Research – #3 Synthesis (Art & Food)

ART 

Combine Painting

Robert Rauschenberg, untitled “combine,” 1963

(http://www.theartstory.org/artist-rauschenberg-robert.htm)

Artwork that incorporates various objects into a painted canvas surface, creating a sort of hybrid between painting and sculpture.

Items attached to paintings might include photographic images, clothing, newspaper clippings, ephemera or any number of three-dimensional objects. The term is most closely associated with the artwork of American artist Robert Rauschenberg (1925–2008)

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COLOURS

Colour interval

(Claude Tousignant. Double quatre-vingt-un (1970))

• Spatial interaction of colours – wet/dry, cool/warm, dark/light

– Wavelength of colours

ART: Pointillism

 

Technique of painting in which small, distinct dots of pure color are applied in patterns to form an image

The technique relies on the ability of the eye and mind of the viewer to blend the color spots into a fuller range of tones.

Painting is inherently subtractive, but Pointillist colors often seem brighter than typical mixed subtractive colors. This may be partly because subtractive mixing of the pigments is avoided, and partly because some of the white canvas may be showing between the applied dots.

(http://scienceblogs.com/cognitivedaily/2009/02/25/visual-illusion-may-explain-th/)

Monnier and Shevell believe this illusion is due to an “antagonism” that occurs in the brain in response to just some the cones used in the eye to detect color: S-cones, which respond to the shortest “blue” wavelengths of light. That’s because the differences between what was perceived and the actual color seen can be completely explained by the S-cone response: no differences in M-cone (green) or L-cone (red) responses were observed.

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CUISINE

Fusion Food

Cuisine that combines elements of different culinary traditions. Cuisines of this type are not categorized according to any one particular cuisine style and have played a part in innovations of many contemporary restaurant cuisines since the 1970s.

Research – #3 Synthesis (Mathematics)*

MATHEMATICS

Combination

(http://en.wikipedia.org/wiki/Combination) 

In mathematics, a combination is a way of selecting members from a grouping, such that (unlike permutations) the order of selection does not matter. In smaller cases it is possible to count the number of combinations. For example given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange. More formally, a k–combination of a set S is a subset of k distinct elements of S.

If the set has n elements, the number of k-combinations is equal to the binomial coefficient

 or written as

Number of k-combinations from given set S of n elements often denoted as C(n,k).

e.g. 3-element subsets of a 5-element set

Bijection between 3-subsets of a 7-set (left) and 3-multisets with elements from a 5-set (right)

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Pascal’s Triangle

In mathematics, Pascal’s triangle is a triangular array of the binomial coefficients. It is named after the French mathematician Blaise Pascal in much of the Western world, although other mathematicians studied it centuries before him in India, Iran, China, Germany, and Italy.

The rows of Pascal’s triangle are conventionally enumerated starting with row n = 0 at the top. The entries in each row are numbered from the left beginning with k = 0 and are usually staggered relative to the numbers in the adjacent rows. A simple construction of the triangle proceeds in the following manner. On row 0, write only the number 1. Then, to construct the elements of following rows, add the number above and to the left with the number above and to the right to find the new value. If either the number to the right or left is not present, substitute a zero in its place. For example, the first number in the first row is 1 (the sum of 0 and 1), whereas the numbers 1 and 3 in the third row are added to produce the number 4 in the fourth row.

Other countries:

Yang Hui triangle

         

Yang Hui (Pascal’s) triangle, as depicted by the Chinese using rod numerals.

Rod numerals are small bars used by mathematicians for calculation in ancient China, Japan, Korea and Vietnam. They are either placed horizontally or vertically to represent any number and any fraction.

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Magic square

(http://en.wikipedia.org/wiki/Magic_square)

In recreational mathematics, a magic square is an arrangement of distinct numbers (i.e. each number is used once), usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the forward and backward main diagonals, all add up to the same number.

Normal magic squares of all sizes except 2 × 2 (that is, where n = 2) can be constructed. The 1 × 1 magic square, with only one cell containing the number 1, is trivial. The smallest (and unique) nontrivial case, 3 × 3, is shown below.

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Geometric Magic Square

(http://en.wikipedia.org/wiki/Geometric_magic_square)

traditional magic square is a square array of numbers (almost always positive integers) whose sum taken in any row, any column, or in either diagonal is the same target number.

                       

A geomagic square, on the other hand, is a square array of geometrical shapes in which those appearing in each row, column, or diagonal can be fitted together to create an identical shape called the target shape.

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Magic circle

(http://en.wikipedia.org/wiki/Magic_circle_(mathematics))

Invented by the Song dynasty (960–1279) Chinese mathematician Yang Hui (c. 1238–1298). It is the arrangement of natural numbers on circles where the sum of the numbers on each circle and the sum of numbers on diameter are identical. One of his magic circles was constructed from 33 natural numbers from 1 to 33 arranged on four concentric circles, with 9 at the center.

Yang Hui’s magic concentric circle has the following properties

• The sum of the numbers on four diameters = 147，
  • 28 + 5 + 11 + 25 + 9 + 7 + 19 + 31 + 12 = 147
• The sum of 8 numbers plus 9 at the center =147;
  • 28 + 27 + 20 + 33 + 12 + 4 + 6 + 8 + 9 = 147
• The sum of eight radius without 9 =magic number 69: such as 27 + 15 + 3 + 24 = 69
• The sum of all numbers on each circle (not including 9) = 2 × 69

There exist 8 semicircles, where the sum of numbers = magic number 69; there are 16 line segments(semi circles and radii) with magic number 69, more than a 6 order magic square with only 12 magic numbers.

Yang Hui 8 magic circles in a square 八阵图

64 numbers arrange in circles of eight numbers, total sum 2080, horizontal / vertical sum =260.

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Patterns obtained

Sierpinski triangle

  

The pattern obtained by coloring only the odd numbers in Pascal’s triangle closely resembles the fractal called the Sierpinski triangle. This resemblance becomes more and more accurate as more rows are considered; in the limit, as the number of rows approaches infinity, the resulting pattern is the Sierpinski triangle, assuming a fixed perimeter. More generally, numbers could be colored differently according to whether or not they are multiples of 3, 4, etc.; this results in other similar patterns.

fractal and attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. Originally constructed as a curve, this is one of the basic examples of self-similar sets, i.e. it is a mathematically generated pattern that can be reproducible at any magnification or reduction.

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 Koch snowflake

The Koch snowflake (also known as the Koch star and Koch island) is a mathematical curve and one of the earliest fractal curves to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled “On a continuous curve without tangents, constructible from elementary geometry”

Tesselation of Koch snowflake

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Fractals by Hausdorff dimensions

(http://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension)

According to Falconer, one of the essential features of a fractal is that its Hausdorff dimension strictly exceeds its topological dimension. Presented here is a list of fractals ordered by increasing Hausdorff dimension, with the purpose of visualizing what it means for a fractal to have a low or a high dimension.

Research – #3 Synthesis (Nuclear Physics & Biology)

FUSION

Nuclear fusion

(http://chemwiki.ucdavis.edu/Physical_Chemistry/Nuclear_Chemistry/Fission_and_Fusion)

Nuclear reaction in which two or more atomic nuclei collide at a very high speed and join to form a new type of atomic nucleus. During this process, matter is not conserved because some of the matter of the fusing nuclei is converted to photons (energy). Fusion is the process that powers active or “main sequence” stars.

A substantial energy barrier of electrostatic forces must be overcome before fusion can occur. At large distances, two naked nuclei repel one another because of the repulsive electrostatic force between their positively charged protons. If two nuclei can be brought close enough together, however, the electrostatic repulsion can be overcome by the attractive nuclear force, which is stronger at close distances.

Fusion power

Energy generated by nuclear fusion processes. In fusion reactions, two light atomic nuclei fuse to form a heavier nucleus (in contrast with fission power). In doing so they release a comparatively large amount of energy arising from the binding energy due to the strong nuclear force which is manifested as an increase in temperature of the reactants. Fusion power is a primary area of research in plasma physics.

The Sun is a natural fusion reactor.

Fusion vs. fission

Fission is the splitting of a heavy nucleus into lighter nuclei and fusion is the combining of nuclei to form a bigger and heavier nucleus. The consequence of fission or fusion is the absorption or release of energy.

The electrostatic force between the positively charged nuclei is repulsive, but when the separation is small enough, the attractive nuclear force is stronger. Therefore, the prerequisite for fusion is that the nuclei have enough kinetic energy that they can approach each other despite the electrostatic repulsion.

Enthalpy of fusion

The enthalpy of fusion also known as (latent) heat of fusion is the change in enthalpy resulting from heating a given quantity of a substance to change its state from a solid to a liquid. The temperature at which this occurs is the melting point.

The ‘enthalpy’ of fusion is a latent heat, because during melting the introduction of heat cannot be observed as a temperature change, as the temperature remains constant during the process. The latent heat of fusion is the enthalpy change of any amount of substance when it melts. When the heat of fusion is referenced to a unit of mass, it is usually called the specific heat of fusion, while the molar heat of fusion refers to the enthalpy change per amount of substance in moles.

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Stellar collision
(http://www.universetoday.com/107244/can-stars-collide/)

Potential stellar collision. Credit: Chandra

Coming together of two stars, which through the force of gravity merge into one larger unit. Astronomers predict that events of this type occur in the globular clusters of our galaxy about once every 10,000 years. Scientists have only recently been able to observe a stellar merger. A series of stellar collisions in a dense cluster over a short period of time can lead to an intermediate-mass black hole via “runaway stellar collisions”.

**merge requires a kaboom to overcome barriers

Colliding Neutron Stars Create Black Hole and Gamma-ray Burst

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BIOLOGY

Sensor fusion

Combining of sensory data or data derived from sensory data from disparate sources such that the resulting information is in some sense better than would be possible when these sources were used individually. The term better in this case can mean more accurate, more complete, or more dependable, or refer to the result of an emerging view, such as stereoscopic vision (calculation of depth information by combining two-dimensional images from two cameras at slightly different viewpoints).

Research – #3 Synthesis (Music)

MUSIC 

Sound synthesis is the technique of generating sound, using electronic hardware or software, from scratch. The most common use of synthesis is musical, where electronic instruments called synthesizers are used in the performance and recording of music. Sound synthesis has many applications both academic and artistic, and we commonly use synthesizers and synthesis methods to:

• Generate interesting and unique sounds or timbres incapable of being produced acoustically.
• Recreate or model the sounds of real-world acoustic instruments or sounds.

Facilitate the automation of systems and processes (text-to-speech software, train station P.A.s)

Research – #3 Synthesis (Philosophy)

PHILOSOPHY

The triad thesis, antithesis, synthesis is often used to describe the thought of German philosopher Georg Wilhelm Friedrich Hegel. Hegel never used the term himself.

• The thesis is an intellectual proposition.
• The antithesis is simply the negation of the thesis, a reaction to the proposition.
• The synthesis solves the conflict between the thesis and antithesis by reconciling their common truths and forming a new thesis, starting the process over.

**Interesting thing to note here, in which the combination of two seemingly conflicted issues would propose a new thesis to reconcile.

Research – #3 Synthesis (Chemistry)

Definition: combination of two or more entities that together form something new; alternately, it refers to the creating of something by artificial means

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CHEMISTRY 

Purposeful execution of chemical reactions to obtain a product, or several products. This happens by physical and chemical manipulations usually involving one or more reactions. In modern laboratory usage, this tends to imply that the process is reproducible, reliable, and established to work in multiple laboratories.

A + B → AB

Organic Synthesis

Special branch of chemical synthesis and is concerned with the construction of organic compounds via organic reactions. Organic molecules can often contain a higher level of complexity compared to purely inorganic compounds, so the synthesis of organic compounds has developed into one of the most important branches of organic chemistry.

Peptide synthesis

In organic chemistry, peptide synthesis is the production of peptides, which are organic compounds in which multiple amino acids are linked via amide bonds which are also known as peptide bonds. The biological process of producing long peptides (proteins) is known as protein biosynthesis.

Electrosynthesis

synthesis of chemical compounds in an electrochemical cell 

The yield of an electrosynthesis is expressed both in terms the chemical yield and current efficiency. Current efficiency is the ratio of Coulombs consumed in forming the products to the total number of Coulombs passed through the cell. Side reactions decrease the current efficiency.

Total synthesis 

complete chemical synthesis of an organic molecule from simpler pieces called precursors. It usually refers to a process not involving the aid of biological processes

Photosynthesis

 

Process used by plants and other organisms to convert light energy, normally from the Sun, into chemical energy that can be later released to fuel the organisms’ activities. This chemical energy is stored in carbohydrate molecules, such as sugars, which are synthesized from carbon dioxide and water.

Photosynthesis maintains atmospheric oxygen levels and supplies all of the organic compounds and most of the energy necessary for life on Earth.

The leaf is the primary site of photosynthesis in plants.

DNA Synthesis

natural or artificial creation of deoxyribonucleic acid (DNA) molecules 

• DNA replication – DNA biosynthesis (in vivo DNA amplification)

In nature, such molecules are created by all living cells through the process of DNA replication, with replication initiator proteins splitting the existing DNA of the cell and making a copy of each split strand, with the copied strands then being joined together with their template strand into a new DNA molecule. Various means also exist to artificially stimulate the replication of naturally occurring DNA, or to create artificial gene sequences.

• Polymerase chain reaction – enzymatic DNA synthesis (in vitro DNA amplification)

e.g. Ethidium bromide-stained PCR products after gel electrophoresis. Two sets of primers were used to amplify a target sequence from three different tissue samples. No amplification is present in sample #1; DNA bands in sample #2 and #3 indicate successful amplification of the target sequence. The gel also shows a positive control, and a DNA ladder containing DNA fragments of defined length for sizing the bands in the experimental PCRs.

A polymerase chain reaction is a form of enzymatic DNA synthesis in the laboratory, using cycles of repeated heating and cooling of the reaction for DNA melting and enzymatic replication of the DNA.

• Gene synthesis – physically creating artificial gene sequences

Artificial gene synthesis is the process of synthesizing a gene in vitro without the need for initial template DNA samples. In 2010 J. Craig Venter and his team were the first to use entirely synthesized DNA to create a self-replicating microbe, dubbed Mycoplasma laboratorium.