fig1 shows an embodiment of the shoe 10 with upper 14 and lower 16 joined along the upper sole 18 extending through the heel portion 20 , instep portion 22 , and toe portion 24 . the blended heel 26 defines a cavity 28 that extends from the rearmost point of the heel portion 20 forward under the instep portion 22 . the blended heel 26 is made from a resilient material , typically rubber so the cavity walls offer some resiliency , but other resilient materials known to persons skilled in the art are within the scope of the present invention . two separate materials may be used , as is shown here , with the layer adjacent the upper sole of a softer material than the remainder of the heel . the mainspring 30 is positioned orthogonal to the longitudinal axis 12 , as shown in fig2 , and under the heelstrike point of the interior of the shoe . the mainspring 30 may be secured by lugs 36 ( upper ) and 38 ( lower ; not shown ) set into recesses 40 and 42 , and provides the majority of resilient force to the wearer &# 39 ; s steps . auxiliary springs 32 and 34 shown in fig2 add stability and enhanced resiliency . in one or more embodiments , a magnetic sleeve 46 is included as shown in fig1 to further enhance the well - being of the wearer with magnetic therapy . also , the pad 48 at the bottom of the blended heel 26 serves not only as a height - enhancer , but also helps to distribute the spring load throughout the heel portion 20 so that the entire shoe is lifted , not just the wearer &# 39 ; s foot . fig2 shows one configuration of the springs . the mainspring 30 is located generally on the longitudinal axis 12 in the center of the shoe width , and the auxiliary springs 32 and 34 are located forward of the mainspring , toward the toe portion 24 and to either side of the longitudinal axis . the lateral spacing of the auxiliary springs 32 and 34 provides overall stability to the shoe and enhances the lift felt by the wearer . one placement of the auxiliary springs 32 and 34 is to have them spaced evenly in front of the mainspring , equidistant from both the mainspring and the longitudinal axis , so that the wearer &# 39 ; s ankle is not turned either inward or outward . also in this configuration , the lift from the springs is directed upward to enhance the lift from the mainspring . on the other hand , strategic placement of the springs offset from each other may aid in the correction of pronation or other ankle alignment problems in other embodiments . fig3 shows the recesses 40 , 52 , 54 for the springs in one embodiment and also shows how there may be other recesses 56 ( rectangular , circular , or of any other shape ) built into the rubber material to aid in overall stability . the design of these various smaller recesses 56 may aid in air circulation within the heel cavity and may work in concert with an air pressure valve to help express air from the cavity on depression thereof . in one or more embodiments , the shoe 10 includes a one - way air exhaust valve 100 as shown in fig3 whereby air is expelled out the valve 100 when the heel 20 is compressed and the volume of the cavity 28 is reduced . the valve 100 is a one - way valve so that water or other unwanted debris is prevented from entering the cavity 28 . the valve 100 is also such that air freely flows out rather than seeking a path in a forward direction through the sole as described in other embodiments herein . fig4 shows one embodiment where a load 80 is placed onto the shoe heel portion 20 so as to compress the mainspring 30 and the auxiliary springs 32 and 34 within the cavity 28 . the cavity 28 is not sealed ( and the one - way air exhaust or exit valve 100 not present ), and thus when the volume of the cavity 28 is reduced air is discharged in a forward direction towards the instep portion 22 and toe portion 24 and through the upper sole 18 as shown in fig4 , which provides overall stability to the shoe and enhances the lift and fresh air feeling felt by the wearer . fig5 shows the air flow depicted in fig4 with arrows in one embodiment within the shoe 10 through a channel structure 82 and channel structure 84 to aeration channels 86 in the instep portion 22 and toe portion 24 of the shoe 10 . fig6 illustrates an embodiment with the upper sole 18 includes a plurality of openings 18 a to further facilitate the flow of air within the shoe 10 . fig7 illustrates another embodiment of a ventilated shoe of the present invention . in this embodiment an air pump 90 is provided in the cavity 28 in the heel portion 20 , rather than the cavity 28 itself in conjunction with the one way valve 100 acting in a similar manner as described above . the air pump 90 is made of a conventional construction well known to persons skilled in the art and is not described in detail here . the air pump 90 is connected to the one - way air suction valve 92 as shown in fig7 and is also connected to the one - way air exhaust valve 100 also as shown in fig7 . the one - way air suction valve 92 is adjacent to the air channel 82 and the air channel 84 , although an intermediate connecting channel 94 can be provided to connect the air channels 82 and 84 to the one - way air suction valve 92 . when the shoe 10 is used for walking , air enters the shoe adjacent to the where the user &# 39 ; s ankle and leg are near to the shoe 10 or at or near the upper 14 . the air flows through the upper sole 18 including through the openings 18 a in the upper sole 18 to the aeration channels 86 on the lower 16 of the shoe 10 . air then flows to the air channels 82 and 84 to the one - way suction valve 92 . the air then enters the air pump 90 and is expelled out the one way air exhaust valve 100 to the exterior of the shoe 10 as depicted schematically in fig7 by arrow 104 . in one or more embodiments , a waterproof ventilation valve 102 is provided on the exterior of the shoe 10 as shown in fig7 to further inhibit water or other debris from entering the shoe 10 or cavity 28 . the air pump 90 operates so that when it is compressed , such as by a wearer &# 39 ; s foot while walking , the air pump 10 is compressed which forces the air in the air pump 90 out through the valve 100 . when the air pump 90 expands , such as when the wearer lifts his foot and heel during a walking stride , air flows into the air pump 90 through the one - way air suction valve 92 . therefore , while walking at even a normal pace , the shoes and thus the feet of the individual wearing the inventive shoes are ventilated with fresh air . alternatively , the air pump 90 could include a small thermoelectric device 91 to remove heat ( or cold ) and humidity from the inside of the shoe . fig8 illustrates an embodiment which includes a lower sole 150 , made from open cell foam or equivalent materials well known to persons skilled in the art , positioned between the upper sole 18 and the aeration channels 86 to further facilitate the flow of air within the shoe 10 with the upper sole 18 having a plurality of openings 18 a as shown in fig8 . alternatively , the lower sole 150 could be made of generally air impervious material having one or more large holes for air to pass from the lower 16 up through the upper sole 18 . fig9 illustrates a second embodiment sport shoe 200 with an upper portion 202 and sole 204 , wherein the sole 204 comprises an outsole 206 , and a midsole 208 . referring to fig1 , the outsole 206 is attached to the midsole 208 , together forming a heel 209 . the midsole 208 includes a first part 210 and a second part 212 . the first part 210 of the midsole 208 is designed to reside substantially under the heel of a wearer , while the second part 212 supports the remainder of the wearer &# 39 ; s foot . referring to fig1 a , a cross section of the sports shoe 200 , outsole 206 , midsole 208 and related structures are shown in an uncompressed state . here , the first part 210 of the midsole 208 is disposed above and engaged by a series of springs 214 . the bottoms of the springs 214 engage the outsole 206 . the second part 212 of the midsole 208 engages the outsole 206 . in this manner , downward pressure by a wearer &# 39 ; s heel is distributed across the springs 214 . fig1 a also illustrates the cavity 216 housing the springs 214 , enclosed by the first part 210 and second part 212 of the midsole 208 , and the outsole 206 . referring to fig1 b , the outsole 206 , midsole 208 and related heel 209 structures are shown in a compressed state . in this state the springs 214 are compressed , reducing the volume of the cavity 216 . the cavity 216 is preferably obscured from view by the outsole 206 forming a sidewall 220 around the heel 209 portion of the shoe 200 . preferably the springs 214 are compression springs wherein the working distance between the minimum operational state and maximum operational state is about 6 mm . optionally , an insole 213 may be installed inside the shoe over the midsole 208 . as the springs 214 compress and cavity 216 volume decreases , the outsole 206 sidewall 220 folds together . the outsole 206 has a bottom pad 222 connected to the springs 214 . the bottom pad 222 makes surface contact while the shoe is under a wearer &# 39 ; s weight . in order to ensure vertical movement of the springs 214 and minimize lateral displacement of the outsole 206 relative to the midsole 208 , the outsole 206 comprises a connecting portion 224 between the sidewall 220 and horizontal pad 222 . as the sidewall 220 deflects downward relative to the bottom pad 222 , the connecting portion 224 folds inward upon itself , sandwiching the bottom pad 222 within the sidewall 220 preventing lateral displacement of the heel 209 . the material comprising the connecting portion 224 is resiliently deformable and is disposed in the outsole 206 between the sidewall 220 and bottom pad 222 . referring back to fig9 and 10 , an air passageway 217 releases the air from the heel 209 . in a preferred embodiment the air passageway 217 comprises a one - way valve 102 ( as illustrated in fig7 ) which expels air , and prevents air , liquid or other debris from entering back into the heel 209 . a thermo - electric cooling ( and / or heating ) device 219 may be installed in the sole to remove heat and humidity and preserve the wearer &# 39 ; s comfort . the outsole 206 is preferably abrasion resistant rubber material . the bottom pad 222 of the heel 209 may be of a softer rubber , such that the bottom pad 222 itself compresses to some extent under the wearer &# 39 ; s weight . the first part 210 of the midsole 208 comprises a rigid material , preferably thermoplastic polyurethane , and may include additives such as silica based or other nanoparticles to increase dimensional stability . the second part 212 of the midsole 208 is of a very lightweight material , preferably ethylene - vinyl - acetate . fig1 through 15 illustrate another embodiment of a resilient shoe sole 500 . in this embodiment the resilient sole 500 comprises a midsole 502 , an upper foundation 504 , and an outsole 506 . a heel cavity 508 is disposed in the sole 500 , and a cap 510 may cover the heel cavity 508 . while the example illustrations show a single heel cavity 508 in the sole 500 , it is contemplated that the sole 500 may have additional cavities [ not shown ] in other locations , and also that the heel cavity 508 may be divided into more than the single heel cavity 508 shown . it is also contemplated that the midsole 502 may be made of softer materials than the outsole 506 , such as ethylene vinyl acetate , while the cap 510 may be made of harder materials , for example thermoplastic polyurethane . in the exemplary embodiment , the heel cavity 508 may house one or more springs 512 . as shown in the figures , a larger spring 512 is seated behind two smaller springs 512 to add support and stability to the sole 500 . it is also contemplated that either a single spring 512 or additional springs [ not shown ] may be incorporated into the sole 500 , including in other areas of the sole 500 . alternatively , springs 512 may be omitted altogether . in one embodiment , the spring ( s ) 512 may have an ideal elasticity of between 50 to 700 lb / ft 2 . trampoline - like rebound in the sole 500 is achieved by the structure of the outsole 506 . in addition to other structures , e . g ., springs , the outsole 506 comprises a platform 514 and a sidewall 516 . the sidewall 516 may be substantially rigid and extend around the heel cavity 508 . in this manner , it may be designed to form the periphery of the sole &# 39 ; s 500 heel area . the platform 514 , while ideally made of resilient material , may be substantially rigid due to its thickness . the pressure required to move the platform 514 relative to the sidewall 516 determines the amount of resiliency and rebound in the sole 500 . the strength of that resiliency is governed by a connector 520 connecting the platform 514 and sidewalls 516 , and by the distance the platform 514 must travel so that both the platform 514 and side wall 516 encounter a common walking surface . referring to fig1 , the connector 520 has a predetermined length 522 as measured from the perimeter wall 526 of the platform 514 , and the inner , substantially vertical surface 528 of the sidewall 516 , and a predetermined thickness 524 , as measured from a top surface 530 of the connector 520 to a bottom surface 532 of the connector 520 . while the length 522 and thickness 524 determine the force necessary to deform the connector 520 , the size of the platform 514 perimeter wall 526 extends below the sidewall 516 determines the amount of rebound achieved by the sole 500 . the thickness 524 determines the shock absorbing properties of the sole 500 and the ability of the sole 500 to deflect upward when compressed on a down step . an increased thickness 524 requires more weight for full deflection . the optimum operational size for the thickness 524 is between 1 mm and 10 mm . the length 522 determines the amount of rebound in the sole 500 after deflection . it operates like a rubber band or sling shot , developing more propulsion the longer the deformable area 520 stretches . the optimum operational size for the length 522 portion of the deformable area 520 is between 1 mm and 10 mm . the platform 514 perimeter wall 526 is used to govern the maximum amount of deflection in the sole 500 . deflection ends once the sidewall 516 of the sole 500 reaches the surface on which the platform 514 rests . the optimum operational height for the perimeter wall 526 is between 2 mm and 25 mm . referring back to fig1 and 13 , in a resting position , the connector 520 of the outsole 506 maintains the platform 514 in a fully extended position . the connector 520 may simply be a portion of the material comprising the outsole 506 . in alternative embodiments , the connector 520 may be made of material having an elasticity differing from the platform 516 , sidewall 518 , or both . referring again to fig1 and 15 , in a deformed position , the connector 520 of the outsole 506 is stretched such that the platform 514 is deflected upward into the cavity 508 until the sidewalls 516 of the outsole 506 reach the surface on which the platform 514 rests . it is contemplated that in certain embodiments the platform 514 may deflect only partially upward into the cavity 508 as shown in fig1 . additionally , while the figures show a substantially planar connector 520 when the platform 520 is in a deflected state , it is contemplated that due to the elastic nature of the connector 520 it may deform into a curved or “ s ” shape when the platform 514 deflects into the cavity 508 . the ratio of the thickness 524 , length 522 , and the perimeter wall 526 height ( and the resiliency of the spring and rubber material ) have different measurements in various shoe designs : for example , it is anticipated dress shoes will be designed with maximum flexibility due to their low - impact use . casual shoes are expected to have a middle range of flexibility for repeated impact during walking . finally , sports or running shoes will have the lowest flexibility due to the great force of impact from sports activities . in some embodiments , the connector 520 may also be of varied size and shape due to shoe size and whether intended for male or female use . for instance , a size seven women &# 39 ; s shoe might be calibrated for around 120 lbs of compression , while a men &# 39 ; s size eleven shoe might be calibrated for 200 or 250 lbs on average . referring to fig1 and 18 , the sole 500 is shown in an uncompressed state incorporated into a sports shoe upper 534 . in this embodiment , the deformable area [ not shown ] would be configured with a greater thickness 524 , length 522 , or a combination of the two . the platform 514 perimeter wall 526 will have a predetermined height adapted to confer maximum stability to the shoe , which is intended for substantial lateral movement and high impact . in one embodiment , the resilient sole 500 may have a window ( not shown ) permitting observers to see the inner workings of the sole 500 . referring to 19 through 22 , a spring - less dress shoe embodiment of the resilient sole 500 is shown . referring to fig1 and 20 , as in other embodiments , the connector 520 in a resting state preserves the platform 514 in a position substantially lower than the remainder of the outsole 506 . referring to fig2 and 22 , as the sole 500 is compressed the deformable portion 520 allows the platform 514 to deflect upward into the heel cavity . also shown in this embodiment is a pneumatic cooling arrangement designed to take advantage of the changing volume of the heel cavity 508 . a one - way valve 536 in the outsole 506 causes air to leave the heel cavity 508 when compressed . as the heel cavity 508 volume increases , air enters through a series of portals 538 in the sole 500 . in this manner a constant flow of cooling air is achieved . it is anticipated that the pneumatic cooling arrangement may be incorporated into casual and sports shoes as well as the illustrated embodiment . it is also anticipated that the heel cavity 508 of the illustrated dress shoe embodiment may include a spring [ not shown ]. the structure of the resilient shoe sole 500 having been described , its operation will now be discussed . after inserting a foot into a shoe having the resilient shoe sole 500 , and lacing or otherwise fastening the foot therein , a wearer may stand , walk , jog or run in any customary manner . on a down step , as the outsole 506 approaches the ground , the platform 514 encounters a surface . as the wearer &# 39 ; s weight is brought to bear against the shoe sole 500 , the deformable area 520 begins to deform , allowing the platform 514 to depend upward into the cavity 508 of the shoe sole 500 . as discussed , the height of the edge 526 of the platform 514 , the thickness of the clip 524 and the width of the lip 522 are predetermined to create a calibrated resistance depending on the weight of the user and the purpose of the shoe . in addition to the dimensions of the edge 526 and deforming area 520 , it is anticipated that choice of materials may play a role in calibrating the shoe sole 500 . although rubber is one preferred material , rubber stock of differing elasticity may be used to strengthen or weaken the deformable area 520 as necessary . other materials having resilient characteristics are also contemplated . while the present invention has been described with regards to particular embodiments , it is recognized that additional variations of the present invention may be devised by persons skilled in the art without departing from the inventive concepts disclosed herein . by way of example , although the preferred embodiments have been shown and described in terms of men &# 39 ; s casual or dress shoes , or sports shoes , the invention as claimed may apply to all types of shoes and even open - toed or sandals and other variations of footwear .