Space is kind of a analog computer for algebra

Since geometry is basically algebra and vice versa, if you draw some triangles and circles you are actually performing algebra and your paper is like it seems an analog computer for the algebra. Or maybe because all algebra is basically geometry with other notation maybe math is all geometry. I guess geometry is then the most basic thing.

In a sense every art piece is a algebraic calculation!?

Similar like an abacus is an analog computer for arithmetic.

And also like a planetarium is an analog computer for the planets.

Oldest planetarium in the world

Veritasium did a great video about it:

What is the golden ratio doing here?!

And,

Then the solutions are:

Source: https://www.wolframalpha.com/input/?i=xy%3Di%2C+x%5E2%2By%5E2%3D1

Just messing around with stuff. I basically combined a circle with a complex hyperbola. Maybe you can get a nice connection with and

Refracting rivers

If you want to show elevation on a map you can use contour lines. Like this:

Now I read in a calculus book the apt observation that a river will always cross perpendicular to these contour lines. This is because it always chooses the steepest descent.

Now I realise you could see rivers like light beam crossing these contour lines, with almost looking like refraction if you make it more clear like this:

If you now look at the fact that rivers carve out their paths, because of erosions their paths change. The rivers change the elevation and the elevation changes the path of the river. This is similar to that quote of wheeler.

This is a nice video about it; https://www.youtube.com/watch?v=8a3r-cG8Wic

Looking at different functions with Taylor series/maclaurin series in polynomial vector space gives a pretty nice analogy

If you type have the full ma

If you look at the polynomial vector space and just ignore the coefficients and only look at if there is an entry or not, than you find a nice summary of these functions

As you can see cos and sine are orthogonal.

Incoherent rambling

So here comes some incoherent rambling …

It has been shown that einsteins field equations are basically thermodynamical equations. Now it also has been suggested that by wick rotations there is a analogy between QFT and statistical thermodynamics. Also isn’t there a theorem that a n dimension field theory can be recast in n+1 dimensional field theory in euclidean space. This sounds holography-ish. I don’t really know what I’m getting at but it seems like this field can be plowed for maybe some more interesting facts.

Why a photon always has to bend when passing an electron, or why boats seem to float.

Water on the road!!

We all have seen the mirage effect or Fata Morgana.

It seems like there are water puddles on the road, or that the car is floating. But you are actually seeing the sky instead of the road. The reason is that light rays bend in the air because of the concentration gradient. In this case because the road became hot from the sun which makes the air just above the road lower in density. Because of the gradient in density the light diffracts or bends.

Nice explanation.

The opposite effect happens on the sea with boats as you can see:

Floating boat!!

We see the boat in the air because of the bending of light. See this diagram from wikipedia:

By Brocken Inaglory, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=17769693

All of the above is the same as simple refraction, but then with a continous gradient.

Simple refraction we learned in high school

So imagine a photon passing an electron/or electron cloud.

Nice Paint skills right?

Because of the probability gradient the photon could deflect or difract just like the mirage and bend around the electron. Obviously this effect is miniscule but I guess it has to be there. It almost is as if there is a force between the photon and the electron, like gravity. Maybe if you scale it up it is the origin of gravity! I wonder if there is experimental evidence of this deflection, in theory this interaction can arise between any particle I guess.

Interesting video about epigenetics

Vicious circle and virtuous circle in parenting

Situation #1

Imagine a couple where the husband is low paid, alcoholic and abusive and the mom is a heroine junkie. They have low education and low intelligence/planning. She accidently gets pregnant and smokes during pregnancy. A child has been born in very bad circumstances and in bad situation. The cause of the problems of the parents is partly genetic, which means this kid will also inherent not optimal genes. He will be brought up in a not optimal education, even though he actually needs extra support and education because of situation.

The childs circumstances demand above average support, but he will get below average support, which will exacerbate the problems. He will get kids on his own who will propagate this problem, in a way a vicious circle started with bad parenting and bad upbringing.

This is obviously a very extreme case which is rare in developed countries, however along the spectrum there will be examples that are more common.

Situation #2

Compare this to two parents who are both highly educated and well paying jobs. They are healthy and planned & prepared to get a child. The mother refrains from any unhealthy behaviour as good as she can around the pregnancy and she goes to the check ups as planned. Because of their wealth they buy lots of good material for the baby, to create a good environment to grow up. Baby grows up and inherents good genes that partly explain the parents succes. At this headstart he even may enjoy even more oppurtinities that his parents create with their wealth and intelligence. Even though the baby already had a headstart, he will get above average support and thus enters a virtuous circle of parenting.

These are examples on the opposite of the spectrum, but I think that is important to make sure that everyone gets to the good side of the spectrum. This will only compound and create more families on the right side of the spectrum.

Noncommutative geometry