Math

I loved this thought experiment because it’s the first instatiation I see of what a truly different kind of math would be like. Just imagine, a math without integers! As Jameson Graber elaborates here, we started with integers and only through calculus first started to truly grasp the continuous. What if there were other paths?

Having thought about this question a good deal, I believe that math is a human construct in that the Math that is possible is far Vaster than we imagine, and from that gnarly Vastness we choose only one thread. That’s what Atiyah’s quote illustrates to me.

Without beings to think it Math exists only in a combinatorial, potential form, just like all that we’ll ever write already exists in a latent form in the alphabet.

As to its universal truth, validity, applicability…, perhaps all that can be said is that empathic nonhumans might be able to get and accept some of it, just as exotic stories start to make sense to us only after we understand the exotic sensibilities that gave rise to it.

Math is not a special, magical kind of thought but simply the ever more sophisticated, ever more rigorous thought that we have. That it is, as it is famously said, “unreasonably effective”, is just an endorsement of thought itself.

Believe the hype. Please take a while and go play with it! Its help, as is Wolfram’s tradition, is excellent, the best introduction.

How to describe it? It’s for data what Google was to text, what Wikipedia was to knowledge. It’s to the calculator what Wikipedia was to the encyclopedia, what Google was to the library catalog. It’s the most exciting, hopeful thing to happen to the web, to the world, since both Google and Wikipedia.

And with a mission “to make all systematic knowledge immediately computable by anyone”, it opens up as big and inspiring a project for this generation.

I believe it’s a historic moment and could not let it pass unmarked.

My answer to life, the universe, and everything:

Randomness begets persistence
Persistence begets replication
Replication begets complexity

Game: 2 players take turns to say a number between 1 and 9. Numbers may not be repeated. The goal is to be the first to say 3 numbers which add up to 15.

Sounds like fun? Try it with a friend!

Fun it ain’t.

It’s hard to remember the said numbers and “playing” is a chore involving many additions in your head. Maybe it’s fun for the better short-term memory endowed or those who enjoy arithmetic but that ain’t me.

Turns out that game above is none other than the beloved tic-tac-toe. You see:

2	7	6
9	5	1
4	3	8

This is what I love about information design (and what I tried to do in my calendars) this is its art, its magic: it can turn a chore into a game! It recasts our weaknesses —linear, verbal processing— into a form suitable for our talents —gestalt visual processing.

In math words: it finds useful language-graph same-shapes (isomorphisms)!

Where, but the web, would you find someone like Oliver Steele? This ain’t no metaphor. That name was a link. I’m not talking about Oliver Steele the person, I haven’t met him (though I apparently am 1-degree of separation from him; weird, that). I’m not talking about the sweating, walking, pinchable, space-and-time-and-flesh-bound avatar, I’m talking about his online persona. And either I’ve gotten crazy enough or technology has advanced enough that I’m ready to treat Oliver Steele —the link, his blog, words, diagrams, code, and further media— as a person by its own merits.

And, boy, is he an interesting guy:

• My no TV. It is, too, one of my most valuable possessions.
  
• Functional JS is a sweet, sweet library, with one of the best documentations I’ve ever seen. Stuff like this is what makes the interwebs the best place on earth. And no, I don’t mean that as a metaphor either.
  
• Addition fractions. Y’know how fractions deal with multiplication? They need not be!
  
  
• Interactive regular expressions. Live regex! Nothing like interaction to make easy and fun once chores.
  
• Why are far things small? and other really hard questions from Steele’s kids.
  
• Visualizing basic algebra.
  
  
• Fluently: a construction kit for chainable methods. Finally, a word for the programming style I’ve been hinting at: Fluent interfaces!
  
• Learning about constraint diagrams
  
  
• A metaphor of computer’s history.
  
• The true advantages of Macs. I agree.
  
• The metaphor of the rock.
  
  
• Aargh!. How to spell it? It’s genius’s mark to have this much fun with such a trivial question.
  
  

I studied math in college because I didn’t believe it. Never could understand how or why someone would come up with the stuff we were being teached. Thanks to some innate verbal ability and motherly discipline, I was thankfully “good” at it though, good enough to realize that what we were “learning” was nothing but mindless regurgitation.

What are you absolutely certain of? Of what are you sure without any conceivable doubt? What is true no matter what? What is necessarily true? Just one thing. Whatever. As long as you’re sure.

I’ve been playing the game for a while and I’ve been shocked to be unable to answer the question. Now, of course I’m familiar with Hume’s skepticism (you don’t really know an apple is going to fall, you’ve just seen all similar objects fall before at similar conditions but you don’t know) and I thought I knew how dear truth was but lately, slowly, I’ve started to realize that not even reason or logic are to be trusted.

Let’s start by quickly demolishing every statement about experience, like, say, that you are, well, you, that you broke your knee when you were fifteen, that your mother exists, that other people exist (solipsism). The usual shortcut is just to ask you how do you know it isn’t all a dream, but I prefer Russell’s more imaginative version, the extreme omphalos hypothesis: how do you know that the world wasn’t created five seconds ago, set in motion, and with fake memories? Clever, huh?

OK, that sweeps off a good big swath of possible answers. As for reason/logic, its problem is that it’s either redundant or not binding at all. But don’t 2 + 2 = 4 whatever fucking nightmare the world might turn out to be? How could time or space not exist? My gosh, can you look me in the eye, and tell me that numbers aren’t infinite? How demented do you need to be to doubt Aristotle’s syllogisms, the very rules of thought (if it’s true that humans are mortal and that Socrates is human, Socrates has to be mortal!)?

But it turns out these conceptual statements aren’t certainties either. When you probe them further, carefully, rigorously, you realize that to advance you have to start defining. If you do it conscientiously, defining or making explicit even the dumbest, most-taken-for-granted assumptions you start to realize that 2 + 2 = 4 because you said so, because you assumed your conclusion from the get-go, and your statements are true in the same empty way that a bachelor can’t be married or a car has to be an automobile too. Yes, it’s a kind of truth, but a rather measly one.

The other thing that usually happens when you probe concepts is one of the most wondrous experiences I know of, exhilarating and unnerving at the same time, dizzying. I call it sense of could. It means taking an entrenched concept and realizing it is not necessarily so, discovering your singularity is just an instance of something subtler, deeper, finding out your rose is one among thousands, seeing that what you thought fixed is just another degree of motion.

Like when Cantor found out there are many kinds of infinities, some bigger than others (!). Like when you realize logic isn’t the complete science Kant thought and open the gates to the non-classical logics. Like when you probe the very fabric of the universe by looking for primitives to space and time. More worldly, like when you question your ethics, your religion, your politics, and you find only possibility where you were looking for necessity.

Now, those two options, redundancy and non-necessity, are the ones I’ve always stumbled upon but I don’t really know that happens for every concept. Or neither do I know if you can dismiss all experience in one fell stroke. That is, I’m, of course, not even sure that you can’t be sure of anything. Would you care volunteering an answer? %(p)Or a question?)%

Charles S. Peirce has been called by Britannica “the most original and the most versatile intellect that the Americas have so far produced.” Bertrand Russell considered him “one of the most original minds of the later nineteenth century, and the greatest American thinker ever,” and Karl Popper goes all out, seeing him as “one of the greatest philosophers of all times.”

I just met him a couple of weeks ago and I couldn’t be more impressed: the man’s a fricking genius, practically inventing semiotics and modern logic, making major contributions to the philosophy of science and epistemology. I would remember him forever just for his offhand naming of math as the “hypothetical or conditional science.” (the could science? the moot science?) and I have the sneaking suspicion that ours will be a lifelong acquaintance.

How not to be intrigued by a man who could explain reason in a sentence?

OK, to fully get the above quote you should be familiar with Peirce’s brilliant and influential classification of signs into ”icons, which signify by virtue of resemblance [think painting], indices, which signify by virtue of a physical connection with the object [think weathervane or tally], and symbols, which signify by virtue of the existence of a rule governing their interpretation [think words].”^SOURCE

Then there’s Peirce “discovery” of abductive reasoning, the third major class of logical reasoning and for which I’ve found no better (or shorter) intro than the logical reasoning pedia.

And to finish this Peirce appetizer you must check out Peter Skagestad’s Thinking With Machines article. He gives a summary of Peirce’s semiotic to make a most intriguing comparison with the thought of human intelligence augmentationists like Doug Engelbart ^ELZR. Fascinating stuff really.

Who would have thought the new Mathematica would introduce one of the coolest interface design innovations in recent years: automatic inteface building?

You should browse this nice showcase of examples but to really grok the idea you’ve got to watch the Author and Deploy an Application in 60 Seconds screencast.

That above is a screenshot of the presentation: the code above generates the application below. Isn’t it beautiful?

Wolfram Research calls it the day documents and applications merged and they’ve got a point. This makes creating an application as automated and straightforward as creating a graph, and similar ease is being introduced for embedding these tiny apps in documents (“Documents are, quite simply, talking things”).

It’s no panacea but it do makes simple things easy, difficult things possible. In Rails jargon, you could call this a very elegant scaffolding functionality, a victory of convention over configuration (:“At its core it means that what you do (especially if you’ve done it a lot) should carry a lot more weight than having to configure (and reconfigure) things over and over”).

A math experiment was carried out recently when Alex Smith —an Electronic and Computer Engineering undergraduate with “a background in mathematics and esoteric programming languages”— proved that the Turing machine below is in fact universal, making it the simplest universal Turing machine possible. In other words, the cute graph below are the instructions for an abstract symbol-manipulating machine that can in principle do anything your computer (or any other computer for that matter) can do.

Stephen Wolfram, who made the conjecture and offered a $25k reward for proving it, reports:

Now, ain’t this just breathtaking?