I was really hoping for a continuous (rather than discrete) fourth dimension. The concept is cool and looks to be well executed, but it's not very different from other alternate reality implementations such as the Dark World in Legend of Zelda.
That would be really cool. The mathematics involved don't seem too difficult; you have to add another axis to your vectors, points, and transform matrices, and you can place and orient your models in 4D space, set up lights and a camera in 4D space, and project the camera's view into 3D space first then onto the 2D display. I think the hard part is creating the models and writing the rendering engine. Creating 4D models, rather than just putting 3D models into 4D space, would be hard to wrap your head around. And the tools, both for world creation and for rendering, are almost certainly limited to 3D so you'd have to write your own tools for everything. No more GPU acceleration, unless your 4D to 3D transformation creates models and textures on-the-fly to pass to the GPU.
This is something I've been working on as a side-project on and off for a while. It's complicated by the fact that every existing engine is built around the assumption that you only want to use 3 dimensions, not four, and not arbitrarily many, so I've been pretty much writing everything from scratch (and very limited GPU acceleration, as you said, because GPUs also assume 2 or 3D). So far, I'm punting on model building by just auto-generating 4D mazes with hypercubical cells, because maze-generation algorithms work in arbitrary dimensions.
For simplicity, my rendering engine is a dead-simple raytracer which doesn't even bother with reflections- just cast rays and record the first surface they run into. Handling rotations and projections is really easy, but there are two problems I have found:
1. It's just really frickin' slow. Raytracing just ain't fast enough, though I may be able to find some additional optimizations to make it better.
2. In terms of gameplay, navigating the space is really, really hard. It is so easy to get completely lost regarding which direction you're facing and what hyperplane you're on when you can make arbitrary rotations in all four dimensions. It might be something I could get used to, but so far I feel like it's practically necessary to have some mechanism that will snap you back into alignment with some set of gridlines.
One possible way of getting around that, stolen from machine learning, is to use colors to represent the fourth dimension, ie, make things darker (or change the hue/saturation) that are bigger in the fourth axis, and vice versa for smaller.
I would just avoid the rotation issue. Time works as a 4th dimension so if you have a charter that can flow backward or forward in time you can 'solve' 4d mazes without major issues. From a game-play perspective plenty of games have you vary limited control over time but you could make some vary interesting puzzles with full control.
EX: walls in the way. <Set bomb off> Walls gone but cave collapses. <walk though wall> <go back in time> <keep walking>.
Or simply let you flip times direction. Going vary slow or backward prevents changing things, but you get to move. So, you might be able to for example walk on water when moving backward in time etc.
That's pretty much the idea of Braid, an awesome indie game. It uses time manipulation in different ways to create mechanics in that vein. Recommended.
There are some simple games like that. 4d mazes, 4d tetris, 4d pong, etc. The problem is it's pretty impossible for people to wrap their mind around it, and it doesn't project very well on 2d screens. Research has shown that people don't get better at it with practice either.
I'm going to google around for this, but do you have any links to the research off hand? I'd be interested in seeing it.
My favorite 2048 variation was the 4D version. It was trippy but I felt like I got my head around that. I think it was because the game rules were so simple that instead of trying to visualize what was going on, my brain just accepted the patterns.
We already have 4-dimensional models; we just keep the 4th dimension separate and call it an animation path. In fact, Skyrim has 5-dimensional models: there are two versions of each walking animation, roughly "feminine" and "masculine," but each character actually uses a specific blend-point between the two. Similar analogies with facegen textures. All the pieces are there, they just need to be glued together right.
Can you clarify why having two animation paths makes 5 dimensions? Surely the dimension is time, you're just deforming the 3 spatial dimensions along two different paths as you progress uniformly along the 4th?
You could probably make something like Minecraft but out of hypercubes and besides turning in three dimensions you can also reorient your three dimensional subspace in the four dimensional world. As you mentioned, the interesting question is how you model objects - are our usual three dimensional things thin sheets in the fourth dimensions or do they have some interesting structure.
I believe there are some good libraries out there for handling quaternions. Can't remember the topic but there was a discussion here within the last 10 days about their application to a similar problem.
It's naturally confusing, because a 4th spatial dimension isn't something we naturally experience.
We can't really say what it represents because it's not real... it's not a model of reality.
We see in 2 dimensions and we infer the third from various cues. (The quote that we are "dimly aware of a fourth", which you may have heard, refers to time and is a different issue than a fourth spatial dimension.)
We have three dimensions, all orthogonal to each other. We can translate, rotate, and project things in between them.
So all we can do is apply those same principles and see what comes out - we shouldn't expect it to match anything recognizeable though.
Mathematically, they're identical to any other dimension. You can move a little bit into a fourth dimension just like moving a little bit left-to-right. Or you can rotate things around the fourth axis just like turning something clockwise. In the case of this game, he only shows a 2D projection of a 3D cross-section of a 4D world, so that might be adding to the confusion. What you see in the video is only 3D "slices" of a 4D object rotating.
One of the axes introduced by the fourth dimension. There are 3 in 3D, 6 in 4D. XYZ space has axes perpenicular to the planes xy, xz, yz. WXYZ space has axes perpendicular to the planes xy, xz, xw, yz, yw, zw.
No. There are only 4 axes in 4-dimensional space - every point is described as a 4d vector, i.e scalar positions along each axis: (x,y,z,w).
xy, xz, etc. are not planes in 4d space - they are 3d-hyperplanes, and perpendicular to them are planes, not axes. Imagine this: you have a 4d vector and you hold x and y constant. You still have 2 degrees of freedom: a plane, not a line.
It might help mentally, but it won't reduce the number of projections. You'd have to be able to see every point in the whole 3D volume, not just the surface.
The game is actually completely continuous. The crazy deforming shape at the beginning of the trailer is a 3D slice of an object called a 120-Cell, which is a true 4D shape.
Isn't that addressed in the additional notes below the video?
There are **infinitely** many 3D worlds stacked on top of
each other, even if in the Wall level the ground texture
makes it seem like there are only two.
Adanaxis is an open source space shooter game that lets you move in all 4 axis, or rotate continuously along any combination of axis. All models are 4 dimensional.
Needless to say, it is confusing to the point of unplayability past a certain point, but utterly fascinating.
You can grab a copy from your Ubuntu, Fedora, or Arch repos, and it is certainly worth trying to wrap your head around for an hour or two, if you are into that sort of thing.
Interesting points, but I don't think the lack of privacy in a small community is very similar to the lack of privacy in a large surveillance ecosystem. If the concern is over the ability to have secrets at all (i.e. to know facts that are unknown to others) then the metaphor works. The problem is that it's not about personal insult or embarrassment, it's about a larger power disparity.
In a small town, the lack of secrecy is (generally) mutual. People are aware of the reputation they gain and can usually address any rumors or allegations directly. Furthermore, there's still the option to physically move away, and one can presume that there will be other communities to join while leaving behind social baggage.
When it comes to the internet, the metaphor breaks down. Most people are (by design) unaware of the degree or even the presence of surveillance around them. The parties collecting the information (corporations, government agencies, and a few individuals) remain unknown, and their motivations reach far beyond those of rumormongers or gossips. Because they don't share in the same small community, the powers that watch us don't have to fear direct or indirect repercussions from the ways they use our data for or against us. This should be much scarier than any threat of individual antagonism or public shame.
There's also no effective way to 'leave' the internet. As this article illustrates, it's difficult or impossible to avoid revealing even a single specific piece of information, let alone your whole identity. It's more than the fact that we "really like" our involvement in the online community, it's a necessity for the vast majority of us to sustain ourselves socially and financially. We will inevitably reveal many things about ourselves by our actions online, and this data will never disappear.
I agree that we need to move forward from the way things are rather than trying to back out at this late hour. However, I very much disagree that this is in any way comparable to the way things have been, or a reemergence of previous societal trends. This is a new problem created from our many advancements, and we need to find new ways to address it.
While it's certainly a good general policy to not abandon significant segments of your user base, this is not a conflict of user ignorance vs developer laziness. The real question is whether preserving IE6-8 functionality is actually a good way to serve your customers. The resources you dedicate to retaining that 10% might be better used to improve your service for the other 90%. Focusing on modern browsers will also help to attract new customers who won't lock you deeper into these technical shackles. While this doesn't have to mean directly antagonizing people, it may involve making the site unusable and 'ruining' the experience for some.
I'd suggest that most organisations that only had to support 10% IE6 use in the past have already actively made the decision not to support it any longer (I know that happened a couple of years ago for all the orgs I was working with).
For other companies, their customers are 90% on IE6. I know that's a hole of their own making, but in some cases it's a massive undertaking to dig out of. There's money to be made in supporting those guys :)
"bro" is a short mnemonic/memetic context which makes the command easier to remember and use. I don't think it has any relation to the intended audience or constitutes an endorsement of the "bro" culture by any means.
It's an interesting example of choosing a name. Some people obviously don't care about $NAME, others have a strong aversion to $NAME. Should the creators consider a name change? What if the product is something you're looking to get funding for?
The advice to "pick anything that isn't going to get us sued for trademark infringement and that doesn't mean 'penis' in some other language" needs some expanding.
Somehow overpopulation didn't make his list of existential risks? Seems like a glaring hypocrisy for someone who claims to have an interest in saving the species.
Overpopulation is not an existential risk: it does not kill the entire human race or permanently curtail/destroy potential. Overpopulation sucks and can cause serious problem for those affected, but it does not threaten all of humanity and to some extent solves itself - you can't go beyond the Malthusian equilibrium.
Not only is overpopulation not an existential risk, it's not even really a risk: look up the demographic transition.
I think it's a very serious issue. Clearly the population will balance itself at some point, whether by education/moderation or mass-starvation. However, I believe we have a finite window of opportunity to make a number of critical scientific and social advancements in order to continue our species' progress in the next few centuries and beyond. This window is defined primarily by the availability of materials and energy which are necessary to support technological development at our current scientific frontiers. Increasing population, especially in the developed world, consumes resources faster and thus shortens the span before many critical materials become scarce. Better extraction and synthesis will likely become available in the future, but first we need to get there.
I am not arguing that we shouldn't have children at all, but responsibly limiting our population seems like a critical supporting factor in any qualitative advancement we want to make as a species. This is especially true since much of the world doesn't seem likely to do the same any time soon.
I think you make some good observations, but I'd wager if you think these statements through a while longer, you'll adjust your position. Jaan (a single high fitness human) having multiple children doesn't connect directly to the real issue of overpopulation. The carrying capacity of the earth (with efficient use of vertical space) is orders of magnitude large than our current population. Survival-necessary resources are not scarce. Depletion of scarce resources causes serious economic and societal impact, but can you name one irreplaceable scarce resource? We're almost out of oil but tech will transition to alternatives soon. I worry about byproducts of overpopulation, like multiple antibiotic resistance bacteria and calcified local optima in social systems.
Your comment didn't address any of my points. Your 'finite window of opportunity', besides being completely unjustified and probably wrong on a long-term time-scale, does not relate to overpopulation rather than, say, Peak Oil, and you ignored my point that the risk simply isn't there due to the demographic transition - which makes your claim that "Increasing population, especially in the developed world, consumes resources faster" simply wrong because places like Japan or South Korea (developed countries by any measure) are projecting decreases in population soon, and even the USA is growing mostly due to immigration.
People often wake up to these things at a certain age or certain phase in life. It's good to encourage and welcome people to do what they can, instead of demanding a 100% conversion to captain planet and perfect history of ecological life choices.
The more relevant question, especially in the context of startup success, is whether George W. Bush is wiser, more forward-thinking, or oriented toward better goals than you. Intelligence is only useful when you're directing it toward the right tasks and your end goals are genuinely beneficial.
what is a "better" goal. The whole point of the article is that things are not black or white - and what you consider right and beneficial may not be the same for someone else :)
In a president specifically, I imagine a "better" goal is one more aligned with the will of the people (even if not specifically in the long-term interest of the people.)
To all the 'justified in my bitterness' responses:
Yes, it's hard work being more knowledgeable, productive, smarter, better, than people around you. This is particularly a problem in software development since it takes an intense and often fleeting concentration to be really productive. Interruptions, especially those stemming from the ignorance or poor choices of others, provoke an immediate frustration and bitterness which seems (and probably is) justified.
Being justified, however, doesn't mean it's helpful. When I'm faced with these situations I often find myself analyzing in my head all the reasons that I shouldn't have to deal with this, why the person who brought it up is an idiot, how much better it would be if I could just be left to get things done. None of this thinking is productive, or even gratifying, except in the shallowest sense.
As hard as it is, the appropriate response to ignorance, idiocy, or other negative stimuli is NOT to be negative, but instead focus on positive solutions. Change the system where you can (as close to the source as possible) but don't compound wasted time by spending your energy being bitter about it.
With their announcement speech so full of contradictions, it seems like they're struggling to differentiate the Mini from the cheaper Nexus 7. The major appeal is its small size, but in comparison to the Nexus 7 they emphasize how much larger it is (albeit lower total resolution). Seems to be a clear case of presenting weaknesses as strengths, which will, unfortunately, probably succeed with many existing Apple customers. The two compelling advantages over the Nexus 7, the presence of a second camera and the availability of cellular capability, were barely mentioned.
I thought this was weird, too. The reason I bought a Nexus 7 was because of the 7in screen. Saying "It's a smaller iPad, but bigger!" just wasn't doing it for me. Maybe it was an attempt to sell people on the higher price tag.
