6 ms·

It’s almost certainly a rational number as activity in the body is finite. There will be an exact point at which a certain molecule has interacted with another

It’s almost certainly a rational number as activity in the body is finite. There will be an exact point at which a certain molecule has interacted with another molecule marking the exact point of perfect sleep. Averaging many rational numbers can’t get you an irrational number. Also it is invalid to compare infinite series like you do in your paracentesis argument, there are infinitely many irrational numbers and infinitely many rational ones. If you do it, you run in to contradictions. (Something which is related to Cantor's paradox)

yakubin 3y ago
The statement OP put in parentheses is a well-defined statement in mathematics. It means that the Lebesgue measure of the set of the rational numbers is zero in the space of real numbers.
- aydyn 3y ago
  That's nice, but reality doesn't live on the real number line.
  - _Algernon_ 3y ago
    "all models are wrong but some models are useful" You're not being clever by being pedantic.
    - aydyn 3y ago
      lol saying that a number in reality will be irrational is peak pedantry. Try again, sweaty.
downvotetruth 3y ago
> will be an exact point at which a certain molecule has interacted with another molecule marking the exact point of perfect sleep Just because the best current theory suggests a smallest observable time span does not mean as a consequence that time is discrete.
- reliablereason 3y ago
  "If the physical property that time meassuring devices meassure is continuous, it must also contain irrational numbers?" Is that what you are refering to? Mabye... To me it seams like nothing is truly continuous i nature. But mabye there is such a thing somewere out there somewere. But irrational numbers require definitions that contain or require recursion. Mabye physical time is built with such a recursive definition?
  - downvotetruth 3y ago
    No, I am not referring to that statement. > irrational numbers require definitions that contain or require recursion The computable reals are also known as the recursive reals, but almost every real number is not computable.
    - reliablereason 3y ago
      Which way was your comment suposed to be interpreted? Was it just a "out of context comment" on something that poped up in your mind as you read the text?
      - downvotetruth 3y ago
        "There will be an exact point at which a certain molecule has interacted with another molecule" statement is contradictory with the uncertainty associated with time as described by quantum mechanics and molecular interactions due to Brownian motion. Material that is returned when searching for those topics will better answer your further questions about them and those above than I here.
        reliablereason 3y ago
        The uncertainty principle is about unavoidable measurement "errors" (measurements that can’t be done). If you are going to measure the time (or anything) you will always get finite values. Finite values are not irrational. Either one talks about the underlying physics or about the measurements of it. If one talks about the underlying physics all bets are of, it is unmeasurable by definition. Anything is possible bellow the measurement threshold(including irrational numbers). If one talks about the measurements you will always get finite rational values.
AprilArcus 3y ago
>There will be an exact point at which a certain molecule has interacted with another molecule marking the exact point of perfect sleep. I have some terrible news for you about statistical mechanics.

yakubin 3y ago

The statement OP put in parentheses is a well-defined statement in mathematics. It means that the Lebesgue measure of the set of the rational numbers is zero in the space of real numbers.

aydyn 3y ago
That's nice, but reality doesn't live on the real number line.
- _Algernon_ 3y ago
  "all models are wrong but some models are useful" You're not being clever by being pedantic.
  - aydyn 3y ago
    lol saying that a number in reality will be irrational is peak pedantry. Try again, sweaty.

downvotetruth 3y ago

> will be an exact point at which a certain molecule has interacted with another molecule marking the exact point of perfect sleep Just because the best current theory suggests a smallest observable time span does not mean as a consequence that time is discrete.

reliablereason 3y ago
"If the physical property that time meassuring devices meassure is continuous, it must also contain irrational numbers?" Is that what you are refering to? Mabye... To me it seams like nothing is truly continuous i nature. But mabye there is such a thing somewere out there somewere. But irrational numbers require definitions that contain or require recursion. Mabye physical time is built with such a recursive definition?
- downvotetruth 3y ago
  No, I am not referring to that statement. > irrational numbers require definitions that contain or require recursion The computable reals are also known as the recursive reals, but almost every real number is not computable.
  - reliablereason 3y ago
    Which way was your comment suposed to be interpreted? Was it just a "out of context comment" on something that poped up in your mind as you read the text?
    - downvotetruth 3y ago
      "There will be an exact point at which a certain molecule has interacted with another molecule" statement is contradictory with the uncertainty associated with time as described by quantum mechanics and molecular interactions due to Brownian motion. Material that is returned when searching for those topics will better answer your further questions about them and those above than I here.
      - reliablereason 3y ago
        The uncertainty principle is about unavoidable measurement "errors" (measurements that can’t be done). If you are going to measure the time (or anything) you will always get finite values. Finite values are not irrational. Either one talks about the underlying physics or about the measurements of it. If one talks about the underlying physics all bets are of, it is unmeasurable by definition. Anything is possible bellow the measurement threshold(including irrational numbers). If one talks about the measurements you will always get finite rational values.

AprilArcus 3y ago

>There will be an exact point at which a certain molecule has interacted with another molecule marking the exact point of perfect sleep. I have some terrible news for you about statistical mechanics.