• 0 Posts
  • 21 Comments
Joined 2 years ago
cake
Cake day: July 25th, 2024

help-circle













  • If you didn’t have plate tectonics, you’d have a lot of problems with the atmosphere, and there’s a decent chance that life wouldn’t evolve, as the energy differentials generated by tectonic activity are those which life hangs onto, from nutrients, to oxidation, to geothermal heat.


  • Again, I think you’re replying to the wrong person. I never disagreed with any of this. I literally learned all of this years ago. I appreciate your attempt to educate, but I’m unclear on its purpose. The dude claimed that the speed of light is defined based on the meter, and that that makes it a tautology. That is simply, provably false. Then the dude tried to move the goalposts. Never did I say that our measurements are anything less than relative. Never did I suggest that our derived units are not based on fundamental constants the nature of which can be only guessed at. Now, you’ve said that the statement I made didn’t tell the dude “how to make use of” dimensionless units, which is a complete non sequitur. If you feel that that lecture is an important one when a dude demonstrates a fundamental misunderstanding of what c even is, that’s your own affair, and I invite you to give this lecture a few comment levels up to the guy who thinks that c is defined based on the meter.


  • I was unaware that the person to whom I was replying, who claimed to be intimately familiar with the complete works of Feynman, needed instruction in how to “make use of” a fundamental constant of nature. If that is something you think is necessary, perhaps you should see to their instruction in such matters, as you are so confident in your faculties of condescending instruction.

    Furthermore, I am acutely aware of the existence and nature of dimensionless constants, thank you very much.


  • c is a measurable constant, not some unit that is arbitrarily defined. Like Boltzmann’s Constant, or the ground state hyperfine transition frequency of the Cesium-133 atom… it just… Is.

    Therefore, it is a useful tool to define units. You claim it is a tautology because we write it in units of meters per second, while the meter is defined based on c. This is easily disproven, as you can represent the speed of light in any unit of velocity. It is a fundamental constant, derivable through experiment without any units a priori.



  • For the uninitiated: this is the current most-efficient method found of packing 17 unit squares inside another square. You may not like it, but this is what peak efficiency looks like.

    (Of course, 16 squares has a packing coefficient of 4, compared to this arrangement’s 4.675, so this is just what peak efficiency looks like for 17 squares)

    Edit: For the record, since this blew up, a tiny nitpick in my own explanation above: a smaller value of the packing coefficient is not actually what makes it more efficient (as it is simply the ratio of the larger square’s side to the sides of the smaller squares). The optimal efficiency (zero interstitial space) is achieved when the packing coefficient is precisely equal to the square root of the number of smaller squares. Hence why the case of n=25, with a packing coefficient of 5, is actually more efficient than this packing of n=17, with a packing coefficient of 4.675. Since sqrt(25)=5, that case is a perfectly efficient packing, equal to the case of n=16 with coefficient of 4. Since sqrt(17)=4.123, this packing above is not perfectly efficient, leaving interstices. Obviously. This also means that we may yet find a packing for n=17 with a packing coefficient closer to sqrt(17), which would be an interesting breakthrough, but more important are the questions “is it possible to prove that a given packing is the most efficient possible packing for that value of n” and “does there exist a general rule which produces the most efficient possible packing for any given value of n unit squares?”


  • I believe that they contribute to understanding, because human minds are wired to engage with stories. If your chemistry teacher was worth their salt, they’d teach you Gay-Lussac’s law by telling you about how, when the hot air balloon was first invented, Gay-Lussac was seen as a mad young upstart by all of the older scientists for wanting to go up in one. Well, not only did he nearly die making measurements, he also showed that, at higher altitudes, there was lower pressure and lower temperature. Then, your chemistry teacher should pull out a spray-can of keyboard cleaner, invert it, spray the liquid into a beaker, and let everyone feel the adiabatic temperature depression from expansion (of course, most of the endothermicity is from the boiling of the liquid, but the point stands) they can explain that any compressed gas gets colder when you release it, whether the keyboard cleaner, spray paint, or the compressed coolant in the coils of your refrigerator. Lower pressure, lower temperature. Gay-Lussac’s law. Now, all of those students will, when they think about the relationship of pressure and temperature, remember Gay-Lussac in a hot air balloon, at low air pressure, and low temperature.