On 25 Mar 2013, at 12:10, Alberto G. Corona wrote:

I mean:
ultimately the aestetic pleasure of Math derives from the natural impulse to search for efficient algoritms useful for deduction

Hmm.... The algorithmic is something both old and new, but it constitutes a little part of math. Theoretical computer science already shows that machines behavior is far beyond the algorithmic. it is easy to find a solution of a diophantine equation (when you have the time), but it can be a matter of extreme complexity to show that there are no solutions, and this can need quite amazing mathematical discoveries.

Mathematics is the study of the mathematical reality.

With comp, you are free to describe the entire mathematical reality as arithmetic, with all the rest belonging to the number's mindscape. It is real and lawful too, and with comp, it can be shown bigger than any formalizable part of the mathematical reality.

With comp it is absolutely undecidable if reality is bigger than arithmetic. Arithmetic, seen from inside, that is from the numbers perspective, is already beyond mathematics.

But not beyond theology. I would say this by definition of theology (you can see it as a theory of everything, from electron to the Mother of God, and Who know What, or don't know What ...).

Bruno







2013/3/25 Alberto G. Corona <agocor...@gmail.com>
I don´t know what Math is.

If math is all that is free from contradictions and can be expressed using the language of mathematics, then any description at any level can be math. For example the set of positions and speeds of the particles of a piece of dirt.

That description has nothing pure to stare at...

I suspect that there must be more in the description to be intuitively called mathematic: short descriptions with general properties applicable to a wide set of different phenomena, whether the descriptions are in some mathematical formalism or not. I think that the concept of math can be subsumed in this last, slightly wider, definition.

That definition is directly related with kolmogorov complexity and Solomonof inductive inference. ultimately the aestetic pleasure of Math derives from the natural impulse to search for efficient algoritms useful for induction, something that a living being do all the time at some basic levels with prefixed algorithms, and humans do at the rational level with their models.

I suspect that the pleasure that these short descriptions widely applicable inspire in the one that aprehend them derives directly from their value as tools to find regularities in the world so that it becomes more predictable.




2013/3/24 Craig Weinberg <whatsons...@gmail.com>
“The things that fascinate me the most about mathematics are logical thought and the great importance attached to the correctness of propositions. Every step made during calculations is conclusive and mathematicians don’t like to make false statements. This is the reason why people from this particular domain contemplate longer before they respond to questions. Recently I read a sentence in a book which summarizes all this fascinating stuff to me succinctly: ‘Mathematics is the purest form of thought.’”
—       
Barbara Meier (via dauphinexvx)

This is an interesting observation, and I don’t disagree that mathematics is the purest form of thought, but what is thought? While we are at it, what is a form?

In the first case, I have proposed that thought is meta-feeling. It is a kind of trick within the interplay of intention and feeling to establish a generalized neutral feeling which can be used like a variable in algebra. A feeling like “I am angry and sad because a tiger ate my kids, but relieved that it was only a dream” can sort of look at itself from a distance and strike all kinds of other thought-like sparks. We can feel fear that dream was a premonition. We can feel motivated to hunt tigers. These need not be thoughts, but emotive dispositions. They don’t entail any awareness about our state or our actions, only a desire for this or that response to a felt condition.

The feeling need not be connected to a real event or a particular event, but as we go up the ladder of meta-abstraction, the absence of immersive personal feeling is replaced by formality and clarity. It is an echo of decoherence, as the living wave of direct feeling ‘collapses’ into a thermodynamically unambiguous state, the flow of participation is deferred into analytical hindsight and strategic foresight.

On some level, it as if we are picking up the stylus from the universal record and holding onto it while we deliberate our options. Thought is born, in my view, as this kind of deferred meta entanglement…a feeling that is whipped up into a frothy foam where it can be used to the sculpt air - turning absence into a virtual presence through surface tension alone. The thought bubble is hypothesis, and the ultimate thought bubble is Mathematics because it seeks only to distill itself into its own purest form. It is, however, still a form. There is still a thinker thinking the thoughts, and the thoughts are still feelings of a living person, but these facts are hidden from view within the mathematical context. The pretense is toward a universal objectivity.

Indeed, it is not incorrect to say that ‘mathematics is the language of the universe’, iff you define the universe to begin with as those forms which can be publicly observed. In my view then, it is really tautological to say that mathematics is the purest form of thought, since mathematics is only the thought of purest forms. What then, are forms?

There are many ways to approach such a general term as form, but I prefer the underlying sense which is shared with formality. A presented shape, yes, but more like the logical essence of a presented shape. It is a presentation of coherent qualities; stability and regularity, reducibility to simpler, universal sub- forms, etc. Mathematics explores this aspect of the universe while eschewing and denying all phenomena which seems exempt from form. All things spontaneous and erratic, non-reducible and proprietary are treated poorly. Emotions, free will, and the “I” to whom they belong are not merely pushed to the back of the bus, but they are pushed out the back door of the bus, to be paved over by the steam roller in hot pursuit.

I sympathize with people who are unable to conceive of a concretely real phenomenon which generates form intentionally rather than is defined by it, but it is harder to be sympathetic when this disability is compounded by the unwillingness to allow that it can be conceived. In my thousands of hours arguing with STEM-minded people online I have found an overwhelming bias against certain kinds of ideas and laughable acceptance of others. Ridiculously grand abstractions like MWI, or replacing every atom in a human brain roll off of the tongue easily, while ordinary terms like free will are brought under Torquemadan hyper-scrutiny. The double standard is tremendous, yet invisible to those who subscribe to it. Physics can be as counter-intuitive and unexplainable as it wants to be, but if you bring up intuition itself, then be prepared to hear a lot of ‘simply’ this and ‘merely’ that.

The good news though, is that through mathematical principles like symmetry, we can move beyond these blind alleys. By applying all of what we know about the public world, its forms and formulations in reverse we can find where the private world of physics begins - not with numbers, but with names; not with abstract thoughts but with sensory experience. To be a living participant in a meaningful universe is to eventually put the stylus down somewhere and let the music play.



The second post is shorter but it has pictures, so probably better to just link it: http://s33light.org/post/46154550763 It's about Tupper's Self-Referential Formula


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http://iridia.ulb.ac.be/~marchal/



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