Philosophy Now Forum

The reason they call it taxi cab geometry is because taxis cannot go in a straight line from A to B. they have to take perpendicular streets. It has nothing to do with square circles. They are saying that if you can only move perpendicular this is how to find the shortest route.

You wrote,"In taxicab geometry, distance is determined by a different metric than in Euclidean geometry, and the shape of circles changes as well."
Of course if space itself is deformed. For example if you are measuring a triangle on a sphere the angles are greater then on a flat plane. That is all they are saying.

raw_thought wrote: ↑Thu Sep 17, 2020 7:54 pm I am using the units in the picture. Its 2 units from the top to the center and only one unit diagonally.

No, you aren't using "the units in the picture". You are using the Euclidian units for "distance".

raw_thought wrote: ↑Thu Sep 17, 2020 8:00 pm Of course if space itself is deformed.

What do you mean by "deformed".

What is the "normal" form of space?

Those distances are PERPENDICULAR they are not a radius.
I can say that I live 80,000 miles from New York by that reasoning. I can go back and forth instead of a straight line.
BTW I admire you. Anyone that defends an impossible position ( that there are square circles ) gets my respect.
Or that Einstein's Relativity is bunk. https://scitechdaily.com/einsteins-gene ... pace-time/ Now of course you will say that I am appealing to authority. And yes, I personally did not do the experiments that confirm Relativity. However, to dismiss facts given by EVERY EXPERT is silly. OK, Relativity was not proven. It is only probably correct. However, I have no problem accepting Relativity's probability of 99%.

I am saying that on a flat plane triangles have angles that add up to 180 degrees. On a sphere they add up to more.

raw_thought wrote: ↑Thu Sep 17, 2020 8:15 pm Those distances are PERPENDICULAR they are not a radius.

They ARE a radius! They are the straightest (possible) line from the centre to the circumference.

raw_thought wrote: ↑Thu Sep 17, 2020 8:15 pm BTW I admire you. Anyone that defends an impossible position ( that there are square circles ) gets my respect.

I am not defending anything. I have given you a counter-example to your non-existence claim: a square circle.

Instead of accepting your error, you are busy rationalising your error now.

You wrote "They ARE a radius! They are the straightest (possible) line from the centre to the circumference." Do you know what a radius is? By definition it is a straight line not a lot of perpendicular steps.

raw_thought wrote: ↑Thu Sep 17, 2020 8:23 pm Do you know what a radius is? By definition it is a straight line not a lot of perpendicular steps.

Those ARE "straigh"t lines!!!!! GIVEN THE GEOMETRY.

They are the shortest distance between center and circumference.

Yes, a Taxi driver cannot drive directly from point A to point B. But that does not mean that a straight line from point A to point B is not the shortest distance.

raw_thought wrote: ↑Thu Sep 17, 2020 8:25 pm Yes, a Taxi driver cannot drive directly from point A to point B. But that does not mean that a straight line from point A to point B is not the shortest distance.

Those ARE the "shortest distances" (straight lines) from A to B !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Show me a distance between the centre and circumference that is less than 4.

You wrote "Those ARE the "shortest distances" (straight lines) from A to B"
On a flat plain a straight line is the shortest distance between 2 points. Yes, on a sphere there is https://www.britannica.com/technology/g ... rcle-route . I remember when I flew from Detroit Michigan to Thailand and went over Alaska! That does not mean that geometry violates logic. Just as a triangle on a sphere has more angles then on a flat plain. There are no contradictions!

No! LOOK AT THE PICTURE YOU SUPPLIED! The dot diagonally from the center is closer to the center than the dot at the top. You cannot see that???

You wrote," Those ARE the "shortest distances" (straight lines) from A to B !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"
hmmm so if I take perpendicular steps rather then a straight line there is no difference in the distance????

You wrote, "Show me a distance between the centre and circumference that is less than 4."
Umm the dot that is diagonal from the center.