View Full Version : Important Numbers

mroulston@yahoo.com

2007-Sep-05, 10:02 AM

After listening to the pod-cast, Important numbers in the universe, It lead me to think ,Are mathematical equations Universal or have they been invented by us? If we run the numbers you can land a rover on mars, its very complicated but it works. The important numbers in the universe look so random yet they are so precise. If they were off by more than 1% we would not be here to think about it! I wonder can we do the maths in Roman numerals or on an abacus? Would those numbers look better if we only had 7 digits to work with or do we need 14 or 25 Digits. Who says 10 Digits are right to do the maths. Hope you get my drift. Our solar system is just right for us. It seems the whole Universe is just right to....

astromark

2007-Sep-05, 10:27 AM

Your interesting point has been touched on by the late Douglas Adams in the trilogy of books "The Hitchhikers Guide to the Universe" Where he suggests that 5x7 is in fact 42. Making the numeric system that humanity has used was wrong...and always has been.

The fact is that the universe does not care what we might call the velocity of C. It is set. At whatever your scale tels you it is. Just because the species of beings that dwell on the surface of the third planet in the Sol system have given a name or number to everything they observe. Does not restrict the number of other possibilities.

Nowhere Man

2007-Sep-05, 12:23 PM

6 times 9, actually. Which does equal 42 in base 13. Which Adams claimed was a coincidence.

You can use whatever number base you want to do the maths. We use base 10, computers use base 2. You can do it in Roman numerals if you're insane enough. The answers are equivalent.

Fred

a1call

2007-Sep-05, 01:53 PM

Mathematics is the true universal language. I believe the SETI project is/was sending prime numbers in sequence to indicate intelligence on Earth. Prime numbers are only divisible by one and themselves in any numeric base and that holds true, through out the Universe.

Saluki

2007-Sep-05, 02:04 PM

After listening to the pod-cast, Important numbers in the universe, It lead me to think ,Are mathematical equations Universal or have they been invented by us? If we run the numbers you can land a rover on mars, its very complicated but it works. The important numbers in the universe look so random yet they are so precise. If they were off by more than 1% we would not be here to think about it! I wonder can we do the maths in Roman numerals or on an abacus? Would those numbers look better if we only had 7 digits to work with or do we need 14 or 25 Digits. Who says 10 Digits are right to do the maths. Hope you get my drift. Our solar system is just right for us. It seems the whole Universe is just right to....

As others have indicated, the actual physical representations of the various universal constants are simply a matter of man's convienience. We select units like meters and kilograms and seconds that represent convienient bundles of whatever quantity we are measuring, and end up with a number that represents the universal constant. We can measure and calculate these universal constants as precisely as necessary for the purpose at hand. Sometimes, 3.14 is an adequate representation of pi, but other times, 3.1415926535897932384626433832795 is not nearly accurate enough. It all depends on the application.

The equations themselves are universal. With a few notable exceptions (temperature usually must be in an absolute scale, and angular measurements are usually required to be in radians), it doesn't matter what units we select. As long as our units are consistant within the equation, we will get numbers that make sense.

An alien race studying the universe would come up with the same constants and equations, but might use quite different units. So, the numerical representations of the constants might be different, but would be easily convertable to our unit systems once conversions were figured out.

Ken G

2007-Sep-05, 02:30 PM

After listening to the pod-cast, Important numbers in the universe, It lead me to think ,Are mathematical equations Universal or have they been invented by us?

I have a different spin on that question that what we've seen so far. I view this is a very deep and very difficult question to answer, that gets right to the heart of what physics is all about. Physics is a search for unifying principles, but these principles require idealizations that are never exactly in play, so they are approximations. As such, all the equations of physics are approximations. Even purely mathematical expressions, like circumference = diameter times pi, become approximate when applied to physics (because of local gravity, this expression is more about the assumed coordinate system, and would require an awkward treatment of time to make that exactly right). And equations like Newton's laws may break down at high speed or on small enough size scales. Physics is pieced together like a tapestry. The numbers come out after you have defined your idealizations and made your equations.

Having said that, it certainly seems like physics is based in something universal, because it works so well. But I don't think that guarantees that advanced alien civilizations would have a physics that would be terribly recognizable to us. There may be alternative ways to look at things that have entirely different principles and use different idealizations, yet are largely equivalent at the end of the day because they have to work as well as ours does, for what it works at. Still, I think it behooves us to bear in mind the potential gap between how we picture reality, and how reality "really is". We don't know a lot about that gap, we can only look at how much our pictures have changed over history. Why would we not expect that trend to continue? And perhaps the only reason we have not seen even more change is that we are coming against the limits of our intellect.

Cougar

2007-Sep-05, 03:09 PM

...we can only look at how much our pictures have changed over history. Why would we not expect that trend to continue? And perhaps the only reason we have not seen even more change is that we are coming against the limits of our intellect.

You are such a pessimist, Ken! It seems so much more likely that fundamental changes and insights are "slowing" because our "approximations" are already close and getting closer to the reality of the situation. When we cut up the area under a curve into thinner and thinner rectangles and add up their areas, we get a good approximation. When we use calculus and approach the appropriate limit, is that just a better approximation, or is it an exact answer?

Physics is a search for unifying principles, but these principles require idealizations that are never exactly in play...

Isn't that the fault of our inexact observation or measurement rather than the phenomenon itself?

Ken G

2007-Sep-05, 05:51 PM

You are such a pessimist, Ken!And like any pessimist, I call it realism! But seriously, I actually think this is the optimistic view-- if there is still much that is a mystery, and will always be a mystery, then it leaves us much more elbow room to believe things are "really" more the way we'd like them to be. Or did that optimistic remark come out pessimistic too somehow?

It seems so much more likely that fundamental changes and insights are "slowing" because our "approximations" are already close and getting closer to the reality of the situation.But that is only true in certain areas. I think of doing physics like eating-- you bite off a piece, and chew and chew, and swallow and digest, and pretty soon you have broken that food down to its basic molecules, you've really reduced it to something fundamental. But what about all that food still on your plate? Were your "eyes too big for your stomach"?

Isn't that the fault of our inexact observation or measurement rather than the phenomenon itself?

The idealizations are not just in terms of our measurements, they are in the reality itself. Physics is all about replacing reality with something simpler (just look at the problems at the end of the chapters of any physics book if you don't believe me), but that also means something different. The differences may or may not matter to us, depending on the application, but they are always there, and always will be. If it's just a matter of precision, it's not that big of a deal, but remember we always have to project reality onto the kinds of questions we can get objective answers to-- and that may be the most violent idealization of all.

hhEb09'1

2007-Sep-06, 10:15 AM

You are such a pessimist, Ken! It seems so much more likely that fundamental changes and insights are "slowing" because our "approximations" are already close and getting closer to the reality of the situation. When we cut up the area under a curve into thinner and thinner rectangles and add up their areas, we get a good approximation. When we use calculus and approach the appropriate limit, is that just a better approximation, or is it an exact answer?And, what if our knowledge was represented by the integral of 1/t, with t starting at 1 and progressing to infinity? The rate of increase of knowledge would continually decrease, but the knowledge left (unknown) would always be infinite.

mroulston@yahoo.com

2007-Sep-06, 12:15 PM

Thanks for all your interesting replies so far. This discussion has to lead to other intelligence in the universe and what we perceive as reality. If we are not here to observe it does anything really matter at all. I guess this line of thought can not really be answered by Astronomy

Cougar

2007-Sep-06, 03:05 PM

And like any pessimist, I call it realism!

:lol:

I think of doing physics like eating-- you bite off a piece, and chew and chew, and swallow and digest, and pretty soon you have broken that food down to its basic molecules, you've really reduced it to something fundamental. But what about all that food still on your plate? Were your "eyes too big for your stomach"?

I'm feeling nauseous.

Just joking. What's the main course? :razz:

Ken G

2007-Sep-06, 06:57 PM

I don't know, but if there is a lot of detailed general relativity it's spinach, and if it involves Feynman diagrams it's Brussels sprouts!

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