Tagmathematics

3 Best University Majors According to Microsoft

Artificial intelligence

These are the areas of concentration Microsoft is most in need of right now, according to its jobs blog:

Data Mining/Machine Learning/AI/Natural Language Processing

Business Intelligence/Competitive Intelligence

Analytics/Statistics – specifically Web Analytics, A/B Testing and statistical analysis

Microsoft Careers Jobs Blog: The Top Three hottest new majors for a career in technology

No surprises there. See “The Coming Data Explosion” for more on the subject of big data.

(via Don)

Update: See also: The Big Data Explosion and the Demand for the Statistical Tools to Analyze It “If The Graduate were remade today, the advice to young Benjamin Braddock might be ‘just one word… statistics.'”

Futurama Writer Invented A New Math Theorem Just To Use In The Show

Futurama math theorm

Ken Keeler, the Futurama writer behind the theorem, actually has a PhD in math, so this was probably just a walk in the park for him. But for the rest of us non math geniuses, his theorem was used to explain a problem with an invention that let characters switch bodies. In the show, you can only switch bodies once with the same pair of people, so they needed an equation to prove that with enough switching bodies around, everyone will eventually end up as who they really are. Insert: funny jokes, robot humor and black comedy and mix accordingly.

Gizmodo: Futurama Writer Invented A New Math Theorem Just To Use In The Show

Help Fund the Punk Mathematics Book

Tom Henderson, who I interviewed on his punk philosophy of mathematics, is writing a book and you can help fund it. He’s already surpassed his fund raising goal, but I’m sure he could always use more.

Punk Mathematics will be a series of mathematical stories. It is written for readers who are interested in having their minds expanded by the strange metaphors and implications of mathematics, even if they’re not always on friendly terms with equations. Better living through probability; the fractal dimension of cities and cancers; using orders of magnitude to detect bullshit; free will and quantum economics; and the mathematics of cooperation in a networked world on the brink of a No Future collapse.

Kickstarter: Punk Mathematics

Hard N Phirm – Pi

I was going to post this last week as part of my post on Pi, but I forgot. So here it is now.

Social Physics with Kyle Findlay – Technoccult Interview

Kyle Findlay

Regular readers of this site may have noticed a large number of posts on this site credited to “Social Physicist” – the Twitter handle of Kyle Findlay (and yes, you could be forgiven for confusing our names). Kyle works for a group within one of the world’s largest market research companies, which he describes as a “mini-think tank” with the purpose of exposing people to new ways of thinking and doing things. Having enjoyed his Twitter stream for the past year or so, I got in touch with Kyle Findlay to ask him about the practice of “social physics.” He talked to me by instant message from from his home in Cape Town, South Africa.

Klint Finley: What, as a “social physicist,” do you actually do?

Kyle Findlay: Well, at the moment I’m on my own in this “field,” if you can call it that. It just seems like the best description of what I do and what interests me so hopefully it sticks.

Basically, my interest is in understanding how people act as groups. As emergent entities that have their own (hopefully) predictable and describable topological forms. That’s the lofty idea anyway. And the tools of chaos theory, systems theory, network theory, physics, mathematics, etc. help describe this.

Do you have a background in physical sciences?

None at all. I studied “business science” at the University of Cape Town. My first job was for a company with a strong academic background, started by a professor of religion and a statistician. They used a 5-dimensional catastrophe cusp model to describe people’s relationships with ideas.

The moment I was exposed to this thinking, something clicked. A lot of contradictions that I saw in the world around me were resolved. Ever since I have had an insatiable desire to understand these areas. Which led me to interact with experts in many disciplines from neuroscience to economics, math, physics, AI, ecology, biology, etc. Every field has a piece of the puzzle. I am lucky to work in an environment that gives me free rein to indulge my passion.

Fractal Zoom
Sketch: Fractal Zoom by Kyle Findlay

Do you think what you do is different from systems thinking or social cybernetics?

They are definitely components. Systems thinking is a broad umbrella term. Cybernetics definitely helps us to understand and describe the patterns and multi-dimensional shapes that society creates. But I think that you need the hard sciences like math and physics to really get at the heart of it. Which is why I am feverishly trying to catch up on many years of missing education.

Do you think there are any dangers in applying models designed for physical systems to human behavior?

Yes there are – you will always be at least slightly wrong. There are a lot of parallels between the way people act in groups and other types of particles. But you also have the same problems of predictability in complex systems: sensitivity to initial conditions, 3-body problem, etc. It’s kind of the paradox of it all, something I am still trying to come to grips with.

What’s the most surprising insight you’ve discovered since you started studying this?

Everything is the same and everything is just information. The universal nature of nature is astounding. You see the familiar signs everywhere: from the atomic through to the cosmic level. It makes me think that there really is only one true science or line of inquiry and that most specialised fields are just facets of this. The more fields I delve into, the more commonalities I discover. It’s become par for the course for me now I think. But in the beginning, it really blew my mind.

Man's Part in the System
Sketch: Man’s Part in the System by Kyle Findlay

Have you been able to apply this stuff in any interesting ways? For example, I know you’ve prepared presentations on network theory and power laws for work.

Those have gone down really well within the silos I work in. People have really been amazed when I’ve shown them these kinds of things. It gets their minds racing.

I’m also doing some work applying systems theory to sports science, which can really benefit from changing the way they view the human body. Music is another area that makes a lot more sense from this point of view.

One of my favourites is understanding how human attention works and how to synchronise communication so that it becomes internalized, but that is very theoretical and could be seen as slightly Machiavellian so I won’t go there.

Also, I’ve been having some interesting chats with a neuroscientist around decision-making, attention, etc. The applications are really endless, it’s just where you choose to focus you own attention.

How would you suggest someone interested get started studying social physics?

Well, considering I’m not 100% sure what falls into the bounds of the field myself, it’s difficult to say. There’s no university course for it as far as I know. I would say that you need to have an intense desire to understand why people do what they do. And a slightly perverse fascination with the human condition. Looking at life from a systems perspective is a good start. Understand that patterns are formed internally, that change is the only constant. You can then use tools like network theory, noise analysis, entropy, etc. to understand these ebbs and flows.

Are you familiar with Stephen Wolfram? He wrote a book called a New Kind of Science.

Yes, I know of Stephen Wolfram from his software and Wolfram Alpha. I’ve been intimidated by the size of his book, though. I struggle justifying devoting so much time to one book, which probably says more about me…

Yeah, I haven’t picked it up yet either.

He sounds like a really bright guy. I think I watched a talk of his at the Singularity Summit or somewhere similar, but to be honest, can’t remember much of it.

Most of my reading is in the scientific literature, interspersed with a good book or graphic novel.

Flatland by Edwin A. Abbott

Speaking of which, do you know of any works of fiction that demonstrate the principles you’re interested in?

Good question. Not too many spring to mind. A classic is Flatland by Edwin Abbot – the quintessential metaphor for perceiving multiple dimensions. The guy wrote a book about perceiving multiple dimensions in the 1800s! Impressive.

A recent book that blew my mind was Accelerando by Charles Stross. He has a great worldview but his insights were more in terms of extrapolating the directions technology is going in.

Yourself? Any suggestions?

Snow Crash seems like it might be relevant. Or the film Run Lola Run.

I am ashamed to admit that I haven’t read Snow Crash. Why do you say Run Lola Run? Time? Sensitivity to initial conditions?

Yep. It shows how tiny changes in a system can have far-ranging results. A starting delay of only a couple of seconds radically changes things for several characters in the different timelines.

True. I’m not going to mention Back to the Future 2 or The Butterfly Effect (although I just did).

Have you heard of the 1990 film, Mindwalk?

No.

It was co-written by Fritjof Capra and consists of several characters discussing the nature of the world from a systems perspective. I have to admit that i fell asleep during it… but I was very tired.

That sounds pretty amazing though.

Yeah – good credentials right there.

My personal favourites are any films or books that push society’s limits. Subversive materials rule in my book (no pun intended). Anything that helps me push back my pre-conceptions and shatter my expectations. They were great at that in the 70s, in music, film and literature. Probably a side-effect of the 60s experimentations. I’m a big fan of exploitation flicks.

Let’s see, what else… I haven’t read Alan Moore’s Big Numbers. But Moore seems to have a pretty good grasp on complexity, judging by Watchmen and From Hell.

I haven’t read Big Numbers either. What elements do you think he draws on in those books?
Watchmen

Watchmen itself seems to be very mathematical – the use of symmetry and so on. In terms of themes, maybe it doesn’t touch on this stuff much, apart from some of Dr. Manhattan’s comments.

Yeah, he definitely weaves a non-linear richness into his tales that is admirable. The way he weaves the various threads of a story together.

I forget why I thought From Hell was relevant. Maybe it’s not.

Also, he calls himself a chaos magician. Watching an interview with him a while back, I could actually identify with a lot of what he was saying.

I wasn’t going to go there, but… have you studying chaos magic or the occult at all?

No I haven’t. That Moore interview is probably as far as I have gone. It’s just not a direction I feel I can go in and remain “grounded” if I want other researchers to take me seriously. But I can definitely see how he got there.

Well, I have and I think you’re better off studying natural sciences, systems, and complexity IMHO.

[Laughs] Cool, thanks for the advice.

But the book Techgnosis by Erik Davis examines a lot of parallels between information theory and cybernetics and mysticism and the occult. I think it stands up pretty well, even if you’re not interested in magic.

I think you have to have a certain detachment to take a step back and observe the world. And when you start seeing everything as inter-related and part of the same thread it becomes easier to start imagining that you can define the tapestry with your perceptions. I guess I don’t want to open that Pandora’s Box. In my view it untethers you. Again, talking from an inexperienced point of view in this area.

Davis’ book sounds interesting though.

From an interview with Manuel DeLanda (who you might be interested in) -conducted by Davis, incidentally:

As Deleuze says, “Always keep a piece of fresh land with you at all times.” Always keep a little spot where you can go back to sleep after a day of destratification. Always keep a small piece of territory, otherwise you’ll go nuts.

Yeah exactly. I find that the concepts I deal with in my day job challenge me enough, and that’s all based on empirically grounded ‘fact’ in the scientific literature.

Most people work very hard to maintain their reality, but I do think that you have to have an affinity towards detachment. A certain world view that is open to having your illusions shattered and actually enjoying that experience. And the cutting edge of science delivers those experiences in spades.

Kyle Findlay

More Info

Kyle on Twitter

Kyle’s Slideshares

Kyle’s Flickr

Pi, Plato and the Language of Nature

Brothers Chudnovsky

After I posted that article about technical analysis a couple people commented that it reminded them of the film Pi, about a renegade mathematician somehow using Pi to search for patters in the stock market with a homemade supercomputer in his crummy Manhatten apartment.

Technical analysis was probably the inspiration for the stock market portion of the film, but did you know that the part about renegade mathematicians building supercomputers in their living rooms to calculate Pi is actually based on a true story? Aronofsky almost certainly took the inspiration from this 1992 New Yorker story:

Gregory Volfovich Chudnovsky recently built a supercomputer in his apartment from mail-order parts. Gregory Chudnovsky is a number theorist. His apartment is situated near the top floor of a run-down building on the West Side of Manhattan, in a neighborhood near Columbia University. Not long ago, a human corpse was found dumped at the end of the block. The world’s most powerful supercomputers include the Cray Y-MP C90, the Thinking Machines CM-5, the Hitachi S-820/80, the nCube, the Fujitsu parallel machine, the Kendall Square Research parallel machine, the NEC SX-3, the Touchstone Delta, and Gregory Chudnovsky’s apartment. The apartment seems to be a kind of container for the supercomputer at least as much as it is a container for people.

Gregory Chudnovsky’s partner in the design and construction of the supercomputer was his older brother, David Volfovich Chudnovsky, who is also a mathematician, and who lives five blocks away from Gregory. The Chudnovsky brothers call their machine m zero. It occupies the former living room of Gregory’s apartment, and its tentacles reach into other rooms. The brothers claim that m zero is a “true, general-purpose supercomputer,” and that it is as fast and powerful as a somewhat older Cray Y-MP, but it is not as fast as the latest of the Y-MP machines, the C90, an advanced supercomputer made by Cray Research. A Cray Y-MP C90 costs more than thirty million dollars. It is a black monolith, seven feet tall and eight feet across, in the shape of a squat cylinder, and is cooled by liquid freon. So far, the brothers have spent around seventy thousand dollars on parts for their supercomputer, and much of the money has come out of their wives’ pockets. […]

Pi is by no means the only unexplored number in the Chudnovskys’ inventory, but it is one that interests them very much. They wonder whether the digits contain a hidden rule, an as yet unseen architecture, close to the mind of God. A subtle and fantastic order may appear in the digits of pi way out there somewhere; no one knows. No one has ever proved, for example, that pi does not turn into nothing but nines and zeros, spattered to infinity in some peculiar arrangement. If we were to explore the digits of pi far enough, they might resolve into a breathtaking numerical pattern, as knotty as “The Book of Kells,” and it might mean something. It might be a small but interesting message from God, hidden in the crypt of the circle, awaiting notice by a mathematician. On the other hand, the digits of pi may ramble forever in a hideous cacophony, which is a kind of absolute perfection to a mathematician like Gregory Chudnovsky. Pi looks “monstrous” to him. “We know absolutely nothing about pi,” he declared from his bed. “What the hell does it mean? The definition of pi is really very simple—it’s just the ratio of the circumference to the diameter—but the complexity of the sequence it spits out in digits is really unbelievable. We have a sequence of digits that looks like gibberish.”

New Yorker: Mountains of Pi

Since the publication of that story, the Brothers Chudnovsky have apparently turned their attentions to applying their expertise in supercomputing to other domains. Richard Preston, author of the original piece, wrote a follow-up for the New Yorker in 2005.

You can learn more about them on this NOVA page.

Reading all of this reminded me of a story I read earlier in the week about someone who claims to have “cracked the code” in Plato’s writings:

The hidden codes show that Plato anticipated the Scientific Revolution 2,000 years before Isaac Newton, discovering its most important idea – the book of nature is written in the language of mathematics. […]

However Plato did not design his secret patterns purely for pleasure – it was for his own safety. Plato’s ideas were a dangerous threat to Greek religion. He said that mathematical laws and not the gods controlled the universe. Plato’s own teacher had been executed for heresy. Secrecy was normal in ancient times, especially for esoteric and religious knowledge, but for Plato it was a matter of life and death. Encoding his ideas in secret patterns was the only way to be safe.

Manchester University: Science historian cracks “the Plato code”

(via Social Physicist)

First Replicating “Creature” Created in Game of Life

A first for the game, the replicator demonstrates how astounding complexity can arise from simple beginnings and processes – an echo of life’s origins, perhaps. It might help us understand how life on Earth began, or even inspire strategies to build tiny computers.

The Game of Life is the best-known example of a cellular automaton, in which patterns form and evolve on a grid according to a few simple rules. You play the game by choosing an initial pattern of “live” cells, and then watch as the configuration changes over many generations as the rules are applied over and over again (see “Take two simple rules”).

The rules of the game were laid down by mathematician John Conway in 1970, but cellular automata first took off in the 1940s when the late mathematician John von Neumann suggested using them to demonstrate self-replication in nature. This lent philosophical undertones to Life, which ended up attracting a cult following.

Life enthusiasts have since catalogued an entire zoo of interesting patterns, such as “spaceships” that travel across the grid, or “guns”, which constantly spawn other patterns. But a pattern that spawned an identical copy of itself proved elusive.

New Scientist:

(Thanks socialfiction)

RIP Martin Gardner

Martin Gardner

James Randi writes:

Martin Gardner has died. I have dreaded to type those words, and Martin would not have wanted to know that I’m so devastated at what I knew – day to day – had to happen very soon. I’m glad to report that his passing was painless and quick. That man was one of my giants, a very long-time friend of some 50 years or so. He was a delight, a very bright spot in my firmament, one to whom I could always turn to with a question or an idea, with any strange notion I could invent, and with any complaint or comment I could come up with.

I never had an angry word with Martin. Never. It was all laughs and smiles, all the best of everything.

James Randi: My World is a Little Bit Darker

Martin Gardner Wikipedia entry

(via Cole Tucker)

Calculus created in India 250 years before Newton

infinite series

Researchers in England may have finally settled the centuries-old debate over who gets credit for the creation of calculus.

For years, English scientist Isaac Newton and German philosopher Gottfried Leibniz both claimed credit for inventing the mathematical system sometime around the end of the seventeenth century.

Now, a team from the universities of Manchester and Exeter says it knows where the true credit lies — and it’s with someone else completely.

The “Kerala school,” a little-known group of scholars and mathematicians in fourteenth century India, identified the “infinite series” — one of the basic components of calculus — around 1350.

CBC: Calculus created in India 250 years before Newton

(via Fadereu)

Math for Primates: Topology Primer: Geometry on Acid

Nicholas  Horton

*Geometry on Acid: The category of Topological spaces and continuous maps.
* Tom has a silly putty reason for everything.
* The continuity of film.
* Did Xeno predict calculus?
* Ms. PacMan also loves donuts.

Download the podcast at Math for Primates

Above: Math for Primates co-host Nicholas Horton, who I have previously misidentified as a “professional weightlifter.” Nick says:

Oh, and while I’m deeply flattered, I’m not a “professional” weightlifter. I’m a competitive weightlifter and a weightlifting coach (that is, I coach other competitive weightlifters and athletes).

Sadly there is no money to be made in American weightlifting, so no matter how good you get (I’m not) you’ll always remain broke. Sure there’s a nice sense of continuity there. But, as such, none of us are allowed to use the prefix “professional” in any technical sense since no one is paying us.

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