This is what I posted on the 'Animal experiments' thread, but it's more appropriate here.
I would say that the fundamental difference between mathematics and physics is the different notion of proof. Mathematics, in my mind, is not a science because it does not conform to the scientific method, in which experiments are held supreme.
The whole of pure mathematics consists of a relatively small number of axioms, with huge chunks of deductive reasoning built around them (though they can never be made to fit together perfectly, as shown by Gödel.) On the other hand physics is composed of principally of many observations and hypotheses, with smaller but more numerous blocks of reasoning binding them together to some extent. Seen from a purely logical point-of-view, physics has a huge number of axioms, some of which have been changed several times, and the resulting system is both incomplete and inconsistent, hence the disunity of the natural sciences.
It's a bit like the difference between carving something out of wood, and carving it out of a single diamond (though perhaps not as extreme.) The former contains carbon, the latter is carbon. The latter is almost indestructible, but the former is far easier to obtain. Even if physics were to stop expanding right now, it would take an enormous effort to cover the ground it has covered already using only deductive reasoning; it may be that no manageable set of axioms is sufficient to give us even an approximate model of the universe on these terms.
Originally posted by pradtfWell I think physics came before math because there was gravity and such before some-one invented math and numbers.
in this thread, we will answer concerns shown about math being before physics, or chemistry being before physics, or physics being phertilizer etc
the phacts will be revealed shortly ...
Originally posted by UncleAdamwell said Acolyte and UncleAdam!
Well I think physics came before math because there was gravity and such before some-one invented math and numbers.
colin that is a good analogy with the carbon for sure and the logic is also thorough (the godel reference was to his incompleteness theorem no doubt) - but then you are a true mathematician.
and thank you adam for your lucid observation that will light the way for many who come to this thread!
it is obvious that right now we three are the only sensible beings on this thread. soon we will be bombarded by the non-believers. but have no fear - we shall overcome the odds.
[{(don't tell anyone, but i have a trump card that will destroy the opposition. i won't play it now, though, because we wouldn't have any phun then.)}]
😉
I would say that they co-existed at the same time. Now while it is true that mathmatics was "invented" so to speak, I also hold that while human beings may not have understood it, it still existed. I could say the same for electricity. It was always there, we just lacked the ability to harness it yet. My opinion is based upon a mental concept existing regardless of whether on not it has actually been thought of yet. Highly debateable, and I am curios to see what others think.
I shall concede that if they did not come to exist at the same time, then I think physics must have been first.
Originally posted by Omnislashwonderful and welcome aboard my friend!
I shall concede that if they did not come to exist at the same time, then I think physics must have been first.
your comments pose an interesting philosophical question. it is along the lines of, "if a tree falls in the forest and no one is listening, is there a sound?" well it would be interesting to see how this would be handled.
some pseudomathematicians would immediately say yes because they can be so attached to the axiomatic way of thinking. the axiom here would be something like if tree falls then sound waves generated by expansion and rarefaction therefore sound (and who cares if anyone is listening). the physicist on the other hand would say how can there be a sound if you can't observe it? the pseudomathematician would sneer and say what about the expansion and rarefactions (ideas that physicists discovered you will note) - they exist regardless of whether you are there to observe or not. the gentle physicist would calmly reply may be so, but we can't be sure if we can't observe it.
now while it may appear that the physicist is being a little indecisive this is not so at all. rather the physicist is taking the possibilities of reality into account rather than relying on the all might axioms. for instance, suppose the tree fell in the forest within a vacuum or suppose the tree was whisked away by a strong wind before it hit the ground or suppose that the ground was a highly dampening quicksand. improbable perhaps, but without an observer who can say? (in terms of your excellent statement of things existing whether we can mentally conceive them or not, the physicist only wants some observational data to work with - that failing a best guess is often quite plausible - but a physicist, who doesn't work in a closed system, would never be so arrogant as to say "i think, therefore the universe can exist".)
here is the point. physics comes from observation initially then flows to hypothesis then to experimentation for verification then to theory - which can be used not so much as an axiom but as dynamic application: the theory may change if the circumstances are changed by better or different observations. hence, physics is primarily an inductive science (with continual refinement).
mathematics is primarily deductive. you start with the axioms and deduce all kinds of stuff from it. indeed it can be powerful and much physics is done using mathematics as a useful tool (more on this in a later post), but to say that math came before physics is like saying we learn to count before we learn to see.
so let us begin by restating the three heinous attacks made recently on physics. (out of courtesy and repect for their personal privacy i will not mention any names. though this inaction may help protect the guilty, rest assured that they know who they are!)
1. the bigmath attack
started like this: in the beginning there was maths, physics was a consquence of mathematics in the universe, chemistry ... afterwards it went on like this: maths can be used independant of phyics, but physics cannot be used independantly of maths, therefore, for physics to exist in the universe maths must already exist therefore maths comes first.
2. chemical a salt
well the assault didn't actually take place but it was threatened (Why I ought to...!), but fortunately the aggressor restrained himself just in time before any testtubes were broken. however, as a parting shot the old alchemy revolt argument was unleashed.
3. fertilibelization
this was not much different than the bigmath attack, but the part about "That statement [mathematics is only numerical physics] is useful only inasmuch as it is good fertilizer" was evidently true. the said statement obviously did fertilize the fantasy of the writer who proceeded to expostulate that mathematics is "defining some underlying rules, and deducing, by logic, all of the consequences of those rules." and then proceeded , no doubt by deducing, that "In that very important and fundamental way, physics is a branch of mathematics. "
as you can plainly see, there is much to set right. we shall begin this honorable opus next day.
I think it doesn't matter. Can't have one without the other. They are tools used to kill gods and devils. Without them, we can't rationalize the nature of the universe without resorting to magic. <even with them, the universe can appear plenty frightening>
"Pure" math might exist in some etherial plane. Problem is, you can't have a corporeal body without physics. Hence my statement "you can't have one without the other." No math no physics. No physics, no "brains". No brains, no math. No math, no physics. ad infinitum
Originally posted by StarValleyWywhile much of what you say is both interesting and accurate, it is not necessary to do physics with math. in fact, much of physics takes place without math. the reason people see math as essential to physics is they usually think of 'chalkboard physics' and have an overwhelming urge to quantify everything. it is also the primary reason that so many students are afraid of' and avoid physics.
[b]I think it doesn't matter. Can't have one without the other.
let me illustrate with a few examples. a while a go, aristotle dropped a feather and a stone and concluded that heavier objects fall faster than lighter ones. a little later gallileo supposedly conducted a similar experiment with 2 canon balls and came to a different conclusion. now neither experiment required math or even arithmetic. we can all go out and do this experiment and we wouldn't have to touch math. (well i suppose some would argue that when you have one object hitting the ground before another that constitutes first and second or considering something heavier than another you are doing math - but that is really being trivial and somewhat spiteful.)
we all do physics. the pole vaulter does physics intuitively not mathematically. so does the person driving a car (yes you can do some arithmetic if you really want to by looking at the speedometer).
even non-humans do physics. the wild tiger carefully calculates its leap on its prey - yes calculates, but not mathematically. in fact, if it were to try to use mathematics, it would probably starve.
even the inanimate world does physics. fire burns, rain falls, planets revolve, and stars shine. this physics takes place whether we choose to quantify it or not. yet physicists have been studying these processes for centuries - before the math had even been invented to handle the stuff.
jearl walker (a physicist who did the amateur scientist column for scientific american for a while) worked very hard to put what he called the 'fun' back into physics:
"Why is physics so badly thought of? ... Here we have a subject that deals with the fundamental clockwork of the universe. We can show students how to piece together the little gears to make a section of their world work... Why is this so unpopular?"
he felt that one of the primary reasons physics was seen as such a detestable topic was that it was usually done in the classroom detached from the world as quantitatively as possible (depending on the level of mathematical ability of the students). he encouraged physics to be taught coupled to everyday phenomena, with humor, drama and emotion. yes mathematics and quantification can definitely be useful in many situations - but there are other ways to do physics and observation and intuition should never be subjugated.
i heard him once telling a delightful story about his grandmother (the most unmathematical person he had ever known), who one day asked him if he knew why a pan of hot water left outside in subzero weather freezes faster than a pan of cold water. he smiled at her and gently said that it was the cold water that froze first. no jearl, the grandmother said, the hot water freezes first. jearl tried explaining the arithmetic behind it to her - how the cooler water has a head start therefore it must freeze first. she said try it jearl. he tried to explain the particle theory of matter, argue the thermodynamics, even in desperation demonstrate the differential equations - but all she would say is try it jearl. so he did try it and then went off to try to figure out why his grandmother was right.
yes we can all explore this universe mathematically or otherwise - and that is the gift physics gives us 🙂
How A Air Plane Flys
The shape of a wing, (the bottom of it is flat and the top side has a hump in the front that comes to a sharp angle on the other side).
The unique shape causes air to go faster over the top of the wing in order to catch of with the air on the bottom of the wing.
The faster moveing air on the top causes the air presser to be lower in the top witch causes lift, and that is how a airplane flys.
This also works for birds and bugs, and they where around before numbers😀
Originally posted by UncleAdam'Tis a bit simplistic, is it not? Numbers are probably much more 'fundamental' than birds or bugs. Mathematics consists of a set of arbitrary rules, and everything that can be logically proven or disproven based on those rules. Mathematics is a subset of the whole set of 'information'. All that a bug is to you or I is a sight, or a buzzing sound, or a stinging sensation, or some other piece of INFORMATION. Thus, as far as you know, a bug is no more 'real' than a number, but a number is a lot cooler!
This also works for birds and bugs, and they where around before numbers😀
Originally posted by pradtfYou have made one of the most interesting posts that I have read in a long time. Excellent. My comments were really to do with the idea that all we can really consider or think about as beings, is done so with our "minds"... whatever that is. 😕
[b]while much of what you say is both interesting and accurate, it is not necessary to do physics with math. in fact, much of physics takes place without math.
Is that true about hot water freezing before cold?! What is the explanation if so? Counter intuitive to say the least.
Originally posted by StarValleyWythank you. i really liked what you said in the animal experimentation thread about the responsibility that must come with dominance - never got around to telling you it in that thread so i do so now.
You have made one of the most interesting posts that I have read in a long time.
Is that true about hot water freezing before cold?! What is the explanation if so? Counter intuitive to say the least.
the water story is true and does happen under certain conditions. it is a phenomenon that people in cold countries are quite familiar with, but seems to bother people in warm countries (according to jearl) 😀
rather than give you the explanation why don't i just let it sit with you for a bit. try it in your freezer if you want - it may work. then you'll have to explain why.
if someone else doesn't post the explanation, i will do so later.
Originally posted by pradtfis it because the hot water loses heat faster then the cool water?
the water story is true and does happen under certain conditions. it is a phenomenon that people in cold countries are quite familiar with, but seems to bother people in warm countries (according to jearl) 😀
rather than give you the explanation why don't i just let it sit with you for a bit. try it in your freezer if you want - it may work. then you'll have to explain why.
if someone else doesn't post the explanation, i will do so later.