Plan B Forum

This:

Let's think of 2 of these rays of light falling on a book you are reading (let's just consider 2 rays, one on one extremity of the book, the other on the other). The rays of light can be considered to form an isosceles triangle. One side of this triangle is about 6 inches long. The other 2 sides are 93 million miles long. Question - what are the internal angles of the triangle?

Any normal person with a reasonable understanding of maths would say "hmmm. Let's pretend that this 93 million miles is infinity." When you do that, the answer becomes 90 degrees, 90 degrees and 0 degrees.

and its progeny do not involve the mathematics of infinitudes.

"Pretend[ing] that this 93 million miles is infinity" is merely an obfuscatory way of saying "Let's round this off to the nearest decimal place" (at whatever the relevant decimal place may be in the circumstances). That does not involve infinity; it is nothing but arithmetic.

I'd hardly call "infinity" the "nearest decimal place" to 93,000,000.

Great to see you posting Grossdad!

Andrew D wrote:This:

Let's think of 2 of these rays of light falling on a book you are reading (let's just consider 2 rays, one on one extremity of the book, the other on the other). The rays of light can be considered to form an isosceles triangle. One side of this triangle is about 6 inches long. The other 2 sides are 93 million miles long. Question - what are the internal angles of the triangle?

Any normal person with a reasonable understanding of maths would say "hmmm. Let's pretend that this 93 million miles is infinity." When you do that, the answer becomes 90 degrees, 90 degrees and 0 degrees.

and its progeny do not involve the mathematics of infinitudes.

"Pretend[ing] that this 93 million miles is infinity" is merely an obfuscatory way of saying "Let's round this off to the nearest decimal place" (at whatever the relevant decimal place may be in the circumstances). That does not involve infinity; it is nothing but arithmetic.

The premise in the original quote was a failure at it's inception.

A Triangle is the product of line segments not rays...

Not to mention the fact that if you are estimating they length of the rays to be 'infinity' then they are parallel by definition and no triangle is created.

BTW Stoat you're up! IIRC it was you who had the audacity to disagree with Andrew on this one.

I myself was in total agreement with Andrew on this subject so I can stand on the sidelines and scoff at those who weren't.

They aren't parallel if they emit from a common point, which (I think) is how a triangle shape is being created.

it was you who had the audacity to disagree with Andrew on this one

Scooter wrote:They aren't parallel if they emit from a common point, which (I think) is how a triangle shape is being created.

Two 90 degree angles would indicate parallel...

Only because 2 arms of 93 million miles and a base of 6 inches is going to mean pretty much as close to 90, 90, and 0 degrees as you can get, but it isn't going to be exactly 90, 90, and 0

Two photons starting from the surface of the sun might have origins further apart, by quite a lot, than the diameter of the earth.

They would not form a triangle at all.

This is an uninteresting point from which to think about infinitude.

yrs,
rubato

Andrew D wrote:"...

"Pretend[ing] that this 93 million miles is infinity" is merely an obfuscatory way of saying "Let's round this off to the nearest decimal place" (at whatever the relevant decimal place may be in the circumstances). That does not involve infinity; it is nothing but arithmetic.

That is an exactly true statement. For a very rare case, you are correct.

yrs,
rubato

Scooter wrote:They aren't parallel if they emit from a common point, which (I think) is how a triangle shape is being created.

My point exactly. Scoot. Either they are parallel or thay are not. If they form a triangle they cannot, by definition, be parallel. If they are not parallel they cannot, by definition, both form 90 degree angles with the same straight line. The problem I have with the example given with the rays of light and the book is that they change from being non-parallel to being parallel midway through the example at a point which suits the author.

I would describe this as mathematical laziness.

Oh dear, this again. I don't currently have much time so I shall post this and might be able to read any replies, but won't try to explain it all again. This is my last post on this because it is getting pointless: in previous posts, when I have quoted subject matter experts, Andrew has simply responded with words along the lines of "they are wrong because they disagree with me". Thus I know that this post won't help - Andrew either cannot or will not understand (or both). But, for what it is worth ...

In the above text, the rays coming from the sun are not parallel. However, for most calculations they can be treated as parallel to make the calculations easier. When they are being treated as parallel, the only way this can happen is if the sun is assumed to be infinitely far away. Andrew, again, there is no such thing as infinity in reality - it is a mathematical abstraction used for these sort of calculations. If you can't get your head around that then why not just accept it? And if you can't accept it then just shout and bluster. I won't bother getting other physicists to cooperate this because Andrew will simply say they are wrong for having the temerity to disagree with him. The great Oz has spoken.

I'm in agreement with everything you have posted there Stoat. The only issue I have is with the description of the rays as being parallel and two sides of a triangle simultaneously. That's not making the calculations easier, that's avoiding calculation completely.

The formula for calculating the angles in an isosceles triangle once height and base are known is relatively simple trigonometry. Since both height and base are known in this example there is absolutely no reason to try to make it easier.

I am very aware that the suns rays are taken to be parallel and have no issue with that. It makes sense. But to then talk of them forming two sides of a triangle is nonsensical to me.

BTW Stoat... I have now been rolling a die for almost 12 months.

Still no six.

Oh and I certainly hope that when you referred to "subject matter experts" you weren't including Dr Math...

Again I must point out that the rays MUST intersect to form a triangle if they never do they never form a triangle.

No matter how acute or obtuse the angles.

GIGO...

Well if they have the same point of origin Keld (which they do), then they have an intersection and therefore form a triangle. Of course having the same point of origin means that they are not parallel.

Sean wrote:Well if they have the same point of origin Keld (which they do), then they have an intersection and therefore form a triangle. Of course having the same point of origin means that they are not parallel.

For that I concur.

So if the internal angles that are considered here are on either side of h the formula requires c which is 93 mil miles to be squared which CAN be done, one cannot however square infinity.

If this is the point Andrew is making I agree 100%

Indeed Keld. If h is known then the calculation is relatively easy. If h=infinity it is not a triangle as the lines would then be parallel.

I do enjoy these discussions where a little thought is required rather than just opinion...

Actually one would be solving for h (and my bad I used c according to this I should have used b):



Fr this example:

Well.

That's quite a run from the simple point that rounding is an arithmetic operation which does not involve infinitudes.

A point on which there appears to be at least near-universal agreement.