What is maths?

[Breakingthewall]

6 minutes ago, Lilia said:

@Breakingthewall Do you think alien minds would do maths differently? 

I don't just mean picking different symbols for shared concepts like addition etc., but perhaps highlighting aspects of reality that humans have no access to due to the way a human mind is configured. 

I do not think so. different symbols sure, but the math has to be the same, there are no other

[gettoefl]

42 minutes ago, Lilia said:

@gettoefl I love how joy found its way into this mixture.

it's the most beguiling mistress ever! you're with her for hours which feels like a minute, and you're like do i really need to sleep today? once she gets her fangs into you, you are putty for life 

[Breakingthewall]

Mathematics governs the functioning of the cosmos. The movement of matter, energy, the organization of atoms and molecules, galaxies, everything is mathematical. and it is incredible that the human brain can deduce all that mathematics in a theoretical way. the theory of relativity for example, without the need for direct experience

[LastThursday]

On 10/28/2023 at 8:07 PM, Lilia said:

Did you understand what maths was about (i.e. a language, a symbolic representation of transformation etc) when you were a kid? Back then, how did you explain to yourself what it was about?

I was pretty young when I became interested. I think at that time it was just a fascination with symbols in general. Playing with a calculator was more like a process of discovery and deciphering what it all meant. But there was an overlap with reading, as I had also recently learned to read (Spanish) too - so I had an unconscious inkling that it was just like another language.

It's only much more recently that the penny dropped about maths being mostly about describing transformations between different patterns.

[An young being]

18 hours ago, Breakingthewall said:

I do not think so. different symbols sure, but the math has to be the same, there are no other

Unless there is an alien with a different logical mind. Maybe they would be explaining gravity with light as a language, who knows!

[Lilia]

@Breakingthewall I hear what you're saying.

I feel like suggesting a flip though: wouldn't it be more precise to say that we're inventing maths when we're observing all those patterns, rather than discovering it? 

[LastThursday]

On 10/28/2023 at 7:22 PM, Lilia said:

So I wonder if there could be a pattern of changing state in that specific way that could be communicated mathematically, with minimum distortion.

I guess you would call Carton Wolf state C and normal human state N. Then you'd have an transformation function called H (for high) and apply it C=H(N). This sort of shenanigans is why the universe is not "made of maths". It only ever maps patterns, it's never the thing itself.

Edited October 30, 2023 by LastThursday

[Lilia]

 

3 hours ago, An young being said:

Unless there is an alien with a different logical mind. Maybe they would be explaining gravity with light as a language, who knows!

I read in one of Robert Monroe's books on astral travel how he got to communicate with 'subtle entities' using something like 'thought blobs' for a language. 

The idea was that an entity sends a mental 'bundle of ideas' to another entity that the latter then has to unpack. Such thought bubbles were rich with information, like what you have in a dream when you understand many things at once without having to go through them sequentially.

Wonder what maths would look like for aliens who communicate like that!

 

[Lilia]

2 minutes ago, LastThursday said:

I guess you would call Carton Wolf state C and normal human state N. Then you'd have an transformation function called H (for high) and apply it C=H(N). This sort of shenanigans is why the universe is not "made of maths". It only ever maps patterns, it's never the thing itself.

Somehow this is the sexiest paragraph I've read in years.

[LastThursday]

3 minutes ago, Lilia said:

Somehow this is the sexiest paragraph I've read in years.

I've never laughed so hard. I feel as though I ought to tell you that you should touch grass occasionally.

To put the cat amongst the pigeons: specifically here he talks about how numbers are not the thing itself.

 

[An young being]

21 minutes ago, Lilia said:

Wonder what maths would look like for aliens who communicate like that!

 

Definitely something weird. They would wonder why humans are taking so much effort to understand simple things using complicated stuff like maths. And our nerd scientists would wonder how they could imagine something as amazing as Maths as weird!

[Lilia]

@LastThursday Loved this cat. Thanks for sharing!

Recently I have been contemplating alternative coordinate systems that could be used to talk about reality. I love creating some and testing them for consistency (perhaps I should go out and touch grass more LOL).

I think it is possible to create many interpretation systems to describe the interplay between the same events. 

Parallel to mathematics, I think psychology is one of such arbitrary systems that we invented and forgot that we did, seeing it now as the way things are but not how we describe them.

 

[Breakingthewall]

4 hours ago, Lilia said:

feel like suggesting a flip though: wouldn't it be more precise to say that we're inventing maths when we're observing all those patterns, rather than discovering it?

We invented mathematical language, but mathematics is invariable. If there are 7 stones and we add another one, there are 8 stones. We could not name the number, but it will continue to exist, and if one of the stones disappears, there will be 7 again, even if no one names it.

Edited October 30, 2023 by Breakingthewall

[LastThursday]

2 hours ago, Lilia said:

I think it is possible to create many interpretation systems to describe the interplay between the same events. 

Philosophy in general seems to be this way. Each philosophy has its axioms or ground truths and you build everything up from there. Mathematics also has this. It's no coincidence I think, mathematics is a form of philosophy, albeit very abstracted away. Also science itself is a branch of philosophy (originally natural philosophy) and has a similar way of working from axioms (called laws there). I think psychology is sort of a hybrid between hard science and philosophy.

There have also been attempts at creating artificial languages that reduce ambiguity. Edward De Bono I think attempted this - see his The De Bono Code Book.

[Lilia]

22 hours ago, LastThursday said:

Edward De Bono I think attempted this - see his The De Bono Code Book.

Thanks for the recommendation. I'll check him out.

[Kuba Powiertowski]

Mathematics is a numerical and conceptual tool used to create maps of reality. Is very related to quantitative logic, although breakthrough discoveries in this field are strongly characterized by qualitative logic lying on the side of intuition. However, no map will reflect the quality of the terrain. The mountain on the map will not tell you about directly experiencing it - whether by looking at it or actively playing together - through skiing, hiking or climbing. I have the impression that it is a more precise tool than, for example, language, but it also operates in different areas. The most important thing for me is how beautifully it captures what we are - infinity. From anxiety to self-delight😉

[Lilia]

On 02/11/2023 at 2:30 PM, Kuba Powiertowski said:

 The most important thing for me is how beautifully it captures what we are - infinity. 

Can you elaborate on the exact ways in which mathematics captures this?

[Kuba Powiertowski]

@Lilia Works of Georg Cantor - Set Theory, Continuum Hypothesis; most of the works of Bernhard Riemann; work of Alan Turing - Turing Machine; works of Kurt Godel - Incompleteness Theorems; works of John Von Neumann. Briefly - several works by these outstanding mathematicians and logicians not only allowed us to learn about infinity from a mathematical (not only) perspective but, most importantly, pointed to the indelible limits of our knowledge. The topic is a river, but damn interesting.

[Breakingthewall]

Mathematics is a mysterious thing. Are they imaginary, or are they real? The human mind partitions reality mathematically. In a basic, innate way, it recognizes quantities. two is more than one. three is even more. From there it begins to structure reality down to the most complex algebra. But is it reality that is structured like this, or is it the mind that invents the structure? Incredibly, both things at the same time. The mind invents mathematics because it is within it. and the physical world is really governed by laws expressible by the mathematics that the mind creates. The orbit of a galaxy about itself is perfect mathematics. Reality is mathematical, and that is why the mind invents mathematics, because the mind it's the reality

Edited November 4, 2023 by Breakingthewall