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Cake day: July 20th, 2023

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  • They need to add heater packs underneath and thermocouple readings. While white is good at rejecting external thermal radiation, it is also poor at emitting thermal radiation. A white surface can be hard to keep cool if the heat comes from within. In particular, white will look like it has a much better comparitive advantage when imaged in IR than is likely to be the case in real usage conditions.

    Yellow, red, and gray may be more comfortable in practice.




  • If her primary concern is drinking water, you can get an under sink RO filter for a couple hundred. They’re very easy to install yourself. I’ve even helped a friend install one connected to their fridge so that the fridge dispenser would taste better. We are on city water that tests well except for microplastics and it sometimes tastes a little bit like soil or musty. The RO systems come with a particulate filter, carbon stage, Reverse Osmosis membrane, and a remineralization stage. RO is the only way to effectively remove microplastics.

    Personally, I would consider having a particulate filter and maybe water softener for the whole house. Neither of those should be crazy expensive. The water softener is only if your city water tests hard or if you have mineral buildup on your shower heads or in your dishwasher. If you’ve done any plumbing work, a particulate filter is pretty easy and affordable to install yourself.

    Reverse osmosis for the whole house is simply unnecessary. Install one yourself at the location your family gets their drinking/cooking water.

    https://www.mcmaster.com/product/4361K71

    This unit from mcmaster carr is what I use. Please be aware that chlorine does damage the RO membrane, so it is important to replace the first two filter stages approximately every 6 months. The fourth stage is recommended to be replaced yearly and the RO stage is supposed to be good for 2 yrs.

    https://www.mcmaster.com/4361K81/ https://www.mcmaster.com/4361K82/ https://www.mcmaster.com/4361K83/ https://www.mcmaster.com/4361K84/

    Express Water also has some decent under sink and counter top options.

    Removing chlorine for the whole home requires a large activated carbon filter. They’re pretty expensive and the media gets saturated and has to be replaced every so often to keep absorbing chlorine. I would only do this if your wife has extremely sensitive skin that is getting irritated from your tap water.

    Oh and Reverse Osmosis systems waste more water than they clean without expensive recirculating pumps and controllers. That’s acceptable for a couple gallons of drinking water a day, but would be very wasteful and expensive in a whole-house system.



  • Marble has a density of 0.098 lbs/in3. So a 500lb sphere has a volume of 500lb/.098lb/in3= 5102 in3. That gives a radius of (5102 in3 * (3/(4pi)))(1/3)= 10.68 in.

    Let’s say the bowl it sits in has 2/3 the radius. So 7.12in. That makes the enclosed surface area pi*( 7.12in) 2= 160in2. So 500lbs/160in2 = 3.14 psi. How fast do you think the water will spray out at 3.14 psi? Without any drag, out of an ideal nozzle, it would be 6.5mph. However, the pressure will actually be higher in the middle and tapers off to 0 at the edge thanks to the flow diverging and drag. So really the pressure drop at the opening is even smaller.

    There’s a lot of lifting area which means you don’t actually need much pressure. You can lift entire buildings with large water bags.








  • Definitely, any changes natural or anthropogenic would be measured and to great accuracy. I just wanted to point out that the notion of the general public, especially if conditioned to distrust scientists and authorities, not noticing changes isn’t the outlandish part. See global warming denial despite years of record setting temperatures.


  • Ignoring conspiracy theory stuff, people aren’t very good at perceiving changes in light levels if they happen gradually. During any solar eclipse there are wide bands where only a partial eclipse is observed. It’s pretty common for people in those bands to not notice that something has changed even with 50% occlusion.






  • Are you familiar with the difference between polar (r, theta) coordinates and cartesian (x,y) coordinates? Parabolas are the solution to gravity that is uniform no matter where you sample. It assumes that gravity points in the same direction with the same magnitude no matter where you are. In this model, gravitational acceleration is always 9.81 m/s^2 in the -y direction. That is a reasonable simplification for things that are at the human scale constrained to near the earth’s surface. Deviations from air resistance will matter far more than errors stemming from that assumption anyway.

    Conic sections are the solutions to gravity that is between two objects where the force is along the line between the center of mass of both objects and the strength is inversely proportional to the square of separation. Now you need polar cpordinates and the direction of gravity changes as things move around. This works pretty well for orbits around the earth and orbits around the sun, because the earth is so much more massive than sattelites that orbit it, and the sun is so much more massive than things that orbit it. If you need really precise orbit trajectories, ellipses aren’t truly accurate either. You need to account for all the orbiting bodies in the system. The 3-body problem famously doesn’t have purely analytical solutions, and you need to resort to numerical methods to calculate trajectories.

    So both solutions come from simplified mathematical models. Despite being simplifications, their predictive power is actually very goood. However, like you are intuiting, it’s important to know when those simplifying assumptions lead to errors that start to become important. It’s hard to come up with a particular threshold for when you need to switch from one model to another, because it really depends on how much accuracy your application needs.