Science – Page 2 – Nima Darabi

Blindspot Dilemma

“We are blind to our blindspots.”

Does this quotation have a name? I couldn’t find, but let’s call it the “blindspot dilemma”.

Blind2 — The image copyright: George Redhawk, an actually blind artist.

From the view point of dominant scientific paradigms [and in fact several of them] this statement amounts to bullshit!

When you mention it and you start to expand on it, mainstream routine scientists start to laugh at you.

Why?

– It is a logical tautology.
– It does not add anything to our knowledge.
– It doesn’t give us any new fact about our environment and how it works.
– It is not testable.
– It is unfalsifiable. (If they think Popper)
– It is unscientific. (If they think Feynman)
– It contains zero amount of information.
– It can’t predict.
– It has no value.
– At best it’s just a definition.

– “We can’t see what we can’t see.”

If you come from science, philosophy, business or what not, the dominant mindsets of your field may be expressed in different forms, but they all – perhaps wrongfully – mean the same thing:

The blindspot dilemma is worthless.

Yet, quite surprisingly, when I think about it, when I apply it to different domains, when I keep it – constantly – in the back of my mind, the conclusions I get are drastically different from before: New things emerge and old things get a different set of explanations. Observations make a better sense in a broader range, and a recursive sense of clarity starts to form.

How can that be worthless?

A month ago I applied this simple recipe to “the range of empathy in humans”. As a result, I was taken by a long trip and came back much more insightful. A whole new world of meanings and insights about morality, empathy, psychopathy started to hit me. I got a different vision of our collective civilization. My relationships with the people improved. Social behaviors made more sense. Everything was shed in an irreversible light!

I applied it to human behavior and I learned new things about politics, conflicts, societies. The way the world works and how it could be dealt with it.

I applied it to data, and I got new approaches, new models, new charts and shapes and values.

I applied it to cognition, and I learned new things about conciousness, and even geometry, math and topology.

Someone please tell me how can such a simple yet useful statement be so worthless?

I think the dominant scientific epistemology that is ruling the way science works is incompetent here. And the harm that is causing us comes exactly from that rigid inadequecy.

From Popper’s “falsificationism” to the statistical null hypothetical testing that is dominating the logic with which we do science, have failed to reflect a sense of recursion that may be more profound to our nature than we think.

The late Feyerabend who eventually went against Popper with refusing to accept the existence of universal methodologies in science was on to something. His anarchistic views of science in his against the method lost the battle of history to the falsificationism of Popper.

Science is so blind to its blindspots that Feyerabend’s “sociology of scientific knowledge” where he started to study science as a man-made cultural product made by the society of scientists (my wording) never took off the way it deserved to.

I don’t have a clear formulation to introduce a paradigm here. But I am sure, as much as Popper was sure of his unfalsifiable theory, that we can and we should formulate the blindness dilemma into scientific paradims in an elegant and ground-breaking way.

Me and myself have a recursive faith that beyond the incompetent tools of our current science and our profound blindness to other potential ways of finding the truth, there must be a formal way to adress the so-called “blindspot dillema”. We must nicely and regretfully invite it back to our toolbox of making sense of the world!

I can only hope we see a paradigm shift before our extinction.

P.S. In a looser reading, one can interprete the two “we”s differently by inviting two different perspectives. Then it is no longer a tautology. There is a model (an interpretation/semantics), for which you get something similar to Dunning-Kruger effect. That is not a tautology either. This is probably where I “cheated” in this passage. But I don’t think of it as cheating and that is the point here.

I am not defending this quick text as a well-thought and accurate post. But hear the idea:

Such a fuzzy freedom of interpretations (such as moving between perspectives) is missing in falsifiablity paradigm.

Even the way the dominant paradigms include uncertainty (e.g. statistical hypothesis testing) is so deterministic that they push uncertainty all the way to a statistical parameter or a random variable.

Such freedoms are in the blindspots of the falsifiability approach without originally being excluded them for a good reason. They are only not included, yet, due to a lack of solid and rigorous formalization.

Synesthesia vs. Dyslexia

I don’t have “dyslexia”.

If you are curious, I am a “grapheme-color synesthete”. It’s a different thing.

Or argualbly of a “phoneme-color” type. (They are sisters)

It’s the most comon type of synesthesia out there. Means seeing inevitably fixed colors in letters and numbers.

It usually helps folks to get better with spelling. In my case too. However, there are corner cases that this ruins life for me. I am blind to them and appear dyslexic.

The [personal] problem is that my consonants have unique and saturated colors. The wovels on the other hand are grayscale and mostly transparent. So the wovels get melted and merged with their consonant neighbors. In fact they get their colors from their neighboring consonants.

That makes mixing vowels much easier. In the particular case of “o” and “u” it’s even worse. They are both quite glassy and they sound similar. So it is random to use them in the right order if they both appear in the same word.

I always thought I am lazy or too dependent on colors for spelling.

But in fact I just can’t learn words that follow that pattern. Words such as “customer” or “corrupt”. As we are blind to our blindspots, I wouldn’t know this without a feedback. I didn’t see those as misspells to judge if they’re systematic or not, until my previous manager pointed out that specific pattern in my reports.

No matter how many times I leave marks or set signs or rules, I will never learn the right spell when it comes to those words and I will end up tossing a coin again. It’s just not worth the effort. Similar issues appear in coding too.

The wovel transparency issue applies to both alphabets that I know (Arabic and Roman). Wovels are transparent / grayish and same-sounding consonants have the same color in both alphabets. When I tried to learn a third alphabet (Cyrillic) things quickly shaped that way, too. Except for the cognitive dissonance of color mismatch between similar looking letters (such as “И” and “N”) that sound different. Which makes it harder to learn them for me.

“И” sounds “I” and should be white/milky transparent but it is red at the first glance because it looks like “N”.

Point, I am not “dyslexic”. I am “wovel color blind”, brought up to outsource spell-checking effort to colors, which did not turn out to be a full-proof approach.

P.S. By the way I live inside my head. I think you should too. As long as you talk about it.

The universe is inside us!

“The universe is inside us. It’s in you and you’re in it.”

1. Conscious realism

In his TED talk, Donald D. Hoffman claims that reality not only is not the same as our perception but also may have nothing to do with it. According to his “conscious realism,” the objective reality can exist as the source of cause and effect in the world. Still, to our counter-intuitive surprise, our perception had not needed to map it in any “real” way, but only in a helpful way for fitness.
According to this approach, the fact that we can “map” the reality and make it in a useful way, such as an objectively verifiable CAD-like software, still does not imply that our very basics of geometric perception have anything to do with reality. Instead, they are just yet another practical approach to interacting with it for survival.
His central thesis that evolution may favor fitness and not reality is hard to grasp for two reasons. First, it is at odds with our dominant scientific belief system, and we are not used to doing science that way. But a greater problem, in my opinion, is that his radical ideas are difficult to grasp for us humans since we may have been deceived by evolution from the very early stages all the way till now. Thus this deception may be deeply rooted in us.

I used to carry similar thoughts when I wrote this piece (Persian, 2003) for the philosophy section of the a popular reformist newspaper in Iran, though the article was not accepted – being labelled as an idealistic subjective viewpoint.

2. Relativism of geometry

I always thought that the geometry of our perception must be deceiving, simply because we have thought and worked it out with our brains. But I never imagined I would go this far to question the whole set of perceptual and intruitive axioms of geometry. And I am intending to do it here.

Let’s break the foundation of a geometric construct, such as any modern axiomatization of a geometry, into two sets:

1. Logical rules of deduction
2. Geometric axioms

Where did we get group 2? From our intuitive perceptual assumptions. They are intuitive so they must be right, we thought.

Playing with these two sets we have constructed intuitive (but not real) geometries that gave us engineering that – so far – helped us to survive better, so we assumed they must represent some sense of an objective truth. What went wrong? We took the latter too seriously. Our “intuitive/perceptive geometric assumptions” did not have to do anything with reality!

Evolutionary biology is the base of geometry, not the other way around.

Evolution is not probably the base of reason and logic (group 1), but it is the foundation of some of the intuitive axioms of geometry (group 2). Because of the intuitive and useful deception of this group, the resulted geometry and thus the whole physics and engineering we built on top of that was only a construct of our basic perceptions. Self-consistent, intuitive, and useful. But not real.

The catch is that the intuitive geometry that we built could be just a random artefact of our evolutionary path. Its axioms come from our profoundly biased perception, and we never fully doubted them, with a systematic and comprehensive map.

It was a historic choice. From Ancient egypt to Pythagoras and then Euclid we based our reasoning and built our sciences on top of a deceiving set of axioms about time, space, scale, and other fitness arteficts of our evolution. They were axioms of survival, not axioms of reality.

Did we make science on top of the most intuitive, yet most deceiving branch of it, geometry? Geometry is not pure math and reasoning. It did not have to be as universally as valid as logic, number theory or algebra. But it was assumed to be. Very simply put, the axioms of group 2 were just the artefact of our evolution and could be theoretically undermined, rewritten or completely deconstructed.

Omar Khayyam of the pioneers of Geometric Algebra said a millennia ago:

“Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras are geometric facts which are proved by propositions five and six of Book two of Elements.”

Khayyam was deceived himself and thought it in vain! Attention must be paid to the fact that algebra and geometry are different, in appearance, and in essence. Algebra *may be* a universal base for reasoning but geometric facts are just deception of our perception thatappear intuitive, to us. He even got the word “trick” right, but mistakenly refered it to “algebra”, instead of the “geometric facts”.

3. Deconstructing intuitive axioms

Things get shorter and more massive when they move, mass is energy, gravity is the curvature of spacetime. Objective experiments showed werid and counter-intuitive results fundamentally different from what our perception had suggested.

In the 20st century, two new perspectives in physics, relativity and quantum theory showed that the geometry of our cosmos may be so different from our basline instinctive or cultural intuisions. Or that the reality may be a generalization of our deceived range-limited perception. It may be far worse than that. The reality may have actually nothing to do with our perception after all.

This is not trivial. If you think this is what quantum mechanics has so far claimed, you are still deceived. This is far more radical. Thinking of cosmos, did we ever manage to remove our basic ingredients of intuitive perception from our written objective math? Even in the context of modern geometries, although we constructed slightly different topologies and geometries (say Riemannian) , weren’t they all still profoundly biased due to some of our wrong yet intuitive axioms?

In my manuscript on higher dimensional Euclidean geometry 20 years ago I touched upon the relativism of geometry. But I – sadly – did not deconstruct the Euclidian axioms and only generalized them to higher arbitrary dimensions. Historic mistake in sync with the society.

It is hard to think and not intuit [perceptually], but setting ourselves free from our perception and knowing that this may actually be a more scientific and “real” approach, although less intuitive (biased), brings new possibilities and we were unaware of those possibilities, as Hoffman says too.

In my interpretation, we never reconstructed it all perception-free. Until recently, and may be in string theory, or M-thoery may be we find axioms that are borrowed from objective experiments more than the perceptual bias? It’s not enough if you ask me.

Reality is not intuitive. But the good news is that it is achievable and objectively testable.

Now, let us deconstruct some basic intuitive axioms in new ways in disagreement with our perception, and still use reason and logicalcomputers (useful Turing machines) to rebuild new profoundly different geometries for cosmos. Then we double check its theoretical results and implications with old or new experiments.

And things start to get interesting:

4. Theory of spacescale

And now, ladies and gentlemen, let me deconstruct one of the most profoundly intuitive axioms of all geometries and sciences that you know of. And then briefly build on it to surprise you with its exotic implications. My time is short to elaborate now, so spitting out the short story:

I am asking, what if “small” and “large” are the same thing?

Of course counter-intuitive, but ignore your bias for a moment and read this:

Hoffman compares the faith of two organisms with simulation: One organism with a realistic perception of the truth, a “linear” fit-ness function of a given resource. The other with a non-realistic, wrong perception of the truth, a bell curve fitness-function. The truth sends the first organism to extinction, because it takes too much or too little of that resource. The deceived organism which has the bell curve fitness function, responds to the “just right” amount of that resource due to the distorted bell curved perception, whereas the organism who saw the truth, dies!

The organisms who could intuit about relativity, quantum entanglement, or wave-particle duality (things that we know from our experiments), die if their true vision did not help them fit from early days. Instead, we, deceived creatures who don’t even understand that time is space, reproduced and survived.

Back to the bell curve perception: We have intuitions about ”left and right” directions, “cold and warm” temperature, ultra and infra” light frequency, “in and out”, “past and future” time, “small and large” size, etc. They are not necessarily telling us how the nature works, but they are two asymmetric sides of a stimulus and have evolved in us to fit and survive.

Now I ask you what if “small and large” are actually the same thing in two different directions? Such as “back and front” in space.

Let’s deconstruct the basic intuition we have about “scale” and build a geometry on top of that exotic axiom where scale is a dimension in space.

Roughly speaking you get what you may call a 4D manifold, made of three spatial dimension, and one “scale” dimension. It’s like spacetime but “time” is replaced with “scale”. And they are unified.

I will get back to you why, with more accurate and formal description of this manifold and possible metrics on it, but for now accept from me that from which ever direction you move on the surface of it you get back to where you are. (the 3D surface of a 4D sphere, as an even-dimensional space can be combed due to the Hairy Ball Theorem, it has no singularity.)

If we simply assume the non-intuitive axiom that “scale” is “space”, despite the fact that just like “time” we perceive it very differently, then it has mind blowing theoretical results. Here’s one of them.

5. The universe is inside us!

This can simply be an implication of unifying scale and space on a combable 3D surface of a 4D sphere (3 space + 1 scale):

Choose a direction around yourself, literally any direction. Up or down, it doesn’t matter. Then zoom in it.

Look at your hand for instance. Say you zoom into one of your cells, any of them. You just keep straight and don’t turn. Then you zoom into it till molecular level. Then atomic level, and you see quarks and what not and when you zoom enough guess what you get: The whole universe! The one and the only universe. The exact same universe that you are in it. And you can repeat.

This video was probably made to demonstrate this visual effect of zooming from intergalactic to sub-atomic levels, but can actually be an implication of the “spacescale axiom”. Ignore the tilts and the cheats and the wrong microscopic objects that it shows, it is a good visualization of what you may expect from this theory.

And yes, it should have approached the woman on a side of the earth when the planet became visible. We expect to lend in the same eye of the same woman, not elsewhere, if we go on a straight line (a geodezy) on the surface of the 4-ball.

This video may be a bit better. It doesn not tilt and its sub-atomic particles seem more size-realistic. But it does not loop.

Here, zoom in scale may be just like moving in a physical dimension. It is not believable, but the theoretical predictions of this theory are objectively testable by experiments.

Just like space and time being the same thing was never intuitive. But was predicted by theory and then approved by experiments.

What if I claim “space”, “time” and “scale” can be all the same thing, and interchangeable? Despite our perceptive bias.

You zoom in something and it gets bigger, and you get close to something and it gets bigger. Same, same. Don’t stay biased. Remove your euclidean axioms.

Scale is just a direction in space? Is it just like “forward and backward” althought we percieve it differently as “in and out”? Just like time that is a dimension but we sense it as “past and future”, although they are just the same and interchangable?

The universe is inside us?

It’s in you? And you’re in it?

It’s not intuitive. But can be real.

P.S. Few days after I quickly drafted this, Alex Grey published his “Body, Mind, Spirit” and appeared on my social network. My claim is this, but in every direction you turn your head:

In fact a one-sided space (such as the Klein bottle) you would actually look into your own eyes, face to face.

I set a mirror in front of your mirror.
To build an eternity,
out of you.
– Shamlou

Revolution or Reform?

Imagine this hypothetical landscape: You live in 2300. Humanity is still around and somehow through calculated global programs, colonizing mars or deadly wars has reduced its earth population from ten down to three billion already. And has fixed it there. The earth is tolerably warm but sustained.

Politics:

Countries are provinces of the world federal government and they have different state rules to practice their local cultural differences.
Different races campaign politically to defend the continuation of their gene traits and complaining about the others reproducing more than regulated.
The word “freedom” has mixed meanings and is used with the word “from” not to be misunderstood.

Economy:

There is no centralized money and even digital currency is just a hidden layer of the world economy that some expert may still look at.
People use public services more than their private properties, however that’s a cultural thing; Everyone is given a minimum of private ownership by birth, and several times during their life span. People can lose their private stuff accidentally or choose to donate it at will, however the world welfare system may restore it for them.

There is a notion of money, but that is negative (like debt) which is calculated by an individual’s cost of living such as their footprint as long as it is calculably affected by their personal choices.
Therefore there is no money. There is fine.

Business:

Growth of companies are limited through regulating their shareholder’s wealth. New-capitalism is practiced safely.
Work is constitutional right but voluntary and companies act more like temporary social games shaped by entrepreneurs and closed and cashed out once they serve their purpose. Land and land resources, infrastructure, utilities, transport and media belong to the public and can not be bought by companies or other legal entities by the world constitution.

Every citizen is granted an equivalent of some work/office space and work equipment after a certain age. They can use the equivalent of their office space for individual business or they can exchange it with an equivalent of that when they get a job or build a company.
Education is too a constitutional right and voluntary. People get educated to fit the available work opportunities. Public education is accessible globally and private education is the service that educational companies serve.

Democracy:

Terms above are regulated by the world federal government, which is a distributed post-digital consensus system on the Internet. Democracy is not a hard-coded system and is a complicated structure for collective decision making by humans (and partly even by pets and rightful animals). It senses and collects data from different levels of humans’ lives and aggregate it organically to sense what people want (implicit voting) and thus regulates the society democratically. It’s optimisation will be focused on human’s psychological level and it’s well being. Feeling good is a constitutional right. Citizens get notified about the important updates of their local or federal rules depending on importance and relevance to their lives, and can always overwrite their predicted vote or temporarily exit the decision-making networks voluntarily. Politicians, lawyers and developers aid the machine. General assemblies are held by politicians who are themselves through the machine. Newer versions of democracies are be deployed. All citizens of the world have constitutional right to access the overall simulations and predictions that the system provide based upon the latest rules. Cultural differences will be shaped by local rules decided by the local people at the time. Climate, genetic differences and culture will self-organise the world to a peaceful multicultural equilibrium.

Legal system:

Over-scaling is a unified crime. Occupying other’s territories, violence, killing of rightful beings, exceeding the individual footprint limit, are all forms of over-scaling and will be fined by custody or private property depending on the degree of crime. People scale for sport in the virtual world.

Celebrities:

Plato, Darwin and Mandelbrot are more famous than Einstein. Few nerds know Obama. No body knows Kanye West. But there’s this terrible dancing monkey all over the fucking virtual world.

Other species:

People talk to pets through chips and devices. Eating animals (and humans!) is highly regulated and lab-grown meat (and a lot of other lab food) has taken off. People consume them according to their fashion, taste and lifestyle.

Animals or humans are not being slaughtered in the real world unless there is a legal warrant or a specific type of digital authorization signed for it. Of course people (and pets) still cheat when you don’t see them, but machines watch, warn and stop the cheaters who kill “rightful animals” illegally. There are debates around the definition of that term. Say there is a list including mammals and big land animals. There are debates and protests to include or exclude a certain species.

In Spain (or north Africa?) they still chase bulls in a safer and non-fatal form of bullfighting. And those who love fishing have to go to, let’s say china, because it’s still legal there.

Parenthood:

There are still families, although people are free to live in different social settings and move on to new groups. This will be reinforced by cultural differences in each region and the cultural differences will be maintained.

Psychology:

People take things for granted. They are civilized and they behave but they can easily get depressed and die a fragile life if they get isolated. It’s called “laziside”.
People have become even lazier than us in a sense that they have outsourced their surviving “actions” to the technology and thus they have also outsourced many of their “sensations” because keeping them is not crucial. Shortly, many sensorimotor functions of the brain are practically outsourced to the machines and that’s worrisome due to the depression and numbness that it creates.

Sport:

For the reason mentioned above, “nature gyms” are all around and somewhat mandatory to train people to practice their sensations in the absence of some practical technologies. Professional sports have become intellectual. People compete over their “nature gym” skills by using their physical, social and cognitive skills to show off that they are best. There are cognitive games in the “nature gyms” where people look into each other’s eyes to read feelings and stuff like that. Sex comes to sport with different forms of convertors.

Architecture:

Nature and civilization are mixed up technologically. Buildings breathe and cities are self-sustained. Rooms rotate and change size and adapt with the light conditions democratically by the wishes of people in them.

The list goes on.

A future landscape that is missing a lot of unimaginable technological advances or their cultural artefacts. Just one in a zillion possibilities. Just fantasize and expand it on your own vision.

Then, question:

Is it fun? Should we start talking about a scenery like this? If yes, should we discuss how we should act accordingly to move towards something like this? And not further away from it? Should we wait till machines do it for us?

Or should we – really painfully – go extinct?

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: 2π 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: π^N/2 / Γ(N/2+1) R^N

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 (R^N) we end up with a magical co-efficient as a function of N:

π^N/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 π^N/2 which also introduces a √π for every added dimension. Thus, for even number of dimensions none of the terms π^N/2 and Γ(N/2+1) introduce a √π and we end up with a rational number multiplied by π^N/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!

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.

New Interview Material for hiring Data Scientists

Hey Business Insider! any publicity is publicity. Plus you don’t need my publicity.

Though when I start my data analysis and warehousing company, I will use your article in the very first interview. If applicants don’t start laughing during the first 10 sec they are out. Unless they cry, or they get angry. Or they double-check the header thinking they are reading the Onion. Anyhow if they finally but late realized or were convinced that this is crap from every single aspect, they will be treated nicely but no job. And if… If they defended the article I would make sure there is a global black list to ban them lifetime from all activities related to data.

How do they allow themselves to publish this when they know “search results varies based on the searcher’s history, the time and place of search”.
Cause “they do say at least a little bit about how countries are perceived”?

Absolutely not.

They haven’t even checked with a friend next door to see s/he would get completely different results. In Norway I and my colleague asked Google the exact formulation:

How much * does cost in New Zeland

Autocomplete gave me: to live, build a house, abortion and to study. My colleague got food, petrol, university, gas, minecraft for NZ. The author got “vasectomy” possibly not even due to his country of search but relevant to his own search history. Then he labels every single country in the world by a totally random buzzword and gets an article in the Business Insider? Bravo!

Asking an uninteresting question, forming an irrelevant hypothesis, doing an absolutely wrong methodology on someone else’s data, representing it with a naive medium of visualization, and then lying in the title.

I had not seen something nearly careless at this level.

I try to summarize: First it gives an impression that these are top searches performed by the people in any country. That comes from the misleading title that actually changed a couple of times and finally got worse. If you struggle to make sense of this and you think it is about other countries’ perception about that country, you are still wrong. Finally you start to doubt the author and think it’s at least about how Americans perceive the world since he lives in the US. Not even that. It’s the authors search recommendation, apparently influenced bye is very own search history .

It’s like publishing an article on your personal recommendation and suggesting it to others as if the recommendation services with their fancy algorithms couldn’t do it for them.

Business Insider doesn’t need to apologize to the world for the silly stereotyping. That’s widely common and you can forgive or pity it as an effort-saving short cut to conserve mental processing energy. This article is unique in terms of ignorance combined with uncalibrated self-confidence. This is too bad to ignore.

Cheryl’s birthday

This has been shared massively around the social media and is a fairly interesting primary school puzzle. Now I tweak it a bit and retry it on you: Bernard’s birthday is on the 1st of April and on his birthday Bernard and Albert are trying to figure out Cheryl’s birthday (Albert and Bernard must lie in all three sentences or a part each, but Cheryl doesn’t lie!). So when is Cheryl’s birthday?

p.s. This tweak could have been a bit more interesting. The problem here is that at last Albert doesn’t know what kind of Lie Bernard is making. So yes it seems both June 18 as well as May 15/16 could hold them liar. The dates can be updated for both versions to satisfy a unique answer. Can’t think of it more now. Any suggestion?