Where is he?

[Paul's Here 0]

Where is the man when he jumps off a bridge?

Some have said: "He's in the air." But that's where he is after he jumps.

Others say: "He's on the bridge." But that is where he is before he jumps.

So, where is he when he jumps?

[Capitalism Forever 0]

Jumping is a process that begins on the bridge, progresses through the air, and ends in the water (or wherever he lands). The question is a bit like asking, where is a man when he travels from Houston to San Francisco? The same kind of answer would apply there.

[Paul's Here 0]

But what is the philosophic (epistemological) explanation? You question can simply be answered by saying he is in whatever location he's in when you ask the question (He's in Las Vegas).

[ruveyn ben yosef 0]

Where is the man when he jumps off a bridge?

Some have said: "He's in the air." But that's where he is after he jumps.

Others say: "He's on the bridge." But that is where he is before he jumps.

So, where is he when he jumps?

His position is a function of time.

Classical mechanics handles this problem very well.

ruveyn

[ewv 0]

Jumping is not a position in answer to the question "where?". It is a kind of action in a trajectory, which itself is a locus of positions.

[Arnold 0]

Fix the time and you fix the position.

[ruveyn ben yosef 0]

Where is the man when he jumps off a bridge?

Some have said: "He's in the air." But that's where he is after he jumps.

Others say: "He's on the bridge." But that is where he is before he jumps.

So, where is he when he jumps?

Have you studied Zeno's "paradoxes" of motion? He raised this very question about 2300 years ago.

ruveyn

[Betsy Speicher 0]

Have you studied Zeno's "paradoxes" of motion? He raised this very question about 2300 years ago.

You'll find an answer to those paradoxes in these lectures available to download for only $2.75.

Achilles, the Tortoise, and the Objectivity of Mathematics (MP3 download)

By Pat Corvini

Philosophers and mathematicians alike have long misunderstood the relation of mathematics to the real world and to the rest of human knowledge. A proper theory of concepts is essential to an understanding of the nature of math. Thanks to Ayn Rand, we now have the basis for such an understanding.

In this course, Dr. Corvini draws on Objectivist epistemology to offer a new identification of how mathematical concepts are related to physical concretes, including a new formulation of the concept of infinity. She uses the easy-to-visualize example of Achilles and the tortoise to make the ideas accessible to a general audience. In the process, she also identifies the fundamental error that underlies Zeno's famous paradox and that has long obstructed men's understanding of mathematical abstractions. Her analysis underscores the importance and power of Ayn Rand's theory of concepts.

(Of interest to anyone interested in epistemology; no prior mathematics background assumed.)

(MP3 download; 4 hours, 12 minutes, with Q & A)

[Kevin Delaney 0]

Where is the man when he jumps off a bridge?

Who cares where he is? To him, the only thing that matters in that moment is where he's going.

[ruveyn ben yosef 0]

Here is another source on the Zeno Paradoxes.

http://en.wikipedia.org/wiki/Zeno%27s_paradox

One point of view says that the modern theory of convergences has not fully addressed the problems that Zeno raised, another point of view says the problem is solved. Judge for yourself.

ruveyn

[Capitalism Forever 0]

But what is the philosophic (epistemological) explanation?

I'm not sure what you would like explained.

You question can simply be answered by saying he is in whatever location he's in when you ask the question (He's in Las Vegas).

No, the question is not where he is now, the question is where he is when he travels. Traveling, like jumping, is a process that takes you from one location to another.

[ruveyn ben yosef 0]

But what is the philosophic (epistemological) explanation?

I'm not sure what you would like explained.

You question can simply be answered by saying he is in whatever location he's in when you ask the question (He's in Las Vegas).

No, the question is not where he is now, the question is where he is when he travels. Traveling, like jumping, is a process that takes you from one location to another.

Define "now": Simultaneity is not absolute. It is relative depending on or motion with respect to the thing observed. Now does not equal Now in different inertial frames of reference. See any treatise on the special theory of relativity or a discourse on simultaneity or "now"

ruveyn

[Paul's Here 0]

But what is the philosophic (epistemological) explanation?

I'm not sure what you would like explained.

You question can simply be answered by saying he is in whatever location he's in when you ask the question (He's in Las Vegas).

No, the question is not where he is now, the question is where he is when he travels. Traveling, like jumping, is a process that takes you from one location to another.

Define "now": Simultaneity is not absolute. It is relative depending on or motion with respect to the thing observed. Now does not equal Now in different inertial frames of reference. See any treatise on the special theory of relativity or a discourse on simultaneity or "now"

ruveyn

I think the question clearly delimits the context, so bringing in moving at the speed of light or near that speed is outside of the context of this discussion.

[Arnold 0]

When you ask where he is, you must at least give a time. The more precisely you fix the time, the more precisely you fix the position.

[ruveyn ben yosef 0]

I think the question clearly delimits the context, so bringing in moving at the speed of light or near that speed is outside of the context of this discussion.

No so. Time varies between any two inertial frames moving with respect to each other. The Einstein formula for time dilation was tested by synchronizing two atomic clocks. On stayed on the ground and the other flew in a jet plane (hardly the speed of light) the clocks differed from each other exactly as the Einstein formula predicted, in this case a few hundred thousandths of a second.

Please see:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html

ruveyn

[Capitalism Forever 0]

When you ask where he is, you must at least give a time. The more precisely you fix the time, the more precisely you fix the position.

BINGO!

[ewv 0]

I think the question clearly delimits the context, so bringing in moving at the speed of light or near that speed is outside of the context of this discussion.

No so. Time varies between any two inertial frames moving with respect to each other. The Einstein formula for time dilation was tested by synchronizing two atomic clocks. On stayed on the ground and the other flew in a jet plane (hardly the speed of light) the clocks differed from each other exactly as the Einstein formula predicted, in this case a few hundred thousandths of a second.

This has absolutely nothing to do with the subject of the thread. It is more perverse, obnoxious interjection by someone who does not understand the topic being discussed, let alone Ayn Rand's philosophy, yet who adopts a self-proclaimed duty to set us all straight and prove we don't know anything because he insists that "someone has to do it".

Such perverse intrusions relying on out of context 'curve balls' or any other gimmick to throw his targets into a state of perpetual befuddlement and paradox do not belong here. It is obnoxious, neurotic disruption in the phony name of facts and genius. It is neither. It's coming from a flailing sub-Normal who can't walk and munch asparagus at the same time, and who perversely refuses serious discussion of relevant ideas, his own past accomplishments, or experiences or values in common with those of us who share them. His sense of self seems to be wrapped up in this perversion and he refuses to budge from it.

For those who are serious and who act an age past about 10, relativity physics does not invalidate the prior physics or the prescientific concepts on which it depends. In particular it does not deny ordinary conceptions and measurements of space, time, position and motion within a reference frame, all of which it explicitly depends on. Effects of relative velocity, of any magnitude, on other measurements taken in frames in relative motion is irrelevant to that.

To claim that reference to a measurement at a specific time is meaningless because of relativity is a stolen concept and not what SR says. Without measurements of position as a function of time there could be no kinematics at all, let alone the SR theory of measurements taken from moving reference frames taking into account signal speeds, let alone the effect of time dilation in accelerated reference frames in general relativity.

[Paul's Here 0]

I think the question clearly delimits the context, so bringing in moving at the speed of light or near that speed is outside of the context of this discussion.

No so. Time varies between any two inertial frames moving with respect to each other. The Einstein formula for time dilation was tested by synchronizing two atomic clocks. On stayed on the ground and the other flew in a jet plane (hardly the speed of light) the clocks differed from each other exactly as the Einstein formula predicted, in this case a few hundred thousandths of a second.

Please see:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html

ruveyn

Wacko nonsense.

[Paul's Here 0]

When you ask where he is, you must at least give a time. The more precisely you fix the time, the more precisely you fix the position.

So the concept "where" implies not only location but a specific time at that location. Would you agree that all action verbs require those two elements?

[Arnold 0]

When you ask where he is, you must at least give a time. The more precisely you fix the time, the more precisely you fix the position.

So the concept "where" implies not only location but a specific time at that location. Would you agree that all action verbs require those two elements?

Asking where someone or thing is, always implies a given time even if it is not explicitly stated. For something in motion, there is no fixed "period" that a location is occupied, but only a point in time that can be narrowed to an infinetly small length, likewise narrowing the accuracy of position. Thus, the car covered 'this distance' in one second, therefore one thousandth the distance in one thousandth of a second and so on. A moving object cannot be stationary for any length of time by definition.

[ruveyn ben yosef 0]

When you ask where he is, you must at least give a time. The more precisely you fix the time, the more precisely you fix the position.

So the concept "where" implies not only location but a specific time at that location. Would you agree that all action verbs require those two elements?

Asking where someone or thing is, always implies a given time even if it is not explicitly stated. For something in motion, there is no fixed "period" that a location is occupied, but only a point in time that can be narrowed to an infinetly small length, likewise narrowing the accuracy of position. Thus, the car covered 'this distance' in one second, therefore one thousandth the distance in one thousandth of a second and so on. A moving object cannot be stationary for any length of time by definition.

You should have underlined the word "length" as well.

Zeno and Eudoxus lacked the mathematical machinery to define an -infinitesimal- which is a quantity not zero but smaller than any positive number. We are brought up on Archimedean algebraic systems which would make this impossible. However Abraham Robinson, around 1960, made infinitesimals mathematically rigorous. Newton and Leibniz used infinitesimals in their construction of calculus. Unfortunately they did not have the machinery to make their mathematical artifact rigorous and consistent. That is why Cauchy invented the rigorous mathematics of -limits- around 1840 or so. The calculus you learned (and no doubt loved!) is based on limits rather than infinitesimals.

It so happens that the infinitesimal is just the mathematical critter that can address Zeno's paradox of the arrow cleanly.

The paradox goes like this: if the arrow is in a definite location at every instant of time (an instant of time is a time interval of zero length) how can it ever move? And the answer is (drum roll) in an infinitesimal interval it -move- an infinitesimal amount. A small quantity that is not zero. So you see, the arrow does move from the bow string to the target after all.

What the operation of integration is, is the addition of an infinite set of infinitesimals to get a quantity that can be finite. If you compute the integral

Integral sign (from t0 to t1) of instantaneous velocity X infinitesimal distance you get a proper finite length. Think of a motion picture show in which an infinite set of infinitesimal frames is run through the projector in a finite interval of time.

thank dog ! If it weren't for the infinitesimal William Tell could not have shot the apple off his son's head and motion picture Hunger Games could never have been made.

ruveyn

ruveyn

[PhilO 0]

Central to this: location is a *relative* concept. It's meaningless to use the word without stating "a location of X *in relation to Y*". If you dropped two objects at the same time off a bridge, and neither of them accelerate at a different rate until hitting water/ground, their relative position will remain unchanged; what will change is each of their positions with respect to the bridge and other things on the earth, and in the universe (and has essentially been noted, those positions can be computed as a function of time using physical principles.)

I might be mistaken but I think that's what Ruveyn was saying in a confusing way - not that the issue is travel near light speed but of stating a reference frame ala Einstein.

[ewv 0]

You don't need calculus to understand the concept of jumping. Without concepts of movement and trajectories there would have been no theory of their analysis using abstract principles of calculus.

[ewv 0]

When you ask where he is, you must at least give a time. The more precisely you fix the time, the more precisely you fix the position.

So the concept "where" implies not only location but a specific time at that location. Would you agree that all action verbs require those two elements?

A time is implicit in any fact. Everything is changing.

All concepts of change include an interval of time but not ot all concepts of change refer to position. An object may change color or temperature but it's position(s) is not what is referred to by that kind of change.

"Jumping" does not refer to a single position. You jump from somewhere to somewhere along a trajectory passing through the locations in between as time passes. Even if you jump "in place" you are moving up and down to return to the approximate starting point. The answer to the question 'where is he' is 'on the path he follows'.

The introduction of Zeno, relativity and calculus is a distraction from a very simple concept.

So is the concept of the bugs in the Forum software changing positioning, nesting, line spacing, quote-tags and headers in the formatting on its own, making it take longer to position the text despite its interference than to type it.

[ruveyn ben yosef 0]

You don't need calculus to understand the concept of jumping. Without concepts of movement and trajectories there would have been no theory of their analysis using abstract principles of calculus.

We have some "wired in" motion processing in our brains. A 5 years old kid can learn to shag a fly ball without knowing a line of mathematics. However, our brains cannot easily deal with turbulence and non-linear perturbations. We can simulate turbulence in fluids by using zillion dollar computers. To internalize such processing we would need 30 lb. brains instead of the 3 lb. model that nature issues to us.

Read Wm. Calvin's -The Throwing Madona-. He points out that the ability to throw rocks accurates in an attribute that Chimpanzees and Bonobos made good use of. Eventually these critters evolved a brain that could do straightforward ballistic motion processing which promoted their reproductive success. We homo sapiens inherited this ability. It is "wired in". We do not need to verbalize to comprehend a simple parabolic ballistic arc.

ruveyn