Sometimes, as I am staring into the deep soul of my monitor, my mind momentarily drifts to thinking about the glimmering pixels which are being updated right before my eyes. Such an extraordinary piece of technology, now just tossed into commonness.
Now, it would be quite comical for a person to become fascinated by every single thing that they see around them but, this makes me wonder: what technology traits make people ‘blow their brains out’. And does this have any dependence on the time they were born into?
Every technology, defined narrowly enough, goes through an S-curve: it starts out small, picks up steam, hits a hockey-stick inflection point, grows exponentially—and then starts to near saturation, slows down, levels off, plateaus.
And regarding how breakthroughs open the flood gates to new invention, he says:
… But when some breakthrough insight creates an entirely new field, it opens an entire new orchard of low-hanging fruit to pick.
I think this is an interesting way to think about progress and would be great to quantify this more rigorously.
Talking about the miracle molecule which keeps us alive, I recommend listening to the episode titled “Breath” from Radiolab. This is a great episode where ” try to climb into the very center of this thing we all do, are all doing right now, and now, and now.“
When people encounter issues with their car or microwave or any man-made object, they are more likely to put on their engineering hats and try to ‘fix’ the problem (oftentimes succeeding in doing so). I find this approach of dealing with ‘man-made’ things rather interesting because, this assumes that there is a solution that exists which can ‘discovered’ upon inspection. This is also common in GitHub repositories where tons of issues get reported regularly and, people are able to eventually resolve them by making changes to the code. Why do we believe that a solution must exist and pursue seeking it? Is it because it was made by another human being and ergo, a solution must exist? I am not sure, but it seems to serve as a motivation to try, which is powerful.
Having said that, I find it hard to transpose the same ‘fix it’ philosophy that applies so well to everyday things, to the study of nature. What are we trying to fix in nature? Well, if we were to let go of our perception that a scientist is someone who works in a lab and looks into a microscope all day, it becomes a little easier to tackle this question.
For example, what if we picture a particle physicist as someone who is fluent in python, QFT, GR and Group theory; works primarily on ‘front-end architecture of atomic particles’ and maintains a GitHub repo titled ‘my-standard-model’ where typical issues in the repo would be along the lines of ‘missing charge’, ‘Help:ValueError: Output contains NaN, infinity or a value too large for dtype(‘float64′).’ and so on; And every couple of months or so, some of these issues end up getting resolved and a PR follows? It sounds a little weird to say it out loud but, certainly conceivable. I guess what I am trying to get at is that, this feedback loop of ‘found issue in model/codebase –> report it –> try to fix it –> if resolved, close issue –> repeat’ might be more universally applicable than we thought.
I was recently watching this vox video and BBC documentary on the Concorde and supersonic travel. The fluid dynamics of air at mach speeds greater than 1 is a fascinating subject on its own accord.
Stagnation enthalpy
Stagnation enthalpy is defined as the ‘Enthalpy of a fluid when it is brought to rest from velocity v isentropically’. Stagnation properties such as Stagnation enthalphy, pressure, temperature are often used to quantify the fast moving air around a flight moving at supersonic speeds.
“For very low Mach numbers, the density of the air is a constant. But as the Mach number increases into the supersonic regime, some of the energy associated with the motion of the object compresses the gas and changes the density from its static value….. As the Mach number increases into the low hypersonic regime, some of the energy of the flow excites the vibrational modes of the diatomic molecules.”
Imaging shock waves in a laboratory can be achieved through specialized tools, but NASA regularly posts images of shock waves around jets flying way up in the sky. How does one begin to visualize shock waves from an around an aircraft at several thousands of feet in the air. This post runs through a few techniques that are commonly employed
Vapor cones and condensation
Slowing down to Transonic speeds, a visible cloud of condensed water form around a fast moving aircraft or object known as a ‘vapor cone’.
This physics today editorial talks about a study which found that as the number of paper in a field increases, it becomes increasingly difficult for researchers to recognize innovative work and progress, as a result, stalls. This got me into thinking about different ways to mitigate this issue:
Parsing journal articles faster?
Some journals include a ‘Plain Language Summary of article’ or ‘Significance of work’ in the abstract section of the paper. These are usually provided by the authors and might help readers parse information faster (although with some clear loss in details). Here are a few journals which have implemented some form of this:
A while ago, I stumbled upon this python module called Sumy and an online web summarizer (ExplainToMe) which were able to summarize contents of HTML pages and documents into a few sentences. And quite frankly. their performance was surprisingly good. Another way to address this issue might be invoke the machines and use NLP to solve this issue.
A more “unbiased” alternative to summarizing articles might be through online discussion (via YouTube, Reddit, twitter, forums, etc). I find Fermat’s library implementation for such a routine quite ideal. They discuss one interesting research article per week but also allow others to annotate and highlight.
When I was learning about commutation relations in QM, this website served as a good resource. Inspired from that here’s a compiled list of commutation results which I found helpful and some notes on how to use index notation to see why that relation would be true.
Approximately two years ago, I wrote a series of posts covering Pilot wave hydrodynamics with Nicole Sharp from FYFD. Since then I have always wanted to try this out at home and visualize the phenomenon. Following is an informal report on how I was able to get this to work from things I found at home:
Things needed
A sub-woofer or a woofer
Petri dish
Dropper
Cardboard
Hot glue
Vegetable/ Silicon/ Linseed oil
Setup
One of the first things that I did was to grab a cardboard and cut it to the size of the sub-woofer.
I then hot-glued a white sheet of paper with grid lines on the cardboard and carefully placed the petridish on the center of this cutout and glued the petridish onto the cardboard.
(Since I was using my personal speaker for these experiments I did not glue the cardboard-petridish setup to the sub-woofer. But if you are dedicating an entire woofer/sub-woofer to these experiments you can glue the setup to the its edges so that it does not wobble when you vibrate it from below)
I finally made a striped color pattern with some strips of paper and placed it in the background such that the reflection of the striped pattern was seen on the petridish. This helps to visualize the perturbations on the surface of the fluid.
Final setup
Connect the speaker to your computer and voila! you have a setup for visualizing pilot wave hydrodynamic phenomenon
Making droplets bounce
I primarily used vegetable oil for most of my experiments. This has the disadvantage that the bouncing droplets do not last for long but it is more commonly available at home. Other oils that offer longer bouncing time are Silicon and Linseed oil.
Pour the vegetable oil on to the petridish*, tune the speaker to 23-33 Hz, and reduce the volume until you do not see any perturbations on the surface (i.e below the Faraday threshold).
Using the dropper take some vegetable oil and carefully drop it on the vibrating bath (see gif below). And you should be able to see a tiny droplet of oil bouncing happily on the surface.
With a bit of patience, it is also possible to make multiple droplets bounce together (known as a droplet lattice. see gif below )
Following are some interesting footage that I shot at 240/1000 fps using this setup on my Galaxy S9:
https://youtu.be/rk8PWaJoGdA
Droplet lattices
Droplet lattices
I strongly encourage the interested reader to try this out. It was a lot of fun to make it and you will not be disappointed at the results. If you have any questions, feel free to email me at 153armstrong@gmail.com, I would be happy to help you out.
Known issues/ Ways to make it better
Since I was using my personal speaker for these experiments I did not glue the cardboard-petridish to the sub-woofer. But doing this would be very optimal. I often had to ensure that petri dish was aligned to the center of the sub-woofer from time to time. This could have been easily resolved by gluing it to the sub-woofer surface
As you can notice from some of the gifs, there were some tiny contaminants in the oil or some air bubbles that got trapped inside. Although I tried to maintain a clean environment it was hard to avoid such contamination entirely.
One of the easiest way to visualize ray diagrams for lenses is by using an array of arrows on the board as the object and the camera on your phone as the screen.
(i) Convex Lens : Arrows on the board are placed outside the focal length of the lens -> Inverted image
(ii) Convex Lens :Arrows on the board are placed inside the focal length of the lens -> Magnified Erect image
(iii) Concave Lens: Irrespective of whether you place the arrows inside or outside the focal length, you get an erect image.
(iv) Convex mirror: Virtually erect image formed from a Christmas ornament
The following video from UCLA extends the ray diagram analysis for concave and convex mirrors:
(This page will be updated as the quarter progresses with other techniques that you will eventually learn about)
There are many way to make things “disappear” and impart the illusion of invisibility. Based on what you have studied so far, here is one possible ways you can do so. (There are certainly other ways and I strongly recommend spending some time thinking about this)
If you want to make something invisible,you have to ensure that the index of refraction of the object and the medium where you are hiding it remain the same and also that the object is transparent and colorless.
The refractive index of a polymer ball is identical to that of water and if you immerse a colorless polymer ball in water, you can make it ‘disappear’ like the animation above shows you.
When you immerse colored polymer balls in water on the other, they seem as if they are 2-d objects although they are spheres!
Colored Polymer balls appear as 2D circles when immersed in water
If you are an astronomer trying to study the cosmos from the earth, this turbulence of air and twinkling of stars is a total nightmare.
The last thing that you want the light that painstakingly took millions of years to get to the earth is to be wiggled away from your telescope through refraction and turbulence!
If you have seen lasers coming out of telescopes. That’s part of the Adaptive Optics system used to correct for atmospheric disturbances due to turbulence and refraction.
But Astronomers found a way to deal with this, a technique called ‘Adaptive Optics’ which uses deformable mirrors to account for the disturbances in the atmosphere.
With and Without Adaptive Optics
Using this technique, the following is the difference between capturing an image with and without adaptive optics.
What can you find with this technique?
Here’s an interesting question: What exactly is at the center of our galaxy? Is there a black hole ? How do we go about studying it?
Prof.Andrea Ghez and her research group at the UCLA’s Galactic center group were inspired by the same question and decided to look at a region in the sky which they believed was the center of our milky way galaxy.
And this is what they found of the trajectories of stars surrounding the proposed center of the galaxy:
The star in the middle is the proposed center of our galaxy.These images were taken through the years 1996 – 2016 (see top right of gif).
The first thing that you notice about these stars is that they are orbiting a point in space. This is very similar of how planets in our solar system are orbiting the sun.
One of the special stars in that animation is S0-2 which completes its elliptical orbit in only 15 years!
S0-2 completes its entire elliptical orbit in just 15 years!
( it takes the sun approximately 225-250 million years to complete one journey around the galaxy’s center )
But having this knowledge of how small the orbit is, we can use Kepler’s law to find out the Mass at the center of the galaxy. And we get the mass of the center of our galaxy as a staggering 4 million times the mass of the Sun
How massive is that?
Let’s take a look at the orbits once again:
The radius of this object at the center, in order to avoid collision with the rest of the objects has to be about the diameter of Uranus’s orbit.
So, an object that has 4 million times the mass of the Sun. and diameter of Uranus’s orbit .. Hmm.. The only astronomical object that would fit this characteristic is a Super Massive Black Hole (SMBH)
And that’s why we believe that at the center of our galaxy is a SMBH: Something we would not have been able to realize without adaptive optics.
So, the next time you go out to gaze at the cosmos, just remember that whatever you are seeing in the night sky right now is through the looking glass of our beloved atmosphere.
And astronomers put in immense effort to nullify the dynamic atmospheric effects that it loves to entertain us with.
All images/animations featured in this post were created by Prof. Andrea Ghez and her research team at UCLA and are from data sets obtained with the W. M. Keck Telescopes
When you search for videos online of plucking a string on an instrument such as the guitar, a surprising number of searches lead you to videos such as the following:
This is not how plucked strings look like! And they don’t have anything to do with Harmonics either! The reason why you are seeing those shapes on the guitar is due to the rolling shutter effect on your camera.
But if you do want to see how plucked strings look like, the following videos would be your best bet:
There is a usually an oscillating paddle( above– used to produce plane waves) or a point source/s ( below – used to produce circular waves ) which are actuated by eccentric motors, solenoids, etc + a shallow tank of water.
And that’s about it! One is ready to visualize wave phenomenon
Here are some of my favorite renditions of physical phenomenon on a ripple tank. Check sources for more. Enjoy!
1. Diffraction
2.Double slit experiment
3. Reflection
4. Refraction
5. Parabolic Reflectors
6. Doppler Effect
Doppler effect is the increase (or decrease) in the frequency of sound, light, or other waves as the source and observer move toward (or away from) each other.
If we have a speaker that is moving to the right (see animation above), if you are standing infront of the speaker you will hear a shorter wavelength- higher frequency sound and if you are standing behind the moving speaker, you will hear a longer wavelength – lower frequency sound.
We experience the Doppler effect everyday whenever a car whizzes past us. Here’s a demo:
In the previous section we took a look at the vibrating string fixed at both ends and found that in order for the boundary condition to be satisfied, the following are the only solutions possible:
The solutions on the left of the image are often termed as ‘Odd Harmonics’ because they have odd number of anti-nodes and the ones of the right have even number of anti-nodes hence ‘Even Harmonics’
If you pluck a string right at the center, you are essentially exciting only the odd harmonic components.
You can test this out by taking a string instrument and plucking it at the center. Download a spectrum app on your phone and take a look at the spectrum
You will see peaks in the spectrum only at the frequencies which correspond to the odd harmonics:
String instruments like the violin or guitar are plucked off-centered, so you get both the odd and even harmonics. But what differentiates one instrument from the other is the amplitude at which these harmonics are expressed when you play them.
Do watch the following video if you would like to know more:
If you have a solid understanding of what Traveling waves are (click here if you need a refresher) then when you add up a sine wave moving to the right with a wave moving to the left, you get a standing wave.
