The Paradox of the Heap: How Small “Yes, Ands” Can Add Up to Big Results

Pile of shiny US pennies

image credit: swisshippo

If I offered you one single penny to do a task you really don’t want to do, would you jump up and say “yes! Yes, I will do that task for a penny!”?

Of course not.

What if I offered you two pennies?


How about three? Four?? Five???

Probably not.

Okay, what if I offered you 100,000,000 pennies (that’s one million dollars); then would you do it?

Almost definitely.

What if I offered you only 99,999,999 pennies?

Still yes, right?

99,999,998? 99,999,997?? 99,999,996???

Yes, of course you would.

The premise here is that if you don’t want to do the task for a certain amount of money, then there is no way that adding one penny would get you to change your mind and say “yes,”

Similarly, if you would be willing to do a task for a certain amount of money, there is no way that taking away one penny would get you to change your mind and say, “no.”

This creates a paradox; If adding one penny won’t make you switch from a “no” to a “yes,” you will never switch. But there is also clearly some amount of money to which you would say, “yes.”


This is an example of the “Paradox of the Heap,” also known as the Sorites Paradox. The Greek philosopher Sorites came up with this using a heap of sand. It is based on the idea that if you take away one grain of sand from a heap, it's still a heap. But if you keep taking away one grain of sand at a time, eventually, the heap will no longer be a heap.

Thinking of pennies or grains of sand is an effective representation, but the important thing about this paradox is that it illustrates how small changes can lead to big differences. Repeated small actions can sometimes seem so small as to make no difference (like adding a single penny), but when added up over time, they can result in a gigantic change.

One powerful place to apply the principle of the Paradox of the Heap is to the idea of saying "yes, and."
When you first learn about the powerful difference between saying, “yes, and” and “yes, but” it can be tempting to jump into saying, “yes, and” to a huge change or goal. The problem is that this can be overwhelming and lead to stress, procrastination, and, quite possibly, giving up.

If, however, you start with small “yes, ands” - ones that may seem almost meaningless on their own - over time they build into something truly impressive and worthwhile.

Start applying the principle of the Paradox of the Heap by setting and acting on small, achievable, “yes, and” goals and you will be amazed at the things you accomplish over time!

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