3,313 reputation
12363
bio website
location Germany
age 49
visits member for 5 years, 1 month
seen 2 hours ago

My interests:

  • abstract structures
    (e.g. graphs, groups, polytopes, spaces, ...)

    in the course of this

  • category theory

  • model theory

  • presentations and representations
    (e.g. of abstract structures by or inside other abstract structures)

    next to this

  • philosophy
    (esp. of mathematics, science, and mind)

    especially concerned with

  • atomism
    (i.e. reductionistic or other theories referring to some kind of "atoms")

  • their refutations


Jan
17
revised Contexts and notations for composing asymmetric simplices
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Jan
17
revised Contexts and notations for composing asymmetric simplices
edited title
Jan
17
revised Contexts and notations for composing asymmetric simplices
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Jan
17
revised Contexts and notations for composing asymmetric simplices
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Jan
17
revised Contexts and notations for composing asymmetric simplices
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Jan
17
revised Contexts and notations for composing asymmetric simplices
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Jan
16
revised Contexts and notations for composing asymmetric simplices
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Jan
15
revised Contexts and notations for composing asymmetric simplices
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Jan
15
revised Contexts and notations for composing asymmetric simplices
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Jan
15
asked Contexts and notations for composing asymmetric simplices
Dec
22
awarded  Nice Answer
Dec
18
awarded  Yearling
Oct
14
awarded  Self-Learner
Oct
14
answered Supervenience in mathematics
Sep
29
comment Rationale behind an requirement on Turing machines
Notice further, that $b$ can not only be read but also be written.
Sep
29
comment Rationale behind an requirement on Turing machines
Re-reading your answer I am still not satisfied: In Hopcroft/Ullman's definition of a Turing machine as a 7-tupel the blank symbol $b$ is distinguished (among the tape symbols), but there seems to be no requirement on a Turing machine involving $b$. Especially the transition function $\delta$ can be defined on the whole tape alphabet (including $b$). The same holds - by the way - for the initial state $q_0$.
Sep
27
awarded  Nice Answer
Sep
24
awarded  Autobiographer
Sep
3
awarded  Peer Pressure
Aug
30
comment When are two algorithms essentially the same?
I didn't want to ask for a single equivalence, sorry if it sounded like this. I am looking for any (sensible) equivalence. One came to my mind only today: $T$ is equivalent to $T'$ when they have the same symbols and blank symbol, compute the same function, have the same number of internal states and there is a bijection $f$ between the states that preserves - among other things - starting and halting, next state $S(f(x),s)$ is $f(S(x),s)$, and so on. One may find this trivial, but it is a sensible equivalence, isn't? And there may be others.