Cosmetics

I wear no cosmetics.

I like to meet women/men with fine make-ups. I also like to see colorful cosmetic items arranged in the shop. Just I don’t wear them myself.

There are some reasons, or backgounds for it.
My late father was a dedicated sales manager of a cosmetics company.
He brought home many samples of cosmetics. So I grew up too close to cosmetics to be attracted to them. They were livelyhood of my family.

And I was faced from so early an age of mine with a fact that a make-up would not improve but rather worsen my appearance.
I tried more than a few times to make my face up with cosmetics which were abundant in my house, and got shocked each time by the result in the mirror.

The last trial was when I was a univ student. There was a boy who was proud of having various skills in life. One day he asked me why I wore no cosmetics.

“That’s the fault of a bad skill for make-up” he said against my answer. “Let me help you with it. Luckily I have a set of cosmetics here. I used them yesterday for a costume party with my friend. And I found I would do quite well as a make-up artist.”

Then he treated my face for a while and said with a chilled smile, “Ah…very well. You look invincible. No one would stand on your way when you go on the street.”

There are many ways to express one’s beauty. As for me, it happened not to be cosmetics.

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Only one wish

(A short story)

One day a man with mysterious appearance visited me and said, “It was good that you saved a spider’s life the other day, so I will realize the only one wish of yours. Tell it to me now.”
“Sir, that spider is my friend, he devours cockroaches in my house. So I don’t think i have done anything to be rewarded.” I said.
“Anyway, it is a fixed fact. Tell your wish to me.”
“Anything I want?”
“Yes.”

I was a pessimistic person as for “wishing a certain number of things”, or I have read too many stories by Ray Bradbury, Fredric Brown, Richard Matheson or Shin-ichi Hoshi.
Such kind of wish would often result in an ironic catastrophe. For example, say “May there be no more war in the world”, and the world would be extinguished, leaving “no more war.” Wish some happiness to yourself or someone else, such happiness would be realized based on other’s tragedy.

“What if I wish you to go away?”
“Then I will go someone else and ask him to wish something in replace of you.”

I didn’t want that. What if that innocent person wished “no more something in the world”?

I had to make up some harmful wish. It must be for as limited use, and temporary as possible. And –

“You could not tell a lie. Tell me just you really wish.”
“I know. Don’t talk to me – What if I wish you would n-” No. I must not use a word “never,” or anything that imply a permanent situation.

Then an idea came to me. If it had already included some defect in itself, the result would not be “ironic.”

So I said to him finally, “I wish Windows8 will be released soon.”

Solar, Fire and Water

The news said a big solar power generation system in Japan had recently started operation.
It could generate 12GWh in a year.
On the other hand, the average power consumption in Tokyo area is 40-45GW in a day.
……
“A sparrow’s tear” is a familiar japanese saying to express very small amount.

“Solar system is not suitable in Japan,” my husband says. “This country is too small and the weather is unstable.”
“We should not expect solar energy to satisfy our own need. Instead, we could develop a leading solar system and export it to the county more suitable to a practical use. That solar plant would have the meaning of a pilot plant.”

“So what would be the best electricity resource for Japan?” I asked to him.
“Mmm, water and fire, at most.”
I was disappointed. “Nothing new?”
“We could improve efficiency instead,” he said. “Don’t you know? In the present much of the heat of steam is discarded unused, because the turbines are unbearable to that heat. If we could develop a bearing more heat-tolerant, we could recover at least 10% additional electricity from the same amount of fuel, under the same infra. Don’t you think it far more efficient than to build a brand-new power plant using a strange alternative resource?”

That’s right. Japanese don’t have a habit to praise a member of their own family in public, but I respect my husband very much.

Hen or Egg

This year I have set myself a slogan: “Don’t leave any minute question unsolved.” If a question occurs me, I will seek the answer by myself, or ask some adequate people.

Recently I have considered again the question I had once tried: Which is the first ancestor, a hen or an egg?

I had been thrown the question at when I was a high school student, as far as I can remember.
It was something like a “Today’s story of the teacher”, where he/she told us as an example of paradoxes or circular reasonings.

At that time I thought the hen was the first.
It would be very difficult to include such a perfect life capsule in a body. So for the first time lives must have been inherited in the form of cell splitting to generate a slightly better half than the original. Then it became gradually possible for a living thing to capsulate a separate life system.

But the above explanation did not answer to the question, where the original single cell had come from.

Now I think, that the first life must have been created, and grown in a closed or half-closed system.
Maybe there was a loaf of very special mixture of materials, which happened to be formed in the chaos, and its surface was hardened into shell, by means of heat, etc. The first life would have been then formed in that shelter.
In this sense the life was originated from an egg. But it happened only once. The first life was not such that could generate an egg within. Instead it created an another life by cell splitting and the things went as I thought before.

So my conclusion is “First something like an egg, then a hen, and then a perfect egg.”

Gravity Center(3)

The final part of explanation on the gravity center of a triangle.

Assume in the below figure that AL=LB and CN=NA.
AM is drawn to join A and G.
But BM:MC is still unknown.
We are going to prove that BM=MC.

We need a supplementary line also this time.
It is drawn from the midpoint L on AB, being parallel to AM.
Let J to denote the intersection of the line with BC.
That is, LJ//AM.

So it is obvious that BJ=JM, because BL=LA.

The we think of another triangle including LG and JM, that is, the triangle CLJ.

In the above figure, it has already been proved that CG:GL=2:1.
Then CM:MJ = 2:1 is derived, because GM, a part of AM, is parallel to LJ.

CM=2MJ
BM=BJ+MJ
and BJ=MJ

So BM=2MJ=CM

Thus it is proved that three medians cross each other with a single point G.

You might think it a meaningless trial to explain where such and such point would be located or what length a line would have. But to prove a geometrical property under a certain condition is to prove that you could control the geometry by fixing conditions. You could get the one and only center of gravity for a given triangle, and triangles are fundamental elements of all polygons.

Gravity Center(2)

When you draw the line from A through G, the intersection of two medians from the other two vertices, the line will be the last midpoint…

To explain the above axiom, we will first explain that the intersection G of two medians BG:GN = CG:GL = 2:1.

If only the case of BG:GN is explained, the same explanation will be valid for the other.

For the discussion a supplementary line is needed. Draw it from the midpoint L to AC, parallel to BN. Let K to denote the intersection of the line and AC.

As AL=LB and LK//BN, AK=KN (This requires a proof, two, but I’d like to skip it, because it would be visibly understandable)

Then it is derived that CN=2NK=2KA, as N is the midpoint of AC.

And BN=2LK, as the triangle ALK is just 1/2 scale of the triangle ABN.

Let’s look at LK in a different triangle, CLK, including a smallaer triangle CGN.

As CN=2NK, CK=3NK.
As G is a point on BN, LK//GN. So the triangle CGN is 2/3 scale of the triangle CLK.
So, LK:GN=3:2.

As BN=2LK, BN:LK:GN=6:3:2.
As BG=BN-GN, BG:GN=4:2=2:1.

In this way, it was proved that BG:GN=2:1 .
It’s a crazy problem of geometry.

Gravity Center(1)

I have been working with a problem of explaining geometrical properties of triangles at school. Recently I met much complicated a problem of the gravity center. I would like to record what I learned, because someone (probably young people in high school) might need it.

The gravity center of a triangle is located at one and only intersection of all three medians. A median is the segment drawn from one vertex to the midpoint of its opposing side of the triangle. And a midpoint is the point on a given side of the triangle, which devides the side into two halves.
The gravity center, on the other hand, devides each medians at 2:1 ratio, the longer part being the side towards the vertex.

That is, in the figure below,
BM=MC
CN=NA
AL=LB
AG:GM=BG:GN=CG:GL=2:1

All three medians will intersect with one another at a unique point – You must prove it, however. It is obvious that two straight lines will have only one intersection, unless they are parallel. But there is no guarantee the third one should also cross the other two at the same point.

Then how can man prove it?
One of the ways is, express the assumption in another way.

Let G to denote the intersection of BN and CL, N and L being the midpoints of BC and CA, respectively.
If you draw a line from A through G to cross the BC. Then the intersection M will be the midpoint of BC.


Fisrt, forget the point M and think of only BN and CL.


Then draw a line from A through G…


That line will go through the midpoint of BC.

The above explanation is in itself complicated. It will need a preparatory explanation that the known medians BN and CL will divide each other at G, with BG:GN = CG:GL = 2:1. That will be discussed in the next post.