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Ultrafilter

Ultrafilters on sets are used in the ultrapower construction of certain fields of hyperreal numbers. The idea of using ultrafilter to define total ordering on hyperreal numbers can suggest an intuitive metaphor to grasp the importance of notion ultrafilter: when transferring relations to “sequences” in a “point-wise” way, the resulting relation will “lose” some nice properties. This can be amended if we make this point-wise transferring in a more sophisticated way: we must “discriminate” positions that “matter”. Any ultrafilter can be used to “discriminate” positions that “matter”, so that the resulting relations have nicer properties. When using a principal ultrafilter, the resulting relation will coincide with one of those we started with, but when using a free ultrafilter, the construct will provide a brand-new relation. See details in article Hyperreal number.

Diagonal lemma

At User:Physis/Language base

Orca vs bird debate

Debate: the English translated Menovshchikov article dealswith sea gull, but the Sirenik book of the same author discusses orca, for which transformability with wolf is stated. Orca? Sea gull? Which one? Let us regard orca as a default. Now the debate:

Pro:

A radio interview with Russian scientists about Asian Eskimos

At least probably…

Subject: Orca: "wolf of the sea" (fwd)

may suggest an ecological and etological justification

Ocra Killer Whale

I cannot see the sources. Suggests mythological connection.

Haida myth

A rather direct evidence, but this is a Haida myth. Same tect on Neander97

North Pacific Native Indian

The same remarks apply

Animals Resource Information: Orca

orca was a wolf

Story 1: Tsimshian Orca Clan Story goes like this: Orca (black and white whale) used to be a white wolf; Noo Halidzoks created only one White wolf and...

In the mythology of the Pacific Northwest of the USA and Canada, the orca is known as the helper of mankind. Native American people in the region regard this creature as the king of the ocean , a sovereign who lives in an underwater city. It was throught that people who drowned went to live with the orcas in their underwater realm.

Orca wolf moiety

Organized into houses, clans, and four crests divided into Orca-Wolf or Raven-Eagle moieties, all inherited through the mother, Tsimshians controlled the ...

Eskimos - Kasatka - Volk

detiled description of these Eskimo thought, and in general man, animal, myth. Because kasatka is said here to help hunters lead the walrusses, I suppose it must be an orca, because a bird could ot do this, and orcas have been seen to cooperate with human in hunting also in reality, see Orca#Co-operating with humans

Orca as sacred

Not very creditful, but it suggests at least that orcas were part of mythology, not indifferent

Mistranslation argument

The English translation sais kingfisher. But the text may be a mistranslation, because the same text says: “causing terror to all coastal inhabitants”. Even, kingfisher do not seem to live in the Arctic.

also in Russian

orcas are called sometimes as wolves of sea.

Reference

in p. 48 of

To do: update Siberian Yupik and medlibrary

Concepts about the animal world around them

The largest Siberian Yupik language spoken in Russia is named after village Ungazik (Chaplino). The pople is called ungazigmik (plural ungazigmit, IPA: as phonemic /uˈŋaziɢmiːt/, as phonetic [uˈŋaʑiʁmʲiːt]; cyrillic: ун'азиг'мит, see tales on pp. 220, 238, 370 of , and also p. 1 of ).

In the tales and beliefs of this people, wolf and a specific sea bird are thought to be identical: this bird can become a wolf or vice versa. In winter, they appear in the form of wolf, in summer, in the form of bird (see tale The orphan boy with his sister, p. 156, note 21).

This bird was believed to help people in hunting on the sea -- thus the boat represented the image of this animal, and the bird's wooden representation hang also from the hunter's belt (see subsection Духовная культура (Spirit culture) of ).

The name of this bird (IPA: [mɨˈɕuŋɨˈɕak], cyrillic: мысюн'ысяк, in English ca. mee-soong-ee-suck) --- is translated

• as касатка in ,
• and as kingfisher in .

Word касатка---it means Anas falcata Georgi, which is falcated duck, so we cannot be sure exactly which bird species is concerned here.

The materials cited above ( ) mention also the spider, whale , raven as revered animals, referring to folklore (e.g. tale) examples.

Bootstrapping

Circularity

“Taming circularity into spirality” ().

Foundations of mathematical logic

How to achieve a foundation of mathmatical logic: we use set theoretical, algebraic concepts — are set theory and algebra not based on mathematical logic? See p. 9 par 3, p. 21 par 4, p. 19 par 2-3 of .

A similar feeling, when I read . I am reading normal text in plain Hungarian, an eventually I begin to understand a new language, sophisticated scientific terms and concepts.

Send message for receiver who does not expect it: language on top of a language

Knocking alphabet

Knocking alphabet was used by Russian prisoners in the Russian Empire: the communication took place between prisoners in separate cells. Knocks on the wall were used as a code to transfer complete messages. For a detailed description, see the here cited example (use this simpler version in case of link problems).

We send a primitive message first, whose only aim is to communicate that it has some meaning, it can be regarded as a message at all. (Maybe, our neighbor does not even know the existence of knocking alphabets!) Thus, first we use a primitive alphabet coding system: coding each letter by so many knocks which corresponds to the position of the letter in the alphabet in a straightforward way. This method is slow, inefficient, but is good for to take the first steps.

Later, on top of it, we teach our listener (if any) a professional, high-tech, fast knocking alphabet system (developed by its experts: among others, practicing common criminals). A coding system for letters using more efficient techniques (like arranging the letters of the alphabet in a matrix, and accessing the letters by indexing this matrix). In other words, we have to construct a “machine”, at least in our mind and in that of our neighbour; and later we shall use this mental machine for coding / decoding our messages.

Plans for messages to extraterrestrial intelligent beings

“We have to communicate first, that it is a message at all, it has meaning, it is different from noise” -- how to achieve this? We read examples for this goal even in fictions: e.g. novel Contact (written by Carl Sagan) mentions the idea of sending first a series of prime numbers (because we do not know abundant natural phenomena emitting prime-number-related patterns -- although see Prime number#Prime numbers in nature, thus we can expect that the receiver will perceive that it is not a noise).

Also the artificial language called Lincos (proposed for sending messages to extraterrestrial intelligent beings by mathematician Dr Hans Freudenthal) is based on the idea of bootstrapping (in the sense as used above in the knocking alphabet example).

See the more general discussion of the topic in article Communication with Extraterrestrial Intelligence: proposed languages, ideas, some of them relating to here.

Idea of specifying a machine

Even the knocking alphabet example used the idea of describing a primitive “machine”, to have a tool to transfer more interesting things. See also the notion of metalanguage (versus object language) and also other meta related things. Consider also if this structural description idea is related to Tarski's structural descriptive name concept , which I used at combinatory logic quine (see Lojban).

The novel Contact may relate to the notion of bootstrapping this way, too: the message contains a technical description of a machine, and the more interesting things will be transferred by the machine itself. A similar motif can be read in A for Andromeda (written by Fred Hoyle).

In ICFP Programming Contest, the task given in 2006 was of a similar taste: the first contest task was to build a “universal machine” (following a given description), the remaining tasks were transmitted by the machine itself. (The relatedness to the notion of bootstrapping may be only partial, because the input of the machine was provided).

Sirenik language

Introduction

Sirenik or "Sirenikskiy" also Sirenik, is an extinct Eskimo-Aleut languages. It was spoken in and around the village of Sireniki (Сиреники) in Chukotka Peninsula, Chukotka Autonomous Okrug, Russia. In January 1997 the last native speaker of the language, a woman named Vyie (Russian: Выйе) died (according to the data of N.B. Vakhtin). Vye (as the last speaker of this special branch of Eskimo languages) is also mentioned by the hompeage of a Russian organization for the rights of Siberian indigenous peples.

It is a remnant of a third group of Eskimo-Aleut languages, in addition to Aleut and Eskimo groups. (Also mentions a “trinity”, but it regards Sireniki as one of the three branches of the Eskimo language family: Inuit, Yupik, Sirenik -- thus, regarding the branching of Aleut vs Eskimo at a higher level -- the Eskimo-Aleut language phylum.) See more details, finer approaches (concept of language continuum etc.) in Eskimo-Aleut languages.

See also

• Siberian Yupik
• Eskimo

Famine

The observations of the Famine Commission of 1880 support the notion that food distribution is more to blame for famines than food scarcity. They observed that each province in British India, including Burma, had a surplus of foodgrains, and the annual surplus was 5.16 million tons (Bhatia, 1970). At that time, annual export of rice and other grains from India was approximately one million tons. The observations of the Famine Commission of 1880 support the notion that food distribution is more to blame for famines than food scarcity. They observed that each province in British India, including Burma, had a surplus of foodgrains, and the annual surplus was 5.16 million tons (Bhatia, 1970). At that time, annual export of rice and other grains from India was approximately one million tons.

In 1966, there was a close call in Bihar, when the United States allocated 900,000 tons of grain to fight the famine. It is the closest independent India came to a famine. The increase in food to the population is also reflected in the fact that in the 50 years of British rule (1891 to 1941) the population grew by 35% (from 287 million to 389 million) whereas in the 50 years of democratic rule from 1951 to 2001 the population grew by 183% (from 363 million to 1,023 million). The fact that there have been no famines even with a population that has almost tripled makes it an even more impressive achievement for the democratic government.

Caegory theory

Saved cleanup grom Adjoint functors:

Formal definitions

A pair of adjoint functors between two categories C and D consists of two functors F : C → D and G : D → C and a natural isomorphism

φ : Mor_D(F–, –) → Mor_C(–, G–)

consisting of bijections:

φ_X,Y : Mor_D(F(X), Y) → Mor_C(X, G(Y))

for all objects X in C and Y in D. Here the naturality of φ means that for all morphisms f : X′ → X in C and all morphisms g : Y → Y′ in D the following diagram commutes:

The horizontal arrows in this diagram are those induced by f and g. We then say that F is a left-adjoint of G and G is a right-adjoint of F, and often write F⊣G.

At this point, one might wonder why we have called φ a natural isomorphism. In fact, we can express the definition of the naturality of φ given above, so that φ truly is a natural isomorphism (under the usual definition of natural isomorphism). The way to do this is to interpret hom-sets as actual functors between suitable categories. To be precise, for any category C, there is a hom-functor Mor(–, –) : C^Op × C → Set. If we interpret the "F" in Mor_D(F–, –) as really representing the "opposite functor" F^Op × id_D : C^Op × D → D^Op × D, defined in the expected way, and if we interpret the "G" in Mor_C(–, G–) as representing the functor id_C^Op × G : C^Op × D → C^Op × C, defined in the expected way, then each of Mor_D(F–, –) and Mor_C(–, G–) is in fact a functor from C^Op × D → Set, and the "naturality" requirement is just equivalent to requiring that these two functors be naturally isomorphic.

---

The new cleanup:

A pair of adjoint functors between two categories C and D consists of two functors F : C → D and G : D → C and a natural isomorphism

Φ : Hom_D(F–, –) → Hom_C(–, G–)

consisting of bijections:

Φ_X,Y : Hom_D(F(X), Y) → Hom_C(X, G(Y))

for all objects X in C and Y in D. Here the naturality of Φ means that for all morphisms f : X′ → X in C and all morphisms g : Y → Y′ in D the following diagram commutes:

The horizontal arrows in this diagram are those induced by f and g. We then say that F is a left-adjoint of G and G is a right-adjoint of F, and often write F⊣G.

In order to interpret Φ a natural isomorphism, one must recognize Hom_D(F–, –) and Hom_C(–, G–) as functors. In fact, they are both bifunctors from C^op × D to Set. See the article on Hom functors for more details.

---

My contributions on Talk:Adjoint functors#Primes put on variables are mispaced?:

Primes put on variables are mispaced?

Is the Oct 5 2006 contribution (done in the Adjoint functors#Formal definitions) correct? It has made a rearrangement of primes on the X, Y objects in case of the f morphism. But I think this rearrangement is mistaken.

In the Adjoint functors#Formal definitions, and important notion is that we regard set of morphisms between between two objects as itself an object in ${\mathcal {SET}}$.

$X,Y,X^{\prime },Y^{\prime }\in \mathbf {Ob} ({\mathcal {C}})$

$f,g\in \mathbf {Ar} ({\mathcal {C}})$

$f\in \mathrm {Hom} _{\mathcal {C}}(X^{\prime },\;X)$

$g\in \mathrm {Hom} _{\mathcal {C}}(Y,\;Y^{\prime })$

Let us note the strange (crossed) arrangement of primes on variables: in case of f it is reversed (compared to the case of g).

Now we build an interesting thing in the ${\mathcal {SET}}$ category out of all these above ${\mathcal {C}}$-things:

$\mathrm {Hom} _{\mathcal {C}}(X,\;Y)\in \mathbf {Ob} ({\mathcal {SET}})$

$\mathrm {Hom} _{\mathcal {C}}(X^{\prime },\;Y^{\prime })\in \mathbf {Ob} ({\mathcal {SET}})$

We have just constructed objects in ${\mathcal {SET}}$ category, built of the above ${\mathcal {C}}$-things. But what about the corresponding morhisms (i.e. ordinary functions) in ${\mathcal {SET}}$? How shall we build them in an appropriate way out of the above ${\mathcal {C}}$-things?

$\mathrm {hom} (f,\;g):\mathrm {Hom} _{\mathcal {C}}(X,\;Y)\to _{\mathcal {SET}}\mathrm {Hom} _{\mathcal {C}}(X^{\prime }\;Y^{\prime })$

defined as

$\forall a\in \mathrm {Hom} _{\mathcal {C}}(X,\;Y)\longmapsto g\cdot a\cdot f\in \mathrm {Hom} _{\mathcal {C}}(X^{\prime }\;Y^{\prime })$

Let us turn back again to the typing of f and g

$f\in \mathrm {Hom} _{\mathcal {C}}(X^{\prime },\;Y)$

$g\in \mathrm {Hom} _{\mathcal {C}}(X,\;Y^{\prime })$

Now the strange, “crossed” arrangement of primes does not look so strange any more — the construction has showed the main point.

I think the 5 Oct2006 contribution (that has made the strange “crossed” arrangement of primes “straight”) was benevolent and (in a sense) logical, but erranous.

Physis 05:36, 16 October 2006 (UTC)

---

Thank You for having corrected it. Now, the above argumentation of mine has lost its original purpose. By the way, is my above argumentation correct at all? I do not really understand much to category theory, The above things are just my conjecture based upon esthetical consideration — I have not proven it. I suppose the answer lies in the article Hom functor…

Physis 02:56, 17 October 2006 (UTC)

Yes, your argument is essentially correct. Thanks for pointing out the mistaken edit. In fancy language one can say that the Hom functor Hom(-,-) is contravariant in the first argument and covariant in the second. Hence the funny arrangement of the primes. -- Fropuff 03:14, 17 October 2006 (UTC)

Thank You very much for Your quick answer. Physis 14:03, 17 October 2006 (UTC)

Check for message on talk pages (e.g. major contributions)

• Domino day
• Shamanism
• Talk:Quine#LISP Quine
• Complete partial order#Examples
• Talk:Adjoint functors#Primes put on variables are mispaced?
• Talk:Markov algorithm#Examples
• Sirenik language
• Theory of computation#Other formal definitions of computation
• Siberian Yupik, because of orca wolf debate
• Signature (mathematical logic)
• Assignment (mathematical logic)
• Non-logical symbol
• Derivative (generalizations)#Type theory
• Zipper (data structure)
• Talk:Eskimo#Deleted from article
  • Talk:Eskimo/Lifting out and hue shade
  • Talk:Eskimo/Eskimo in the Platonic realm
• Ultrafilter#Applications
• Many-sorted logic
• Talk:Diagonal lemma/Proof with diagonal formula
• Talk:Diagonal lemma/Proof with diagonal formula/Conjunction and equality reduced to substitution

Make a computing scheme, based on

• logically: combinatory logic
• physically: domino computer

• Gödel numbering for sequences
• Hilbert-style deduction system

Smaller contrib

• hu:Matematikafilozófia

Linkspam

Used Textbooks for Anthropology A site that offers a free student-to-student anthropology textbook exchange

Debated, by let us see

People whom I shall write to

Khanti

If anyone wants samles of Khanti & Manshi folk-songs, I recorded some when I was in Siberia in summer 1996. So please feel free to contact me.Kaz 12:59, 3 September 2006 (UTC)

Talk:Eskimo#Add Smithsonian link?

Hello! I am a writer for the Smithsonian's Center for Education, which publishes Smithsonian in Your Classroom, a magazine for teachers. An online version of an issue titled "Teaching from Objects and Stories, Learning about the Bering Sea Eskimo People" is available at this address:

http://www.smithsonianeducation.org/educators/lesson_plans/eskimo/start.html

If you think your audience would find this valuable, I wish to invite you to include it as an external link. We would be most grateful.

Thank you so much for your attention.

Mathematics and antropology and linguistics

Wrting to User:James Crippen, mentioning

• combinatory logic
• universal attribute grammar
• revitalizing Eskimo
• native marinal biology project
• blurring noun-verb & active-passive… (Jurgen (?) principle)

Linguistics and constructed languages

Applicative and many other jokes at a Tolkien-like contructed language. See for help:

• Applicative voice
• Valency (linguistics)

See also “my page” Lojban

Matter and energy

Main articles: Matter and Energy

Some fields of science see nature as "matter in motion", obeying certain "laws of nature" which science seeks to understand. For this reason the most fundamental science is generally understood to be "physics"—the name for which is still recognizable as meaning that it is the study of nature.

Matter is commonly defined as the substance of which physical objects are composed. It constitutes the observable universe. According to the theory of special relativity, there is no unchangeable distinction between matter and energy, because matter can be converted to energy (see annihilation), and vice versa (see matter creation). The visible components of the universe are now believed to compose only 4 percent of the total mass. The remainder is believed to consist of 23 percent cold dark matter and 73 percent dark energy. The exact nature of these components is still unknown and is currently under intensive investigation by physicists.

The behavior of matter and energy throughout the observable universe appears to follow well-defined physical laws. These laws have been employed to produce cosmological models that successfully explain the structure and the evolution of the universe we can observe. The mathematical expressions of the laws of physics employ a set of twenty physical constants that appear to be static across the observable universe. The values of these constants have been carefully measured, but the reason for their specific values remains a mystery.

See also: Chemistry and Physics

na-lang-stub

Eskimo shamanism

User:Physis/Eskimo shamanism

User:Physis/I put a subpage for the details

User:Physis/baby section comes from this book

User:Physis/Eskimo shamanism2

User:Physis/Eskimo shamanism3

User:Physis/Yksin1

User:Physis/Eskimo shamanism4

User:Physis/Yksin2

User:Physis/Fenevad1