So, I've been thinking a lot lately about intuition and how we develop it. As a result of some recent discussions, I decided to write something about where I get my intuitions from for scientific areas I simply don't have the math for.

It's no secret that I'm pretty much a dunce when it comes to mathematics. My formal education ended at rudimentary algebra, and I never had a reason to look at algebra again until I got an office job many years later and had to use a spreadsheet, at which point I had to start again.

However, and I have a good deal of experience working in a host of live and recording situations as musician, performer or engineer, and this experience has given me a very good feel for the behaviour of waves, as well as a smattering of rudimentary information theory, and almost everything I've encountered in physics, for example, has been in some way reducible to the behaviours of waves, at least intuitionally. In fact, some of the more counter-intuitive things in QM really don't feel at all counter-intuitive to me. The uncertainty principle reflects a general uncertainty in waves; a note of extremely short duration has a lot of uncertainty in its pitch. Wave interference in the double-slit experiment is what we refer to in audio as 'comb-filtering', often seen as poor studio design or mic placement, as early reflections from a surface arrive at the mic slightly out of phase, resulting in destructive interference. Noise-cancelling headphones and the removal of expletives in recordings employ the same physics. The list goes on.

Recently, I've been working a bit on filling in some of the conceptual mathematical gaps, and it's been interesting in that it's given me a map of my intuitions and why they worked. I'm still not going to be finding any exact solutions to the Schrödinger Equation, but I can see the logic of it and how it marries with my intuitions of how waves behave.

The idea of developing better intuitions and replacing what "we" think of as common sense as something a lot more common and a fuckton more sensible is pretty much where all my thought is right now, and it's fairly well understood that we explain (and develop intuitions for) things by comparing them to things we already understand. I'd be interested to see if others could point to an instance like the above, where some comparison made something click for you.

Got any?

Nothing comes to mind at the moment. Currently I'm trying to get a better grasp of electromagnetism so I can get a better grasp of direct current systems. I found myself trying to compare them to alternating current circuits in residential applications, and kept failing to really grasp the specific quirks of direct current.

Oddly enough, it feels very counterintuitive to my previous experience with electrical; I sometimes even wonder if my past experience is a barrier to understanding as opposed to an asset.

What in particular are you struggling with? We have bods around here with good knowledge.

I'm also math challenged but have reasonably understanding of how things work tho I must admit got initially fooled by DWFTTW until some visuals came out and I watched the the America's Cup AC70s.
Then it clicked.

I think having visuals of science concepts are a great aid to those of us who can't do the math or wade through dry textbooks to come to an understanding.


A good animation can affirm an intuition ....or just bust it to pieces for me. The DWFTTW animations knocked my intuition flat.

Also the subconcious has a strong role in dealing with problems that the concious mind struggles with. Benzine ring comes to mind.
https://medium.com/@jahnavimandadapu/th ... c7e270c90c

hackenslash wrote:What in particular are you struggling with? We have bods around here with good knowledge.

Honestly, I have to just learn direct current from the ground up; someone talks to me about a circuit, I start talking about the negative leg like it's a neutral, and I'm told that, no, no it's not. I imagine that such is as basic as it gets.

But I did find a whole lecture series on electricity and electromagnetism. Walter Lewin at MIT.

Macdoc wrote:I'm also math challenged but have reasonably understanding of how things work tho I must admit got initially fooled by DWFTTW until some visuals came out and I watched the the America's Cup AC70s.
Then it clicked.

I did as well. Indeed, I seem to recall I posted rather indignantly about it at Talkrat. For me, it was all about finding a differential in the system that could be exploited. Once I found that, it became obvious that a lot of energy is being wasted in rolling friction and subsequently lost to heat dissipation beyond the natural entropy of the system.

I think having visuals of science concepts are a great aid to those of us who can't do the math or wade through dry textbooks to come to an understanding.


A good animation can affirm an intuition ....or just bust it to pieces for me. The DWFTTW animations knocked my intuition flat.

Also the subconcious has a strong role in dealing with problems that the concious mind struggles with. Benzine ring comes to mind.
https://medium.com/@jahnavimandadapu/th ... c7e270c90c

Indeed. And it isn't alone, either. How did Einstein end up thinking about the occupants of an elevator?

Greg the Grouper wrote:

hackenslash wrote:What in particular are you struggling with? We have bods around here with good knowledge.

Honestly, I have to just learn direct current from the ground up; someone talks to me about a circuit, I start talking about the negative leg like it's a neutral, and I'm told that, no, no it's not. I imagine that such is as basic as it gets.

But I did find a whole lecture series on electricity and electromagnetism. Walter Lewin at MIT.

I seem to remember that Khan Academy did some really good videos on this. I'll be doing a paragraph or two in this post I'm working on, because it's an excellent example of wave behaviour, particularly alternating frequencies and their impact on things. For example, when you see flickering of a light source on a video, the rate of flicker is exactly twice the frequency that the current is alternating at, as the light dims each time the current reverses direction. I once attempted to construct an analogy for the broken symmetry in the twins paradox based on this principle, because it's the broken symmetry in changing inertial frames that results in the temporal difference, in exactly the same way that the symmetry is broken when the current changes direction and the light momentarily flickers.

It's all waves, man. Somebody should tell Paul...

Greg the Grouper wrote:Oddly enough, it feels very counterintuitive to my previous experience with electrical; I sometimes even wonder if my past experience is a barrier to understanding as opposed to an asset.

This is a massively important point, and it relates to what Mac and I were talking about. DWFTTW runs hard up against some important and reliable intuitions about things like Noether's Theorem and conserved quantities. It probably didn't help that all of us first encountered it in exactly the sort of venue in which people would regularly bowl up with a method for extracting water from the atmosphere or some over-unity or perpetual motion device, and that cart looked entirely indistinguishable on cursory inspection from one of those. It's so easy to develop a quick intuition and then cling on to it to the exclusion of evidence.

It was really surprising to encounter the cart after a decade, and after having been built and demonstrated to work, and to find that people are still arguing over whether it works, even to the extent that physicists are doing the inverse of what they all did with the Michelson-Morley experiment, and trying to find what he did right to make it look like the observed result is not because he's right.

Macdoc wrote:I'm also math challenged but have reasonably understanding of how things work tho I must admit got initially fooled by DWFTTW until some visuals came out and I watched the the America's Cup AC70s.
Then it clicked.

I think having visuals of science concepts are a great aid to those of us who can't do the math or wade through dry textbooks to come to an understanding.


A good animation can affirm an intuition ....or just bust it to pieces for me. The DWFTTW animations knocked my intuition flat.

Also the subconcious has a strong role in dealing with problems that the concious mind struggles with. Benzine ring comes to mind.
https://medium.com/@jahnavimandadapu/th ... c7e270c90c

My math grades took a nosedive in diffeq class which was calc2 in the system I was in and I never pursued it beyond that but I find that when I encounter an application, I can generally learn what I need to for that purpose. I have been told that if I had linear algebra there are things I could do that don't occur to me now. All that said, beyond topics that are specifically math centric (physics and some aspects of information science mostly) visuals are the central method of intuition pumping for me. Or, more specifically, I can almost always draw a picture of what I'm thinking about that informs intuition. But I think it boils down to how we each construct narrative.

hackenslash wrote:...

Recently, I've been working a bit on filling in some of the conceptual mathematical gaps, and it's been interesting in that it's given me a map of my intuitions and why they worked. I'm still not going to be finding any exact solutions to the Schrödinger Equation, but I can see the logic of it and how it marries with my intuitions of how waves behave.

The idea of developing better intuitions and replacing what "we" think of as common sense as something a lot more common and a fuckton more sensible is pretty much where all my thought is right now, and it's fairly well understood that we explain (and develop intuitions for) things by comparing them to things we already understand. I'd be interested to see if others could point to an instance like the above, where some comparison made something click for you.

Got any?

I too am seeking some mathematical rigour to bolster my intuitive thinking. I learned early on that I'm not a mathematician but the equations and short hand methods of getting ideas written down has always impressed me in books on the subject.

This time, I'm thinking about the formation of dense material around the centres of neutron stars beyond Pauli Exclusion such that collapse to a gravitational black hole may proceed without the requirement to invoke a singularity (a thing I dislike). I've read things about quark-plasma soups, quark stars and I really like some of the drawings of that mathematics guy I recently brought to another topic hereabouts (Elliot Kienzle, iirc). I also learned about shells of material and how they act like point masses from a great distance but also have no net gravitational pull for an observer inside the shell. Trying to combine some consequences of relativity theory, like those in Bell's paradox in SR and extreme Weyl curvature in GR, with facts about symmetric boson and anti-symmetric fermion wavefunctions in QM + my intuitions => room for me to wibble about such things.

I've made a blog post about the topic in an effort to gather the intuition and my maths bumbling together but, seeing as its unlikely I'll ever reach the position of testing the ideas against observations, I have some reluctance to take things much further... Hey ho.

newolder wrote:I also learned about shells of material and how they act like point masses from a great distance but also have no net gravitational pull for an observer inside the shell.

This made me laugh out loud. I remember a conversation years ago wherein we were trying to explain to somebody why an observer wouldn't feel any gravity right at the Earth's core, and I drew a crappy diagram, for which I took a shitload of abuse from Twist and Campy.

I've spent the last few days looking for a good graphing solution for diagrams, and that's opened up more intuitions. My current plans are this post on waves, then a post about vectors, and then the wavefunction and the Schrödinger equation. This is all laying groundwork.

I found a nice solution for graphing, if you like, and there are oodles of resources in terms of diagrammatic animations. I took an existing sin(x) graph today and cobbled this together in pretty short order, where I can set the slider to complete the curve.



Also does 3D graphing.

www.geogebra.org

I'm sure I/we covered the (Newtonian) Shell Theorem as undergraduates and the wiki page is a useful resource for the required sums...

Graphing solutions are always a good thing (I find wolframalpha can build some useful command lines too) and that link is now bookmarked in my toolbox folder (?!). Thanks!

hackenslash wrote:

newolder wrote:I also learned about shells of material and how they act like point masses from a great distance but also have no net gravitational pull for an observer inside the shell.

This made me laugh out loud. I remember a conversation years ago wherein we were trying to explain to somebody why an observer wouldn't feel any gravity right at the Earth's core, and I drew a crappy diagram, for which I took a shitload of abuse from Twist and Campy.

I've spent the last few days looking for a good graphing solution for diagrams, and that's opened up more intuitions. My current plans are this post on waves, then a post about vectors, and then the wavefunction and the Schrödinger equation. This is all laying groundwork.

I found a nice solution for graphing, if you like, and there are oodles of resources in terms of diagrammatic animations. I took an existing sin(x) graph today and cobbled this together in pretty short order, where I can set the slider to complete the curve.



Also does 3D graphing.

http://www.geogebra.org

That's pretty nifty.