Philosophy
Plato's myth of the cave is an allegory that tries to make the point that there may be more to reality than meets the eye, that our experience is simply of a very limited and lowly aspect of reality. Given the knowledge and technology of the time, Plato's use of puppets and shadows in his ancient writing is brilliant in conveying the difference between the real and the apparent, but in the 1800's, Edwin Abbott took this idea much further, and in a way more rigorously and convincingly, as he was able to tell it through a creative exploration of mathematical space:
Compare the experience of a creature from three-dimensional space against one from a two-dimensional world. Easy, and completely reasonable to understand why the two-dimensional figure was skeptical of "more" dimensions, even if it was wrong, right? Well, apply the same reasoning to the difference between four-dimensional space and the three-dimensional space we're all used to. Wouldn't the reasoning you applied in the first case also apply to this one? And just like that time we were introduced to these ideas by the irreplaceable Carl Sagan, when he tried to show us the projection of a tesseract, here's a fun little animation to inspire your imagination and help you explore the beauty of mathematical space that can be understood by the mind even if it cannot be always perceived by the senses :)
Now, are there 'really' more dimensions than the three spatial ones we're used to or is this just a fancy mathematical abstraction? That's a topic for another discussion :p
- The Realization Of The Galaxy
Nick LaClair Book Seven of The Republic of Plato clearly illustrates the classic metaphor of someone being blinded from reality, and then revealed to a unfamiliar new world. We see this as the subjects have lived in the cave their entire life, completely...
- The Allegory Of Truman
The Allegory of the Cave Travis Larkin Book VII outlines the most famous metaphor in the novel and philosophical writings in our human history. The allegory of the cave is this metaphor, it tells of a dark scene in which a group of people has been living...
- (a) Explain Plato?s Analogy Of The Cave (25 Marks)
Again this has been written in a time limit. I allow 30 mins for part (a). In Republic book VII Plato explains his analogy of the cave (an analogy is a simple story that has metaphorical meaning). Plato uses the analogy to help describe his philosophical...
- Horizon - What Is Reality?
Ancient Greek philosophers like Parmenides, Zeno and Plato stumbled upon a radical discovery: the distinction between appearance and reality. If we are to ask the question of what reality is (and how we can know this), our best bet at finding some sort...
- Deceased--john R. Stallings Jr.
John R. Stallings Jr. 1935 to November 24th, 2008 "John R. Stallings Jr., 73, California Mathematician, Is Dead" by Kenneth Chang January 19th, 2009 The New York Times John R. Stallings Jr., who found a proof for part of the Poincaré Conjecture, one...
Philosophy
Flatland - Exploring Other Dimensions
Compare the experience of a creature from three-dimensional space against one from a two-dimensional world. Easy, and completely reasonable to understand why the two-dimensional figure was skeptical of "more" dimensions, even if it was wrong, right? Well, apply the same reasoning to the difference between four-dimensional space and the three-dimensional space we're all used to. Wouldn't the reasoning you applied in the first case also apply to this one? And just like that time we were introduced to these ideas by the irreplaceable Carl Sagan, when he tried to show us the projection of a tesseract, here's a fun little animation to inspire your imagination and help you explore the beauty of mathematical space that can be understood by the mind even if it cannot be always perceived by the senses :)
Now, are there 'really' more dimensions than the three spatial ones we're used to or is this just a fancy mathematical abstraction? That's a topic for another discussion :p
- The Realization Of The Galaxy
Nick LaClair Book Seven of The Republic of Plato clearly illustrates the classic metaphor of someone being blinded from reality, and then revealed to a unfamiliar new world. We see this as the subjects have lived in the cave their entire life, completely...
- The Allegory Of Truman
The Allegory of the Cave Travis Larkin Book VII outlines the most famous metaphor in the novel and philosophical writings in our human history. The allegory of the cave is this metaphor, it tells of a dark scene in which a group of people has been living...
- (a) Explain Plato?s Analogy Of The Cave (25 Marks)
Again this has been written in a time limit. I allow 30 mins for part (a). In Republic book VII Plato explains his analogy of the cave (an analogy is a simple story that has metaphorical meaning). Plato uses the analogy to help describe his philosophical...
- Horizon - What Is Reality?
Ancient Greek philosophers like Parmenides, Zeno and Plato stumbled upon a radical discovery: the distinction between appearance and reality. If we are to ask the question of what reality is (and how we can know this), our best bet at finding some sort...
- Deceased--john R. Stallings Jr.
John R. Stallings Jr. 1935 to November 24th, 2008 "John R. Stallings Jr., 73, California Mathematician, Is Dead" by Kenneth Chang January 19th, 2009 The New York Times John R. Stallings Jr., who found a proof for part of the Poincaré Conjecture, one...