Posts by Rod P

41

Can you solve this paradox?

by Rod P in

jw
friends

you have a bow and arrow.

you shoot the arrow with the bow from point a to point b.. but the arrow will never reach point b, it's destination.

before the arrow can reach point b, it must first travel half way (let's call that point c).. but before the arrow can reach point c, it must first travel half way (let's call that point d).. but before the arrow can reach point d, it must first travel half way (let's call that point e).. do you see the problem?

Rod P

On the Mirror question, Yes, there is a reverse image.

Try this experiment. Take a piece of paper and a pen. Now, sit at a table, and place the paper on the underside of the table. Now write your name on the paper while it is on the underneath side. Now look at the paper, and what do you see? Your name will be written backwards. Now go to the mirror and hold up your paper to the mirror. What do you see?

Now, take a piece of paper or a small card and write the following letters:

b q

d p

Look at this in the mirror. You would see in the mirror the same thing that you would see if you could hold the paper up to a light, and then looked at the letters from the other side of the paper.

What if we could turn this paper (card) over (i.e. rotated it about the vertical axis)? Here's what we would see:

p d

q b

In other words, the image would be reversed left-right.

What if we rotated this card or paper 180 degrees (i.e. rotate it about the horizontal axis), so that it is now upside down. Now look at this upside down paper in the mirror, and what do you see? It would look lke this:

p d

q b

In other words, it will be reversed up-down. This is true, regardless of whether we look at it in the mirror, or if we looked at the letters thru the backof the paper (card).

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On the question of Protagorus versus Euathlus:

Where Euathlus went wrong was he was a Defendant in his own lawsuit. (He had a fool for a client). What if Euathlus had hired another lawyer to handle his case. Then if his lawyer won the case for him, then Euathlus would still not have won his first case. That way, according to the terms of the original contract, Euathlus would have to pay Protagorus only on the condition that Euathlus won his first case, and under these circumstance, it could still be said that Euathlus was not yet practicing law, and so had yet to win his first case. Therefor, Euathlus should not have to pay.

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Outoftheorg,

If you go back to Page 1 of this thread, you will see the explanation of Zeno's Paradox that explains the fact that the arrow does move from Point A to Point B, which is mathematically consistent with both space and time.

Terry,

On Page 1 of this thread, in my reply to Dr. Mike, I stated why I avoided taking this paradox analogy down to the minute or sub-atomic particle level.

The Heisenberg Principle of Uncertainty is primarily about the consciousness of the observer affecting the thing being observed, so that one can never know with certainty its exact location/position or speed. I see how the Heisenberg Principle is materially relevant when it comes to the tiniest particles and sub-stomic particles of the universe. But I hardly think this would be all that relevant at the scale of the arrow in the "normal" observable day-to-day world we live in. When we get to the point of measuring the infinitely small units of time and distance remaining for the arrow, I doubt that our observation of the arrow in flight would materially influence its position in space and time. In other words, Heisenberg does not influence, or interfere with, the problematic nature of this paradox.

Rod P.

41

Can you solve this paradox?

by Rod P in

jw
friends

you have a bow and arrow.

you shoot the arrow with the bow from point a to point b.. but the arrow will never reach point b, it's destination.

before the arrow can reach point b, it must first travel half way (let's call that point c).. but before the arrow can reach point c, it must first travel half way (let's call that point d).. but before the arrow can reach point d, it must first travel half way (let's call that point e).. do you see the problem?

Rod P

Double Edge,

I have heard of that one many years ago; now you have brought it all up again.

But no, I cannot remember the answer. Just don't know what it is, at the moment.

So now, I am going on a random search, based on this understaindting (Halleluja! Hallejuja!)

So why do I suddenly feel go sad???!!!!.

.

59

Dead Relative Due To Blood Policy?

by AlanF in

.

i'd like to hear comments from anyone who had a relative die because of the watchtower society's misguided policy on blood transfusions.. alanf

Rod P

This whole thing is very sad, and very sick. There are people on the inside of the organization who know better than anyone, that the thinking of the Borg is beginning to rethink its polcy on blood!"

48

Ex elders, have you apologized to anyone you df'd?

by avishai in

jw
friends

for instance, especially kids under the age of eighteen, or dfing folks for questioning the society?

i think if i had been involved, i'd have to get on the horn with everyone i'd df'd.

except the child molesters

Rod P

Well, Yes! They have some answering to do, don't they?????

Where is everyone one on this one?????

41

Can you solve this paradox?

by Rod P in

jw
friends

you have a bow and arrow.

you shoot the arrow with the bow from point a to point b.. but the arrow will never reach point b, it's destination.

before the arrow can reach point b, it must first travel half way (let's call that point c).. but before the arrow can reach point c, it must first travel half way (let's call that point d).. but before the arrow can reach point d, it must first travel half way (let's call that point e).. do you see the problem?

Rod P

Dr. Mike,

You are right, of course.

I deliberately avoided particle physics and all those arcane and esoteric discussions that would cause almost everyone one else on this forum to "virtually" disappear. I know that modern day scientists and mathmaticians have taken this whole paradox into an entirely new level that the Greeks would never have contemplated.

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On a lighter note, What is a paradox?

Answer: A couple of Doctors.

Rod P.

5

The Perfect Map

by Rod P in

jw
friends

"the perfect map" is a paradox.. where would we be without maps?

they provide us with much information to give us directions, pinpoint locations, quantify distances and areas, and identify landmarks (roads, tracks, intersections, towns, cities, signs, etc.

it is a scale drawing of the real world.

Rod P

Ballistic,

You have made some interesting comments. I was aware of fractal theory (at an introductory level).

I am also familiar with what happens to a coastline, say if you could reconfigure it into a straight line. The distance or length would be quite astounding.

Your point about the amount of detail (albeit in your example, at the subatomic level) is precisely the point I am trying to make about the map paradox, namely that if you made a map on a scale of 1:1, then such a map, in all of its (infinite) detail, would no longer be needed. It would defeat the purpose for the map in the first place.

41

Can you solve this paradox?

by Rod P in

jw
friends

you have a bow and arrow.

you shoot the arrow with the bow from point a to point b.. but the arrow will never reach point b, it's destination.

before the arrow can reach point b, it must first travel half way (let's call that point c).. but before the arrow can reach point c, it must first travel half way (let's call that point d).. but before the arrow can reach point d, it must first travel half way (let's call that point e).. do you see the problem?

Rod P

Iggy,

Yes, it is one of Zeno's several paradoxes, and your explanation isn't too bad.

The answer is very well explained at the following website:

www.mathacademy.com

Allow me to paraphrase their explanation (to fit my example of the arrow):

"What this actually does is to make all motion impossible, for before the arrow can cover half the distance it must cover half of half the distance, and before it can do that it must cover half of half the distance, and so on, so that in reality it can never move any distance at all, because doing so involves moving an infinite number of small intermediate distances first.

Now, since motion obviously is possible, the question arises, what is wrong with Zeno? What is the "flaw in the logic?"

Suppose the arrow was to travel one mile from point A to point B. Now suppose we take Zeno's Paradox at face value for the moment and agree with him, that before the arrow can travel a mile, it must first travel a half-mile. And before the arrow can travel the remaining half-mile, it must first cover half of it, that is, a quarter mile, and then an eighth-mile, then a sixteenth-mile, and then a thirty-secondth mile, and so on. Well, suppose the arrow could cover all these infinite number of small distances, how far should it have travelled? One mile! In other words:

1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 +...........

At first this may seem impossible: adding up an infinite number of positive distances should give an infinite distance for the sum. But it doesn't- in this case it gives a finite sum; indeed, all these distances add up to one (1)! A little reflection will reveal that this isn't so strange after all: if 1 can divide up a finite distance into an infinite number of small distances, then adding all those distances together should just give me back the finite distance I started with. (An infinite sum such as the one above is known in mathematics as an infinite series, and when such a sum adds up to a finite number we say that the series is summable.)

Now the resolution to Zeno's Paradox is easy. Obviously, it will take the arrow some fixed time to cross half the distance to the other side of the room, say 1/2 second. How long will it take to cross half the remaining distance? Half as long- only 1/4 second. Covering half of the remaining distance(an eighth of the total) will only take 1/8 of a second. And so on. And once the arrow has covered all the infinitely many sub-distances and added up all the time it took to traverse them? Only 1 second, and here the arrow is on the other side of the room after all.

41

Can you solve this paradox?

by Rod P in

jw
friends

you have a bow and arrow.

you shoot the arrow with the bow from point a to point b.. but the arrow will never reach point b, it's destination.

before the arrow can reach point b, it must first travel half way (let's call that point c).. but before the arrow can reach point c, it must first travel half way (let's call that point d).. but before the arrow can reach point d, it must first travel half way (let's call that point e).. do you see the problem?

Rod P

Puternut,

First of all, I talked with Robin Hood, and he gave me the name and location of his tailor, who I visited. I paid this guy $500.00 to make you the best stockings in the world on the same quality level as Robin Hood himself. The only difference was that they were custom made to fit you to perfection.

Now, you take the world's most powerful bow and shoot the world's most aerodynamically efficient arrow, and shoot that arrow with maximum force, so that the arrow will reach it's theoretical physical distance limit. Now let's call that distance limit "Point B". There is no such thing as shooting the arrow past this Point B. The arrow can only travel between Point A and Point B, and that's the reality here.

So now, smarty pants, how ya gonna get that arrow to Point B when before it gets there, it must first travel half-way (Point C)? And before it gets to Point C, it must first go half of that distance (to Point D). And so on...

googlemagoogle,

The number of half-ways is INFINITE, which means there are so many of them you cannot possibly count them. And because the arrow must first travel half-way of any distance between Point A and Point B in a straight line trajectory, it cannot ever get beyond the half-way point of any point along the way to its Point B destination. Therefore, it cannot logically reach Point B.

Rod P.

5

The Perfect Map

by Rod P in

jw
friends

"the perfect map" is a paradox.. where would we be without maps?

they provide us with much information to give us directions, pinpoint locations, quantify distances and areas, and identify landmarks (roads, tracks, intersections, towns, cities, signs, etc.

it is a scale drawing of the real world.

Rod P

"The Perfect Map" is a paradox.

Where would we be without maps? They provide us with much information to give us directions, pinpoint locations, quantify distances and areas, and identify landmarks (roads, tracks, intersections, towns, cities, signs, etc.)

What exactly is a map? It is a scale drawing of the real world. It's purpose is to convey to the reader a picture of the reality it represents.

Different maps have different scales. Some maps, for instance, have scales where one inch on the drawing equals one mile in real world. If you measured 10" on the map, you would realize that on that scale, you were looking at a representation of 10 linear miles of the real world at that geographic location. And one square inch on the map (i.e. 1" x 1") = 100 square miles in reality (i.e. 10 x 10).

So now, what if you changed the map scale? Suppose that two inches on the map would represent the 10 linear miles. Or four square inches (i.e. 2" x 2") would equal the same 100 square miles in reality (i.e. 10 x 10).

From this we can deduce that when you double the square dimensions in, you actually make it possible to provide four times as much information, because you have four times the square inches available in the larger scale. For if the same four square inches on paper provides details on 100 square miles, that means you can include 4 times as much information as you would be able to if you had to draw information for 100 square miles in only one square inch.

What would happen if you used a scale of 10" on the map equals 10 linear miles. Or 100 square inches (i.e. 10" x 10") would equal the same 100 square miles in reality (10 miles x 10 miles)? This means you would now have ten times as much detailed information, because you have ten times the square inches available in the larger scale. For if the same one hundred square inches on paper provides details on 100 square miles, that means you can include 100 times as much information as you would be able to if you had to draw information for 100 square miles in only one square inch.

Therefore, the larger the scale, the more detail you can include on the map, the more accurately you can represent or depict reality on paper. Which means, the more detail you have on your map, the more useful and valuable it becomes in terms of the amount of information it can give you.

What then is the perfect map? What is the perfect scale?

The perfect scale would be when one mile on the map equals one linear mile in reality, or one square mile (i.e. 1 x 1) on paper equals one square mile in the real world. This is the perfect map, because this would provide sufficent space on the map to literally draw 100% of everything that was out there in the real world. No detail would be left out or missing, with the perfect map.

So here is the paradox: The minute you have created the perfect map, that is precisely the moment when you have created a map that is now completely useless. You no longer need the map, because you need only walk around in the real world to get all of the details you need. The perfect map is perfectly useless!

Rod P.

41

Can you solve this paradox?

by Rod P in

jw
friends

you have a bow and arrow.

you shoot the arrow with the bow from point a to point b.. but the arrow will never reach point b, it's destination.

before the arrow can reach point b, it must first travel half way (let's call that point c).. but before the arrow can reach point c, it must first travel half way (let's call that point d).. but before the arrow can reach point d, it must first travel half way (let's call that point e).. do you see the problem?

Rod P

You have a bow and arrow. You shoot the arrow with the bow from Point A to Point B.

But the arrow will never reach Point B, it's destination. Here's why:

Before the arrow can reach Point B, it must first travel half way (let's call that Point C).

But before the arrow can reach Point C, it must first travel half way (let's call that Point D).

But before the arrow can reach Point D, it must first travel half way (let's call that Point E).

Do you see the problem? In other words, before an arrrow can travel anywhere, it must first travel half-way, no matter how short or how small the distance. It will always be half way before it can reach the whole of any distance. This half-way can divide and sub-divide, and sub-sub-divide ad infinitum. Therefore logically, the arrow can never reach its final destination. Yet we all know that the arrow does reach Point B from Point A.

This is a paradox. How do you explain it?

Rod P.