the invention will now be described with reference to the preferred embodiment shown in fig1 . fig1 is an exploded perspective view of a preferred embodiment of a midsole 103 and an outsole 105 of the shoe . the outsole 105 is not part of the midsole 103 . as shown in fig1 , 2 and 2 a , the outsole 105 is below the midsole 103 when the shoe is in its normal , upright position . this normal , upright position is shown with respect to the ground 100 in fig5 a - 5d . as used herein , “ above ” and “ below ” refer to relative locations of identified elements when the shoe is in this normal , upright position as shown in fig5 a - 5d . the midsole 103 is located between the shoe upper 106 and the outsole 105 . the midsole 103 , as shown in fig1 , 2 and 2 a , comprises an upper layer 107 , a shank 111 , and a lower layer 109 . the upper layer 107 and / or the lower layer 109 may each comprise two or more sub - layers . as described more fully hereinafter in an alternative embodiment , the upper layer 107 may also be eliminated completely . in the preferred embodiment shown in fig1 , 2 and 2 a , upper layer 107 has a top surface 113 substantially opposite a bottom surface 115 . top surface 113 is shown in fig6 a . bottom surface 115 is shown in fig6 b . the shank 111 has a top surface 181 substantially opposite a bottom surface 183 . top surface 181 is shown in fig6 c and bottom surface 183 is shown in fig6 d . the shank has a top portion 186 and a bottom portion 187 . top portion 186 and bottom portion 187 are shown in fig3 . the lower layer 109 has a top surface 117 substantially opposite a bottom surface 121 . top surface 117 is shown in fig6 e . bottom surface 121 is shown in fig6 f . the outsole 105 has a top surface 119 substantially opposite a bottom surface 123 . as shown in fig1 , when the shoe is in its normal , upright position , the shank 111 is below the upper layer 107 . the lower layer 109 is below the shank 111 , and the outsole 105 is below the lower layer 109 . fig2 is a side elevation view of an embodiment of the midsole and outsole of the shoe . the shoe has a front tip 140 located at the farthest point toward the front of the shoe and a rear tip 142 located at the farthest point toward the rear of the shoe . the upper layer 107 includes a toe region 151 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that begins in the vicinity of the front tip 140 and extends from there to a location that is approximately one third of the distance toward the rear tip 142 . the shank 111 includes a toe region 251 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that begins in the vicinity of the front tip 140 and extends from there to a location that is approximately one third of the distance toward the rear tip 142 . the lower layer 109 includes a toe region 161 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that begins in the vicinity of the front tip 140 and extends from there to a location that is approximately one third of the distance toward the rear tip 142 . the outsole 105 includes a toe region 171 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that begins in the vicinity of the front tip 140 and extends from there to a location that is approximately one third of the distance toward the rear tip 142 . the upper layer 107 includes a heel region 153 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that begins in the vicinity of the rear tip 142 and extends from there to a location that is approximately one third of the distance toward the front tip 140 . the shank 111 includes a heel region 253 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that begins in the vicinity of the rear tip 142 and extends from there to a location that is approximately one third of the distance toward the front tip 140 . the lower layer 109 includes a heel region 163 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that begins in the vicinity of the rear tip 142 and extends from there to a location that is approximately one third of the distance toward the front tip 140 . the outsole 105 includes a heel region 173 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that begins in the vicinity of the rear tip 142 and extends from there to a location that is approximately one third of the distance toward the front tip 140 . the upper layer 107 includes a middle region 152 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that extends approximately between the toe region 151 and the heel region 153 . the shank 111 includes a middle region 262 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that extends approximately between the toe region 251 and the heel region 253 . the lower layer 109 includes a middle region 162 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that extends approximately between the toe region 161 and the heel region 163 . the outsole 105 includes a middle region 172 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that extends approximately between the toe region 171 and the heel region 173 . typically , the lower layer 109 of the midsole 103 is on average thicker in the heel region 163 than it is in the toe region 161 . the upper layer 107 has a first density . the lower layer 109 has a second density different from the first density and is typically less dense than the first density . the upper layer 107 has a first compressibility and the lower layer 109 has a second compressibility that is different from the first compressibility . the compressibility of the lower layer 109 is typically relatively high . due to this relatively high compressibility , the lower layer 109 undergoes a relatively high amount of deformation when subjected to a given load . the upper layer 107 is typically made from polyurethane , polyvinyl chloride , rubber or thermal plastic rubber . however , the upper layer 107 can be made from any other material without departing from the scope of the present invention . typically the upper layer 107 will have a durometer hardness between about 45 and about 65 on the asker c scale . fig2 a is an exploded side elevation view of fig2 . the lower layer 109 is made of a compressible and deformable yet resilient material which may or may not be the same material of which the upper layer 107 is made . typically the lower layer 109 will have a durometer hardness between about 20 and about 45 on the asker c scale . the top surface 113 of the upper layer 107 is typically positioned below an insole board ( not shown ) which is typically positioned below a sockliner ( not shown ). as shown in fig2 and 2a , the bottom surface 115 of the upper layer 107 is in substantially continuous contact with the top surface 181 of the shank 111 . due to this substantially continuous contact between the bottom surface 115 of the upper layer 107 and top surface 181 of the shank 111 in this embodiment , bottom surface 115 of the upper layer 107 substantially conforms to top surface 181 of the shank 111 . in other embodiments , such substantially continuous contact between bottom surface 115 of the upper layer 107 and top surface 181 of the shank 111 may not be present . the upper layer 107 has a bottom surface 115 that may be connected to the top surface 181 of the shank 111 by either friction and / or an adhesive and / or other similar means . alternatively , substantially the entire bottom surface 115 of the upper layer 107 may be molded to substantially the entire top surface 181 of the shank 111 . alternatively , the upper layer may be eliminated in alternative embodiments . the shank 111 has a frontmost point 250 and a rearmost point 255 . the shank 111 can be made from polyurethane , polyvinyl chloride , rubber , thermal plastic rubber , carbon fiber or carbon fiber reinforced plastic . however , the shank 111 can be made from any other material without departing from the scope of the present invention . typically the shank 111 will have a durometer hardness between about 50 and about 70 on the shore d scale . the outsole 105 typically curves upwardly in the heel region . the outsole 105 has a frontmost point 170 and a rearmost point 174 . when the shoe is in its typical upright , unloaded state , the frontmost point 170 and the rearmost point 174 are both relatively high above the ground 100 . from a point at or near the vicinity of the frontmost point 170 , the outsole 105 has a gradual downward curve 195 that continues through at least a portion of the toe region 171 of the outsole 105 . starting in the middle region 172 , the outsole 105 has a gradual , upward curve 196 that continues to curve upward through at least a portion of the heel region 173 of the outsole 105 . this gradual upward curve 196 typically continues until the outsole 105 approaches the vicinity of the rear tip 142 of the shoe . this upward curve 196 is typically sharper than downward curve 195 in the toe region 171 . upward curve 196 may be substantially sharper than shown in fig2 a or substantially shallower than shown in fig2 a . the outsole 105 has a bottom surface 123 that typically contains grooves and / or patterns for optimal traction and wear . fig3 is a side elevation view of a preferred embodiment of the shank 111 . in the preferred embodiment , the shank 111 comprises a top portion 186 and a bottom portion 187 . the shank 111 has a top surface 181 and a bottom surface 183 . the bottom surface 183 of the shank 111 has a longitudinal concavity 303 , a longitudinal convexity 305 and another longitudinal concavity 307 . the bottom surface 183 of the shank 111 has a longitudinal concavity 303 that comprises at least a downward curve 190 located in at least a portion of the heel region 253 . “ downward curve ,” as used here and throughout this specification , unless otherwise noted , refers to a direction that moves toward the ground 100 from any specified location on the shoe when the shoe is oriented in its typical upright position in which the bottom surface 123 of the outsole 105 is in unloaded contact with the ground 100 . the shank 111 has a frontmost point 250 and a rearmost point 255 . downward curve 190 of the longitudinal concavity 303 begins at or near the vicinity of , the rearmost point 255 of the shank 111 and gradually and continuously descends downwardly from there through a point at or near the vicinity of the middle region 262 . the portion of the shank 111 indicated by lines extending from , and associated with , reference numeral 303 indicates the approximate range wherein longitudinal concavity 303 is typically primarily located . longitudinal concavity 303 may , or may not , be entirely located within the range indicated by the lines extending from , and associated with , reference numeral 303 . longitudinal concavity 303 , as shown in fig2 a , is relatively shallow due to its large radius of curvature or radii of curvature . longitudinal concavity 303 may comprise a curve or curves in addition to downward curve 190 . the radius of curvature throughout longitudinal concavity 303 may be completely constant , may have one or more constant portions mixed with one or more non - constant portions , or may be completely non - constant . downward curve 190 , as well as any other curve or curves that are part of longitudinal concavity 303 , may , at any point on any of those curves , have a slope that is gradual , moderate or steep . although downward curve 190 of longitudinal concavity 303 is shown in fig2 a as beginning near the rearmost point 255 , downward curve 190 of longitudinal concavity 303 may instead begin at some other location on the bottom surface 183 of the shank 111 . although longitudinal concavity 303 is shown in fig2 a as ending at a location in the middle region 262 or the location where the heel region 253 transitions into the middle region 262 , longitudinal concavity 303 may end at some other location on the bottom surface 183 of the shank 111 . the bottom surface 183 of the shank 111 , as shown in fig2 a , has a longitudinal concavity 307 that comprises at least an upward curve 192 located in at least a portion of the middle region 262 . “ upward curve ,” as used here and throughout this specification , unless otherwise noted , refers to a direction that moves away from the ground 100 from any specified location on the shoe when the shoe is oriented in its typical upright position in which the bottom surface 123 of the outsole 105 is in unloaded contact with the ground 100 . upward curve 192 of longitudinal concavity 307 begins at , or near the vicinity of the middle region 262 of the bottom surface 183 and gradually and continuously ascends upwardly from there through at least a portion of the toe region 251 . the portion of the bottom surface 183 indicated by lines extending from , and associated with reference numeral 307 indicates the approximate range wherein longitudinal concavity 307 is typically primarily located . longitudinal concavity 307 may , or may not , be entirely located within the range indicated by the lines extending from , and associated with , reference numeral 307 . longitudinal concavity 307 , as shown in fig2 a , is relatively shallow due to its large radius of curvature or radii of curvature . longitudinal concavity 307 may comprise a curve or curves in addition to upward curve 192 . the radius of curvature throughout longitudinal concavity 307 may be completely constant , may have one or more constant portions mixed with one or more non - constant portions , or may be completely non - constant . upward curve 192 , as well as any other curve or curves that are part of longitudinal concavity 307 , may , at any point on any of those curves , have a slope that is gradual , moderate or steep . although upward curve 192 of longitudinal concavity 307 is shown in fig2 a as beginning near the middle region 262 , upward curve 192 of longitudinal concavity 307 may instead begin at some other location on the bottom surface 183 . although longitudinal concavity 307 is shown in fig2 a as ending at a location in the toe region 251 , longitudinal concavity 307 may end at some other location on the bottom surface 183 of the shank 111 . the bottom surface 183 of the shank 111 , as shown in fig2 a , has a longitudinal convexity 305 that is defined by downward curve 190 and upward curve 192 and that is typically located in at least a portion of the middle region 262 . longitudinal convexity 305 may , or may not , be entirely located within the range indicated by the lines extending from , and associated with , reference numeral 305 . longitudinal convexity 305 , as shown in fig2 a , is relatively shallow due to its large radius of curvature or radii of curvature . longitudinal convexity 305 may comprise a curve or curves in addition to upward curve 192 and downward curve 190 . the radius of curvature throughout longitudinal convexity 305 may be completely constant , may have one or more constant portions mixed with one or more non - constant portions , or may be completely non - constant . downward curve 190 and upward curve 192 , as well as any other curve or curves that are part of longitudinal convexity 305 , may , at any point on any of those curves , have a slope that is gradual , moderate or steep . although longitudinal convexity 305 is shown in fig2 a as ending at a location where the middle region 162 transitions into the toe region 161 , longitudinal convexity 305 may end at some other location on the bottom surface 183 of the shank 111 . the shank 111 , has a cavity 309 which is formed by the top portion 186 and bottom portion 187 . the cavity has a beginning point 311 and an end point 313 . the cavity 309 begins at the beginning point 311 longitudinally closer to the heel region . the cavity 309 terminates at end point 313 closer to the middle region . the shank 111 has a bottom surface 183 that may be connected to the top surface 117 of the bottom layer 109 by either friction and / or an adhesive and / or other similar means . alternatively , substantially the entire bottom surface 183 of the shank 111 may be molded to substantially the entire top surface of the bottom layer 109 . as shown in fig2 and 2a , the top surface 117 of the lower layer 109 is in substantially continuous contact with the bottom surface 183 of the shank 111 . due to this substantially continuous contact between the top surface 117 of the lower layer 109 and bottom surface 183 of the shank 111 in this embodiment , top surface 117 of the lower layer 109 substantially conforms to bottom surface 183 of the shank 111 . in other embodiments , such substantially continuous contact between top surface 117 of the lower layer 109 and bottom surface 183 of the shank 111 may not be present . fig3 a is a front elevation view in cross section of an embodiment of the shank 111 along line 3 a - 3 a in the direction of the appended arrows . as shown , the bottom surface 183 of the shank 111 along line 3 a - 3 a is straight . fig3 b is a front elevation view in cross section of an alternative embodiment of the shank 111 along line 3 a - 3 a in the direction of the appended arrows . as shown , the bottom surface 183 of the shank 111 along line 3 a - 3 a contains a transverse concavity . fig3 c is a front elevation view in cross section of another alternative embodiment of the shank 111 along line 3 a - 3 a in the direction of the appended arrows . as shown , the bottom surface 183 of the shank 111 along line 3 a - 3 a contains a transverse convexity . fig4 is a perspective view of a preferred embodiment of the shank 111 as seen in fig1 , 2 , 2 a and 3 . fig4 illustrates the cavity 309 being open from the lateral to medial side of the shoe . in normal use of the shoe , each forward step taken by the user begins when the heel region 173 of the outsole 105 begins to make contact with the ground 100 . the lower layer 109 of the midsole 103 in the heel region 163 that is made of less dense and more readily compressible material then begins to compress and deform , allowing the heel of the user &# 39 ; s foot to sink toward the ground 100 to a greater extent than it would sink while wearing a conventional shoe . due to longitudinal concavity 303 , the lower layer 109 is relatively thick in the heel region 163 . since this relatively thick heel region 163 of the lower layer 109 is also relatively soft and highly compressible , it mimics the effect of walking or running on a sandy beach , thereby requiring the user to exert more energy while walking or running than would be required when walking or running while wearing conventional shoes . additionally , since the heel region 163 of the lower layer 109 is relatively thick and highly compressible , it has a degree of inherent longitudinal and transverse instability that is not present in conventional shoes . this inherent instability forces the user to engage in a balancing effort and use muscles and muscle control and coordination to maintain a normal walking gait that would not be required with conventional shoes . however , while also maintaining an inherent instability due to the lower layer 109 as discussed above , the shank 111 , due to its rigidity and structure is able to provide proper support to the user &# 39 ; s heel so that although the heel region 163 compresses and provides instability , the shank 111 provides stability and does not compress . as the step continues , the user &# 39 ; s weight shifts to the middle regions 152 , 162 , 262 , and 172 and the shoe rolls forward in a smooth motion without the user having to overcome any abrupt pivot point . the lower layer 109 of the midsole 103 in the middle region 162 then compresses and deforms , allowing the user &# 39 ; s foot in that region to sink toward the ground 100 more than it would sink if the user were wearing conventional shoes , due to the inherent instability due to the lower layer 109 as discussed above . as with the above , the shank 111 , due to its rigidity and structure is able to provide proper support to the user &# 39 ; s midfoot area . the cavity 309 in the shank 111 , may cause the bottom portion 187 of the shank 111 to compress a small amount in the area directly below the cavity 309 . this compression provides cushioning and imparts some instability , but the shank 111 still maintains adequate support to the user &# 39 ; s foot . as the step continues , the user &# 39 ; s weight then shifts to the toe regions 151 , 161 , 251 , and 171 . the lower layer 109 of the midsole 103 in the toe region 161 then compresses and deforms , allowing the user &# 39 ; s foot in that region to sink toward the ground 100 more than it would sink if the user were wearing conventional shoes . as shown in fig2 a , the thickness of the lower layer 109 in the toe region 161 is typically not as great as it is in the heel region 163 . this decrease in thickness of the lower layer 109 results in relatively more stability in the toe region 161 . this allows the user , when completing his / her step more control when pushing off with the forefoot ball of the user &# 39 ; s foot . all of this simulates the effect , and imparts the fitness benefits , of running or walking on a sandy beach or on a giving or uneven soft surface regardless of the actual hardness of the surface . fig5 a - 5d show a side elevation exterior view of a representative shoe that embodies the instant invention . fig5 a shows this representative shoe in a fully unloaded state . fig5 b , 5 c , and 5 d show this representative shoe undergoing normal loading that occurs when a user walks or runs while wearing the shoe . in fig5 a - 5d , the shank 111 does not undergo a significant amount of compression aside from the area occupied by cavity 309 . thus the compression of the shank is not shown aside from the area occupied by cavity 309 . in fig5 a - 5d , the straight lines identified by , respectively , reference numerals 501 a - 501 d , 502 a - 502 d , and 503 a - 503 d each represent the thickness of the upper layer 107 at the location where each such straight line 501 a - 501 d , 502 a - 502 d , and 503 a - 503 d appears . the straight lines identified by , respectively , reference numerals 504 a - 504 d , 505 a - 505 d , and 506 a - 506 d each represent the thickness of the lower layer 109 at the location where each such straight line 504 a - 504 d , 505 a - 505 d , and 506 a - 506 d appears . the straight lines identified by , respectively , reference numerals 509 a - 509 d each represent the area occupied by the cavity 309 . a decrease in the area represented by numeral 509 a - 509 d represents a compression in the cavity 309 of shank 111 . as shown in the unloaded state in fig5 a , the upper layer 107 and lower layer 109 are not undergoing any compression . as also shown in fig5 a , the outsole 105 is not undergoing any deflection or deformation . in this fully uncompressed state , the thickness of the upper layer 107 and the thickness of the lower layer 109 are each at their respective maximum thickness . this maximum thickness is indicated by , and corresponds to , the length of each straight line 501 a - 506 a , each one of which is at its maximum length as shown in fig5 a . furthermore , the area occupied by the cavity is at its maximum . this maximum area is indicated by and corresponds to the length of the straight line 509 a . fig5 b shows the representative shoe in an orientation where the user &# 39 ; s heel ( not shown ) is imparting a load in the heel regions 153 , 163 , 253 , and 173 , shown in fig1 and 2 . in normal use of the shoe , each forward step taken by the user begins when the heel region 173 of the outsole 105 begins to make contact with the ground 100 . the lower layer 109 of the midsole 103 in the heel region 163 that is made of less dense and more readily compressible material then begins to compress and deform , allowing the heel of the user &# 39 ; s foot to sink toward the ground 100 to a greater extent than it would sink while wearing a conventional shoe . due to longitudinal concavity 303 , the lower layer 109 is relatively thick in the heel region 163 . since this relatively thick heel region 163 of the lower layer 109 is also relatively soft and highly compressible , it mimics the effect of walking or running on a sandy beach , thereby requiring the user to exert more energy during use than would be required with conventional shoes . additionally , since the heel region 163 of the lower layer 109 is relatively thick and highly compressible , it has a degree of inherent longitudinal and transverse instability that is not present in conventional shoes . this inherent instability forces the user to engage in a balancing effort and use muscles and muscle control and coordination to maintain a normal gait that would not be required with conventional shoes . however , while also maintaining an inherent instability due to the lower layer 109 as discussed above , the shank 111 , due to its rigidity and structure is able to provide proper support to the user &# 39 ; s heel so that although the heel region 163 compresses and provides instability , the shank 111 provides stability and does not compress . under this loading condition , the heel region 153 of the upper layer 107 is undergoing a relatively small amount of compression . this relatively small amount of compression results in a relatively small decrease in the thickness of the heel region 153 of the upper layer 107 . this relatively small decrease in thickness is indicated by 501 b . under this same loading , the heel region 163 of the lower layer 109 is undergoing a relatively large amount of compression . this relatively large amount of compression results in a relatively large decrease in the thickness of the heel region 163 of the lower layer 109 . this relatively large decrease in thickness is indicated by 504 b . under this same loading , the heel region 173 of the outsole 105 is undergoing a relatively large amount of deflection . this relatively large amount of deflection in the heel region 173 of the outsole 105 is caused by the heel region 173 conforming to the ground 100 as it bears the load of the user . this deflection and conformity of the heel region 173 of the outsole 105 is indicated by the straight portion of the outsole 105 where it contacts the ground 100 as shown in fig5 b . fig5 c shows the representative shoe in an orientation where the user &# 39 ; s foot ( not shown ) is imparting a load in the middle regions 152 , 162 , 262 , and 172 , shown in fig1 and 2 . as the step continues , the user &# 39 ; s weight shifts to the middle regions 152 , 162 , 262 , and 172 and the shoe rolls forward in a smooth motion without the user having to overcome any abrupt pivot point . the lower layer 109 of the midsole 103 in the middle region 162 then compresses and deforms , allowing the user &# 39 ; s foot in that region to sink toward the ground 100 more than it would sink if the user were wearing conventional shoes , due to the inherent instability due to the lower layer 109 as discussed above . as with the above , the shank 111 , due to its rigidity and structure is able to provide proper support to the user &# 39 ; s midfoot region . the cavity 309 in the shank 111 , may cause the bottom portion 187 of the shank 111 to compress a small amount in the area directly below the cavity 309 . that compression provides cushioning and imparts some instability , but the shank 111 still maintains adequate support to the user &# 39 ; s foot . under this loading condition , the middle region 152 of the upper layer 107 is undergoing a relatively small amount of compression . this relatively small amount of compression results in a relatively small decrease in the thickness of the middle region 152 of the upper layer 107 . this relatively small decrease in thickness is indicated by 502 c . under this same loading , the middle region 162 of the lower layer 109 is undergoing a relatively large amount of compression . this relatively large amount of compression results in a relatively large decrease in the thickness of the middle region 162 of the lower layer 109 . this relatively large decrease in thickness is indicated by 505 c . under this same loading , the middle region 172 of the outsole 105 is undergoing a relatively large amount of deflection . this relatively large amount of deflection in the middle region 172 of the outsole 105 is caused by the middle region 172 conforming to the ground 100 as it bears the load of the user . this deflection and conformity of the middle region 172 of the outsole 105 is indicated by the straight portion of the outsole 105 where it contacts the ground 100 as shown in fig5 c . furthermore , the area occupied by the cavity 309 is decreased due to the weight of the user &# 39 ; s foot with respect to the ground . the decrease in area of cavity 309 is shown in line 509 c . fig5 d shows the representative shoe in an orientation where the user &# 39 ; s foot ( not shown ) is imparting a load in the toe regions 151 , 161 , 251 , and 171 , shown in fig1 and 2 . as the step continues , the user &# 39 ; s weight then shifts to the toe regions 151 , 161 , 251 , and 171 . the lower layer 109 of the midsole 103 in the toe region 161 then compresses and deforms , allowing the user &# 39 ; s foot in that region to sink toward the ground 100 more than it would sink if the user were wearing conventional shoes . as shown in fig2 a , the thickness of the lower layer 109 in the toe region 161 is typically not as great as it is in the heel region 163 . this decrease in thickness of the lower layer 109 results in relatively more stability in the toe region 161 . this allows the user , when completing his / her step more control when pushing off with the forefoot ball of the user &# 39 ; s foot . under this loading condition , the toe region 151 of the upper layer 107 is undergoing a relatively small amount of compression . this relatively small amount of compression results in a relatively small decrease in the thickness of the toe region 151 of the upper layer 107 . this relatively small decrease in thickness is indicated by 503 d . under this same loading , the toe region 161 of the lower layer 109 is undergoing a relatively large amount of compression . this relatively large amount of compression results in a relatively large decrease in the thickness of the toe region 161 of the lower layer 109 . this relatively large decrease in thickness is indicated by 506 d . under this same loading , the toe region 171 of the outsole 105 is undergoing a relatively large amount of deflection . this relatively large amount of deflection in the toe region 171 of the outsole 105 is caused by the toe region 171 conforming to the ground 100 as it bears the load of the user . this deflection and conformity of the toe region 171 of the outsole 105 is indicated by the straight portion of the outsole 105 where it contacts the ground 100 as shown in fig5 d . the area in the cavity 309 is now returned to its original state as shown in line 509 d , which is equal to line 509 a . fig7 , 8 and 8 a show another embodiment of the invention . the midsole 703 in this alternative embodiment does not have an upper layer but rather is comprised of a shank 711 and a lower layer 709 . the lower layer 709 can be comprised of two or more sub - layers . in this alternative embodiment , lower layer 709 has a top surface 717 substantially opposite a bottom surface 721 . the shank 711 has a top surface 781 substantially opposite a bottom surface 783 . the shank has a top portion 786 and a bottom portion 787 similar to the embodiment of shank 111 shown in fig3 . the outsole 705 , which is not part of the midsole 703 , has a top surface 719 substantially opposite a bottom surface 723 . as shown in fig7 , when the shoe is in its normal , upright position , the lower layer 709 is below the shank 711 and the outsole 705 is below the lower layer 709 . fig8 is a side elevation view of the alternative embodiment . the shoe has a front tip 740 located at the farthest point toward the front of the shoe and a rear tip 742 located at the farthest point toward the rear of the shoe . the shank 711 includes a toe region 851 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that begins in the vicinity of the front tip 740 and extends from there to a location that is approximately one third of the distance toward the rear tip 742 . the lower layer 709 includes a toe region 761 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that begins in the vicinity of the front tip 740 and extends from there to a location that is approximately one third of the distance toward the rear tip 742 . the outsole 705 includes a toe region 771 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that begins in the vicinity of the front tip 740 and extends from there to a location that is approximately one third of the distance toward the rear tip 742 . the shank 711 includes a heel region 853 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that begins in the vicinity of the rear tip 742 and extends from there to a location that is approximately one third of the distance toward the front tip 740 . the lower layer 709 includes a heel region 763 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that begins in the vicinity of the rear tip 742 and extends from there to a location that is approximately one third of the distance toward the front tip 740 . the outsole 705 includes a heel region 773 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that begins in the vicinity of the rear tip 742 and extends from there to a location that is approximately one third of the distance toward the front tip 740 . the shank 711 includes a middle region 862 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that extends approximately between the toe region 851 and the heel region 853 . the lower layer 709 includes a middle region 762 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that extends approximately between the toe region 761 and the heel region 763 . the outsole 705 includes a middle region 772 that extends substantially from the medial side of the shoe to the lateral side of the shoe at a location that extends approximately between the toe region 771 and the heel region 773 . fig8 a is an exploded side elevation view of fig8 . the lower layer 709 is made of a compressible and deformable yet resilient material . typically the lower layer 709 will have a durometer hardness between about 20 and about 45 on the asker c scale . the top surface 781 of the shank 711 is typically positioned below an insole board ( not shown ) which is typically positioned below a sockliner ( not shown ). as shown in fig8 and 8a , top surface 717 of the lower layer 709 is in substantially continuous contact with , and substantially conforms to , the bottom surface 783 of the shank 711 . in other embodiments , such substantially continuous contact between top surface 717 and bottom surface 783 may not be present . the bottom surface 783 of the shank 711 , as shown in fig8 a , has a longitudinal concavity 782 that comprises at least a downward curve 790 located in at least a portion of the heel region 853 . the shank 711 has a frontmost point 750 and a rearmost point 755 . downward curve 790 of longitudinal concavity 782 begins at , or near the vicinity of , the rearmost point 755 of the shank 711 and gradually and continuously descends downwardly from there through a point at or near the vicinity of the middle region 862 . the portion of the bottom surface 783 of the shank 711 indicated by lines extending from , and associated with , reference numeral 782 indicates the approximate range wherein longitudinal concavity 782 is typically primarily located . longitudinal concavity 782 may , or may not , be entirely located within the range indicated by the lines extending from , and associated with , reference numeral 782 . longitudinal concavity 782 , as shown in fig8 a , is relatively shallow due to its large radius of curvature or radii of curvature . longitudinal concavity 782 may comprise a curve or curves in addition to downward curve 790 . the radius of curvature throughout longitudinal concavity 782 may be completely constant , may have one or more constant portions mixed with one or more non - constant portions , or may be completely non - constant . downward curve 790 , as well as any other curve or curves that are part of longitudinal concavity 782 , may , at any point on any of those curves , have a slope that is gradual , moderate or steep . although downward curve 790 of longitudinal concavity 782 is shown in fig8 a as beginning near the rearmost point 774 , downward curve 790 of longitudinal concavity 782 may instead begin at some other location on the shank 711 . although longitudinal concavity 782 is shown in fig8 a as ending at a location in the middle region 862 or the location where the heel region 853 transitions into the middle region 862 , longitudinal concavity 782 may end at some other location on the bottom surface 783 of the shank 711 . the bottom surface 783 of the shank 711 , as shown in fig8 a , has a longitudinal concavity 785 that comprises at least an upward curve 792 located in at least a portion of the middle region 862 . upward curve 792 of longitudinal concavity 785 begins at , or near the vicinity of , the middle region 862 of the lower layer 709 and gradually and continuously ascends upwardly from there through at least a portion of the toe region 851 . the portion of the bottom surface 783 of the shank 711 indicated by lines extending from , and associated with , reference numeral 785 indicates the approximate range wherein longitudinal concavity 785 is typically primarily located . longitudinal concavity 785 may , or may not , be entirely located within the range indicated by the lines extending from , and associated with , reference numeral 785 . longitudinal concavity 785 , as shown in fig8 a , is relatively shallow due to its large radius of curvature or radii of curvature . longitudinal concavity 785 may comprise a curve or curves in addition to upward curve 792 . the radius of curvature throughout longitudinal concavity 785 may be completely constant , may have one or more constant portions mixed with one or more non - constant portions , or may be completely non - constant . upward curve 792 , as well as any other curve or curves that are part of longitudinal concavity 785 , may , at any point on any of those curves , have a slope that is gradual , moderate or steep . although upward curve 792 of longitudinal concavity 785 is shown in fig8 a as beginning near the middle region 762 , upward curve 792 of longitudinal concavity 785 may instead begin at some other location on the bottom surface 783 of the shank 711 . although longitudinal concavity 785 is shown in fig8 a as ending at a location in the toe region 851 , longitudinal concavity 785 may end at some other location on the bottom surface 783 of the shank 711 . the bottom surface 783 of the shank 711 , as shown in fig8 a , has a longitudinal convexity 789 that comprises the downward curve 790 and upward curve 792 and that is typically located in at least a portion of the middle region 862 . longitudinal convexity 789 may , or may not , be entirely located within the range indicated by the lines extending from , and associated with , reference numeral 789 . longitudinal convexity 789 , as shown in fig8 a , is relatively shallow due to its large radius of curvature or radii of curvature . longitudinal convexity 789 may comprise a curve or curves in addition to upward curve 792 and downward curve 790 . the radius of curvature throughout longitudinal convexity 789 may be completely constant , may have one or more constant portions mixed with one or more non - constant portions , or may be completely non - constant . downward curve 790 and upward curve 792 , as well as any other curve or curves that are part of longitudinal convexity 789 , may , at any point on any of those curves , have a slope that is gradual , moderate or steep . although longitudinal convexity 789 is shown in fig8 a as ending at a location where the middle region 762 transitions into the toe region 761 , longitudinal convexity 789 may end at some other location on the bottom surface 783 of the shank 711 . as shown in fig8 and 8a , the outsole 705 typically curves upwardly in the heel region . the outsole 705 has a frontmost point 770 and a rearmost point 774 . when the shoe is in its typical upright , unloaded state , the frontmost point 770 and the rearmost point 774 are both relatively high above the ground 100 . from a point at or near the vicinity of the frontmost point 770 , the outsole 705 has a gradual downward curve 795 that continues through at least a portion of the toe region 771 of the outsole 705 . starting in the middle region 772 , the outsole 705 has a gradual , upward curve 796 that continues to curve upward through at least a portion of the heel region 773 of the outsole 705 . this gradual upward curve 796 typically continues until the outsole 705 approaches the vicinity of the rear tip 742 of the shoe . this upward curve 796 is typically sharper than downward curve 795 in the toe region 771 . upward curve 796 may be substantially sharper than shown in fig8 a or substantially shallower than shown in fig8 a . fig9 a depicts a top plan view of the top surface of an alternative embodiment of a shank 901 along line 6 c - 6 c in the direction of the appended arrows . as shown , the shank 901 shown in fig9 a differs from the shank 111 shown in fig6 c . the shank 901 , instead of having a fork - like structure as shown in 6 c , does not have any open areas and occupies substantially all of the area from the medial to the lateral side of the shoe between the rear tip 142 and the front tip 140 . fig9 b depicts a top plan view of the top surface of another alternative embodiment of a shank 903 along line 6 c - 6 c in the direction of the appended arrows . as shown , the shank 903 shown in fig9 b differs from the shank 111 shown in fig6 c . the shank 903 , instead of extending from the rear tip 142 to the front tip 140 , extends only from the rear tip 142 to an area close to the middle region 262 and does not extend to the front tip 140 . while the foregoing detailed description sets forth selected embodiments of a shoe in accordance with the present invention , the above description is illustrative only and not limiting of the disclosed invention . the claims that follow herein collectively cover the foregoing embodiments . the following claims further encompass additional embodiments that are within the scope and spirit of the present invention .
a shoe having a toe region , a middle region , a heel region , and a multi - layer , multi - density midsole ; the midsole being comprised of at least a shank and a lower layer ; the bottom surface of the shank having at least one longitudinal concavity and at least one longitudinal convexity , the longitudinal concavity typically occupying a substantial portion of the heel region and the longitudinal convexity typically occupying a portion of the middle region . collectively , these elements contribute to making the shoe appropriate for both walking and higher impact activities such as running , and simulating the effect , and imparting the fitness benefits , of use on a sandy beach or on a giving or uneven surface regardless of the actual hardness of the surface .