Great points about the energy minimisation issue. Funnily enough, this is actually a problem with de-novo protein design at the moment: the designed proteins are _too_ stable! Compared to natural proteins. Protein are often not static shapes, they are machines that need to be dynamic - in other words what you said, they do not live at some deep global optimum.
> I think what you said only depends on the minimum being relatively flat (instead of deep); but it doesn't matter whether it's global or local
No. There is no such thing as a "global minimum" energy conformation, because the conditions vary wildly. Many protein structure changes are brought about by changes in the local chemical potentials and even electric fields. This is not something you can get a good grip on by thinking in terms of "flat minima".
Aether refers to some historical ideas (which evolved over time), and though the word isn’t in use anymore the current model of fields has similarities (ofc in many ways very different). Have just been reading some of the history of this (Einstein plays a big role), it’s very interesting, thank you! :) You might be interested in this discussion https://news.ycombinator.com/item?id=27942970
Wilczek points out that field theories are aether theories — as is relativity.
“Aether just means this one particular historical model!” is branding more than reality; and hides the fact that modern theories also describe an everywhere substrate of which particles are localized excitations and gravity is localized warping.
I strongly disagree with the approach of avoiding complex numbers because its "so complicated that most scientists and engineers can't spare the time to learn or use it". Full disclosure though: my training is physics, so I'm pretty biased (and will use 'i' instead of 'j' with great prejudice).
E.g. frequency mixing without complex numbers is a mess of trig-identities, and (at least to me) it's not clear at all why multiplying various terms should eventually result in the desired outcome. Whereas with complex numbers: exp(2pi i f1 t) exp(2pi i f2 t) = exp(2pi i (f1+f2) t). Other concepts are similar.
In my mind the beauty of DSP is one can work directly with complex base-band signals, rather than splitting into I and Q and then doing all sorts of shenanigans which obscure the underlying modulation/demodulation schemes - which are often quite simple but appear complicated once physical components are required (vs doing it all in software). From a historical perspective of course that stuff is all very interesting, but less helpful if you want to learn the core concepts.
The author also says most textbooks do use complex numbers which I don't doubt, but most of the resources I've found online avoid them, I usually find I can understand what's going on much better after converting it back (and hence eliminating 3/4 of the maths).
If this interests anyone - I started making a little tutorial on GMSK out of frustration about this issue, currently no actual notes, just implementations (which may not be perfect! I am not an expert) https://github.com/gabi-a/DSP_SatComms_Tutorial/blob/main/Si...*
You're right that complex numbers simplify the math incredibly. Being able to move everything to the baseband is a huge help.
I think the fundamental problem is that:
1) there isn't a whole lot of comfort with complex numbers generally, so getting rid of them makes the material seem more approachable - at the cost of being significantly more complicated, and
2) a lack of good resources for implementing common DSP algorithms in actual hardware. The jump from Matlab to raw C is mystifying to many people (myself included in many cases).
I actually prefer Lyons's Understanding Digital Signal Processing as an intro text over this one.
I also really benefitted from having a good teacher in this stuff. Dan Boschen with DSPrelated runs some great online classes on DSP that helped me immensely in understanding this material. About $200 for five classes, with tons of great iPython notebooks of examples. (He was the one who helped me get the "all math works the same at baseband" advantage of complex numbers.)
Based on the current trend the wireless modulation eco-system is moving towards time-frequency-spatial-polarization for better capacity and reliability. Not unlike the 3D graphics/multimedia eco-system sooner or later quaternion math will soon be a common thing, and textbook need to be re-written, expanded and updated due to complex number's limitations.
Worth noting that complex numbers are not avoided entirely in Smith's DSP book, they are introduced in the last few chapters. FWIW Smith's book was the one that helped me (who didn't take any math classes after high school) get a basic grasp on audio DSP principles.
Makes no sense to me, imaginary numbers came into the first year engineering course when I studied it. There's no way it would be either too hard or unfamiliar to engineers.
"39. (alternate formulation) The three keys to keeping a new human space program affordable and on schedule:
1) No new launch vehicles.
2) No new launch vehicles.
3) Whatever you do, don't develop any new launch vehicles."
Notably, SpaceX did not develop the Falcon 9 as part of their human spaceflight program, and it was in fact not rated for carrying humans for many years. They instead developed their launch vehicle as part of a standalone "launch vehicle program" then later committed to building a human spaceflight program on top of their existing rocket.
Starship _is_ being developed as part of a human spaceflight program, and we have yet to see whether this violation of Akins Laws will be justified.
I had the opposite thought. SLS/Artemis is a “new human space program” that includes a new launch vehicle and it is hopelessly unaffordable and off schedule. SpaceX developed one of the most affordable human launch systems ever made, in a reasonable amount of time, by using their pre-existing cargo launch vehicle. Even Boeing will likely have Starliner, which also uses an existing workhorse launcher, flying humans before SLS launches anything.
SLS reuses almost everything (with modifications) from the shuttle program. These are 40 year old designs. Falcon Heavy reused a 10 year old design (Falcon 9).
edit: If we count back to the first successful propulsive landing, the technology was only 5 years old. Falcon Heavy had been planned since way back in 2005.
This is not really the case. Everything about SLS was specified by Congress to be similar enough to Shuttle to require all of the same contractors, but different enough to require everything to be redesigned from scratch. No part of it should be thought of as having flight heritage.
The central tank is kind of like Shuttle’s, to justify building it in the same factory in Louisiana, but it’s a different diameter, so it had to be a clean-sheet design and all of the tooling had to be created from scratch. The solid rocket boosters are similar to Shuttle (the good Senator from Utah, with all his engineering expertise, required SLS to use solid fuel boosters that only one company in Utah can make), but a different number of segments in length, requiring them to be designed from scratch.
Early in the process of SLS (under its original name, Ares V), a group of NASA engineers lobbied for a true Shuttle-derived version, which would have been much cheaper and quicker to create, with the benefit of lots of flight heritage. Of course they got nowhere, because none of that was why SLS was the way it was. Everything about SLS is designed for the sole purpose of funneling the maximum amount of money to the right contractors in the right states for as long as possible. Thus, it is acceptable that it has never flown even after so many years and so many billions—indeed it’s desirable! If the costly design phase goes on for as long as possible, the money spigot will dispense much more than if it proceeded into operations.
But, just in case, SLS will undergo two costly redesigns after coming into service: a whole new upper stage and new boosters. That should keep the gravy train running for a good long while.
In addition to the Shuttle-industrial complex which must be kept running with make-work, there is now a Station-industrial complex which must receive the same treatment, in the form of an utterly useless lunar-orbit station called Gateway. I’m not sure if you can tell but I’m fairly bitter about all this.
Not mentioned in the above link was an amateur group developing VTVL tech around the San Francisco bay area in the 90's. IIRC, it was EPRS. FWIW, they also invented a multi-rotor platform to test their conrol system that evolved into the modern drone.
Valid point. Also, if one wants to stretch the envelope, Harold Graham, flying the Bell Rocket Belt, performed the first rocket powered landing, April 20th, 1961 at Bell Aerospace, upstate New York. This development footage opens with that flight:
https://www.youtube.com/watch?v=gxmxbMdToR4
Not quite, spacex changed quite a few things every launch or at least every version, that's why the first falcon 9 is very different compared to one from today. The one carrying humans is called block 5 of the full thrust version (version 1.2).
SpaceX was neither affordable nor on schedule. If you wanted someone up there cheaply and on time 5 years ago, you should just buy a seat on a Soyuz.
However, #39 doesn't say “don't ever develop new launch vehicles”, rather “don't develop new launch vehicles if staying in budget and on timeline is your priority”.
SpaceX did not develop a new launch vehicle for a human space program. SpaceX developed two new reusable launch vehicles for transfering cargo, whilst not cutting the corners that could not be cut if it were used for a human space program. Then when it came time to put humans on it, it already had a legacy.
Starship, however, is in fact designed for humans. But it is not part of a "human space program", rather it is a multi-purpose vehicle. It is yet to be seen towards which human space programs it will be applied, but even with the Artemis bid many aspects of Starship were clearly designed without the Artemis bid as a specific target.
Starship is intended to be a dual-purpose cargo and human flight vehicle and Falcon 9 + Dragon were iteratively improved through many cargo launches before Dragon 2 for human flight.
What has likely changed is that there is sufficient demand for cargo flights to bootstrap an affordable human flight program on top of it.
The vast majority of structures in the protein data bank are determined by crystallography, which involves putting the protein in a chemical cocktail that causes it to crystallize. The cocktail is very different to the chemical environment in which the protein functions, so an open question is whether the protein structure determined by crystallography (and hence learned by AlphaFold) is representative of the structure in it's natural environment.
It would be very interesting if there was a way to use computational techniques to go beyond what crystallography and other experimental techniques (Cryo) can accomplish and determine the protein structure in it's true biological setting. Some research into experimental methods for this include high power X-ray pulses.
The effect of a spacetime transformation isn't just to redefine straight lines along which particles move. It means measurements (e.g. lengths, areas, time intervals) are different depending on where you are in the spacetime. The are forces don't come with these "extra" effects - an EM field doesn't stretch and contract space.
However, there are a lot of parallels between electromagnetism and relativity! Quite often relativity effects are introduced with an EM analogy, e.g. gravitational waves (which have polarisation) and electromagnetic waves ie photons (which also have polarisation). Note though it really is an analogy - they are fundamentally different things in both reality and mathematical form.
The main difference though is that gravitation (probably) doesn't have a mass of its own, while EM fields do. Plus, matter does not react to EM fields in the way it does towards gravitation. I.e. light is not "pulled" by EM fields. However, these are technicalities. If all matter reacted to EM fields the same way it would to gravitation, would that make EM fields no force either? Or put another way, gravitation act universally on all particles, while EM fields do not. That necessarily has consequences when it comes to relativity. However it seems odd to argue that general relativity would exclude gravitation from being a force. If it acted only on a subset of particles, it would likely be in the same position as EM fields, and suddenly become a force again?
> The main difference though is that gravitation (probably) doesn't have a mass of its own, while EM fields do.
Both gravity and EM fields have energy which is what couples to the gravitational field. Neither of the fields has mass, though.
> If all matter reacted to EM fields the same way it would to gravitation, would that make EM fields no force either? Or put another way, gravitation act universally on all particles, while EM fields do not. That necessarily has consequences when it comes to relativity. However it seems odd to argue that general relativity would exclude gravitation from being a force. If it acted only on a subset of particles, it would likely be in the same position as EM fields, and suddenly become a force again?
This is very well thought. Indeed, the equivalence principle, the fact that gravity couples to everything in exactly the same way (and that includes gravity itself as per the previous clarification) lurks behind our ability to reinterpret gravity in a geometric fashion. After all, if something didn't interact with gravity in the same way as everything else we could establish an experiment to differentiate if a spaceship is accelerating or stationary under a gravitational field (see Einstein's mental experiment) by measuring how that thing behaves. And that same fact would stop us from interpreting gravity as curvature of spacetime itself.
To your last point, speaking of forces is probably antiquated anyway, although still in use partly for historical reasons partly abuse of terminology. Preferably we should use the term "interactions", after all some of the "forces" do not result in push or pull as we usually understand a force in Newtonian mechanics but in things like color change. Others, like the gravitational "force" can be expressed entirely as spacetime geometry. But discussing semantics is quite pointless so as long as everyone understands in what way the term "force" is an abuse of terminology it's OK to keep using it.
Also a layperson here. Can you give an example of how we can tell that EM fields don't "stretch" space, but gravity does? Is it just about how light behaves in those fields or is there something more to it?
As mentioned below, one way to think about it is that EM only affects charged particles (and depends on their charge), whereas because gravity is acting on the underlying space-time it has a universal effect on everything (including light).
We can pretty much boil EM down to: like charges repel, unlike attract, strength is charge1*charge2/distance^2. What about magnetic field, photons, QFT etc?? None of this exhibits effects which could be described as stretching space-time either.
But we cannot do the same with gravity. An explanation like the above but for gravity (which is traditional Newtonian) leaves out many, now observed effects such as:
-> time dilation (GPS relies on this calculation) (measures time stretching and contracting)
-> gravitational waves (LIGO) (measures space stretching and contracting)
How do we _know_ any of this? People propose theories, those theories are then tested against experiment. AFAIK to date there is no experimental evidence suggesting EM stretches space, and no theory proposed that includes such an effect and correctly matches experimental data. That's the most holistic answer (but unfortunately one you just have to believe unless you have a lot of spare time!)
SatNogs is fantastic for satellites operating in the amateur band. A global coordinated ground station network and community with loads of expertise. They have on at least a couple occasions (including a cubesat mission I was involved in) found satellites (ie tracked and identified from beacons) after deployment before the satellite operator. Hoping to add a station to the network sometime in the next 12 months. The grafana dashboard they set up is super cool also.
I claim that pretty much any post with "Hacker News" in the title will attract attention. And after all, attention from others what we all want, right? (I'm too lazy to verify this, but at least it sounds plausible.)
Author here! Super excited to share what I and a whole bunch of people have been working on the past year. Ask me anything!