Why is the physical world so amenable to mathematical description?

[Heuristic]

Why can we describe the physical world so well in mathematical terms? Is there simply a coincidental similarity between the properties of items of analysis in the physical world and in the mathematical world? Is it the design of God? Evidence of the human mind imposing its own order on experience?

 

[L2R]

our maths evolved in this physical world and is therefore tailored to it. our units of measurement are essentially arbitrary, had the physical world been different somehow, units and maths would have evolved differently.

 

[Raw Evil]

Mathematics is a system we developed through inference by observing phenomena in the outside world, thus this is what it reflects. If one were to instead analyse the rules of a game, they would derive a different system of rules, but these would describe the game world as accurately as the person performing the analysis was capable.

 

[ebola?]

Our engagement of the world (a way in which the universe folds in on itself, partially perceiving and acting upon itself in time in the way we do) implies the project of mathematized concepts produced in this interaction. What is description other than rendering parts of the amorphous whole into comparable, discrete, static units amenable to quantification? This process is the order arising of chaos, to return to the latter at some point.

While we know not the universe 'as such' (for we encounter nothing of the sort), it's not just cognitive imposition going on here; the act of creation is at once an act of discovery, two sides of the same coin. This could account for why the universe 'for us' is amenable to mathematization. We 'discover' the creations wrought of the conditions of possibility for our investigation, in our case mathematized.

Now what of the universe 'as such'? Serving as the preconditions of possibility for mathematized description, this universe cannot itself be captured entirely therein. However, the property of the engaged universe as mathemized and the question as to why the universe is so will arise solely to the degree that this universe has investigated itself to the point of establishing mathematized constructs (anthropic principle).

well, not eloquent enough for now...will revisit.
Still...I feel as if the description's not quite there...bitta repetition already too...

ebola

 

[Heresy]

Supposedly modern science was an idea that came to Renee Descartes in a dream when an angel told him "The conquest of nature is achieved through measurement and number"

 

[Draigan]

All of the world is math. Everything in the obersevable world fits into properties that we analyze and process into units. We simply invented a system for measuring life. I dunno what your talking about with this god or humans imposing on our own experience.

 

[nautilus]

Perhaps the creator saw symmetry, exactness, and repetition as characteristics of beauty. Since we are made in his image, we share the same belief and seek to measure such things.

 

[L2R]

This process is the poisoned devil pride apple knowledge ego arising of God, to return to the latter at some point.

ficksed

 

[chitowndown]

i got a D in math

 

[aanallein]

units are not math and I don't believe that's what Heuristic is talking about.

I think with Heuristic is asking is why does the universe fit so well with our system of mathematics when mathematics could be created independent of physical form?

The way math works so eloquently and simultaneously reflects so many aspects of the physical universe while at the same time being completely abstract in and of itself is remarkable.


I think the best explanation is that mathematics are the pure essence of logic. There are axioms of algebra and higher level rules that exist in the mathematical world and they shape the way math functions. The universe is similar to this. Whether there is a god or no god or whatever is irrelevant because what maters is that for the universe to exist, it must follow certain principals and rules. It cannot be random/chaotic but rather very structured. Since both systems are based on logic and concrete rules they seem to pair with each other perfectly. Their origin is pretty much a philosophical debate (did man or god create math or did it need creating at all?).

 

[RedLeader]

[...]for the universe to exist, it must follow certain principals and rules. It cannot be random/chaotic but rather very structured.

Prima facie, this seems blatantly false. Can you give any support for this statement?

Heuristic, I'm just curious - do you think that God is a BLer? Because that's the only way that this question is ever going to get properly answered.

In all seriousness, philosophers (and mathematicians to some degree, although they tend to avoid this type of discussion) have debated this issue for over 2,000 years, and they've gotten absolutely nowhere. This is the kind of philosophical question that simply isn't very amenable to rational discussion, for several reasons. Chief among them is simply that a person's answer to the question is going to be very heavily, if not completely, dependent upon his prior philosophical worldview. As nautilus suggests, the idea of a Creator both fashioning the physical universe by number and imparting upon the human mind that same frame of mathematical understanding is, all things considered, probably the most elegant solution to the problem. And yet, this answer obviously depends on not only a theistic, but a broadly Biblical worldview (the idea of man being created in God's image). Similarly, the suggestion that mathematics is a filter through which the human mind orders the noumenal realm (which in itself is unknowable) is an elegant solution as well, but it already depends on a Kantian metaphysics. And, unfortunately, no amount of specialized mathematical knowledge can help us with regard to this problem. A person with a PhD in mathematics won't be able to lend any more insight here than a person who barely got through high school math. It cannot really be "unlocked from the inside," so-to-speak.

 

[Pythagoras]

Mysterium tremendum et facinans!

I think the question is more than 2000 years old, hence the screen name. Redleader is right though that this is a tawdry question of metamathematics and philosophy of mathematics. Where people like Cantor, Godel and Russell have trod, and come up short, I dare not tread. Given that we are still devoid of a convincing explanation for basic mathematics, for instance - What IS the number 3? And have done little better with higher-order mathematics.

I personally hold to Platonic maths (plenitudinous Platonism to be precise), where number and arithmetic are Forms, that have objective, abstract reality. It seems that thought on the matter has come full circle and rests on a fundamental ontological understanding of What exists? The pre-Socratics essentially offered the two extremes - All is Flux, and all is unchanging - one allowing for number abstracted from discrete 'objects', the other offering an answer to the continuum problem, and fixing problems of infinity.

I think in the final analysis (if such a thing is possible) that mathematics is a phenomenalistic 'explanation' of our encounter with the noumena. Higher mathematics is perhaps purely phenomenalistic, which might explain why is is non-computational. All that said I still hang to the Pythagorean/Platonic solids as having abstract reality, even if that reality is reality-as-such - with Mathematics offering an explanatory-predictive system of our phenomenalistic experience.

What I do know is that if a Blue-lighter could answer this mysterium tremendum et facinans they would probably scoop a Nobel Prize.

 

[ebola?]

There ain't no Nobel prize for ontology, epistemology, etc.

the idea of a Creator both fashioning the physical universe by number and imparting upon the human mind that same frame of mathematical understanding is, all things considered, probably the most elegant solution to the problem.

Well...elegant in terms of requiring the introduction of a single assumption. . .but inelegant (lacking parsimony) in terms of this assumption's reach...(likely all obvious).

Similarly, the suggestion that mathematics is a filter through which the human mind orders the noumenal realm (which in itself is unknowable) is an elegant solution as well, but it already depends on a Kantian metaphysics.

I dunno. There are similar solutions, many playing with the phenomenal-noumenal relation, that assume metaphysics other than Kunt's.

ebola

 

[Pythagoras]

Shape not number?

There ain't no Nobel prize for ontology, epistemology, etc.


ebola

I was thinking Mathematics, anone who can resolve set theory with peono arithmetic might stand a chance. I agree that the solution lies somewhere in the relation of the nouminal and phenomenal, somehow squared ('scuse pun) with a Platonic theory of number is where the solution lies.

I also think that geometry, not number, is what the forms are. Science often tells us that mathematics is the universal language of the universe but unless aliens know the Greek alphabet and indo-European numerals I doubt it...I think a dodecahedron would make more sense to them.

this

rather than this

 

[aanallein]

Prima facie, this seems blatantly false. Can you give any support for this statement?

how so? the universe is incredibly structured. from the way chemicals and molecules work to the speed of light and sound.. the universe is not a series of chaotic and unpredictable forces but behaves in very predictable ways.

 

[L2R]

^a matter of perspective, perhaps. one can observe just as much chaos in nature as order depending on where you look. meybe even moreso, but it's hard to compare the fuzzy with the definite.

 

[yougene]

I think it's a sign of a universe that shows self-similarity/structural isomoprhisms across every level of complexity.

The mapping of math onto the world works the same reason metaphor works.
The types of relationships, objects take on with one another are the same from one ontology to the next. For example, I can tell you that a computer is organized like a nested Russian doll, or I can tell you that a computer can be seen as a partially ordered set of circuits. You can get a good description of any 2 of these via isomorphisms of the 3rd one.



The question could be reworded as "why do all phenomena map so well onto the ontological schema of wholes, parts, and relations?"

 

[L2R]

The question could be similarly reworded as "why do all phenomena map so well onto the ontological schema of wholes, parts, and relations between
parts?"

maybe i'm missing something here, but i really have difficulty fathoming how phenomena can not do this.

 

[yougene]

No, that's the point. The schema is the universal construct through which we all grasp the world. Mathematics is a distillation of this schema to the lowest common denominator.

The phenomena don't actually do those things. Our consciousness projects those schemas onto phenomena. I think The structure of the schema is isomorphic to the structure of the phenomena if it can be said to have such a thing.

 

[L2R]

so, isn't that more indicative of us than the universe? i mean, had we evolved differently to have a slightly different form of maths and logic then we'd be observing a slightly different way. the same stuff but in a different language (so to speak).

i think it's a bit egocentric to assume that we, by chance, have a stumbled onto a definitive grasp and comprehension of things. what we have is extremely useful and relatively objective, but i'd hardly consider it truely objective.

consider language for instance. in a time and/or place where migration between borders and language did not take much place, an inhabitant with no exposure to another tongue may be forgiven to believe that theirs is the definitive one, but as we know that would be incorrect. the same could be said of cultures and traditions. the same in terms of religion and belief causes a great deal of conflict. how is that any different to our earth-centric mode of maths and logic?


edit: nb. "earth-centric" meaning perspective from our capable yet limited sensory limits and within our common "dimensional" place (if there are any others) .