Recent content by erobz

Start working with it (AI). Consider it a genius level mathematician that can help you explore, learn, and create (possibly) influential work.

Sorry. A friend of mine isn't entirely happy about the arguments so far. They point out that the standard formula for arc length is: $$L=\int_a^b\sqrt{1+[f'(u)]^2}~du,\qquad a<b$$ This suggests that the more general expression for the arc-length element should be...

I would say avoid the ##( -dy )## thinking - it's corrupt. The delta ##\Delta## or ##d## captures change in either direction ( ##\pm##), it's going to lead to errors if you start thinking that it is signed. Use $$ s = \int_0^a \sqrt{ 1 + ( y' )^2 } ~dx $$ and it will all work out.

The math looks fine, but it's not realistic. Tension isn't going to be developed in the front leg unless the chair is pinned to the ground there. The rear constraint can be met by normal forces and static friction, but basically static analysis is telling me that a "functionally normal chair"...

There is a lot of geometry to track if you are trying to be precise? I think I diagram of the free body in certain positions is a great place to start. Then you likely have to make some reasonable assumptions, maybe even a video of yourself completing a pushup is warranted so you can see the...

Not sure I completely follow, but the butter will not slide uphill once it gets a layer of melted butter beneath it. In your experiment, when you exaggerate the incline of your pan (such that the heat source is higher like shown) do you observe the butter pad climb from the bottom of the pan...

The butter is experiencing a force ( frictional) that is holding it in place against basically imperceptible elevation gradient ( a bubble level measurement ) and/or temperature gradients are changing the pans geometry as its heated asymmetrically. When the heat reaches the butter pad, it begins...

Exactly my point. There is nothing inherent in a blip that makes it distinguishable as a particular phenomenon...it becomes distinguishable as a particular phenomenon via the current world model you are using.

You're missing my point. I'm not arguing the models are limited by what we can directly perceive by sensory input. Let's look at UV. We don't directly sense it, but we deduced something was "there" in our world model. So we use our world model machinery to build instruments that interface with...

For the skeptics on my post... When you open your eyes in the morning do you experience the universe as it is? No. You see a wall, you hear a coffee pot, you feel a crick in your neck, etc... all of the input available to our sensory system constructs the world around us as we become...

Since everything "found/examined/observed" in the physical world is mediated by the mind; At a fundamental level it actually is the case that what we "are experiencing as the physical world" is in fact just our internal mathematical constructs of it compiled from incomplete sensory input (a...

If it doesn't exist, how do you suppose it works so consistently on such deep levels? All of these things that you say "do exist", are also inescapably constructions of the mind. Can you observe the "physical universe" without a mind? A universe devoid of consciousness is no universe at all.

I got Chat GPT to look at the Fluid Mechanics approach. After it fixed a sign error i made in the flux term It gets what @haruspex, and @TSny get too. $$0 = \frac{d}{dt}\left( ( M+m)v \right) - \rho A u ( u-v)$$ It doesn't work with the integral, it instead works with ##\dot{m}## which we...

as far as I can tell that is what is happening. The bottom temperature is leading during the transient phase while a significant the thermal gradient is being established ( its penetrating depth is ## x \propto \sqrt{\alpha t } ## ). Initially ( 0s - 25 s ) Your blue line is climbing while your...

It's not difficult, but I do recall "getting it"(I learned algebra mostly as an adult though). I teach my kids by balance scale type problems. There is an intuitive understanding about physical balance at a pretty young age. You might balance shapes with them, and you can use other balance...