math

[CovenantJr]

What does philistine mean?

Main Entry: Phi·lis·tine
Pronunciation: 'fi-l&-"stEn; f&-'lis-t&n, -"tEn; 'fi-l&-st&n
Function: noun
1 : a native or inhabitant of ancient Philistia
2 often not capitalized a : a person who is guided by materialism and is usually disdainful of intellectual or artistic values b : one uninformed in a special area of knowledge


From www.m-w.com

[Revan]

What does philistine mean?

Main Entry: Phi·lis·tine
Pronunciation: 'fi-l&-"stEn; f&-'lis-t&n, -"tEn; 'fi-l&-st&n
Function: noun
1 : a native or inhabitant of ancient Philistia
2 often not capitalized a : a person who is guided by materialism and is usually disdainful of intellectual or artistic values b : one uninformed in a special area of knowledge


From www.m-w.com

I'm not disdainfl of intellectual or artistic values. Quite the opposite. I love smart people (Aside from the fact that they made me feel bad) I can't stand people without at least, an average intelligent to get by in life. I'm not disdainful Ur-Vile, I'm just lazy.

[dlbpharmd]

And the funny part is that Fermat claimed to have a proof that people tried to figure out for about 350 years!

Uh, yeah - that's uh - really funny.

It's clear to me now why you call yourself "Fist."

j/k - I'm glad someone can understand all of this crap, uh, I mean math.

[Gil galad]

Cool what other maths can we talk about now

[I'm Murrin]

Cool what other maths can we talk about now

How about √(-1) ? Utter nonsense, of course, but occasionally makes working out a problem a little easier.

[Nathan]

1+infinity=infinity
2+infinity=infinity

therefore by rearrangement

1=infinity-infinity
and
2=infinity-infinity

and therefore

1=0
and
2=0

and, to carry it to its logical (!) conclusion:

0=1=2

Put that in your pipe and smoke it.

[Fist and Faith]

And that, friends, is what happens when you try to apply the laws of finite sets to infinite sets! Good work, Nathan.

Let's give a clearer example. The rule is: A part is less than the whole. That's simple enough to see for finite sets. Obvious, really. There are more examples than we could possibly name. The set of all dogs has more members than the set of all black dogs. The set of all knives has more members than the set of all butter knives.


Now how about infinite sets? The natural numbers - the counting numbers - is infinite. 1, 2, 3, 4, 5,... Let me know when you're finished.

But what if we only look at every other number. 2, 4, 6, 8, 10,... Once again, it's infinite.

You could count forever, and never get to the end of either set. Each has an infinite number of members. The set of counting numbers does not have more members than the set of even numbers.

hmmm....

[Nathan]

Glad to be of assistance

[Fist and Faith]

OK Avatar, let's see what's up with math. (Wanna play, CJ? ) Let's start at the very beginning, and see where it leads/where your distrust, or discomfort, or whatever it is, lies.

So if you have a chair, and you get another chair, you now have two chairs. Difficult to disagree with that. Is the problem that you don't feel confident removing actual objects from the picture, and having numbers that don't represent anything? (There are mathematicians who actually disdain mathematics that have practical applications! ) Do you maybe think we cannot know that 1 plus 1 always equals 2?

Or is the problem much further along, past addition, subtraction, multiplication, and division?

[Avatar]

Much further along than what I'll call arithmetic rather than mathematics.

I'm perfectly comfortable with the fact that 1+1=2, and that it always will. Afterall, these numbers are simply place-holders for any given object, whether it's apples or nuclear submarines.

I'm pretty comfortable with geometry and even simple algebra as well. At least as far as if 1+x=20, then x must = 19. That's straightforward enough, x is simply the unknown in the equation, which can be deduced by simple logic, (or trial and error. )

I can survive statistics too, which gives me a handle on probability, (Stats A was a required subject at Varsity for me, (and the only one that I ever struggled with (my own lazy-ass fault) but I passed it eventually. )

Even there, the expressions of the formula are simply placeholders for variables which we can determine, right? Like those old "triangular" formulae which I can't reproduce here, with the representation of, say, force in the top, and time and speed say, at the bottom, where one is the sum of the others, and therefore, a different one must be the product of the remainder, etc. (Yes, I know, those example don't work out, but you know what I'm talking abot, right?)

I can "see" how all those work on the whole.

It's when we get into the "pure" mathematics that I lose all coherence. Where a mathematical proof of something serves to underscore an observed event/whatever.

When it comes to these more complex expressions, the way it looks to me is that the person has taken an observed event, (say gravity, although even that is probably too simple to really count here) and then played with numbers until he gets an answer that matches what he's observed.

In other words, they start with an answer, and then reverse engineer it so that the equation comes out to that answer.

(I'm not sure if this makes it easier to understand my problems with math, but let's see what happens. At least it's a starting point so you can point out any misconceptions I may be under. )

Don't get me wrong, I find it very interesting. But like statistics, I think the answers seem not only inferential, but easily manipulable.

--A

[Fist and Faith]

OK, I see what you mean. Yeah, they might originally come up with some weird math in the way you're talking about. The thing is, like a scientific theory, that math has to stand up to scrutiny. Remember Zen and the Art of Motorcycle Maintenance:

"Well, it's quite a bootstrap operation. It's analogous to the kind of hang-up Sir Isaac Newton had when he wanted to solve the problems of instantaneous rates of change. It was unreasonable in his time to think of anything changing within a zero amount of time. Yet it's almost necessary mathematically to work with other zero quantities, such as points in space and time that no one thought were unreasonable at all, although there was no real difference. So what Newton did was say, in effect, 'We're going to presume there's such a thing as instantaneous change, and see if we can find ways of determining what it is in various applications.' The result of this presumption is the branch of mathematics known as the calculus, which every engineer uses today. Newton invented a new form of reason..."

I don't really know, but I assume that's how calculus got its start. And even if not, the principle is: If the newly invented math doesn't stand up the next time its needed, it has to be thrown out, or refined. Either Newton got it all right the first time around and his math held in all following times of need, or it was corrected and refined through the years.

Meh?

[Avatar]

I must read that again. Been far too long.

So you're not disagreeing with me then. Math is simply another way of describing it. It's no more real than words, just more detailed?

The very fact that it may not stand up illustrates what is, for me, the illusory nature of mathematics. It is, at best, a detailed description of some event/whatever.

It's an explanation that depends on current understanding, and even the "imagination" of how current understanding will change. It is, is essence, a science of assumption. Newton assumed that change could be instant.

His theory therefore is based on something he couldn't prove, show, or demonstrate. Fair enough, like any science, (and this is what I love about science), it's prepared to be wrong. But math is rarely (if ever) presented as such.

If something can be proved mathematically, it's assumed proved. Not, "proved pending better information" or a better understanding, or proved pending later data doesn't show that we've been making a fundamental mistake.

It's simply that I don't see it as the rock-solid "proof" of anything that it's usually touted as.

--A

[Fist and Faith]

Yes, I agree with all you said. As I recently said somewhere, there are mathematicians who don't like math that has practical applications. But even their math must at least follow the rules of mathematics. They may go into areas that, since they don't have any bearing on the real world, are more entertainment (and I find such things as entertaining as any other intellectual exercises) than anything else, but they still have to follow math's axioms, and all that jazz.

My high school physics teacher said, "Don't say this to a mathemetician, but math is just a tool for science." No scientific theory will be given any consideration at all if the math is not done correctly. Can you imagine:
"I've proven the existence of dark matter!!"
"But in your third equation, 1 plus 1 equals 3."
"Yes... Well... I had to do that, or I couldn't prove dark matter exists."

So does dark matter exist? Well, there are observable facts that suggest something we can't directly detect exists. The math is checked over and over, and it seems that bodies should be moving at speeds, and in directions, other than they are. No, that math doesn't prove dark matter's existence, but it gives us reason to develop the theory. And the math must hold up, or that theory is wrong.

[Avatar]

Damn, that was a short debate. Fun though, and it's given me a better way of looking at the way I've been thinking about it at least.

Math, it seems, doesn't prove anything. But it's good for working out if I can afford something or not.

Still, for all my complaints, anything that gives us another way of looking at the world is a good thing, as far as I'm concerned. And not being mathematically inclined, that's about the best description of math that I can give.

--A

[ur-bane]

OK. I may as well ask this here. Fist, you would probobly know.
It doesn't really have anything to do with the topic other than it is math related (with a bit of philosophy sprinkled on.) But I am interested in the term itself.

I cannot for the life of me remember the word for describing questions like "How many Angels can you fit on the head of a pin." Those types of unverifiable questions where one aspect can be measured (the pinhead) and another canot (how big is an angel?) have a specific name....do you remember what it is (I think it starts with the letter "c"....but I am not sure.)

I wanted to use the word in a response elsewere, but I couldn't remember it.

[Fist and Faith]

Hmm, that is a conundrum, ur-bane. I'll think about it for a while. Maybe I'll figure it out.

...anything that gives us another way of looking at the world is a good thing, as far as I'm concerned. And not being mathematically inclined, that's about the best description of math that I can give.

Sure! J.S. Bach looked at the world his way, Picasso his way, Einstein his way. Mathematicians see reality as numerical relationships between everything. All are correct, for each viewer. Here's Jung.

The only things we experience immediately are the contents of consciousness. In saying this I am not attempting to reduce the “world” to our “idea” of it. What I am trying to emphasize could be expressed from another point of view by saying: Life is a function of the carbon atom. This analogy reveals the limitations of the specialist point of view, to which I succumb as soon as I attempt to say anything explanatory about the world, or even a part of it.

[Avatar]

Always quite liked Jung.

And as you know, I too subscribe to the idea that, to the viewer, his specific view is always correct.

--A

[Zarathustra]

Avatar, I think your view of math is incorrect. It is not always the case that the world is viewed first, and then reverse engineered to find the mathematical formula that describes it. Sometimes mathematicians discover things in their equations that don't fit their expectations, and it is only after a new observation of the world that they understand what their equations were telling them to begin with. The expansion of the universe. The existence of anti-matter. Fractal nature of physical phenomena. These things were "discovered" first as purely mathematical oddities, and it was only later that physicists realized that there were real features of reality that conformed to these mathematical patterns.

And often, the observation and the formula happen simultaneously, as with Galileo discovering the way falling objects accelerate. He timed falling (actually rolling) objects and found that what we had been observing for millenia--falling objects--were not moving the way we had assumed. It was only when he measured this motion that it was truly observed in its true form. Something that happens right under our nose--so to speak--is not actually SEEN as it really exists until it is seen through the lense of numerical interpretation. The non-numerical interpretation was the illusion, not the measured, formulated interpretation. So it is a false assumption to think we see the world the way it really is, and then apply an artificial formula to describe it. Math is, in a sense, MORE real than the world of phenomena. It is a transcendental truth, a truth that transcends subjectivity and individual observations.

[Avatar]

Although I see what you're saying, (and I note that you qualify it with "sometimes," which suggests that both views can be correct at different times), I'm not exactly clear on your reasoning.

How do you find something in your equation that you didn't expect, unless it is in the sense that although the equation looks right, it is still not explaining it?

Take the fractal nature of physical phenomena -- how does an equation tell us that things are fractal? Surely only the failure of an equation to describe something accurately can lead to the formation of a new formula that does seem to describe things better?

(I freely admit of course, that I know next to nothing about math, so I may well be missing or ignorant of, something obvious. I'm not saying you're wrong, I'm saying I don't understand. )

For example, Galileo and the speed of falling objects: It was assumed that objects fell at different speeds, right? So he came up with a test to measure those speeds -- but the formula was based on the observation or at least, the assumption, that the speed was not uniform. Applying it though, showed that despite the assumption, it still wasn't working out, so had to be reconsidered. (Of course, I may be totally wrong, in which case, please don't hesitate to disabuse me. Maybe you'll get a convert. )

--A

[Zarathustra]

Av, you are right to note my qualifier. This is an issue that is up for debate. I'm not sure that anyone knows just exactly why the universe is so aptly described with numbers and equations. But even if it's just one hell of a coincidence, it's still one HELL of a coincidence! Since no one knows for sure, I guess I was just trying to knock you out of your dogmatic way of thinking about it.

I used to know the historical examples much better, but without doing any research to refresh my memory, I'll try to explain them. With the antimatter example, physicists found than their equations came down to both a positive solution and a negative solution. The math was right, but they couldn't make sense of the fact that a negative solution would occur simultaneously with the positive solution. This led them to postulate a negative particle that at the time had never even been imagined. A little bit of exploration, and presto! we discovered antimatter.

With the expansion of the universe example, Einstein realized that one of his equations didn't make sense unless you assumed that the universe was expanding. Since no one suspected such a fact, he inserted an *ad hoc* "cosmological constant" into the equation so it would make sense. But then when Hubble discovered the expansion of the universe, Einstein quickly removed the cosmological constant and said it was one of his worst blunders.

Fractals were discovered as purely mathematical oddities. They were just toys mathematicans played with, with no practical applications. Then people started realizing that coast lines and snowflakes and millions of other things followed the patterns of these equations.

It's as if the math already, always existed as a realm to discover, rather than something we invent after the fact to fit our observations. So "reverse engineering," as you put it, may happen sometimes or even most of the time. But this still doesn't explain why the world can be reverse engineered in the first place. Why do physical structures so easily and prolifically conform to non-physical, immaterial patterns of pure abstraction? What is the link between these two seemingly disparate realms?