Media for Thinking the Unthinkable | Hacker News Reader

Media for Thinking the Unthinkable

worrydream.com

409 pointsespeed78 comments

https://dl.dropboxusercontent.com/u/17455578/unthinkable_tho...

"Evolution, so far, may possibly have blocked us from being able to think in some directions; there could be unthinkable thoughts."

Which prompts today's startup idea:

1. Use Silk Road imitators to send hallucinogens to Amazon Mechanical Turk workers

2. Ask workers to solve impossible problems

3. Pass responses into machine learning algorithm

4. Gain godlike insight

5. Rescue humanity from self-destruction

Your algorithm becomes a bit implausible at step 4 & 5.

How inspiring it is that Bret Victor diligently designs the presentation of his content: to me this is one of the reasons he's apart from others, where often even a great design thinker simply leaves a talk or slides or an essay to be presented however it will, like a philosopher who sets aside her inquisitive attitude in real life.

Counterpoint: he notes our techniques are based on writing, but it goes deeper: our symbolic writing (including mathematical notation) is based on speech, for which we have dedicated linguistic structures in our brains, much as we have a visual center. It is deep-seated, and many have argued fundamentally entwined with sapience. Thus, even if it's not theoretically the best way, it might be the best way for us. But I'm going to argue it is the theoretically best way:

Linguistic descriptions have a key advantage over pictorial in that they represent or reference rather than show. This enables them to be compact, and omit unnecessary detail. (Of course, showing rather than telling is a strength of visual representation).

Yes, you can have a hierarchy of visual systems, and zoom-in or hide. But a fundamental problem here I think is in choosing the hierarchy - that is, the way the system is modularized.

Different modularizations of the same system are often appropriate for different uses of that system, or for considering different aspects of it. For even a slightly complex system, there are a huge number of different modularizations possible, and not all of them are useful. Often, you'll start with a poor one, and eventually have insights moving you towards the ideal one. (Of course, sometimes the "right" modularization is obvious, especially for well-known families of problems).

All this is very difficult. My point is that it is easier to switch modularities linguistically than pictorially, by changing your concepts. Without the right modularity, it's difficult to pictorially show just the aspects of interest instead of the whole picture. In contrast, one can linguistically omit detail by referencing it (implicitly, as a separate module).

Maybe it's possible to do this visually, though I suspect it thereby would have become linguistic!

[Though the above is a counterpoint, I'm very impressed with the talk. He's working both ends of abstraction, with concrete working software demonstrating cool useful practical techniques that, while not universal, would be helpful in many domains; and also framing it within, and using it to illustrate, the deep universal and philosophical idea of unthinkable thoughts. BTW e.g. uncomputable numbers.]

My gut reaction is to say that all three of these ways of thinking (interactive, visual, and symbolic) are all useful and should be used where their advantages can be best applied. As a shallow example, I think that the basic visual/interactive representations can be fantastic teaching tools, and once you get an intuitive feel for how the system behaves, you can then switch to symbolic representation and move on to the more higher-order systems which those building blocks are composed of.

I thought it was interesting that when he compressed the paragraph describing an equation to is algebraic representation (x2 + 2x = 10), we immediately grokked the algebraic version better, because we have loads of experience reading and manipulating the algebraic expression. If I think back to my own learning career, however, I learned the basic tenets of algebra using -- you guessed it -- interactive and visual representation through Hands-On Equations [1]

[1] http://www.borenson.com/

(now that I think about it, Hands-On Equations serves as a very nice "tldr" for this speech and the related concepts)

I don't know, maybe the good old separation between soft and hard science can help here. On the speech side, in soft science, I think the most powerful transmission of knowledge if by pure speech, oral speech, like in podcasts. A good lecturer will branch his brain on yours and will have a very high and precise throughput, only by spoken words. That's for history, politics, philosophy, soft sciences. The best example I know of this effect is the courses of Jankelevitch (in French), it's really like a good ride on the back of an experimented motorbike driver knowing the region like the back of his hand.

On the other side, the pinnacle of hard sciences, geometry, logic, topology, are very visual and symbolic by essence. A proof is only an explanation of a truth that is already there, that some can "see in their mind". I wouldn't imagine being able to follow a math class without a black board, that would be like a piano lesson without a piano.

Albert Einstein in a letter to Jacques Hadamard:

The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced and combined. .... This combinatory play seems to be the essential feature in productive thought before there is any connection with logical construction in words or other kinds of signs which can be communicated to others

Good thought doesn't have to be linguistic.

I speculate that the reason most of us only think in words because it's the way we're taught. We can hear the word "dog" because at a young age we were told about the association from each letter => sound. "What does A sound like? aaaaah". But what if instead our parents and teachers taught us that A was a picture? A could be a red square, and B a purple box. "DOG" might be a pink triangle next to a red and a green circle. Great, then you start to remember those three shapes as one image, just as you remember the sounds "duh" "aww" "guh" as one. And you would learn to assemble them together in all the same ways. I bet you would get very good at it.

I think that every verbal system could be represented in a visual system by just replacing each sound with a shape. I actually know of people who do this, who do this fully, just not with boxes and circles. The deaf. They can learn how to read despite having no hearing. They will report that instead of using sounds they think in a combination of hand signs and images. This is the only group of people I know that replaces all sounds with images, but there are a lot of examples of in-betweens too.

Vladimir Nabokov, the author of Lolita:

The long "a" of the English alphabet has for me the tint of weathered wood, but a French "a" evokes polished ebony. This black group also includes hard "g" (vulcanized rubber) and "r" (a sooty rag being ripped). Oatmeal "n", noodle-limp "l", and the ivory-backed hand mirror of an "o" take care of the whites. I am puzzled by my French "on" which I see as the brimming tension-surface of alcohol in a small glass.

Richard Feynman:

When I see equations, I see the letters in colors – I don't know why. As I'm talking, I see vague pictures of Bessel functions from Jahnke and Emde's book, with light-tan j's, slightly violet-bluish n's, and dark brown x's flying around. And I wonder what the hell it must look like to the students.

tl;dr you can do everything visually. Or you can mash up visuals and words. The problem of "choosing between hierarchies" isn't actually a problem, because just as you can make a sound to decide, you can make a visual symbol. If this were false then you would have to explain how sign language works.

Bret Scares me. He makes feel inadequate on so many levels. Am I alone on this? I don't care for most 'successful' startup people and others, but Bret in particular - is amazing.

"Count your blessings, not your troubles." -Dale Carnegie.

Bret is a lovely and amazing person, but don’t sell yourself short. I guarantee you if you come up with a topic or problem to work on, and devote 10+ years to full time reading/tinkering/inventing/implementing in the field, allowing yourself to be creative, sweating the tiny details, and worrying more about making your inventions wonderful than profitable, you will be able to amaze yourself and all of the rest of us with what you make.

This is quite astute. Truly, I only dream of what the world would be like were we free to pursue our most profound curiosities instead of only our most profitable ones.

We are.

The we you're referencing includes very few people in the world.

I would think the number of people who are free to do this is significantly higher than the number of people who actually do it.

Freedom is a continuous unit. Just because I can take risks doesn't mean I will, or that I am necessarily "free" to do so, or that that freedom isn't highly limited (for example, I may be free to start a company with a 2-year ramp and some expected gain, but I'm not able to take 10 years with no income to pursue some ideas that interest me).

If so many people are truly free to pursue higher callings, why don't they? Look at reality, not theory. Find some answers to that question and you'll start to discover the wide and complex range of restrictions on true freedom.

Thanks for the encouragement, needed it.

One of my favorite parts of his website is the Links section: http://worrydream.com/#!/Links

It reminds me that the way to be amazing is to do an amazing amount of work.

He's kind of woken up my personal motivation to do cool shit, actually. He doesn't scare/intimidate me; its more a sort of reminder that in fact if you work hard on something you love, you do it well and have a good time. So I'm getting on with it, all the while appreciating the genius that I am able to access ..

I'm always torn whenever I see a Bret Victor talk.

On one hand, I agree with almost everything he says in the talk, amazed by the prototype tools he presents, the concepts he discovered to make those tools usable. And I can see that in each talk he has some new insights to present, deeper connections, better and more general creations - and thats really exciting.

On the other hand, his attitude that he doesn't plan to turn the tools into products, that they're just prototypes, that he expects someone else to come and create actual products - that rubs me the wrong way.

The thing is, we've found excellent collaboration platforms exactly for these kind of prototypish things that we don't plan to make a product of yet we would like other people to toy around with the general idea. The most recent incarnation is GitHub.

So why not publish some of these prototypes? Its not about the code, its about forming a community that will build upon those ideas. Its about kick-starting the construction, setting it in motion. As far as I can see, that is what Victor is hoping for - people taking these ideas close to their hearts and building them in reality.

Is the idea not ready yet? Not exactly polished enough or general enough to be published? The visualization drawing / exploration tool looks like an awesome start to me...

I don't understand.

Edit: Oh wait. https://github.com/damelang/nile contains the presented Nile viewer. Nevermind.

One particular tweet from Victor explains his point of view quite poignantly, in what he calls the dichotomy between industry and research:

"An 'Industry vs Research' dichotomy that I sketched at a conference. I probably should elaborate on it sometime. https://twitter.com/worrydream/status/392335781374619648/pho...

One can understand why, given the options as viewed by Victor, one would choose "research" if given the choice.

I get an error that the page doesn't exist.

The last " is sticking to the link. Delete that and it works. https://twitter.com/worrydream/status/392335781374619648/pho...

Going through that list, this is what I think github style open-source prototype publishing would mean for the points made there:

Left side of the board:

- No need to ship anything. Its possible to just put whatever you have out there and let people play with it by forking it. It doesn't even have to "build", e.g. other people could start by making it build reliably. There really are no limits.

- All code is immediately applicable for builders, even prototype code. Immediately applicable means that they'll be able to read it, study it, toy with it (possibly interactively), see how it works, make some changes => get inspired

- github is not results-driven. No pressure to "ship it", on the contrary - if you want to ship something, the common path is to fork and get it there by yourself, right?

- build and exit - the exit part doesn't even apply.

Right side of the board:

- Source code does export knowledge to be built upon - and its even more knowledge than just old-fashioned media (videos and articles) - it exports hands-on, interactive, reshapeable, remixable, engaging knowledge.

- its perhaps not long-term enough, but on the plus side it actively engages a much larger number of people.

- it could indeed distract from deeper, foundational work but I think there is enough room for anyone to choose what kind of work they want to do - no need to centralize it all. For example, people could "pull" new foundational work from Victor into their own projects.

- its definitely exploratory - massively exploratory as it engages more people actively on many levels and causes an innovation ripple effect.

A tiny example: as soon as V8 implemented generators in JavaScript, the node.js community started experimenting with async runners. Lots of async runners were produced and ideas are still studied, analyzed and exchanged between various projects. But before V8 published it, it was all just excitement and discussion about the possibilities with zero hands-on experimentation and a much smaller number of ideas.

- it is indeed ongoing - nothing needs to be shipped, no project need necessarily be done.

Additionally:

- it represents extreme transparency - everything open to the public - which nicely matches the scientific method.

Percieved but non-existant downside:

- personal recognition is harder - not quite true. Its easy to think that some things may get lost in the mass of people, but usually the contrary happens - the pioneers always get the recognition. [citation needed - this one is based on personal observations]

Possible downsides:

- academic recognition: no idea how academy (and related publishers) treat open-source in general. It seems like they would be a perfect match for each other as they share a lot of common principles, but so far it hasn't engaged researchers more massively...

Its a third category - different from traditional research and different from industry. I believe its worth considering.

As a developer I really appreciate his position personally. I think one of the reasons he's so brilliant is that he's a pioneer in pushing interface abstraction back and forth between the science and art worlds. I'm not sure he'd be so competent were he working under the constraints of commercial development.

What I yearn for is about 20 more Bret Victors to appear in such a way that they'd all get together in the same room for a few weeks and do some cool shit. Maybe thats where he's headed?

Don't you see? Just by giving these talks he is building a community. Releasing the products makes everyone focus on the specific things he's made and not the things these products represent. The ideas are much more important, and he wants people to push past the things he's made and invent entirely new things.

This got posted to HN twice in April and died with only a few points and no comments. glad to see it's finally finding an audience here.

Yeah, the video got posted a while back, but at the time he hadn't created the interactive page. It's cool to see how much thought he puts into presenting each idea. He doesn't stop with just the talk.

Bret Victor also has many other amazing and thought provoking talks:

Inventing on Principle: http://vimeo.com/36579366

Stop Drawing Dead Fish: http://vimeo.com/64895205

Drawing Dynamic Visualizations: http://vimeo.com/66085662

The Future of Programming: http://vimeo.com/71278954

IMO - Abstraction is almost a prerequisite for creating anything interesting or innovative.

Meaning: my best ideas always come from playing in non-traditional representational systems within a certain medium. Particularly drawing. I find sketching/scribbling/drawing things generates ideas that I could not have thought of by just writing/brainstorming. You may even be able to apply it to the example of how software development models have jumped paradigms into mainstream business management (eg, agile teams). Bret's onto something here.

The scientific paper isn't designed for people who need explanation/visualisation of a logarithmic curve. People who read that paper should be able to quickly decipher what the authors have written – their writing is consistent with normal mathematical instruction.

The electrical drawing would be obvious to anyone who is used to working with them.

There are obvious places where this would work– dissemination of material is always useful in many different forms. But this is NOT an answer to a question that is being asked. Rather, it is an alternative form of dissemination to an alternative audience.

Fully admitting I've only read the website's summary bullets: I disagree. The point to me is not as much dissemination of material but thinking through materials in a language other than left to right words or symbols. It harkens back to renaissance books in which words and scribbles mixed together in what was, for the times, a coherent mixture. We're talking note-taking for instruction, tools to think about and optimize problem solving ... tools for thinking rather than sharing, even if the source appears to be sharing or instruction right now. That may not be true in the future... I, for one, am sick of OneNote being "the best thing since lined paper" and living otherwise with notepad.exe alternatives. What, precisely, will bring the tablet from its consumption roots into a true work/thinking device? There's a lot of room for more visual note-taking apps, and eventually that will be the new low-hanging fruit of computer vision and natural language input. Someday, for some tasks, at least.

How did the people who read that paper get to the point that they are able to quickly decipher what the authors had written? Brute force repetition.

Back in high school I played a musical instrument. I practiced my scales, was quizzed on them, then practiced them some more for years. I got pretty high-school-good at this instrument, enough to earn a small scholarship. I never continued it into engineering school though, and one of the milestones I never reached was the ability to improvise within a key. You see, despite practicing the fingerings of the different keys hundreds of times, it wasn't enough to gain the intuition needed to just feel it out on my own.

Those people who read that paper and could decipher what the authors had written HAD practiced their scales enough times to develop that intuition.

Bret isn't trying to provide the most compact representation out there. He's trying to present the best model that helps you build that intuition the fastest. In music, you had to spend hours repeating the same scales so your fingers would get hard-wired into the valid combinations for a specific keys... the question is how can we build tools and techniques that help us reach that level of effortless mastery faster.

I'm a big fan of Bret Victor's thinking, but this part struck me as indicative of the criticisms he'll receive:

"here, they are discussing some relationships: the regular latice, L grows linearly with n, we see L growing linearly with n, and we see C is staying constant. In the random network, L grows logarithmically, and we see L growing logarithmically, we see C going as a reciprocal relationship. When we read the word "logarithmic", we don't need to reconstruct that relationship in our head, you can just see it"

Does the average reader of Nature need to be shown a graph of what a linear, constant, logarithmic, and inverse relationship looks like? I don't think so.

That said, I imagine there are highly terse and technical ideas that cannot be simply represented in the current mediums of publication and which could benefit greatly using a presentation using an interactive widgets, making more complex ideas more easily communicable.

The average reader can probably easily imagine y=2 to y=2x to y=X^2 relationship, but its becomes harder when the rates change. Visualizing y=N to y=Nx to y=x^N where N is any given number is fairly hard to see accurately in my head since it adds a new dimension (time) to the visualization.

Giving a slider where N can be visualized over time shows how changes in N accelerates y=x^N away y=Nx. These compound complexities better seen in interactive widget as the average mind is not well equipped to visualize them.

When introducing a new visualization, First you show familiar curves such as y=x and y=x^2 as context for more complex curves that follow.

The point is now someone who isn't the average reader of Nature can understand the concept...

Sometimes I feel like nerds kind of enjoy the exclusivity provided by "cryptic" notation. What Bret is doing is not genius level stuff, he's just doing what a lot of people don't have the balls to do. Attempt to make "hard" things easy enough for "regular" people to understand by appealing to the right side of their brain.

Jargon and specialized notation is sometimes cryptic as an unintentional side effect of communicating efficiently between specialists. To suggest they should communicate findings in a less efficient way that's understandable by laymen who haven't put in the effort to learn the jargon / notation is silly.

But I think Bret's point isn't that every research paper should be as verbose as an introductory textbook, but rather that interactive widgets can express ideas which text and static images in published papers can't.

"interactive widgets can express ideas which text and static images in published papers can't"

This. I had such hopes for iBooks, but then making widgets is hard, and making a Microsoft Word for widgets, harder still.

Sorry, but that is not the point.

This is not just about simplifying scientific notation so it is easier to digest for an untrained audience: it is about using tools to remove as much cognitive "shit work" as possible, so that our minds (including those of experts) are free to think the "unthinkable thoughts" of the title.

But you see, once you get the point where no one can draw pretty pictures about what you are working on requires your mind to be trained in this cognitive shit work (imagination?). So we'll develop a generation of people who never really learn to think creatively. Everything is just handed to you in a pretty little interactive diagram.

Learning is hard, but that is a good thing. It's like exercise. The more you work at it, the easier it becomes.

Are you seriously saying that if scientific papers contain parts that lets us visualize their contents interactivity human being will lose the ability to think creatively?

What I am saying is that the intended audience of those scientific papers rarely need the interactive diagrams (the equations & math are enough - most of us for example can visualize logarithms quite trivially).

But those who do not have the necessary math background - this will not really help them at all. Sure they might have some understanding of this particular algorithm - but when it comes to abstraction and extending that knowledge to other problems I do not believe it will scale. You do not have the fundamentals to think creatively (in a mathematical sense).

The circuit for example. They might now understand how that circuit behaves. But if I show them a completely different circuit can they infer how it behaves? Likely no, they were not able to pick up on all the non-linear behavior that occurs within circuits.

Yours is a very sad comment.

The author gives a good example here, if you choose to read it:

http://worrydream.com/MediaForThinkingTheUnthinkable/note.ht...

Basically, Claude Shannon was able to create his information theory because he could use things like calculus, probability, stochastic processes and graph theory to aid his thought process. He needed those tools to be able to think things that would have been unthinkable without them.

Of course I read it. Just like I watched all of his videos. There is no substance. Of course he was able to create information theory because of calculus, probability, stochastic processes, and graph theory. Yet for none of those did he need Brett Victor's cute little animations. I am merely stating that Brett is adding nothing to the equation here.

Don't get me wrong, I understand what you're saying. The point I was trying to make is that this opens up new potential.

Years ago, before there were power tools, all furniture was crafted by hand. Painstakingly. It would take a craftsman years to develop his craft. Eventually though, power tools lifted a lot of the learning curve. It became easier and faster to create furniture. Eventually a lot of those power tools were replaced with automated CNC machines. With these machines you can pretty much throw anyone from the street who can read on the machine. Productivity has increased so much that you can pretty much buy furniture these days for not that much more than the cost of materials alone! It really is an incredible statement.

Now not to take the metaphor to far. I realize you can't turn science into an industrial process... it is a creative process as much as anything. The main point is that as you lower the learning curve, you enable a few more people to gain the new skills required.

Again, i'm not suggesting this was ACTUALLY the point which motivated him to come up with the concept. But to me, this is the really cool potential outcome.

Not a good analogy really. CNC requires careful programming of the machines; now you wind up with CNC object creators and people who work the assembly line feeding the machines.

Not only does it reduce the time to create, it reduces the skill required, the flexibility of product, and the overall level of craft.

Ignorance is not something we should aspire to or assist others in attaining.

The main take away I got here was that using a representation that decompresses the terse mathematical notation that you can interact with builds intuition about the system. If you already have the intuition then these interactions with the system add little value to your understanding of the system.

> Does the average reader of Nature need to be shown a graph of what a linear, constant, logarithmic, and inverse relationship looks like? I don't think so.

Representing simple, familiar relationships visually and interactively may indeed not offer much clarity, just as a single brick may not offer much shelter.

> average reader of Nature

His point is, this average can change, and its the quality of the symbols which deduces the set of readers.

Didn't know about this. Blew me away. The editor looks really awesome. What is the software called?

I am somewhat intrigued by the idea to represent arbitrary systems. I wonder where you might hit a wall within the editor, and how you can extend the editor to be able to visualize what might be possible to vizualize now. Like Emacs paired with these capabilities?

AFAIK, it's just a prototype Bret built to illustrate his point.

Bret Victor is awesome. Check out his website - when I first discovered it, I spent hours there, reading even his poems.

ALBATROSS gave me the chills.

Same here! His thinking had a huge impact on my thinking.

i know you all hate on mathematica but isn't this what the CDF computable document format is all about? text, systems modelling and dynamic movement all in the one language/system? (NB i'm not a mathematica user but have always wanted an excuse to get into it)

>This page is an attempt to "explode" a demo-driven talk into a skimmable, browsable, gistable form, where individual ideas can be quickly referenced later.

This reminds me of another tool, Korsakow[0], which attempts to do a similar thing in a different way with documentary material, by presenting it in "shortest narrative units" or SNUs that relate to each other. It is one of a number of "interactive documentary" tools (like Mozilla's Popcorn [1] to some extent) but I wonder if it could be repurposed to "explode" a talk in a slightly more digestible way that could be reproduced by those of us who don't have Bret Victor's skillz.

[0] www.korsakow.org

[1] www.popcornjs.org

Thanks for posting both of these! I'm very interested in tools that allow you to switch between the linearity of narrative (e.g., a film) but then break out into the non-linearity of systems.

I think these tools could be especially useful for helping people understand systems like climate change.

I wonder if Powerpoint (or Visio, OneNote, VS) will eventually evolve this way. My prediction? We'll see lots of bad examples for 10+ years once software for this takes off, until people actually write up what better ways exist through documenting the good stuff. Oh and geeks will use Latex-style power tools that no one else can figure out :) Perhaps I'm talking about the web once alternative layouts and HTML5 component libraries start taking off... Maybe we'll see the return of Quartz Composer someday. When Apple actually takes non-linear programming seriously.

If you don't have enough time to watch the entire video, just watch the "Linked representations" which starts at 24 minutes (4 minutes long).

It's on a 2D graphing library but his visualizations are incredible.

I knew the name sounded familiar. Bret Victor also gave a great talk called Inventing on Principle (http://vimeo.com/36579366).

If you enter through the home page, you can see a list of his other talks: http://worrydream.com/#!/InventingOnPrinciple

A lot of the stuff here (especially the circuit simulator) were discussed in Inventing on Principle.

I think one major reason why Victor's talks are so appreciated is that he shows a deep and serious engagement with humanism, tapping into the same vein as Christopher Alexander, Alan Kay, Jef Raskins, Seymour Papert, and others.

Where can I get the tool he showed? Did he publish it?

A friend of mine asked him this after we saw it in his "Inventing on Principle Talk". Here is his response:

> Thanks! The tools I showed were just prototypes that I made for the talk. I don't have plans to make them into products myself. (But someone else might!)

Thanks, I can not wait for it. Anybody take this job?

Not that I'm aware of, which is rather unfortunate. One way to do this might be to take an existing open source SPICE implementation such as NGSPICE (http://ngspice.sourceforge.net/) and build a GUI around it that provides the real-time visualization of the signals.

In the meantime, if you're looking for a free, easy-to-use circuit simulation tool, I've used LTSpice (http://www.linear.com/designtools/software/) in the past for my EE classes. The Windows version runs pretty well under Wine and the UI isn't too shoddy. It's pretty far away from Bret Victor's vision though, as you need to rerun the simulation again in order to see a new plot of the node voltages and currents.

Is anyone else having trouble with the video on Vimeo?

yes, but you can just download it and watch it with VLC :)

This will for sure speed up research. Thinking all the extensions of this technology is impossible... or is it? ;)

I 'm not convinced. Such a "media" for thinking the unthinkable already exists. It's called "written language" plus maybe a drawing here or there. Has been used for millennia and once internalized by a mind willing to spend the effort to parse it has never failed to convey the unthinkable, the sublime or the transcendent.

So, it would suck to introduce you to this guy named Ludwig Wittgenstein.

Inability to hold educated conversation on Wittgenstein should not be taken to reflect badly on anyone's intellect.

I see your point. However, these tools for thinking, they give you time to think more things and also allow you to think on new levels, which may let you attain the previously unthinkable. And you might be able to combine different ideas to understand new systems and conceive of new tools to discover more.

Further, on an individual level, each person might be able to think what maybe they personally couldn't think otherwise. And in that, communication might happen which gives rise to new thoughts.

I tend to agree, though I suppose it's not entirely proven that it's never failed. But the "unthinakble thoughts" argument seems to be to go in two different directions - the analogy to sound is misleading; we have reason to believe in the existence of ultrasonic vibrations, and they don't require us to hear or not hear them. But thoughts don't exist separate from our minds. Truly unthinkable thoughts wouldn't be thoughts at all. What the concept seems to represent here is "novel ways of thinking" and those are in fact generally not impossible to share with other thinkers (luckily).

Did you even watch the entire talk? He mentioned the written language very early on ... but then moves forward significantly.

brilliant!

Haven't watched the whole thing, but scrolling down and reading his closing makes me not want to watch it. He complicates the simple procedure "Completing the Square" (http://en.wikipedia.org/wiki/Completing_the_square). Take half of the b coefficient, square it, and add it to both sides gives x^2 + 10x + 25 = 64 or the completed square (x+5)^2 = 64 or x+5 = 8 or x=3.

That's a quote from al-Khwārizmī[1], the medieval Persian mathematician whose name the word "algorithm" comes from.

Victor didn't complicate the process. He used that quote to illustrate his claim that it's precisely because of innovations in symbolic representation (i.e., representing the equation as x^2 + 10x + 39) that you are able to think of the process as simple.

[1] http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C...

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