4 ms·

Paradoxes, from Your Coffee to Calculus

31 points by yarapavan 8y ago

neonate 8y ago
http://archive.is/CeB4C http://archive.is/CeB4C
- bena 8y ago
  BTW, this is an archive link to the article that bypasses the paywall.
bena 8y ago
The article is also just fluff. The central premise is that paradoxes allow us to change our way of thinking. Some examples: can't find your glasses because you can't see without them; can't make coffee because you need coffee to wake up in order to make it; how can you be intolerant of intolerance etc. They then describe the barber paradox and some of Zeno's paradoxes. How the barber paradox informs us how important it is for us to define things and set limits. And how Zeno's paradoxes led us to calculus. They then say that they resolve their paradoxes by having a place they put their glasses, setting up the coffee machine the night before, and hating the sin, not the sinner. And that's pretty much it. Over a thousand words to say that she's a tolerant person who hates intolerance.
- s-shellfish 8y ago
  How is what you do any different? Paradoxes can change how we reason. Being able to think about them allows oneself to refine an understanding to a static context of parts. Once that is complete, a paradox can be resolved by defining a logic of which no paradox arises, and testing it to ensure that, which is still NP hard to prove but, for real life, some people just like to make points and feel smart and talk about things they maybe never got to talk about before. https://en.m.wikipedia.org/wiki/Paraconsistent_logic https://en.m.wikipedia.org/wiki/Paraconsistent_logic
  - bena 8y ago
    Huh? I wasn't really disagreeing with anything, I was breaking down the article for people who don't have a WSJ subscription, don't want one, and don't want to bother with the archive link. I feel the article is mostly pedantic fluff, reiterating a concept that most people are already familiar with in order to just say what she says in the final paragraph: That she can be a tolerant person, tolerate people, while still disagreeing with their viewpoint. Basically responding to the whole "you can't be tolerant and hate intolerance" canard. My issue isn't with her stance on paradoxes, it's with the fact that she doesn't say anything.
    - s-shellfish 8y ago
      That's really not fair to women who want to be known as logical thinkers and are just starting to grow into it externally. You can call it pedantic fluff, I call it a coupled fear of having one's own mind appear hypermasculinized while maintaining sensitivity to multiple perspectives of listening to many individuals without being listened to directly. Big picture. The devil is in the details. Edit: maybe wait a few hours before downvoting next time? at least give me the opportunity to not see it as being likely to be you
      - mirko22 8y ago
        are you saying women somehow need to choose to think logically and are illogical by default or what? cos your comments makes very little sense.
        s-shellfish 8y ago
        Nope, I'm projecting from my own personal experience of having to combine everything I've ever read, learned, listened to, and thought with logic. And I'm female, oh no! Huzzah! Keep insulting -> make my perspective stronger.
        mirko22 8y ago
        who is insulting who? in original comment you were claming that “she wants to think logically” as if women don’t do that, and that statement sounds insulting to women... so...
1996 8y ago
I believe Wittigstein said it best: philosophical paradoxes (if a tree falls in forest with no one around to hear it, does it make a noise?) are just word play, due to the inconsistencies of human language. Adequate language or computer code makes them go away. You are not blind without glasses - you can distinguish shapes and remember the shape of the room and where you may have left glasses and probe with your hand to find them. You are not comatose without coffee - you are conscious, and take coffee just to feel more alert. And so on, that with the right language (but it is easier to do that with mathematics or code) the paradox goes away. Like the Zeno paradox with calculus.
- justifier 8y ago
  i'd say planck did more for zeno than calculus https://en.m.wikipedia.org/wiki/Ultraviolet_catastrophe https://en.m.wikipedia.org/wiki/Ultraviolet_catastrophe
- s-shellfish 8y ago
  No, paradoxes exist for people in real life. Study zen buddhism, if you want evidence.
  - 1996 8y ago
    I did study, at length. Maybe too much. But I found no evidence and dropped many aspect of religion from my life. Care to give me some examples?
    - s-shellfish 8y ago
      http://flatbedsutra.com/flatbedsutrazenblogger/?p=1714 http://flatbedsutra.com/flatbedsutrazenblogger/?p=1714
      - 1996 8y ago
        Not a paradox for a buddhist. Answering will make him open his mouth and lose his grip. Thinking about answering will cause the want, and the suffering as he can not answer without forfeiting his life. The answer is unthinking- as in meditation, clear thoughts from the mind. It is designed to show how the right answer is no answer, in both senses! With the proper understanding, there is no paradox. I agree with you that noticing a potential paradox is sometimes a souce of inspiration to learn, mostly when you can not show the way and when it must come by self discovery. I do not know how familiar you are with Buddhism. If you want to keep learning, ask yourself: if Kyogen was asked 3 times, would he change his "answer" ?
n4r9 8y ago
I like the insight about applying set-theoretic, Russell's-paradox-circumventing thinking to everyday scenarios. Not to detract from that, but I think the coffee and glasses situations are perhaps better described as "deadlocks" than "paradoxes".
- kqr 8y ago
  It depends on how you choose to view them. The article chose to use imperative-sounding wording, but you could just as well look at them as declarative statements of logic: (1) Operating a machine implies having been drinking coffee. (2) Drinking coffee implies having operated the coffee making machine.
raincom 8y ago
Paradoxes arise due to our descriptions or understanding or theories we use to understand a phenomenon. If we keep this distinction betweeen a phenomenon and its description, paradoxes tell us that we don’t understand the phenomenon very well. The other issue is the theory-laden ness of observations. Every observation is theory laden. Most of the time we don’t even perceive this theory-ladenness because we see them as some atomic facts. The trick here is to describe the phenomenon at a lower level when paradoxes arise at higher level.

31 points by yarapavan 8y ago

neonate 8y ago

http://archive.is/CeB4C http://archive.is/CeB4C

bena 8y ago
BTW, this is an archive link to the article that bypasses the paywall.

bena 8y ago

The article is also just fluff. The central premise is that paradoxes allow us to change our way of thinking. Some examples: can't find your glasses because you can't see without them; can't make coffee because you need coffee to wake up in order to make it; how can you be intolerant of intolerance etc. They then describe the barber paradox and some of Zeno's paradoxes. How the barber paradox informs us how important it is for us to define things and set limits. And how Zeno's paradoxes led us to calculus. They then say that they resolve their paradoxes by having a place they put their glasses, setting up the coffee machine the night before, and hating the sin, not the sinner. And that's pretty much it. Over a thousand words to say that she's a tolerant person who hates intolerance.

s-shellfish 8y ago
How is what you do any different? Paradoxes can change how we reason. Being able to think about them allows oneself to refine an understanding to a static context of parts. Once that is complete, a paradox can be resolved by defining a logic of which no paradox arises, and testing it to ensure that, which is still NP hard to prove but, for real life, some people just like to make points and feel smart and talk about things they maybe never got to talk about before. https://en.m.wikipedia.org/wiki/Paraconsistent_logic https://en.m.wikipedia.org/wiki/Paraconsistent_logic
- bena 8y ago
  Huh? I wasn't really disagreeing with anything, I was breaking down the article for people who don't have a WSJ subscription, don't want one, and don't want to bother with the archive link. I feel the article is mostly pedantic fluff, reiterating a concept that most people are already familiar with in order to just say what she says in the final paragraph: That she can be a tolerant person, tolerate people, while still disagreeing with their viewpoint. Basically responding to the whole "you can't be tolerant and hate intolerance" canard. My issue isn't with her stance on paradoxes, it's with the fact that she doesn't say anything.
  - s-shellfish 8y ago
    That's really not fair to women who want to be known as logical thinkers and are just starting to grow into it externally. You can call it pedantic fluff, I call it a coupled fear of having one's own mind appear hypermasculinized while maintaining sensitivity to multiple perspectives of listening to many individuals without being listened to directly. Big picture. The devil is in the details. Edit: maybe wait a few hours before downvoting next time? at least give me the opportunity to not see it as being likely to be you
    - mirko22 8y ago
      are you saying women somehow need to choose to think logically and are illogical by default or what? cos your comments makes very little sense.
      - s-shellfish 8y ago
        Nope, I'm projecting from my own personal experience of having to combine everything I've ever read, learned, listened to, and thought with logic. And I'm female, oh no! Huzzah! Keep insulting -> make my perspective stronger.
        mirko22 8y ago
        who is insulting who? in original comment you were claming that “she wants to think logically” as if women don’t do that, and that statement sounds insulting to women... so...

1996 8y ago

I believe Wittigstein said it best: philosophical paradoxes (if a tree falls in forest with no one around to hear it, does it make a noise?) are just word play, due to the inconsistencies of human language. Adequate language or computer code makes them go away. You are not blind without glasses - you can distinguish shapes and remember the shape of the room and where you may have left glasses and probe with your hand to find them. You are not comatose without coffee - you are conscious, and take coffee just to feel more alert. And so on, that with the right language (but it is easier to do that with mathematics or code) the paradox goes away. Like the Zeno paradox with calculus.

justifier 8y ago
i'd say planck did more for zeno than calculus https://en.m.wikipedia.org/wiki/Ultraviolet_catastrophe https://en.m.wikipedia.org/wiki/Ultraviolet_catastrophe
s-shellfish 8y ago
No, paradoxes exist for people in real life. Study zen buddhism, if you want evidence.
- 1996 8y ago
  I did study, at length. Maybe too much. But I found no evidence and dropped many aspect of religion from my life. Care to give me some examples?
  - s-shellfish 8y ago
    http://flatbedsutra.com/flatbedsutrazenblogger/?p=1714 http://flatbedsutra.com/flatbedsutrazenblogger/?p=1714
    - 1996 8y ago
      Not a paradox for a buddhist. Answering will make him open his mouth and lose his grip. Thinking about answering will cause the want, and the suffering as he can not answer without forfeiting his life. The answer is unthinking- as in meditation, clear thoughts from the mind. It is designed to show how the right answer is no answer, in both senses! With the proper understanding, there is no paradox. I agree with you that noticing a potential paradox is sometimes a souce of inspiration to learn, mostly when you can not show the way and when it must come by self discovery. I do not know how familiar you are with Buddhism. If you want to keep learning, ask yourself: if Kyogen was asked 3 times, would he change his "answer" ?

n4r9 8y ago

I like the insight about applying set-theoretic, Russell's-paradox-circumventing thinking to everyday scenarios. Not to detract from that, but I think the coffee and glasses situations are perhaps better described as "deadlocks" than "paradoxes".

kqr 8y ago
It depends on how you choose to view them. The article chose to use imperative-sounding wording, but you could just as well look at them as declarative statements of logic: (1) Operating a machine implies having been drinking coffee. (2) Drinking coffee implies having operated the coffee making machine.

raincom 8y ago

Paradoxes arise due to our descriptions or understanding or theories we use to understand a phenomenon. If we keep this distinction betweeen a phenomenon and its description, paradoxes tell us that we don’t understand the phenomenon very well. The other issue is the theory-laden ness of observations. Every observation is theory laden. Most of the time we don’t even perceive this theory-ladenness because we see them as some atomic facts. The trick here is to describe the phenomenon at a lower level when paradoxes arise at higher level.