December 11th, 2010, 09:37 AM
Hi
I am writing an essay on how mathematics can be found in nature. my title is "is nature just another equation?"
I have found some interesting ways to prove the title, such as equations for flowers, the golden spiral relating to sea shells, movement in beehives and planetary motion.
However I need to disprove the title in order to have a "discussion" in my essay which is where I am stuck...I would appreciate it if anyone could give me ideas.
thanks
Suggest you examine randomness in nature, such as radioactivity, genetic mutation, etc.True randomness is essentially a natural process and cannot be explaned/described by a mathematical equation.
Thanks that is really helpful MigL
There is an area of mathematics that deals with "randomness". It is probability.
http://en.wikipedia.org/wiki/Probability_theory
http://mathworld.wolfram.com/Probability.html
Interesting topic.
I suspect (important word) that anything considered random is in fact not random if enough information is available about the event. The roll of a single die has equal probability assigned to any single outcome, one through six. However, I believe if we knew the initial position of the die being thrown and all of the relevant information about its throw, i.e., force apllied, axis of rotation, height above the table, etc., that the outcome could be predicted by classical mechanics and probability wouldn't apply.
There are lots of things considered random that, like the throw of a die, are considered random because we lack the appropriate information about the events themselves.
So, is nature just another equation? Well, the way the question is worded doesn't really do it justice, but yes, I suspect (there's that word again) it is. Nevertheless, it doesn't explain its existance (nature's) nor does it imply a deterministic system. The fact that we keep finding math and science at the bottom of our questions doesn't mean that's all there is to it.
Like I said, interesting topic.
That doesn't really work though since, for various reasons (Heisenberg, etc.), we can't know the initial conditions well enough.
Also, at the quantum level, it's been shown (Bell's Inequality) that no local hidden variable model can explain quantum uncertainty. This means that either things really are random, or there's some global hidden variables.
Perhaps mankind has not progressed far enough to understand these phenomena as well as we understand other things.Originally Posted by MagiMaster
No. We've progressed far enough to understand that there are some things that really are random and really are unknowable.
Here's Bell's theorem; http://en.wikipedia.org/wiki/Bell's_inequality
It would seem that we have a reductio ad absurdum of the stochastic nature of the quantum.
I also submit that, logically, the observed phenomena of choice precludes an absolute determinism.
Because the term "free will" might be construed to indicate an infinite number of degrees of freedom I have chosen to use the term "choice".
As obviously as nature is not absolutely deterministic neither is it absolutely random or chaotic. It(nature) is probabilistic within deterministic boundaries.
Considering that probabilities can be mathematically modeled, I submit that the whole of nature can be expressed through the use of equations and inequalities.
As Aristotle was confident that falling objects fall faster as they approach the earth because they become more jubilent as the approach their resting place?
I think we have a lot to learn, that's all.
Actually Aristotle thought that heavier objects fell faster than lighter objects. This was due to the failure to conduct experiments and use empirical observation. Modern science doesn't have this problem. We do have a lot to learn, but what we "know" we know for some pretty good reasons.As Aristotle was confident that falling objects fall faster as they approach the earth because they become more jubilent as the approach their resting place?
I think we have a lot to learn, that's all.
Aristotle may have believed as you said, but he also did indeed attribute faster falling to becoming more jubilant as they neared the earth.Actually Aristotle thought that heavier objects fell faster than lighter objects. This was due to the failure to conduct experiments and use empirical observation. Modern science doesn't have this problem. We do have a lot to learn, but what we "know" we know for some pretty good reasons.As Aristotle was confident that falling objects fall faster as they approach the earth because they become more jubilent as the approach their resting place?
I think we have a lot to learn, that's all.
The only point I'm making here is what history has taught us about 'truths' we have held (we as in mankind).
Regarding this forum topic, there are lots of equations about nature that we didn't have going back in time. I don't think we are finished adding to the list just yet. That's why I often smile when people talk about 'what they know' when they are really stating current popular knowledge that is often quite transient over time.
Look four "post's" up. I think we crossposted and you missed that one Ledger.
Rubbish.
This demonstrates a complete lack of understanding of the term "equation", and more profoundly the nature of science. This is the sort of statement commonly made by pseudo intellectuals who have no idea what they are talking about. Not a clue.
Mainstream scientific theories are accepted within a domain of validity, and only within a domain of validity on the basis of predictive power that is 100% consistent with a mountain of experimental and observational data.
Modern science progresses as a series of successive approximations with enlarging domains of validity. But established theories are refined, not overturned.
That smile is quite commonly found on the countenance of a fool.
I thought chaos theory provided a mathematical model for sensitive dependence on initial conditions, or is it just pie in the sky, or my misunderstanding it?
That depends on your definitions of refined and overturned. I have seen it persuasively argued that Newton was wrong. Period. Sure he had a nice approximation that seems to work just fine at low speeds, but basically he was wrong. W R O N G, wrong.
In geology and in biology I can give you a bunch of theories that have been overturned in the last century and a half. Not a refinery in sight.
I agree.
Sounds like a statement from a philosopher, and one pays attention to philosophers only at great risk.
There is no position so ridiculous that it has not been held by some philosopher. – Cicero
Newtonian mechanics and the subsequent refinement by Einstein's relativity is the poster child for progress by refinement. Look up "correspondence principle" and the importance of same to Einstein.
Newton's gravity and mechanics are used to calculate the orbits of all satellites, and they seem to follow the predicted orbits.
By that reasoning all physical theories are wrong. But physics, chemistry, and even engineering seem to be managing somehow.
If you found that argument persuasive, then you need to brush up on your reasoning.[/list]
True, but coupled with Heisenberg's uncertainty principal, which, in a round-about way, says we can't know the initial conditions to an arbitrary precision, it means that even purely deterministic systems can be impossible to predict in the long run. (Statistics can still give us useful ranges though.)I thought chaos theory provided a mathematical model for sensitive dependence on initial conditions, or is it just pie in the sky, or my misunderstanding it?
Godel's incompleteness theorem says that in any given system, there are some things that are unknowable.
And the Bell inequality says that there are some things that really are random (in the most likely case).
Going back to the essay title, "Is nature just another equation", I am discussing how the equation R= 1-sin(Nx) can be polar plotted to produce a flower, where "N" determines the number of petals on the flowers(this can be tried out using any graph plotter on the internet such as wolfram or using excel-work in radians).
I was wondering how I can show specific objections to my point (or special case scenarios where euqtions are unlikely in flowers-please explain why).
Ihave already discussed the fact that the above equation is specified to special types of flowers and that a general equation can not be derived.
thank you
Insane ide mayby, I cant say im operating in my own system:P
I think that the only thing math cant discribe is the evulution of it self, and what it can not describe.
First of all its a techincal thing like a showel or an adjectiv, you can improve the shovel by making a better grip for exampel.
An adjectiv describes a property of a thing and we can invent better adjectives that describe the properties better but the adjectiv will never describe all properties of a substantive. Because then the adjective would be a substantive.
You can also improve math by inventing new things like the "polar system" with out it
the flower making equation wil become useless.
You can se it as a way to describe an avarge flower the shortest way possible and that is what I think math is all about, to describe things as short and as correctly as possible, so how can we describe things like quantum mechanics with a multi tool like math that hasent got any attatchment designed to handle QM(multi tool=swiz armyknife).
What I'm trying to say is that the only thing math cant describe shorter then it is, is it's own flawes and possibiltys.
Max Planck's view was that science progresses as a series of successive approximations with enlarging domains of validity.
This is somewhat analogous to Darwinian natural evolution.
Both processes are punctuated by 'catastrophes', called 'paradigm shifts' in science.
An example is the 'ultraviolet catastrophe', which Planck himself resolved by the introduction of the 'quantum' in December 1900.
An equation is simply an expression containing the equality sign (=) of the form t = u ,stating that the two terms u and v
have the same value in some valuation system, such as algebra.
Parts of nature may be described by equations, such as E = mc2.
Expressions which are not equations may also describe (parts of) nature.
For example Heisenberg's uncertainty relations, use inequalities.
Both equality and inequalities are relations.
There's always going to be some relation involved, because that's what they (scientists) are trying to do - relate things into
conceptual schemes, more and more comprehensive (cf. 'Theory of everything').
Reminds me of what Bertand Russell once said: 'In mathematics we are trying to call everything by the same name'.
every thing cant be explained in equations ., like
smile of a child,
enormity of universe,
coldness of water,
phobias and manias,
sweetness of your LOVE,
the desire for something,
blessing of god,
complexity of life,
human intelligence, etc
quality/quantity of nature is highly ambiguous/relative term. you must have to set some standards.
and remember that you can make any equation easily, if you observe nature closely. this shows that math is dependent on nature and not vice versa. this point is very important in this discussion. more you make equations more you will feell a gap between what is real and what is not real.
May be or not but the topic is superb and great i like it very much . i ll also think about it
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