Order of Kilopi
No one said math has all the answers. You are still arguing against a straw man.Originally Posted by dusthurricane
Without quantitative analysis, how can your theory be proved correct?Yes , this is a theory. Please do not ask for quantitive analysis ? Observation will prove me correct or the contrary.
On the other hand, simple observations appear to show it to be trivially false.
Member
I think the episode Dusthurricane is referring to is "What Happened Before the Big Bang", which was broadcast last year in the UK (not sure about other countries). It discussed the causes and origins of the big bang with a large selection of "luminaries" from the world of physics, cosmology, astrophysics, etc. etc.
However, there was a great deal of mathematics in evidence, and if any reference was made to needing new ideas, it was along the lines of "current mathematics isn't enough to answer these questions, and we may need some new approaches" - not that mathematics was irrelevant.
The programme included a visit to something called "The Perimiter Institute" (which I hadn't heard of before) where a number of theoreticians were trying to better understand the big bang, some of them coming to the conclusion that perhaps there was no such thing - but that's another debateIt maybe seemed like a large collection of people, all eagerly working on the problem, but I'd reckon probably no more than 20 - 30 were actually there. (I'm also just home from ESTEC in Holland - now that is like a small town dedicated to science!!)
Horizon has gone through cycles of good and poor quality science reporting, sometimes highly technical, sometimes overly simplistic and "popularisational". Currently it seems to be on an upswing and most of the recent episodes have been pretty good - the above mentioned one included.
I think the OP may have misinterpreted what was said in this particular programme, as it certainly, from my recollection, didn't even look at non-mathematical approaches to understanding the universe.
Established Member
I think the limitation of Math is the existence of "infinities". But the other meaning of it (the symbol of infinity) is 'undefined'. Could it be that why infinities occur in equations is because our knowledge is indeed limited? How about infinitely small? Does it mean there's no such thing as a "zero size"?
Moderator
For some reason, this morning, I found that funny on at least three different levels.
Order of Kilopi
For some reason, this morning, I found that funny on at least three different levels.,
and
?
Last edited by caveman1917; 2012-May-26 at 05:07 PM. Reason: english, not dutch, even if only for a single word :)
Established Member
May I know what that reasons, if you may?For some reason, this morning, I found that funny on at least three different levels.
Order of Kilopi
One of them is, I believe, the idea of "infinities" as a "limitation." I know (and I'm sure grapes knew) that you didn't mean it that way, but it's still an interesting phrasing.
As above, so below
Order of Kilopi
Another reason may be the interesting question of whether infinities "exist." I can't think of a third one.
Also interesting thing (going back to the thread topic) that to make the point, grapes used the very mathematical concepts of "three" and "at least." I suspect it would be difficult to express these ideas without math.
As above, so below
Order of Kilopi
Zero is the opposite of infinity. Saying "infinitely small" is like saying "infinitely large" the first is just "Zero" the second is just "infinite"
Established Member
Surely infinitesimal means infinitely small, zero means it has no size. The dx in basic integration is a good example, it means an infinitely small step (but not one that is zero).
Established Member
Infinitesimals are avoided in standard analysis by using limits.
Order of Kilopi
The fact that mathematics formally defines infinity (infinities) and therefore this cannot be a limitation of mathematics?
Established Member
This is just my opinion (I don't making any new theory) - zero can exist as a point of reference, but to think a 'zero size' is unachievable, in a sense that it is only "an idea"- like infinities, as some thing which give us or lead us to a mathematical limitation, that, we cannot truly define (reason why sometimes we call the sign of infinity as "undefined"). Possibly, the reason why early philosophers like Aristotle believe that matter is composed of infinitely small particles is what our world (or universe), really is - no end to discovering things in a box within boxes...
Established Member
I agree that mathematics is indeed important. But maybe, the interpretation of how we observe the Universe through "mathematical analysis" (integration, differential math or what so ever) is still lacking or the approach is a bit off track. But I believe, one day we can solve it. with the help of computers
Established Member
The basic principles of computers come from mathematics. You start with something like Boolean logic (a branch in maths), and work your way up from there. Whether your hardware solution uses semiconductors or one-bead abacuses and a person flipping through the instructed maneuvers doesn't really matter.
Established Member
Indeed, but that was not my point. My point was a size of zero is not infinitely small - it is zero sized. Something infinitely small has an infinitesimal size.
Established Member
Although it is possible to build a consistent axiomatic development of infinitesimals, such a theory is non-standard. Calculus as we have it does not require the concept of an infinitely small quantity, and is based on the well defined real numbers.
The reals form an Archimedean field. Briefly, for any real number d greater than 0, there exists an integer n such that nd is greater than 1.
Whether or not non-standard analysis adds anything to applicable mathematics, I believe that it remains the case that all the mathematics applied in astronomy remains firmly within the structure of standard analysis.
I will admit that there are posters to BAUT who disagree with me.
Established Member
I don't know if you agree with me when I say:
"You can draw a perfect circle but never can measure it (that circle), perfectly"
Why I said that? It is possible to draw a circle with a compass with a given exact measure of radius (example, let radius = 1 centimeter) but its circumference will never be an exact measurement because
pi = 3.141592653589793238462643383279502884197169399375 10582097494459230781640628620899862803482534211706 7...
Reason why I believe math has limitation and agree that any science can be described 'even' without math.
Established Member
No offense... just like to know how large is an infinitely large?
Order of Kilopi
Infinitely. Of no finite size.
How exactly is being able to handle the concept of unbounded, unlimited values a limitation?
Order of Kilopi
That is irrelevant. The accuracy with which we can measure the circumference of a circle has got nothing to do with the nature of Pi.
I can just as accurately say: "You can draw a perfect square but never can measure that square perfectly"
If you draw a square with a side of 1cm, you can measure its perimeter just as accurately as you can measure the circumference of the circle. Remember, the perimeter is: 4.000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 000000...
Not 4.000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 000010...
Also, you can't make the radius "exactly" 1cm any more than you can measure the circumference exactly.
So this isn't a limitation of math (quite the reverse: mathematics tells us exactly what the circumference is) it is a limitation of our measuring tools.
I don't know how any science can usefully be described without math. Let's try a simple example:Reason why I believe math has limitation and agree that any science can be described 'even' without math.
Q1: If a stone of unknown weight falls from a building of unknown height, what speed will it be travelling when it hits the ground?
A: Unknown. (What is "weight"? What is "height"? What is "speed"?)
Q2: Is the weight of the stone relevant to the answer to Q1?
A: Unknown.
Q3: Is the height of the building relevant to the answer to Q1?
A: Unknown.
Not very useful, is it?
Established Member
Sorry to say but I don't agree with you in this case. In measuring a "square", it could be an excuse that it is due to limitation of a measuring tool but not a circumference of a circle where a "pi" is a non- ending or a non-terminating value.
Sorry if you misinterpreted me. I said is, "any science can be described 'even' without math". I didn't mean to say that "math is not important". As a tool, it DOES NEEDED. But mere describing a certain phenomenon w/out the strict mathematical accuracy is still ACCEPTABLE. How come early people know when to plant and when to harvest their crop w/out the accurate details that we know now-a-days because of modern science. I think if for mere investigating the accuracy of a certain event, MATH IS INDEED IMPORTANT. There's no disagreement to that.
Order of Kilopi
Why is that relevant? We know exactly what the circumference of a circle with diameter of 1cm is.
In fact, how is pi different from 4.000... in that respect?
And what about 1/3? Does that have the same problem?
Are you confusing the notation used with the accuracy with which we can know something?
Moderator
Naturally it is completely possible to make a circle with exactly a circumference of 4, one takes a strip of paper of length 4 and rolls it into a circle, no problem whatsoever.
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Order of Kilopi
The nonterminating decimal nature is purely an artifact of decimal representation. In base pi, a circle with a diameter of 1pi will have a circumference of 10pi. And a circle can just as easily have an integer circumference in whatever units you're using. This has nothing whatsoever to do with measurement. And given that pi can be expressed exactly, regardless of number system, as "pi" (or if you like, "π"), what exactly is the problem?
Um, it's likely that calendar systems for timing crop plantings were one of the earliest uses of mathematics.
Established Member
I don't intend to make an argument about how to create a circle or make a circle out of a given measurement. It is true that in any measurement, there is what we call 'clearance' or tolerance of error, which even in engineering , is, indeed acceptable.. I'll just go back to my 'philosophical' phrasing that it is true, we can draw a perfect circle but the mere fact that radical numbers do exist that it is impossible to make the 'exact' measure of it. We always accurately measure it nearest 'approximation' but we could never really know the exactness of it. Such as 1/3 = 0.333333 that if we multiply it by 3, that is 3 x 0.333333 = 0.9999999 or approximately 1 but never exactly equal to 1
Order of Kilopi
All computers do is maths, very very quickly.
Established Member
This is a science board, not a philosophy board.
Established Member
Better yet: Draw a circle, and arbitrarily declare that its circumference is exactly 4. In hipster units, which are very obscure and you've probably never heard of them.
Fred
"For shame, gentlemen, pack your evidence a little better against another time."
-- John Dryden, "The Vindication of The Duke of Guise" 1684
Order of Kilopi
30 days = ATM thread closed, but for the sake of mainstream science and math I need to point out that 1/3 = 0.3... and 3 x 0.3... = 0.9... which equals (not approximates) 1.
Get up, a get-get, get down.
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