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> [re a slide-to-unlock patent] Apple’s .. argument is that “a tap is a zero-length swipe.” That’s silly. It’s like saying that a point is a zero-length line.

by mikek 14y ago

> [re a slide-to-unlock patent] Apple’s .. argument is that “a tap is a zero-length swipe.” That’s silly. It’s like saying that a point is a zero-length line. But a point is a zero-length line.

cwp 14y ago
Yes, and a tap is, technically, a zero length swipe. But there is nevertheless a distinction between taps and swipes just as there is between points and lines. Apple's API distinguishes between the two gestures, even if Apple's lawyers don't. Claiming that tap-to-unlock violates a swipe-to-unlock patent is silly. The whole point of swipe-to-unlock is that a tap doesn't unlock the phone.
- vacri 14y ago
  This is what I thought the judge was getting at - yes, you can define a point as a zero-length line in theoretical space, but when you apply it to something like finger movements in the case in front of him, it's a big pile of horseshit. Describing a point as a zero-length line is a mathematical trick used to help understand a concept; it's not a real-world application of mathematics.
planetguy 14y ago
If my high school maths teacher were here he'd say that a point is a zero-length line segment.
- cglace 14y ago
  Except it isn't. Doesn't a line segment required two distinct endpoints?
- ktizo 14y ago
  Sometimes it is useful to think of a really short line becoming a point, like in calculus, but that doesn't mean a point is a really short line any more than its a really tiny triangle or anything else we want to scale to a point.
seanalltogether 14y ago
Only if you have a jury full of mathmeticians
famousactress 14y ago
Is it? Maybe a zero length line segment. In geometry terms, lines are infinite, aren't they?
- tankenmate 14y ago
  No. Yes.
colanderman 14y ago
Your statement would imply that a point has a direction, which it does not. Also, a line does not have a length; both you and Posner meant line segment. So a correct statement would be: A zero-length line segment is a point. Edit: not even this is true if your definition of a line segment explicitly states that the endpoints must be distinct, as does PlanetMath's definition, as Aethaeryn points out below.
- Aethaeryn 14y ago
  > A zero-length line segment is a point. The Wikipedia definition of a line segment says that it is bound by two endpoints.[1] It provides a reference to Planet Math that goes into specifics.[2] In this page, it is made clear that the two endpoints cannot be equal. Planet Math provides an equation for a closed[3] line segment: L = {a + tb | t in [0, 1]} This means that a line segment can be expressed as all of the points a + tb, where t is the range [0, 1] (which contains 0, 1 and all the points between them). It also limits a, b as real or complex numbers with b != 0. In other words, any line segment is just "morphing" the basic 0 to 1 range, with a shifting it and b scaling it. Now, since b can't be 0, and 0 != 1, you're not going to get the endpoints of the range 0 and 1 to equal each other no matter how you scale them with b or shift them with a.[4] In other words, line segments will always have length. Because you cannot get the endpoints to equal each other, a point cannot be thought of as a line segment under what appears to be the common definition. ----- [1] https://en.wikipedia.org/wiki/Line_segment https://en.wikipedia.org/wiki/Line_segment [2] http://planetmath.org/encyclopedia/LineSegment.html http://planetmath.org/encyclopedia/LineSegment.html [3] Open is the exact same thing, except with (0, 1) instead of [0, 1] and it doesn't include the points 0 and 1. [4] Of course, if b = 0 was allowed, you could just say that points are where b = 0 for all a.
  - colanderman 14y ago
    Ah good I was looking for the restriction b ≠ 0 but couldn't find in on the Wikipedia page. Forgot to check out PlanetMath, thanks.
    - 14y ago
TeMPOraL 14y ago
A zero-dimmensional equivalent of line, maybe?
johnpmayer 14y ago
Depends on your definition. In my interpretation, to be considered a line in any number of dimensions, it must be specified by no fewer than two points. This puts a lower bound on the amount of information to specify "lines", a bound strictly greater than specifying a "point" in a space of similar dimensions. Otherwise, is point also a polygon consisting entirely of zero-length sides? But anyway, I think it was only meant to highlight the Judge's opinion of the absurdity of some claims. edit: so glad this tiny portion was the subject of the most discussion
- deleted 14y ago
  [deleted]
twelvechairs 14y ago
Yeah. This struck me as well. I think what you say is right, but probably the 'silly' part comes from the context of the legal argument. For instance, You could also say a point is also something with 132 dimensions of data - all but one or two of which are set to 0. Does that mean if we patent ways of working with 132-dimensional data that our patents should apply to anything with fewer dimensions? Of course that would be silly....
meson2k 14y ago
A zero-area polygon. A zero-volume hedron. etc. etc.
- SilasX 14y ago
  Such degeneracy!
hristov 14y ago
Not exactly. Even if you disregard the definition arguments discussed below, and allow the definition of "line segment" to include "point" I would not say that a point is a zero length line segment. It seems to me that the "lenght" of a point, if such a concept is to be allowed, is infinitely small but not zero. Thus, a point has length of lim(x->0) x. To me, a zero length line segment would be nothingness. But putting the math aside, in the context of patent law, it is important to follow the commonly accepted definitions. A person should not be able to change the meaning of his claims by suggesting new definitions. And it seems obvious that, as others have pointed out, the accepted definition of a line segment is something with finite length, and the accepted definition of a swipe is something that (obviously) results from swiping, i.e. some movement of the finger.
- throwaway___ 14y ago
  Euclid, Book 1, Definition 1. "A point is that which has no part."
- trowftd 14y ago
  A point has no dimensions whatsoever. No length, width, or area. A point is not a zero length line segment, but not because of the reason you mention.
strictfp 14y ago
That is the point he is trying to make. A point _can be seen_ as a zero-length line, but this is really on the boundary of the definition of a line. Likewise a zero-length swipe is a tap, but that is really stretching the definition of a swipe. Basing a court case on such a stretched definition is what he is opposing.
jsprinkles 14y ago
I'm beyond disappointed that the article is about the most important ruling regarding patent law in recent memory, and the overwhelming majority of this thread is arguing about the geometry cited in the judge's order. Rational people understood what he meant, even if maybe it's not 100% mathematically sound. This pedantry really frustrates me, and it extends beyond Hacker News. It's pervasive in conversations I've been having recently as well, as if we're all looking for the slightest thing wrong with what someone has said so that we can achieve some kind of acclaim by pointing it out. I made a point recently about how people need to work together and cited a Star Trek film as a joke, and some jackass in the group decided to go to the mat with me on the fact that I had cited the wrong Star Trek film (my quote was in III, not II). There is nothing more frustrating than a pedant. It seems like it's tech people that do it most, too, which makes sense, but still.
- ars 14y ago
  > and the overwhelming majority of this thread is arguing about the geometry cited in the judge's order. Rational people understood what he meant, even if maybe it's not 100% mathematically sound. > This pedantry really frustrates me People are well aware that they are nit picking, but they enjoy the resulting discussion! Intellectually inclined people enjoy discussing minutia with other like minded people. They are perfectly aware that it makes no difference, and they don't care - it's just something interesting to talk about. It's no longer nit picking about the original (i.e. the practical use is settled), at that point it becomes a discussion for its own sake. Do you never learn or do anything just for the sake of doing it, rather than in order to accomplish something useful? > and some jackass in the group decided to go to the mat with me on the fact that I had cited the wrong Star Trek film He was showing off. If you don't wish to participate in the Star Trek memorization culture just ignore him - his comment was geared to other members of his group who do like doing that. Or simply acknowledge that he was right and move on. Clearly you don't care about that topic, so that acknowledgement shouldn't cost you too much ego. That's also the point of threads: You can ignore an entire thread that is off topic - but it also gives people who found something interesting a place to talk about it without disturbing the rest of the conversation.
  - 14y ago

by mikek 14y ago

cwp 14y ago

Yes, and a tap is, technically, a zero length swipe. But there is nevertheless a distinction between taps and swipes just as there is between points and lines. Apple's API distinguishes between the two gestures, even if Apple's lawyers don't. Claiming that tap-to-unlock violates a swipe-to-unlock patent is silly. The whole point of swipe-to-unlock is that a tap doesn't unlock the phone.

vacri 14y ago
This is what I thought the judge was getting at - yes, you can define a point as a zero-length line in theoretical space, but when you apply it to something like finger movements in the case in front of him, it's a big pile of horseshit. Describing a point as a zero-length line is a mathematical trick used to help understand a concept; it's not a real-world application of mathematics.

planetguy 14y ago

If my high school maths teacher were here he'd say that a point is a zero-length line segment.

cglace 14y ago
Except it isn't. Doesn't a line segment required two distinct endpoints?
ktizo 14y ago
Sometimes it is useful to think of a really short line becoming a point, like in calculus, but that doesn't mean a point is a really short line any more than its a really tiny triangle or anything else we want to scale to a point.

seanalltogether 14y ago

Only if you have a jury full of mathmeticians

famousactress 14y ago

Is it? Maybe a zero length line segment. In geometry terms, lines are infinite, aren't they?

tankenmate 14y ago
No. Yes.

colanderman 14y ago

Your statement would imply that a point has a direction, which it does not. Also, a line does not have a length; both you and Posner meant line segment. So a correct statement would be: A zero-length line segment is a point. Edit: not even this is true if your definition of a line segment explicitly states that the endpoints must be distinct, as does PlanetMath's definition, as Aethaeryn points out below.

Aethaeryn 14y ago
> A zero-length line segment is a point. The Wikipedia definition of a line segment says that it is bound by two endpoints.[1] It provides a reference to Planet Math that goes into specifics.[2] In this page, it is made clear that the two endpoints cannot be equal. Planet Math provides an equation for a closed[3] line segment: L = {a + tb | t in [0, 1]} This means that a line segment can be expressed as all of the points a + tb, where t is the range [0, 1] (which contains 0, 1 and all the points between them). It also limits a, b as real or complex numbers with b != 0. In other words, any line segment is just "morphing" the basic 0 to 1 range, with a shifting it and b scaling it. Now, since b can't be 0, and 0 != 1, you're not going to get the endpoints of the range 0 and 1 to equal each other no matter how you scale them with b or shift them with a.[4] In other words, line segments will always have length. Because you cannot get the endpoints to equal each other, a point cannot be thought of as a line segment under what appears to be the common definition. ----- [1] https://en.wikipedia.org/wiki/Line_segment https://en.wikipedia.org/wiki/Line_segment [2] http://planetmath.org/encyclopedia/LineSegment.html http://planetmath.org/encyclopedia/LineSegment.html [3] Open is the exact same thing, except with (0, 1) instead of [0, 1] and it doesn't include the points 0 and 1. [4] Of course, if b = 0 was allowed, you could just say that points are where b = 0 for all a.
- colanderman 14y ago
  Ah good I was looking for the restriction b ≠ 0 but couldn't find in on the Wikipedia page. Forgot to check out PlanetMath, thanks.
  - 14y ago

TeMPOraL 14y ago

A zero-dimmensional equivalent of line, maybe?

johnpmayer 14y ago

Depends on your definition. In my interpretation, to be considered a line in any number of dimensions, it must be specified by no fewer than two points. This puts a lower bound on the amount of information to specify "lines", a bound strictly greater than specifying a "point" in a space of similar dimensions. Otherwise, is point also a polygon consisting entirely of zero-length sides? But anyway, I think it was only meant to highlight the Judge's opinion of the absurdity of some claims. edit: so glad this tiny portion was the subject of the most discussion

deleted 14y ago
[deleted]

twelvechairs 14y ago

Yeah. This struck me as well. I think what you say is right, but probably the 'silly' part comes from the context of the legal argument. For instance, You could also say a point is also something with 132 dimensions of data - all but one or two of which are set to 0. Does that mean if we patent ways of working with 132-dimensional data that our patents should apply to anything with fewer dimensions? Of course that would be silly....

meson2k 14y ago

A zero-area polygon. A zero-volume hedron. etc. etc.

SilasX 14y ago
Such degeneracy!

hristov 14y ago

Not exactly. Even if you disregard the definition arguments discussed below, and allow the definition of "line segment" to include "point" I would not say that a point is a zero length line segment. It seems to me that the "lenght" of a point, if such a concept is to be allowed, is infinitely small but not zero. Thus, a point has length of lim(x->0) x. To me, a zero length line segment would be nothingness. But putting the math aside, in the context of patent law, it is important to follow the commonly accepted definitions. A person should not be able to change the meaning of his claims by suggesting new definitions. And it seems obvious that, as others have pointed out, the accepted definition of a line segment is something with finite length, and the accepted definition of a swipe is something that (obviously) results from swiping, i.e. some movement of the finger.

throwaway___ 14y ago
Euclid, Book 1, Definition 1. "A point is that which has no part."
trowftd 14y ago
A point has no dimensions whatsoever. No length, width, or area. A point is not a zero length line segment, but not because of the reason you mention.

strictfp 14y ago

That is the point he is trying to make. A point _can be seen_ as a zero-length line, but this is really on the boundary of the definition of a line. Likewise a zero-length swipe is a tap, but that is really stretching the definition of a swipe. Basing a court case on such a stretched definition is what he is opposing.

jsprinkles 14y ago

I'm beyond disappointed that the article is about the most important ruling regarding patent law in recent memory, and the overwhelming majority of this thread is arguing about the geometry cited in the judge's order. Rational people understood what he meant, even if maybe it's not 100% mathematically sound. This pedantry really frustrates me, and it extends beyond Hacker News. It's pervasive in conversations I've been having recently as well, as if we're all looking for the slightest thing wrong with what someone has said so that we can achieve some kind of acclaim by pointing it out. I made a point recently about how people need to work together and cited a Star Trek film as a joke, and some jackass in the group decided to go to the mat with me on the fact that I had cited the wrong Star Trek film (my quote was in III, not II). There is nothing more frustrating than a pedant. It seems like it's tech people that do it most, too, which makes sense, but still.

ars 14y ago
> and the overwhelming majority of this thread is arguing about the geometry cited in the judge's order. Rational people understood what he meant, even if maybe it's not 100% mathematically sound. > This pedantry really frustrates me People are well aware that they are nit picking, but they enjoy the resulting discussion! Intellectually inclined people enjoy discussing minutia with other like minded people. They are perfectly aware that it makes no difference, and they don't care - it's just something interesting to talk about. It's no longer nit picking about the original (i.e. the practical use is settled), at that point it becomes a discussion for its own sake. Do you never learn or do anything just for the sake of doing it, rather than in order to accomplish something useful? > and some jackass in the group decided to go to the mat with me on the fact that I had cited the wrong Star Trek film He was showing off. If you don't wish to participate in the Star Trek memorization culture just ignore him - his comment was geared to other members of his group who do like doing that. Or simply acknowledge that he was right and move on. Clearly you don't care about that topic, so that acknowledgement shouldn't cost you too much ego. That's also the point of threads: You can ignore an entire thread that is off topic - but it also gives people who found something interesting a place to talk about it without disturbing the rest of the conversation.
- 14y ago