Chuluundorj.B

20191

Interdisciplinarity and Multidisciplinarity

in research

PART I

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Imagination is more important than

knowledge (Albert Einstein)

Knowledge creation is a integral process.

Каждый день создается 2,5 нониллиона 1035 байтданных (Журавлева ЕЮ Вызовы технологиибольших данных для современных гуманитарныхнаук ВФ 2018 №9, стр 51)

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Peter V. Coveney. (Big data need big theory too)

We would need some 1032 bits of information to definethe human body.

Example:

Analysis of big data associations between air quality andhealth – extra ordinary complexity of biomedical data

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Human brain, in that’s way human behavior, psychology arean object of interdisciplinary study.

In quantum physics brain waves are most dynamicphenomena of analysis (quantum entanglement,superposition - Christof Koch, Klaus Hepp

2006. Quantum mechanics in the brain)

Example:

Application of electromagnetic and gravitational forces in themedicine, neuropsychology, computer science and militaryresearch. (MRI, x-ray, EEG)

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In terms of methodology, human behavior, psychologypresent broad area of research in terms of scalar field andvector, tensor fields in 2D and 3D

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Vector analysis

Set of Neurons

Brain waves

Semantic symbols

Mental or semantic structures

Object of analysis:

EEG + vector analysis

Object of analysis in

vector/tensor space

According to Civon der Malsburg, brain states may be regarded as semanticsymbols. (Nervous structures with dynamical links. 1996, Germany)

Human memory organization: Words and numbers

Two-dimensional semantic (metric) space - a distance between components of

subsets is measured by using standard Euclidean distance function:

нөхөр-friend,

амьтан- animal,

нохой- dog,

муур-cat,

чоно-wolf.

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Cosine similarity, cosine of two vectors (Euclidean dot product) must be

applied to analysis of distance between components of a set, analysis of

values or benefits affecting custom decision making (as comparison of two

vectors using angular distance between them)

Dot product 𝑎 ∙ 𝑏𝐴 ∙ 𝐵 = 𝐴 𝐵 cos 𝜃𝑊 = 𝐹 ∙ 𝑥 = 𝐹 𝑥 cos 𝜃

Vector space analysis of consumer’s product valuation and benefits

Values: Personal values – closely linked to needs (PV)

Consumption values – elegant house, prestigious car etc. (CoV)

Cultural values – socio - cultural environment, beliefs (CV)

Benefits: social benefits – social status (SB)

affective benefits – feelings (AB)

functional benefits – concrete attributes for using (FB)

epistemic benefits – curiosity, novelty (EB)

aesthetic benefits – sense of beauty (AeB)

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𝑑 𝑥, 𝑦 =

𝑖=1

𝑛

(𝑥𝑖 − 𝑦𝑖)2

Distance metrics

𝑑 𝑥, 𝑦 =σ(𝑥𝑖𝑦𝑖)

σ(𝑥𝑖)2σ(𝑦𝑦)2

cosine correlation

PS: PV, CoV, CV depend the age and life style

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Vector analysis

Val

ues

Reaction time (waves)

There is used Euclidean dot product formula sl.13

(𝐴𝑖 𝑎𝑛𝑑 𝐵𝑖 are components of vector A and B respectively)

𝑃𝑉

Co𝑉

𝐶𝑉

Analysis of common effect of values or benefits - Vector addition

Values: (x)

Personal value - PV

Consumption value - 𝐶𝑜𝑉

Cultural value - CV

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Benefits (y)

Social status – SB

Function benefit – FB

Aesthetic benefit – AB

values

ben

efit

s

x

y

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x - 𝐹𝑣

y - 𝐹𝑏

Pythagorean theorem - resultant displacement

𝑐2 = 𝑎2 + 𝑏2 → 𝑐 = 𝑎2 + 𝑏2

In this case: 𝑑2 = ∆𝑥2 + ∆𝑦2 → 𝑑 = ∆𝑥2 + ∆𝑦2

tan 𝜃 =Δ𝑦

Δ𝑥→ 𝜃 = tan−1

Δ𝑦

Δ𝑥

Sum of values 𝐹𝑣 and benefit 𝐹𝑏

If only two components:

Vector addition summary effect of valuesIf three and more components:

Values (x)

Personal value - PV

Consumption - 𝐶𝑜𝑉

Cultural - CV

CV

y

x

𝑅𝑥 = 4 + 6 + 13 = 23𝑅𝑦 = 2 + 5 + 9 = 16

𝑅𝑥 = 𝐶𝑉𝑥 + 𝐶𝑜𝑉𝑥 + 𝑃𝑉𝑥

𝑅𝑦=𝐶𝑉 𝑦+𝐶𝑦𝑉 𝑦+𝑃𝑉 𝑦

D-distanceT-time

F (wave)

Distance-xT time -y

Value affecting

human decision

making – brain

wave takes some

distance in someshirt time 15

Sum of values/benefit in human decision Linear effect

making presented in the form of net force NON - Linear effect

Vector addition

𝐹𝑛𝑒𝑡 =𝐹𝑖 = 𝐹1 + 𝐹2 + 𝐹3 +⋯

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a specific case for neuro-

marketing, strong involvement

of the right hemisphere.

Distance (metrics) based or cosine similarity measurement is one of

effective instruments for classification (clustering) of objects according to

its properties and features.

Human semantic vocabulary classification is a result of human perception

of reality – N (static) – V (dynamic)

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Human mental (perceptual) classification of objects must be interpreted in terms

of algebraic operation (Boolean algebra)

This is one simple example of universality of human, psychological mechanism and actions

What about animal perception of feeds or?

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Decision making in 2D and 3D

Inspirational applications

Different observes will disagree or agree with the speed of light how axes are rotated.

Minkowski Space – time: Space–time in special relativity

Top: frame F′ moves at velocity v along the x-axis of frame F.

Bottom: frame F moves at velocity −v along the x′-axis of frame F′.[11]

Some ideas of theory of relativity is applied in psychology, for example in the perception of color, size, sharp, distance

Decision making as psychological act takes place in different frameworks which must be described as different

coordinates

Differences in life style, social status and cultural and consumption values must be described in different coordinates20

Different choices – neural computation non–linearity in decision making

Coordinate system in curved space - different frameworks for human perception

Contravariance the vector component has gotten bigger as thecoordinate system length unit has gotten smaller.. Covariance thevector component has varied in the same way as the coordinatesystem length.

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Reg vector is an eigenvector of the linear transformation

Case: Basic differences in culture, life style and its perception by people of different

social and cultural backround.

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In human behavior, psychology:

Handling internal and external negative influences as a

resisting forces (financial etc), change of motivation,

stresses

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Cross product

Cross product 𝑎 × 𝑏

𝐴 × 𝐵 = 𝐴 𝐵 sin 𝜃

torque Ԧ𝐹 ⊗ Ԧ𝜏 = 𝐹 𝜏 sin 𝜃

Counter clockwise – positive direction

𝐹 sin 𝜃

𝐷 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝐹 cos 𝜃

W (work)=F∙AB

A B

F

D (distance)

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To explore this idea:

Motivation and inspiration through non-Linear processes overcoming external influences:

Torque 𝜏 = 𝐹𝜏

Ԧ𝜏 = 𝐹 𝜏 sin 𝜃

Torque is the tendency to produce a change in rotational motion.

Torque is proportional to the magnitude of F and to the distance 𝜏 frome the axis.

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There an idea to study non-linearity in human behavior, psychology:Emotional or motivational force applied to direction “x” is transformed to a force in direction “y”

Vector/tensor space: Advertising space on the Internet- the primary source of revenue – sale of advertisingspace - Nash equilibrium – Game theory. (Nash, JohnEquilibrium points in n-persons game 1950. NAS)

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PART II

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If I have seen further it is by standing on

the shoulders of Giants (Isaak Newton)

Prime number are building blocks of all numbers, in that’sway – of our understanding of the nature.

Prime numbers and fundamental particles, basiccomponents of thinking (symbols, concepts, prototypes)

Primes behave almost like a crystal (quasicrystal) (canonly divided by 1 and themselves).

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Number sequences and operations

Comparison of the spontaneous activity of the brain neurons

with the random properties of the sequence of prime numbers

can shed certain light on the problem: Whether mathematics

belongs completely to the outer world or it is a production of our

brain activity.

All types of information are encoded by nerve cells into

sequences of pulses of similar shape. (A, Bershadskii. Hidden

periodicity and chaos in the sequence of prime numbers).

Where is some similarities (or basic differences) between number sequence and sequence of phenomenon in the nature and human life.

Arithmetic Sequence

In an Arithmetic Sequence the difference between one term and the next is a constant.

Constant – based Linear changes (Linear function)

Geometric Sequences

In a Geometric Sequence each term is found by multiplying the previous term by a constant.

Linear and NON-linear changes: (Linear and exponential growth function)

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Fibonacci Sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ….

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For example 5 and 8 make 13, 8 and 13 make 21, and so on

This spiral is found in nature!

Fibonacci Sequence

Suppose you have some amoebas in a petri dish (glass to culture cells such asbacteria). Every minute, all adult amoebas produce one child amoeba, and all childamoebas grow into adults

The equation of this system is

adultst+1 = adultst + children1

childrent+1 = adultst

which we can rewrite in matrix form like

Vt+1 = A ∙ Vtadultst+1childrent+1

= 1 11 0

∙ adultstchildrent

The total population is the Fibonacci Sequence.

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The system goes toward the green line, which is an eigenspace with λ=(1+ 5)/2>1

Mona Lisa eigenvector transformation.35

Prime numbers can explain why in music some complexrhythms take a long time to repeat (Mongolian traditionallong song?)

Музыкальное чередование звуков имеетаритмологический характер для объяснения чегоиспользуется теория прерывных функций (БугаевН.В.1905)

Repetitive structures in music, rhythmic beats and loopingbreaks (Beatles’ song, Mozart) have analogy tomathematical structures and number operations inspatial-temporal reasoning.

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Два эстетических идеала: идеал текучести (народныйтанец, классический балет) и идеал расчлененного,изолированного движения (постмодерн) – оба этихидеала резонируют с идеями гармонии. (Сироткина И.ЕДискретное и континуальнее в танце. ВП 2016. №10. 138)

Music also has fractal side

Price change as a behavior of markets also has fractal side

So primes are used for analysis of fractals of different types.

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Sequence of components in human perception and its reflection in sequence of verbal structures (syntax)

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adj 1 adj 2 adj 3 adj 4 N

Хуучин жижиг хүрэн модон байшин

(Old small brown wooden house)

adj 1 adj 2 adj 3 adj 4 N

New Japanese red sport car

𝒂 + 𝒃 𝒎+ 𝒄 + 𝒅 𝒏

c d n a b mНамхан цэнхэр хаалгатай өндөр төмөр хашаа

𝒄 + 𝒅 𝒏 + 𝒂 + 𝒃 𝒎a b c d e f j

Old large wooden house with extra bedroom decorating.

𝒂 + 𝒃 + 𝒄 𝒅 + 𝒆 + 𝒇 ∙ 𝒋

Sequence of components as a reflection of object features or properties (size, color, shape etc)

human visual perception in space – time coordinate simultaneous, its verbal interpretation is

not-simultaneous and has linear sequence. Is it phenomenon.

Number (and vector) operations in relation to verbal structures

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Хар цамц (black shirt)

Хар шөл (meat soup),

Хар шөнө (dark night),

Хар санаа (hostility)

addition and multiplication in mental verbal structures

1+1+4=2×3

1+4+1=3×2

Number operations

PEMDAS presents an effective instrument of analysis at discourse level.

Order of Operations

Do things in Parentheses First

Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract

Multiply or Divide before you Add or Subtract

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Order of operations /үйлдлийн дараалал/

BEDMAS (PEDMAS)

B-Brackets

P-Parenthesis

E-Exponents

D-Division

M-Multiplication

A-Addition

S-Subtraction

Some order of operations in

human verbal syntax best

way to develop NLP

Following propositions must be described in terms of BEDMAC and (PEMDAS).

1.Гэр хорооллын оршин суугчдыг орон сууцтай болгох – public housing

2.Байрны зээлийг бага хүүтэй олгох – decreasing loan percentage

3.Эрчим хүчний хангамжийг шийдэх – improving electricity delivery

4.Утаа арилж агаарын бохирдол буурах – cleaning up the smoke and reducing air pollution

5.Хүн амын эрүүл мэндэд учрах эрсдэл буурах – decreasing health risks for people

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Propositions {1; 5}Propositions (2; 3)Propositions [(2+3)∙ 1]Propositions [4+5]

Concluding propositions:

(2+3)∙ 1(1+4)∙5

topic 5 – эрүүл аж төрөх

Alternative or text analysis in computer science

topic 1 – байртай болох

Sequence of number operations - Randomization of text (data)structures according to its degree of significance, hierarchy of logico-semantics relations.

Order of operations supports to build mental mapping as a logico-semantics tree of a text, web

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Comments on prime (number) factorization and structural analysis.

GCF, GCD and LCM must be applied to research in linguistics, computer science, economics and psychology.

factors of 15 are: 1, 3, 5, 15

factors of 30 are: 1, 2, 3, 5, 6, 10 15, 30

divisors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54

divisors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

multiplies of 4 are: 4, 8, 12, 16, 20, 24, 28…

multiplies of 5 are: 5, 10, 15, 20, 25, 30, 35…

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15-GCF

6-GCD

20-LCM

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Prime factorization in arithmetics and linguistics

Following trees present another case to use GCF in the syntax:

Prime factorization is used

for clustering of objects and structures,

analysis of complex problems leading into subproblems,

building decision tree

Хамгийн бага нийтлэг үржвэр

Хамгийн их нийтлэг фактор (хуваагч)

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LCM - common semantic component in metaphor:

Metaphors on economics:

A useful metaphor for production in an economy comes from the kitchen

Economic growth springs from better recipes, not just from more cooking

multiples of 3:3, 6, 9, 12, 15, 18 …

multiples of 5:5, 10, 15, 20, 25 … LCM=15

What is a common component in production

and kitchen

What is a common component in economic

growth and recipes

Number theory → to cryptology, digital signatures, useridentification, breaking of codes (of computers or credit cards)

RSA algorithm Rivest R.L, Shamir A, Adleman L; Method forobtaining digital signatures and public key cryptosystems(ACM V.21. 1978) is used for on-line transaction.

Factoring digits to find a prime number → to secure or breakcodes.

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RSA algorithmPublic key modulus “n” and exponent “e” Private key modulus “n” and exponent “d”19x31=589 589 – result of multiplying two primes (19, 31)To try all of the primes that are less than 589To find which prime numbers multiplied together come to 589This works for smaller numbers

Is it like structural analysis to find two smallest components (elements) of key number….?Principle of binarity….?

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The way public key cryptography works, is to attach largenumber such as 384 119 982 448 028 as a “key” to a secretmessage.

But it is very difficult to find the prime factors of a large number.

If you find it….

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Science is a way of thinking much more than it is a

body of knowledge

Carl Sagan

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