The Maths Book of the Future
Mathigon presents the first fully interactive and adaptive mathematics textbook. Using beautiful graphics and animated simulations, it makes advanced mathematical ideas accessible to the general public.
Seriously cool website and a lot of fun to browse. Checkit.
Omg this is so fucking cool. Can we turn this into a learning device with that same interface and just 3d print em en mass to poor communities lacking educational outlets???
I’m still not over this site.
NEW AVAILABLE ART PROGRAM
It seems to be a mix between SAI and photoshop, simplified. It even has a stabalizer that works even with the mouse.
Best of all, it’s free, and works for both Mac and Windows.
To give it a try, head right on down to http://firealpaca.com/
Reblogging for artsy people that follow me. Also a lovely name for a program.
THIS IS MY FAVORITE PROGRAM. LIKE HOLY @#!*% I DIDN’T LIVE UNTIL I USED THIS.
Theoretical Physics: The Origins Of Space And Time
Many researchers believe that physics will not be complete until it can explain not just the behaviour of space and time, but where these entities come from.
“Imagine waking up one day and realizing that you actually live inside a computer game,” says Mark Van Raamsdonk, describing what sounds like a pitch for a science-fiction film. But for Van Raamsdonk, a physicist at the University of British Columbia in Vancouver, Canada, this scenario is a way to think about reality. If it is true, he says, “everything around us — the whole three-dimensional physical world — is an illusion born from information encoded elsewhere, on a two-dimensional chip”. That would make our Universe, with its three spatial dimensions, a kind of hologram, projected from a substrate that exists only in lower dimensions.
This ‘holographic principle’ is strange even by the usual standards of theoretical physics. But Van Raamsdonk is one of a small band of researchers who think that the usual ideas are not yet strange enough. If nothing else, they say, neither of the two great pillars of modern physics — general relativity, which describes gravity as a curvature of space and time, and quantum mechanics, which governs the atomic realm — gives any account for the existence of space and time. Neither does string theory, which describes elementary threads of energy.
Van Raamsdonk and his colleagues are convinced that physics will not be complete until it can explain how space and time emerge from something more fundamental — a project that will require concepts at least as audacious as holography. They argue that such a radical reconceptualization of reality is the only way to explain what happens when the infinitely dense ‘singularity’ at the core of a black hole distorts the fabric of space-time beyond all recognition, or how researchers can unify atomic-level quantum theory and planet-level general relativity — a project that has resisted theorists’ efforts for generations.
“All our experiences tell us we shouldn’t have two dramatically different conceptions of reality — there must be one huge overarching theory,” says Abhay Ashtekar, a physicist at Pennsylvania State University in University Park.
Finding that one huge theory is a daunting challenge. Here, Nature explores some promising lines of attack — as well as some of the emerging ideas about how to test these concepts (see 'The fabric of reality').
Loop Quantum Gravity
Even if it is correct, the thermodynamic approach says nothing about what the fundamental constituents of space and time might be. If space-time is a fabric, so to speak, then what are its threads?
One possible answer is quite literal. The theory of loop quantum gravity, which has been under development since the mid-1980s by Ashtekar and others, describes the fabric of space-time as an evolving spider’s web of strands that carry information about the quantized areas and volumes of the regions they pass through6. The individual strands of the web must eventually join their ends to form loops — hence the theory’s name — but have nothing to do with the much better-known strings of string theory. The latter move around in space-time, whereas strands actually are space-time: the information they carry defines the shape of the space-time fabric in their vicinity.
Because the loops are quantum objects, however, they also define a minimum unit of area in much the same way that ordinary quantum mechanics defines a minimum ground-state energy for an electron in a hydrogen atom. This quantum of area is a patch roughly one Planck scale on a side. Try to insert an extra strand that carries less area, and it will simply disconnect from the rest of the web. It will not be able to link to anything else, and will effectively drop out of space-time.
One welcome consequence of a minimum area is that loop quantum gravity cannot squeeze an infinite amount of curvature onto an infinitesimal point. This means that it cannot produce the kind of singularities that cause Einstein’s equations of general relativity to break down at the instant of the Big Bang and at the centres of black holes.
In 2006, Ashtekar and his colleagues reported7 a series of simulations that took advantage of that fact, using the loop quantum gravity version of Einstein’s equations to run the clock backwards and visualize what happened before the Big Bang. The reversed cosmos contracted towards the Big Bang, as expected. But as it approached the fundamental size limit dictated by loop quantum gravity, a repulsive force kicked in and kept the singularity open, turning it into a tunnel to a cosmos that preceded our own.
This year, physicists Rodolfo Gambini at the Uruguayan University of the Republic in Montevideo and Jorge Pullin at Louisiana State University in Baton Rouge reported8 a similar simulation for a black hole. They found that an observer travelling deep into the heart of a black hole would encounter not a singularity, but a thin space-time tunnel leading to another part of space. “Getting rid of the singularity problem is a significant achievement,” says Ashtekar, who is working with other researchers to identify signatures that would have been left by a bounce, rather than a bang, on the cosmic microwave background — the radiation left over from the Universe’s massive expansion in its infant moments.
Loop quantum gravity is not a complete unified theory, because it does not include any other forces. Furthermore, physicists have yet to show how ordinary space-time would emerge from such a web of information. But Daniele Oriti, a physicist at the Max Planck Institute for Gravitational Physics in Golm, Germany, is hoping to find inspiration in the work of condensed-matter physicists, who have produced exotic phases of matter that undergo transitions described by quantum field theory. Oriti and his colleagues are searching for formulae to describe how the Universe might similarly change phase, transitioning from a set of discrete loops to a smooth and continuous space-time. “It is early days and our job is hard because we are fishes swimming in the fluid at the same time as trying to understand it,” says Oriti.
Journey into a Schwarzschild black hole.
The simplest kind of black hole is a Schwarzschild black hole, which has mass yet no electric charge or spin. This black hole geometry was discovered by Karl Schwarzschild in 1915, shortly after Einstein presented his final theory of General Relativity. The gifs above are created from a simulation depicting what you would theoretically see if you traveled towards a black hole, against a panorama of our Milky Way.
First of all, as you approach, you clearly see gravitational lensing taking place, with the black hole bending light around it. It appears to ‘repel’ the Milky Way radially, which then stretches the image transversely. The sections closer to the black hole experience greater ‘repulsion’, so the image appears to be compressed radially.
You then take note of the Einstein Ring seen around the black hole, occurring because of the bright objects lying directly behind it. Due to the aforementioned gravitational lensing, the light from these bright objects is bent around the black hole and forms this ring.
Fortunately (or maybe unfortunately), as you get closer, the trajectory of your journey does not have enough angular momentum to go into an unstable circular orbit. If you had slightly more, you would find yourself orbiting this black hole, which would, in fact, make for a fairly nice view. However, you carry on travelling towards the center.
Next, you swiftly pass through the photon sphere,where light rays can orbit the black hole in unstable circular orbits. However, you do not see anything of particular interest, but are more concerned with your forthcoming fall through the horizon.
As you travel, you would not know at what point you fell through the black hole’s horizon. However, as you do pass through it unaware, it apparently splits in two, explained nicely by these Penrose diagrams (if you have the chance to give them a quick glance over whilst you’re hurtling towards your inevitable death). Here, space is falling faster than light, meaning you are carried inexorably inward.
Anyone who happens to be watching your spectacular journey would see you as fairly dim and red. This effect is due to red shift, with anything falling past the black hole’s horizon appearing this way to an observer outside of this point.
As you get closer and closer to the center, the black hole’s tidal forces begin to wear on you. Presuming you are travelling feet first, you feel a greater force of gravity in your lower half than up by your head. Due to these forces, you are stretched vertically and crushed horizontally; this is known as spaghettification. These forces also mean that your view of the Universe beyond is blue shifted and bright around your waist, but red shifted and dim above that; a strange sight.
Despite having been utterly torn apart from the tidal forces, a tenth of a second later you reach the black hole’s singularity, the center point of infinite curvature. Here, space and time as you know them come to an end, and so does your exciting journey.
It must be remembered that real black holes are probably much more complicated than Schwarzschild black holes; they likely spin and are not isolated, so a journey into a normal black hole could be slightly different adventure.
The Blue Mosque
Edirne, Turkey via Architecture Daily
Leonardo da Vinci’s Geometric Sketches.
Da Vinci illustrated Divina proportione, supplying sixty plates for the work.
For the Platonic solids, Da Vinci supplied two views: a plane view and a “vacua” or empty view where he removed the sides to better reveal the complete structure of the polyhedron. These “nets” of vertices and edges illustrate the artist’s graphic genius.
Besides the sphere, can you identify the 5 platonic solids?
The first geologic eon began with the formation of the Earth about 4,600 million years ago and ended 4,000 million years ago.
More broadly: abiogenesis - the natural process by which life arises from simple organic compounds. The earliest life on Earth existed at least 3,500 million years ago, at the beginning of the Archean Eon when sufficient crust had solidified following the molten Hadean Eon
First geologic period of the Paleozoic Era, lasting from 541 to 485 million years ago. Although complex, multicellular organisms gradually became more common in the millions of years immediately preceding the Cambrian, it was during the Cambrian that life exploded, rapidly diversifying and producing the first representatives of many modern phyla, However, while diverse life forms prospered in the oceans, the land was comparatively barren.
A geologic period of the Paleozoic Era that occurred from 419 to 358 million years ago. This was the first significant adaptive radiation of terrestrial life.
The all-white reinvention of Medieval Europe commonly depicted in popular fiction, films, tv shows and art is entirely that: a fiction. An invention. An erasure. Obviously, people of color have been an essential and integral part of European life, European art, and European literary imagination since time immemorial. To cite “historical accuracy” as a means to project whitewashed images of the past into the future to maintain a fiction of white supremacy is an unconscionable farce.
People of Color are not an anachronism.
The above images depict the scope of study in science.
Science today, is the crème de la crème of human knowledge and the center of our tech-savy culture. It is the quintessential ‘double edged sword’; it can be used for achieving the sheer amazing or the macabre destruction of everything. With science in our hands, mankind has ambled to the greatest of heights and also the lowest of low.
But at heart, it is all pure. There is nothing else that can be more euphoric, exalting, exasperating, head breaking, heartwarming and overawing all at the same time. The goal of science is quite audacious—if not a little chutzpah. It’s nothing less than to understand it all: atoms, cells, life, death, the universe and beyond.
It is by nature, a very human endeavor; an extension of our curiosity. Great minds have dedicated all to this most prodigious of human undertaking. The far reaches of the universe and the befuddling land of the tiny, all are in grasp when we delve into science. So, what exactly is this science?
The etymology of the word science stems from the Latin word scientia, meaning knowledge. And during the early ages, it was exactly that; any form of knowledge was called science. Be it about the natural world or about abstract mathematics, all of this was called to science.
Then during 17th and 18th century, the Age of Enlightenment and the Renaissance, people started to rediscovery ancient Greek texts, and Newton came up with his classic laws. It was a time of revelation; the pillars of modern science such as Newtonian physics, thermodynamics were all established during this time.
It was also during this time that the meaning of science got closer to what used to be called ‘natural philosophy’, namely the study of natural phenomenon. This is modern science; it includes physics, chemistry and biology as broad categories.
Modern science is built on the strict ideals of empiricism, falsification and the scientific method.
Science and Its Products
We have been talking so much about science; yet, we have not formally defined it. ‘Science is the means of organizing and pursing knowledge, through testable predictions.'
Notice that I said that it is the means of pursing the knowledge; the knowledge itself is not science, rather they are products of it. The manner if obtaining knowledge is judged as scientific or not; not the knowledge itself.
Science is more than just facts. It is an ideology; a way of thinking. In science, nature is considered not to be capricious. Nature is governed by laws, and those laws are universal and completely understandable by probing it, i.e., doing experiments. Thus, experiments form the very veritable substratum of science. All knowledge is a posteriori, i.e., only experiments can confirm a hypothesis. This ideology is called empiricism.
The means of carrying out an experiment—so central to science—is by using the scientific method. It is the pièce de résistance of any endeavor in science. It consists of a series of steps as described below:
- Observation: This requires observing the natural phenomenon and recording data.
- Pose a question: If such data cannot be expounded by current theory, a question should be posed as to why this is so? Do we need a new theory?
- Hypothesis: An appropriate answer should be formulated for the above question. It would be sort of like a hunch or a guess that you have.
- Make some predictions: This is the important bit. After formulating the above hypothesis, some testable predictions should be made. These are extensions of the hypothesis; the extrapolation of your hypothesis to other situations. Science is based on empiricism and falsification, where a hypothesis should be able to make predication that can be easily tested to ascertain the hypothesis.
- Experimentation: These predictions are now tested.
- Results: The results of the experiment are taken and checked to see if the predictions match the results. If they don’t, we need to start all over again and come up with another hypothesis.
- Theory: If a hypothesis has passed all this, it is accepted into the general scientific community, and is called a theory. A theory accurately explains the phenomenon in question, and it is generally accepted as ‘true’.
The word ‘theory’ in science does not mean the same as it does in common parlance. In common language, it generally means something that is not proven. But as far as science is concerned, a theory is an accepted explanation for a phenomenon; it is proven to be right to the best of our knowledge.
The hallmark of a good hypothesis is its ability to produce large amounts of testable predictions (which should come true of course!). The process of obtaining scientific knowledge from testable experiments is called the scientific inquiry. It is very important for a hypothesis to produce some viable statements and predictions, which can then be tested.
Keep in mind that even if a hypothesis becomes a theory, it can still be rejected later if new experiments and evidence refute it. And this brings us to the next section.
Best Fit Theory
Due to the nature of science, no theory can be perfect. There is no permanent or absolute truth. Falsification demands that even if one trifle shred of evidence is found that contradicts a theory, it should be rejected. In that sense, no theory is the absolute and dogmatic truth, and that is why scientists call a good theory a ‘best fit’ one, i.e., the one that best explains the body of evidence discovered currently.
It may happen that some new technologies and new evidence may contradict a well-established theory in the future, and in that case it will have to be removed from the textbooks (or at least altered).
Take the example of Newtonian Mechanics. For over two centuries it was unchallenged and accepted as true. But, in the 20th century, new evidence, taken with more precise instruments, found it deviating from the experimental data. So it had to be rejected, since new evidence was found that contradicted Newton’s theory, and modern mechanics—most notably by Einstein, Bohr, Planck, and others—was developed.
But again, this does not show that all scientifically accepted theories are intrinsically unstable or untrue. If a theory is accepted into science, it is scientifically true and, it can be used to explain a multitude of phenomena. But, those same rules of science that give credibility for a hypothesis to become theory, also give the freedom to undermine it if new research and evidence does not corroborate with it.
Some people cannot get their heads around this concept. So, let us make an analogy. Science is almost like a democracy, where the people of the scientific community are citizens of this democracy. These citizens vote for the leader who will best adapt to the needs and situation of the country at that time; in the same way, scientists favour or ‘vote’ a theory that best suites the evidence. So for this particular time period, that person who was elected is called the ruler. Akin to this is when we call our theory as the ‘truth’.
Now if the situation in the democracy were to change to a state in which the incumbent ruler would be unable to rule decisively, he would then be replaced. Taking the analogy forward, a theory would be ‘replaced’ if it is found that it cannot cope with some new evidence found.
In short, one can say that a theory is a ‘scientific’ truth, but not the ‘absolute’ truth.
We can conclude therefore, that science is an ongoing process; it is never ‘finished’. New questions are always being formulated, and new answers are being thought of for whilom questions.
Science in Our Genes
Science is the most human of activities; our DNA is endowed with it. All of us have a restive passion for discovery. Nature has always intrigued us; it truly piques our curiosity, and stokes our fervor for discovery.
Also, science is a very democratic endeavor; no theory is allowed to exist if it doesn’t deserve to. It is egalitarian, in the sense that any theory can replace another if it has sufficient evidence (remember our earlier example?). Through the principle of falsification described above, no theory can claim to be the permanent truth. This stops science from being a dogmatic creed, and prevents it from receding into the abyss of pseudo-science. This maintains the consistency of our knowledge.
We do science, not because we can make new technologies but, because we can satisfy our insatiable curiosity and zest for learning. The search for answers and the meaning among it all veritably is the most powerful drive of humanity and the foremost of human expression. We were built for undertaking science, and it would be a sin if were not to oblige to this calling.
Picture: Sprawling aerial view of Mexico City, one of the most densely populated places in the world.
Photograph: Pablo Lopez Luz/Barcroft Media