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blogjou

It seems like at least the European CORONA crisis is coming to an end, so I need another socially accepted excuse for never being around anywhere. A blog!

  • Demonstrating and Evaluating Teaching Proficiency

    SLU guidelines

    • provide support to demonstrate teaching skills or assess them

    1. Teaching proficiency - a short background

    • proficiency: ability to perform instruction and carry out examination
    • late 20th century: paradigm shoft from “providing instruction” to “producing learning”
    • teaching proficiency: proficiency in planning, performing and evaluating teaching, including ability to motivate teaching methods and refklect on them
    • teaching skills requirement for professor or lecturer, equal weight to scientific skills
    • good practice in education:
      1. Encourages contacts between students and faculty
      2. Develops reciprocity and cooperation among students
      3. Uses active learning techniques
      4. Gives prompt feedback
      5. Emphasizes time on task
      6. Communicates high expectations
      7. Respects diverse talents and ways of learning
    • 4 dimensions: Context –> Knowledge and approaches – Planning –> Teaching
    • 3 progressive levels of early stage teachers’ views:
      1. Who the student is: learning is primarily defined by the students’ personal characteristics: some ar gifted and some are not
      2. What the teacher does: learning is primarily defined by what the teacher does: how she teaches
      3. What the student does: learning is a result of the learning activities the students engage in, and it is determined by the students’ previous experiences and the learning environment they find themselves in
    • also 3 progressive levels for proficient teachers:
      1. excellent: proficient in the classroom, teaching is experienced as effective by colleagues and students
      2. expert:
        • excellent plus theoretical knowledge about teaching and learning
        • combine subject knowlege and practical knowledge of teaching
        • continuous self-development and adaptation in teaching methods
      3. scholarship of teaching and learning: excellent + expert + sharing and promoting knowledge on the general development of teaching: conferences, articles, etc.

    2. Documenting teaching skills - the teaching portfolio

    • two types of teaching portfolios:
      • personal:
        • extensive documentation together with reflections
        • course evaluations, testimonials from course leaders, material produced, certificates, etc.
        • all kind of situations you helped people, being a coach, private support
        • include negative experiences
        • everything is valuable
      • specific: assembled for special purpose
      • What have I done? How did I do it? Why did I do it this way? What was the result?

    What serves as evidence of teaching proficiency?

    • pedagogical self-reflection:
      • What I teach
      • How I teach
      • Why I teach the way I do
      • What results do I achieve
    • teaching philosophy (pedagogical standpoint):
      • what is knowledge
      • existing limits for what is possible to know
      • how learning happens
      • what is important to know
      • how should we teach
      • should match your actual way of teaching
    • A well-structured philosophy can be formulated citing the literature.

    • most important: philosophy in action
    • self-reflection:
      • penetrate all aspects of a teacher’s role
      • trace own development as a teacher over time
      • include merits
        • for example self-development during participation in a teaching course
          • Constructive alignment
          • important is what the students do, not what the teacher does
          • deep knowledge needs personal activity
          • active learning way more useful than just bein able to preach
          • rather teach less but deeper
        • mere participation does not demonstrate teaching skills
        • desciption of significance of the course for own development
        • expansion of vision as a teacher, influence on student learning
      • ideas for future development (personal, at the department)

        3. Requesting or writing a testimonial of teaching skills

        To be done.

    4. Evaluating teaching proficiencey

    To be done.

    My questions and comments

    • In the seven principles for good teaching (Table 1), what does “Emphasizes time on task” mean?
    • My teaching was long ago, I did not care about certificates, course evaluations, or testimonials for in Germany nobody cares about. How does this impede future applications in Sweden?
  • Biodiversity as insurance: from concept to measurement and application

    Abstract

    • biodiversity will make aggreagate ecosystem properties vary less
    • insurance and portfolio theory connected to biodiversity
    • distinction between effects on mean and variability
    • application to ecosystem management

    I. Introduction

    • decrease variation (buffering), increase mean (performance enhancing)
    • often happen at the same time

    II. Insurance and portfolio theory in economics

    • trade-off between decreasing variance and increasing mean
      • portfolios: different stocks
      • options: permission to delay a decission until more information is available
      • insurance: an insurer is paid to cover the highest risk scenarios

    (1) Portfolios

    • maximize expected returns by a given level of risk by choosing not highly positively correlated assets
    • mean-variance trade-offs not yet applied in ecosystem functioning

    (2) Options

    • option value determined by Black and Scholes
    • increased return if ill-suited species are lost, cynical toward biodiversity and stability theory

    (3) Insurance

    • paying the insurance premium lowers wealth but saves from disaster
    • ecology: conservation strategies?

    III. Insurance and portfolio theories in ecology

    (1) Similarities and differences between insurance and portfolio theories in ecology

    • a zero-correlation assumption is ridiculous, apart from being separeted in space maybe
    • the shared ecological driver (climate) by all species will have an increasingly negative impact which makes portfolio and insurance theory less likely to increase mean returns, no matter how it’s done; planting species more suitable for a new climate might be useless for trees that grow to slowly compared to current climatic changes

    (2) Mechanisms of biological insurance

    • important: asynchronous fluctuations
    • while competition does contribute to increase the level of asynchrony of population fluctuations, which has a stabilising effect on ecosystem properties, it simultaneously increases the amplitude of population fluctuations, which has a destabilising effect

    • one should expect reduction of competition, i.e. niche complementarity, not competition, to favour ecosystem stability

    (3) Distinguishing between the effects of biodiversity on the mean and variability of ecosystem properties

    • in ecology often trade-off between mean and variablity not yet consindered
    • Therefore, for clarity’s sake, we propose that the performance-enhancing effect be renamed a selection effect

      • Who selects better than nature itself?
    • It may be worth recalling here that the selection effect does not conflict with the positive effects of biodiversity. Not only does it require the maintenance of biodiversity at larger spatial and temporal scales (Loreau, 2000), it even turns into functional complementarity when considered at larger scales because selection of the best-performing species under each environmental condition tends to increase the average level of ecosystem properties across space or time

      • Large scale spatial diversity is not the same as small scale spatial diversity for, let’s say small animals living in such ecosystems, who may depend on different species and cannot just wander around between different ecosystems on a daily basis

    (4) Spatial insurance

    • large spatial scales, but low diversity on small scales

    IV. Applications of biological insurance in ecosystem management

    (1) Agriculture

    • local diversity for single farmers as biological insurance instead of economical insurance against extreme events
    • on country-wide scale: spatial diversity/insurance

    (2) Fisheries

    • high species diversity allows simpler adaptation to market requests

    (3) Forestry

    • under current future climate, mixed-species stands seem inevitable
    • portfolio theory over the last 20 years shows that mixed stands are both more stable and more ecomicially useful
    • pure poductivity without looking at the economic aspect does not make much sense
    • Ecological knowledge on the mechanisms that provide biological insurance has yet to be integrated into applications of biological insurance and portfolio theory to forest management. For example, García-Robredo (2018) recently demonstrated that reduced competition and facilitation between mixtures of two tree species can lead to overyielding, increased economic return and reduced financial risk. Most studies so far, however, have focused on demonstrating the positive effects of managing different types of stands (often monospecific) and have ignored complementarity effects within stands. Moreover, portfolio studies have not considered the variability in site conditions across the managed forest landscape and have disregarded spatial ecological insurance.

    V. Synthesis

    (1) Shared features across disciplines

    • ecology: fixed species value, variable abundance
    • economy: changing stock value, fixed abundance (on first investment)

    (2) Contrasts between ecological and economic concepts

    • economics:
      • no spatial insurance effect for a single asset
      • automatic mean-stability trade-off
    • ecology:
      • spatial insurance also for single species
      • increase of performance and decrease of risk possible by complementary species effects

    VI. Future challenges

    (1) Linking the effects of biodiversity on ecosystem functioning and stability

    (2) Incorporating multiple functions and feedbacks

    • Future developments of biological insurance theory may require a clearer formulation and justification of the assumed objective function.

    (3) Developing new approaches to partition biodiversity effects across scales

    (4) Extending biological insurance theory to complex interaction networks

    VII. Conclusions

    • biological insurance theory becoming mature
    • need to distinct between effects on mean and variablity of ecosystem properties
    • much more to do in this growing research field

    Personal questions and remarks

    • What corresponds to “the market” and its fluctuation?
    • Scale (time oe space) must be large enough, a stand is probably not enough.
    • One should put infinite costs on the extinction of a species (policy-wise).
    • Portfolios: many pure spruce stands yield high productivity, but are susceptible to bark beetle outbreaks: mix the stands with different species
    • Option pricing in ecology seems cynical to me. Wait a while to learn whether or how much an intact ecosystem if beneficial before we decide to gradually destroy it opens Pandora’s box, in particular at incomplete information of species’ values and their interactions. Insurance: store seedlings and genes in huge protected databases in case a species goes extinct
    • an insurance strategy: reduce plant density to avoid spread of infections
    • It seems to me that when they mention an example of a quantity to be stabilized in the first place, they speak about stock (productivity). It’s not about species conservation or bioderversity in itself. Biodiversity is only considered as means to help ensure productivity (biomass, yield, salmon catches).
    • Best-performing species might deplete soil nutrients or other resources that are simply not part of the equations here.
  • Multidimensional tropical forest recovery

    Tropical forests disappear rapidly because of deforestation, yet they have the potential to regrow naturally on abandoned lands. We analyze how 12 forest attributes recover during secondary succession and how their recovery is interrelated using 77 sites across the tropics.

    Network analysis shows three independent clusters of attribute recovery, related to structure, species diversity, and species composition. Secondary forests should be embraced as a low-cost, natural solution for ecosystem restoration, climate change mitigation, and biodiversity conservation.

    • tropical forest regrowth on many agricultural sites left because of loss of fertitlity, migration, or alternative livelihhod options
    • resilience: ability to resist disturbance and to recover from disturbance
      • resistance: difference between the value of a specific forest attribute at the start of succession and the average old-growth forest value
      • recovery: ability to return to old-grown forest attribute values after succession
    • succession: change in vegetation structure, species composition and ecosystem functioning over time after a disturbance
    • secondary succession: on previously vegetated lands when a disturbance removes most of the above-ground vegetation and can proceed at fast rates due to legacy effects of previous forest or previous land use

    Pace of recovery

    • soil resistance was high, indicating that agricultural use does not disturb it too much; fast recovery

    Wood density (WD) is the stem-wood dry mass divided by stem volume, and it increases tissue longevity and carbon residence time in trees and forests. Specific leaf area (SLA) is the leaf area divided by the leaf mass. It reflects leaf display cost and scales positively with photosynthetic capacity and forest productivity and negatively with leaf longevity. WD and SLA change during secondary succession because pioneer species are typically replaced by later-successional species with opposite trait values.

    Nitrogen fixation is generally high early in succession when irradiance is high and trees can support their nitrogen-fixing symbionts with carbohydrates and declines over time as forests regrow, light availability in the stand drops, and nitrogen fixation becomes too costly.

    • fast plant functional recovery after short-lived pioneer species, with similar traits

    Structural heterogeneity (SH) refers to the tree size variation in a plot; it increases light capture and ecosystem productivity and contributes to biodiversity conservation by providing a habitat for different species.

    • forest structure recovers at intermediate pace
    • species diversity and composition recovers at intermediate to slow pace

    Network properties and proxies for multidimensional recovery

    The first network analysis was based on pairwise correlations among all 12 attributes and showed that recovery of attributes occurred in parallel, with the highest expected influence (i.e., many links with other attributes) for SC, followed by the three structural attributes and soil C.

    The clustering of forest attributes into multiple groups suggests that recovery of different forest attributes is shaped by different drivers or processes. For example, recovery of biodimeversity attributes may be driven by the land-scape context, land-use history, and the availability of seed trees and dispersal vectors, whereas recovery of structural attributes may be driven by resource availability [i.e., water availability, soil fertility (16), and remnant trees].

    We hypothesized that AGB would be the best predictor of multidimensional recovery because ecosystem processes and flux rates strongly depend upon the amount of vegetation. Instead, we found that recovery of Dmax had the highest influence.

    Resilience

    • overall return time about 120 years
    • fast forest recovery during secondary succession because of many legacies and productive, warm, and wet conditions

    Applied implications

    we urge the embrace of SFs as a low-cost, nature-based solution to meet the United Nations’ Sustainable Development goals and the United Nations’ Decade on Ecosystem Restoration goals (where needed with some assistance from management: control of invasive species, seed availability)

  • Tips from neuroscience to keep you focused on hard tasks

    Understanding cognitive control can help your working life, says David Badre.

    Hard tasks

    • solve a methodological hurdle
    • design an elegant experiment
    • make sense of a puzzling result
    • work on a new model
    • write a paper or grant proposal

    Make space

    In practice, returning to a hard task in this way comes with a ‘restart’ cost.

    Switching frequently between tasks makes producing quality work harder.

    Be consistent. We should try to reserve a consistent time and place for our hard work and be protective of it.

    Minimize distraction and never multitask

    Even cues that we simply associate with other tasks, such as seeing our phones on the table, can distract us. As much as possible, we should keep our space and time for hard work clear of other distracting tasks.

    Beware the allure of easy tasks.

    Engage in good problem-solving habits

    In general, we can get better at structuring hard problems with experience.

    Interact with others. Just like taking a break, interacting with others can help us conceptualize a problem in new ways. Talking to people with diverse backgrounds, perspectives and viewpoints that differ from our own can be a powerful way to break out of a rut and make progress, as well as get some perspective.

    Personal comments

    • don’t get overwhelmed by the entire task, do it step by step
    • maybe step back a level of abstraction and ask yourself, what is the goal
  • Carbon Sequestration in Forests - Addressing the Scale Question

    Whether young or old forests sequester or store more carbon, is a heated debate. Depending on the consideres scale in time, space, and involved proces, there are arguments for either side. This controversy is resolved at the landscape scale.

    Young forests are growing faster, while old forests have more dead trees and decomposition. On the other hand, replacement of older forests by young forests will result in a net release of carbon.

    • process of defining a problem should include specifying a spatial, temportal and process level
    • processes involved:
      • tree growth
      • photosynthesis
      • plant respiration
      • tree death
      • litter production
      • decomposition
      • formation of stable organic matter in soil
      • disturbances (e.g., harvesting and fire)
      • manufacture use
      • disposal of forest products
      • substitution of fossil fuels
    • young forests often have a high amount of slash: high decomposition
    • detritus, soil, and forest products can be long-term storages
    • a single dead tree decomposes and loses mass, but an accumulation of many dead trees can accumulate mass
    • NPP = gross growth (in forestry terms)
    • If one considers the average production over the length of a rotation, then older forests may be lust as productive as younger ones. This is because no forest can be $X$ years old without having been $X-1$ years old.

    • given enough time, ecosystems’ carbon accumulation ability vanishes
    • Although old forests have a substantial amount of dead and dying material, these losses are roughly offset by the production of this material. Ironically, it is the very production of that dead and dying material that prevents the older forest ecosystem from being a net carbon source to the atmosphere.

    • at large spatial cases with many age classes, effects might cancel out
    • disturbances less severe and less frequent: higher carbon storage (and vice versa)
    • increased NPP (by climate change) far too small to offset losses caused by conversion of older forests to younger forests

    Personal comments

    • all the analyses are done in terms of carbon (tons/ha, tons/ha/yr)
    • we can do similar analyses in terms of transit time
  • On the value of preprints: An early career researcher perspective

    The publication of preprints, publicly available scientific manuscripts posted on dedicated preprint servers prior to journal-managed peer review can play a key role in addressing these ECR challenges such as timely publication and increased interdisciplinarity in life sciences research.

    Introduction

    • research output comes in very many varieties: research articles, reviews, commentaries, perspectives, theory manuscripts, methods, data, reagents, model organisms, computational models, patents, drugs, vaccines, software, and highly trained researchers
    • still the only “currency” is published articles in peer reviewed journals
    • preprints: online, freely available (open-access) scientific manuscripts posted by authors on dedicated servers prior to peer review and publication in an academic journal
    • sometimes concurrently to journal submission, sometimes sole way of publication
    • no peer review, only screening for appropriate topic
    • some journals do not accept preprinted articles

    Values of preprints for ECRs

    Preprints accelerate science communication that facilitates ECR career progression

    • long duration of traditional journal publishing can negatively impact ECRs seeking funding, promotion, and hiring
    • added benefit of encouraging collaboration, informal discussion, and sharing and receiving data
    • some funding agencies take preprints into account, in order to evaluate the researcher based on quality of work not only publications

    Preprints increase ECR visibility and facilitate networking

    • increase networking
    • discussion in social media
    • higher citation rates of later publications

    Preprints can help ECRs accelerate training time and optimize research design and quality

    • faster knowledge and data dissemination with all its benefits like steeper learning cuves, reduction of costs, avoidance of redundancy

    Preprints allow ECRs with limited funds to publish their findings with open access

    • low costs open access publishing

    Preprints in public health and medical research can boost ECR research

    • Was it used much to fight the pandemic?

    Preprints can accelerate the peer-review process to make ECRs more efficient

    • useful if the author has no experts at hand in the field
    • feedback through email or social media
    1. researchers can begin to respond to preprint comments before journal-solicited reviews are received
    2. researchers can submit higher-quality articles to journals after getting feedback from preprint readers
    3. with the exception of a few journals [1], the journal peer review process remains largely opaque and confidential.

    If open preprint peer review were to become common practice, rereviewing of the same article could be avoided.

    Preprint commenting can help ECRs develop their reviewer skills

    Only 20% of scientists perform 69% to 94% of the all journal-solicited peer reviews culminating to 63.4 million review hours a year, 15 million of which are spent rereviewing rejected papers [3,44].

    • Commenting on preprints by ECRs is an opportunity to sharpen their reviewing skills and to give them a voice in academic publishing that can expand and diversify the pool of peer reviewers.
    • more and more interdisciplinary research needs more and more reviewers
    • there are platforms for preprint reviews

    Preprints helps ECRs perform corrections via revisions

    • easy corrections instead of retractions

    Publishing all research findings and conditions in preprints can benefit ECRs

    • negative results, replication studies

    Perceived concerns by ECR on preprinting

    Preprinting leads to scooping

    • preprints come with a DOI
    • depends on whether journals allow citing preprints and whether they accept being second

    Preprinting prevents publication

    • unclear publisher and journal policies
    • closer collaboration and reverse links between journals and preprint servers could help

    Preprints have low visibility

    • any publishing option will benefit ECRs who need to prove productivity over a short period of time
    • some results might not be published at all otherwise
    • preprint search engines are improving

    Conclusions

    Preprints are already benefiting ECRs and life scientists at large, but we argue that they are underutilized and can be used in new ways to aid ECR development and increase the efficiency of scientific research.

    Personal comments

    • I remember a case in which I read a paper on entropy rates in marked Poisson processes and got totally stuck for quite some time. Only to learn much later that this was a preprint and they had several errors in the equations… That was rather annoying.
    • Recently I reviewed a paper and got stuck with some formulas. But it was a review, I knew there might be something wrong, noted it down in my report, and the authors corrected it. So the actual reader later does not have to go through this process anymore, maybe without knowing, it has not been double checked.
    • Sometimes it takes forever to find reviewers, but PhDs need the publications. What does it help however, if preprints are not accepted by the university?
    • Preprints empower authors to decide when their work is ready to be shared with the scientific community.

      • This might be too early.
    • another means for networking, in particular now in Corona times
    • For example, in the biophysics and fluorescence microscopy fields, preprinted methods were used well in advance of the peer-reviewed publication in sample labeling [19–20], instrument design [21–22], and image analysis [23].

      • This is kind of dangerous.
    • might be a first or one of many steps away from the ridiculous current publication system
    • I might consider my Landau constants paper for preprint for I have no expert in the field at hand. Furthermore, I have a negative result that could go on arXiv.
    • How does it help the system if every ECR can publish more and faster?
    • I know that at Imperial College London, they have an internal preprint server.
  • Some Prescriptions for How to Escape into a Deeper Basin

    Some of the suggestions for speeding upt the process of conceiving a creative idea fit in well with the pircture of using a controlled level of noise to avoid getting stuck in too shallow a basin of attraction. One can try to escape from the original basin by means of a random perturbation – for example Edward DeBono recommends trying to apply to a problem, whatever it is, the last noun on the front page of today’s bewspaper.

    Another method is akin to brainstorming, which has been used throughout the postwar era. Here several people try to find a solution to a problem by meeting for a group discussion in which one is encouraged to build on someone else’s suggestion but not to attack it, no matter how bizarre it is. A crazy or self-contradictory proposal can represent an unstable state of thinking leading to a solution. DeBono likes to cite as an example a discussion of river pollution control, in which someone might say, “What we really need is to make sure that factories are donwstream from themselves.” That is a manifestly impossible suggestions, but someone else might then come up with a more serious proposal, saying “You can do something like that if you require the intake of water at each factory to be downstream from the effluent.” The crazy idea can be regarded as a rise on a fitness landscape that can lead to a much deeper basin than the one from which the discussion started.

  • For a case more like that of biological evolution...

    For a case more like that of biological evolution, we can turn to the competition among human societies in the past. To a great extent, fitness was measured by population. In Southeast Asia, for instance, some ethnic groups practiced irrigated rice agriculture while others raised dry rice, often by slashing and burning the forest. The irrigated-rice peoples, such as the Central Thai, the Lao, or the Vietnamese, were able to put many more individuals on the ground per unit area than their neighbours. Denser population helped them to dominate the dry-rice peoples, and in many cases to drive them back into remote hilly terrain. Looking toward the future, we may well ask whether it is desirable for density or total numbers to continue to determine winners and losers in the same way.

  • Deception Among Birds

    For amusing examples of the exploitation of opportunities by species interacting with other species, we can turn to lying as practiced by animals other than humans. Deception by mimicry is well known; the viceroy butterfly, for instance, resembles the monarch and thus profits by the bad taste of the latter. The cuckoo (in the Old World) and the cowbird (in the New World) practice another kind of deception by lazing their eggs in the nests of other birds; the intrusive chicks then do away with the eggs or chicks that belong in the nest and monopolize the attention of the foster parents. But actual lying?

    We are accumstomed to hearing people lie, but it is somehow more surprising in other organisms. When the Argentine Navy spots a mysterious periscope in the estuary of the Río de la Plata just before the budgets of the armed forces are to be considered by the legislature, we suspect that deception is being practiced so as to capture additional resources, and we are not particularly astonished. But the analogous behaviour among birds is more unexpected.

    One such case was discovered recently by my friend Charles Munn, an ornithologist studying mixed feeding flocks in the lowland tropical forest of Manu National Park in Peru. Some species forage together in the understory or lower canopy of the forest and others in the middle canopy, where they are sometimes joined by colorful fruit-eating tangers from the upper canopy. (Amon the species found in those flocks in winter are a few North American migrants. Further north in South and Central America there are many more. We residents of North America know them as nesting species in the summer and are intrigued to find them leading a very different life in a distant land. If they are to return zear after year to nest, their habitats in the southern countries will be jeopardized if North American forests are chopped up into still smaller parcels than the ones now remaining. For one thing, thinning out the forests permits further inroads bei parasitic cowbirds.)

    In each mixed feeding flock, there are one or two sentinel species, which move about in such a way that they are usually near the center of the flock or just below. The sentinels warn the others by a special call of approaching bird that might turn out to be raptors. Charlie noticed that the sentinels for the understory flocks sometimes gave the warning signals even when no danger was apparent. Looking more closely, he found that the fake alarm often permitted the sentinel to grab a succulent morsel that another member of the flock might otherwise have eaten. Careful observation revealed that that the sentinels were practicing deception about 15 percent of the time and often profiting by it. Wondering if the phenomenon might be more general, Charlie examined the behavior of the middle canopy flocks and found the sentinels there are doing the same thing. For the two species of sentinels, the percentage of false signals was about the same. Presumably, if the percentage were much higher, the signals would not be accepted by the rest of the flock (recall the story The Boy Who Cried “Wolf”), and if it were much lower, the opportunity for the sentinel to obtain extra food by lying would be partially or wholly wasted. I am intrigued by the challenge of deriving by some kind of mathematical resoning the figure of about 15 percent; in a plausible model, might it come out one divided by two pi? When I asked that question of Charles Bennett, he was reminded of something his father had told him about the Royal Canadian Air Force units based in England during the Second World War. They found it useful, when sending out a fighter and a bomber together, to attempt occasionally to deceive the Luftwaffe by positioning the fighter below the bomber rather than above. After a good deal of trial and error, they ended up following that practice at random one time in seven.

  • Quantum Theory

    I am not sure where this project belongs. It is not like classically reading a paper and it is not about classically citing some quotes of enjoyable books. For starters, I would like to note my impressions. I need to study physics to understand the simplest of Bohm’s arguments, I do not have the time, and the energy to do so fainted as well. So I try to make the best of it and note down what I feel most interesting.

    Chapter 1

    • in three dimensions, a transverse wave (the link helped me a lot to understand the concept of polarization) has two options for polarization
      • Are there always $d-1$ options for polarization if $d$ is the space dimension?
        • No! Only $d-1$ basis directions, any combination is possible, the wave could also be tilted.
      • What is a longitudinal wave?
    • Maxwell’s equations and Fourier mathematics lead to a perfect blackbody radiation theory, as long as the frequency is not too high (Rayleigh-Jeans law)
      • Fourier mathematics, as is mentioned in a footnote on page 10, works as long as the function is piecewise continuous, which I find a pretty remarkable footnote in the realms of the borderline between classical physics and quantum mechanics
    • both Maxwell’s equations and Fourier mathematics are undisputable, but something is wrong when it comes to measurements at high frequencies
    • Max Planck (Einstein is also mentioned, Nobel Prize?) comes with the idea, that quantized energy packets might do the trick
    • it was not ovious earlier noted because the frequency-dependent package size $h\,\nu$ is small enough to make quantum theory look continuous at not too high frequencies
    • Maxwell’s distribution reconciles both the Rayleigh-Jeans law and the Wiener law, his new law interpolates even everything in between very well
    • most of the things are just greek to me but I hope I got the gist