1A) Michael Nielsen Principles of Effective Research (link)
1B) A classic by Jacques Hadamard: The Psychology of Invention in the Mathematical Field (link)
2) Einstein as a Student (by Dudley Herschbach)
3) Einstein 1905: The Standard of Greatness (by John S. Rigden)
4) Missed Opportunities (by Freeman Dyson)
6) How different people think (some people think abstractly, some think visually) (interview of Temple Grandin)
7) Notes from the book Einstein: 1905 (by John S. Rigden)
a) Working from the contradictions. Contradictions stimulated him
b) “The antipathy of those scientists towards the atomic theory can be indubitably traced to their positivistic philosophical attitude. Even scholars of audacious spirit can be obstructed in the interpretation of facts by philosophical prejudices. The prejudice ... consists in the faith that facts themselves can and should yield scientific knowledge without free conceptual construction”
Einstein rejected this exclusively fact-based philosophy. Such a philosophy constrained the creative mind which, he believed, was capable of developing general laws that went beyond the description of known facts and, in the process, led to new knowledge.
c) The March 1905 paper exposes the way Einstein’s mind worked. He begins his March paper in typical Einstein fashion. Here is the first sentence:
There exists a profound formal difference between the theoretical conceptions physicists have formed about gases and other ponderable bodies, and Maxwell’s theory of electromagnetic processes in so-called space.
The issue appears here in stark contrast: the discontinuity of gases consisting of localized atoms and the continuity of light (electromagnetic processes) propagating in empty spaces. Einstein immediately directs our attention to the fundamental nature of the issue. He often worked from generalizations or principles that were seen as contradictory – they fueled his imagination. Once he identified a contradiction, Einstein would generalize it and then be guided by its implications until a resolution was found, frequently in the form of profound new insights. In addition, he often showed how long-held preconceived notions were invalid. This same approach appears again in his May and June papers.
In Einstein’s “profound formal difference” merely an abstract, academic issue? Not at all. Many phenomena of Nature are a direct consequence of mutual interactions between unlocalized (continuous) radiation and localized (discontinuous) matter and it is when radiation and particles must be treated together, as in the case of blackbody radiation, that problems emerge. Forty years later, in his “Autobiographical Notes,” Einstein referred to the 1905 period and wrote that “one is struck by the dualism which lies in the fact that the material point in Newton’s sense and the field as continuum are used as elementary concepts side by side.” Einstein recognized this in 1905. He was convinced that his problems with the juxtaposition of particles and waves. His March paper was a direct outcome of that knowledge.
d)
In addition to a substantive base, the papers of 1905 also provided Einstein with a procedural base. Einstein started his March and June papers with contradictory images and new physics resulted when Einstein resolved the contradictions. In the March and June contradictions, there is irony. In March Einstein could be seen as rejecting Maxwell’s electromagnetic wave theory of light in favor of a particle theory; then in June, three months later, Einstein could be seen as contradicting himself by rescuing Maxwell’s electromagnetism from internal contradictions. Einstein used contradictions because they opened avenues of reflective thought that led him to issues deeper than the apparent contradiction. Anyone can see contradictions, but Einstein saw in the contradictions what others did not. All physicists saw light as continuous waves and matter as discontinuous particles, but no physicist other than Einstein saw in this a contradiction.
Einstein was driven to simplify and unify. These two principles dominated his approach to physics. In his March 1905 paper, Einstein brought radiation and matter together by making radiation, like matter, particle in nature. At the same time, Einstein recognized that the facts, interference and diffraction, fit beautifully with the wave theory of light. So, driven by his need to bring disparate views together, Einstein called for “a kind of fusion” of the wave and particle theories of light.
The June paper exudes simplicity. The entire special theory of relativity is derived from two simple principles, the concepts of space and time, which are unified and brought out of their Newtonian isolation. A world with absolute space existing apart from and independent of absolute time was turned into a world where space and time are joined. Energy and mass, never before regarded by any physicist as having anything to do with each other, were made one as a result of Einstein’s September paper.
8) Excerpt from The Meaning of Relativity (by Albert Einstein)
The theory of relativity is intimately connected with the theory
of space and time. I shall therefore begin with a brief investigation
of the origin of our ideas of space and time, although in
doing so I know that I introduce a controversial subject. The
object of all science, whether natural science or psychology, is
to co-ordinate our experiences and to bring them into a logical
system. How are our customary ideas of space and time related
to the character of our experiences?
The experiences of an individual appear to us arranged in a
series of events; in this series the single events which we remember
appear to be ordered according to the criterion of \earlier"
and \later," which cannot be analysed further. There exists,
therefore, for the individual, an I-time, or subjective time. This
in itself is not measurable. I can, indeed, associate numbers with
the events, in such a way that a greater number is associated
with the later event than with an earlier one; but the nature of
this association may be quite arbitrary. This association I can
de.ne by means of a clock by comparing the order of events furnished
by the clock with the order of the given series of events.
We understand by a clock something which provides a series of
events which can be counted, and which has other properties of
which we shall speak later.
By the aid of speech di.erent individuals can, to a certain
extent, compare their experiences. In this way it is shown that
certain sense perceptions of di.erent individuals correspond to
each other, while for other sense perceptions no such correspondence
can be established. We are accustomed to regard as real
those sense perceptions which are common to di.erent individuals,
and which therefore are, in a measure, impersonal. The natural
sciences, and in particular, the most fundamental of them,
physics, deal with such sense perceptions. The conception of
physical bodies, in particular of rigid bodies, is a relatively constant
complex of such sense perceptions. A clock is also a body,
or a system, in the same sense, with the additional property that
the series of events which it counts is formed of elements all of
which can be regarded as equal.
The only justi.cation for our concepts and system of concepts
is that they serve to represent the complex of our experiences;
beyond this they have no legitimacy. I am convinced that
the philosophers have had a harmful e.ect upon the progress
of scienti.c thinking in removing certain fundamental concepts
from the domain of empiricism, where they are under our control,
to the intangible heights of the a priori. For even if it should
appear that the universe of ideas cannot be deduced from experience
by logical means, but is, in a sense, a creation of the
human mind, without which no science is possible, nevertheless
this universe of ideas is just as little independent of the nature
of our experiences as clothes are of the form of the human body.
This is particularly true of our concepts of time and space, which
physicists have been obliged by the facts to bring down from the
Olympus of the a priori in order to adjust them and put them
in a serviceable condition.
essential here also to pay strict attention to the relation of
experience to our concepts. It seems to me that Poincar.e clearly
recognized the truth in the account he gave in his book, \La
Science et l'Hypothese." Among all the changes which we can
perceive in a rigid body those are marked by their simplicity
which can be made reversibly by an arbitrary motion of the
body; Poincar.e calls these, changes in position. By means of
simple changes in position we can bring two bodies into contact.
The theorems of congruence, fundamental in geometry, have to
do with the laws that govern such changes in position. For the
concept of space the following seems essential. We can form new
bodies by bringing bodies B, C, . . . up to body A; we say that
we continue body A. We can continue body A in such a way that
it comes into contact with any other body, X. The ensemble of
all continuations of body A we can designate as the \space of
the body A." Then it is true that all bodies are in the \space of
the (arbitrarily chosen) body A." In this sense we cannot speak
of space in the abstract, but only of the \space belonging to a
body A." The earth's crust plays such a dominant r^ole in our
daily life in judging the relative positions of bodies that it has
led to an abstract conception of space which certainly cannot be
defended. In order to free ourselves from this fatal error we shall
speak only of \bodies of reference," or \space of reference." It
was only through the theory of general relativity that re.nement
of these concepts became necessary, as we shall see later.
I shall not go into detail concerning those properties of the
space of reference which lead to our conceiving points as elements
of space, and space as a continuum. Nor shall I attempt
to analyse further the properties of space which justify the conception of continuous series of points, or lines. If these concepts
are assumed, together with their relation to the solid bodies of
experience, then it is easy to say what we mean by the three dimensionality
of space; to each point three numbers, x1, x2, x3
(co-ordinates), may be associated, in such a way that this association
is uniquely reciprocal, and that x1, x2 and x3 vary continuously
when the point describes a continuous series of points
(a line).
9) How to write (the daily routines of famous writers)
http://www.brainpickings.org/index.php/2012/11/20/daily-routines-writers/
from brainpickings.org
10) The Pleasure of Finding Things Out (Interview of Richard Feynman)
11) Letters to a Young Scientist (EO Wilson)
a) Look for a chance to break away, find a subject you can make your own
b) 40 hours - teaching, 10 hours for study in your specialty, 10 hours research. Take chance for sabbatical, dodge admin work
c) You will become most devoted to research in science through images and stories that affected you early in childhood
d) Successful research does not depend on mathematical skill, talent etc. ... choosing an important problem and finding a way to solve it, even if imperfectly at first. Often ambition and entrepreneurial drive beat brilliance. (solved biogeography problem by using pesticides to wipe out all insects on island)
e) there exists a discipline in science for which that level of mathematical competence is enough to achieve excellence
f) for every problem, there is a solution; for every solution there is a problem that it can be applied to