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The Mandelbrot Bet (2016)
Dirk Strasser

Contributed by Vijay Fafat

The byline of the story is: "Does mathematics truly describe the physical universe, or is the world of mathematics actually the universe itself? And what do these concepts have to do with the hopes and fears and passions that we human beings feel with every beat of our hearts?" I think both parts of this are enormous in their scope and it is hard to do justice to them in combination in a short story. Dirk Strasser tries this by focusing on one problem which evidently worries every sentient race in the universe - how to stave off the heat death of the universe (With Dark Energy, the actual worry may be cosmic isolation and inexorable loneliness...).

A quantum computer expert, Daniel Rostrum, is a Hawking-like figure, except he has little Physics training. Wheelchair bound due to muscular dystrophy, but all the access to latest technology. He starts thinking about the fractal nature of the Mandelbrot set, its boundary and the escape-behavior of the points outside the set. A lot of mumbo-jumbo is conjured up ("I have developed the idea to include a time dimension" to the calculation of the boundary of the Mandelbrot set and somehow recursively bootstrap out to the future. "The important thing is I’ve tied the behavior of Mandelbrot-like time dimensions to quantum computing") to give Daniel Rostrum the ability to send not just his mind but the entire body more than a quadrillion years into the future. There he meets a universal hive-mind, an Oversoul-like non-corporeal Voice which explains to him how the last black dwarf is about to be formed, how this means the termination of Reality, how they need his mind to try and stave off the Universal Death and how this one problem has vexed them for "millions of years". You can get a sense of of all this from some excerpts below but....

... it all sounds very farcical and "not even wrong". The universe does not end when the last star becomes a black dwarf. Energy conservation is violated when you send your body into the future. Timescales are important for narrative consistency. One man - a human - does not a savior make for the universe, etc. etc. Even the central math part is incorrect, where he speaks of using 4 variables, including time, to speak of his Mandelbrot transportation (the traditional Mandelbrot set appears on the complex plane with 2 variables, through the squaring-iteration of complex number inputs. Higher-dimensional sets in even dimensions can be defined using quaternions and octonions while odd-dimensional extensions are more ad hoc). Despite these shortcomings, it could have been a great story if the author had expounded much more on at least the second part of the tagline - the anguish of Sentience at the prospect of extirpation. Bertrand Russell, for e.g., had poignantly written:

"All the labors of ages, all the devotion, all the inspiration, all the noon-day brightness of human genius, are destined to extinction in the vast death of the solar system, and that the whole temple of Man's achievement must inevitably be buried beneath the debris of a universe in ruins.".

Or Shakespeare, who scribbled:
"Our revels now are ended. These our actors,
As I foretold you, were all spirits, and
Are melted into air, into thin air:
And like the baseless fabric of this vision,
The cloud-capp’d tow’rs, the gorgeous palaces,
The solemn temples, the great globe itself,
Yea, all which it inherit, shall dissolve,
And, like this insubstantial pageant faded,
Leave not a rack behind. We are such stuff
As dreams are made on; and our little life
Is rounded with a sleep."

So anyway, here are some excerpts from the story:

(quoted from The Mandelbrot Bet)

"The escape-time algorithm is the simplest algorithm for generating a representation of the Mandelbrot set. The answer lies in the infinity of the escape-time algorithm. Repeat the calculation for each x, y, z, t point and make your decisions based on the behavior of that calculation. Pick a value for time, t, square it, add a constant. Take the new number, square it, and add the same constant. Forever, do it forever. Simple."

(quoted from The Mandelbrot Bet)

"The loner physicist has the added handicap that he or she is not working as part of a team. Are great discoveries still achievable by individuals working alone? A case in point is the work of Daniel Rostrom, a man with little formal physics training who brought his skills from other fields such as computer science, art, and geography to bear on the complex field of time travel speculation. The jury is still out whether Daniel Rostrom was the greatest polymath and deepest thinker of our century, a brilliant hoaxer, or a fringe-dwelling crackpot. Rostrom, whose muscular dystrophy meant he was wheelchair-bound for much of his life, presents us with the most detailed insight into the loner physicist."

(quoted from The Mandelbrot Bet)

"One of two things always happens in a Mandelbrot set: either an iterated point jumps up to two units away from the origin or it jumps further away. The result is a shape that is finite but an edge that is infinite. It’s all about the edge. The line. It’s a monster. The more you magnify it, the more complex it becomes. It never settles down. Ever. I know this is the key. Somehow a Mandelbrot set has only two dimensions, yet it also possesses another dimension. What if that other dimension was time? With the right procedure it must be possible to both orbit close to an origin and jump in ever-increasing spans."

(quoted from The Mandelbrot Bet)

"It’s just a matter of applying the right iterative algorithm to time travel. Quantum computers are powerful enough to do it and quantum computers don’t get much more powerful than my chair. I just have to get the sequence of qubits right. Of course I don’t know for certain what will happen, but possibility theory tells me the likelihood."

(quoted from The Mandelbrot Bet)

"As eons passed, other sentient races came to the same point in their evolution and first unified as a race and then joined us. As it became clear that the universe was dying, the main aim of sentient beings was to find ways to prolong its life, or at least to find a way of prolonging sentient life. Those beings that had not joined us, knew that they now had no choice. The only hope for us all was to collectively put all our knowledge into solving the ultimate problem. That is what we have been doing for millions of years. And it is what we continue to do even now.”

(quoted from The Mandelbrot Bet)

"Our last best hope is that assimilating your mind will enable us to devise a solution to stop the last white dwarf turning black. You are the last time traveler. No one will arrive after you. There is no time anymore."

The Mandelbrot Bet was published in 2016 in the collection of "hard" SF stories called Carbide Tipped Pens (Ben Bova and Eric Choi, eds.). However, I agree with Vijay Fafat that the mathematical ideas here are garbled and I found their connection to the protagonist's supposed ability to travel to the end of the universe weak. Consequently, IMHO, this is closer to the "gosh, wow!" pulp SciFi stories in which mathematical nonsense is used to justify fantastical conclusions than it is to the more realistic and thought provoking genre of "hard SF".

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Works Similar to The Mandelbrot Bet
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. The Simplest Equation by Nicky Drayden
  2. Emmy's Time by Anthony Bonato
  3. Music of the Spheres by Ken Liu
  4. The Square Root of Summer by Harriet Reuter Hapgood
  5. The Woman Who Shook the World-Tree by Michael Swanwick
  6. Permafrost by Alastair Reynolds
  7. I’ll Follow The Sun by Paul Di Filippo
  8. The Pythagoras Problem by Trevor Baxendale
  9. Location, velocity, end point by Matt Tighe
  10. Nuremberg Joys by Charles Sheffield
Ratings for The Mandelbrot Bet:
RatingsHave you seen/read this work of mathematical fiction? Then click here to enter your own votes on its mathematical content and literary quality or send me comments to post on this Webpage.
Mathematical Content:
3/5 (1 votes)
Literary Quality:
2/5 (1 votes)

GenreScience Fiction,
MotifTime Travel, Math as Beautiful/Exciting/Useful,
TopicMathematical Physics, Chaos/Fractals,
MediumShort Stories,

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Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in non-fictional math books let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.

(Maintained by Alex Kasman, College of Charleston)