Well first of all, surface area is not width x height. Not even volume. That's area. Second, that's an issue with measurement, not with the model itself.

No, it's not an issue with measurement at all. The issue is that mathematics (particularly geometry) are fundamentally conceptual and make no effort whatsoever to bridge the gap to reality. And that's fine. That's a good thing. But we shouldn't pretend like we can use geometry to measure the world, only to solve conceptual problems.

I'm only responding to say that what you just wrote does not justify a response.

Yes, it is. If you could measure all the peaks and valleys, you could use geometry and calculus to compute the volume and surface area.


We can, for large objects. Elementary equations work fine for testing if two farts pit together, as long as said parts are manufactured within tight enough specifications.

hahahahaha

I'd go with Physics. Math, while immensely important, is just a code that the sciences attempt to use to model reality.

I'm an engineer though, so I am biased in how I see the world.

edit: bias being lack of "respect" for softer sciences.

Physics is easily the most fundamental science. Chemistry and biology are just specialised applications of Physics.

Mathematics is a much more complicated issue. What is mathematics? This is a very deep and difficult question, and I can only say that it is so much more than what any of you guys in this thread seem to think it is.

Mathematics is more than just a 'tool' occassionally used by scientists. You can't do any science whatsoever without mathematics, mathematics is something intrinsic to reality. 2+2 will always be 4, and it has always been 4. It is not something we 'observe', we do not have keep checking this by adding two things to two other things and making sure we still have four things, it is true because it must be true. It doesn't matter what symbol we use for '2', or '+', or '=', or '4', the statement expressed in '2+2=4' will always be true.
The same applies with Pythagoras theorem. We do not need to observe all right-angled triangles, we do not need to observe any right-angled triangles to prove Pythagoras' theorem and this is still true for all right-angled triangles that have ever existed and will ever exist. It is true because it must be. Mathematics is an expression of perfect truths; it is the only expression of perfect truths. The 'limitations' of any proof are explicit in the derivation, in the assumptions it makes (Pythagoras theorem assumes Euclidean geometry, and non-Euclidean geometries are constructed specifically to investigate geometries that do not satisfy this theorem).

Mathematics is not just a tool, or a language, or some human construct created for to serve a purpose. Mathematics exists outside of human construction, and mathematical truths are independent of any observer. Mathematics is reality. As science is the study of reality, it is necessarily inseparable from mathematics.



You write this as if you have some alternative to mathematics. How exactly are you going to 'measure the world' without mathematics?

ok.

I hereby redefine the equation "width * height" to mean "the area of an orthographic projection of a surface using the negative of the normal of that surface as a view angle".

I also redefine the equation "width * height * depth" to mean "the most probable volume of the electric field produced by a rectangular prism of matter where the vector field is of sufficient magnitude to repel the electric field of a carbon atom moving at high terrestrial velocities".

are we happy now

holy crap, you're back!

Any microscopic calculation must reduce to the macroscopic value at some appropriate distance. That's simply common sense. If you calculate the surface area of your desk at a macroscopic level of width*height, it must be roughly the same as measuring the surface area spanned by each individual atom multiplied by the number of atoms. They represent the same physical object, so there is no concievable way that they can be in disagreement by 'several orders of magntiude'. You'll get the same answer, to a lot more (completely unnecessary) decimal places, with the microscopic measurement.

I think what he's suggesting is that math should make all measurements useless for their intended purpose. And that atoms have surface area.

You know how you can measure the volume of something by dropping it into a marked container of water? Think about doing that, only in 2D. Just think about it.

This is why math is good and why some people shouldn't be allowed near electron microscopes.

Well that's your problem right there. Don't disagree with Hawking.

For most surfaces, couldn't the heights of peaks and valleys be modeled as a normal distribution according to the central limit theorem? If so, the volume would be unaffected by the variation, to a rather high degree of precision.

*Note I'm talking about volume not surface area.

I wrote the original post when I was really tired and having a difficult time formulating my opinions. My initial point was that Philosophy is a more fundamental study than physics because logic (which is just applied math) can show us how our basic wiring effects our perception of the world.



You misunderstand my evoking the word 'philosophy.' While the mind is simply physics, and our experience and thoughts are byproducts of that physics, physics (math) cannot describe why Two Plus Two Equals Four is "correct."

But I'm now starting to think Logic is the fundamental field, and math, physics, and philosophy are all different ways of applying logic.

Your words are all wrong.

Why did you say "physics (math)"? Physics has nothing to do with why 2 + 2 = 4. Math, on the other hand, describes that 2 + 2 = 4 by the very definition of the terms involved.

I was under the impression that mathematics had been proven by Gödel to be incomplete (as with any sufficiently powerful and consistent code). That is why I take issue with referring to Mathematics as "reality."

Clarification: my main engineering interest is in Control Systems. Studying the modeling of systems has given me some appreciation for the difference between a mathematical model and reality.

I appreciate that I am an Engineer, not a Physicist or Mathematician, and as such I experience more of the applied and less of the pure science. That having been said, let me know if I am mistaken.

You have it backwards. Logic is algebraic in nature.

I was trying to make the point that 2 + 2 = 4, or the force of gravity still require I conceptualize two and plus and two and equals and four and gravity itself. Not just their value as far as language goes, but what my experience of that truth is. My original argument would be that Philosophy debates and describes what 2 + 2 = 4 means. Now I'm calling it logic that discerns what the "reality" of 2 + 2 = 4.

I mean, we dissect which science is most fundamental using logic itself, don't we?

Logic is a subset of mathematics.

tl dr

IE, a subset of logic. It is used as a tool, and it can be because it involves totally abstract true axioms. It is possible for us to err in it's use but by nature it cannot be flawed. I have to say though, you kind of short change the concept by describing it in terms of time.

Math is true, and it contains truths, but it's not truth. It's abstract.



Either way, it doesn't matter. It's just a matter of terms.

Except mathematics and logic are inextricably linked and form the basis of all sciences - indeed, the scientific method itself. You literally cannot form a cogent hypothesis if you are unable to collect observations as statistics and derive a logical (mathematical) expression from them.

I'd still suggest that physics is the most "fundamental" science simply due to the fact that it's the study of "fundamentals". Physics is the study of the nature of the universe. Chemists figured out the structure of molecules thanks to Rutherford and Bohr. Biologists might not have such a great idea about certain organic structures if de Broglie hadn't figured out that electrons behave like waves or if Einstein hadn't believed him. All of our modern technology exists because Maxwell, Volta, Coulomb, Kirchoff, Hertz and Ohm were very smart people.

Psychology, on the other hand, is basically voodoo magic and it has been ever since B.F. Skinner. I'm pretty sure there isn't any important research to be done from the manager's office of a Dairy Queen, is all I'm saying.

Huh? Modern psychology uses the scientific method... it's just very difficult considering variables are very hard to isolate. The field is populated with trash, unfortunately.

Am I the only one who thinks that Computer Science is the most fundamental science?

Maybe you're the only person here with an extra chromosome as well.

Submerse in liquid, only good for very broad measurements I guess.

Information Theory might be the most fundamental science. If we're counting out math.

What? Computer science isn't even science. It's all applied mathematics.

Computer Science is a combination of physics and information theory (Both of which are applied mathematics)

I'm still stumped on the "we are 3 dimensional people in a 6 dimensional world" bit. How does that even work? I can't even follow the train of logic to reach that conclusion.

what

Computer Science is the science of solving problems with a computer. That does not mean programming, people! In fact, a high degree of Computer Science is mathematical. Finite State Automata, algorithm analysis, etc. I had a math professor who taught data structures without writing one single line of code. Proving why your algorithm is O(nlg n) isn't using a merge sort and comparing against bubble sort, it's a mathematical proof.

Yeah, you think that wasn't intentional? You're just saying that you're too stupid to figure out when someone is emphasizing a subtle distinction between two like concepts.

I'm obviously poking fun at your poor language skills.

i like mittens

Wow, how did I do that?

But typo or no, you're still wrong.