만류 귀종(萬流 歸宗)
학문은 숨겨진 연관성을 찾는 것

경험•현상들에 대한 식견
1. Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically....real successes come to those who start from a physical point of view,

2. 물리 속의 수학:
① The glory of mathematics is that we do not have to say what we are talking about. The glory is that the laws, the arguments, and the logic are independent of what “it” is... 수학과 물리 차이
② the important thing to learn and to remember is the relationship, not the proof...attention should be given not to the trick exactly, but to the mathematical idea involved.
nature does not have to go along with our reasoning

3. This self-reproducing factor of Newton’s laws is thus really not a fundamental feature of nature, but is an important historical feature... 뉴튼의 제2법칙에 대하여
① 양자역학이 고전(경험)역학과 다르다는 파인만 의견은 틀렸다. '역사는 되풀이한다'라는 격언이 입증하듯, 모든 것은 self-reproduce, 지표 정리(Poincaré-Hopf, 아래)를 모르고 하는 소리.
4. a strange thing occurs again and again
5. 충돌•접촉은 에너지 교환: 굴러온 돌이 박힌 돌 뺀다
6. 다른 상황에서의 같거나 비슷한 법칙, 역사는 되풀이 된다

7. 꿈보다 해몽: The trouble with quantum mechanics is not only in solving the equations but in understanding what the solutions mean!

Poincaré-Hopf 정리. Let $M$ be a compact closed surface and $v : M -> TM$ a smooth vector field with isolated zeros. The sum of the indices at the zeros equals the Euler characteristic of $M$.
예: 지구 전체가 물로 덮여 있고 아무런 동요가 없다고 하자. 그 상태에서 물 방울 하나가 떨어져 파문이 생긴다. 그 파문은 vector field를 형성할 것이고 위 정리에 의해 구(sphere)의 오일러 넘버는 2. 그는 그 파문이 영원히 없어지지 않는다는 것. 여기서 물론 지구는 구조적으로 '기' closed, just like 하모닉 진동의 stored 에너지
=> 빛 흡수 및 반사

② 고전(경험) 물리 결과를 확률적 측면으로 본다 => Boltzmann’s law의 상대적 해석

Potential, kinetic energy를 타고난 것과 노력으로 대응

평균(Average), 무게 중심(center of mass): 기체 등 집단적 움직임
1. 기체 분자 압력과 kinetic 에너지,  기체 분자 압력과 kinetic 에너지2
2. quantum number 평균,  quantum number 평균2
* adiabatic 어원 및 그 의미,   average 중요성

일대일 대응 전환(One2one & onto): 답을 직접적으로 구하기 어렵거나 불가능한 때의 우회적 수단
Galois가 5차 방정식의 일반적 radical solution이 존재할 수 없다는 걸 증명하기 위해 그룹과 필드 사이의 one to one& onto를 사용했듯...

1. Galilean 상대성 공리: 정지 좌표계와 등속 좌표계 사이의 일대일 대응 전환
예1: $m_u=\frac{m_0}{\sqrt{1-u^2/c^2}}$ 증명, 예2: inelastic 충돌 경우, 운동량 보존 입증, 예3: elastic 충돌

2. Fourier transformation

* 일반화된 우회 방법
예1: 적분 문제
예2: 속도와 에너지 관계

특수한 경우 일반화: 특례로부터 얻은 intrinsic 성질들을 일반 공리화
1. 드브로이 물질파
2. 유클리드 공간(Euclidean space)의 벡터를 스테이트 벡터(state vector)로
3. 에테르에 대한 지구 속도 측정 불가능을 모든 현상에로의 일반화한 상대성 원리
4. double-slit experiment, Schrödinger equation, Dirac equation 등 주로 전자들만의 연구 결과들 바탕으로 양자 역학 이론 전개
5. 비교: 다르지만, 이상 기체에서 얻은 식을 일반적인 엔트로피로 정의

6. 포텐셜 에너지의 일반화? Topological 에너지(* 하모닉 진동의 stored 에너지, 2021.7.1)
① 포텐셜 에너지와 기체 분포: 고정된 포텐셜 경우 => 포텐셜과 분포 관계가 dynamic 경우로
혼합 기체, 퀀텀 넘버
A toplogical view of a molecule along free electrons trajectories

인간의 보존 속성
어리석은 대중(The presence of the other particles increases the probability of getting one more)

Some proofs
Poynting























Neurophilosophy Science
Genetically engineered 'Magneto' protein remotely controls brain and behaviour

“Badass” new method uses a magnetised protein to activate brain cells rapidly, reversibly, and non-invasively
The toroidal magnetic chamber (Tokamak) of the Joint European Torus (JET) at the Culham Science Centre. Photograph: AFP/Getty Images
The toroidal magnetic chamber (Tokamak) of the Joint European Torus (JET) at the Culham Science Centre. Photograph: AFP/Getty Images

Researchers in the United States have developed a new method for controlling the brain circuits associated with complex animal behaviours, using genetic engineering to create a magnetised protein that activates specific groups of nerve cells from a distance.

Understanding how the brain generates behaviour is one of the ultimate goals of neuroscience – and one of its most difficult questions. In recent years, researchers have developed a number of methods that enable them to remotely control specified groups of neurons and to probe the workings of neuronal circuits.

The most powerful of these is a method called optogenetics, which enables researchers to switch populations of related neurons on or off on a millisecond-by-millisecond timescale with pulses of laser light. Another recently developed method, called chemogenetics, uses engineered proteins that are activated by designer drugs and can be targeted to specific cell types.

Although powerful, both of these methods have drawbacks. Optogenetics is invasive, requiring insertion of optical fibres that deliver the light pulses into the brain and, furthermore, the extent to which the light penetrates the dense brain tissue is severely limited. Chemogenetic approaches overcome both of these limitations, but typically induce biochemical reactions that take several seconds to activate nerve cells.

The new technique, developed in Ali Güler’s lab at the University of Virginia in Charlottesville, and described in an advance online publication in the journal Nature Neuroscience, is not only non-invasive, but can also activate neurons rapidly and reversibly.

Several earlier studies have shown that nerve cell proteins which are activated by heat and mechanical pressure can be genetically engineered so that they become sensitive to radio waves and magnetic fields., by attaching them to an iron-storing protein called ferritin, or to inorganic paramagnetic particles. These methods represent an important advance – they have, for example, already been used to regulate blood glucose levels in mice – but involve multiple components which have to be introduced separately.

The new technique builds on this earlier work, and is based on a protein called TRPV4, which is sensitive to both temperature and stretching forces. These stimuli open its central pore, allowing electrical current to flow through the cell membrane; this evokes nervous impulses that travel into the spinal cord and then up to the brain.

Güler and his colleagues reasoned that magnetic torque (or rotating) forces might activate TRPV4 by tugging open its central pore, and so they used genetic engineering to fuse the protein to the paramagnetic region of ferritin, together with short DNA sequences that signal cells to transport proteins to the nerve cell membrane and insert them into it.
In vivo manipulation of zebrafish behavior using Magneto. Zebrafish larvae exhibit coiling behaviour in response to localized magnetic fields. From Wheeler et al (2016).

When they introduced this genetic construct into human embryonic kidney cells growing in Petri dishes, the cells synthesized the ‘Magneto’ protein and inserted it into their membrane. Application of a magnetic field activated the engineered TRPV1 protein, as evidenced by transient increases in calcium ion concentration within the cells, which were detected with a fluorescence microscope.

Next, the researchers inserted the Magneto DNA sequence into the genome of a virus, together with the gene encoding green fluorescent protein, and regulatory DNA sequences that cause the construct to be expressed only in specified types of neurons. They then injected the virus into the brains of mice, targeting the entorhinal cortex, and dissected the animals’ brains to identify the cells that emitted green fluorescence. Using microelectrodes, they then showed that applying a magnetic field to the brain slices activated Magneto so that the cells produce nervous impulses.

To determine whether Magneto can be used to manipulate neuronal activity in live animals, they injected Magneto into zebrafish larvae, targeting neurons in the trunk and tail that normally control an escape response. They then placed the zebrafish larvae into a specially-built magnetised aquarium, and found that exposure to a magnetic field induced coiling manouvres similar to those that occur during the escape response. (This experiment involved a total of nine zebrafish larvae, and subsequent analyses revealed that each larva contained about 5 neurons expressing Magneto.)

In one final experiment, the researchers injected Magneto into the striatum of freely behaving mice, a deep brain structure containing dopamine-producing neurons that are involved in reward and motivation, and then placed the animals into an apparatus split into magnetised a non-magnetised sections. Mice expressing Magneto spent far more time in the magnetised areas than mice that did not, because activation of the protein caused the striatal neurons expressing it to release dopamine, so that the mice found being in those areas rewarding. This shows that Magneto can remotely control the firing of neurons deep within the brain, and also control complex behaviours.

Neuroscientist Steve Ramirez of Harvard University, who uses optogenetics to manipulate memories in the brains of mice, says the study is “badass”.

“Previous attempts [using magnets to control neuronal activity] needed multiple components for the system to work – injecting magnetic particles, injecting a virus that expresses a heat-sensitive channel, [or] head-fixing the animal so that a coil could induce changes in magnetism,” he explains. “The problem with having a multi-component system is that there’s so much room for each individual piece to break down.”

“This system is a single, elegant virus that can be injected anywhere in the brain, which makes it technically easier and less likely for moving bells and whistles to break down,” he adds, “and their behavioral equipment was cleverly designed to contain magnets where appropriate so that the animals could be freely moving around.”

‘Magnetogenetics’ is therefore an important addition to neuroscientists’ tool box, which will undoubtedly be developed further, and provide researchers with new ways of studying brain development and function.

Reference

Wheeler, M. A., et al. (2016). Genetically targeted magnetic control of the nervous system. Nat. Neurosci., DOI: 10.1038/nn.4265 [Abstract]