What is Insights: Definition and 40 Discussions

Insight is the understanding of a specific cause and effect within a particular context. The term insight can have several related meanings:

a piece of information
the act or result of understanding the inner nature of things or of seeing intuitively (called noesis in Greek)
an introspection
the power of acute observation and deduction, discernment, and perception, called intellection or noesis
An understanding of cause and effect based on the identification of relationships and behaviors within a model, context, or scenario (see artificial intelligence)An insight that manifests itself suddenly, such as understanding how to solve a difficult problem, is sometimes called by the German word Aha-Erlebnis. The term was coined by the German psychologist and theoretical linguist Karl Bühler. It is also known as an epiphany, eureka moment or (for cross word solvers) the penny dropping moment (PDM). Sudden sickening realisations often identify a problem rather than solving it, so Uh-oh rather than Aha moments are further seen in negative insight. A further example of negative insight is chagrin which is annoyance at the obviousness of a solution missed up until the point of insight, an example of this being the Homer Simpson's catchphrase exclamation, D'oh!.

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  1. P

    Bug Cannot comment on the Insight Blog

    Every time that I click to comment on a Insight Blog article I get redirected to a new page that says: But clicking there gets me to back to the forums and not to the Insight article. Is this a bug?
  2. benorin

    I I would like opinions of the latest draft of my note - Integration

    The note is entitled: Evaluation of a Class of n-fold Integrals by Means of Hadamard Fractional Integration. 4 pgs pdf format. I assure you that you need not know anything about fractional calculus at all to understand this note that Howard Cohl helped me with. We only use a single...
  3. benorin

    This is for an Insights article: Bivariate induction proof using Calc3

    Link to my insight Article it's right where I need you to start checking, read the above boxes to, check out the picture to see examples of the kind of sequence of sets we are dealing with. I need you to read the section jusr below the first picture entitled "3.0.2 Lemma 2.1: Nesting Property of...
  4. M

    What is Fermat's Theorem on Light?

    Hi, I'm Michael, a high schooler very passionate about physics. My favorite physics theorem is Fermat's Theorem on light. I'm also very into computer science and math. I run a physics blog. I look forward to discussions on physics forum!
  5. B

    Insights for a Mechanical Engineering student

    Hello everyone, I'm a mechanical engineering student, I'm italian, so, sorry for my bad english. In this moment i am studying the following subjects: Mathematical Analysis II (multivariable calculus), Physics II (eletctromagnetism), Mechanical design and fundamentals of structural mechanics...
  6. benorin

    I Gamma function/partial fractions (a problem from my Insights article)

    I'm typing up answers to the exercises in my Insight article "A Path to Fractional Integral Representations of Some Special Functions", this problem is from section 1 (Gamma/Beta functions). I need a bit of help with this one: The problem statement: 1.9) Use partial fraction decomposition to...
  7. jtbell

    I New insights in penguin physics

    Projectile Trajectory of Penguin’s Faeces and Rectal Pressure Revisited (PDF, ArXiv) There's an even better diagram related to fluid pressure, but I'll let you see it in the paper. :cool:
  8. J

    Studying Approaching difficult problems and gaining insights

    I find that on encountering a tricky problem for which I have to look up the solution, I tend to 'understand' the solution yet over a period of time 'forget' it. On seeing the solution I understand the logical flow of the solution but on seeing the same problem over time I am often unable to...
  9. Bandersnatch

    Can Insights Articles Be Translated and Shared with Attribution?

    1. If somebody wanted to translate one or some of the articles, would it be doable to include the translated text with the original Insight? 2. Alternatively, would publishing such a translation elsewhere (with full attribution of course) be o.k.? Questions mostly directed to @Greg Bernhardt...
  10. Q

    I What are the insights into the Total Derivative formula?

    I’ve always been confused by the formula for the Total Derivative of a function. $$\frac{df(u,v)}{dx}= \frac{\partial f}{\partial x}+\frac{\partial f }{\partial u}\frac{\mathrm{d}u }{\mathrm{d} x}+\frac{\partial f}{\partial v}\frac{\mathrm{d}v }{\mathrm{d} x}$$ Any insight would be greatly...
  11. Lukeblackhill

    Developing more practical insights into real situations in Physics

    Good Evening Mates, I've been following up with the Forum for a couple of months now, and I've noticed how some of the members are able to give some deep answers for seemingly simple questions. I'm in my second year of undergrad's school, and have studied the basis of Mechanics, Thermodynamics...
  12. Arceus74

    What is Electricity? Insights please....

    I have some couple of questions about this topic to keep this as concise. 1)First of all why does electricity flow in the opposite direction to electron flow? 2)What is electricity in relation with a electron? I know it is the proportional to electric charge, but what relation does it hold? Is...
  13. S

    Bug Can I Leave Comments Using the Insight Form?

    Clicking on "3 comments" in the "Partial Differentiation Without Tears" insight doesn't work for me. No comments appear. But clicking on the "4 Comments" in "Solving The Cubic For Dummies" does work.
  14. B

    Other Do "older" books provide unique insights?

    Dear Physics Forum personnel, I am curious what are your opinions about the "older" books in mathematics and physics (i.e. Neumann, Schrodinger, Dirac for QM, Hawking/Ellis for relativity, Russell for mathematics, etc.). From my experience with mathematical books, I found that I have liking to...
  15. ibkev

    Relativity Sleeping Beauties in Theoretical Physics: 26 Surprising Insights

    This book Sleeping Beauties in Theoretical Physics: 26 Surprising Insights sounds pretty cool as something to read for fun. Has anyone looked at it yet? I'm wondering also what level of reader it's been written for? https://www.amazon.com/dp/3319134426/?tag=pfamazon01-20
  16. jim mcnamara

    LaTeX Latex in pervect's comments at bottom of insights article

    https://www.physicsforums.com/insights/a-problem-from-incandescence/ For me, many blank lines where I'm sure there should be something . Latex is just fine everywhere else on PF. Thanks for any help.
  17. Ygggdrasil

    Bug Comments on Insights: BBCode Issues on Wordpress Site

    For the Insight articles, I noticed that the comments on the Wordpress side of the site do not correctly process BBCode written on the forum side of the site. For example, see some of the later comments on https://www.physicsforums.com/insights/when-did-mitochondria-evolve/ The url tags are...
  18. Greg Bernhardt

    Praise Happy 1yr Anniversary for PF Insights

    The first Insight was published on April 28th, but I can't wait to celebrate :partytime:. I am brimming with pride and amazement at how awesome this resource has become. We got something really really special here. 240 published Insights with well over 1 million views :oldsurprised:! All glory...
  19. micromass

    Other Micromass' Insights on how to self-study mathematics

    How to self-study mathematics https://www.physicsforums.com/insights/how-to-study-mathematics/ How to self-study basic high school mathematics https://www.physicsforums.com/insights/self-study-basic-high-school-mathematics/ How to self-study calculus...
  20. Greg Bernhardt

    Insights PF Insights Scavenger Hunt - Comments

    Greg Bernhardt submitted a new PF Insights post PF Insights Scavenger Hunt Continue reading the Original PF Insights Post.
  21. E

    I Example of a linear combination, anyone have any insights?

    According to A Borobantu, regarding superposition, where Ψ is a state vector or a wave amplitude, given Ψ1, Ψ3, Ψ3... Ψncan by physically realized, then the following statement holds for all linear combinations Ψ = ∑ciΨi where ci can satisfy 1 = ∑|ck|2 to be called a complete and closed...
  22. PhysicsKid0123

    Insights on future prospects: Applied vs Computational Math

    Hello Physics Forums community, I'm looking for opinions, advice, really anything, to help me better understand what I'm going into and what may be better for me after gradation. I am posting this under academic guidance because these are decisions that I need to make while I am in college. This...
  23. Stephanus

    LaTeX Latex Issues with PF Insights in Chrome

    Dear PF Forum, I use Google Chrome Version 43.0.2357.130 m My browser doesn't display LaTex in PF Insights. But it display latex on PF Forum other area. Forum and conversation but not in PF Insights. Even in chat window my browser display LaTex, but a mentor told me that typing latex in chat...
  24. PsychonautQQ

    I'm stuck on a proof that's probably trivial, any insights?

    Given polynomial P(a,b,c,d,e,f...n) = (a^0)(b^1)(c^2)...(n^n) show that the sum of P(a,b,c,d,e,f...x) when acted upon by the symmetric group of order n and each time multipled by the sgn function (1 if even and -1 if odd); that this sum is equal to the vandermonde determinant of these...
  25. H

    How to be more insightful? (AHA insights)

    Hi guys:It's a general question about mathematics so I figure it best belongs to the general math forum.I would like to know how to be more "AHA" insightful, often time when I look at a math problem/puzzles, there's always these little things (observations, reasoning) that would enable one to...
  26. G

    Some insights about the Riemann hypothesis needed

    The Riemann hypothesis states, whenever the Riemann zeta function hits 0, the real part of the input must be 0.5. Does any input with real part being 0.5 make the function hit 0? Also, assuming the hypothesis is true, would it suffice to prove that if the input's real part is not 0.5, then the...
  27. D

    Advice for EE Degree: Current Students & Engineers Share Their Insights

    My name is Patrick, I'm 25 and for the first time I'm going to be going to school for my EE degree. I was curious if any current students could suggest books, links or anything that you can think of that will make my time in school either be easier or more successful or feel free to just post...
  28. S

    Testing the Limits of Special Relativity: Questions and Insights

    1. Consider a correlation function between two points `A(x1,t1)` and `B(x2,t2)`, we need to integrate over paths which could be infinite long. But the time length `(t1-t2)` is finite, so if A and B are the coordinates of one single particle, then all of the paths from A to B should be time-like...
  29. A

    Insights on high GPA - for nonprof blog

    Hey guys, I'm a 3rd year studying mechanical engineering. I blog for a nonprofit that helps first generation students get access to higher education; in my next blog, I'd like to have a community created list of advice, tips, tools, and quirky methods of how other students have achieved a...
  30. P

    When Does This Equation Hold True?

    Hi. Sorry I couldn't think of a more appropriate title for this thread. I'm doing some calculatons and I arrived at an equation with this form f(t')|_0^t = \int_0^t f(t')dt' I was just wondering if anyone as any insight into the interpretation of such an expression. All I can think...
  31. M

    3D Programming: Experiences and Insights

    Was just wondering if anyone here has tried 3D programming. If you have, what language did you write in, what difficulties did you have, and what did you find interesting about it? As of now I know of Direct3D and OpenGL, but, if I'm not mistaken, you can use different languages to write...
  32. R

    Exploring F@H Stats with My Friend: The Hidden Insights

    My friend and I have begun work on a folding at home statistics site. I'm going to break F@H down for you all real quick. Every 3 hours a Team submits more points and "Units" to their total points and Unit count. (The unit is where the points come from). So every 3 hours Point and Unit...
  33. W

    Entanglement - the Latest Insights?

    Dr Chinese has an admirable exposition of Bell's Inequality, here: http://www.drchinese.com/Bells_Theorem.htm From this it appears (and please correct me if I am wrong) that a pair of entangled particles each have opposite spin BUT this spin is NOT a hidden value waiting to be revealed by...
  34. R

    Looking for insights about this sequence:

    1 2 3 4 5 6 1, 1, 2, 3/2, 4/(3/2), 5/(4/(3/2)), ... I suppose there are a lot of variations, but the general idea is the terms are defined by: f(n)*f(n+1)=n, where n is an integer. The top row is the term # (n), and the bottom one is the actual value of...
  35. B

    Any insights on the Lymphatic System?

    Homework Statement My teacher wants us to do a report on the lymphatic system but I'm stuck on the part where we have to predict and give insights on improvements of the lymphatic system in the future and original ideas. Help? Homework Equations The Attempt at a Solution
  36. rootX

    Which Country Leads in Physics Forum Interest?

    http://google.com/insights/search/#cat=&q=physics%20forum&geo=&date=&clp=&cmpt=q India seem to beat everyone else. I thought US would be at 1. 1. India 100 2. Canada 84 :biggrin: 3. Australia 71 4. United States 70 5. United Kingdom 66 6. Germany
  37. M

    What are some nifty and clever discoveries in mathematics?

    I was reading the general discussion section and noticed that someone came with a thread about cleaver ideas. I was thinking that there may be some clever ideas, tricks, or insights that many of you experienced mathematicians may have come across. If you have anything you think it is of worth...
  38. iansmith

    How Did Irish Researchers Discover New Introns in Worm Genomes?

  39. U

    Discussing Interesting Links and Insights

    Ok somebody was bound to post a thread on this so what the hell, anybody got any interesting links or insights into this ?
  40. iansmith

    Uncovering New Insights on SARS Virus Transmission

    Yesterday I was a at special SARS conference and here what I have learn and did not see on the news: - Virtually all infected people show SARS viruse in the fecals matter only 50% show SARS viruses in the resporatory system. Therefore SARS viruse would be transmitted from air to air, fecal to...