I implemented this in python as a command line program that saves those as svg images. Below I will explain the math behind it and show some images.
The process of generating an Apollonian gasket roughly works like this:
We start with a triple of circles, each of which touches the other two from the outside. Now we try to find a fourth circle that is also tangent to each of the three. It’s easy to see that there are two possibilities for this: Either it lies in the middle of the three given circles (externally tangent) or it encloses them (internally tangent).
Left: Three circles with different radii. Each is tangent to the other two.
Right: Two possibilities for a fourth circle that is tangent to the first three. Externally tangent (pink) or internally tangent (green). Read the rest of this entry »
Herr told the story of his transformation from double amputee after a climbing accident, to exceeding what he was previously physically capable of on the rock face.
With technology I am released from these shackles of disability – we will end disability in this century
Herr was told by doctors that there were many things he would never be able to do in life, let alone ever climb again. However, 24 hours after hearing that news he decided the doctor was wrong.
“Technology is not invariant; it’s being upgraded all the time. My body was completely fine, beautiful and powerful. The only hold back was technology and bad design. Technology changes and we can innovate. I climbed at a superior level after my limbs were amputated.”
We will design nature and change nature under our own power – we will give ourselves new bodies
Herr said he embraced the challenge of what his new limbs could be, thinking of a “bionic limb”, rather than a fake-looking human false leg.
“I can be any height I want – think Inspector Gadget. I could climb where no one had before, with three-metre legs. A few people actually said ‘you’re cheating’.”
Herr said it was within our capabilities to fundamentally transform the biological brain and body, extending the sensory experience. He painted a picture of using technology to enhance our bodies.
“We will design nature and change nature under our own power. In the future people will be wearing robots. You don’t need a missing leg to exploit this technology – we will give ourselves new bodies.”
Herr said that in 30 year from now, everyone will be able to modify and sculpt their bodies in a way they see fit.
If you look at a photo after my legs were amputated, do you see the potential for a human who will go beyond human capability?
“Our bodies are plastic and malleable, our very identities are plastic and malleable. A year after I was told I was crippled, I was even more powerful and strong.
“If you look at a photo of me after my legs were amputated, do you see the potential for a human who will go beyond human capability?”
Herr believes that “disability will be overcome” through creativity and innovation.
“You can’t, with a straight face, say that I’m disabled. With technology I am released from these shackles of disability. We will end disability in this century.”
Herr concluded: “In the future, humans will experience a transformation in how they sense, think, feel and move. I dream of a world without disability; I ask you to dream with me.”
If you fall within the Gen-Y era like us, chances are you’ve given a bunch of thought as to how you would raise your own children in this day and age (assuming you don’t have children already). Especially with technology, so much has changed since our childhoods in the 90s. Here’s one question: Would you introduce the technological wonder/heroin that is the iPod and iPad to your kids?
Steve Jobs wouldn’t, and for good reason too.
In a Sunday article, New York Times reporter Nick Bilton said he once assumingly asked Jobs,“So your kids must love the iPad?”
Jobs responded: “They haven’t used it. We limit how much technology our kids use at home.”
Especially in Silicon Valley, there is actually a trend of tech execs and engineers who shield their kids from technology. They even send their kids to non-tech schools like the Waldorf School in Los Altos, where computers aren’t found anywhere because they only focus on hands-on learning.
There is a quote that was highlighted in The Times by Chris Anderson, CEO of 3D Robotics and a father of five. He explains what drives those who work in tech to keep it from their kids.
“My kids accuse me and my wife of being fascists and overly concerned about tech, and they say that none of their friends have the same rules… That’s because we have seen the dangers of technology firsthand. I’ve seen it in myself, I don’t want to see that happen to my kids.”
If our current addictions to our iPhones and other tech is any indication, we may be setting up our children for incomplete, handicapped lives devoid of imagination, creativity and wonder when we hook them onto technology at an early age. We were the last generation to play outside precisely because we didn’t have smartphones and laptops. We learned from movement, hands-on interaction, and we absorbed information through books and socialization with other humans as opposed to a Google search.
Learning in different ways has helped us become more well-rounded individuals — so, should we be more worried that we are robbing our children of the ability to Snapchat and play “Candy Crush” all day if we don’t hand them a smartphone, or should we more worried that we would be robbing them of a healthier, less dependent development if we do hand them a smartphone? I think Steve Jobs had it right in regard to his kids.
So the next time you think about how you will raise your kids, you may want to (highly) consider not giving them whatever fancy tech we’ll have while they are growing up. Play outside with them and surround them with nature; they might hate you, but they will absolutely thank you for it later, because I’m willing to bet that’s exactly how many of us feel about it now that we are older.
Last year, Apple announced a technology that will let you control the appliances in your home with Siri.
It’s called HomeKit. And if Apple’s plans work out, it will turn your home into one giant computer — like the iPhone, but everywhere.
The iPhone, like any other computer, is a piece of hardware built by a certain company that can run apps and games built by other companies and developers all over the world.
These apps expand the functionality and usability of your phone — if you could only use apps made by Apple on your iPhone, imagine how limiting the experience would be.
Apple is opening up similar opportunities with HomeKit by allowing developers to build new features and apps that run your home. Read the rest of this entry »
We propose a method for propagating edit operations in 2D vector graphics, based on geometric relationship functions. These functions quantify the geometric relationship of a point to a polygon, such as the distance to the boundary or the direction to the closest corner vertex. The level sets of the relationship functions describe points with the same relationship to a polygon. For a given query point we ?rst determine a set of relationships to local features, construct all level sets for these relationships and accumulate them. The maxima of the resulting distribution are points with similar geometric relationships. We show extensions to handle mirror symmetries, and discuss the use of relationship functions as local coordinate systems. Our method can be applied for example to interactive ?oor-plan editing, and is especially useful for large layouts, where individual edits would be cumbersome. We demonstrate populating 2D layouts with tens to hundreds of objects by propagating relatively few edit operations.
If we could pause your mind at this instant and look carefully inside your brain, we would see that some brain cells are active and others are inactive. How long these neurons continue to fire after we unpause your mind is determined by how much input they are getting from other active neurons. If they are not being sent more than the requisite number of messages from their peers, they slow down or turn off. Some of the currently active neurons will remain active for only a few milliseconds, others for large fractions of a second and others for several seconds. None remain active indefinitely, but rather they each persist for different durations. The pattern of activity in the brain is constantly changing, but because some individual neurons persist during these changes, particular features of the overall pattern will be conserved over time. In other words, the distribution of active neurons in the brain transfigures gradually from one configuration to another, instead of continually changing all at once. I believe that the persistence of certain neurons allows the temporary maintenance of mental imagery which is a central hallmark of consciousness and working memory. I also believe that this persistence lends continuity to the train of thought.
Six years ago I was waiting at a bus stop wondering how my mind is different from that of other animals. I realized that my thoughts can extend further in the sense that I can carry a complex concept out to its logical conclusion. I can take more information with me through time before I lose it and forget what it was I was just thinking about. Psychologists agree that working memory, or the ability to preserve information and perform manipulations on it, is more highly developed in humans. Influenced by the various lengths of different pine needles on a Douglas fir at the bus stop, I concluded that human thoughts were somehow “longer.” But if thought has a length associated with it, then it must have a beginning and an end too. I wondered for a while if thoughts really do begin and end, and if so, on what time scales. I now believe that it is possible to answer these questions using the reasoning in the previous paragraph.
Thoughts have length in a sense, but thoughts do not have a clear beginning or an end. Thoughts are “longer” in humans because they are composed of elements (that correspond to individual neurons, or neural assemblies) that remain active for longer periods than they do in other animals. Our large prefrontal cortex and association areas keep some neurons online for several seconds at a time, whereas in our pets, for example, most neurons remain active only very briefly. So it is not that individual human thoughts are longer, it is that our thoughts are composed of elements that remain coactivated for longer. The neurons that persist stop and go at different intervals. It is not the case that all of the neurons that persist turn on and off simultaneously. In fact, the beginning of the activity of one neuron will actually overlap with the tails of others. The neurons act like racecars that join in and drop out of a race intermittently. Their behavior is staggered, insuring that we continually have a cascade of cognitive elements that persist through time. Thus there is no objective stopping or starting point of thought. Instead, thought itself is composed of the startings and stoppings of huge numbers of individual elements that, when combined, create a dynamic and continuous whole.
Sensory neurons in the back of the brain do not usually remain active for long. It is the anterior, association areas, especially the prefrontal cortex that contains neurons that stay online for seconds and even minutes at a time. These neurons, by remaining active, can mete out sustained signaling to other neurons, insisting that the representations that they code for are imposed upon the processing of other neurons that are firing during their span of activity. This is why the prefrontal cortex is associated with working memory, mental modeling, planning and goal setting. The longest, most enduring element or neuron would correspond to what the individual is most focused on, the underlying theme or element that stays the same as other contextual features fluctuate.
Thought changes incrementally during its course. We picture one scenario in our mind’s eye and this can often morph into a related, but distinctly different scenario. Our brain is constantly keeping some elements online whether they are representations of things that are concrete and tangible or abstract and conjunctive. I think that neural continuity as described here is an integral element of consciousness and may be a strong candidate for the “neural correlate of consciousness.” Philosophers and neuroscientists have identified many different elements of brain function (thalamocortical loops and reentrant cortical projections) and attempted to explain how these may lead to conscious experience. I think that the present concept of “continuity through differential temporal persistence of distributed neural activity” is instructive and I even feel that it is the core aspect of conscious experience, qualia and phenomenality.
Figure A shows two time points and the change in activation over time. Undoubtedly the longer the separation in time between time one and time two, the fewer reactivated elements. Figure B shows the time course for eight hypothetical neurons. Note how some remain activated for longer than others and that they overlap frequently.