Can we use the most powerful abstract entity known to Human Race for describing and solving problems with the assistance of computer?
Is abstract expressiveness important? What is number?
When is circle a circle?
Should we even ask those questions?
This book is introductory material.
Introduction to what?
How can above questions even have a common ground?
I see no other choice but to use descriptive language as much as I can, along with additional, hopefully searching questions. Maybe you are aware of the literary device that is sometimes used when writers need to illustrate unimaginable advance, powerful and wise alien race? Basically, they point out that their language, mathematics and poetry are one. That device is so old, that there is no mention of computers in it.
Well, that is us, now.
Admittedly, not all of us are familiarly comfortable with the archetypes of one cultural genre, so I'll try again. Imagine that all of areas of mental endeavor are actual “realms”. We can imagine maps of them, undoubtedly having an entertaining time while composing them, but that is not what I am aiming at. While we are imagining, let us imagine that they are “natural borders” between those “realms”.
As history teaches us, some were able to negotiate them. Therefore, metaphorically speaking, we just started to negotiate, we finally dared, a natural obstacle from which we can see all those realms.
What is that obstacle? A mountain, mountain chain? How many summits does it have? While we are at it, it simply is not true that we can “see” all those realms at the same time, we are not able to see 360 degrees around us, aren't we? This analogy also explains why are we currently more interested in these new vistas in front of us, then we are into gaining new views into already familiar surroundings. Where we are now, everything is new to us. Behind every bush can be a new path, above every tree is a fresh, new view into Universe above us.
How come we suddenly have Universal Languages? What happened?
Nothing happened. Sad truth is, we had them for quite a while, but we just didn't pay any attention to them.
We are very good at willful ignorance, aren't we?
Is abstract expressiveness important? What is number?
When is circle a circle?
Should we even ask those questions?
This book is introductory material.
Introduction to what?
How can above questions even have a common ground?
I see no other choice but to use descriptive language as much as I can, along with additional, hopefully searching questions. Maybe you are aware of the literary device that is sometimes used when writers need to illustrate unimaginable advance, powerful and wise alien race? Basically, they point out that their language, mathematics and poetry are one. That device is so old, that there is no mention of computers in it.
Well, that is us, now.
Admittedly, not all of us are familiarly comfortable with the archetypes of one cultural genre, so I'll try again. Imagine that all of areas of mental endeavor are actual “realms”. We can imagine maps of them, undoubtedly having an entertaining time while composing them, but that is not what I am aiming at. While we are imagining, let us imagine that they are “natural borders” between those “realms”.
As history teaches us, some were able to negotiate them. Therefore, metaphorically speaking, we just started to negotiate, we finally dared, a natural obstacle from which we can see all those realms.
What is that obstacle? A mountain, mountain chain? How many summits does it have? While we are at it, it simply is not true that we can “see” all those realms at the same time, we are not able to see 360 degrees around us, aren't we? This analogy also explains why are we currently more interested in these new vistas in front of us, then we are into gaining new views into already familiar surroundings. Where we are now, everything is new to us. Behind every bush can be a new path, above every tree is a fresh, new view into Universe above us.
How come we suddenly have Universal Languages? What happened?
Nothing happened. Sad truth is, we had them for quite a while, but we just didn't pay any attention to them.
We are very good at willful ignorance, aren't we?
