Random Thoughts 7

[fresh_42]

Do I need to put an insulating barrier between my pressure-treated woods and my natural woods to prevent galvanic corrosion?

The question is probably more about different levels of humidity and possible mold.

 

[WWGD]

I hate English. Autocorrect wants me to write webserver as web server, but if I apply it to web sites, it insists on one word, <grrrr>. Why is vector space two words and eigenspace only one?

And what is it with the hyphenation? Are there rules, or is it an on-the-spot decision?

I've found to deal differently at different times when I use the same word.

 

[DaveC426913]

I hate English. Autocorrect wants me to write webserver as web server, but if I apply it to web sites, it insists on one word, <grrrr>. Why is vector space two words and eigenspace only one?

And what is it with the hyphenation? Are there rules, or is it an on-the-spot decision?

Isn't that because website is a word and webserver is not?

eigenspace is a word (because Germans hate space characters) and vector space is not German?

 

[BillTre]

 

[Jonathan Scott]

Something slightly related which has always amazed me (assuming of course that I've remembered it correctly): If you roll a ball over the surface another fixed one of the same radius without slipping or twisting, the orientation of the rolling ball only depends on where it is, not how it got there. The set of relative orientations of the rolling ball is equivalent to aligning it first with the orientation of the fixed ball then rotating the rolling ball by a half turn about the radius through the point of contact (so the moving ball has the same orientation at opposite points on the surface).

 

[WWGD]

I ran into this student from the beginning of my former adjunct days that I had impacted not so positively. I was writing on the board and a fly was buzzing around me and I couldn't find a way of getting rid of it, until at one point, I just pounded the fly dead into the blackboard. This did seem to traumatize her to the point I remember her just looking away when I directed my sight in her direction. She also seem to avoid me if she saw me outside of class. Weird story.

 

[WWGD]

Troubling

 

[WWGD]

Nothing says love and caring like " I made this for you. It was in the fridge and it was going to spoil otherwise".

 

[Mayhem]

If you are good at seeing connections between things, people will think you are smart.

If you are too good, they will think you are insane.

 

[WWGD]

Rowan is sitting in row two. What happened to the fixed point?

 

[WWGD]

Another one that passed me by was Malliavin.

 

[WWGD]

Vector Calculus _ Stokes_ my curiosity.

 

[fresh_42]

Vector Calculus _ Stokes_ my curiosity.

Gauss you have to be Cauchy?

 

[WWGD]

Gauss you have to be Cauchy?

Did you include Malliavin Differential in your pantheon of derivatives? Or Frechet?

 

[fresh_42]

Fréchet and Gateaux in Part 2, and material in Part 4, also known as

Euler operator
advective derivative
convective derivative
derivative following the motion
hydrodynamic derivative
Lagrangian derivative
substantial derivative
substantive derivative
Stokes derivative
total derivative

Source: https://www.physicsforums.com/insights/pantheon-derivatives-part-iv/#A-–-Material-Derivative

but I avoided stochastics.

 

[WWGD]

Fréchet and Gateaux in Part 2, and material in Part 4, also known as

Euler operator
advective derivative
convective derivative
derivative following the motion
hydrodynamic derivative
Lagrangian derivative
substantial derivative
substantive derivative
Stokes derivative
total derivative

Source: https://www.physicsforums.com/insights/pantheon-derivatives-part-iv/#A-–-Material-Derivative

but I avoided stochastics.

Maybe I could do some myself into an insight. Though ito is more of an actual net infinitesimal change and not a rate of change as a derivative.

 

[fresh_42]

sMaybe I could do some myself into an insight. Though ito is more of an actual net infinitesimal change and not a rate of change as a derivative.

I think we could need quite a few insights from stochastic, and statistics in general. I have observed that they are a very frequent topic on MSE, and we are not specifically good at it, maybe with the exception of @Dale. (I only had a B-C in my exam on a Rosenmontag.)

The different perspectives alone (Bayesian or not, the various common distributions, measure theory approach, stochastic analysis like the Malliavin calculus, statistical tests) would deserve an article, not to mention the standards like the laws of large numbers or the $\chi^2$-test, and as we are a physics website, probably Brownian motions, time series, and Boltzmann.

This field is large!

 

[BillTre]

 

[WWGD]

View attachment 362255

Anyone heard of those new super-fast chargers? Supposedly take just 10-15 minutes for a full charge 0-100%.

 

[WWGD]

Another win in my quartel against ETS: the ratio of the area of a circle inscribed in an equilateral triangle is fixed. Thus knowing the radius of the circle is enough to know that of the inscribing triangle.

 

[WWGD]

Another win in my quartel against ETS: the ratio of the area of a circle inscribed in an equilateral triangle is fixed. Thus knowing the radius of the circle is enough to know that of the inscribing triangle.

After teaching/tutoring GMAT and similar tests, I decided to tell my students that the ratio of area of an equilateral triangle to a circle it's inscribed in is $\frac{\sqrt 3 \pi}{9}$, and the converse , of an equilateral triangle inscribed in a circle is $\frac{3\sqrt{3}}{4\pi}$. Just got tired of solving the problem so many times.

 

[Jonathan Scott]

After teaching/tutoring GMAT and similar tests, I decided to tell my students that the ratio of area of an equilateral triangle to a circle it's inscribed in is $\frac{\sqrt 3 \pi}{9}$, and the converse , of an equilateral triangle inscribed in a circle is $\frac{3\sqrt{3}}{4\pi}$. Just got tired of solving the problem so many times.

I'm just wondering why you don't show it in a form that makes it directly clear that the ratio of the larger triangle to the smaller one is 4, for example by making the first one $\frac{\pi}{3\sqrt{3}}$.

 

[WWGD]

I'm just wondering why you don't show it in a form that makes it directly clear that the ratio of the larger triangle to the smaller one is 4, for example by making the first one $\frac{\pi}{3\sqrt{3}}$.

The ratio between the two is
$\frac{4\pi^2}{27}$~$1.46$.

 

[Jonathan Scott]

The ratio between the two is
$\frac{4\pi^2}{27}$~$1.46$.

I mean that if you have an equilateral triangle inside a circle inside a triangle, the larger triangle is four times the area of the smaller one, and that is clear from the ratios if you rewrite $\frac{\sqrt{3}\pi}{9}$ as $\frac{\pi}{3\sqrt{3}}$ for consistency with the other ratio. The smaller triangle in terms of the larger one is then simply as follows: $$\frac{\pi}{3\sqrt{3}} \cdot \frac{3\sqrt{3}}{4\pi} = \frac{1}{4}$$

 

[fresh_42]

 

[WWGD]

Troubling : What ChatGpt does with your data:

 

[fresh_42]

I watched a documentary yesterday about our development as a species throughout the various ages of Earth, with an emphasis on the changing climates. Someone said in an interview that, after all, we stem from a tropical area and are not specifically prepared to cope with ice ages. I hate hot weather. And I am a European, hence I carry Neandertal genes. I assume that mine are significant. I should let them be tested.

 

[WWGD]

One day late:

 

[Ibix]

Ah, British trains. In the last fifteen minutes we have advanced less than one mile. And the air conditioning is broken.

Edit: oh, and although we're at a station they can't open the doors so we can get some fresh air because the (alleged) express is longer than the platform at this tiny stop and they can't only open some doors and if they open all of them some idiot will step out without looking to see if there's a platform and then sue.

 

[WWGD]

Ah, British trains. In the last fifteen minutes we have advanced less than one mile. And the air conditioning is broken.

Edit: oh, and although we're at a station they can't open the doors so we can get some fresh air because the (alleged) express is longer than the platform at this tiny stop and they can't only open some doors and if they open all of them some idiot will step out without looking to see if there's a platform and then sue.

Literally a not very cool part of Summer.