## We live in a shadow universe

14 Jul

It is not uncommon to have a sensation that we live in a kind of downgraded universe and science sustains this feeling in a mathematical ground. This 4-dimensional universe we live in, the space-time framework where life and phenomena unfold, is a reduced version of much more complex worlds, or universes, that somehow prevails over ours. Science, theoretical physics, start unveiling a hidden aspect of our universe. Big data collected worldwide by astronomers and spacecraft are strongly suggesting that ours might well be just a projection, a hologram that forms and where we are in (see Fig.1).

At a more down-to-Earth approach, we all may feel when we sleep and dream, that the wake-up process appears to our senses and feelings as if we were suddenly disconnected from a cosmic current, a stream of energy and information that we are not capable to define clearly. For now, we can only conjecture. So, we may imagine that we are a kind of “virtual beings”. As we know from Quantum Field Theory, “virtual particles” represent a disturbance in a field caused by the presence of other particles, often of other fields. Could we be just a shadow of other, more complete beings, “real” beings living in more expanded dimensions?

In mathematics, we use “real numbers” to quantify what is real. Economists, bankers, and bookkeepers do not use imaginary numbers or the more elaborate hypercomplex numbers and spinors (mathematical objects that represent all “ordinary matter” in our universe) to make business or understand economic-social phenomena. Physicists and mathematicians do. Because to understand our world, they need to understand the other more elaborate world from which ours are nothing else but a projection, a shadow. Perhaps, the fact that we need to use hypercomplex numbers to predict the outcome of events in Quantum Mechanics, we have a lot of troubles to understand Quantum Mechanics. Those numbers are not of our world. It is remarkable that somehow we are able to intuit their existence, to somehow remember them, as discussed by Plato in the Allegory of the Cave.

As scientists are nowadays attempting to communicate with whales and dauphins, one day, science will take seriously the task of communicating with the deads. “Dead” is just a word of ignorant minds, unaware of the enriching process and transformation when a soul is transferred to a higher reality. What we call life, is just this phenomenon of a projection of higher realm beings to a reduced dimensional universe where necessary information must be lost, compactified for lack of spatial memory in this reduced mathematical form, kind of $(x,y,z,t)$ universe.

When we die, probably we regain conscience of the higher complexity and richness of the other worlds from were, for some reason, we were transferred. Believing in karma and Eastern philosophies, maybe this transference to our cosmos is nothing else than an opportunity to redeem our souls from some flaws, hopefully.

A clear vision of our world and the others may help us to overcome the fear of death, and give hope that one day, we will have the technology to communicate with the deaths, if, remotely, they still remain interested in having a connection with us, in this reduced form of the realm.

## The power of networks…

20 Mar

«As the number of connections between people and things adds

up, the consequences of those connections multiply out even faster so that initial successes aren’t self-limiting, but self-feeding.

Mathematics says the sum value of a network increases as the square of the number of members. In other words, as the number of nodes in a network increases arithmetically, the value of the network increases exponentially.

A good definition of a network is organic behavior in a technological matrix.

Every day we see evidence of biological growth in technological systems. This is one of the marks of the network economy: that biology has taken root in technology. And this is one of the reasons why networks change everything.» – Kelly K., in New Rules for the New Economy (1999)

20 Mar

## 10 Rules of Good Studying

1. Use recall. After you read a page, look away and recall the main ideas. Highlight very little, and never highlight anything you haven’t put in your mind first by recalling. Try recalling main ideas when you are walking to class or in a different room from where you originally learned it. An ability to recall—to generate the ideas from inside yourself—is one of the key indicators of good learning.
2. Test yourself. On everything. All the time. Flash cards are your friend.
3. Chunk your problems. Chunking is understanding and practicing with a problem solution so that it can all come to mind in a flash. After you solve a problem, rehearse it. Make sure you can solve it cold—every step. Pretend it’s a song and learn to play it over and over again in your mind, so the information combines into one smooth chunk you can pull up whenever you want.
4. Space your repetition. Spread out your learning in any subject a little every day, just like an athlete. Your brain is like a muscle—it can handle only a limited amount of exercise on one subject at a time.
5. Alternate different problem-solving techniques during your practice. Never practice too long at any one session using only one problem-solving technique—after a while, you are just mimicking what you did on the previous problem. Mix it up and work on different types of problems. This teaches you both how and when to use a technique. (Books generally are not set up this way, so you’ll need to do this on your own.) After every assignment and test, go over your errors, make sure you understand why you made them, and then rework your solutions. To study most effectively, handwrite (don’t type) a problem on one side of a flash card and the solution on the other. (Handwriting builds stronger neural structures in memory than typing.) You might also photograph the card if you want to load it into a study app on your smartphone. Quiz yourself randomly on different types of problems. Another way to do this is to randomly flip through your book, pick out a problem, and see whether you can solve it cold.
6. Take breaks. It is common to be unable to solve problems or figure out concepts in math or science the first time you encounter them. This is why a little study every day is much better than a lot of studying all at once. When you get frustrated with a math or science problem, take a break so that another part of your mind can take over and work in the background.
7. Use explanatory questioning and simple analogies. Whenever you are struggling with a concept, think to yourself, How can I explain this so that a ten-year-old could understand it? Using an analogy really helps, like saying that the flow of electricity is like the flow of water. Don’t just think your explanation—say it out loud or put it in writing. The additional effort of speaking and writing allows you to more deeply encode (that is, convert into neural memory structures) what you are learning.
8. Focus. Turn off all interrupting beeps and alarms on your phone and computer, and then turn on a timer for twenty-five minutes. Focus intently for those twenty-five minutes and try to work as diligently as you can. After the timer goes off, give yourself a small, fun reward. A few of these sessions in a day can really move your studies forward. Try to set up times and places where studying—not glancing at your computer or phone—is just something you naturally do.
9. Eat your frogs first. Do the hardest thing earliest in the day, when you are fresh.
10. Make a mental contrast. Imagine where you’ve come from and contrast that with the dream of where your studies will take you. Post a picture or words in your workspace to remind you of your dream. Look at that when you find your motivation lagging. This work will pay off both for you and those you love!

## 10 Rules of Bad Studying

Excerpted from A Mind for Numbers: How to Excel in Math and Science (Even if You Flunked Algebra), by Barbara Oakley, Penguin, July, 2014

Avoid these techniques—they can waste your time even while they fool you into thinking you’re learning!

1. Passive rereading—sitting passively and running your eyes back over a page. Unless you can prove that the material is moving into your brain by recalling the main ideas without looking at the page, rereading is a waste of time.
2. Letting highlights overwhelm you. Highlighting your text can fool your mind into thinking you are putting something in your brain, when all you’re really doing is moving your hand. A little highlighting here and there is okay—sometimes it can be helpful in flagging important points. But if you are using highlighting as a memory tool, make sure that what you mark is also going into your brain.
3. Merely glancing at a problem’s solution and thinking you know how to do it. This is one of the worst errors students make while studying. You need to be able to solve a problem step-by-step, without looking at the solution.
4. Waiting until the last minute to study. Would you cram at the last minute if you were practicing for a track meet? Your brain is like a muscle—it can handle only a limited amount of exercise on one subject at a time.
5. Repeatedly solving problems of the same type that you already know how to solve. If you just sit around solving similar problems during your practice, you’re not actually preparing for a test—it’s like preparing for a big basketball game by just practicing your dribbling.
6. Letting study sessions with friends turn into chat sessions. Checking your problem solving with friends, and quizzing one another on what you know, can make learning more enjoyable, expose flaws in your thinking, and deepen your learning. But if your joint study sessions turn to fun before the work is done, you’re wasting your time and should find another study group.
7. Neglecting to read the textbook before you start working problems. Would you dive into a pool before you knew how to swim? The textbook is your swimming instructor—it guides you toward the answers. You will flounder and waste your time if you don’t bother to read it. Before you begin to read, however, take a quick glance over the chapter or section to get a sense of what it’s about.
8. Not checking with your instructors or classmates to clear up points of confusion. Professors are used to lost students coming in for guidance—it’s our job to help you. The students we worry about are the ones who don’t come in. Don’t be one of those students.
9. Thinking you can learn deeply when you are being constantly distracted. Every tiny pull toward an instant message or conversation means you have less brain power to devote to learning. Every tug of interrupted attention pulls out tiny neural roots before they can grow.
10. Not getting enough sleep. Your brain pieces together problem-solving techniques when you sleep, and it also practices and repeats whatever you put in mind before you go to sleep. Prolonged fatigue allows toxins to build up in the brain that disrupt the neural connections you need to think quickly and well. If you don’t get a good sleep before a test, NOTHING ELSE YOU HAVE DONE WILL MATTER.

## A valuable collection of educational vintage films

19 Mar

Please, click on the topic to access the video.

Frames of reference

Electric Motors: AC motors and generators

DC motors and generators

## Otto Lilienthal, pioneer of aviation

18 Mar

Insects fly since 300 millions year from now. Naturally, by observing the various modes of flying that natural world show to all of us, create the desire to fly in humans, and Icarus, the son of the master craftman Daedallus that invented the labyrinthus, wanted to fly to the Sun and fall.

A long time after the Greek mythology evoked this desire to fly, Leonardo da Vinci dreams to fly and design several flying machines.

But it was Otto Lilienthal (23 May 1848 – 10 August 1896), a German pioneer of aviation, and also known as the “flying man” that, with braveness and a systematic series of experiments that opened the skies to us.

He made his own hill and glider, and systematically investigate the behavior of different airfoils and the principles of gliding, on how to generate lift and control of flight. He collected a lot of data, later used by the Wright brothers. Unfortunately, on 9 August 1896, while testing a new glider, the airfoil stalled and he falls from above 15 m, breaking his neck and dying the next day. Fearing to have the same fate, the Wright brothers, Orville and Wilbur, used the wind tunnel to be sure that the aircraft was stable, were controllable, and they flew about 6 meters above the ground… With the obsession of stability, in Europe, people were building aircraft so stable that was impossible to make a turn, but the Wright brothers succeed to make the airplane stable but also sufficiently agile in order to make turns with it. They succeed in making the first circular flight by a powered airplane on September 20, 1904.

Astonishingly, from Otto Lilienthal to the Boeing 747 only about one hundred years elapsed…

## What is Loop Quantum Gravity?

15 Mar

Loop Quantum Gravity (also known as Canonical Quantum General Relativity) is a quantization of General Relativity (GR) including its conventional matter coupling. It merges General Relativity and Quantum Mechanics without extra speculative assumptions (e.g., no extra-dimensions, just 4 dimensions; no strings; not assuming that space is formed by individual discrete points). LQG has no ambition to do unification of forces or to add more than 4 spacetime dimension, nor supersymmetry [1]. In this sense, LQG has a less ambitious research program than String Theory and is its biggest competitor.

General Relativity envisages spacetime and the gravitational field as the same entity, “spacetime” itself, that, in many ways, can be seen as a physical object analog to the electromagnetic field. Quantum Mechanics (QM) was formulated by means of an external time variable t like it appears in Schrödinger equation

$i\hbar\frac{\partial}{\partial t}\left|\Psi(t)\right>=H\left|\Psi(t)\right>$

Fig. 1 below shows the solutions of SE when applied to the simplest atom in Nature, the hydrogen atom, where the potential is $V=\frac{1}{r}$. Electrons that rotate around the positive nucleus have the energy is quantified according to the law $\latex E_n=\frac{13.6}{n^2}$ and the wave function $\latex \Psi$ are given by the mathematical functions given in Figure 1.

However, in General Relativity (GR) this external time (represented above by the letter t) is incompatible because the role of time becomes dynamical in the framework of Minkowski spacetime. Time is no longer absolute (as Sir Isaac Newton once stated) but is relative to a frame of measurement. In addition, GR was formulated formerly by Albert Einstein in the framework of Riemannian geometry, where it is assumed that the metric is a smooth and deterministic dynamical field (Fig.2).

Fig.2 – Example of Riemann surface. Image courtesy: http://virtualmathmuseum.org (See for details about this specific surface here: http://virtualmathmuseum.org/Surface/riemann/riemann.html

This raises an immediate problem, since QM requires that any dynamical field be quantized, that is, be made of discrete quanta that follows probabilistic laws… This would mean that we should treat quanta of space and quanta of time…

All the known forces in the universe have been quantized, except gravity. The first approach to quantization of gravity consists of writing the gravitational field as composed of the sum of two terms, a background field $g_{background}$ and a perturbation $h(x)$. So, its full metric $g_{\mu \nu}$:

$g(x)=\eta_{background} (x)+ h(x)$

where $\eta_{\mu \nu}$ represents the background spacetime, normally Minkowski) and $h_{\mu \nu}$ a perturbation of the field (representing the graviton). The Minkowski space united space and time as a single entity introducing the new concept of space-time manifold where two points are distant by

$ds^2= c^2 dt^2-d \bf{x}^2$.

The problem resides in the intrinsic difficulty that this approach face when describing extreme astrophysical (near a black hole) or cosmological scenarios (Big Bang singularity). The inconsistency between GR and QM becomes more clear when looking at Einstein equation of GR:

$R_{\mu \nu} - \frac{1}{2}gR=\kappa T_{\mu \nu}(g)$

$R_{\mu \nu}$ is the Ricci curvature tensor, $R$ is the curvature, and $T_{\mu \nu}$ is the energy-momentum tensor. $\kappa \equiv \frac{8 \pi G}{c^4}$. While the left-hand side is described by a classical theory of fields, the right-hand side is described by the quantum theory of fields…

LQG avoids any background metric structure (described by the metric g), choosing a background independent approach, along the suggestion of Roger Penrose on the spin-networks where a system is supposed to be built of discrete “units” (anything from the system can be known on purely combinatorial principles) and all is purely relational (avoiding the use of space and time…) In GR spacetime is represented as a well-defined grid of lines, even if curved in the presence of a massive body, such as

In LQG, spacetime is represented rather as background-independent, the geometry is not fixed, is a spin network of points defined by field quantities and angular momentum, more like a mesh of polygons; spacetime is more a derived concept rather than a pre-structure, pre-concept on which events take place, as shown here

Image credit: http://www.timeone.ca/glossary/spin-network/

This new representation of fields has the advantage of representing both their intrinsic attributes but also their induction attributes. That is, the field quantities depend not only of the point where it exist but also on the neighboring points connected by a line. That’s why the mathematical idea that best express this representation is the holonomy of the gauge potential $A$ along the loop (line) $\alpha$, $U(A,\alpha)$, which is given by the integral

$U(A,\alpha)=exp{\int_0^{2\pi} ds A_a(\alpha(s))\frac{d\alpha^a(s)}{ds}}.$

REFERENCES:

[1] Carlo Rovelli, Quantum Gravity (Cambridge University Press, Cambridge, 2004)

## Vermeer and the Masters of Genre Painting: Inspiration and Rivalry

4 Oct

Johannes Vermeer is best known for his meticulously rendered images of women in light-filled domestic interiors. A slow and methodical painter, Vermeer produced relatively few paintings (34 have been attributed to him) but was a modest celebrity in his hometown of Delft during his lifetime. After he died, he fell into obscurity until the 19th century when he was rediscovered by German art historian Gustav Friedrich Waagen and French journalist and art critic Théophile Thoré-Bürger. Vermeer is now considered one of the greatest painters of the Dutch Golden Age. [from https://www.artsy.net/artist/johannes-vermeer]

The exhibition, Vermeer and the Masters of Genre Painting: Inspiration and Rivalry opens on October 22 at the National Gallery of Art and closes January 21, 2018.
Useful resources for Art collecting and information is offered by the Artsy team, at the site https://www.artsy.net, Artsy’s mission is to make all the world’s art accessible to anyone with an Internet connection.

Vermeer’s Art of Painting or The Allegory of Painting (c. 1666–68), Image credit: Wikipedia

## Colin Maclaurin popularized the physico-mathematical work of Isaac Newton

17 Feb

Colin Maclaurin (1698-1746), in Scottish Gaelic his name pronounce Cailean MacLabhruinn, was a Scottish mathematician who made important contributions to mathematics, in special, he is known by his Maclaurin series. He was the first one to popularize the physico-mathematical work of sir Isaac Newton publishing An Account of Isaac Newton’s Philosophical Discoveries (see link below). This publication raised a so great interest and admiration that for some it constituted the “great intellectual affair of the century: …the application of the experimental and geometrical method of Newton to the study of human nature, now stripped of the trappings of theology”[2].

Sir Isaac Newton contributed decisively to the Enlightenment (reason as the primary source of authority and legitimacy). There is great evidence, and several historians of science soustain the argument, that Adam Smith and other intellectuals had the “secret ambition” to make parallelism of his theories, to imitate Newton, and Adam Smith work shows is efforts to discover general laws of economy, inspired by the success of Newton and his discovery of the natural laws of motion

REF:

[1] An Account of Isaac Newton’s Philosophical Discoveries, by Colin Maclaurin

[2] Political Economy in the Mirror of Physics: Adam Smith and Isaac Newton, by Arnaud Diemer and Hervé Guillemin, Revue d’histoire des sciences, 2011/1 (Volume 64)

## When all are equal, can one make the difference?…

23 Sep

Scientific research can help society to progress, but can also be deceptively dangerous… Research in the field of statistical physics shows that the collective behavior of population can have a ‘giant response’ if an individual is properly tuned. So, the task of social media is to avoid, or strongly reduce the possibility for this situation to happen… Then “spontaneous symmetry breaking” occurs and “someone, no matter who, has to do the job”… The work done by Federico Corberi, a Researcher at the Salerno University, in Italy, was published in Journal of Physics A: Mathematical and Theoretical. [1]

REF:

[1] When all are equal, one can be very different [http://iopscience.iop.org/journal/1751-8121/labtalk/article/63268]

## Can we survive after-death?…

12 Jun

Can we (i.e. our soul, our consciousness, our spirit, our élan vital,…) survive after death?…A scientific study points for that possibility… At least, and for now, according to Dr. Parnia, in the interview stated: “The evidence thus far suggests that in the first few minutes after death, consciousness is not annihilated. Whether it fades away afterwards, we do not know, but right after death, consciousness is not lost.

We know the brain can’t function when the heart has stopped beating. But in this case conscious awareness appears to have continued for up to three minutes into the period when the heart wasn’t beating, even though the brain typically shuts down within 20-30 seconds after the heart has stopped. This is significant, since it has often been assumed that experiences in relation to death are likely hallucinations or illusions, occurring either before the heart stops or after the heart has been successfully restarted. but not an experience corresponding with ‘real’ events when the heart isn’t beating. Furthermore, the detailed recollections of visual awareness in this case were consistent with verified events”.

The important research accomplished may represent the first step towards the “proof” that our soul, conscience, spirit, survive after our body dies…