Among my passions, I love to check financial data about companies I like. Recently I was looking for a quick way to get reliable financial information for comparative analyses. At the same time, I was looking for shortcuts to perform that analysis.

I was researching for myself. I thought why waste so much time on scraping financial reports? While surfing the web, I was looking for a solution and a term popped to my eyes "**computational engine.**"

Wolfram Alpha! That search opened me a universe I wasn't aware of. Yet that universe wasn't only about a fantastic tool I learned to use in several ways. I found out the most amazing entrepreneurial story. That is how I jumped in and researched as much as I could about this topic! Why is this story so remarkable?

Imagine a kid that as many others, is struggling at arithmetic. Imagine that same kid at 12 years old building a physics dictionary and by the age of 14 drafting three books about particle physics. A few years later at 23, that kid, now a man gets awarded as a prodigious physicist. We could stop this story here, and it would be already one of the most incredible stories you'll ever hear.

Yet this is only the beginning. In fact, what if I told you, that same person turned into a successful entrepreneur, which built several companies and a whole new science from scratch! (Let's save some details for later)

That isn't only the story of Wolfram Alpha, a tool that I learned to use and cherish. That is the story of one of the smartest people of our century, a shrewd entrepreneur, and polymath, which turned to influence and being influenced by people like Steve Jobs and Benoit Mandelbrot.

This is the story of Stephen Wolfram.

Writing this post for me has been a pleasure and torture. On the one hand, I jumped into Stephen Wolfram's videos, books, and articles. The more I found out, the more I wanted to know. It was an endless loop.

However, the unbounded intelligence of Stephen Wolfram is such that trying to circumscribe it in one post, it is like trying to close the universe in a box. Yet more than a post this is an e-book, and I hope you'll enjoy reading it as much as I enjoyed writing it!

Contents

# The Quest to Unfold Complexity: who is Stephen Wolfram?

Because, after all that's what technology is all about: setting up systems to achieve human purposes

Stephen Wolfram in Computation and the Future of the Human Condition

Stephen Wolfram is the founder of Wolfram Alpha, a powerful computational engine (more about what a computational engine is later on). Yet the path that brought Stephen Wolfram to the launch of its latest creature looked more like a life-long quest.

Born in London in 1959. Stephen Wolfram showed incredible qualities since a young age. In fact, by age 15 he had drafted three physics books and his first scientific paper. By the age of 21, he had received an important fellowship, which launched him on a life-long quest: understanding complex systems by stripping out their complexity.

Yet Stephen Wolfram approach was unique for a couple of reasons, I believe.

First, he understood that computation was the most compelling discovery of the past century. Therefore, he focused since the beginning of using machines to enhance human abilities.

Second, he believed that to understand complexity he had to look at natural processes to find the most essential programs that mother nature used by time to time to run the show of life.

Yet Stephen Wolfram didn't spend his life as a hermit (except when, for practical purposes, he had to put together a book, which would become a New Kind of Science) or isolated from the world. Instead, he understood the importance of more practical matters, such as managing people.

The quest to complexity started from the study of cellular automata, which launched him to formulating a computing theory of everything. So, what are cellular automata?

## Computing a theory of everything

So I want to talk today about an idea. It's a big idea. Actually, I think it'll eventually be seen as probably the single biggest idea that's emerged in the past century. It's the idea of computation. Now, of course, that idea has brought us all of the computer technology we have today and so on. But there's actually a lot more to computation than that. It's really a very deep, very powerful, very fundamental idea, whose effects we've only just begun to see.

Cellular automata are programs that follow simple deterministic rules but show complex behaviors, the more steps they take along their evolution. What does that mean and what makes them so valuable from a scientific standpoint?

Imagine starting playing a game with fundamental and straightforward rules. Chances are you'll start projecting yourself at the end of the game, foreseeing a particular scenario. However, as much as you would love to imagine, even if you had Albert Einstein's or Salvador Dali's ability to day-dream you will never manage to foresee the complex behaviors that will arise along the way from those trivial programs.

How is that possible that from such simple programs spring up so much complexity of behavior? The answer lies in rule number 30! Let's dive a bit into it to see how it works.

## Rule Number 30: simplicity as the mother of all creations

The weather has a mind of its own” isn’t such a primitive thing to say: the fluid dynamics of the weather is just as sophisticated as something like a brain

Stephen Wolfram, on blogs.scientificamerican.com

It probably was the summer of 1985 - as recalled in Idea Makers - when Steve Wolfram stumbled upon something that would leave a mark on his life and guide him toward a life-long quest. What was that?

It all started from rule number 30. As someone that found computation as the most important discovery of the past century Stephen Wolfram didn't waste time doing calculations. Rather he let computers run all the possible programs that could be found in nature, as simple cellular automata and look at what behaviors they would show.

That is what happened that summer in 1985. Cellular automata are self-replicating systems showed as a grid of changing cells. Each cell in the grid reacts based on the neighboring cells. In other words, you start from a grid like the one below

A simple rule determines whether a cell will be on or off in the next generation based on the configuration of its neighborhood. For instance, if a cell is white, and the one on its left and right are white, then the cell stays white. Instead, if a white cell falls in-between two black cells, then it turns black. And so on for all the possible arrangements.

The possible configurations on a grid comprised of three cells as you can see from the red rectangle above are eight. But the possible combinations, given the fact that each cell can be either black or white (in a binary state) can be 256 - 2 ^ 8 (therefore the two possible states, black or white, at the power of the eight possible combinations).

We start by letting the cellular automaton take 20 steps,

We can see already a more complex behavior so far. Yet nothing exciting.

When we start taking additional steps, the more steps we take, the more complexity arises.

That is what we get after 100 steps. As you can see the patterns created by a simple cellular automaton starts to become kind of interesting.

**Source**: blog.stephenwolfram.com

When in the 1980s Stephen Wolfram observed this kind of behavior he was shocked. That kind of shock that changes your life, the aha moment! In fact, the more steps he let rule 30 take, the more complexity arose out of simple deterministic rules!

The fact that simple rules could replicate nature is pretty counter-intuitive, yet quite effective.

*Cone Snail, Photographer: Richard Ling Cellular Automata Rule 30 *

**Source**: artfail.com

The most powerful part is that to build such complexity you don't need a super powerful computer, but only a three-digit number grid that follows super simple rules. Rule number 30 above all, was the beginning of a quest that would lead Stephen Wolfram to formulate a New Kind of Science.

It also opens up a new way of thinking, where intelligence isn't solely a human thing, but it can be found anywhere in nature. Therefore, the complexity arising from our brain isn't different from what happens in nature. Both are described well by computations. Before we dive more into what would become the principles of Stephen Wolfram's book, A New Kind of Science, let's dive more into his life.

# Before Wolfram Alpha

If you've been using the iPhone, chances are you've also been using Wolfram Alpha all along. In fact, you may not know it, but your built-in intelligent assistant, Siri, uses Wolfram Alpha's API to provide answers to any question.

Yet before we dive into the technical stuff, how did it all start? From studying Stephen Wolfram's life, I understood one fundamental concept, which before was a bit elusive for me. In short, technologies, ideas, and enterprises don't come in isolation. More often than not they spring up from people's lives context.

In other words, if you want to understand an idea or a technology better probably the best place to start isn't how it works but how it originated in that person's mind. Also before that, you may want to investigate what, who, where and when inspired those ideas, if you want to understand the why.

As trivial as it may sound, I ended up discovering quite a few interesting facts by using Stephen Wolfram's approach. The paradox is that his approach helped me to better understand him as a person, therefore as an entrepreneur and scientist.

It all started from a life-long friendship with an incredible man, which for better or for worse (according to your perspective) revolutionized our times, Steve Jobs.

## NeXT, Mathematica and the batch of computers that built the Web

**Source**: Commons.Wikimedia.org

According to Stephen Wolfram, in his book Idea Makers, he first met Steve Jobs back in 1987. At that time Steve Jobs was focused on building what would become the first NeXT computer.

In fact, business magnate Ross Perot, founder of Electronic Data Systems, which was sold to General Electric in 1984 for $2.4 billion had enough liquidity to make risky investments. Therefore, in 1987 Perot invested $20 million, in Steve Jobs' startup, NeXT, which although valued about $125 million hadn't yet released any product.

In 1996 Apple bought NeXT for $429 million. After that, when Steve Jobs, in July 1997 took back the reins of Apple, NeXT experience played a vital role. In fact, Steve Jobs installed his NeXT executive team at Apple.

Goin back to our story, at the time (1987) Stephen Wolfram was as busy in figuring out the details of what would later become his first company, Mathematica. It turns out that in a way or another Steve Jobs played a key role in Stephen Wolfram's company success and vice-versa.

## Why is it called Mathematica?

Stephen Wolfram was undecided about how to call the company he was about to launch. Among the names he had in mind - as he reported in Idea Makers - there was either Omega or PolyMath. Yet one day by talking to Steve Jobs, he told him "you should call it Mathematica."

According to Stephen Wolfram, Jobs had a theory about company's names. In short, you start with a very generic concept, and then you romanticize it. That is where Mathematica came from.

## What is Mathematica?

Mathematica is a software that does scientific computations of any kind. From data analysis to visualizations and much more, Mathematica laid the foundations for what would later become Wolfram Alpha.

One interesting fact is that Mathematica walked hand in hand with NeXT. In fact, Steve Jobs intuition made him realize that each NeXT should have been bundled with Mathematica and that is what happened.

The most interesting part of the story - as explained by Stephen Wolfram in Idea Makers - is that a batch of NeXT computers would later be given to the CERN of Geneva. In other words, NeXT computers bundled with Mathematica happened to be the computers used to develop the web!

Yet between Mathematica and the launch of Wolfram Alpha, Stephen Wolfram put together the ideas he had observed throughout his scientific discoveries, in a controversial book, A New Kind of Science.

**A New Kind of Science **

Stephen Wolfram's A New Kind of Science is a remarkable book in many ways. It is certainly the most arrogant piece of science writing I have ever read. It also displays a jaw-dropping ignorance of some key issues, of which more later. Yet, despite its shortcomings, it may be the most important contribution to science this decade.

by Chris Lavers on theguardian.com

In 2002, Stephen Wolfram's book A New Kind of Science was out, and it was quite controversial. That is also clear if you look at its Amazon reviews,

One thing I understood by looking at Stephen Wolfram's personality is either you love him, or you hate him. More precisely either you think he's a genius or you think he's mad. In fact, it is also funny to see how polarised are the feedbacks about his book,

The book has as much 1 star reviews, then 5-star ones. You may think that those one-star reviews are from people that were not erudite enough to comprehend it, and vice-versa the five-star came from the scientific community. That is not the case,

Throughout my research, I've come to "know" Stephen Wolfram at a personal level (take it with a pinch of salt). Since the beginning, I tried to keep a neutral view about him. Yet I found his ideas original and refreshing in many ways.

Of course, it can be argued that his ego is massive. However, if you look at his life, you realize that he's one of the greatest minds of our times. It is very hard to understand how a person is contributing to our history until that person is no longer alive. We love to look at things with a nostalgic eye. That is why things from the past always have this halo that makes them look almost mystic and mysterious.

That is why when you see Stephen Wolfram comparing himself to Isaac Newtown you get the goosebumps. Only time will tell us what impact Stephen Wolfram's ideas will have.

Going back to A New Kind of Science, one of the people who contributed to Stephen Wolfram's growth was physicist Richard Feynman. Although they had two very different mindsets, they shared a common passion, physics.

They met when Stephen Wolfram was 18, while Richard Feynman was 60. Stephen Wolfram first met Richard Feynman at Caltech. After that they also worked together for a company called Thinking Machines Corporation (once a successful tech company then bankrupted in 1994).

Richard Feynman loved to do calculations for the sake of feeling the pleasure of discovery. Stephen Wolfram instead, loved to automate processes for the sake of understanding the principles underlying, so that unknown would eventually become more relatable.

I leave the judgment on whether a New Kind of Science's ideas are worth or not your attention to Richard Feynman. In fact, when Stephen Wolfram stumbled upon rule 30 Richard Feynman told him,

OK, Wolfram, I can't crack it. I think you're on to something. (source: Idea Makers)

Let's dive into a couple of core principles from Stephen Wolfram's book.

## The principle of computational equivalence

As Stephen Wolfram reminds us nature has no constraints when it comes to computation. In other words, mother nature can pick up whatever "little computational program" exist out there to start building complex stuff.

However, that complexity always springs from a low level of sophistication, which is equal for all the "programs" that you can ever find in nature. In other words, it doesn't matter how complicated the outcome or a process it seems. What's behind it are always relatively simple deterministic rules!

Why is this principle staggering in a way? If you didn't realize, this principle contradicts something which humans always believed to be true. The fact that something complex is at its root complex. Also that in some way our intelligence us unique or in some way distinct from any other natural process.

Yet what Stephen Wolfram shows us is the opposite. Nature works through computational equivalence. Instead, human processes evolve through the purposes that by time to time become relevant. At times what becomes relevant by human standard may well be "an accident."

For instance, as Stephen Wolfram recollects, if you take mathematics, that is based on a few axioms. But are those the only possible axioms? Of course, they are not. There are infinitely many other ones. Instead, the mathematics we have today is only "an historical accident."

Therefore, many technological inventions often carry the heavy baggage of history.

That also brings us toward another pillar of the New Kind of Science: computational irreducibility.

## Computational Irreducibility: how does our universe work according to Stephen Wolfram?

If complexity in nature arises from simple deterministic rules, does that mean that if we figure out those simple rules, we will also be able to predict the outcome of the system?

The answer to that is controversial. According to Stephen Wolfram's computational irreducibility, we won't be able to out-compute a system unless we take each step of it. In short, it doesn't matter if you're able to understand the underlying deterministic rules that are behind a complex system.

If you don't follow how the system evolves at each stage, you won't be able to know what the output of that system will be. Therefore, you will not be able to predict its behavior. In part, this is reassuring as it gives us back our free will. Why? For most cases, we don't have a choice but wait and see how the behavior unfolds.

However, this isn't always true. As Stephen Wolfram suggests for certain processes, there are always endless of what he calls "pockets of reducibility" which allow at least some kind of predictions.

Now that we covered most of Stephen Wolfram's life, and how his mains ideas formed, we can look more at the entrepreneurial side of the story.

# The launch of Wolfram Alpha

On May 18, 2009, finally, Wolfram Alpha launch was announced. At the eye of the average onlooker that seemed the start of something entirely new. Yet instead, it was only the next stage in the evolution of Stephen Wolfram's research he had put together throughout his whole life.

In fact, Wolfram Alpha was launched as a spin-off of Wolfram Research, Inc., the company that developed Mathematica back in 1986.

As an LLC Wolfram Alpha was launched without outside investments.

## How does Wolfram Alpha work?

When you surf the web, you use search engines. For instance, each time you ask something to Google, it is providing you answers based on what it finds by crawling, indexing and ranking the web pages available.

Eventually, you will get links to pages that exist on the web. Those pages though are manufactured by other humans. Wolfram Alpha instead, computes answers to specific questions using its knowledge base and algorithms.

You may think that Wolfram Alpha is more like a fact-based engine. And in fact, compared to Wikipedia, it gives facts not narratives.

In short, Wolfram Alpha goes into its internal knowledge base, made of several official sources and curated data and computes the answers, based on which ones seemed to be the most appropriate for the query.

The answer to a query comes from an algorithmic computation that looks into the internal knowledge base, with its extensive internal semantics and ontology.

To read the users' queries, Wolfram Alpha does not use traditional NLP because it has to deal with linguistic fragments rather than full grammatical sentences.

The technologies behind Wolfram Alpha can be divided into four key general areas:

- a data curation pipeline
- an algorithmic computation system
- a linguistic processing system
- an automated presentation system.

Currently Wolfram Alpha comprises more than 10 million lines of symbolic *Mathematica* code, together with many terabytes of data. When you type your queries into Wolfram Alpha, you're making it better and better. In fact, it looks at the user behavior to understand more about linguistic and compute better answers.

**Source**: WolframAlpha.com

## How does Wolfram Alpha make money?

Wolfram Alpha makes money in a few ways:

**iPhone/iPad Apps**

Each App ranges from $0.99 up to $2.99 (even though I can see that on the European App Sore some apps are priced around €3.49, about $4.16).

Therefore, its business model is based on selling these apps. How much money are they making with that? It is very hard to give this answer considering that I couldn't find any announcement from the company stating how much money they are making.

I used Similar Web to understand how many installs the main app had.

Assuming that each install is a paying customer they made on that single app anywhere from $1.5 up to $3 million for a single app. My assumption (take this premise like a pinch of salt) is that overall the other apps may have paid off about the same. Therefore, if I have to give a rough estimate, I would say they made anywhere from $1 million up to $5 million on all the apps they sold so far.

**API**: those are a set of prepackaged instructions to integrate an application within another platform. For instance, as we saw throughout this research, the iPhone and other Apple devices use Wolfram Alpha API to make their built-in intelligent assistant, Siri, provide the answers to its users.

API usually have a cost based on the volume of calls you make through queries. Therefore, the more queries go through Wolfram Alpha, the more it will cost regarding API. Based on what they have on the website this is the price of Wolfram Alpha's API for a thousand queries,

I believe this is where most of the company's revenues come from. In fact, if I had a business that has to offer a certain amount of computational power to my users I would use Wolfram Alpha rather than going through the process of developing a new stack of technologies.

Now, the hardest question. How much money does Wolfram Alpha make with its API?

I assume that Apple is Wolfram Alpha largest client. If back in 2012, Siri's queries drove 25% of Wolfram Alpha, if this still holds true we can run some rough estimates.

If there are 3.3 million hits per day, if we assume a hit is a query, then there are about 825,000 queries coming from Siri, which translates into about 825 API calls by a thousand queries per day. If we assume that Siri calls are "Full Results API" this means that they are priced $50 per thousand calls, which would cost over $15 million annually.

Hits per day |
3,300,000 |

25% coming from Siri | 825,000 |

Divided by 1,000 | 825 |

Cost of API per day | $41,250 |

Total API cost |
$15,056,250 |

I don't think Apple is paying Wolfram Alpha that much for several reasons. First, being featured in Siri is already free marketing for Wolfram Alpha. Second, the more API calls you buy, the better deal you will get. Therefore, I believe if ever Apple does pay Wolfram Alpha, the price it pays is well below the $50 mark per a thousand.

However, I do believe that the API is the most important part of Wolfram Alpha business.

Also, apparently Siri isn't the only intelligent assistant powered by Wolfram Alpha. In fact, Cortana may be using it too.

**Pro Version**: you can get the PRO version of Wolfram Alpha (ranging from $5.49 up to $9.99 per month) which includes enhanced features,

It's impossible to determine the exact number of PRO users since they don't share that info. However, since Wolfram Alpha is a Freemium, we can assume that their rate of conversion may be anywhere from 0.5% up to 27%.

**Source**: process.st

Let's assume the lowest conversion rate, 0.5%, which means that Wolfram Alpha (I don't see any strategy which is focused on improving its conversion rates) might have about ten thousand paying customers each year (0,5% times 1.9 million daily visitors, assuming they are returning). It means about $77,400 in revenue each year (I took the average of the two packages, student for $5.49 and educator for $9.99, and multiplied it by 10,000, the number of paying customers each year.

This is how the Wolfram Alpha business model is organized.

Now the hardest question,

## Is Wolfram Alpha profitable?

I'm not going to do crazy calculations to figure this out. Since for a software company the greatest cost is related to its personnel, according to CrunchBase, Wolfram Alpha has about 19 employees, including Stephen Wolfram as a founder.

I also looked at the whole Wolfram Research profile on Glassdoor,

I wanted to have a rough idea about the average salary paid by the company,

I will never stop saying, my analysis is full of assumptions and estimates based on those. Therefore, take it as an att

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