> [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.
But a point is a zero-length line.
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.
> A zero-length line segment is a point.
L = {a + tb | t in [0, 1]}
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.
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[1] https://en.wikipedia.org/wiki/Line_segment
[2] 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.
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[1] http://mathworld.wolfram.com/LineSegment.html
[2] Just saying 'two distinct endpoints' instead of 'two endpoints' would work, so it's literally just one word that makes a big difference!
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
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.
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....
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.
> 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.
Also, I like to think of myself as intellectually inclined, and I simply hate discussing and arguing minutia like this. It just doesn't matter, and my time is limited. I don't want to argue with you on what Dickens meant by a certain character's dialogue in David Copperfield, I'd just like to enjoy it as a great novel. (That is fairly specific, and there are instances where it's fun to think about, but in general it isn't.)
> Clearly you don't care about that topic, so that acknowledgement shouldn't cost you too much ego.
Not about my ego, oddly (most everything else is, but this isn't). It undermines the opinion or discussion at hand from everybody else's perspective, however subtly. It's an annoying opportunity to show off, as you say, like those people that get up at conferences and ask a question that shows off at the expense of everyone listening. Both are distractions from the topic and are a detriment to the conversation, regardless of their original purpose.
I really don't think they are doing that. They understand that for the normal purpose he's right, they are just talking about mathematics, or general cases. At this point it's removed from the original, they are no longer talking about him (the Judge) they are talking about the concept in general.
> I like to think of myself as intellectually inclined
and
> and there are instances where it's fun to think about
There you go. There is no rule that says you have to enjoy talking about the same things as someone else. Each person likes their own stuff.
I would guess that people who are in certain professions which require precision would be more likely to act this way. Because lack of precision would cause the plane to crash or the bridge to fail or the code to croak. Medicine (drugs) for example is not really super precise when you think about it. Dosing isn't so critical that if you take a little more or a little less you end up dead or sick. You have latitude. (Of course someone who knows more than I about this would point out that coumadin (Warfarin) dosing is quite critical and correct me.)
Have you found that to be the case in your IRL conversations?
Pedantry like that indicates that the person may be suffering from OCD, not that they have a high IQ. There is a correlation between intelligence and anxiety-spectrum disorders but there are, ofcourse, many anxious people who have low IQ's too.
It's so much easier to do this as a result of information so readily available at your finger tip. So any statement anyone makes can be quickly verified and corrected with pretty good precision. Wondering if the people who corrected you in conversations looked up the fact on their iphone (or whatever) while you weren't looking.