What is the relationship between the abstract world of mathematics and the material universe?

[Moontown_Rabbit]

A minor change, obviously, but a very different technique.

I used average deviation, you are using statistical deviation. We used average deviation in the engineering program because it can be calculated more quickly, something that is quite significant during an exam. No doubt statistical deviation is slightly more accurate.

 

[tonyrey]

If mathematics were an arbitrary set of axioms and rules there would be no reason why it is applicable to reality.

Maths is not arbitrary. 2+3=/8 or 5 or 545 Once the rule is set it is ruled till the end no matter what.

How that applies to nature, FOR ME, is one of the strongest proves of the existence of God. God makes the bridge between what is merely spiritual and what is material.

Physical laws use maths to rule on physics. But you have got an ideal physic and a material physic. You may imagine the 10th dimension or the Chords of the Universe or worlds being created and destroyed.

But in practice, you must compromise between exactitude and possibility of the material world to reflect the spiritual mind. It is very, very difficult, even for NASA brilliant minds, to make the crafts behave the way the imagine and want and dreamed. Maths is not arbitrary. 2+3=/8 or 5 or 545 Once the rule is set it is ruled till the end no matter what.

How that applies to nature, FOR ME, is one of the strongest proves of the existence of God. God makes the bridge between what is merely spiritual and what is material.

Physical laws use maths to rule on physics. But you have got an ideal physic and a material physic. You may imagine the 10th dimension or the Chords of the Universe or worlds being created and destroyed.

But in practice, you must compromise between exactitude and possibility of the material world to reflect the spiritual mind. It is very, very difficult, even for NASA brilliant minds, to make the crafts behave the way the imagine and want and dreamed.

Precisely! (A particularly appropriate term in this context…

 

[Pfaffenhoffen]

There is no doubt that persons on this planet are members of the species homo sapiens.

I stated that “it needs to be proved that persons are no more than animals”. In other words I don’t believe persons are **merely **animals! The onus is on those who do to explain, for example, why animals don’t appear in court.

sorry language problems, for me

it needs to be proved that persons are no more than animals"

means that that must be proven that persons are just animals but it seems the meaning is reverse…
I cannot still catch the logic of it…

 

[Pfaffenhoffen]

In Platonic terms there is no perfect triangle in the material world, however there is such a thing as a perfect ideal triangle that we can represent mathematically. Your comment about accuracy is related to this distinction. When I studied engineering, I came across a mathematical solution to this problem of inaccuracy, namely the introduction of error ranges. Thus I can say

distance (d) = 1561 meters +/- 2 meters
time (t) = 25.3 seconds +/- 1 seconds
speed (s) = (d / t) +/- ((∆d / d) + (∆t / t)) * (d / t)

therefore

s = (1561 / 25.3) +/- ((2 / 1561) + (1 / 25.3)) * (1561 / 25.3)
= 61.7 +/- (0.040806 * 61.7)
= 61.7 m/s +/- 2.52 m/s

The inclusion of the error range makes the mathematical statement entirely valid.

No Plato said that the Perfect Triangle existed in the World of Ideas.
Actually it exists in Maths but not in the real world.
Hence your +/- solution, that, obviously, I follow at large, but cannot interpret finely.

Of course, engineers built valid solutions, brilliant one, each time more brilliant, but math is the ideal perfection.

 

[Pfaffenhoffen]

Weird, I was always told that compounding errors for multiplication/division was

s[sub]x[/sub]=x * ( (s[sub]a[/sub]/a)[sup]2[/sup]+(s[sub]b[/sub]/b)[sup]2[/sup]+…)[sup]1/2[/sup]

where s[sub]x[/sub] is the uncertainty of the total measurement, s[sub]a,b[/sub] are the uncertainty of the individual measurements and a,b are the measurements themselves. So, in my method and with your numbers, the error of measurement would be

s[sub]speed[/sub] = 61.7 ( (2/1561)[sup]2[/sup]+(1/25.3)[sup]2[/sup] )[sup]1/2[/sup]=2.44

A minor change, obviously, but a very different technique.

I do not understand, hence, it must be good.

 

[Alberti_Devoveo]

I used average deviation, you are using statistical deviation. We used average deviation in the engineering program because it can be calculated more quickly, something that is quite significant during an exam. No doubt statistical deviation is slightly more accurate.

Ah, I see. I guess I never learned average deviation because we were allowed calculators on our exams in physics .

 

[Moontown_Rabbit]

Ah, I see. I guess I never learned average deviation because we were allowed calculators on our exams in physics .

We had calculators as well, but the difficulty is that one solution often used up five or six pages of the exam booklet and you would typically have five such problems to solve. You can imagine how a more complicated error calculation would snowball as it was carried through a hundred calculations, resulting in many more button presses, with each button press a possible mishit, and so on, and so on…

 

[Alberti_Devoveo]

We had calculators as well, but the difficulty is that one solution often used up five or six pages of the exam booklet and you would typically have five such problems to solve. You can imagine how a more complicated error calculation would snowball as it was carried through a hundred calculations, resulting in many more button presses, with each button press a possible mishit, and so on, and so on…

I can see that being an issue. We’d have a similar set of problems for a test, but error analysis was just one of those problems and not something we had to do for each problem.

 

[Pfaffenhoffen]

More one reason for considering Math a science of the spirit.

Never thought physics ( I am on the Humanities side!) deviated to much !!! It seems that there is as much deviation as good solutions for the problems.

I was told of the 2nd Law of Thermodynamics, which I do not understand how came into being a Law (nor did I ever see the formula), but which says that phenomena tend to entropy. That is my favorite proof of the existence of God but this should be flawed for entropy came to me out of the blue: if everything tends to entropy, then there must be an Organizer who goes against it to for hipyer-complex molecules and cells, and organs, and functions and organisms.

So, in this world, you need Math to put order in Physics…

 

[tonyrey]

More one reason for considering Math a science of the spirit.

Never thought physics ( I am on the Humanities side!) deviated to much !!! It seems that there is as much deviation as good solutions for the problems.

I was told of the 2nd Law of Thermodynamics, which I do not understand how came into being a Law (nor did I ever see the formula), but which says that phenomena tend to entropy. That is my favorite proof of the existence of God but this should be flawed for entropy came to me out of the blue: if everything tends to entropy, then there must be an Organizer who goes against it to for hipyer-complex molecules and cells, and organs, and functions and organisms.

So, in this world, you need Math to put order in Physics…

There is also good reason to believe Physics can ultimately be explained in terms of mathematical equations! Chaos is at the opposite extreme…

 

[Pfaffenhoffen]

There is also good reason to believe Physics can ultimately be explained in terms of mathematical equations! Chaos is at the opposite extreme…

It seems that Chaos is being studied in Maths.

 

[Alberti_Devoveo]

More one reason for considering Math a science of the spirit.

Never thought physics ( I am on the Humanities side!) deviated to much !!! It seems that there is as much deviation as good solutions for the problems.

There is much deviation! Physics studies the real, mathematics generally does not.

I was told of the 2nd Law of Thermodynamics, which I do not understand how came into being a Law (nor did I ever see the formula), but which says that phenomena tend to entropy. That is my favorite proof of the existence of God but this should be flawed for entropy came to me out of the blue: if everything tends to entropy, then there must be an Organizer who goes against it to for hipyer-complex molecules and cells, and organs, and functions and organisms.

There isn’t really a formula for the 2nd Law, it’s just a statement. The closest you could come to an equation would, I guess, be the dS >= dQ/T where S is the entropy, Q is the heat transferred between two objects/systems, and T is the equilibrium temperature of the two objects; in words this would be “the infinitesimal change in entropy is greater than or equal to the infinitesimal change in heat divided by the equilibrium temperature.”
In Fr Spitzer’s New Proofs, there’s a nice sub-chapter in the first chapter about the entropy argument for a Creator; it’s worth the read if you haven’t already.

So, in this world, you need Math to put order in Physics…

I disagree with this. Mathematics is merely a tool to help describe things that one sees in the real world. As I’ve stated before, does an apple fall from a tree due to y=0.5gt[sup]2[/sup] (equation for free fall) or because of gravity? The former is the mathematical equation for it while the latter is the physical reason for it.

 

[lemondiesel]

the cognition of math is abstract, but things still exist…

 

[Pfaffenhoffen]

There is much deviation! Physics studies the real, mathematics generally does not.

There isn’t really a formula for the 2nd Law, it’s just a statement. The closest you could come to an equation would, I guess, be the dS >= dQ/T where S is the entropy, Q is the heat transferred between two objects/systems, and T is the equilibrium temperature of the two objects; in words this would be “the infinitesimal change in entropy is greater than or equal to the infinitesimal change in heat divided by the equilibrium temperature.”
In Fr Spitzer’s New Proofs, there’s a nice sub-chapter in the first chapter about the entropy argument for a Creator; it’s worth the read if you haven’t already.

I disagree with this. Mathematics is merely a tool to help describe things that one sees in the real world. As I’ve stated before, does an apple fall from a tree due to y=0.5gt[sup]2[/sup] (equation for free fall) or because of gravity? The former is the mathematical equation for it while the latter is the physical reason for it.

Thanks for your piece of information.
Thanks for the quote of Fr. Spitzer.
Now “because of gravity” means that “g” is the cause of “y” and there is a “t2” on the way, so both say the same thing, no?

 

[Alberti_Devoveo]

Thanks for your piece of information.
Thanks for the quote of Fr. Spitzer.

Not a problem!

Now “because of gravity” means that “g” is the cause of “y” and there is a “t2” on the way, so both say the same thing, no?

Yes and no. The equation describes the motion as it actually happens (neglecting air resistance of course), but that equation is not the cause of the motion. And that is one of the big distinctions that must be made! Mathematical equations are useful in relating variables (mass, length, temperature, etc) to other variables, but they don’t cause the relationships to occur. It is reality that causes the relations, and physics describes reality using both words and mathematics.

 

[Pfaffenhoffen]

There is also good reason to believe Physics can ultimately be explained in terms of mathematical equations! Chaos is at the opposite extreme…

How come Chaos is being studied?: the flight of birds, the swimming of schools of fishes, the traffic flow, and so on…

 

[Pfaffenhoffen]

Not a problem!

Yes and no. The equation describes the motion as it actually happens (neglecting air resistance of course), but that equation is not the cause of the motion. And that is one of the big distinctions that must be made! Mathematical equations are useful in relating variables (mass, length, temperature, etc) to other variables, but they don’t cause the relationships to occur. It is reality that causes the relations, and physics describes reality using both words and mathematics.

Next post.
I am enjoying yours.

 

[wcknight]

Every physicist should be introduced to more abstract Mathematics. Then they would realize that Mathematics has far out distanced the physical universe in which they have limited themselves.

Granted that early mathematics was developed to try to explain or describe the physical world around us. Theoritical Mathematics has long left physical reality behind.

SOme would question the need to study anything that does not have an applicable use in the real physical world, BUT the fact is that some physical entities and realities have been discovered and proven to exist simply because the mathematics pointed to such anamolies or realities and scientist then went about to search for such things… stuff such Black holes, anti matter and dimensions outside the four that we can physically describe.

While some may scoff at studying math involving N-dimensional vector spaces when N is greater than 4, we now know that at the time of the big bang or very shortly thereafter, there were at least 16 or 17 dimensions.

It may have been true that many many years ago that physics was the driving force to develop the mathematics to explain or assist with describing the physical universe. But The last century or two and certainly for most of the 1900’s, theoritical Mathemathics has ventured out on its own frontiers, to the point where there are several if not many theoritical Mathematics sub fields that are areas of study in and of themselves. Most physicists end their mathematics study with multi dimension calculus, but theoritical Mathematics extends far beyond that.

Consider that there are at least 30 classes in advanced Mathematics that Physics majors are not even required to take. You can have a PHD in Physics, and not be introduced to dozens of theoritical Mathematics topics.