Jake: Math prodigy proud of his autism
Tuesday, December 31, 2013
Saturday, December 28, 2013
On zero and infinity
Yesterday, while looking for examples of Strange Attractors on YouTube I came across a video of a high school student discussing the fourth spacial dimension. He made a reference in passing to a theory that dimensional space may be circular. Its an old theory, and it seems to tag along with the theory of 4th and n-dimensional space. I don't particularly go along with this school of thought (circular space) so I'm posting a link instead to someone I think you'll really like - a 4th-dimensional space advocate who is cute as cupcake as well... (and its not Rocky or Bullwinkle, but 13yo Jacob Barnett...)
n-Dimensional space may well be one way of modelling something that exhibits unusual properties, but to understand the model of the physical universe we must necessarily first embrace the idea of the infinite physical spacial dimension. Curved space is necessarily finite, and is offered as an alternative to an infinite spacial dimension. To me curved space theorists don't accept the infinite spacial universe. However while I accept circular dimensional space as interesting in itself, I don't accept the idea of our spacial universe being finite.
The Horizon video below covers several contemporary views of Infinity. Infinite (ie linear) space seems to be something most people struggle with, however, the idea of infinite space is really quite easy to grasp when considered in the context of a finite physical universe contained within an infinite void. Whether or not this is actually the case for our physical universe is not of concern here, as it is simply the concept of infinite space we want to grasp. This is analogous to the way Cantor conceptualised infinity - by containing it in an abstract form.
So by defining the void that contains our physical universe as completely and utterly empty of everything, including light, we not only define the boundary of the ever expanding physical universe, but can now conceptualize in a very simple way how the physical space beyond the boundary of the defined physical universe can indeed be infinite, because there is absolutely nothing there. Because there is nothing beyond the defined limit of the physical universe, there is no purpose in persisting with notions of what exists beyond. We already know. Nothing exists, and it has no limit. It can be defined as the boundary of all physical existence, or the limit of the finite universe and the start of the infinite universe. Zero, then, can help us understand infinity.
The Horizon video below covers several contemporary views of Infinity. Infinite (ie linear) space seems to be something most people struggle with, however, the idea of infinite space is really quite easy to grasp when considered in the context of a finite physical universe contained within an infinite void. Whether or not this is actually the case for our physical universe is not of concern here, as it is simply the concept of infinite space we want to grasp. This is analogous to the way Cantor conceptualised infinity - by containing it in an abstract form.
So by defining the void that contains our physical universe as completely and utterly empty of everything, including light, we not only define the boundary of the ever expanding physical universe, but can now conceptualize in a very simple way how the physical space beyond the boundary of the defined physical universe can indeed be infinite, because there is absolutely nothing there. Because there is nothing beyond the defined limit of the physical universe, there is no purpose in persisting with notions of what exists beyond. We already know. Nothing exists, and it has no limit. It can be defined as the boundary of all physical existence, or the limit of the finite universe and the start of the infinite universe. Zero, then, can help us understand infinity.
Thus there is nothing to prevent our mind from embracing the certainty that a void, at least, can indeed be infinite, in a tangible and physical way. With this firmly established, it becomes easier to entertain how infinity can present itself in our daily existence without involving circular special dimensions, even if they can be constructed in the scientific model.
n-dimensional space is not new to IT. Multi-dimensional cubes are an important analytical tool. These dimensions are not spacial, but they can be and there can be many more than 4. Robotics for instance makes use of sets of connected spacial dimensions that while persisting in the same 3-D physical world, nevertheless give rise to situations where interactions could be considered in a n-Dimensional spacial map. Fractal math also introduces the idea of partial dimensions - another interesting possibility. However these views of the physical world tend to complicate our understanding, and are really only useful in solving specific problems, such as modelling how two objects might interact as they collide.
But all this is pretty meaningless if you cant handle the relatively simple idea of an infinite universe.
n-dimensional space is not new to IT. Multi-dimensional cubes are an important analytical tool. These dimensions are not spacial, but they can be and there can be many more than 4. Robotics for instance makes use of sets of connected spacial dimensions that while persisting in the same 3-D physical world, nevertheless give rise to situations where interactions could be considered in a n-Dimensional spacial map. Fractal math also introduces the idea of partial dimensions - another interesting possibility. However these views of the physical world tend to complicate our understanding, and are really only useful in solving specific problems, such as modelling how two objects might interact as they collide.
But all this is pretty meaningless if you cant handle the relatively simple idea of an infinite universe.
Monday, December 16, 2013
Subscribe to:
Posts (Atom)