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	<title>shortest &#8211; Fountain Magazine</title>
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		<title>How Do Ants Know Trigonometry?</title>
		<link>https://fountainmagazine.com/all-issues/2020/issue-138-nov-dec-2020/how-do-ants-know-trigonometry/</link>
		
		<dc:creator><![CDATA[The Fountain]]></dc:creator>
		<pubDate>Sun, 01 Nov 2020 18:03:08 +0000</pubDate>
				<category><![CDATA[Issue 138 (Nov - Dec 2020)]]></category>
		<category><![CDATA[ant]]></category>
		<category><![CDATA[ants]]></category>
		<category><![CDATA[day]]></category>
		<category><![CDATA[desert]]></category>
		<category><![CDATA[direction]]></category>
		<category><![CDATA[distance]]></category>
		<category><![CDATA[entomology]]></category>
		<category><![CDATA[find]]></category>
		<category><![CDATA[food]]></category>
		<category><![CDATA[home]]></category>
		<category><![CDATA[hypothesis]]></category>
		<category><![CDATA[legs]]></category>
		<category><![CDATA[nest]]></category>
		<category><![CDATA[nests]]></category>
		<category><![CDATA[researchers]]></category>
		<category><![CDATA[return]]></category>
		<category><![CDATA[Science]]></category>
		<category><![CDATA[scientists]]></category>
		<category><![CDATA[shortest]]></category>
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		<guid isPermaLink="false">http://107.21.79.195/all-issues/2020/issue-138-nov-dec-2020/how-do-ants-know-trigonometry/</guid>

					<description><![CDATA[Think of yourself as a desert ant. You leave your nest to search for food early in the morning in the deserts of Tunisia, except you do not know where to find food. You, therefore, walk randomly in the desert in a circuitous outward path from your nest until you find food. If you would [&#8230;]]]></description>
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<p>Think of yourself as a desert ant. You leave your nest to search for food early in the morning in the deserts of Tunisia, except you do not know where to find food. You, therefore, walk randomly in the desert in a circuitous outward path from your nest until you find food. If you would find food, how do you get it back to your home? How do you go back without having left for yourself any traces or signs in the wasteland, without knowing where you located, and most importantly, without ending up stranded in the scorching heat of the desert? Could you accomplish coming back each day with food? Well, desert ants can.</p>
<p><span id="more-5675"></span></p>
<p>To find out how ants can do this, scientists observed their behavior, and surprisingly they have found that ants did not follow back on the same trail they randomly took after they left their nests. Instead, ants took a direct route as if they already knew where the nest exactly located. How do these ants find the closest way and shortest distance to their nest from their current locations? Former studies had found that red and forest ants secrete a chemical substance to mark their paths. They leave a trail of chemical scents or visual traces behind them—like leaving a trail of breadcrumbs to help you find your way home. However, the structure of desert sands and conditions are not consonant with containing chemicals that will carry an odor or leave visual cues. Even if such markings have made, it is hard to guarantee that they will remain intact long enough considering the harsh conditions of the desert. As in Hansel and Gretel fairy tale kids who could not return home for the breadcrumbs they had left on the trail eaten by birds. Therefore, these desert ants must be equipped with another cognitive mechanism so that they can return to their nests before succumbing to the midday heat.  </p>
<p>Black desert ants (<em>Cataglyphis fortis</em>) emerge from their nests in the heat of desert sand, which rises to 70 degrees with the rise of the morning sun, to search for the remains of other insects that were not as heat resistant as they are. They can only survive for one hour on the hot sand and under the blazing sun, which means that within an hour, they must find their food and bring it back home without getting lost. The journey is quite arduous and dangerous each day. If the slightest confusion occurs and they are not able to return to their nest in time, then it could cost them their lives.</p>
<p>Scientists conducted a series of research in the scorching deserts of Tunisia to find out how desert ants take their food to their nests in the shortest route possible. Researchers first determined an anthill and plotted the terrain around it to set up a coordinate plane. They observed that the ants left their nests very early in the morning to begin their daily search for food, and many of them eventually found grubs that had been planted by the scientists. However, researchers moved the ants to locations that they had not previously been to after the ant began carrying the food back to their nests. The attempt was to understand whether there was a “sign placement system” within the ants. This system would encourage the ant to find its last known location, in this instance where it had picked up, then find its way back home. However, the ant instead began heading directly to its nest. It was as if the ant determined its position concerning its nest and set off for it immediately. This experiment was repeated on many ants numerous times and with the same consistent results. The ants, as soon as they had placed on the ground, moved to the nest relative to there. With a wondrous intrinsic coding of some neurons in their nervous systems, they traveled the distance between their new location and the nest in the shortest way possible. In addition to this, the margin of error was very nominal; they found their nests with a ten percent error in the average distance of 500-meters and with an error of only two degrees in angle. Additionally, a fascinating discovery revealed that the ants could calculate errors in their navigation systems. As they approach their destination, they would make adjustments if they need to by moving back and forth in parallel lines to reach the nest with minimum error. </p>
<p>Scientists determined that desert ants have about a thousand lenses in their compound eyes (remember that a human eye has only one lens) and 80 lenses in each of their eyes that can detect polarized light that comes from different points in the sky. Polarized light occurs when sunlight enters the atmosphere of Earth, hits air molecules and other particles, and then scatters in all directions. This dispersion leads to polarization, and the light that starts to vibrate in many planes begins to vibrate in only one plane. Therefore, the strongest of them is a distinct polarization that always makes a 90-degree angle towards the sun. The lens system in the eyes of desert ants uses this polarization to form a kind of Sky Map. These ants will occasionally stop and robotically move their heads while returning to their nest. This brief period allows the ants to make this sky map by surveying the sky and making a mental note of its layout. Researchers believe that ants can then calculate the direction that they need to travel to return to their nest. They repeat this movement along the way to continually update their sky maps. If they cannot find their home, then they utilize a patterned search method with a set of circular motions. It means that each ant knows how far it is from their nest at every point of their journey.</p>
<p>Then, how do ants find their direction to the nest? Perhaps they were guided by the position of the sun in the sky is. To test this hypothesis, researchers placed a set of mirrors to make ants perceive the sun in a different state than where it ordinarily would be. It observed that the ants changed their directions according to the new state of the sun. However, this finding raised another question; researchers wondered how the time of day would affect the ants since the sun moves across the sky during the day. However, this finding raised another question; researchers wondered how the time of day would affect the ants since the sun moves across the sky during the day.</p>
<p>In another part of the experiment, the researchers caught the ants after they found the bait, closed a box over them, and kept them inside the box for several hours so that they could not see the sun and its movements. It expected that the ants would have trouble finding their way back after they were released since a long time had passed, and the sun was in a drastically different position in the sky. However, they once again returned home by using the shortest distance possible. It understood that the desert ants were aware that time was passing even though they could not see the sun.</p>
<p>We now understand that ants determine their direction home by using the sun, but we still do not know how they figure out the distance they must travel to return to their nest. Researchers have developed three hypotheses to explore this phenomenon. The first hypothesis was the energy hypothesis. According to this hypothesis, the ants were able to know how much energy they needed on the way back by calculating it they had spent until they reached their food. The depletion of their energy meant the end of their journey. An ant loaded with extra weights to test this hypothesis as soon as it reached its food. The scientists thought that if their body weight increased, then they would not be able to strike reach the nest since they would spend more energy on the return trip. However, in this case, it did not affect the ants, and they returned home in the shortest way possible regardless of their weight.</p>
<p>The second hypothesis was the optical-flow hypothesis. In this hypothesis, it believed that the ants had visual memory, and this was how they remembered the way back. To prove this, scientists prevented the ants from seeing their surroundings by blindfolding the ants when they found their food source. However, the blindfold did not prevent the ants from obtaining the shortest distance back home. As a follow-up to this experiment, the researchers placed an extensive television screen in front of the ants showing an endless desert on the television screen to make the ants feel as if they had crossed the entire desert in this simulation. They used various types of simulations, but the result did not change; the ants found their way. </p>
<p>The last test involved the pedometer hypothesis. It surmised that ants could be counting their steps to determine how far they had traveled. To test whether they were doing so, researchers attached stilts made of hair strands to the legs of one group of ants after they found the food. As their legs now extended, they could move with longer scale steps. Another group of ants had their legs cut below the knee, thus shortened to increase the number of steps needed to walk the required distance back. They then observed the return journey of both groups of ants. The results were astounding; the ants with shorter legs had concluded their course before reaching the nest, while the ants with longer legs ended up passing the nest. Thus, it understood that the ants counted their steps according to the distance they traveled.</p>
<p>The findings reveal that the ants are created with an internal system that keeps track of the steps they take and re-calibrates itself on the way back. People make these complex calculations with measuring instruments and by knowing the laws of trigonometry. However, these small creatures find their way directly back without using any tools or computer applications. They do not use their perception to find direction, and they do not use any other directional methods because they all remember direction and distance as they move forward. If you look at this situation, what would be your simplest explanation? You can only have one definition: These little creatures can measure distances and angles precisely by applying mathematical calculations and trigonometry within their conditions. Since the first day of their existence, these creatures show only a few of the shreds of evidence of the divine power created them out of nothing with wondrous systems and superior abilities in their bodies.</p>
<blockquote>
<p>I have put my trust in God, my Lord, and your Lord. No living creature is there, but He holds it by its forelock and keeps it under His complete control. Undoubtedly, my Lord is on a straight path (He governs all that exists and carries out His decrees rightly and with absolute justice). (Surah Hud, 56)</p>
</blockquote>
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			</item>
		<item>
		<title>Action and Coincidence</title>
		<link>https://fountainmagazine.com/all-issues/2009/issue-71-september-october-2009/action-and-coincidence/</link>
		
		<dc:creator><![CDATA[Louima Cunningham]]></dc:creator>
		<pubDate>Tue, 01 Sep 2009 00:00:00 +0000</pubDate>
				<category><![CDATA[Issue 71 (September - October 2009)]]></category>
		<category><![CDATA[ball]]></category>
		<category><![CDATA[center]]></category>
		<category><![CDATA[close]]></category>
		<category><![CDATA[distance]]></category>
		<category><![CDATA[figure]]></category>
		<category><![CDATA[lines]]></category>
		<category><![CDATA[longer]]></category>
		<category><![CDATA[needles]]></category>
		<category><![CDATA[number]]></category>
		<category><![CDATA[player]]></category>
		<category><![CDATA[point]]></category>
		<category><![CDATA[probability]]></category>
		<category><![CDATA[result]]></category>
		<category><![CDATA[route]]></category>
		<category><![CDATA[Science]]></category>
		<category><![CDATA[shortest]]></category>
		<category><![CDATA[situation]]></category>
		<category><![CDATA[speed]]></category>
		<category><![CDATA[time]]></category>
		<category><![CDATA[times]]></category>
		<category><![CDATA[universe]]></category>
		<guid isPermaLink="false">http://107.21.79.195/all-issues/2009/issue-71-september-october-2009/action-and-coincidence/</guid>

					<description><![CDATA[It is not easy for people living today to believe that every object, every law and every incident in the universe is planned in a very detailed way. However, it is a fact that there is a seen and unseen algebraic reality to everything moving in the universe. This situation amazes the distinguished scholars roaming [&#8230;]]]></description>
										<content:encoded><![CDATA[<p>It is not easy for people living today to believe that every object, every law and every incident in the universe is planned in a very detailed way. However, it is a fact that there is a seen and unseen algebraic reality to everything moving in the universe. This situation amazes the distinguished scholars roaming on the lace of science.</p>
<p><span id="more-1064"></span></p>
<p>Physicists study on the biggest and smallest physical measures, on the strongest and weakest forces, and they have calculated the ratio between some of them and attained results close to 1040 several times. For example, it has been proven that “strong nuclear force,” which keeps protons and neutrons in the atomic nucleus together, is 1040 times stronger than the force of gravity. Although some consider this situation a result of coincidence, there are also some people who have shown the courage to question the accuracy of this result and open it to discussion. Since then, obtaining the same number several times has inevitably led to the belief that the number was determined and calculated before. This situation resembles the situation of a chess player who hears somebody telling him the opponent’s next move, or the situation of a composer who hears a melody from upstairs that perfectly fits his lyrics while he is trying to write the melody for his lyrics. Is it not amazing when somebody says what is going to be especially at a time when you least expect such a vision? Questions emerge: Have all actions and incidents in the universe and the values corresponding to them been determined in advance? Is there a certain logic behind the behavior of materials without intellect or consciousness?</p>
<p>Perhaps when Comte de Buffon (1707–1788) started to do research into probability calculations concerning falling matches and needles three centuries ago, he did not think that he would make such an astonishing discovery. According to his calculations, the probability of dropped needles hitting a pair of parallel lines that are drawn a certain distance apart is proportional to the number pi (&amp;#960;) (Figure 1–2). When the distance between the parallel lines are drawn the length of a match, this probability becomes exactly 2/&amp;#960;. This was a theoretical result that was calculated on paper, but trying it out would raise interesting results. In other words, when a certain number of tests were conducted, it could be expected that a number of matches equal to the number that was found through the theoretical calculations would hit the lines; and, indeed, that was what happened. In addition, mathematicians found another way to calculate pi by using this method since the ratio of the number of matches or needles that hits the lines to the total number of matches or needles should give a pi-proportioned number. In 1901, Mario Lazzarini threw one needle 3,408 times and, as a result, got the ratio 355/133 or 3.1415929; the difference between this value and the real value is only 0.0000003.</p>
<p>The experimental proof of this fact is not difficult. When the experiment, which has been conducted thousands of times up to today, was first tried by a group of mathematicians dropping 3,000 needles, the number of the needles that touched the lines was close to 1,900, which was the desired result, and the result was amazingly found to be proportionate to pi.</p>
<p> </p>
<p>Although the real relation is like the equation given in Figure 3, when the length of the needles and the distance between the lines are equalized, the desired ratio becomes 2/&amp;#960;. What does this mean? Does the number pi, which was created with the universe and which we meet in different fields, play a role in showing the manifestation of the Majestic Will about where an object will fall-through having a result that can not be explained by coincidence? Is falling not an ordinary incident?</p>
<p>While this reality makes even falling an extraordinary incident, it opens a perspective on understanding the reality behind the verse: “…it was not you (O Messenger) who threw but God threw,” which was revealed about the Battle of Badr in the Qur’an. Actually, it is impossible even for a leaf to fall without the knowledge and the calculation of Our Lord, who is closer to us than our jugular vein.</p>
<p>Let us think about a group of creatures that lives with different physical laws in a different universe. Assume that they live on a flat, circular world (Figure 4) and their steps get longer when they come close to the center. For this kind of creature, the shortest distance between two points is not a straight line as it is for us (A–B). Since their steps get longer as they get closer to the center, they travel close to the center. Yet, since they make the way a little longer in this way, the shortest distance would be an oblique line that takes these two variables into account and that passes by partially approaching the center. So, what would we think if we saw these creatures walking in this way all the time? Or if we knew that the creatures acting in this way were inanimate beings? In these circumstances, we might wonder whether these beings are very intelligent or whether One who knows and sees everything, and is present in every place at every time, directs them.</p>
<p>For a soccer forward to find the best time to attack when he is facing the goal keeper or for a tennis player to choose the best timing and position to hit the ball requires a fine calculation. In tennis, the player sometimes approaches very close to the net to meet the ball. In this way, the player gains great advantage since, by his or her positioning, the player reduces the area into which the ball can fall to the minimum, and increases his or her own chances of returning the ball (Figure 5). Nevertheless, since the ball reaches the player faster and harder, there is also a raised probability of the player’s failing to return the ball. Therefore, advancing right up to the net may not always be advantageous. Thus, the best position for the player may lie at any point between the net and the baseline when area and speed variables are considered. Similarly, the most advantageous point for the goal keeper lies between the attacking forward and the goal line, at a point which depends upon the variables of the speed of the ball and the area.</p>
<p>Naturally, we do not find tennis and soccer players’ positionings as described above strange since we expect them, as reasonable people, to play in this way. Yet, how would we interpret and explain it if we saw inanimate things acting in the same way? There is a phenomenon that applies this logic consciously but itself does not have consciousness. A phenomenon that astonishes people: light.</p>
<p>Let us think of a rectangular racetrack with points A, B, C, D. While the shortest distance for a horse that will run from one end of this racetrack to the other is the AC diagonal when the ground is homogenous, there will be a reroute if the ground is not homogenous. Assume the length of the racetrack is 80 meters and its width is 60 meters. Half of it is grass and the other half is sand (Figure 6). Also, assume the horse’s speed on the sand is half of its speed on the grass (it runs 10 meters in 1 unit of time on the grass). Under these circumstances, the horse will run the AC diagonal in 15 units of time while it will run AEC route in 14.5 units of time. The ABC route is much longer. Thus, any route which passes between these two routes will be shorter than these two. The point O, which the shortest route (AOC) passes, will be between the points M and E. When we look carefully, we understand that this is the route light follows as it enters environments of different densities; for example, the route it follows when passing from air to water (see a spoon’s broken image in a water-filled glass). As you see, light finds that specific mysterious point and follows that particular path. In other words, while entering different environments of varying densities, it finds the shortest way and follows it in an amazing way.</p>
<p>All these detailed calculations and functioning with great wisdom show that even inanimate beings and atoms are in the hands of a Majestic Will.</p>
<p><em>Every atom contains two truthful testimonies to the Necessarily Existent Being’s Existence and Unity. Despite being powerless and insentient, it bears decisive witness to the Necessarily Existent Being’s Existence by carrying out important duties and functions as though it were conscious. It also testifies to the Unity of the same Being, Who owns all material and immaterial dominions, by conforming to the universal order in general, and to the rules of each place it enters in particular. It settles in every place as if it were its homeland. All of this shows that the One Who owns the atom owns all the places it enters. By carrying out very heavy duties incompatible with its size and weakness, the atom shows that it acts at the command and in the name of One with absolute power. (</em><em>The Thirtieth Word, Second Point, Risale-i Nur Collection)</em></p>
<h3><b>Notes</b></h3>
<ol>
<li>See Al-Anfal 8:17.</li>
<li>“… And He knows whatever is on land and in the sea; and not a leaf falls but He knows it” (Al-An’am 6:59).</li>
</ol>
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