#### Re: Analogies and scientific knowledge

Hello, Khimik, you wrote: K> Now I will give an example, as by means of analogies it is possible to study properties...  from the cradle learn all using analogy...

#### Re: Analogies and scientific knowledge

...Everyone  ... K> a question - that such generally analogies? You for what purpose are interested? Can it is necessary take the appropriate professional literature and to read? https://www.google.com/search?q=analogi … rogramming

#### Re: Analogies and scientific knowledge

Hello, Khimik, you wrote: K> From pictures it is visible that the total of corners of a triangle turns out less than 180 degrees. Really, in Lobachevski geometry there is such theorem: And you in which of geometries considered this total?

#### Re: Analogies and scientific knowledge

K>> From pictures it is visible that the total of corners of a triangle turns out less than 180 degrees. Really, in Lobachevski geometry there is such theorem: S> And you in which of geometries considered this total? The second and the third (Poincare's model and upper halfplane model). There in pictures it is visible that it is less 180.

#### Re: Analogies and scientific knowledge

Hello, Khimik, you wrote: K> 1) the Internal surface of sphere. K> we assume, there is a sphere surface in three-dimensional space. Between two points of this surface it is possible to draw a straight line (in three-dimensional space). Also between two points it is possible to lead a line on surfaces, as though a shade from the first straight line if at sphere center there was a light source (and further to continue this line in both sides that the circle on a sphere surface turned out). K> we name these abstractions accordingly "a line in the first sense" and "a line in the second sense". K> Now we invent a homonym - "straight line" so-called which means both that and that. K> Now we receive "the theorem" corresponding to Lobachevski geometry: K> Through set by a point it is possible to lead any number of "straight lines", parallel given "straight line". I here did not understand Something. How though one parallel line to lead? They all are intersected on sphere. The sphere surface has the positive curvature, there the total of corners is more 180, it not that at Lobachevsky.

#### Re: Analogies and scientific knowledge

Hello, Khimik, you wrote: K> In spite of the fact that we cannot imagine the same Lobachevski geometry, we can successfully study its properties by means of a method of analogies. K> Here there is a question - that such generally analogies? The mathematician would tell that the analogy is a forgetting functor. https://ru.wikipedia.org/wiki/%D0%97%D0 … 0%BE%D1%80 actually, all essence of the category theory just that we study things through their relations. The more we know about relations, the we know about object though inside we can and not look more. Just as learning something through analogies. (And it too analogy)

#### Re: Analogies and scientific knowledge

Hello, D. Mon, you wrote: DM> I here did not understand Something. How though one parallel line to lead? They all are intersected on sphere. Why are intersected? Unless parallels of the Earth (a line, parallel to equator) are intersected? DM> the sphere Surface has the positive curvature, there the total of corners is more 180, it not that at Lobachevsky. Truth is more 180? It is sad...

#### Re: Analogies and scientific knowledge

Hello, Khimik, you wrote: DM>> I here did not understand Something. How though one parallel line to lead? They all are intersected on sphere. K> why are intersected? Unless parallels of the Earth (a line, parallel to equator) are intersected? Parallels of the Earth - not straight lines in this sense, them not to receive the method described by you. The immediate analog of a straight line on sphere is geodesic, "the big circle". Such, as meridians, as equator. And all of them are intersected. DM>> the sphere surface has the positive curvature, there the total of corners is more 180, it not that at Lobachevsky. K> truth is more 180? It is sad... Truth. As a classical example - a triangle made of two perpendicular meridians and equator. At it all corners straight lines, the total 270. At other triangles the total can be less, and at small will come nearer to 180, but all the same always hardly more than 180 will be.

#### Re: Analogies and scientific knowledge

Hello, Khimik, you wrote: K>>> From pictures it is visible that the total of corners of a triangle turns out less than 180 degrees. Really, in Lobachevski geometry there is such theorem: S>> And you in which of geometries considered this total? K> the second and the third (Poincare's model and upper halfplane model). There in pictures it is visible that it is less 180. In pictures of it it is not visible, ....

#### Re: Analogies and scientific knowledge

Hello, D. Mon, you wrote: K>> Truth is more 180? It is sad... DM> Truth. As a classical example - a triangle made of two perpendicular meridians and equator. At it all corners straight lines, the total 270. At other triangles the total can be less, and at small will come nearer to 180, but all the same always hardly more than 180 will be. Any analogy gives any correct predictions, and any wrong. The "more strongly" (more close) the analogy, the is more percent of the correct predictions. It is possible to take as an example analogy between atom and solar system. She allows to foretell that if kinetic energy of an electron will be enough high, it departs from a kernel on infinity. On the other hand, from this analogy the wrong prediction follows that the electron should radiate energy and gradually fall on a kernel. As I already wrote, the amount of analogies can compensate quality. In an initial post 4 analogies are resulted, from them two or most likely three foretell that the total of corners is less 180, and one (first) - that is more than all 180. Therefore as a whole these analogies predict properties of Lobachevski geometry.

#### Re: Analogies and scientific knowledge

K>>>> From pictures it is visible that the total of corners of a triangle turns out less than 180 degrees. Really, in Lobachevski geometry there is such theorem: S>>> And you in which of geometries considered this total? K>> the second and the third (Poincare's model and upper halfplane model). There in pictures it is visible that it is less 180. S> In pictures of it it is not visible, .... You look inattentively (the last pictures with places of honor).

#### Re: Analogies and scientific knowledge

Hello, Khimik, you wrote: K>>>>> From pictures it is visible that the total of corners of a triangle turns out less than 180 degrees. Really, in Lobachevski geometry there is such theorem: S>>>> And you in which of geometries considered this total? K>>> the second and the third (Poincare's model and upper halfplane model). There in pictures it is visible that it is less 180. S>> In pictures of it it is not visible, .... K> you look inattentively (the last pictures with places of honor). And you a case do not operate with Euclidian geometry, including corners which are drawn in a projection non-Euclidean on ?

#### Re: Analogies and scientific knowledge

Hello, Sheridan, you wrote: K>> you look inattentively (the last pictures with places of honor). S> And you a case do not operate with Euclidian geometry, including corners which are drawn in a projection non-Euclidean on ? Did not understand a question. All four models naturally imply Euclidean geometry.