Re: Are plane tickets real?
« Reply #160 on: April 12, 2020, 03:13:29 PM »
It occurred to me following my last post that the results given by the independent implementation of Haversine and Bing are so very close that perhaps there was an extra step I could take to eliminate the difference altogether. I had another look at the rounding idea and realised that I'd converted a result to km and then rounded it, so out of interest, I tried this the other way around, i.e. round first and then convert to km.

Now the results look like this:

Comparison between 1000000 locations
Min variation 0.0mm
Max variation 0.0mm
Avg variation 0.0mm
Min variation(%) 0.0
Max variation(%) 0.0
Avg variation(%) 0.0
Min dist 4km
Max dist 20029km
Avg dist 10014km

So no further excuses, this version of Haversine correlates 100% with the results from Bing over a million random pairs of distances.

Code is included as an attachment to this post as before. Instructions to run as per my earlier post.

Offline iamcpc

  • *
  • Posts: 832
    • View Profile
Re: Are plane tickets real?
« Reply #161 on: April 13, 2020, 03:55:52 PM »
It occurred to me following my last post that the results given by the independent implementation of Haversine and Bing are so very close that perhaps there was an extra step I could take to eliminate the difference altogether. I had another look at the rounding idea and realised that I'd converted a result to km and then rounded it, so out of interest, I tried this the other way around, i.e. round first and then convert to km.


Code is included as an attachment to this post as before. Instructions to run as per my earlier post.


I'm not getting any results. I got the website, I put the code in, i hit the play button and nothing happens. I'm only trying to do 100 locations. It just says "Page Unresponsive". What browser are you using to do this?

Re: Are plane tickets real?
« Reply #162 on: April 13, 2020, 04:07:52 PM »
It occurred to me following my last post that the results given by the independent implementation of Haversine and Bing are so very close that perhaps there was an extra step I could take to eliminate the difference altogether. I had another look at the rounding idea and realised that I'd converted a result to km and then rounded it, so out of interest, I tried this the other way around, i.e. round first and then convert to km.


Code is included as an attachment to this post as before. Instructions to run as per my earlier post.

I'm not getting any results. I got the website, I put the code in, i hit the play button and nothing happens. I'm only trying to do 100 locations. It just says "Page Unresponsive". What browser are you using to do this?

Chrome on Windows 10.

Also just tried it in Edge and Internet Explorer 11. Works on all 3 for me.

Did you just change nlocations in settings (to 100) or anything else?
« Last Edit: April 13, 2020, 04:12:31 PM by robinofloxley »

*

Offline JSS

  • *
  • Posts: 1618
  • Math is math!
    • View Profile
Re: Are plane tickets real?
« Reply #163 on: April 13, 2020, 04:54:04 PM »
I'm not getting any results. I got the website, I put the code in, i hit the play button and nothing happens. I'm only trying to do 100 locations. It just says "Page Unresponsive". What browser are you using to do this?
Chrome on Windows 10.

Also just tried it in Edge and Internet Explorer 11. Works on all 3 for me.

Did you just change nlocations in settings (to 100) or anything else?

I just tried it and set it to 100 and got this:

Comparison between 100 locations
Min variation 0.0mm
Max variation 0.0mm
Avg variation 0.0mm
Min variation(%) 0.0
Max variation(%) 0.0
Avg variation(%) 0.0
Min dist 756km
Max dist 18819km
Avg dist 10346km

Seems to be working fine for me.  Chrome on Windows 10.

Offline iamcpc

  • *
  • Posts: 832
    • View Profile
Re: Are plane tickets real?
« Reply #164 on: April 13, 2020, 09:19:43 PM »
Seems to be working fine for me.  Chrome on Windows 10.

It looks like it's because I made some changes to the minimum and maximum distances. I wanted to try a few distances that were between 8 and 10 KM or a few that were between .1 and .4 KM. It ran for 10 minutes trying to do one comparison with a min distance of .4 and a max distance of .4. Very strange that this thing is unable to do smaller distances.


I feel like, if we are going to compare distances, the smallest distance should be something less than 756 KM. Why is it that we are unable to do 100 samples of 0-1 KM and 100 samples of 2-10 KM etc.
« Last Edit: April 13, 2020, 09:28:02 PM by iamcpc »

Re: Are plane tickets real?
« Reply #165 on: April 13, 2020, 09:50:13 PM »
Seems to be working fine for me.  Chrome on Windows 10.

It looks like it's because I made some changes to the minimum and maximum distances. I wanted to try a few distances that were between 8 and 10 KM or a few that were between .1 and .4 KM. It ran for 10 minutes trying to do one comparison with a min distance of .4 and a max distance of .4. Very strange that this thing is unable to do smaller distances.


I feel like, if we are going to compare distances, the smallest distance should be something less than 756 KM. Why is it that we are unable to do 100 samples of 0-1 KM and 100 samples of 2-10 KM etc.

Ah, OK that makes sense. The way it works is that it generates a completely random pair of locations, which could be any distance apart, then works out the distance between them. If this distance falls outside the min/max distance setting then it is discarded and it just generates another pair and tries again and again until it gets a good pair. This is simple to implement, but wasteful. If your distance range is set to 0 - 20,000km, then every pair will be within range so you'll generate (say) 1000 pairs and all 1000 are valid. Halve that range and you'll have to generate twice as many pairs to get 1000 useful ones etc. etc. The smaller the range, the worse it gets.

If you are trying to use a range of say 2 - 10km, then you're probably generating thousands or maybe even millions of out of range ones just to get one in range. I did wonder about making the pair generation a bit more intelligent, but wanted to keep the code simple and easy to understand.

I'll have a think about this and come up with an improved version.

*

Offline JSS

  • *
  • Posts: 1618
  • Math is math!
    • View Profile
Re: Are plane tickets real?
« Reply #166 on: April 13, 2020, 10:03:56 PM »
It ran for 10 minutes trying to do one comparison with a min distance of .4 and a max distance of .4. Very strange that this thing is unable to do smaller distances.

If you were asking for distances between .4 and .4 then it would never find any as there are 0 numbers between them.

If you meant .1 and .4 then it will take a LONG time to run due to how random numbers are being used.  It's not strange at all, I can see the code myself and that's completely expected for those values.

Hmm, that's an interesting problem, how to get two sets of numbers within a specific distance of each other on a sphere. I'll be curious to see what robinofloxley comes up with. I can't think of any quick ways that don't use a bunch of extra math which would be confusing. The code as it stands is pretty minimal and easy to understand.

*

Offline stack

  • *
  • Posts: 3583
    • View Profile
Re: Are plane tickets real?
« Reply #167 on: April 13, 2020, 11:14:12 PM »
I ran it for 100 pairs at 0 to 10 km. It took a really, really long time to run. But when it completed, the results are as predicted (Chrome 80, Mac 10.15.3):


Offline iamcpc

  • *
  • Posts: 832
    • View Profile
Re: Are plane tickets real?
« Reply #168 on: April 14, 2020, 04:53:33 AM »
I ran it for 100 pairs at 0 to 10 km. It took a really, really long time to run. But when it completed, the results are as predicted (Chrome 80, Mac 10.15.3):

the issue that I have here is that the only way you were able to make them match was by rounding the number. The issue with that is that there could be one distance which is 1.1 KM away from another distance. When you round to the nearest kilometer we are unable to see those kinds of differences as demonstrated before when the numbers were different and you were not rounding.

Re: Are plane tickets real?
« Reply #169 on: April 14, 2020, 03:32:34 PM »
Well inevitably the code is a bit more complex, so I'll explain what I've done.

I have a new function to generate a dependent pair of random locations. The start location is entirely random as before, generated in the same way.

Then I generate a vector in the form of a pair of numbers, a bearing and a distance. The bearing is just a random angle between 0 and 360. The distance is a random number between the min and max settings. If the max is set too high, then I just use 1/2 way around the world, i.e. around 20,000km instead to prevent any nasty overflows.

Then I add the vector to the start location to give me a destination a suitable distance away. This means all my generated pairs of locations are sensibly separated and I'm not having to throw anything away.

To make things a bit more flexible, the settings object now allows you to choose to use the old or new method for pair generation and whether or not you want any rounding. Without rounding, expect to see variations of up to 5mm or so. To change features, just comment out the one you don't want (add a // to comment) and uncomment the one you do want. I think you'll understand what I mean if you look at the code. So for example, use dontRound to avoid rounding and round2dp to round to 2 decimal places.

Web site to use is as before, https://www.bing.com/api/maps/sdk/mapcontrol/isdk/layerevents#TS

The code for Haversine and the code to allow me to add the vector come from https://www.movable-type.co.uk/scripts/latlong.html
« Last Edit: April 14, 2020, 04:30:29 PM by robinofloxley »

Re: Are plane tickets real?
« Reply #170 on: April 14, 2020, 03:54:28 PM »
I ran it for 100 pairs at 0 to 10 km. It took a really, really long time to run. But when it completed, the results are as predicted (Chrome 80, Mac 10.15.3):

the issue that I have here is that the only way you were able to make them match was by rounding the number. The issue with that is that there could be one distance which is 1.1 KM away from another distance. When you round to the nearest kilometer we are unable to see those kinds of differences as demonstrated before when the numbers were different and you were not rounding.

When I looked at the values I was getting back from Bing, it looked to me like they had been rounded to the nearest cm, which IMHO is a reasonable thing for them to do. If you accept just for the sake of argument that they are using Haversine, that means they are using a perfect sphere as an approximation for an imperfectly shaped earth, so calculating distances to tiny fractions of a millimetre is a bit pointless. If I'm right, then to match the code I'm using with the Bing code, I need to do the same as they do.

If Bing are either not rounding at all or rounding to something else, such as the nearest mm or nearest metre then if I round my results (not Bing's, I'm not touching Bing's results at all) when I shouldn't or get the rounding wrong, I'll see a mismatch. On the other hand if my to-the-nearest-cm results match exactly with the unadulterated results from Bing, then I'm doing it right.

Re: Are plane tickets real?
« Reply #171 on: April 20, 2020, 09:38:22 AM »
A while back in this thread I said:

I originally got involved in this thread talking about distances on Bing maps. After a lot of back and forth discussion, I finished with a post where I showed the line of code calling the Bing API to calculate a distance, showed the official Bing documentation for this code, where it tells you they use the globe based Haversine formula. In my view, that's beyond reasonable doubt - Bing maps under the hood is clearly based on a Globe model. Since then, silence, tubleweed, nothing, nada, no response.

I get that people have lives and it's unreasonable to expect responses all the time, but I've seen this before. Once the scales start to tip irretrievably in the direction of the RE in a discussion, it dies silently.

That prompted a revival of the thread which was then very active right up until I posted a modified version of a piece of code which addressed all of the criticisms of the earlier versions. Specifically, this new code:

Allows you to specify very small distances to measure.
Allows you to specify a very large number of tests to perform and completes in a reasonable time.
Gives precisely identical results to the Bing API.

Just a reminder, here are the results for 200 million tests between 0.1 and 0.4km:

Comparison between 200000000 locations
Min variation 0.0mm
Max variation 0.0mm
Avg variation 0.0mm
Min variation(%) 0.0
Max variation(%) 0.0
Avg variation(%) 0.0
Min dist 0.10001km
Max dist 0.39999km
Avg dist 0.25km

i.e. Bing maps API distance calculations correlate 100% with an independently developed Haversine formula having compared distances between 200 million random pairs of locations.

So the jury have come back in...

On the charge of Bing documentation having been accused of being accurate when they assert they use the spherical Haversine formula for distance calculations - guilty as charged due to overwhelming evidence. Bing uses Haversine for distances.

On the charge of Bing maps distances having been accused of being "based on measured distances in our 3d world" (i.e. incorporating elevation changes) - case dismissed as the prosecution failed to provide any evidence whatsoever.

And now we're back to silence, tumbleweed, nothing, nada, no response.
« Last Edit: April 20, 2020, 01:43:04 PM by robinofloxley »

Offline iamcpc

  • *
  • Posts: 832
    • View Profile
Re: Are plane tickets real?
« Reply #172 on: April 20, 2020, 04:29:12 PM »

Comparison between 200000000 locations
Min variation 0.0mm
Max variation 0.0mm
Avg variation 0.0mm
Min variation(%) 0.0
Max variation(%) 0.0
Avg variation(%) 0.0
Min dist 0.10001km
Max dist 0.39999km
Avg dist 0.25km

i.e. Bing maps API distance calculations correlate 100% with an independently developed Haversine formula having compared distances between 200 million random pairs of locations.

So the jury have come back in...

On the charge of Bing documentation having been accused of being accurate when they assert they use the spherical Haversine formula for distance calculations - guilty as charged due to overwhelming evidence. Bing uses Haversine for distances.

On the charge of Bing maps distances having been accused of being "based on measured distances in our 3d world" (i.e. incorporating elevation changes) - case dismissed as the prosecution failed to provide any evidence whatsoever.

And now we're back to silence, tumbleweed, nothing, nada, no response.

There is still this issue of rounding which is very unclear to me. Is the variance on these short distances 0 because they are rounded down to the nearest KM which is 0 KM? If so then this is overwhelming evidence that the Bing API is not based on the haversine formula because the haversine formula does not include any rounding.

*

Offline JSS

  • *
  • Posts: 1618
  • Math is math!
    • View Profile
Re: Are plane tickets real?
« Reply #173 on: April 20, 2020, 04:47:28 PM »
There is still this issue of rounding which is very unclear to me. Is the variance on these short distances 0 because they are rounded down to the nearest KM which is 0 KM? If so then this is overwhelming evidence that the Bing API is not based on the haversine formula because the haversine formula does not include any rounding.

The answer is that Bing uses the haversine formula and then rounds down. You can see they round down using the measurement tools, they always show exactly one decimal place of accuracy. It will show 2.4km, not 2.412834756384976529385465362783664578234km.

The script that was posted does this, and matches EXACTLY the results Bing does.

I'd say getting the exact results over two hundred million calculations is pretty solid evidence the methods are the same.

Re: Are plane tickets real?
« Reply #174 on: April 20, 2020, 04:52:41 PM »

Comparison between 200000000 locations
Min variation 0.0mm
Max variation 0.0mm
Avg variation 0.0mm
Min variation(%) 0.0
Max variation(%) 0.0
Avg variation(%) 0.0
Min dist 0.10001km
Max dist 0.39999km
Avg dist 0.25km

i.e. Bing maps API distance calculations correlate 100% with an independently developed Haversine formula having compared distances between 200 million random pairs of locations.

So the jury have come back in...

On the charge of Bing documentation having been accused of being accurate when they assert they use the spherical Haversine formula for distance calculations - guilty as charged due to overwhelming evidence. Bing uses Haversine for distances.

On the charge of Bing maps distances having been accused of being "based on measured distances in our 3d world" (i.e. incorporating elevation changes) - case dismissed as the prosecution failed to provide any evidence whatsoever.

And now we're back to silence, tumbleweed, nothing, nada, no response.

There is still this issue of rounding which is very unclear to me. Is the variance on these short distances 0 because they are rounded down to the nearest KM which is 0 KM? If so then this is overwhelming evidence that the Bing API is not based on the haversine formula because the haversine formula does not include any rounding.

The implementation of haversine I am using is internally working in metres. The values it calculates are first rounded to 2 decimal places, i.e. to the nearest cm. Then the value is converted to km and returned.

The reason for rounding at all is simply that when I looked at the values Bing was returning, they appeared to have been rounded. I experimented with different roundings of my own and when I tried to the nearest cm rounding, suddenly all my results matched with Bings.

If I had rounded to the nearest 10cm or the nearest 0.1cm then the results would not match.

It's a similar to me asking you what is 1/6 as a decimal. If you give me the answer 0.17 rather then 0.167 or 0.1667, then I'm going to guess that you're giving me the answer rounded up to the nearest 2 decimal places, so if I then ask what is 2/3, I'm guessing you will be consistent and tell me 0.67 rather than 0.667 or anything else.

Re: Are plane tickets real?
« Reply #175 on: April 21, 2020, 09:02:55 AM »
...because the haversine formula does not include any rounding.

I realise I didn't address this point.

Just to refresh the memory, here's what the Bing documentation has to say (my emphasis)...

Quote
Calculate the distance between two locations on the surface of the earth using the Haversine formula.

In other words, their getDistanceTo method isn't directly an implementation of Haversine, it is a method which uses an implementation of Haversine. It clearly does other things as well. For example you can ask it to return the distance in a number of different units: feet, kilometres, metres, miles, nautical miles or yards. It also rounds to the nearest cm. Just to be clear, haversine neither rounds nor converts, but the getDistanceTo function, which uses it, does both.

My code didn't reflect that crucial difference and actually violates a principle of software design - single responsibility. My distance calculation function was doing two distinct jobs, directly calculating a haversine distance and then post-processing this result to give a rounded value in km. This is not what the Bing documentation says should happen, I should have a separate function which uses a pure implementation of haversine to get a result and then post-process the result.

So I've changed the code. Now I have a pure implementation of haversine (onlyHaversine) which does no conversion or rounding - just as you say it should - and a separate distanceUsingHaversine function which is the analogue of Bings getDistanceTo. The distanceUsingHaversine function now uses haversine (onlyHaversine), it does not implement haversine.

Functionally the code is identical. All I've done is split my original function in two and moved the code across so both functions now have a single job to do (the single responsibility principle).

One last thing. If you switch off the rounding, the max variation you see is exactly 5mm. What does that tell you? Well if Bing does round to the nearest cm, then that means values such as 1.50 cm get rounded up to 2, which is a 5mm difference. You can never get more than a 5mm variation when rounding to the nearest cm and if you have enough random numbers, you are bound to see a 5mm variation. The presence of a 5mm max variation actually tells you what rounding strategy they are using. I didn't spot this myself at first, but when you do, it's obvious isn't it.

Offline iamcpc

  • *
  • Posts: 832
    • View Profile
Re: Are plane tickets real?
« Reply #176 on: April 21, 2020, 09:58:08 AM »
There is still this issue of rounding which is very unclear to me. Is the variance on these short distances 0 because they are rounded down to the nearest KM which is 0 KM? If so then this is overwhelming evidence that the Bing API is not based on the haversine formula because the haversine formula does not include any rounding.

The answer is that Bing uses the haversine formula and then rounds down. You can see they round down using the measurement tools, they always show exactly one decimal place of accuracy. It will show 2.4km, not 2.412834756384976529385465362783664578234km.

The script that was posted does this, and matches EXACTLY the results Bing does.

I'd say getting the exact results over two hundred million calculations is pretty solid evidence the methods are the same.



They were not the same until we did some creative rounding. I could make a distance formula and round it to the nearest light year. I could measure the length of my roof with a tape measure and round it down to 0 light years and it would match the haversine formula. Does that mean I used the haversine formula to measure my roof? No I used a tape measure.



And now we're back to silence, tumbleweed, nothing, nada, no response.

Dude you have gotten many many responses. It's hit an impasse. We're trying to guess at what the Bing API is doing without seeing the source code. The only thing that I have learned is that, if the bing API does use the haversine formula, it does some pretty creating rounding.


In other words, their getDistanceTo method isn't directly an implementation of Haversine

Hmmm welcome to what I've been weary of this entire time....


it is a method which uses an implementation of Haversine. It clearly does other things as well. For example you can ask it to return the distance in a number of different units: feet, kilometres, metres, miles, nautical miles or yards. It also rounds to the nearest cm. Just to be clear, haversine neither rounds nor converts, but the getDistanceTo function, which uses it, does both.

exactly why we need to see the source code to know for sure. These exercises have just shown that, without the source code, it's very difficult to know what exactly is happening.
« Last Edit: April 21, 2020, 10:02:35 AM by iamcpc »

Offline ChrisTP

  • *
  • Posts: 926
    • View Profile
Re: Are plane tickets real?
« Reply #177 on: April 21, 2020, 11:11:45 AM »
Quote
They were not the same until we did some creative rounding. I could make a distance formula and round it to the nearest light year. I could measure the length of my roof with a tape measure and round it down to 0 light years and it would match the haversine formula. Does that mean I used the haversine formula to measure my roof? No I used a tape measure.
This is probably one of the dumber arguments you've made and it's really showing that you simply don't want to believe you could be wrong. Rounding numbers does not mean the math in the code or the method used isn't accurate, it's just for peoples ease when displaying large numbers... And the point being that it still shows that Bing maps is based on a globe and visually distorted to conform to a rectangle. If it weren't then you'd find the numbers in the higher northern and lower southern areas of the world would be way more off.
Tom is wrong most of the time. Hardly big news, don't you think?

Re: Are plane tickets real?
« Reply #178 on: April 21, 2020, 01:55:35 PM »
I'd say getting the exact results over two hundred million calculations is pretty solid evidence the methods are the same.

They were not the same until we did some creative rounding. I could make a distance formula and round it to the nearest light year. I could measure the length of my roof with a tape measure and round it down to 0 light years and it would match the haversine formula. Does that mean I used the haversine formula to measure my roof? No I used a tape measure.

If you'd like to go out and measure 200 million different roofs to the nearest 1cm and find some simple mathematical formula which would give identical results without needing to go anywhere or take any measurements at all, I reckon you'd make a few $1m from that.

And now we're back to silence, tumbleweed, nothing, nada, no response.

Dude you have gotten many many responses. It's hit an impasse. We're trying to guess at what the Bing API is doing without seeing the source code. The only thing that I have learned is that, if the bing API does use the haversine formula, it does some pretty creating rounding.

Yes I did and the topic was very active for a long while, but then you complained about not being able to work with small distances and complained about rounding, so I went away and within 24h produced an improved solution to deal with the distance limitations and (I thought) answered your question about rounding. Then it all went quiet for a week, so from my perspective, a very active discussion appeared to have died for no apparent reason. I'm glad that you have re-engaged, so thank you for that.

I don't understand what you mean by creative rounding. 200 million Bing results are being returned with answers given in km to 5 decimal places. That means a 1cm resolution. It doesn't make any sense at all to quote distances on this scale to nanometer accuracy so it's perfectly sensible for the developers to round these values and a 1cm resolution is a good choice. When you compare with a non-rounded haversine value, you end up with a max variation of 0.5cm. This is a dead giveaway that they are rounding to the nearest cm. It's not creative rounding at all, it's an entirely sensible way to do it and it's a very simple bit of basic detective work to figure out this is what they've done.

In other words, their getDistanceTo method isn't directly an implementation of Haversine

Hmmm welcome to what I've been weary of this entire time....

In much the same way as a pineapple in a paper bag isn't a pineapple, it's a pineapple in a paper bag. So what.

it is a method which uses an implementation of Haversine. It clearly does other things as well. For example you can ask it to return the distance in a number of different units: feet, kilometres, metres, miles, nautical miles or yards. It also rounds to the nearest cm. Just to be clear, haversine neither rounds nor converts, but the getDistanceTo function, which uses it, does both.

exactly why we need to see the source code to know for sure. These exercises have just shown that, without the source code, it's very difficult to know what exactly is happening.

There are only two possibilities left here. A) Microsoft are telling the truth and they are using haversine. The very extensive testing strongly supports that hypothesis. B) Microsoft have deliberately published misleading documentation which claims they are using haversine, when they are not.

For the sake of argument, let's assume the latter. Let's assume Microsoft have developed a distance method which is indistinguishable from a haversine formula distance, to the nearest 1cm over distances ranging from 0.1 to 20,000km. Why would they even bother doing this when they could just use the very simple haversine formula in the first place. What would be the point? Does it even matter if we can demonstrably swap out the Microsoft implementation for our own and literally nobody could tell the difference. Either Bing is based on a globe model or it isn't, but it might as well be because you literally can't tell the difference.

And having gone to all the trouble of developing a new method, so far unknown to mankind, which leads to results which are indistinguishable from haversine, they then decide to lie about it and claim it is haversine. They could self-evidently save themselves an awful lot of time, trouble and money by just doing what they say they do and use haversine.

You yourself have said on a number of occasions there is no such thing as proof, which means you investigate, gather evidence, weigh the evidence and decide on the balance of probability where the truth lies. The trouble is you are simultaneously ignoring overwhelming evidence, demanding absolute proof and yet claiming there is no such thing as absolute proof.

From time to time cases come before courts where one songwriter claims plagiarism because another is using their song or parts of it. A famous example is George Harrison's My Sweet Lord and the similarities with The Chiffon's He's So Fine. Imagine if the two pieces of music were literally identical in every way. Every note, every instrument, every word, melody, harmony, beat, everything identical and indistinguishable. Your argument is "well we're at an impasse Judge, we'll never know".

*

Offline GreatATuin

  • *
  • Posts: 310
  • It's turtles all the way down
    • View Profile
Re: Are plane tickets real?
« Reply #179 on: April 22, 2020, 05:36:30 AM »
Quote
They were not the same until we did some creative rounding. I could make a distance formula and round it to the nearest light year. I could measure the length of my roof with a tape measure and round it down to 0 light years and it would match the haversine formula. Does that mean I used the haversine formula to measure my roof? No I used a tape measure.
This is probably one of the dumber arguments you've made and it's really showing that you simply don't want to believe you could be wrong.

He's nitpicking over rounding distances to the nearest cm. At this point, I think the most plausible explanation is that iamcpc was trolling all along. Someone who calls rounding distances on a map to the nearest cm "creative rounding" just cannot be serious.
« Last Edit: April 22, 2020, 05:38:27 AM by GreatATuin »
Nearly all flat earthers agree the earth is not a globe.

you guys just read what you want to read