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tcaudilllg
Dragonmaster
Joined: 20 Jun 2002
Posts: 1731
Location: Cedar Bluff, VA
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 Posted: Fri Jun 24, 2005 8:33 pm Post subject: |
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...I research every day. :P You have no idea how much resource material I have on my HDD.
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LeoDraco
Demon Hunter
Joined: 24 Jun 2003
Posts: 584
Location: Riverside, South Cali
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| Posted: Fri Jun 24, 2005 11:07 pm Post subject: |
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| LordGalbalan wrote: | | ...I research every day. :P You have no idea how much resource material I have on my HDD. |
No, we don't. Mostly because you never actually reference anything.
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"...LeoDraco is a pompus git..." -- Mandrake
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Nephilim
Mage
Joined: 20 Jun 2002
Posts: 414
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| Posted: Sat Jun 25, 2005 12:51 am Post subject: |
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| LordGalbalan wrote: | | One need not understand the "math" to understand a theory. The math is just a tool to arbitrarily apply the theory with. Understanding it, or rather, the difficulty thereof, rests on the tradition of mathematicians to use archaic symbols that can often have varying meanings from equation to equation. |
I'm sorry, but you're just showing your ignorance here. I'm not a physicist, so I can't address your thoughts on physics, but as a mathematician, I know a bit about mathematics.
To say that you don't need to understand the math to understand a theory is like saying you don't need to understand English to understand a sentence spoken to you in English. Math is the language of science, and it can be used to communicate ideas across cultures and native spoken languages. In almost all cases where math comes into play, the math IS the exposition of the theory in its most succint and usable form. If you don't understand this about mathematics, I seriously doubt that you understand the physics you are going on about. You gotta learn to walk before you can run.
Furthermore, mathematics is all about rigor. If you try to use and apply a theory, but dismiss the mathematics as secondary, you're far more likely to misapply it, leading to faulty thinking and therefore faulty conclusions in many cases.
| LordGalbalan wrote: | | So to say, there is no comparison between a mathematical formulation of a principle, and an alogorithm of the same in C. The C algorithm is by far superior. |
What the hell are you talking about? Any C implementation of a mathematical principle is going to be inferior to the principle itself, if only because it is shackled to the procedural and physical nature of a computer. (If nothing else, the mathematical principle can be used during a power outage.) And you're assuming that a C algorithm can even be formulated for a given mathematical principle.
In fact, it's the very fact that a computer algorithm is inferior to the mathematical principle behind it that gives us technologies like public key cryptography. The C implementations of finding large primes and multiplying them are fast, but the C implementation of factoring the result is very slow. Put those two things together, and you have a "trap door" function that can be used to perform cryptography to any level of hardness you want - just use big enough numbers, and no one can write C code to crack the code before the value of the information has passed.
But maybe you're getting at something that I'm missing, so let's do a little experiment and see what happens. I'll give you a mathematical principle, and you show me the C code that is "far superior" to it.
To keep things simple, let's take a very straightforward mathematical expression: D=RT (distance equals rate times time). What is the "far superior" C equivalent of that mathematical principle? I predict that it will be more obfuscated and less useful than the simple mathematical expression D=RT.
Remember that the mathematical principle is stateless - it doesn't assume which variables you know and which ones you don't know, or even that you know any of them, and it communicates HOW the variables are related on an abstract level outside of computation, so that you can apply the principle to a problem before you even deal with data. Expressing an idea as a mathematical expression buys you a lot, because you can harness all sorts of powerful tools once it is in that form (including writing computer code for computation purposes!).
It's easy to write C code for a particular application of the principle. It looks like this:
Almost as succinct as the mathematical expression itself, although it is cluttered a bit with the necessary operator symbol and the semicolon statement terminator (and I'm omitting all the variable declarations, output statements, function declarations, etc. that have to be present in order for that C command to actually do anything). But still, it's nowhere near as useful as the principle itself. That's just an application of the principle where you know r and t and are looking to find d.
To do the same thing as the mathematical principle itself, your code will need to be able to (among other things):
* Compute distance given rate and time.
* Compute time given distance and rate.
* Compute rate given time and distance.
* Communicate the relationship between the variables in an abstract fashion, like "If R is halved and D is held constant, how does T change?"
* Work in conjunction with other unforseen equations or relations so you can do things like computing the cost of travel and performing optimization computations.
* Work with itself as a system of equations to compute all unknown variables (or indicate that the equations are mutually dependent).
* Work with irrational numbers without data loss or approximation.
I look forward to seeing your "far superior" expression of the principle D=RT in C code.
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tcaudilllg
Dragonmaster
Joined: 20 Jun 2002
Posts: 1731
Location: Cedar Bluff, VA
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| Posted: Sat Jun 25, 2005 5:04 pm Post subject: |
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| Quote: | To do the same thing as the mathematical principle itself, your code will need to be able to (among other things):
* Compute distance given rate and time.
* Compute time given distance and rate.
* Compute rate given time and distance.
* Communicate the relationship between the variables in an abstract fashion, like "If R is halved and D is held constant, how does T change?"
* Work in conjunction with other unforseen equations or relations so you can do things like computing the cost of travel and performing optimization computations.
* Work with itself as a system of equations to compute all unknown variables (or indicate that the equations are mutually dependent).
* Work with irrational numbers without data loss or approximation.
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I skimmed that dissertation faster than you would think. ;) Thank you for insulting my intelligence, which is equal to yours but from a perpendicular tangent, mister INTP.
No I can't write a program that does that... oh wait yes I can. I need to write a neural network simulation that operates on a concentration gradient, like unto your own brain. But I digress, writing such a thing would take years and it would hobble any computer made in the next ten.
Let me add a little judgement to your rigor, sir. The "mathematical principle" you favor so highly is not expressed by "d = rt". (which in some contexts may not mean d = r * t; one only needs to observe the mess of dx/dy in calculus to understand that, and that's exactly my point in saying the C expression is superior from a judge's perspective) That grouping of letters means what it does only because you don't draw conclusions about anything, and yet actually know where those conclusions came from. Yes, sometimes I'm wrong, and sometimes, so are you. Sometimes, so is anyone.
If it will help to cite references, then I will. I avoid citing them because it encourages people to disdain leadership and run after the "superiority" of people who quite frankly just followed the crowd on a larger level. Power to the individual, let the unbalanced order of the mob be damned.
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Nephilim
Mage
Joined: 20 Jun 2002
Posts: 414
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| Posted: Sat Jun 25, 2005 11:03 pm Post subject: |
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| LordGalbalan wrote: | | No I can't write a program that does that... oh wait yes I can. I need to write a neural network simulation that operates on a concentration gradient, like unto your own brain. But I digress, writing such a thing would take years and it would hobble any computer made in the next ten. |
So how is the C version better than the principle itself, then?
| LordGalbalan wrote: | | Let me add a little judgement to your rigor, sir. The "mathematical principle" you favor so highly is not expressed by "d = rt". |
Actually, it is.
| Quote: | | (which in some contexts may not mean d = r * t; one only needs to observe the mess of dx/dy in calculus to understand that |
Then I question your understanding of that. Even in calculus, D=RT still means exactly the same thing - the principle is unchanged, and still expressed in the same fashion. If you want to find the distance travelled, you multiply the time interval by the speed you were going, whether the time interval is an hour, a minute, or near zero. The "mess of dx/dy," as you call it, has exactly zero to do with the D=RT principle - that comes from the process of using calculus, which can be applied to practically any principle that can be expressed as a function.
(Also, I think you mean "dy/dx" if you mean the typical expression of computing under a y-curve with calculus.)
| Quote: | | and that's exactly my point in saying the C expression is superior from a judge's perspective) |
I must not be understanding what criteria you have in mind for judging the usefulness of a mathematical principle and its use in C code, because I really don't see the connection of how the fact that D=RT can be used in calculus demonstrates that "the C expression is superior from a judge's perspective." If you want to solve the same problem with C, you're still going to need to use the principle, aren't you? The C code needs the principle in order to exist, but the principle does not need the C code.
Again, maybe an example would help clarify your point. You say above that the "mess of dx/dy" demonstrates the superiority of the C code. Give an example of the mathematical calculus expression with dy/dx in it, and then the companion C code, and explain why you think the C version is so superior.
| Quote: | | That grouping of letters means what it does only because you don't draw conclusions about anything, and yet actually know where those conclusions came from. |
What do you mean that I "don't draw conclusions about anything?" And how can I know where they came from if they never got drawn? If you mean that it's an abstracted expression of the principle, with specifics undefined until the principle is applied, then that's exactly why the principle is so powerful. It's why it can be applied to ad-hoc mental computations as well as detailed calculus-based investigations. If this is not what you mean, then please clarify.
| Quote: | | Yes, sometimes I'm wrong, and sometimes, so are you. Sometimes, so is anyone. |
True. Your point being...?
| Quote: | | If it will help to cite references, then I will. I avoid citing them because it encourages people to disdain leadership and run after the "superiority" of people who quite frankly just followed the crowd on a larger level. Power to the individual, let the unbalanced order of the mob be damned. |
Wow, you seem to have a real chip on your shoulder about the scientific and mathematics communities. I think your characterization is mean-spirited and quite unfair to the people who honestly and humbly toil for years to, for instance, find the effect different amounts of water have on a particular food crop. It's true that science does not value the individual, but that's intentional - the individual can easily be dead wrong about whatever theory he's pushing. The whole point of science is to try to control for human fallibility in the pursuit of knowledge. The more people who check out a theory from more angles and in more contexts, and find evidence to support the theory, the more likely that theory is to be correct. Not 100%, but certainly better than what any individual can claim.
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tcaudilllg
Dragonmaster
Joined: 20 Jun 2002
Posts: 1731
Location: Cedar Bluff, VA
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| Posted: Sun Jun 26, 2005 6:24 pm Post subject: |
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Not 100%, but certainly better than what any individual can claim. |
To that, I'll quote Einstein:
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"...Then I feel sorry for the dear Lord! The theory is right."
- A. Einstein, when asked about what his response would be if one of his key proofs of general relativity, the dilation of light during the solar eclipse of 1919, were demonstrated not to be apparent in experiment.
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Absolute truth is absolute truth and absolute truth exists, surely as there is absolute life and absolute death. Case closed.
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biggerUniverse
Mage
Joined: 18 Nov 2003
Posts: 326
Location: A small, b/g planet in the unfashionable arm of the galaxy
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| Posted: Sun Jun 26, 2005 6:49 pm Post subject: |
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I by no means want to be involved in this dance, nor am I taking sides, but I would like to point out that I think LG is attempting to state this: D=RT contains several implicit functions that we as humans naturally understand. Nephilim, you have explicitly defined them in one post, but just saying "D=RT" is like saying "Z=XY"- there are no established definitions around the latter, and without knowledge of the former, you would have no idea how to interpret. If it were written out fully as you defined in C code, then one would need only knowledge of that language (I consider it a natural language unto itself) to understand the entire algoritm and perhaps even the proof.
This does not, however, make the C code superior, it simply establishes the entire definition of D=RT. Any language could have done that.
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tcaudilllg
Dragonmaster
Joined: 20 Jun 2002
Posts: 1731
Location: Cedar Bluff, VA
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| Posted: Sun Jun 26, 2005 7:43 pm Post subject: |
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The C code is more accessible.
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Mandrake
elementry school minded asshole
Joined: 28 May 2002
Posts: 1341
Location: GNARR!
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| Posted: Mon Jun 27, 2005 12:24 pm Post subject: |
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Absolute truth is absolute truth and absolute truth exists, surely as there is absolute life and absolute death. Case closed.
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Yeah, and if everyone followed exactly what Einstein said, we would not have the beautiful uncertainty of Quantum Mechanics today. Einstein isn't really all that impressive of a thinker. Most of his ideas are just modernized simplifications of stuff that German mathematics discovered in the 1200's. He just simplified the equations. Hell, he didn't even do it all by his lonesome, either. To quote Einstein himself, he "stood on the shoulders of giants". Which is to say, all he did was make a tiny leap on somebody else's already complex groundwork.
Now, Georg Cantor. He was fucking awesome. I'm just so sick of whenever anyone mentions the word Genius, Einstein's name pops up like a bad rash. There are people in history who have done so much more, were so much smarter.
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tcaudilllg
Dragonmaster
Joined: 20 Jun 2002
Posts: 1731
Location: Cedar Bluff, VA
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| Posted: Mon Jun 27, 2005 11:53 pm Post subject: |
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Anyway, the reason I don't like being at the bottom of the mathematical totem pole, and not having an entertaining way up (equations are the ultimate in boredom) is this:
I'll post it tomorrow.
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Nephilim
Mage
Joined: 20 Jun 2002
Posts: 414
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| Posted: Tue Jun 28, 2005 6:43 am Post subject: |
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| biggerUniverse wrote: | | I would like to point out that I think LG is attempting to state this: D=RT contains several implicit functions that we as humans naturally understand. Nephilim, you have explicitly defined them in one post, but just saying "D=RT" is like saying "Z=XY"- there are no established definitions around the latter, and without knowledge of the former, you would have no idea how to interpret. |
True, but very seldom do you encounter random math expressions out of context like that. Of course a math expression is meaningless if you divorce it from all context. But anyone who deals regularly with math-based discussions knows that the context is generally very well defined in the interest of rigor.
If LG was indeed referring to a math expression presented out of context, then the C code case would need to be similarly adjusted. In order to compare apples to apples, you'd have to strip the companion C code of all reference to context too - no comments, no output, inscrutable variable and function names, etc. - at which point it would become equally meaningless.
On a side note, biggerUniverse, I was intrigued by your mention of C being a "natural language" which could perhaps communicate to the reader the proof of an assertion in its code. Would you mind elaborating on that point?
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Mandrake
elementry school minded asshole
Joined: 28 May 2002
Posts: 1341
Location: GNARR!
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| Posted: Tue Jun 28, 2005 11:51 am Post subject: |
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LJ:
If you think equations are boring, than maybe you should persue a different endeaver? I would suggest philsophy, but if you find equations boring you will probably find the countless abstract way of "proofing" theories in philisophy equally so.
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tcaudilllg
Dragonmaster
Joined: 20 Jun 2002
Posts: 1731
Location: Cedar Bluff, VA
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| Posted: Tue Jun 28, 2005 9:24 pm Post subject: |
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LJ:
If you think equations are boring, than maybe you should persue a different endeaver? I would suggest philsophy, but if you find equations boring you will probably find the countless abstract way of "proofing" theories in philisophy equally so.
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No way. I want to know it all. I want the Knowledge Key.
Rigor = painstaking. (for me, and hell, every judge out there, and I don't think the Xs like LeoDraco find it that enjoyable either. Sorry, LeoDraco, just using you as a reference)
Behold the ArVix
http://arxiv.org/
The absolute cutting edge. Of everything in science. Half coded in knowledge, and half in that damnable mathematical rigor. Just enough coded in rigor to leave one wondering how to get more out of all this information than the knowledge it provides directly.
Err didn't I make a comment that Mandrake was into Georg Cantor just because he was the same type as Mandrake is? ENTJ?
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Terry
Spectral Form
Joined: 16 Jun 2002
Posts: 798
Location: Dublin, Ireland
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| Posted: Tue Jun 28, 2005 9:51 pm Post subject: |
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| Quote: | | Rigor = painstaking. (for me, and hell, every judge out there, and I don't think the Xs like LeoDraco find it that enjoyable either. Sorry, LeoDraco, just using you as a reference) |
Personally, I love the maths bit of science. I actually started in a TP course when I went to college first, and changed into pure maths when I realised that I couldn't even get the pendulums to work. Tut.
So there's at least me, and loads of other people (I can tell you from experience) who find the rigor fun, in fact, much more fun that all that tedious lab work and experimentation is.
As for your thought experiments approach... what age are you? Seriously?
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tcaudilllg
Dragonmaster
Joined: 20 Jun 2002
Posts: 1731
Location: Cedar Bluff, VA
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| Posted: Tue Jun 28, 2005 9:58 pm Post subject: |
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