Sorenography

Introduction

This is Soren.

Soren

His owner (whom I won’t tag for security reasons) is traveling for two months and so this fluff stays with me for a couple of months. Soren is a mixed breed called Hymalayan. They are Persian cats bred with some Siamese gene that makes them smarter. They have the fluff and laziness from the Persians and intellect and analytical skills from Siamese. For the same reason they are vocal. They talk to express themselves. His owner told me that sharing space with him will help to decode his language soon. So far I’ve recognized three distinct sounds referring to:
– I’m starving
– Stop ignoring me reciprocally
– Don’t you sit on me!

Liquidity

The molecular structure of cats makes them liquid but it doesn’t mean that you can pour a cat into more than one bucket. Here is a drop of cat for example:

Soren drop

The Dishwasher

The puzzle of Soren’s love for the bathroom, the mystery of him disappearing a couple of times where no one could find him, the problem of unpleasant smell that I couldn’t sniff where it comes from, all solved when I wanted to do laundry! ‪#‎cat‬ ‪#‎urine‬ ‪#‎inside‬ ‪#‎washingmachine‬

Soren Dishwasher

The Alarm

Fluffy alarm goes off again. 6AM in the morning…

Soren Alarm

The Other Cat in Karl Johan

Born in the wrong species

This girl is a cat. She realized it when she was sixteen and came out later. I had seen her before through my window and the scenes you see in this video are just down my apartment. I was confused many times what Soren is reacting to when there’s no other cat. Now I know she is one of the reasons that he leaves marks by the window, to spread his smell and to show his territory.

The Wine

So a normal man has a wife who kisses him good night. I have Soren (If you don’t know him, he’s a 7-year-old non neutered Himalayan cat who bites me goodnight). Usually he’s gentler than this but tonight he bit me really hard while I was petting him. My hand was hurt and he felt guilty enough to hide himself and didn’t show up as usual to sit on my head or to hump the pillow. It could be the night for me to sleep uninterrupted.

And it was until I woke up by the sound of dripping water in the kitchen. Then it was the smell of wine. Apparently one full bottle out of twenty bottles of home-made banana wine – recently arrived from Trondheim – had just cracked and spilled all over. I cleaned it up and examined the scene. Soren playing a role in this is very unlikely since he is still under the bed. The bottle had cracked horizontally but standing still. So some physical effect like explosion due to gas pressure or temperature change is to blame. Still strange though!

Just in case I displaced all the bottles and kept ignoring his presence. He’s still under the bed and seems a little depressed.

If there will be more casualties tonight, yet he does not show up on the bed as he usually do then he’s in charge of these plots.

Unless he reads this post which is a different story! ¯\_(ツ)_/¯

3:30 AM – OSLO

Soren Wine

p.s. 5AM! He just, NOW, shat and made too much unnecessary noise. Purposefully digging the earth and playing with hard objects 5 in the morning. As he realized that I woke up he ran under the bed again. Still not showing up on the bed. He’s making me very suspicious…

The escape

So Soren had escaped and was gone for a night. The poor thing was discovered sleeping in the sun in the backyard not in his most charming shape. We don’t know where he has been and what parties he has crashed but he has possibly digested some grass that made him vomit. Or at least doctors suspect so. Soren is deffinitely not vegan. Like any other cat he is an absolute carnivor. He doesn’t even eat other things than the cat food, made from chicken, turkey and fish. Even if he is hungry he refuses any other thing. So it’s odd if he has tasted some fiber that would make him like this. Out of curiosity may be?

He is in a good shape now and will respond to his emails at his convenience.

The catch of the day is though: There actually exist vegan dogs and cats out there! There are dogs (and even cats) who are on a cruelty-free vegan diet because of their vegan owners. And they manage to live long. Can you believe it?

Table Manners

Although Soren is humble and nice to other pets, he is still classy and elegant. He has the manners and etiquette of eating properly and sometimes when he meets some of his friends who don’t do this right, he humbly tries to show them the correct style. So they can also be more successful pets in their lives. Check the video!

Soren from Inside

Soren-badass

I must add that baby sitting is not a totally correct word since he is a 40-year-old big bearded muscular man and a bad-ass alpha mail from inside. He looks cute from outside but if you normalize him within his species you get Tom Hardy or Bruce Willis. Hi beats the shit out of other cats and sometimes dogs and he can be super confident, determined and someitmes rude, but very kind and caring at the same time. For real!

Soren is gone

Soren_gone
So the cat is gone. The owners came back from the long journey and claimed it back. They had a bunch of ridiculous reasons such as Soren is used to their home for 7 years, or that they have a bigger place and the cat is more comfortable there. And that they are a couple and have more time to spend with the cat. But on top of their arguments was that they should have the cat back because he is their cat. Seriously? And that’s how things are. Soren is gone…

Hectic weekend!

Left to the airport after my work on Friday and landed in Trondheim midnight, partied with friends and had fun big time, met with the accountant to close the company, finished the tax return forms (s), picked up the neon lights and other branded material from the cafe to ship to Oslo, took over my so-missed apartment and signed a contract renting it out again from tomorrow, gave away the last unwanted items both from the cafe and the apartment, went through around 50 unchecked letters and acted upon them, met with as many Zedgers as I possibly could passed a midnight and even got time to drop by the once in a year underground electro scene in Trondheim which luckily coincided my trip. It would have been awesome to get the chance to meet the magicians and it turned out that today is the yearly meeting of the association in Trondheim! Had more to do but sadly not possible on a weekend. I guess I am ready to head back to work in Oslo tomorrow (Monday) early morning!

Karma is a bitch!

It saddens me in my bones, thinking that  horrible things like our animal farms or Auchwitz are so insignificant compared to the amount of suffering that may be going on beyond our galaxy in all those trillions of planets roaming around. If evolution of life is universal and ego and greed comes with it like it did for us, then Karma is truly a bitch!

For the Pi Day

This post may be a bit technical for general audience (as if anybody is reading this!). Although, if you do and happen to have any popular interest in Pi, the mathematical constant π=3.141592…, since it’s the day of Pi, consider to scan it through and get to the end point, if I manage to make it!

From 20 to 18 years ago I attempted to build an algebraic axiomatic system to reformulate geometry. The goal was to generalize the theorems of Euclidean geometry to a version independent from the number of its dimensions.

I didn’t know how big the world is and that my work must be redundant. So I put the effort and called it “geometry beyond dimensions”. Soon after renamed to “multidimensional Euclidean geometry” (word by word translation from Persian).

My ambitions were beyond speculating about the “flatlanders” and generalizing their problem: Oh, poor flatlanders don’t know about us three dimensional beings, so we too must learn about four dimensions and higher.

No, the point was that there is a lot more to linking geometry and algebra. Still an unacomplished mission.

Anyhow, learning two and three dimensional geometry was mandatory at school and I extended it from N=2, 3 to any number. It was a mechanical and labor intensive work using the principles of induction and a minimal set of “bridging” axioms on top of the existing literature, our school books.

Not only the concept was beyond my intuitive perception, the formulation could also get weird quickly, but it was possible after all to get familiar and use tricks to grasp the concepts and proceed.

To see how it looked like before it escalates, here is an example axiom (a bulding block for more complicated structures and proofs that came later in the book):

There exists exactly one N-dimensional space passing through any N+1 points not lying on the same straight N-1-dimensional space.

A bit weird, huh? But you could put N=1 to get the following axiom in planar geometry, more intuitive:

There exists exactly one line passing through any two distinct points.

Or N=2:

There exists exactly one plane passing through any three points not lying on the same line.

It took some 80 theorems till it covered a satisfactory area and I wrapped it up. And although I was quite obsesssed with its mechanical accuracy, I remember it still had few holes and gaps.

Now let’s get closer to the Pi:

One of the wheels I reinvented in that work was calculating the volume of n-ball, or a multidimensional hypersphere. Of course I didn’t just write an integral to solve it; I proved dozens of theorems to justify that my integral is legit and comes only from the few axioms that were introduced at the start of the book, and assumes no more.

The final result was mysterious in terms of its connection with the Gamma function and Pi. And this is where it can take us beyond a dimension-agnostic theory of geometry: discovering the nature of Pi!

Now, I refer to the pages 45 to 56 in my book (Sorry it’s all in Persian!) But I will make a simpler point here. Let’s try to formulate:

0. Consider the volume of a 0-sphere: How many dots are in a dot? 1 (or 1.R0)

1. And the volume of a 1-sphere with radius R: What is the length of a line segment with radius R: 2 R1

2. The volume of a 2-sphere: What is the surface of a circle with radius R: R2

3. How about the volume of a 3-sphere? 4/3π R3

4. And it turns out that the volume of a 4 dimensional sphere (all the points on a 4D space that are as far from one point in a 4D space) is: π2/2 R4

N. In general the volume of N-ball, an N-dimensional hypersphere with radius R turns out to be: πN/2 / Γ(N/2+1) RN

You can find the full proof in the book in Persian (pages 45 to 56), and perhaps somewhere on the net in English. Now, ignoring the trivial part of the formula (RN) we end up with a magical co-efficient as a function of N:

πN/2 / Γ(N/2+1)

Where Γ  is the Gamma function. Now the value of this function for its integer arguments is straight ahead. It ends up equal to the famous factorial function, multiplication of all integers from 1 to that number [minus one]:

Γ(n) = (n-1)! = 1*2*3*…*(n-1)
Γ(n+1) = n* Γ(n) (n) = 1*2*3*…*n

For non-integers though it will take on funny values to interpolate the factorial results between two integers. For example for the half values right in the middle of two integers, it ends up a rational number (a number that can be written in a form of an integer devided by another one) multiplied by an irrational number which is Γ(½) and happens to be the square root of π, that is not only irrational but transendental:

Γ(n+½) = (n+½)*(n-½)*…*Γ(½)

Now the strange part is that the argument of the Gamma function in our formula is N/2+1. It gets one unit higher for every second added dimension! And that for odd dimensions it will not be an integer or a rational and will include the term Γ(½)=√π.

On the other hand the gamma function in our formula is multiplied by another term of πN/2 which also introduces a √π for every added dimension. Thus, for even number of dimensions none of the terms πN/2 and Γ(N/2+1) introduce a √π and we end up with a rational number multiplied by πN/2 where N/2 is an integer. For odd numbers both of these terms introduce a √π that divides and vanishes. So, there will not be a √π in any of the integer dimensions, even or odd.

It is not a √π introduced to the formula for every added dimension, instead is it an extra π coming to multiply, for every even number of dimensions. Odd dimensions (extending from a point to a line, or from a circle to sphere) do not introduce a new π to the co-efficient, only a rational number. The even numbers (going from a line to a circle) bring in a π to the play! A strange asymmetry between the odd and even dimensions, I would say.

Ignoring the rational part of our magical co-efficient, for every second added dimension there will be just one π introduced and the co-efficient for dimensions from 0, 1, 2, 3, … will be as the following:

0 -> 1
1 -> 2
2 -> 2π
3 -> 4/3.π
4 -> 1/2.π2
5 -> 8/15.π2
6 -> 1/6.π3
7 -> 16/105.π3
8 -> 1/24.π4
9 -> 32/945.π4

Where does π come from? One intuitive way is that it comes from the comparison of the space a hypersphere takes to that of a hypercube. But one π for every second dimension. Why every second? Well, this happens in Euclidean geometry where distances are Euclidean and the ball is defined as a set of points equally far from a center, using a “two” norm distance metric. You take another distance measure and the math will change. But I would argue that Euclidean distance is the only legit metric at least when it comes to defining a ball, as it is the only metric that maintains the shape of the ball when we rotate the axes. So the key is that when you go beyond one dimension something called “shortcut” comes to existance. And there’s a straight shortcut that for some reason follows the Pithagorean theorem and that defines the perfect curvature. I couldn’t reveal how these are connected, but if I ever want to speculate about the nature of π, here would be my starting point.

p.s. I read a bit more on the topic. I opened that back door in my head and it was two decades of silence and spiders ran off quickly. My friend Sajad gave me a torch, albeit a map: Quite surprisingly the Pi day coincided this news on some weird statistical behavior of the Prime numbers. I realized that I was brought up in a typical middle class (and 3-dimensional!) family. Dimension-deprievation is the evolutionary intution of 0, 1, 2, 3 only. That is too few to realize that all dimensions do not have to be symmetric because they are all numbers. The number of dimensions, even or add, prime or divisible, affects how N-space behaves and just like number theory it doesn’t have to inherit it all from N-1-space. Do all numbers exhibit the same properties cause they are all numbers? so why should they when they count dimensions. I think this is actually what numbers are made for: counting dimensions. And the historic fact that we count 1, 2, 3 and we “…” the rest is not pure coincidence. Sounds poetic, but read it logically:

3 doesn’t get every property of 2, neither does a ball from a circle. To my previous wonder, a ball (3-sphere) did not inherit an additional π from a circle in the calculation of the volume, but 4-sphere did. Is it weird? No, 3-sphere introduces singularity too, two poles in the hairly ball theorem, that are the two ends of a segment (1-sphere), but 4-sphere doesn’t: A circle (2-Sphere) can go round on another full circle around a point and you get a 3-torus or a 4-Sphere that you can comb (no singularity) and they both happens to have π2 in the volume and surface formula. Now you try to rotate the circle, not like you just did on both dimensions of a full circle and around one point, but instead around a segment on its own disk space. And you get a ball (3-sphere) with two inevitable South and North poles (singularity) and this time it does not give you that extra π. So, 3-sphere is just a product of a circle and a line segment (thus singularity, thus no extra π). The product of two circles (3-torus or 4-sphere) gets that extra π and you can also comb it (no singularity)!
This is a short summary of the common stories that two formal proves tell. The same thing happens in both: The multiplication of a new π in the volume of n-sphere on every second dimension in my [redundant] proof (A), and the generalized hairy ball theorem for 2n-spaces (B).

Is there an established field on the intersection of algebraic topology and number theory?

Wear you later!

I was fantasizing and day-dreaming about exotic forms of life. This topic is very much not within my expertise, but it is fun to let your thoughts play with the idea of life somewhere else.

No, I am not going to talk about whether we are alone! There is a consensus that we are probably not. But I wanna ask who are the others. How do they look like? What do they do?

And this was not really a dream. It was rather a guided semi-concious train of thoughts with closed eyes on the way to a powernap. So it may sound trivial, or wrong, or stupid. Nevertheless I explored some fantasies and I share them with you.

Rethinking loud…

Ok, In our terrestial life on Earth we *consume* each other in different forms for our survival. We eat, we mate, we socialize…

Eating:
living organisms enjoy other creatures as nutrition to obtain energy and mass they need. So we all somehow eat for movement and for growth. Eating may have universal rules. I think creatures eat things that are not so much like them. But that can be a coincidence on our Earth and canibalism could be more widespread gallactically. And creatures don’t eat things that are so different from them, afterall they need to process the matter and rebuild they bodies, or burn it to be able to move. So some universal laws agreed on the issue of food.

Mating:
living organisms sometimes need to meet each other and do something funny in order to reproduce. Let’s be polite and without the use of the F-word remember how our fellows across the animal kingdom rape or hump or bang each other with or without consent in order to pass on their genes. And well as opposed to eating, mating (if done with another being) is probably done with something that is more alike to us, and not that different, right? Cause then a legitimate question would arise: what kind of baby would come out of that interspecious act of sex!

Mingling:
well it doesn’t have to be socializing in a bar or coexistance of ants and termites, but we sometimes need to meet each other and collaborate on overcoming the problem of survival in other creative ways.

Sure we may do other things with each other directly and indirectly and these acts have been evolved, thus formed slowly over generations and generations.

Now there are other fundamentally different actions of survival that we could do to each other cause they seem very logical to me but we don’t! Or I couldn’t find immediate examples since I don’t know biology.

And I’d like to believe these exotic acts of life are actually happening somewhere out there on another planet on other stars, albeit other galaxies, right now as you read this.

What else could we do to each other? Three guesses!

WEARING:
So among other ways of consuming another live being, one animal could possibly wear another animal to protect against hazards, such as some poisonous matter, a colony of contagious and alive microorganism or some deadly radiation. I am aware that in our vicinity crabs move into new shells but this is not quite the same thing as shells are dead. And we wearing fur doesn’t count either. I am talking about life forms that are alive both as non-wearable and wearable. Or at least in the latter form.

CLEANING WITH:
Next time you take a shower imagine that water was a life form. And that your interaction was not that boring and static, like now that you two (you and water) are linked simply by gravity. Or by drowning. Let’s say the drops or the shower head could escape from you, or you had to trick and manipulate it somehow to wash and clean your body. If this example is not clear, try wiping your ass with a soft and fluffy rabbit next time.

SENSING THROUGH:
My inspiration here is a cool gif animation of an E.T. that put on a pair of eyes from his plate into his hands and started to see the world (I can’t find it now). And this is where there is no limit to imagination. And gamble with a risky bet that: Whatever you imagine exists somewhere out there!

So, imagine an animal that wears another compatible animal temporarily or lifetime, to sense the environment better. What if some animal takes onother poor creature like a pair of glasses to see or hear or touch better? Or to recieve electrical signals more effectively? This must be more painful than joyful if it doesn’t somehow endanger the survival of the pray. Then pray will not decide and volunteer to be worn and well it will suffer. Hunted against its will, just like food or even worse if it us an unpleasant lifetime imprisonment!

Or let’s hope that karma is not that bitch and in most of such colonies of life, creatures enjoy being “sensed through”.

Thanks for following till this point. Now wake up and get back to life. To this very form you are used to.

Wear you later!

Smart house

I just woke up from a dream that we were in a smart house and lots of weird things were connected to the Internet of Things (IoT). Several interesting products in that house that all doesn’t make sense to me now. I mention two:

There were smart plates and people were playing an eating game based on the dart game 301. So we started eating random portions of a soup and the goal was to finish it up just with the right portion on the last spoon. It was not allowed to tilt the plate at the end of the game.

And this one: Upon exiting the house there were animated carpets!

Darvin IV

There are billions of galaxies out there, billions of stars in each of them. There are trillions or quadrillions of planets in our universe and some of them harvest life. What happens in the bottom of our own oceans surprises us, let alone far planets around other stars in other galaxies (and assume that’s the only recipe for life).

Other life forms are extremely far and unreal, as if they don’t exist. But they most likely do, and so many of them indeed. But how do they look like? I think although our universe is ruling them all similarly, the potential is so huge that anything we can imagine proably exists somewhere. And anything that our imaginary creatures can imagine, could as well.

What other life forms may look like has not really captured our imaginations. Alien Planet – Darwin IV is the best (realistic, still very earthly) animation I have come across. There are many documantaries out there but no fictional motion pictures that I know of. If you know of some pleases hint me. If you haven’t watched this, give it a try. Don’t think fiction but more science. Think reproduction, growth, survival, energy, memory, intelligence. Think life! It’s fun.

The long tail of terrestial life

If you are an organic molecule, a molecule of terrestial life, is it more likely for you to be a part of a big animal, or a microorganism?

Let’s say you break (or not), you will travel from body to body, from a plankton to a fish, then bacteria, a tree, to a pig, or to a human. You spend there short or long. But where will you spend most of your lifetime? A big or a small host?

I would say both.

Could there be a simple answer to this, that applies to every other livable planet, at any stage of their evolution?

On ours, among uniqe species krills consist most of the biomass, human are second, arguably more than pigs and cows (still farmed by us). Though if you count thousands of species of ants as one, they win over all.

Still, seems all sizes are involved at this stage of life.

Geometrically I would say big should win at the end of the game. (Feel a jar with big marbles, then smaller, then sands, etc.)

Economy of scale aside.

Non-existentialism

I had a nightmare that I didn’t exist. But I was there hearing an explanation justifyng why I don’t exist. It was not that I had died, but I was never even born:

“The exact combimation of the matter like you – statistically – has ended so many times before, but has never started once yet. That’s why you never existed.”