I think we have to expand our thinking about the toroidal sphere even more. When looking at maps, I noticed the da Vinci map, from 1514, which uses the Reuleaux Triangle. This triangle is formed from 3 intersecting circles, and is in the center of a trefoil.

"You don't see radio changing gradually and suddenly become radar. #Darwin's theory doesn't work for #technology, and we have to make a new observation."

- W Brian Arthur at SFI today

#evolution #innovation #invention

"Novel technologies are constructed from existing technologies. These offer themselves as components for the construction of further technologies."

- W Brian Arthur at SFI today

#evolution #innovation #invention #technology #engineering #design

Unlike the two-parent #inheritance typical to (but not ubiquitous among) #complex organisms, #technology inherits features from n parents - a "vast ancestral #network" more like horizontal gene transfer networks in #bacteria.

W Brian Arthur on sumulating #invention on a chip:

Does #Archaeology support the Theory of the #AdjacentPossible - that #innovation is combinatorial, persistent, cumulative?

In short, yes. SFI's Tim Kohler on the #Paleolithic data of #technology #evolution & the #prehistory of the infamous "hockeystick" curve:

😉 @SAPIENS_org

#Economist Roger Koppl of @SyracuseU presents a model for the #AdjacentPossible at SFI.

Output = "a combinatorial explosion" or #singularity, albeit one that arguably occurred millions of years ago, or in the distant future (since the model doesn't specify t = 0):

1/

Get a cup of coffee.

In this thread, I'll help you understand the basics of Binomial Thinking.

The future is always uncertain. There are many different ways it can unfold -- some more likely than others. Binomial thinking helps us embrace this view.

2/

The S&P 500 index is at ~3768 today.

Suppose we want to predict where it will be 10 years from now.

Historically, we know that this index has returned ~10% per year.

If we simply extrapolate this, we get an estimate of ~9773 for the index 10 years from now:

3/

What we just did is called a "point estimate" -- a prediction about the future that's a single number (9773).

But of course, we know the future is uncertain. It's impossible to predict it so precisely.

So, there's a sense of *false precision* in point estimates like this.

4/

To emphasize the uncertainty inherent in such predictions, a better approach is to predict a *range* of values rather than a single number.

For example, we may say the index will return somewhere in the *range* of 8% to 12% (instead of a fixed 10%) per year.

5/

10 years from now, this implies an index value in the *range* [8135, 11703]: