13 ms·

How does the periodicity of the sine function depend upon the infinitude of primes?

pierre_d528 10y ago
Because real numbers and infinities are a fairy tale. This enlightening video makes it clear: https://youtu.be/4DNlEq0ZrTo?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf&t=2577 https://youtu.be/4DNlEq0ZrTo?list=PLIljB45xT85Bfc-S4WHvTIM7E...
- schoen 10y ago
  This argument is seemingly related to Gregory Chaitin's views on noncomputability and nondefinability. Chaitin observes that almost all real numbers cannot be referred to, or singled out, by any mathematical method available to us -- for example because definable numbers using a language or notation must have the cardinality of the natural numbers, but we know from Cantor that the cardinality of the reals should be larger. Chaitin simply thought this was an impressive fact about the reals and the limitations of mathematics -- a way in which mathematics contains randomness and that many or most facts are "true for no particular reason". This author instead seems to conclude for a related reason that the reals don't exist because we have (and could have) no usable technique to distinguish most real numbers from one another. His complaint in this video is a Chaitin-like observation that we have no way to distinguish real number A from real number B in a finite amount of time or with a finite amount of reasoning or information, and an un-Chaitin-like conclusion that maybe we then have no reason to believe that these numbers exist and are distinct from each other. Edit: and he emphasizes later that if we believe in the reals, numbers must exist that we can't actually do arithmetic with (which I would suggest is sometimes for the Chaitinesque reason that we can't name or define them, or other times for the weaker Chaitinesque reason that we can't calculate their values), so he seems to ask what good such numbers are to us or what reason we could have to believe that they are real.
- JulianWasTaken 10y ago
  (For anyone else reading this who might be misled, note that OP's position is generally considered to be "crank" mathematics)
  - schoen 10y ago
    It is definitely not a standard or mainstream view, but it could be a flavor of https://en.wikipedia.org/wiki/Finitism https://en.wikipedia.org/wiki/Finitism which has been defended by a very small but not infinitesimal :-) number of professional mathematicians and which isn't a logically inconsistent position.
    - 4ad 10y ago
      Personally, I am an ultrafinitist. By that I mean that I believe that physical systems can be completely described by constructive mathematics based on intuitionistic logic[2] operating on computable reals[3]. I believe that any other kind of mathematics, e.g. classical logic with axiom of choice can create unphysical models. That being said, I don't object to classical logic as a purely abstract concept. Everything proved in ZFC is certainly true in ZFC! And I don't think any finitist will contest that. [1] https://en.wikipedia.org/wiki/Ultrafinitism https://en.wikipedia.org/wiki/Ultrafinitism [2] https://en.wikipedia.org/wiki/Intuitionistic_logic https://en.wikipedia.org/wiki/Intuitionistic_logic [3] https://en.wikipedia.org/wiki/Computable_number https://en.wikipedia.org/wiki/Computable_number
  - pierre_d528 10y ago
    What a rigorous way to defend your position! Calling names! I bet you are an infinitely good Cantorian ! Did you speak with God recently?
    - mikeash 10y ago
      You got as much rigor as you gave. Disproving every wacky position with a careful analysis is impossible, nobody has that much time.
      - xenadu02 10y ago
        Indeed, there are an almost infinite number of crank theories because they don't require logic, evidence, or proof - just belief. One crank can churn out a hundred nonsense theories in the time it takes someone to validate one scientific idea or mathematical proof. This has a corollary in the startup world: everyone has an idea, what matters is execution.
- jackmaney 10y ago
  Uhhhh...no. Take a look at Dedekind cuts.
  - schoen 10y ago
    The linked video is largely a critique of Dedekind cuts, arguing that they don't in general let us recognize, distinguish, or perform arithmetic on most real numbers. (Almost all of the informational input to a Dedekind cut for a randomly chosen real couldn't be written, remembered, or specified in any way by a human being.) I think the presenter in the video is trying to justify a kind of finitist attitude based on the inaccessibility and unspecifiability of reals-in-general to us. This could also be advocating a position something like https://en.wikipedia.org/wiki/Computable_number#Can_computable_numbers_be_used_instead_of_the_reals.3F https://en.wikipedia.org/wiki/Computable_number#Can_computab... Edit: or perhaps https://en.wikipedia.org/wiki/Constructive_analysis https://en.wikipedia.org/wiki/Constructive_analysis (I didn't watch enough to understand exactly what alternative he proposes)
    - jackmaney 10y ago
      > Almost all of the informational input to a Dedekind cut for a randomly chosen real couldn't be written, remembered, or specified in any way by a human being. Well, yes. The reals are uncountable.
jsprogrammer 10y ago
It's stated in the only english text of the "proof": >If the set of primes is ﬁnite All conclusions are true when your premise is false: https://en.wikipedia.org/wiki/Truth_table#Logical_implication https://en.wikipedia.org/wiki/Truth_table#Logical_implicatio... "the set of primes is finite"? What is "the set of primes" ??????

Because real numbers and infinities are a fairy tale. This enlightening video makes it clear: https://youtu.be/4DNlEq0ZrTo?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf&t=2577 https://youtu.be/4DNlEq0ZrTo?list=PLIljB45xT85Bfc-S4WHvTIM7E...

schoen 10y ago
This argument is seemingly related to Gregory Chaitin's views on noncomputability and nondefinability. Chaitin observes that almost all real numbers cannot be referred to, or singled out, by any mathematical method available to us -- for example because definable numbers using a language or notation must have the cardinality of the natural numbers, but we know from Cantor that the cardinality of the reals should be larger. Chaitin simply thought this was an impressive fact about the reals and the limitations of mathematics -- a way in which mathematics contains randomness and that many or most facts are "true for no particular reason". This author instead seems to conclude for a related reason that the reals don't exist because we have (and could have) no usable technique to distinguish most real numbers from one another. His complaint in this video is a Chaitin-like observation that we have no way to distinguish real number A from real number B in a finite amount of time or with a finite amount of reasoning or information, and an un-Chaitin-like conclusion that maybe we then have no reason to believe that these numbers exist and are distinct from each other. Edit: and he emphasizes later that if we believe in the reals, numbers must exist that we can't actually do arithmetic with (which I would suggest is sometimes for the Chaitinesque reason that we can't name or define them, or other times for the weaker Chaitinesque reason that we can't calculate their values), so he seems to ask what good such numbers are to us or what reason we could have to believe that they are real.
JulianWasTaken 10y ago
(For anyone else reading this who might be misled, note that OP's position is generally considered to be "crank" mathematics)
- schoen 10y ago
  It is definitely not a standard or mainstream view, but it could be a flavor of https://en.wikipedia.org/wiki/Finitism https://en.wikipedia.org/wiki/Finitism which has been defended by a very small but not infinitesimal :-) number of professional mathematicians and which isn't a logically inconsistent position.
  - 4ad 10y ago
    Personally, I am an ultrafinitist. By that I mean that I believe that physical systems can be completely described by constructive mathematics based on intuitionistic logic[2] operating on computable reals[3]. I believe that any other kind of mathematics, e.g. classical logic with axiom of choice can create unphysical models. That being said, I don't object to classical logic as a purely abstract concept. Everything proved in ZFC is certainly true in ZFC! And I don't think any finitist will contest that. [1] https://en.wikipedia.org/wiki/Ultrafinitism https://en.wikipedia.org/wiki/Ultrafinitism [2] https://en.wikipedia.org/wiki/Intuitionistic_logic https://en.wikipedia.org/wiki/Intuitionistic_logic [3] https://en.wikipedia.org/wiki/Computable_number https://en.wikipedia.org/wiki/Computable_number
- pierre_d528 10y ago
  What a rigorous way to defend your position! Calling names! I bet you are an infinitely good Cantorian ! Did you speak with God recently?
  - mikeash 10y ago
    You got as much rigor as you gave. Disproving every wacky position with a careful analysis is impossible, nobody has that much time.
    - xenadu02 10y ago
      Indeed, there are an almost infinite number of crank theories because they don't require logic, evidence, or proof - just belief. One crank can churn out a hundred nonsense theories in the time it takes someone to validate one scientific idea or mathematical proof. This has a corollary in the startup world: everyone has an idea, what matters is execution.
jackmaney 10y ago
Uhhhh...no. Take a look at Dedekind cuts.
- schoen 10y ago
  The linked video is largely a critique of Dedekind cuts, arguing that they don't in general let us recognize, distinguish, or perform arithmetic on most real numbers. (Almost all of the informational input to a Dedekind cut for a randomly chosen real couldn't be written, remembered, or specified in any way by a human being.) I think the presenter in the video is trying to justify a kind of finitist attitude based on the inaccessibility and unspecifiability of reals-in-general to us. This could also be advocating a position something like https://en.wikipedia.org/wiki/Computable_number#Can_computable_numbers_be_used_instead_of_the_reals.3F https://en.wikipedia.org/wiki/Computable_number#Can_computab... Edit: or perhaps https://en.wikipedia.org/wiki/Constructive_analysis https://en.wikipedia.org/wiki/Constructive_analysis (I didn't watch enough to understand exactly what alternative he proposes)
  - jackmaney 10y ago
    > Almost all of the informational input to a Dedekind cut for a randomly chosen real couldn't be written, remembered, or specified in any way by a human being. Well, yes. The reals are uncountable.

jsprogrammer 10y ago

It's stated in the only english text of the "proof": >If the set of primes is ﬁnite All conclusions are true when your premise is false: https://en.wikipedia.org/wiki/Truth_table#Logical_implication https://en.wikipedia.org/wiki/Truth_table#Logical_implicatio... "the set of primes is finite"? What is "the set of primes" ??????