Humans grow linearly, companies grow exponentially – interview with Khalid Halim
Following links in the OP to<p><a href="http:&#x2F;&#x2F;firstround.com&#x2F;review&#x2F;hypergrowth-and-the-law-of-startup-physics&#x2F;" rel="nofollow">http:&#x2F;&#x2F;firstround.com&#x2F;review&#x2F;hypergrowth-and-the-law-of-star...</a><p>see in part and relevant to the title of this thread<p>&gt; “Human beings grow biologically and linearly. A year from now, you will be a year older — there&#x27;s no growth hacking we can do to make that happen faster. Even if we were looking at the metrics of ‘you’—the age of your bones, your height, everything — you&#x27;re not going to grow exponentially. You&#x27;re going to grow linearly because all biological systems do that,” says Halim. “A company, which is a collection of biological systems called humans, can grow exponentially. Especially in tech, companies exist in a world in which you can be serving 100 customers one day, and a million a year later.”<p>Want to find the root of a function?  Under mild assumptions, Newton iteration gives accuracy that improves as an exponential function of the number of iterations.  This situation is especially well known and easy to see for finding square roots.<p>I will make an argument the other way around, that it&#x27;s humans who can grow exponentially (for a while) and companies grow at best linearly!!<p>Okay, the first example is Leo Szilard walking across a street and then soaking in a bathtub:  He thought, one neutron hits one uranium nucleus which emits two neutrons, ..., four neutrons ... and after positive integer n such <i>generations</i> we have 2^n neutrons emitted.  So, that was exponential growth, all from just Leo walking and later soaking in a bath tub.<p>Then for an organization, at Oak Ridge the were getting about, what was it, 10 grams a day of separated uranium.  So, for 100 grams a day, have 10 times more working units, that is, linear growth.<p>Then when it appeared that maybe one approach to uranium enrichment might not work, try three.  Linear growth.<p>When it appeared that uranium might be too tough to get, try plutonium.  Work with two elements instead of just one, double the number of elements, people, facilities, money, results, etc. and get two paths to success instead of one.  All linear.<p>Then Edward Teller had another <i>exponential</i> idea:  Let the X-rays from fission squeeze deuterium for another essentially exponential growth rate.<p>For another example, Alan Guth wanted to do something so dreamed up the big bang, where exponential growth seems even an understatement.  So, Guth had exponential growth.<p>Since then various organizations have gotten data that confirm what Guth thought, and the growth of those organizations have been essentially linear, that is, twice as much money, people, time yield twice as many new results, e.g., the 3 K background radiation and accelerating growth of the universe.<p>For more, for the traveling salesman problem in Euclidean spaces, R. Karp had an idea --  on problems with positive integer n cities, for any probability p &lt; 1, and for any epsilon &gt; 0, a simple application of minimum spanning trees will as n grows, with probability greater than p get feasible solutions within epsilon percent of optimality.  So, as n grows, the number of traveling salesman tours grows exponentially, really n! (use Sterling&#x27;s approximation to get an exponential), and Karp&#x27;s idea was <i>exponentially</i> powerful, that is, the minimum spanning tree effort grows only as a polynomial in n but <i>beats</i> the exponential challenge of the problem.<p>For another, linear programming commonly has the number of feasible region extreme points growing exponentially with problem size, but the polynomial algorithms can find the possibly unique extreme point in only polynomial time.  If divide by the polynomial, then get linear effort, and the exponential number of extreme points divided by the polynomial is still exponential.  So, the polynomial algorithm idea, one of them from the head of just one person, was exponentially powerful.<p>For another example, Moore&#x27;s law, so far still exponential but from the brains of mostly just a few people and brought to market by essentially linear time, money, people, etc.  Want twice as many chips?  Okay, that linear; build two fabs instead of one and get twice as many chips -- linear.<p>For another, Alexander Fleming looked at some bread mold and how it fought off some bacteria.  Presto, bingo, he had penicillin that saved <i>exponentially</i> many lives.<p>There are lots of other examples where people <i>grew</i> by having <i>exponentially</i> powerful ideas while organizations were limited by twice as much in people, time, and money gives at best, twice as much revenue, maybe less due to the quadratic growth of the overhead of internal communications as the number of people in the organization grows.<p>Net, the big stuff, the stuff with exponential power, is from people, commonly one or at most only a few people, where a company to exploit the exponentially powerful work grows only linearly, that is, twice as many people, etc. in the company result in twice as many customers served.