“Why should the thirst for knowledge be aroused, only to be disappointed and punished? My volition shrinks from the painful task of recalling my humiliation; yet, like a second Prometheus, I will endure this and worse, if by any means I may arouse in the interiors of Plane and Solid Humanity a spirit of rebellion against the Conceit which would limit our Dimensions to Two or Three or any number short of Infinity.” -Edwin A. Abbott, "Flatland: A Romance of Many Dimensions" (1884)

Some of you may have ended up here by random chance, but most of you may be here just out of curiosity on what we’re all about. For that maybe you can go to our “ABOUT US” page, as there’s no point in having redundant discussions.

But this initial post is here to address a question that most people have asked us the moment they’re on this site: what’s up with your logo?

And as per our tradition of avoiding redundancies, this article will explain our logo and the philosophy behind it. But just to be extremely clear, no, it’s not a doughnut.

But this initial post is here to address a question that most people have asked us the moment they’re on this site: what’s up with your logo?

And as per our tradition of avoiding redundancies, this article will explain our logo and the philosophy behind it. But just to be extremely clear, no, it’s not a doughnut.

The logo is a stylized tesseract, that is, a fourth dimensional analog of a cube. We have chosen the tesseract as it symbolizes quantifiable truth even for the unobservable. For a tesseract, even if it is difficult (impossible?) for us to imagine, project, illustrate and shape it, it can be mathematically proven. And there is nothing more certain in this world than maths.

How do we know this? If you want to build a tesseract, first you have to start the zeroth spatial dimension, that is, the point. The point have no length, height or width, it simply is and of itself – the alpha and the omega, the first and the last, the beginning and the end.

Who says mathematicians aren’t philosophers?

To get to a one-dimensional object, double the number of that point and attach the two with a line – in geometry this is called a ‘line segment’. It has length, but neither width nor height. While extending it in the same way (doubling the number of points) would then result in a two-dimensional object – a square.

But a square is not just a square, it depends on what sort of geometry we’re dealing with – whether it’s the one we’re used to in day-to-day life, or the one that is best left unknown (until we cover it, that is). For the sake of your sanity, we’re just going to use the plain version.

Extend the square again by doubling the number of points and voila, a three-dimensional cube. This is by far the most familiar object to us as we can shape it in the real world, but what would happen if we were to extend this most plain of objects further?

We’re familiar with the three-dimensional concepts of length, height and width; a fourth spatial dimension adds another, inconceivable factor. How then would we justify IFSA’s logo? Easy, we just repeat the same method we used to attain higher spatial dimensions, doubling the point and linking them…which results in the abomination below.

How do we know this? If you want to build a tesseract, first you have to start the zeroth spatial dimension, that is, the point. The point have no length, height or width, it simply is and of itself – the alpha and the omega, the first and the last, the beginning and the end.

Who says mathematicians aren’t philosophers?

To get to a one-dimensional object, double the number of that point and attach the two with a line – in geometry this is called a ‘line segment’. It has length, but neither width nor height. While extending it in the same way (doubling the number of points) would then result in a two-dimensional object – a square.

But a square is not just a square, it depends on what sort of geometry we’re dealing with – whether it’s the one we’re used to in day-to-day life, or the one that is best left unknown (until we cover it, that is). For the sake of your sanity, we’re just going to use the plain version.

Extend the square again by doubling the number of points and voila, a three-dimensional cube. This is by far the most familiar object to us as we can shape it in the real world, but what would happen if we were to extend this most plain of objects further?

We’re familiar with the three-dimensional concepts of length, height and width; a fourth spatial dimension adds another, inconceivable factor. How then would we justify IFSA’s logo? Easy, we just repeat the same method we used to attain higher spatial dimensions, doubling the point and linking them…which results in the abomination below.

But wait, isn’t that just a cube in the first picture? The second picture is even further from a cube. But the last one seems familiar, no? Where have we seen that before?

All three images are of a single four-dimensional tesseract, which is seen from different ‘angles’ (we should use this term cautiously), and by the fact that we could never project it fully whether in 2D (a computer screen or drawings) or 3D (objects we can hold) forms.

The same way drawing a cube on a piece of paper doesn’t fully represent a real cube; the human mind cannot fully grasp the form of a four-dimensional object. Not yet at least.

In addition to that there is another reason why it’s difficult for us to perceive higher dimensions, although we live in a three dimensional world, our binocular eyes are viewing it in two dimensions. If you cover your left eye, your ability to perceive depth is greatly reduced. Having two eyes set slightly apart from each other gives our brain enough information to cheat the system – by comparing the differing inputs and estimating depth from two independent sources of information.

The limitations of our eyes are due to its structure. The image formed at the back of our retina is perceived in two dimensions due to the layout of our photoreceptor cells – flat and along the inner surface of our retina. If we can somehow enhance our vision, by engineering artificial eyes which can sense the breadth, height and depth of the light that goes into it, now that’s a true 3D eye.

This hypothetical 3D eye may then have the advantage of perceiving a higher dimensional structure of, for instance, a tesseract. Want to get an idea of how that might look like? Try traversing through a 4D maze.

All this may seem confusing, and we did pass through both the fields of philosophy, mathematics and biology, but this being the inaugural post, serves to give you a taste of what’s to be expected from IFSA.

All three images are of a single four-dimensional tesseract, which is seen from different ‘angles’ (we should use this term cautiously), and by the fact that we could never project it fully whether in 2D (a computer screen or drawings) or 3D (objects we can hold) forms.

The same way drawing a cube on a piece of paper doesn’t fully represent a real cube; the human mind cannot fully grasp the form of a four-dimensional object. Not yet at least.

In addition to that there is another reason why it’s difficult for us to perceive higher dimensions, although we live in a three dimensional world, our binocular eyes are viewing it in two dimensions. If you cover your left eye, your ability to perceive depth is greatly reduced. Having two eyes set slightly apart from each other gives our brain enough information to cheat the system – by comparing the differing inputs and estimating depth from two independent sources of information.

The limitations of our eyes are due to its structure. The image formed at the back of our retina is perceived in two dimensions due to the layout of our photoreceptor cells – flat and along the inner surface of our retina. If we can somehow enhance our vision, by engineering artificial eyes which can sense the breadth, height and depth of the light that goes into it, now that’s a true 3D eye.

This hypothetical 3D eye may then have the advantage of perceiving a higher dimensional structure of, for instance, a tesseract. Want to get an idea of how that might look like? Try traversing through a 4D maze.

All this may seem confusing, and we did pass through both the fields of philosophy, mathematics and biology, but this being the inaugural post, serves to give you a taste of what’s to be expected from IFSA.

###### Ponder this

How would a fifth-dimensional analogue of a tesseract look like?

How would a fifth-dimensional analogue of a tesseract look like?

###### Discuss

Assuming there’s a higher fourth-dimensional being, how would it perceive us and our world? And how would it perceive the fifth dimension? How would one come about designing a 3D eye? How are we to accommodate sensing the depth of an image formed in our eyes? How would the world look like through a hypothetical pair of binocular 3D eyes?

###### Further readings

Edwin A. Abbott (1884), Flatland, A Romance of Many Dimensions.

Michio Kaku (1994), Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension, Oxford University Press.

Thomas F. Banchoff (1990), From Flatland to Hypergraphics: Interacting with Higher Dimensions.