Predicting earth radius
TODO: this was an attempt at round-earth vs. flat-earth using empirical data about travel times to predict curvature
Bahrain, Munich, Vladivostok, Astana
Munich-Bahrain: 4135 km Bahrain-Vladivostok: 7410 km Vladivostok-Munich: 8308 km Munich-Astana: 4202 km Bahrain-Astana: 3300 km Vladivostok-Astana: 4529 km
Arbitrarily fix Astana at (0,0). Arbitrarily fix Munich’s latitude at 0. Then we find: long for Munich (1 var), lat/long for Bahrain and Vladivostok (4 vars). to minimize error in predicted distance between all places.
There’s only one curvature which can make all these distances consistent. We first try with a flat earth and see what minimum error we get.
earth radius (1 var).
If the earth is flat, all these distances would be consistent.
Let’s start by driving from Astana to Munich. We find the distance to be 4202 kilometers. Starting with this, we can begin to model our flat world.
import tensorflow as tf astana_lat = tf.constant(0., tf.float32) # Since the origin is arbitrary, astana_lon = tf.constant(0., tf.float32) # we fix Astana there to reduce variables. munich_lat = tf.constant(0., tf.float32) # Since rotation is arbitrary, we fix Munich at 0 latitude. munich_lon = tf.Variable(10., tf.float32) def distance_flat_earth(a_lat, a_lon, b_lat, b_lon): return tf.sqrt(tf.square(a_lat - b_lat) + tf.square(a_lon - b_lon)) astana_munich_distance_prediction = distance_flat_earth(astana_lat, astana_lon, munich_lat, munich_lon) DISTANCE_KM_ASTANA_MUNICH = 4202 loss = tf.square(astana_munich_distance_prediction - DISTANCE_KM_ASTANA_MUNICH) train_step = tf.train.GradientDescentOptimizer(0.1).minimize(loss) with tf.Session() as sess: tf.global_variables_initializer().run() for _ in range(100): sess.run(train_step) print("Final Munich lon: %s" % sess.run(munich_lon)) print("Final Error: %s" % sess.run(loss))
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