# 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:** 3
### Author:  [@The\_Hamster\_King](https://boards.straightdope.com/u/The_Hamster_King)
#### Post date: [May 19, 2009, 4:08pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/41 "2009-05-19T16:08:00Z")
> [@straggler](#):
>
> How so?
Say t = an infinitesimally small interval of time.
How long does (t + t) take?
How about (t + t + t + t + t + t + t + t + t + t + t + t + t + t + t)?
No matter how many infinitesimally small intervals of time you string together, their combined duration is still infinitesimally small.
In your example you’re assuming that you have an infinite number of \*finite \*intervals. But you’re overlooking the fact that as the number of intervals becomes infinitely large, their duration becomes _infinitely small_. The two infinities cancel each other out and you reach your destination in a finite amount of time.
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### Author:  [@Lemur866](https://boards.straightdope.com/u/Lemur866)
#### Post date: [May 19, 2009, 4:08pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/42 "2009-05-19T16:08:35Z")
What he’s saying is that there’s no such entity as a “two” in reality. There’s a concept of two things…if you have a rock and another rock then you have two rocks, and if you have two rocks and another two rocks then you have four rocks. But where’s the two? Where’s the four? Where’s the one? You can’t hold a naked two in your hands, you can only apply the concept of two to real world objects. Therefore, “two” is a theory you have about the way the universe works. 2+2=4 is another theory. And sometimes 1 object plus another object doesn’t give you two objects, it gives you something different. What happens when you add a proton to an antiproton?
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### Author:  [@Rolken](https://boards.straightdope.com/u/Rolken)
#### Post date: [May 19, 2009, 4:11pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/43 "2009-05-19T16:11:11Z")
> [@straggler](#):
>
> I don’t accept these examples as self-evidently obvious. Even without having the real explanations as to how either of these things are possible, one could speculate a plausible scenario that makes them possible.
And others don’t accept your proposals as self-evident, which is why self-evidence isn’t sufficient in scientific theory. Everyone has their own standards of self-evidence; mathematics and measurements make a theoretician put his money where his mouth is, so to speak.
> [@straggler](#):
>
> I happily open up my example to wild speculation for you explain a way that it might not be true.
My point has never been that your interpretation is impossible. My point is merely that there is a wide range of possibilities, and you are not offering anything that elevates yours over any other.
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### Author:  [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)
#### Post date: [May 19, 2009, 4:11pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/44 "2009-05-19T16:11:19Z")
straggler, all your objections seem to come down to the standard argument of “I don’t understand infinite math so I won’t accept it.” Therefore you throw out not just the math of infinities but also the calculus and the theory of limits which depend on the summation of infinite quantities. Can you explain how your mathematical system works if you toss all these fundamental elements out the window?
Remember, if you reject infinities so that space is quantized you must also then explain how every single aspect of reality that uses limits or the calculus is changed by the removal of infinities.
Please be mathematically rigorous when you do so.
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### Author:  [@Kimmy\_Gibbler](https://boards.straightdope.com/u/Kimmy_Gibbler)
#### Post date: [May 19, 2009, 4:12pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/45 "2009-05-19T16:12:55Z")
> [@straggler](#):
>
> …I was highlighting the point that in reality, you can not sum infinity.
Suppose I (like you) assert without proof that all space is infinitely divisible (of course, you assert the opposite, but with the same quantum of evidence) and that when you cast your gaze over a item of finite extension, you observe–in the real world–the infinite summation of increasingly small fractions producing a finite number.
What defect does this argument have that your own does not?
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### Author:  [@straggler](https://boards.straightdope.com/u/straggler)
#### Post date: [May 19, 2009, 4:23pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/46 "2009-05-19T16:23:19Z")
> [@The\_Hamster\_King](#):
>
> Say t = an infinitesimally small interval of time.
>
> How long does (t + t) take?
>
> How about (t + t + t + t + t + t + t + t + t + t + t + t + t + t + t)?
>
> No matter how many infinitesimally small intervals of time you string together, their combined duration is still infinitesimally small.
How are you defining infinitesimal? My understanding of infinitesimal means something that is too small to be measured. Assuming there is such a thing as an infinitesimal amount of time, you _could_ eventually sum enough of them to reach something measurable.
> [@](#):
>
> In your example you’re assuming that you have an infinite number of \*finite \*intervals. But you’re overlooking the fact that as the number of intervals becomes infinitely large
What do you mean by “becomes infinitely large”? Either the number of intervals is infinite or it isn’t. If they are infinite, and each one takes time, then the destination is unreachable.
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### Author:  [@Kyrie\_Eleison](https://boards.straightdope.com/u/Kyrie_Eleison)
#### Post date: [May 19, 2009, 4:24pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/47 "2009-05-19T16:24:42Z")
> [@Lemur866](#):
>
> What he’s saying is that there’s no such entity as a “two” in reality. There’s a concept of two things…if you have a rock and another rock then you have two rocks, and if you have two rocks and another two rocks then you have four rocks. But where’s the two? Where’s the four?
This, but more importantly, I’m trying to explore and challenge your notion of “in reality.” You manipulate the symbols that represent a finite series of numbers to correctly arrive at their sum, and claim that you’re doing so in reality. **Roken** manipulates the symbols that represent a converging infinite series, and correctly arrives at their sum, and yet you say that is _not_ in reality. I don’t see the distinction – for any definition of “in reality” either both are in reality, or neither is.
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### Author:  [@The\_Hamster\_King](https://boards.straightdope.com/u/The_Hamster_King)
#### Post date: [May 19, 2009, 4:29pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/48 "2009-05-19T16:29:57Z")
> [@straggler](#):
>
> How are you defining infinitesimal? My understanding of infinitesimal means something that is too small to be measured. Assuming there is such a thing as an infinitesimal amount of time, you _could_ eventually sum enough of them to reach something measurable.
Yes, you’re right. I was speaking casually without considering the precise meaning of the term “infinitesimal”. Substitute “infinitely small” in my argument above.
> [@](#):
>
> What do you mean by “becomes infinitely large”? Either the number of intervals is infinite or it isn’t. If they are infinite, and each one takes time, then the destination is unreachable.
But each one doesn’t take time. Some of the intervals you’re adding up are infinitely small.
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### Author:  [@straggler](https://boards.straightdope.com/u/straggler)
#### Post date: [May 19, 2009, 4:30pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/49 "2009-05-19T16:30:01Z")
> [@Rolken](#):
>
> And others don’t accept your proposals as self-evident
If one step takes _some_ time, and if all steps are sequential, and if some process requires an infinite number of steps to occur before the result can be reached, then said result is unreachable. The standard of accepting a statement as factual does not sit _beyond_ the example I have described here. I’d sure love to see what your idea of a more robust piece of logic looks like.
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### Author:  [@The\_Hamster\_King](https://boards.straightdope.com/u/The_Hamster_King)
#### Post date: [May 19, 2009, 4:34pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/50 "2009-05-19T16:34:08Z")
> [@straggler](#):
>
> If one step takes _some_ time … .
That’s a big “if” … .
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### Author:  [@gazpacho](https://boards.straightdope.com/u/gazpacho)
#### Post date: [May 19, 2009, 4:35pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/51 "2009-05-19T16:35:23Z")
Your are assuming that summing up an infinite number of things does not converge on a finite number. This is not always true. Until you buy into this or convince us otherwise there will not be a meeting of the minds.
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### Author:  [@straggler](https://boards.straightdope.com/u/straggler)
#### Post date: [May 19, 2009, 4:38pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/52 "2009-05-19T16:38:05Z")
> [@The\_Hamster\_King](#):
>
> Yes, you’re right. I was speaking casually without considering the precise meaning of the term “infinitesimal”. Substitute “infinitely small” in my argument above.
What do you mean by “infinitely small”?
> [@](#):
>
> But each one doesn’t take time. Some of the intervals you’re adding up are infinitely small.
But that’s impossible. You can not have movement through space without time elapsing. Time is a measure of change.
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### Author:  [@Colophon](https://boards.straightdope.com/u/Colophon)
#### Post date: [May 19, 2009, 4:39pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/53 "2009-05-19T16:39:30Z")
> [@straggler](#):
>
> What do you mean by “infinitely small”?
> But that’s impossible. You can not have movement through space without time elapsing. Time is a measure of change.
You can if the movement is infinitely small… 🙂
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### Author:  [@straggler](https://boards.straightdope.com/u/straggler)
#### Post date: [May 19, 2009, 4:39pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/54 "2009-05-19T16:39:42Z")
> [@Kimmy\_Gibbler](#):
>
> Suppose I (like you) assert without proof that all space is infinitely divisible (of course, you assert the opposite, but with the same quantum of evidence) and that when you cast your gaze over a item of finite extension, you observe–in the real world–the infinite summation of increasingly small fractions producing a finite number.
>
> What defect does this argument have that your own does not?
This part: “you observe–in the real world–the infinite summation of increasingly small fractions producing a finite number.”
We do not, in real world, observe an infinite anything.
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### Author:  [@Rolken](https://boards.straightdope.com/u/Rolken)
#### Post date: [May 19, 2009, 4:39pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/55 "2009-05-19T16:39:54Z")
> [@straggler](#):
>
> If one step takes _some_ time, and if all steps are sequential, and if some process requires an infinite number of steps to occur before the result can be reached, then said result is unreachable. The standard of accepting a statement as factual does not sit _beyond_ the example I have described here. I’d sure love to see what your idea of a more robust piece of logic looks like.
You still haven’t explained why it should take infinite time to traverse finite space, rather than finite time to traverse infinite space for that matter. Both time and space are subject to the same infinite sums if we’re assuming continuity for the sake of disproving it, so why the distinction between the two?
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### Author:  [@straggler](https://boards.straightdope.com/u/straggler)
#### Post date: [May 19, 2009, 4:41pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/56 "2009-05-19T16:41:56Z")
> [@gazpacho](#):
>
> Your are assuming that summing up an infinite number of things does not converge on a finite number.
I am suggesting that you can’t sum an infinite amount of things in the first place.
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### Author:  [@The\_Hamster\_King](https://boards.straightdope.com/u/The_Hamster_King)
#### Post date: [May 19, 2009, 4:43pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/57 "2009-05-19T16:43:55Z")
> [@straggler](#):
>
> What do you mean by “infinitely small”?
The reciprocal of infinity.
> [@](#):
>
> But that’s impossible. You can not have movement through space without time elapsing. Time is a measure of change.
Yup. When the duration of each successive subdivision becomes infinitely small you stop, having arrived at your destination in a finite amount of time.
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### Author:  [@The\_Hamster\_King](https://boards.straightdope.com/u/The_Hamster_King)
#### Post date: [May 19, 2009, 4:45pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/58 "2009-05-19T16:45:04Z")
> [@straggler](#):
>
> I am suggesting that you can’t sum an infinite amount of things in the first place.
Then what is calculus?
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### Author:  [@straggler](https://boards.straightdope.com/u/straggler)
#### Post date: [May 19, 2009, 4:45pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/59 "2009-05-19T16:45:28Z")
> [@Rolken](#):
>
> You still haven’t explained why it should take infinite time to traverse finite space, rather than finite time to traverse infinite space for that matter. Both time and space are subject to the same infinite sums if we’re assuming continuity for the sake of disproving it, so why the distinction between the two?
Time and space, as I have suggested, are inextricably linked. If there has been “no change”, ie, no movement through space, then there is no time elapsed. The smallest, indivisible unit of time could be represented by the fastest possible movement through one space unit.
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### Author:  [@Colophon](https://boards.straightdope.com/u/Colophon)
#### Post date: [May 19, 2009, 4:46pm UTC](https://boards.straightdope.com/t/what-ramifications-will-my-scientific-breakthrough-have/496889/60 "2009-05-19T16:46:17Z")
> [@straggler](#):
>
> I am suggesting that you can’t sum an infinite amount of things in the first place.
Which, as several posters have pointed out, is simply incorrect. Look here for starters: [Series (mathematics) - Wikipedia](http://en.wikipedia.org/wiki/Series_(mathematics)#Convergent_series)
If you’re talking about maths, you can’t just pick and choose which bits you believe in.
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