupid remark false, is silly (though,
>> hardly inconsistent with my expectations).
moggin:
> See above.
The "above" doesn't address my point - it only assists me in compiling a
very unflattering assessment of your mental adroitness.
moggin:
>>> Why ever should those be the only possiblities? It's easy to
>>> imagine that Hyppolite asked an unclear question that Derrida was
>>> able to understand, regardless, or which Derrida thought he was able
>>> to understand. Happens all the time in conversations.
Hardy:
>> Yes it does - usually in silly conversations.
moggin:
> In all kinds.
Judging by the nonsense you have taken to disseminating until now, I can
only conclude that you are drawing deeply on personal experience here.
moggin:
>>> Now let's look at Derrida's words again. (Again remember that
>>> we're ignoring the bulk of both Hyppolite's question and Derrida's
>>> reply in order to focus on one, particular detail.) Derrida says:
>>>
>>> "[It] is not a constant, is not a center. It is the very
>>> concept of variability -- it is, finally, the concept of the
>>> game. In other words, it is not the concept of some_thing_ --
>>> of a center starting from which an observer could master the
>>> field -- but the very concept of the field which, after all, I
>>> was trying to elaborate."
>>>
>>> You no longer have to assume that Derrida is talking about c,
>>> so you no longer have to conclude that his statement is meaningless
>>> or false. We're left to figure out what he _is_ talking about, but
>>> it's now possible that he's making an arguably valid observation
>>> about certain elements of relativity -- in other words, that there
>>> exists an [it] which fits his comments. Maybe you could make some
>>> suggestions. Personally, I'd guess he's referring to the lack of
>>> absolute space and time.
Hardy:
>> After much elaborate sleight of hand, all you've managed to tell me is
>> that, if we're exceedingly charitable towards Derrida, and assume that
>> "Einsteinian constant" is not in fact Einstein's constant, then his
>> comment *need* not be false. You still don't have a clue as to what
>> Derrida is actually saying *about* the "Einsteinian constant".
>> Consequently, you stand absolutely no chance of determining what the
>> "Einsteinian constant" actually is. In fact, your grand hypothesis is:
>> Derrida says that for some constant c, and some predicate P, P(c)
>> obtains.
moggin:
> There was nothing elaborate about it at all -- I just paid
> some attention to what Hyppolite and Derrida were saying to each
> other. That allowed me to remove the premise of your reading,
> which prevented you from understanding them, and replace it with
> one that makes more sense, if you accept my interpretation (and
> I don't see you arguing with it). There's no need for charity
> toward Derrida, since the term "Einsteinian constant" came from
> Hyppolite -- on my reading, Derrida corrects it. And although
> you don't seem to have noticed, I also handed you a clue to the
> meaning of Derrida's reply.
The "premise" (and I quote you with trepidation, for it has already
become clear that you don't understand the relationship between
antecedents and consequents in conditional expressions) to which you
refer was that "Einsteinian constant" means, in fact, just that -
Einstein's constant. This didn't render Derrida's remark unintelligible
to me, as you allege, but merely false.
I haven't resisted your attempts to replace the conventional
interpretation of "Einsteinian constant" with something more fanciful,
because it hasn't been necessary. But, since you insist, I will. You've
offered "lack of absolute space and time" as a possible interpretation.
Explain, then, to what extent is such a concept Einsteinian, and to what
extent is it constant?
Furthermore, committing yourself to a project of finding an alternative
interpretation for Hyppolite's (and Derrida's - since he didn't object
to the words "Einsteinian constant" being used, and continued to refer
to them throughout his statement) use of a pretty well-understood
concept, *just* because the conventional interpretation means that
Derrida was wrong, is weak scholarship.
Hardy:
>> I'm flabbergasted. How can you possibly spew shit like: "We're left to
>> figure out what he _is_ talking about..." and "it's now possible that
>> he's making an arguably valid observation about certain elements of
>> relativity", and offer it as a defence of the truth and
>> intelligibility of Derrida's claims?
moggin:
> You claimed that what Derrida said was wrong or meaningless;
> I showed that you were full of crap. Mission accomplished.
I say: "Derrida's remark is wrong, or meaningless". You say: "No, if we
interpret him in a certain way, he *need* not be meaningless or wrong -
we just have to figure out what he _is_ talking about". Well, my dear
gollum, *until* you have figured out what he *is* talking about, how do
you know that its meaningful or true?
You may well consider your mission accomplished, but *you* certainly are
not.
moggin
> If you want to go on to discuss what he meant and whether it's true,
> you don't need an invitation; but I gave you one, anyhow, along
> with my guess about his meaning. Your response was to say, "I'm
> flabbergasted," and accuse me of spewing shit. Well done.
Again, the very fact that you concede, here, that we may still "discuss
what he meant and whether it's true", clearly indicates, by your own
admission, that you have not yet falsified my claim that Derrida's
remarks are either false, or meaningless. If you have demonstrated that
Derrida's words are meaningful *and* true, why must we discuss anything?
Why must you "guess about his meaning" still?
My accusation still stands.
Hardy:
>> It's time to stop dithering - do you, or don't you know what Derrida
>> meant in his much-quoted conversation with Hyppolite? I have claimed
>> that what he said was either false, or meaningless - my claim awaits
>> falsification.
moggin:
> I already showed that your claim was false, and told you
> what I thought he meant. Your reply, such as it is, is above.
Falsifying my claim entails finding an interpretation for Derrida's
remark which is both reasonable and true. You tentatively proffered one
silly hypothesis for what "Einsteinian constant" may mean, but failed to
demonstrate reasonableness. Furthermore, you were, in your own mind,
unsure of whether this is what Derrida meant, and of whether or not it
makes his grand pronouncements true. Consequently, you have still failed
to locate an interpretation with the desired qualities. Ergo, you
haven't falsified my claim.
Cheers,
Hardy
Subject: Re: Hermeneutics and the difficulty to count to three...
From: moggin@mindspring.com (moggin)
Date: 13 Nov 1996 11:58:43 GMT
Anton Hutticher:
>>>Our definitions are as good as yours.
moggin
>> Not to mention Humpty Dumpty's.
caj@moriarty.math.niu.edu (Xcott Craver):
> What what WHAT??? Please, Moggin, *just this once* let's settle
>a quibbling petty side-thread in a direct manner, without one-liners,
>without semantically jumping ship. I can't see how you can do anything
>other than (perhaps grudgingly) agree on this point, because it's a
>point you yourself have made countless times!
> You have in the past emphasized this in our own articles: there
>is no universal strict definition of such words, and nobody has the right
>to insist that theirs is the right one. You keep insisting that if it's
>flat, then by definition it's not a hill. That's just one definition,
>albeit a common one. It is quite contradictory to your usual behavior
>to assert this usage of "hill" as if it were strict and universal, and
>not just your opinion, your definition. Indeed, many sciency types fear
>your ability to escape a losing argument by claiming different def's
>of terms your opponents used.
> Remember months back to that yammering about syllogisms and
>validity? I foolishly assumed that my definition of "valid" was
>universal, and you were quick to point out that it was wrong to do so,
>even if it's the definition logicians agree upon. Not everyone is a
>logician, and certainly a word like "valid" has many connotations.
>I was forced to agree. I still agree. Why are you suddenly doing a
>180? I mean, if you saw someone behave this way you'd (IMHO) say
>the same thing Anton did. Do principles and opinions get tossed aside
>or reversed so easily in the name of word games?
> Agree or disagree, with no sarcastic frosting: it's a loose
>use, but not any more or less correct, to consider a flat plane a
>hill? Yes? No? A single straight answer would quite brighten my
>day.
Sorry for not answering your earlier post (I lost it, along with a
few others) -- if I had, it might have saved us this confusion. You'll
be glad to learn that I agree with your basic point -- my citation of
the esteemed Mr. Dumpty notwithstanding. _Pace_ Hardy, I never
studied with him, but as a philosopher of language, he has few equals.
I can agree with you without grudge, quibble, or (I'd better make
this plain) sarcasm: there isn't any universality to my sense of
the term "hill." You're fully entitled to use a different one, if you
see fit. And if you apply a definition which differs from mine, it's
entirely possible that you would arrive at a different conclusion.
Please note that I did not make a U-turn. I'm capable of driving
like a bootlegger, but here I was out for a Sunday cruise -- agreed
that I _would_ be reversing myself if I insisted that my sense of
"hill" was exclusively valid -- but you'll notice that I'm not. I've
got no desire for you to adopt it, if you don't so choose.
I admit, it's hard for me to grasp the idea of a hill that's flat,
but that's probably because I'm thinking of my sort of hills -- if
you're giving the term your own definition, there's no reason in
the world hills couldn't possess flatness as a characteristic. I
wouldn't even call that a "loose" use of the word, since there's no
larger notion of hilliness for me to measure by -- it's just a
different way of using the term.
-- moggin