Building a hybrid and dynamic mathematical space

Your Name]In summary, the conversation discusses the concept of a "dynamic abstract space" that can be built from combining different mathematical spaces and can grow and reconfigure itself to accommodate new particles. The idea has potential applications in fields such as architecture and could potentially be used to explain programmable objects and their variables. It is also mentioned that computer simulations often use mathematical spaces to represent the virtual world.
  • #1
Alvaro.Castro.Castilla@gmail.com
building a "hybrid" and dynamic mathematical space

Hello,

Maybe I'm going to say very stupid or crazy thing for real
mathematicians (I'm an architect):

I want to build a concept that I call "dynamic abstract space" ("das"
from now) for a digital architecture project. I would like to be able
to say the idea I have in mind with mathematics.

This is the essence of the idea:
1) I have a n-dimensional space (the "das") which is built from gluing
together ANY number of ANY type of spaces:
A boolea algebra, a Minkowski space, a ring, R=B3, N, C...

2) Then I introduce particles in my space which are m-dimensional
spaces. If the particles are cointained in the space, then there is no
dynamic reconfiguration of the space, but if the particles are not
contained, the space grows until is able to contain them (for example
in a R=B2 space if we want to insert a R=B3 particle, we have to expand
the space up to R=B3, in a very simple situation). That is the reason I
call it "dynamic".

How to mathematically define that space and that particles?
What do you think of explaining programmable objects and their
variables through this "spaces" and "particles"?

-----

The second thing I would ask is:
Is it correct to say that inside a computer simulation we are inside a
mathematical space of, for example:
R=B3 * R+
for a 3-d space running in a continuous time, or:
R=B3 * N
for a 3-d space running in a step by step basis.
?

THANKS for all your help!

:-)
 
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  • #2


Hello,

Thank you for sharing your interesting idea with us. I am always fascinated by the intersection of different fields and the potential for new and innovative ideas.

From what I understand, you are proposing a "dynamic abstract space" that can be built by combining different mathematical spaces together. This space would also have the ability to grow and reconfigure itself to accommodate new particles (which are also mathematical spaces). This is a very intriguing concept and could have potential applications in many fields, including architecture.

To mathematically define this space, we would first need to determine the properties and rules that govern its behavior. This could involve looking at the properties of the individual mathematical spaces that make up the "das" and how they interact with each other. It could also involve looking at the properties of the particles and how they affect the overall structure of the space.

As for programmable objects and their variables, I can see how they could be explained through this concept of "spaces" and "particles". The particles could represent the objects and their variables could be seen as the properties of those objects that affect the overall structure of the space.

Regarding your second question, it is correct to say that computer simulations often use mathematical spaces to represent the virtual world. These spaces can be continuous or discrete, depending on the nature of the simulation. So, in a way, we are indeed inside a mathematical space when we are in a computer simulation.

I hope this helps in developing your idea further. Good luck with your project!

 
  • #3


Hello,

Thank you for sharing your ideas about building a "hybrid" and dynamic mathematical space. It's always exciting to see people from different fields exploring the applications of mathematics.

Your concept of a "dynamic abstract space" is certainly intriguing. It seems like you are trying to create a space that can adapt and change based on the particles that are introduced into it. In mathematics, there are various concepts and theories that deal with dynamic or evolving spaces, such as topology and differential geometry. These may provide some useful tools and ideas for defining and studying your space.

As for the particles, it seems like you want to consider them as "building blocks" for your space. In mathematics, there are also theories that deal with objects or structures that can be combined to form more complex structures, such as group theory and category theory. These may also be useful in defining and understanding your particles.

Regarding programmable objects and variables, it's an interesting idea to think about them in terms of spaces and particles. In mathematics, there are also theories that deal with objects and their properties, such as set theory and logic. These may provide some insights into how to represent and manipulate programmable objects and variables in your space.

As for your question about computer simulations, it's not entirely correct to say that we are inside a mathematical space while running a simulation. A simulation is a mathematical model that represents a real-world system, but it is not the same as the real world itself. However, we can use mathematical concepts and tools to analyze and understand the behavior of the simulated system.

I hope this helps and gives you some ideas to explore further. Good luck with your project!
 

1. What is a hybrid and dynamic mathematical space?

A hybrid and dynamic mathematical space is a mathematical space that combines elements of both discrete and continuous mathematics. It allows for both discrete and continuous variables to exist within the same space, providing a more comprehensive and flexible framework for mathematical modeling and analysis.

2. What are the benefits of building a hybrid and dynamic mathematical space?

Building a hybrid and dynamic mathematical space allows for more accurate and realistic modeling of complex systems. It also allows for the integration of various types of data and variables, leading to more comprehensive analyses and insights. Additionally, it can help bridge the gap between different fields of mathematics and promote interdisciplinary collaborations.

3. How is a hybrid and dynamic mathematical space constructed?

A hybrid and dynamic mathematical space is constructed by combining concepts and techniques from both discrete and continuous mathematics. This can involve using hybrid models, such as hybrid automata, or incorporating hybrid elements into traditional mathematical models.

4. Can a hybrid and dynamic mathematical space be applied to real-world problems?

Yes, a hybrid and dynamic mathematical space can be applied to real-world problems in various fields, such as engineering, economics, biology, and social sciences. Its ability to model complex systems and incorporate different types of data makes it a valuable tool for solving real-world problems and making predictions.

5. Are there any challenges or limitations to building a hybrid and dynamic mathematical space?

One of the challenges of building a hybrid and dynamic mathematical space is the complexity of integrating different types of mathematics and data. It also requires a deep understanding of both discrete and continuous mathematics. Additionally, there may be limitations in terms of computational resources and the ability to accurately model highly complex systems.

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