mc ☕ @mc@qoto.org

@Pat
Okay lady... I'm puzzled now.

I've been trying to figure out how you got to the factorials formula.
Could not be empirically. (Could it?)

So, how did you get there? Please.

> These #chocolate #cherry #brownies are insanely fudge like, gooey, and rich. They take less than 10 minutes to prep and less than 30 minutes to bake.
#recipe

https://organicallyaddison.com/chocolate-cherry-brownies/

@freemo
I was going to use the formula "break a leg", but... I'll just wish you good luck.

My kind of girl.
#flexible #Parcour #gal

https://foto.dapor.org/picture.php?/8840

@Pat
> Isn’t learning fun…

absolutely fascinating... For approximately 1% of the world population.

So, in spite of being "not a math gal" you got it.

Well, I'm impressed.
...
I never thought that Wikipedia would have such good math articles.

You also seem very comfortable discussing physics.

The #Orange #Almond #Cake You Should Make This #Weekend! 😋

https://www.marilenaskitchen.com/2021/12/09/orange-almond-cake/

@Pat
> Of course you could just use the summation symbol in an equation or the sum function in mathlab or julia

That'll do, as long as I know how the sum function works. 😃

@freemo
Congratulations.
Nice video. Not much color, tough.
2 questions:
- Those iron structures are part of some project to populate bare sand sea bottoms?
- Some sounds recorded seem those of airplanes. Is that place near an airport?

@Pat
Perhaps you can find some relation between the heights of the successive tet.s? (If youhave the time and he will to do it, of course.)

@Pat
> My unconscious brain keeps interrupting my day with ideas on this…

OMG! What have I done? I'm sorry, really didn't mean to... 😅

> the solution should be the formula for the volume of a tetrahedron

Wouldn't it be nice if it could be so simple? 😃

> Do you already know what the general formula is?

Nope. But I trust you will find it. Some authors say that obsessive thinking is the start of the 'Eureka' moment. 🤭

(as #promised)

```
2. Generalizing the function for any number of days:

```
function allgifts2(days)
dg = [] # daily gifts storage
for d in 1:days
d = sum(1:d) # daily gifts from day 1 to days
push!(dg, d) # storing each day gifts
end
print(sum(dg)) # showing total number of gifts in storage
end

# There are actually 13 days from 25 Dec to 6 Jan
# Let's add to the list Thirteen puzzlers puzzling
# > allgifts(13)
# 455
```
```

Did The Wise Men (Magi) Arrive 12 Days After Jesus’ Birth?
https://reasonsforhopejesus.com/did-the-wise-men-arrive-12-days-after-jesus-birth-or-much-later/

**Happy Three Kings Day**

"C'est la guerre qui fait fleurir les #mathématiques appliquées dans toutes sortes de domaines et y convertit provisoirement la quasi totalité des #mathématiciens disponibles : ondes de choc, « surface waves in water of variable depth », calculs "hydrodynamiques" pour les bombes atomiques, dynamique des gaz, optimisation statistique des bombardements aériens, tir contre avions, recherche opérationnelle, etc. Certains mathématiciens de l'industrie commencent à dire (Thornton C. Fry, Bell Labs, 1941) que lesmathématiques "pures" ou "supérieures" ne sont, après tout, que des branches des mathématiques appliquées qui n'ont pas encore trouvé un vaste champ d'applications « and hence have not as yet, so to speak, emerged from obscurity » (12).
...
On fait alors appel, pour le Japon, aux services d'une équipe dirigée par un #statisticien de Berkeley, Jerzy Neyman, qui applique à ce problème et à d'autres des méthodes qui le rendront célèbre après la guerre (13). En 1943, Richard Courant, s'appuyant sur la méthode d'approximation qu'il a utilisée en 1928 avec Friedrichs et Lewy pour établir l'existence de solutions d'équations aux dérivées partielles, explique à Hans Bethe, chef de la #physique théorique à Los Alamos, comment calculer numériquement le comportement d'une sphère de #plutonium comprimée par une onde de choc convergente (Nagasaki) ; de cette technique fortement poussée par von Neumann sortira l'intérêt de celui-ci pour le premier #calculateur #électronique qu'il rencontrera l'année suivante , l'#ENIAC; c'est pour ce calcul que l'on a déjà commandé en 1943 des machines IBM à cartes perforées incomparablement moins rapides. ..."

#Science, #technologie, armement by Roger Godement (pdf)
https://rogergodement.com/gallery/extraits%20de%20la%20pr%C3%A9face%20&%20postface%20int%C3%A9grale%20issues%20de%20analyse%20math%C3%A9matique%20(1997).pdf

@sprkwd@mas.to
Shouldn't it be 'Explore'?

@Pat
> I looked up “arithmetic progression” and this doesn’t fit the definition

Of course it does not fit... Did I say it was an arithmetic progression? OG, what was I thinking?!

Sorry. Now I'm focused. It's just a triangular numbers sequence with accumulation of all previous results.

@Pat
Apparently this is the Unix sysadmin way, not using any shell math features ;)

```
for i in `seq 1 12`; do for j in `seq 1 $i`; do head -c $j /dev/zero; done; done | wc -c

```

...
Care for a #nappuccino?

If a plain #nap just isn't doing enough for you, Banks does have another hack up her sleeve, one that will be especially exciting for #coffee enthusiasts.

"One of our team published a paper last year on the 'nappuccino'," she tells ScienceAlert. "It's basically having a coffee before you have a nap."

Why does this work? Along with other physical effects, #caffeine blocks a compound called adenosine from accumulating in our brains. Adenosine reduces the brain's firing rate, and helps us get to sleep; then, once we do sleep, it's whisked away to start the day (or afternoon) afresh.

So, coffee and sleep together makes you wake up even more refreshed than either alone. Banks loves coffee, and sees it as the easiest sleep hack we all have access to.

"It's a little bit boring in terms of a hack, but there are ways to more strategically use caffeine," she says.

"The average person has a big cortisol spike – a stress hormone – in the morning to get us going. That's a very normal thing. So, we actually don't need to have coffee first thing in the morning, but people want to have it because they feel a little bit sluggish."

Instead, having caffeine in the late morning would help you get through the afternoon, without keeping you awake throughout the night.

As with many other variable traits within our species, some people also just get lucky with their genetic sleep lottery.

"There is a big range – some people need more and some need less. There are some people who naturally can get by with a much shorter amount of sleep," says Banks. You can think of it like a spectrum, similar to normal ranges in height or weight.

"Now, those politicians that say they could get by on just a couple of hours sleep, I don't believe them. I think that maybe they're catching up on their sleep through naps or maybe being asleep in Parliament."

Again it all comes down to naps... even while making decisions for the nation.

Of course, getting less sleep and chugging coffee aren't just about maximizing productivity. Some people have insomnia or anxiety around sleep, and knowing that your health is incurring damage without the right number of hours is unlikely to help quieten the voices in one's head.

So it's reassuring to know that once you do get back to a normal sleep schedule, the brain has a surprising ability to bounce back – and many of the problems associated with sleep deprivation do actually get better.

"To follow up all that doom and gloom, when we change our sleep habits and get more sleep again, we also see that some of those mental and physiological effects go away," says Banks.

Edison, for what it's worth, would fall asleep under his desk or in meetings – sometimes he'd just pass out wherever he was. His wife installed a cot in the corner of his office so he'd at least have somewhere to lie down.

So, the next time you feel like a nap might be a waste of time, remember it's just the opposite. If you can get it, there's truly no better productivity hack than a quick nap.
___

The #Science of a Good Nap
https://www.sciencealert.com/the-cult-of-the-sleepless