Today I Learned #4: Somewhere, something incredible is waiting to be known.

[Takhisis]

I don't think you can join without taking the test (I don't think: I know), and I am not sure if such is provided here (there is one, in Athens).

And if you did you might have to satisfy their Europhilia, so maybe better not.

 

[Kyriakos]

All the same, you can't take something from one not having it - as was famously said in the Dialogues of the Dead, by Lucian of Samosata.

 

[Takhisis]

Also in the famous Lazarillo de Tormes, when the beggars discuss whither to go to ply their trade.

 

[Kyriakos]

Well, not "learned" (technically I knew it is true, before), but TI Undestood/formed a stable understanding of why:

From my perspective, the most intuitive way to understand this is that the infinite sum of the values y in the derivative, multiplied by dx, covers the accumulation of the value of y of the original function between the points (eg a,b) taken in both.
Still, nice to acquire an actually definitive hold of it, regardless of this not negating possible future other angles. I am just happy that I realized why it's a tautology
(going by my diary, it seems to have taken me 8 days to do so, which is "not great, not terrible" )

 

[Kyriakos]

Yil how to optimally divide a number of 50 euros notes, if I am told by some gray alien in a blackcoat that he will give me the product of the two parts I chose.
Next stop, e.

 

[Takhisis]

Yil how to optimally divide a number of 50 euros notes, if I am told by some gray alien in a blackcoat that he will give me the product of the two parts I chose.

Make the number of notes in each stack equal to the other, or as close to that as possible, if I remember correctly.
The difference rises by 1-3-5-7, etc. so
10×10 = 100
9×11 = 99
8×12 = 96
7×13=91
and so on.

 

[Kyriakos]

Make the number of notes in each stack equal to the other, or as close to that as possible, if I remember correctly.
The difference rises by 1-3-5-7, etc. so
10×10 = 100
9×11 = 99
8×12 = 96
7×13=91
and so on.

Yes, it is exactly the same to the other(s)
One of the proofs in the spoiler ^_^

Spoiler :

This proof uses calculus, but starts with the usual algebra:
Since you split the original sum (let's call the sum n) to two parts, one part is x and the other inevitably is (n-x). So the multiplication gives: x(n-x)= xn-x^2

Now, in calculus, to find the slope of a y (in this case y=xn-x^2), you find its derivative, which in this particular case (won't explain why ) is n-2x.
So, the slope of y is a formula (unless y is linear), so varies according to what the value of x is. But it is known that the maximum and minimum points always have a slope of zero (because the curve becomes horizontal there), so n-2x=0
=> n=2x=>x=n/2

There you have it, regardless of the starting number (n), you always take its half. Also is true for other number of parts, eg if you have three parts, all should be equal to each other.

 

[Gori the Grey]

Using zero math, that would have been my hunch.

 

[Takhisis]

One of the proofs in the spoiler ^_^

Yes, I remember having to actually prove that in an exam about derivatives and limits and what-not.

Of course, if you have to split an uneven number, it holds true anyway
10×9=90
11×8=88
12×7=84
13×6=78

Just a thought, as always.
(and I need to resume studying higher mathematics at some point)

^_^

 

[Kyriakos]

@Takhisis , would be good to return to Nim-Wolf too, if you recall

 

[Takhisis]

I remember the game of Nim-wolf. Something should come of that.

 

[Kyriakos]

Using zero math, that would have been my hunch.

Which is very good.
But can you, also without using any math, come up with answering what the two parts should be in order to get the smallest possible product? ^^
Let's say some tormentor entered your cell and told you that you can cut the whip he has to two parts, and in the end you will be hit by a whip the size of the first part multiplied by the second

Spoiler :

It is the other way around: you need to find where the slope becomes the largest, which is where y is the largest, which is where n-2x tends to be equal to n (this is because, by definition, x can't be zero nor negative). In other words, y is the largest when x tends to zero, so you cut an infinitesimal part of n to make your x. Eg you had a whip of size 20, so if you take 0.1 this gives 19.9(0.1)=1.99 of the original whip to hit you. If the bit was 0.01, the final whip would be 19.99(0.01)=0.1999, and so on.

I remember the game of Nim-wolf. Something should come of that.

There might!

 

[Takhisis]

Which is very good.
But can you, also without using any math, come up with answering what the two parts should be in order to get the smallest possible product?

Well, if making them as close in number to each other as possible makes them larger, then making them as far from each other as possible should make them smaller. E.g., ultimately in the above demonstration:
1×19 = 19
2×18 = 36
3×17 = 51
4×16 = 64
tapering off to
10×10 = 100

There might!

YEEEAAAHHHHHHHHHH!

 

[Gori the Grey]

But can you, also without using any math, come up with answering what the two parts should be in order to get the smallest possible product? ^^
Let's say some tormentor entered your cell and told you that you can cut the whip he has to two parts, and in the end you will be hit by a whip the size of the first part multiplied by the second

Well, if it were the money-stacks, I would ask if I am allowed to have zero in one stack and still count it as a stack, b/c multiplying anything by zero makes the whole thing disappear, and I'd scape whipping. But since you've shifted to a rope that has to be cut somewhere, I know that's not allowed. Still, multiplying by one doesn't multiply, so I'll take the twenty, cut it nineteen and one and take my deserved lashing with a nineteen foot rope.

But those answers do involve math: my knowledge of how zero and one work as multipliers.

But what I'd really do in that case, is have the tormentor split the rope evenly. Then, after his multiplication, he'd have a hundred-foot rope. And that would be so unwieldly that he wouldn't be able to deliver painful lashes with it.

 

[Kyriakos]

Nice and sufficiently sneaky idea; but the tormentor would clearly be a monster of a man, so he would manage

Also, since this would be a physical whip, even if you wanted to you'd be unable to cut it at exactly a 1-unit mark (nothing can provide so precise a cut, in nature; only in our mental world ^^), and so it was also to be inferred that you could cut any bit, regardless of its exact ratio to the full whip (=>x/whip size doesn't have x needing to be an integer, even if it could, which in nature it cannot). Ideally, of course, the solution is in my spoiler (essentially your idea of zero, only in this case since you cannot by definition have zero, the bit would need to tend to zero), but even with the physical restraints you could cut so tiny a bit that the product is itself tiny and thus painless

I also agree on your point, that the answers do involve math regardless. Because everything does - one can assume that any thinking progression itself can be mathematically presented, if not now then in some future, and ultimately it may be broken down entirely to the same fabric its solution was (itself more evidently) of.

 

[Gori the Grey]

it was also to be inferred that you could cut any bit, regardless of its exact ratio to the full whip (=>x/whip size doesn't have x needing to be an integer, even if it could, which in nature it cannot)

He told me I could cut it into the parts I wanted. I want an integer. If that's physically impossible to achieve, that's his problem, not mine.

I force a kind of Dormammu stalemate and scape whipping, safe in the interval between math and physics.

 

[Kaitzilla]

Youtube devoured me today and I watched the Napoleonic Wars by Epic TV for 5 straight hours!

The pictures and production quality were amazing!

Spoiler :

I watched the last video about Waterloo and wondered what the hell happened, but the sophomoric effort and poor quality was because they made that video 1st, years before they made all the others.

Spoiler :

Truly an unbelievable history.

The best was of course cavalry officer Marshall Ney, the most badass guy in history.

Michel Ney - Wikipedia

en.wikipedia.org

Spoiler :

When Napoleon was defeated, dethroned, and exiled for the second time in the summer of 1815, Ney was arrested on 3 August 1815. After a court-martial decided in November that it did not have jurisdiction, he was tried on 4 December 1815 for treason by the Chamber of Peers. In order to save Ney's life, his lawyer André Dupin declared that Ney was now Prussian and could not be judged by a French court for treason as Ney's hometown of Sarrelouis had been annexed by Prussia according to the Treaty of Paris of 1815. Ney ruined his lawyer's effort by interrupting him and stating: "Je suis Français et je resterai Français!" (I am French and I will remain French!).[19] When the Peers were called to give their verdict, a hundred and thirty-seven voted for the death penalty, seventeen for deportation, and five abstained. Only a single vote, that of the Duc de Broglie, was for acquittal.[20] On 6 December 1815, Ney was condemned, and on 7 December 1815 he was executed by firing squad in Paris near the Luxembourg Gardens. He refused to wear a blindfold and was allowed the right to give the order to fire, reportedly saying:

Soldiers, when I give the command to fire, fire straight at my heart. Wait for the order. It will be my last to you. I protest against my condemnation. I have fought a hundred battles for France, and not one against her ... Soldiers, fire![21]

Ney's execution deeply divided the French public. It was an example intended for Napoleon's other marshals and generals,[citation needed] many of whom were eventually exonerated by the Bourbon monarchy. Ney was buried in Paris at Père Lachaise Cemetery.

 

[Kyriakos]

But not intelligent enough to realize horses won't gallop onto pikes regardless ^^
The end was underwhelming, and before that there were the russian campaign and the peninsular war fiascos.

 

[Kaitzilla]

But not intelligent enough to realize horses won't gallop onto pikes regardless ^^
The end was underwhelming, and before that there were the russian campaign and the peninsular war fiascos.

Ney was a bit of a blockhead ya.

A new video just got released today!
Napoleon in Italy, 1796.

 

[Kaitzilla]

Am I crazy or does Justinian I of the Byzantium have a duck on his right shoulder?

Justinian I - Wikipedia

en.wikipedia.org

I've looked around, but nobody seems to ever talk about it.

Here is another one @3:54

I get it though.
The duck is the only animal that operates with total superiority on land, air, and water.