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Let's go back 10,000-12,000 years, when humans have yet to make strides in basic machines. In our world, the invention of the wheel makes things easy to move, starting a transportation revolution. This will eventually lead to new technologies, and eventually the rise of more complicated machines.
What if the wheel was never invented? In this world, humans discover a gel-like substance that, when put on an object, immediately reduces friction. All of a sudden, pushing a boulder across a grassy field is more like pushing a boulder across an icy pond - but even easier. The effects of friction can be almost totally neglected.
This leads to a different type of transportation revolution. All of a sudden, the coolest new way to get around is in large sleds with their undersides coated with this gel. Soon, horses are domesticated - way ahead of schedule - as it becomes clear that putting them side by side in front of a sled is a great way to pull heavy loads.
Will this society ever be motivated to invent the wheel (assuming that pulleys are created not out of axles, but out of gel-coated blocks)?
Related points can be found in In a society of flying beings, would the wheel ever be invented?, especially related to pulleys and the application of the wheel to transportation.
4It seems extremely unlikely that such an elementary tool would never be invented, even by a civilization that reached the technological age we now find ourselves in. Depending on the properties of your magic gel it might never have a practical application, but given the mathematically interesting properties of circles, I would be surprised if engineers could avoid ever creating one. Gel scarcity or shortage is also a real concern to motivate wheel invention / adoption. – Avernium – 2015-12-21T22:13:13.877
6Not to mention all the slimy gel trails left everywhere. Eventually there would be a lot of buildup. People would be tracking it into the house, and slipping and breaking things. Bleh :) – Francine DeGrood Taylor – 2015-12-22T01:16:43.790
1@FrancineDeGroodTaylor Hopefully it washes away eventually! Otherwise, I anticipate a huge market for cleaning supplies. . . – HDE 226868 – 2015-12-22T01:17:43.430
What about highly uneven ground? Stone and small ledges would stop a sled in a way that wheels may be able to roll over with enough force. A sled may need to be lifted to get over things that wheels could handle regardless of friction. – shiningcartoonist – 2015-12-22T15:31:42.110
@shiningcartoonist I think it depends on the sled you're thinking of. If it has a curved front (it's not a wheel!), the lack of friction might get you over ledges that a wheel would roll over. – DoubleDouble – 2015-12-22T16:31:28.287
Wheels have a wonderful property of being nearly frictionless in one directly, but very friction-y in the direction 90 degrees from that. Those properties allow wheeled "vehicles" to "park" sideways on a hillside, with very little danger of them rolling to the bottom of the hill. Any gel-covered objects of yours would always tend to slide to the bottom of a hill, gully, etc. (Just a thought, not an answer.) – BrettFromLA – 2015-12-22T18:52:36.677
The egypts had no wheel as far as i know and they were pretty okay. Using wheels just makes transport easier but not impossible. Once we have lowcost teleporters we dont even want to have the wheel. Why should invent it when we can transport thinhs faster and cheaper with teleportation? – BlueWizard – 2016-01-01T00:42:37.383