Isn't it mathematically impossible for an object to reach another object?

Question

Let's say I start out at one end of a football field and begin walking toward the other end zone. When I reach the 50, it would be accurate to say that I have halved my original distance from the end zone. When I reach the 25, it would be accurate to say I've halved that remaining distance, and when I'm 12 and a half yards away, it would be accurate to say that I've halved that remaining distance. So one accurate description of my approach would be "continuously halving remaining distances from the end zone."

We know from mathematics that a number can be infinitely halved and will never reach zero because there will always be some infintesimal fraction remaining. Nevertheless, I will eventually find myself in the end zone, having not only reached zero, but surpassed it.

Is it actually inaccurate to describe me as halving the distances, and, if so, why does this seemingly incontrovertible description fail? Or is it that something I do not understand happens when I get there

Answer 1

This is called Zeno's Paradox. It's a mathematical fallacy rather than a true paradox.

Mathematics is not a perfect predictor of physical reality. That's why scientific experiments are necessary to evaluate a theory.

This is because mathematical reality and fantasy are made of the same stuff and where they divide is not clearly defined.

Math may or may not successfully predict physical reality. There is no 100% way to know for sure unless we put the theory to the test, but that is not always possible.

The physical fact that you can reach an object ahead of you is clear proof the mathematical theory is invalid.

http://faculty.washington.edu/smcohen/320/zeno1.htm

Answer 2

You can totally reach the end zone, even mathematically speaking. Imagine you have the number 50 and you keep subtracting 1 from it. You will get down to 0 and even to negative numbers (IE leaving the stadium). In your analogy, this is the mathematical representation of what you are doing, not halving numbers. If you want to represent that, say you're at the 50 yard line, and say "I'll halve my distance to the end zone" so you walk down to the 25. You could do that again, walk to the 12 and a half, and again and again. Doing so, you would never reach the end zone. But you will get within inches of it. Fractions of an inch, even. However, if you decide to take a step into the end zone, you aren't halving, you are, in effect, subtracting. That's how you end up in the end zone. Touchdown!

Answer 3

If you haven’t heard of "Zenos" he is the guy who pulled this crap on the Greeks with "Zeno's Paradox--Achilles & the Tortoise."

If you listen to Zenos, 1/3 = .333333.... To infinity
So 1/3+1/3+1/3 =. 99999999...to infinity
But it doesn't 1/3+1/3+1/3= 1

This is old news.

The dichotomy paradox leads to the following mathematical joke. A mathematician, a physicist and an engineer were asked to answer the following question.
A group of boys are lined up on one wall of a dance hall, and an equal number of girls are lined up on the opposite wall. Both groups are then instructed to advance toward each other by one quarter the distance separating them every ten seconds (i.e., if they are distance d apart at time 0, they are d/2 at t==10, d/4 at t==20, d/8 at t==30, and so on.) When do they meet at the center of the dance hall?

The mathematician said they would never actually meet because the series is infinite.

The physicist said they would meet when time equals infinity.

The engineer said that within one minute they would be close enough for all practical purposes.


Yours: Grumpy

Answer 4

Your getting stuck on the half issue. instead of progressing by halves, if you moved by the whole distance you would have achieved your goal.

What's really going to get you is the difference between exact and precise. If you take a real world example, one object can't exactly be measured to reach another. However this is possible mathematically because you are nolonger using measurements.

It's impossible to measure exactly 60 seconds, but you can precisely count 60 seconds. Only facts can be exact, such as there are 60 seconds in a minute.

Answer 5

If you tried to reach the end zone by continuously halving the remaining distances, you would never get there. But you're not. You're just walking to the end zone. Therefore, you arrive.

Answer 6

Yes its inaccurate in halving the distances. Your theory only works if you exactly half the distance ans stop after each half while attempting to approaching the end. Its similar to half life theory

Answer 7

The only way that you would not be able to reach the end is if you were under the restriction of only being able to halve your distance every time, you are not, so therefore you can reach the endzone.

Answer 8

In theory I accept as true with the first respondent (that gravity has no decrease) with one exception. Gravity, like each thing else, is constrained by technique of relativity - the outcomes of gravity at one factor might want to correctly be felt at a 2d think about uncomplicated words as as right now as person-friendly might want to be able to commute between those 2 factors. (the immediately ahead get at the same time is that the earth might want to proceed to orbit the solar inspite of if the solar disappeared for a jiffy till the "message" reached the earth that the solar grow to be lengthy gone). The universe is increasing, and so some distant areas are shifting faraway from us at speeds that exceed the speed of light (which they could do because they don't look to be shifting by skill of area yet with area). Gravity is then constrained because gravity from the solar, as an get at the same time, will by no skill "seize up" to galaxies in those distant areas of area. In essence, the decrease to gravity is defined by technique of the era of time that the source of that gravity has been in existence.

Answer 9

If you keep doing a halve of a halve of a halve, yes you will be doing this for the rest of your life, your children's lives, and and your grandchildren's lives, etc... I don't know about the other stuff you're talking about.

Answer 10

You are subtracting, not halving, not dividing by two. By moving in distances, addition (of positive or negative real numbers) is applied. You are using an incorrect application of operations.