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Show ALL Forums  > Science/philosophy  > I could use a good mathematician here...      Home login  
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 scorpiomover
Joined: 4/19/2007
Msg: 3
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I could use a good mathematician here...Page 1 of 2    (1, 2)

Whilst I understand the checks and balances he's speaking of, I get lost at why he says "Euclidian or other practical measuring systems". I get the gist of it, but why specifically Euclidian and what other measuring systems may he be speaking of?
He's talking about Euclidean geometry which is the basis of Newtonian gravity, as opposed to non-Euclidean geometry, which is the basis for Einsteinian relativity.

The type of geometry you use, affects how you measure things, because geometry is the study of shapes and sizes of objects, and so different geometries have different measurements of their shapes and sizes, for the same objects. So a circle in Euclidean geometry would have a different area than a circle in non-Euclidean geometry.

From what I remember, Euclidean vs non-Euclidean geometries have different metrics, ways of measuring the distance between 2 points, which are the basis of all of the differences. So you could say that they have different "measuring systems". To read more, see here:

http://en.wikipedia.org/wiki/Euclidean_geometry

But usually, when you say "different measuring systems", most people think of litres vs pints, or cms vs inches, and different geometries are much more different than which ruler you use. So most of us wouldn't say that.

However, in TNG, they like to make out that the future is far more advanced, and that everyone is much more knowledgeable than us. But the writers usually stuck to using most scientific theory that was currently accepted at the time, to make it more palatable to the general public, rather than have really outstanding ideas that scientifically creative types would love, but that would alienate the rest of the viewing public, who find wholly new ideas very disturbing.

So they took an existing idea, that of Newtonian vs Einsteinian physics, which is known to parallel Euclidean vs non-Euclidean geometry, and give it another name to make Picard sound much smarter than us, without giving him an idea that goes right over our heads.

FYI, on the dimensional front, back in the mid-90s, a friend of mine in uni told me that some versions of string theory included as many as 26 dimensions. I think that was along the lines of what they referring to.
 scorpiomover
Joined: 4/19/2007
Msg: 5
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I could use a good mathematician here...
Posted: 6/19/2009 6:01:32 AM

Thank you very much, scorp. So I'm guessing what he's really saying is that regardless of how we measure it, the reality of our existence superscedes anything that we understand in any practical way. I do understand the difference in measuring things in a Newtonian vs. Relativity sort of way. I just had a hard time wrapping my head around what he was saying. It's odd how the simplest things can confuse us sometimes. Thank you again.
You're welcome.

I think what Picard was alluding to, was just that we thought the universe was Euclidean, and now we think it isn't, that we can never really know what reality really is. We just get more understanding of it. But we never really know what it is, and there will always be more within reality than we really understand.
 2hi-iq-4u
Joined: 5/29/2009
Msg: 7
I could use a good mathematician here...
Posted: 6/19/2009 11:19:42 AM
Euclidian geometry assumes 3 dimensions, and for all practical purposes; doesn't even encompass time as a fourth. An object is measured in height, depth, and width, and movement across space over time hardly enters the equation. Everything moves. We are moving at about 1000 miles an hour without leaving our desks if one considers only the rotation of the earth. When you consider the movement of the earth around the sun, we are moving even faster. 93 million miles times 2 pi per year. Figure it out in miles per hour.

The entire solar system orbits the black hole at 220 km per second.

Funny, I don't feel like I am moving. Is there a brake pedal? Who is driving, anyway? At this speed, I hope we don't collide with anything.
 Mister Logic
Joined: 3/5/2009
Msg: 8
I could use a good mathematician here...
Posted: 6/19/2009 1:25:14 PM
Start at the North pole. Head due South in a straight line for 100 miles.

What if you start at the North pole and try to head due North?

It's a bit redundant to say "Head due south". Every way is south.
 Twill348
Joined: 12/20/2008
Msg: 9
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I could use a good mathematician here...
Posted: 6/19/2009 2:34:26 PM
"And as an addendum, speaking of dimensions, how many are there beyond the obvious 4"

What is a dimension? If you can define that, then perhaps the question can be answered.

There are qualites, realities, of existence, that some have labled as "dimensions". But those are concepts, not realities. The word dimension is a description, it is not the being, the totality. Hence, I would posit it to be a meaningless question, in this context.

In other words, please show me the beach ball that is missing a dimension.

Also, people often confuse "dimension" with a row of data in a database.
 Twill348
Joined: 12/20/2008
Msg: 10
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I could use a good mathematician here...
Posted: 6/19/2009 2:40:29 PM
"Start at the North pole. Head due South in a straight line for 100 miles. Make a right turn 90 degrees. Continue for 100 mile and make a right turn 90 degrees. You should now be heading north for 100 miles to a place where you originated from. You just made a triangle with more than 180 degrees in it. "

Not an expert, but I don't think thats right. It depends on how you define "triangle".
 Mister Logic
Joined: 3/5/2009
Msg: 11
I could use a good mathematician here...
Posted: 6/19/2009 3:28:12 PM
What is a dimension?

A "dimension" is not necessarily limited to being a "spatial" entity. "Dimensions" can refer to any set of linearly indepent parameters of a system.

For example, a given location in the earth's atmosphere can have (in addition to x, y, and z coordinates) attributes of temperature, chemical composition, air pressure, etc. Each of these parameters represents a component of the "state" of the system as a whole. (I.e., they are the "dimensions" that specify a particular instance of the "atmosphere".)
 NotGorshkovAgain
Joined: 4/29/2009
Msg: 12
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I could use a good mathematician here...
Posted: 6/19/2009 5:44:48 PM

:
Start at the North pole. Head due South in a straight line for 100 miles.

What if you start at the North pole and try to head due North?

It's a bit redundant to say "Head due south". Every way is south.

Depends on which north you're at, and which one you're measureing from.

I've spent over a year in Alert, NWT, just over 420 miles south of the north pole. MAGNETIC north was over 800 miles south-southeast - compass correction was something over around 120 degrees or something like that - it was a long time ago, but it made using map and compass VERY confusing :-)
 Mister Logic
Joined: 3/5/2009
Msg: 13
I could use a good mathematician here...
Posted: 6/20/2009 12:20:35 PM

Start at any point say Times Square for example, head due North 100 miles, then turn face due West and travel 100 miles, again turn face due South and travel 100 miles. At each point you turn you can make a cross in the road and turn 90 degrees...You will end up back where you started in Times Square...

Uh... not quite! If you travel on three 100-mile segments, you will end up a little more than 100 miles west of Times Square. And even if you make a fourth turn and then travel 100 miles East, you will still fall slightly short of where you started (Times Square), because the "Southern" leg of the spherical rectangle is slightly longer than the "Northern" leg.
 Mister Logic
Joined: 3/5/2009
Msg: 14
I could use a good mathematician here...
Posted: 6/20/2009 2:36:59 PM
If after turning west, you continue always traveling west, you will not be travelling on a great circle of the earth. Instead you will be travelling on a constant latitude line. Then, when you later turn south and travel south along a longitude line (which is a great circle) to reach a different latitude, you will then have to travel east more than 100 miles in order to reach your initial starting point (because, in the northern hemisphere, lines of longitude get farther apart as you travel south). It's all very elementary spherical geometry. (If you're having trouble understanding it, just look at a globe of the earth. )
 Mister Logic
Joined: 3/5/2009
Msg: 15
I could use a good mathematician here...
Posted: 6/20/2009 7:17:20 PM

...starting at point x and travelling a distance (a) on a sphere making a 90 degree turn, travelling any distance (b) then making another turn 90 degrees and travelling distance (a) will bring you back to x where you began..

Yes, I have no disagreement with this new statement that you just made. But, that's not what you initially said!(Go back and reread your original post. )
 Mister Logic
Joined: 3/5/2009
Msg: 17
I could use a good mathematician here...
Posted: 6/21/2009 9:37:37 PM

... That's clearly not understanding what spherical geometry is all about.

The real problem that we seem to be having in our discussion here is not a lack of proper understanding of spherical geometry on either of our parts (at least, not on my part... my professional education is in physics and astronomy). No, the real problem seems to be in your use of the English language (which is somewhat surprising... seeing as you live in the UK! )

For example, as part of your post #17 you first said: "...head due North 100 miles, then turn face due West and travel 100 miles." From your wording, it wasn't clear whether you were saying to follow a great circle of the earth (in which case you would not be heading due west at every point of that 100 mile leg. Or were you saying to head west and continue heading due west at every point (in which case you would be travelling along a line of constant latitude)?

Next, you said: "...turn face due South and travel 100 miles." Ok, so now you've just travelled due south for 100 miles. But then, you immediately contradicted yourself in your very next sentence by saying: "At each point you turn you can make a cross in the road and turn 90 degrees". Er... Um... please make up your mind! Are you travelling due south (like you originally claimed)? Or did you now change your mind and decide to use the 90 degree vector pointing toward the south-east instead? You can't have it both ways!

I'm sure that you knew what you meant to say, but what you did say was quite confusing! If you could have presented your example a little more consistently (and less ambiguously) by using the the proper wording, we would not have had to engage in any of this nit-picky discussion.
 Mister Logic
Joined: 3/5/2009
Msg: 18
I could use a good mathematician here...
Posted: 6/21/2009 10:41:26 PM
Continued...

The spherical triangle that you were trying to create (by going north 100, then west 100, and then south 100) will only work if you start at the south pole of the earth. It will not work from Times Square, since the three "legs" from there don't even close to form a triangle. And as for your comment to me:

Go here for a basic maths lesson

http://en.wikipedia.org/wiki/Non-Euclidean_geometry

and then come back here with the correct answer.

Let this be a lesson to you... Be careful about merely glancing at pictures in Wikipedia's article on "Non-Euclidean geometry", and then drawing false conclusions by not properly understanding what you see.
 Mister Logic
Joined: 3/5/2009
Msg: 19
I could use a good mathematician here...
Posted: 6/22/2009 9:50:46 AM

...however as we have started at times square and turned left on a non-Euclidean plane the pole (new North pole) is now at times square...

The new North pole is now at times square??? I didn't know that the earth had more than one geographic north pole!

Your comments are starting to become just a little bit too silly for me, so I'm afraid that I am going to have to bow out of this comedy routine of yours. (And it appears that I must also retract my concession about you having a proper understanding of spherical geometry.)

Perhaps other members of this forum will be able to help you out. Or you might go and actually read about spherical coordinates and analytic geometry (instead of merely looking at the "pretty" pictures on a Wikipedia webpage and not properly understanding them).

Bye
 Mister Logic
Joined: 3/5/2009
Msg: 20
I could use a good mathematician here...
Posted: 6/22/2009 12:01:11 PM

Explain the significance of the poles on a sphere, isn’t every point on a sphere the same?

I don't think that any amount of "explanation" is ever going to convince you of your fallacious reasoning. So the best thing for you to do is... don't take my word for anything. Instead, simply go out and try it for yourself:

Pack a big lunch, and spend a few bucks (or "Pounds", or "Euros", or whatever) and hire a pilot to fly you north 100 miles, then west 100 miles, and then south 100 miles. Next, tell him to look for an open field somewhere and land the plane. Then, while you're eating your lunch, take out a pencil and send me a postcard saying: "HELP! I'm Lost!"

Yes, really do go on that journey. (Don't just do a "thought experiment" and "pretend" that you did.) Only then will you be truly convinced of your errors.

End of discussion.
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