Exponential functions! Or why you probably still massively underestimate Steemit.com. No, you probably don’t really understand them!

Curious about how long it could theoretically take to reach 50.000.000 users* on STEEMIT.COM? Read on!
“The greatest shortcoming of the human race is our inability to understand the exponential function.” Dr. Albert A. Bartlett

Source picture: https://zedie.wordpress.com/tag/ray-kurzweil/

*Disclaimer! my math skills are very rusty and I made some gross assumptions about average growth rates on Steemit.com , for this one I needed to break out pen and paper. I might have screwed up here or there in the examples but the overall gist is certainly true. I would appreciate any corrections, because I believe this is so important to understand!!!!
Feel free to add corrections or comments on the math! All projections on my part are just to ILLUSTRATE exponential growth.

What's the exponential function?
It is behind interest and the huge changes we will see in our society, economy and technological development.
I believe Steemit.com and Steem itself CAN BE exponential ideas, which is why even the most optimistic persons on this board are more than likely underestimating
how big it really is and how much Steem and other crypto-currencies CAN get.
(There WILL be catastrophic failures along the way, any cryptocurrency has risks too and some can and will fail including STEEM)
I am not making any predictions how big it will actually get, I am explaining with this post what exponential change is and why our brain is underestimating its growth potential. And how fast it can go.

The exponential function is used to describe the size of anything that is growing steadily by a fixed fraction of it self, like e.g. 5% a year (or per month, per day,…)

So the time(e.g. a year, week, month) needed for the growing quantity to increase by this fixed fraction (say 5%) is constant.
So 5% per year growth.

That does not sound very impressive. But how long would it take for something that grows at 5 % a year to double in size?
How do you calculate the doubling time?

You take 70 and divide it by % growth (5%) = 70/5 = 14

So at 5% a year it takes 14 years for the size to double
5% a month it would take 14 Months or a year and two months to double
5% a week, 14 weeks or 3.5 months!

(why 70? You don’t need to remember, but it is an approximation of 100 x ln2 = 69.3 or approximately 70 Ln2 is the Natural logarithm of 2 explained in

See https://en.wikipedia.org/wiki/Natural_logarithm )

Wanna know the time it takes to triple? Easy:
100*Ln3 = 109.86 approx 110 (check Wolfram Alpha https://www.wolframalpha.com/ if you need a scientific calculator)

So 5% per year 110/ 5 = 22 Years to triple
So 5% per month 110/ 5 = 22 months or a little under 2 years!
So 5% per week 110/ 5 = 22 weeks or 5.5 months to triple!

So from this you can see that growth rates of 5% per week seem small but actually they can double something in 3,5 months and TRIPLE in less than 6 months.

What does that mean for Steemit?
Going from https://steemit.com/steemit/@penguinpablo/look-what-happened-on-steemit-over-the-weekend-guys

It seems that from graph 4 “New accounts created”
Since over a month there are about a 1000 new accounts a day, and accelerating. Lets assume that it can maintain the % of growth:

Today there are 180000 accounts and growing with about 4% a week on averaged taken for the last month.
(VERY approximate quick and dirty calculation, just trying to illustrate exponential growth)

So where does that lead? Assuming that rate will remain constant of course (actually it might even accelerate see below)

4% a week = 70 / 4% = 17.5 weeks or about 4.3 months to DOUBLE the amount of members
But 110/4% = 27.5 or 6,8 months to TRIPLE the amount of members
Quadruple the amount of members? 140 / 4% = 35 weeks or 8,7 Months !

To one million? (someone check my math please)
That's 5,5 times 180.000 the accounts a few days ago
So assuming a steady 4 % growth (improbable) = 100 * ln 5.5 = 170
170/ 4% = 42 weeks or 10,6 months or LESS THAN A YEAR to reach a million!

Ok now let’s get really ambitious:
10 million! That is 55 times the number of current members 180.000.
Assuming 4% growth /week ( and again that is unlikely)
100*ln55 = 400
Or at 4% a week = 400 / 4% = 100 weeks or LESS THAN 2 years to reach 10 million.

Mind-blowing? What about 50 million? That requires multiplying current membership 277 * 180000 = 50.000.000
So 100*Ln277 = 560 or there abouts
Or at a steady growth of a humble 4%/week as we have been doing for the last month = 560 / (4%/week)= 140 weeks = approx 980 days or about 2,6 years to reach 50 million!

Here is how that looks on a graph:

Days Members
1 180000
121 360000
179 500000
300 1000000
703 10000000
985 50000000


That’s exponential growth! And the reason why you are probably underestimating Steemit.com´s growth POTENTIAL .
I am not saying it will get there, it is simply illustrating what exponential growth really means.

If Steemit goes on that curve and can maintain it, less than 1000 days is what it could take to reach 50 million users.

You probably think I am crazy at this point, “a couple of million maybe” you think, but 50 million? Forget it…

To illustrate that, how about other social networks? How long did it take for them to reach 50 Million?

Source https://plus.google.com/+PaulAllen/posts/EwpnUpTkJ5W

Looks suspiciously familiar doesn’t it?
Disregarding Google which had a huge advantage already, other social networks took about 1000 days to reach 50 million viewers.

What is going to drive this growth and the value of STEEM?

Other exponential changes are going on that will help fuel this growth and potentially accelerate it further!

You have to realise that the value of a network is an exponential function in and of itself.
So assuming that the value of STEEM is linked to the value of STEEMIT.com as a network we have to take something else into account.

This is called Reed´s law:
From https://en.wikipedia.org/wiki/Reed%27s_law
Reed's law is the assertion of David P. Reed that the utility of large networks, particularly social networks, can scale exponentially with the size of the network.
The reason for this is that the number of possible sub-groups of network participants is 2N − N − 1, where N is the number of participants. This grows much more rapidly than either
the number of participants, N, or
the number of possible pair connections, N(N − 1)/2 (which follows Metcalfe's law).
so that even if the utility of groups available to be joined is very small on a peer-group basis, eventually the network effect of potential group membership can dominate the overall economics of the system.
From David P. Reed's, "The Law of the Pack" (Harvard Business Review, February 2001, pp 23–4):
"[E]ven Metcalfe's law understates the value created by a group-forming network [GFN] as it grows. Let's say you have a GFN with n members. If you add up all the potential two-person groups, three-person groups, and so on that those members could form, the number of possible groups equals 2n. So the value of a GFN increases exponentially, in proportion to 2n. I call that Reed's Law. And its implications are profound."
Source Wikipedia https://en.wikipedia.org/wiki/Network_effect
So assume that we double the amount of members, if Reed’s law holds true the value of that network is not simply x2 but 2^2 or 4 times the previous value each time it doubles in size!

Think about it this way: say you are the very first person to buy a fax machine (back in the day).
It is useless! Now your friend buys one as well. Great! You are in business let's say the value is 1 now.
What happens if you double the people in your network from 2 to 4? Now value of that network is not simply double but 2^2 or four times from when you were just 2.
Because you now have more people to fax to, but also everyone else sees an exponential increase in the number of potential connections!
Now for everyone else that sees that increased utility it has become much more attractive. That is the network effect in a nutshell:
“This creates a positive externality because a user may purchase a telephone without intending to create value for other users, but does so in any case. Online social networks work in the same way, with sites like Twitter and Facebook becoming more attractive as more users join.” (see the above link)
In the fax example there is also a warning, what if something comes along that has a greater utility than a fax, and a greater network say a smartphone. Well the fax network becomes irrelevant. So the lesson to remember is that the value of the network is undermined by technological and societal changes too.

But that is not the only exponential growth curve that can influence steemit.com’s growth.

The internet itself and its expansion itself is on an exponential curve. Google, Facebook, SpaceX and others are working hard to connect the rest of the world in the next 5 years. Their idea is to provide the whole world with broadband sky based internet (Satellites or globes, drones, etc.)
Because they understand the network effect! A mere billion users is not enough for Facebook. The incentive to connect the rest of the world is huge! If they double their users, they can expect to quadruple their company value!
Take a look at this table:source https://www.internetworldstats.com/stats.htm

That is the connection potential and various companies are working hard to connect people with affordable high-speed internet. What about the computers themselves? Well those prices are also an exponential function : basically Moore´s law https://en.wikipedia.org/wiki/Moore%27s_law

It is now possible to buy a smartphone with the same performance of the first Iphone for less than 30 USD. (At some point they offered it for 5 USD in India but that turned out to be scam) http://www.businessinsider.com/onyx-connect-making-30-dollar-smartphone-in-africa-2017-5

So, there are still about 4 billion people who are NOT on the internet! That means that even starting in 2017, the internet can still roughly DOUBLE. It is becoming fast technologically feasible and affordable for developing nations to participate MASSIVELY on the internet. And most of those will join us in the coming 5 years.
Again, this is not just double of what we have now, it will change everything.
Think the internet is valuable now? It will be peanuts compared to what its value will be in 5 years....

Other incentives for Steemit.com particularly
Like you already see with Venezuela, the incentive to publish creative work is huge!
Do you realise how far 20 USD goes these days in Venezuela? That is a month of food!!! (btw please support those guys they really need it!)
Most of the developing countries that are connecting to Steemit.com are going to profit from geo-arbitrage.
Even small sums of money gained through Steemit.com will be worth it to put in significant effort!
The incentive for developing countries to connect to Steemit.com will be a lot higher than existing users of Facebook etc. My wife is from Venezuela; if you are educated and lucky enough to have a job, your salary probably does not cover grocery money for that month! So expect a lot of highly educated, motivated people to contribute and the few cents you can spare will make a world of difference for them!
Unfortunately, people in Venezuela are not unique, there are other similar situations, like the Middle Eastern refugees who all could immensely benefit from a functioning Steemit.com income even though it's only a few dollar a day!

There are of course also things that can put a brake on Steemit.com's growth:

• adoption of internet is mainly driven by mobile these days, if Steemit.com and its content does not play nice with basic smartphones most of that potential public will not connect

• cryptocurrency currently is a pain in the ass, getting easier but still a threshold to overcome!

• language barriers (most growth potential probably is in places that use different languages e.g. Indonesia, China, India, Latin America) (people who speak these languages though have a "yyyyuuuge" first mover advantage. Imagine being the first Indonesian influencer to connect and grow a Indonesian speaking community on Steemit.com !
  That's currently 50 million people potential customers with the potential to connect 200 million more in the next few years! Most of them are young and becoming more and more tech savvy)

• The language barriers also might however also create ghettos on Steamit.com where the value might not get evenly distributed because the rich influencers simply do not see original contributions in other languages. (Automatic AI translation might help eventually.)

• other networks will develop along the same lines (but it is not a zero sum game, the race is on not necessarily to steal Facebook users but to conquer the rest of the world, although eventually FB users will ditch FB as well for various reasons eventually)

• it might be acqui-hired/ or eliminated through buyout or currency manipulation by the big boys which don't mind dumping 50 Million to crush a potential competitor.

• the sky might fall. etc. etc.

If you are interested in the power of exponential technology here are some interesting sources:
Kevin Kelly : The Inevitable http://kk.org/books/the-inevitable/
Peter Diamandis also has perfected this pitch of exponential change in many fora:

I'm super interested in other sources if you have them would appreciate it in the comments! Would be interested to hear your arguments pro or con why Steemit.com and Steem are potential exponential ideas.