# What ramifications will my scientific breakthrough have?
**URL:** https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889
**Category:** Factual Questions
**Created:** [May 18, 2009, 7:24pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889 "2009-05-18T19:24:12Z")
**Posts on this page:** 20
**Page:** 1
### Author:  [@straggler](https://boards.straightdope.com/u/straggler)
#### Post date: [May 18, 2009, 7:24pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/1 "2009-05-18T19:24:12Z")
A thought occurred to me today, and I did a quick bit of Googling but couldn’t find anything on the subject. I am wondering if my hypothesis has already been suggested and dismissed by physicists.
I propose that _space is **not** infinitely divisible_. Any given chunk of space is composed of a finite number of “space units”, nothing can be smaller than 1 space unit. In terms of matter that occupies a space unit, it’s all or nothing. Either the space unit is occupied by matter or it’s empty. Think of it like bytes in computer memory. A space unit is either full (1) or empty (0). There is no “half a byte”, and there is no “half a space unit”.
Here is my proof that space is indivisible:
Given that the following statement is true: If something could only be achieved “after” an infinite number of steps, and each step must be completed sequentially (ie, one step at a time), and each step takes up at least _some_ time, the “result” is unachievable.
That statement is true, yes?
Now let’s apply this to space and distance. Let’s say there is an apple sitting arm’s length away from me. I intend to reach over and grab the apple. Now, in order for my arm to reach the apple, it must first traverse _half_ of whatever the remaining distance is, and this will take some _time_. Once there, my arm must now travel to the new half-distance, and this again will take time. My arm, as it turns out, needs to traverse an infinite number of “half distances” to reach the apple, which is of course impossible. Clearly, if I go to grab the apple, I won’t reach it.
Unless…
My arm only needs to traverse the finite number of space units between it and the apple.
Where can I get my Nobel?
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### Author:  [@beowulff](https://boards.straightdope.com/u/beowulff)
#### Post date: [May 18, 2009, 7:26pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/2 "2009-05-18T19:26:03Z")
> **[Planck units](https://en.wikipedia.org/wiki/Planck_length)**
>
> In particle physics and physical cosmology, Planck units are a set of units of measurement defined exclusively in terms of four universal physical constants, in such a manner that these physical constants take on the numerical value of 1 when expressed in terms of these units. Originally proposed in 1899 by German physicist Max Planck, these units are a system of natural units because their definition is based on properties of nature, more specifically the properties of free space, rather than...
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### Author:  [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)
#### Post date: [May 18, 2009, 7:27pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/3 "2009-05-18T19:27:55Z")
> [@straggler](#):
>
> A thought occurred to me today, and I did a quick bit of Googling but couldn’t find anything on the subject. I am wondering if my hypothesis has already been suggested and dismissed by physicists.
Based on articles I have read in Scientific American, it’s an open question that gets studied regularly. If I remember right, loop quantum gravity is one of the theories of non-continuous space.
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### Author:  [@Duckster](https://boards.straightdope.com/u/Duckster)
#### Post date: [May 18, 2009, 7:28pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/4 "2009-05-18T19:28:22Z")
So I guess that means **straggler** can walk the Planck …
The last step is a doozy.
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### Author:  [@Qadgop\_the\_Mercotan](https://boards.straightdope.com/u/Qadgop_the_Mercotan)
#### Post date: [May 18, 2009, 7:35pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/5 "2009-05-18T19:35:06Z")
Then there’s also Planck time, the unit of time necessary for a photon to travel the Planck Length.
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### Author:  [@Kimmy\_Gibbler](https://boards.straightdope.com/u/Kimmy_Gibbler)
#### Post date: [May 18, 2009, 7:37pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/6 "2009-05-18T19:37:25Z")
> [@straggler](#):
>
> A thought occurred to me today, and I did a quick bit of Googling but couldn’t find anything on the subject. I am wondering if my hypothesis has already been suggested and dismissed by physicists.
>
> I propose that _space is **not** infinitely divisible_. Any given chunk of space is composed of a finite number of “space units”, nothing can be smaller than 1 space unit. In terms of matter that occupies a space unit, it’s all or nothing. Either the space unit is occupied by matter or it’s empty. Think of it like bytes in computer memory. A space unit is either full (1) or empty (0). There is no “half a byte”, and there is no “half a space unit”.
>
> Here is my proof that space is indivisible:
>
> Given that the following statement is true: If something could only be achieved “after” an infinite number of steps, and each step must be completed sequentially (ie, one step at a time), and each step takes up at least _some_ time, the “result” is unachievable.
>
> That statement is true, yes?
>
> Now let’s apply this to space and distance. Let’s say there is an apple sitting arm’s length away from me. I intend to reach over and grab the apple. Now, in order for my arm to reach the apple, it must first traverse _half_ of whatever the remaining distance is, and this will take some _time_. Once there, my arm must now travel to the new half-distance, and this again will take time. My arm, as it turns out, needs to traverse an infinite number of “half distances” to reach the apple, which is of course impossible. Clearly, if I go to grab the apple, I won’t reach it.
>
> Unless..
>
> My arm only needs to traverse the finite number of space units between it and the apple.
>
> Where can I get my Nobel?
Zeno of Elea! You finally got your NetZero account!
Please, this is like 2500 years old. Now I am going to read the “Engineers are so s-m-r-t, unlike humanties majors” thread and choke on some irony.
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### Author:  [@Dewey\_Finn](https://boards.straightdope.com/u/Dewey_Finn)
#### Post date: [May 18, 2009, 7:59pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/7 "2009-05-18T19:59:01Z")
Two hetero males are standing on one end of a long corridor. One is a mathematician and the other is an engineer. A stunningly attractive naked woman who is at the other end offers herself to them to do with what they will. The mathematician thinks about it but hesitates because Zeno’s Paradox tells him that he will never get to her. The engineer promptly starts in her direction, figuring that he can get close enough for all practical purposes.
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### Author:  [@Chief\_Pedant](https://boards.straightdope.com/u/Chief_Pedant)
#### Post date: [May 18, 2009, 8:31pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/8 "2009-05-18T20:31:00Z")
Nominated for match of OP’s handle and OP query.
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### Author:  [@Keeve](https://boards.straightdope.com/u/Keeve)
#### Post date: [May 18, 2009, 9:01pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/9 "2009-05-18T21:01:29Z")
**beowulff** gave the answer that I was thinking of.
**Kimmy\_Gibbler** and **Dewey Finn** also gave perfect answers, but their link is [http://en.wikipedia.org/wiki/Zeno%27s\_Paradox](http://en.wikipedia.org/wiki/Zeno%27s_Paradox).
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### Author:  [@Xema](https://boards.straightdope.com/u/Xema)
#### Post date: [May 18, 2009, 9:24pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/10 "2009-05-18T21:24:00Z")
> [@straggler](#):
>
> If something could only be achieved “after” an infinite number of steps, and each step must be completed sequentially (ie, one step at a time), and each step takes up at least _some_ time, the “result” is unachievable.
> That statement is true, yes?
That statement is false.
In Zeno’s time this was fully plausible - possibly even obvious - to nearly everyone. But it’s now well understood that the sum of an infinite series of positive values can in fact be finite.
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### Author:  [@Derleth](https://boards.straightdope.com/u/Derleth)
#### Post date: [May 18, 2009, 10:06pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/11 "2009-05-18T22:06:47Z")
> [@Kimmy\_Gibbler](#):
>
> Now I am going to read the “Engineers are so s-m-r-t, unlike humanties majors” thread and choke on some irony.
Only if I can judge the current state of English Ph.D. courses by reading High School “Huckleberry Finn” papers.
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### Author:  [@panache45](https://boards.straightdope.com/u/panache45)
#### Post date: [May 18, 2009, 10:31pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/12 "2009-05-18T22:31:52Z")
> [@straggler](#):
>
> Here is my proof that space is indivisible:
>
> Given that the following statement is true: If something could only be achieved “after” an infinite number of steps, and each step must be completed sequentially (ie, one step at a time), and each step takes up at least _some_ time, the “result” is unachievable.
>
> That statement is true, yes?
This is neither a proof nor true nor original.
No Nobel for you!
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### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [May 18, 2009, 10:41pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/13 "2009-05-18T22:41:53Z")
Here’s some food for thought: Suppose there were a minimum possible length. Suppose now that I have a right triangle, two of whose legs are this minimum possible length. What is the length of the hypotenuse?
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### Author:  [@Kimmy\_Gibbler](https://boards.straightdope.com/u/Kimmy_Gibbler)
#### Post date: [May 18, 2009, 10:58pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/14 "2009-05-18T22:58:05Z")
> [@Chronos](#):
>
> Here’s some food for thought: Suppose there were a minimum possible length. Suppose now that I have a right triangle, two of whose legs are this minimum possible length. What is the length of the hypotenuse?
It is perfectly consistent to say that no length _of material_ of that precise distance would exist in this world with a fundamental minimum length. We suffer all sorts of mathematical entities whose real world bases are less than readily apparent: irrationals, imaginaries, etc.
After all, to say that you have a rope whose length is an irrational number is to say that if you held your rope up against an infinitely zoomable yardstick, you would find, however much you zoomed in, it always terminated between two of the ruler’s tick marks. I don’t think this is any more satisfying on an intuitive level than a world where we cannot cut a line of rope to perfectly fit a right triangle composed of even integer length legs.
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### Author:  [@Keeve](https://boards.straightdope.com/u/Keeve)
#### Post date: [May 19, 2009, 2:33am UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/15 "2009-05-19T02:33:24Z")
> [@Chronos](#):
>
> Here’s some food for thought: Suppose there were a minimum possible length. Suppose now that I have a right triangle, two of whose legs are this minimum possible length. What is the length of the hypotenuse?
(This post may or may not contain the same ideas as **Kimmy\_Gibbler** ’s post. My apologies in advance, Kimmy; I’m not trying to steal your thunder.)
Before I respond to **Chronos** ’ question, let me talk about other things: Let’s start with a circle. I don’t care how big the circle is. But if we accept the idea of “a minimum possible length” (i.e. Planck length), then the radius of that circle will be a precise and finite number of those units. In addition, _circumference_ of that circle will be a precise and finite number of those units. That is, there will be an integer which tells us the radius, and another integer which tells us the circumference. Given that pi is an irrational number, this is clearly impossible.
We are entering into the realm of ridiculous impossibilities. Let’s zoom in on this circle, all the way to the scale where we can see these Planck lengths. Is the edge of the circle smooth? Or is it made of pixels, like on a computer monitor, or a piece of graph paper? If there is a “minimum possible length”, then a square is an integer, and it cannot be filled in halfway. But then we can ask how far it is from one corner of each square to the corner diagonally opposite, and that will have to be either 1 or 2. There is no longer any room for 1.4141.
One might suggest that we’re not dealing with squares on graph paper; maybe it’s all a bunch of dots. That won’t help us, because we will still ask how those dots are arranged.
And that brings us to the conundrum of Chronos’ Triangle. Is it truly a right triangle? It can’t possibly be a right triangle, because, as Chronos asks, “What is the length of the hypotenuse?” If it is longer than the other sides, then (since fractions are not an option) it must be twice as long as each of the other sides, which is the same thing as both of the other sides put together, which means we have a line not a triangle. But if it is _not_ twice as long as the other sides, then it is equal to the other sides, and we don’t have a right triangle any more - we have an equilateral! What the hell is going on – is a right angle really only sixty degrees?
The answer to all these questions, and to Chronos’ question, is that – as **Kimmy\_Gibbler** wrote – any tangible circle will be imperfect, and all its dimensions can be counted in finite integers of Planck units. It is only the conceptual circle whose precise circumference, divided by its precise diameter, will yield precisely pi.
(I was tempted to phrase that last paragraph in romantic terms about “the world of the infinitely small.” But the truth is that although Planck units are ridiculously small, they are not infinitely so. They have very real and specific sizes. It is very easy to talk about lengths which are half of a Planck length, or even a millionth of a Planck length; they’re just not real in the physical world.
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### Author:  [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)
#### Post date: [May 19, 2009, 2:50am UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/16 "2009-05-19T02:50:35Z")
> [@Xema](#):
>
> That statement is false.
>
> In Zeno’s time this was fully plausible - possibly even obvious - to nearly everyone. But it’s now well understood that the sum of an infinite series of positive values can in fact be finite.
True, although there’s a catch to it.
1/2 + 1/4 + 1/8 + 1/16 … is certainly equal to 1. But if each step took the same amount of time to realize, we would never reach 1 in a finite universe. We get to one only because time as well as distance decreases for each step.
Given that every other statement in straggler’s OP is wrong, he probably was thinking of each step taking an equal time. And in that case it would be true that the result was be unachievable. But since each step takes only half the time as well as half the distance of the one before, the result is quite achievable.
The real question is: does straggler really not know of Zeno’s paradox or have we been whooshed?
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### Author:  [@Xema](https://boards.straightdope.com/u/Xema)
#### Post date: [May 19, 2009, 3:51am UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/17 "2009-05-19T03:51:36Z")
> [@Exapno\_Mapcase](#):
>
> … he probably was thinking of each step taking an equal time.
His statement was “each step takes up at least _some_ time…” which I (perhaps naively) took to imply that he was not thinking the time was the same for each step.
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### Author:  [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)
#### Post date: [May 19, 2009, 4:10am UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/18 "2009-05-19T04:10:03Z")
> [@Xema](#):
>
> His statement was “each step takes up at least _some_ time…” which I (perhaps naively) took to imply that he was not thinking the time was the same for each step.
Yes, I’m also making a guess since the original statement was itself unclear, although that’s probably the heart of the OP’s confusion.
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### Author:  [@straggler](https://boards.straightdope.com/u/straggler)
#### Post date: [May 19, 2009, 12:06pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/19 "2009-05-19T12:06:49Z")
Thank you, **beowulff** , for the link to the article on Planck length.
**Keeve** , Zeno’s Paradox is only a paradox if space is infinitely divisible, or if motion can be made in infinitely smaller increments.
**Xema** and **Panache45** , I’d like to know why you think this statement is false: “_If something could only be achieved “after” an infinite number of steps, and each step must be completed sequentially (ie, one step at a time), and each step takes up at least some time, the “result” is unachievable_”.
**Chronos** , your triangle would be impossible to construct in a universe consisting of a minimum possible length, or “space unit”. It would be akin to challenging someone to draw a triangle within the grid below, using only horizontal and straight lines that connect between dots:
. . .
. . .
. . .
**Exapno Mapcase** , you said “_he probably was thinking of each step taking an equal time_”. It doesn’t matter whether each step takes an equal amount of time, or different amounts of time. The important thing is, does each step take _some_ time, each step be taken sequentially (ie, no two or more steps at the same time), and there being an infinite number of steps.
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### Author:  [@straggler](https://boards.straightdope.com/u/straggler)
#### Post date: [May 19, 2009, 12:13pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/20 "2009-05-19T12:13:29Z")
Should be..
> [@straggler](#):
>
> It would be akin to challenging someone to draw a triangle within the grid below, using only horizontal and **vertical** lines that connect between dots
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