Responses by Stephen Wolfram to an “Ask Me Anything” on Reddit.

Q: I guess you are a heavy reader. Can you list some of your favorite books? (Not just novels) —notg3orge

SW: I have altogether about 4000 physical books, though I pretty much stopped buying new ones a decade ago. (There’s actually a list of many of my books, as “NKS references” at http://www.wolframscience.com/reference/books/.)

On my desk I have to say I have only one book: A New Kind of Science. And I refer to the paper version with some regularity. (I used to have a physical Mathematica book too, but that’s now been completely superseded by what’s online.)

But within reach … I have a bunch of reference books that I’ve been using as benchmarks for Wolfram|Alpha … as well as a few “classics” that I just feel I should have nearby.

Let’s see … there’s Newton, Darwin, Euclid, Galileo, Boole, D’Arcy Thompson, Linnaeus. (I used to have Turing’s collected works, but they seem to have gone missing.) (In addition to the famous books by these folk, I see I also have e.g. Darwin’s autobiography, D’Arcy Thompson’s book on greek fishes, Darwin on barnacles, and Newton’s chronology of ancient kingdoms…)

Q: About 6 weeks ago, I found two bugs in Mathematica where it would compute a specific integral and return an incorrect answer. I submitted the bugs with my full documentation and proof of the correct solutions and spoke to someone at Wolfram about it. I then suggested that you award some kind of bounty to those of us that find actual mistakes in the software (similar to what Knuth does). Nothing special, just a cool piece of Wolfram swag. What do you think?

I would also like to say that I met you right around the time ANKOS came out at UIUC (I was a math major there). Jerry Uhl was my mentor there and I know that you knew him also. He is the reason I was a math major and the reason that I am doing a PhD in applied math right now. Thank you for a wonderful product. I am very big fan of yours! —microwave_safe_bowl

SW: We could have bankrupted Don Knuth when we first started automatically generating TeX from Mathematica years ago!

We are always very grateful for feedback and bug reports for Mathematica, Wolfram|Alpha, and our other products. And the most important thing we do is try to fix problems people report.

For years, I’ve insisted that we let people know when we’ve fixed a problem they told us about. Sometimes years can go by before we overhaul some area and fix an obscure bug. But we always try to let the original reporter of the bug know when we’ve fixed it. Though sometimes a decade may have elapsed … and it can be nontrivial to find the original reporter.

Q: [A watercolor of Stephen Wolfram] —Shitty_Watercolour

SW: Cute. Looks like I need a haircut….

Q: Given that you received your PhD at such a young age compared to many others in your field, what was that experience like in the formative years of your career? —Vintagecoats

SW: It was great! It was really nice to be “launched” and not to have years of school ahead of me.

It’s a little weird now, because my “contemporaries” 30 years ago were quite a bit older than me … so while I think I’m still in my prime, a lot of my contemporaries are retiring etc.

Q: Hey, read NKS and a few other things. You have a great many very powerful points, but 1 question I always had for you was this:

You seem to be fixed on the concept of finite state automata in nks, why not continuous state systems?

I say this because the concept of finite state automata seems to belie the fact that there has to be an underlying mechanism there, they are not, imho, mathematically pure, compared to an infinite state machine, such as waveforms. One can implement a finite state machine by taking continuous state machines and adding quantization, one cannot go the opposite direction, as information is lost.

I thought, as a fundamental theory, fundamental mathematic completeness would be required. Now we have a greater understanding/respect for emergent phenomena, would you find a place for continous state automata in your theory?

Also, thanks for Wolfram Alpha! Go Sox! —PubliusPontifex

SW: A fundamental question is whether continuous variables are really things that can concretely exist in our universe, or whether they’re just mathematical abstractions. (Or in the words of Kronecker: “God made the integers; all else is the work of man”.)

My guess is that ultimately the universe is discrete. But even so, it can be useful to use continuous variables (e.g. for the pressure of a fluid, even though ultimately the fluid is made of molecules). But in practice, continuous variables tend to be hard to work with except in simple settings. It’s great when one can get an exact algebraic answer to something (using Mathematica!). But when things get complicated, that’s impossible … and one ends up having to use “numerical approximations”, which in turn involve discretization. And the worst part is that after that discretization it’s very hard to tell if the answers one gets are “correct” in terms of the idealized continuous variables.

In the book I actually do talk a certain amount about continuous systems: e.g. http://www.wolframscience.com/nksonline/chapter-4 But my main conclusion is that the basic phenomena are the same as in discrete systems—just more difficult to identify.

I even have my favorite PDE, which shows rule-30-like behavior—but which ultimately kills all known numerical PDE solving schemes (it’s been a great test for NDSolve in Mathematica for years).

Q: Hi Stephen. Concerning this blog post on your personal analytics. Don’t you find scary to look one day back and see what you’ve done in such a detail? All your achievements but at the same time all captured all your live captured in these plots and numbers. Do you think from time to time about the direction of your life? Don’t these analytics sort of make you do what they seem to suggest you to do rather than stop and ask you what other things you could do? —BeingDigital

SW: I spend most of my time just “doing things”, but I’ve always effectively allocated a little time to thinking about what I should be doing.

Typically I have a bunch of ideas and projects that I kick around for many years (and quite often decades). Sometimes other people end up doing the projects, so then I don’t need to. But more often, the ambient technology etc. isn’t yet there to make the projects doable. When it exists, then I get serious about doing the projects.

I also think about how I feel about things I’ve done in the past … and that helps me figure out what it makes sense for me to do in the future. And I gradually learn what things I’m better and worse at doing…

Q: I read your amazing post on your blog about personal analytics –

• how did you capture this data

• do you see a commercial application from you in this space

• what format do you keep this data in

Also, loved your post about Steve Jobs, great reading, thanks :) —felixthehat

—and—

Q: Absolutely this. It is the most interesting post I have ever read online. The sheer amount of time put into this “experiment” is astounding. I would love to know more about this.

It has been pointed out that there is a post for the email data, but I am more interested in the rest of it (the email seems the most straight forward).

The keystrokes were fascinating, seeing how you have progressed over the years (it would have been interesting to see a metric on typing speeds too). What software did you use for capturing this? Does it allow you to encrypt it? etc.

Calls are the other interesting one. How on earth did you manage to capture all this data? Was the phone VoIP or a regular telephone?

Finally the file. Oh wow, the files. This is pretty straight forward, but how on earth did you manage to keep those files for so long? And are they still useful?

Love your AMAs. I hope that you continue to do them. —man1979

SW: I’ve used different keystroke capturing software at different times and on different computers. It tends to be rather messy, and it was a bit of a challenge pulling all the data out of weird obsolete databases etc. to do the analysis.

About phones: yes, I’ve been able to get this data because I’ve always had a phone that’s connected to our company’s phone system (formerly a PBX, now VoIP).

My general principle about files and data in general is that the only way to keep it properly is to have it always online. Dealing with old physical media is a mess…

Q: Five years ago, you announced a $25,000 prize for a proof that a 2,3 Turing machine you proposed in NKS is universal. A few months later, you announced that Alex Smith had won the prize, and that his proof would soon be published in your journal Complex Systems. Today, however, the proof still remains unpublished in any peer-reviewed journal. What happened? —ou81also

SW: It should have been published long ago. In fact, I ask about this quite regularly. I keep on being told that it’s waiting for the author to make some minor clarifications that will make the proof easier to read. I have no idea why it’s taken this long. It seems bizarre to me…

Perhaps this is one of these cases where I need to forget about delegation and do something myself. Come to think of it, I’m going to be at several Turing centenary events … and we suggested Alex Smith be invited too … so perhaps I can see to this in person…

The paper about the proof is available in preprint form, though … and it’s been very thoroughly gone through now by all sorts of people…

[I don’t know what it is about universality proofs … but it seems as if almost all of them have long publishing delays. Perhaps it’s in part because they end up getting “written” in something that’s almost machine-code-like, and it’s not very exciting for humans to read, or write.]

Q: Why did you name your book A New Kind of Science and why it is new? —BeingDigital

SW: I think it might take a whole book to answer that :-)

Perhaps the opening of the book gives some indication: “Three centuries ago science was transformed by the dramatic new idea that rules based on mathematical equations could be used to describe the natural world. My purpose in this book is to initiate another such transformation, and to introduce A New Kind of Science that is based on the much more general types of rules that can be embodied in simple computer programs.”

I thought about many many different titles for the book. I thought about trying to name the science. And that turned out to be really really difficult. Partly because the concepts it involves are new, and themselves don’t have names. The names that were runners-up mostly had to do with the “computational universe”—my name in effect for the space of all possible programs.

Q: Hello Stephen Wolfram and thank you for the IAmA! Now for the questions:

1. What do you recommend for current students who are interested in STEM carriers and want to make a difference?

2. Is there any validity in the talk about the Singularity and Transhumanism?

3. How much of a hassle was creating WolfromAlpha and Mathematica?

4. Will we ever formulate the Grand Unified Field Theory, or will it always be a mystery to us?

—relativisticmind

SW:

1. I’m a huge believer in people doing projects they care about. Learn the basics. Learn the best tools. Then try doing projects. I’m not sure if I’m suitably unbiased in this, but I have to say that I think learning Mathematica is a really good start. It depends on your detailed interests, but I certainly think NKS is a really interesting area that connects to a huge number of things. And what’s great about it is that it’s such a new field that it’s still very easy to make interesting discoveries in it. A general piece of advice about careers is to pick an area that’s small and young now, but you think is going to expand. We’re thinking of doing more directly in education, particularly emphasizing projects. Two initiatives we have are: https://education.wolfram.com/summer-school/ and http://www.mathematica-camp.org/ Another direction is: http://www.computerbasedmath.org/

2. Transhumanism: yes. Singularity: depends what one means. I don’t think it’s going to be a dramatic moment; more a process.

3. Hassle? Well, we’ve been working on Mathematica for 25 years, and Wolfram|Alpha for nearly 10. And they’re incredible complicated pieces of technology. But I certainly consider working on them to be a lot of fun…

4. It’s hard to know for sure … but my guess is that we will find an easy-to-describe theory of physics. It might even happen soon. I’m guessing we have the science and technology needed to do it. Now it’s just a question of deciding it’s possible, and putting all the effort in…

Q: Do you have any sci-fi type ideas that you really think are achievable within your lifetime? Faster than light travel, meeting extraterrestrial intelligent life, things of that sort. —Eagleheardt

SW: Well … some things may actually be impossible … and I even wrote an essay about that a little while ago: https://www.stephenwolfram.com/publications/what-ultimately-possible-physics/

Some things may happen gradually; others may be the result of a sudden discovery.

I’m guessing “AI” (with some footnotes about what it means) will happen gradually, as will the merger of humans with machines.

Something like cryonics might happen suddenly. Effective human immortality will probably be gradual.

I’m guessing faster-than-light travel is outright impossible in the way we currently think about it. But somehow when our existence is more virtual and distributed it may seem like less of an issue.

Extraterrestrial intelligence: I’ve been interested in that one for a long time… I have a bad feeling, though, that the question doesn’t even really make sense. As a consequence of the Principle of Computational Equivalence, lots of things in our universe should really be thought of as “intelligent” … and we have to be more specific, asking about human-like civilization histories … and that’s a very different story.

Q: First, let me say that, as an academic mathematician, I use Mathematica nearly everyday and my job would be much more difficult without it.

Now for a question: What is your response to the criticisms and accusations made about yourself and NKS here: http://bactra.org/reviews/wolfram/ and elsewhere?

For example, how do you respond to accusations that you tried to publish a theorem regarding rule 110 without attributing Matthew Cook who claims to have done most of the work proving the theorem? —anonymous

SW: “A Rare Blend of Monster Raving Egomania and Utter Batshit Insanity” is a great title for something that’s written about one … but I have to admit I didn’t get further than that in reading this piece; the title didn’t make it seem likely to be very reasoned or reasonable.

I wrote a blog post a few days ago about general responses to the NKS book: http://blog.stephenwolfram.com/2012/05/living-a-paradigm-shift-looking-back-on-reactions-to-a-new-kind-of-science/ I consider it a fascinating study in the history and sociology of science.

About rule 110: the easiest thing to do is just quote the NKS book! “Following my ideas about class 4 cellular automata I had come by 1985 to suspect that rule 110 must be universal. And when I started working on the writing of this book in 1991, I decided to try to establish this for certain. The general outline of what had to be done was fairly clear—but there were an immense number of details to be handled, and I asked a young assistant of mine named Matthew Cook to investigate them. His initial results were encouraging, but after a few months he became increasingly convinced that rule 110 would never in fact be proved universal. I insisted, however, that he keep on trying, and over the next several years he developed a systematic computer-aided design system for working with structures in rule 110. Using this he was then in 1994 successfully able to find the main elements of the proof. Many details were filled in over the next year, some mistakes were corrected in 1998, and the specific version in the note below was constructed in 2001.”

Matthew worked for me for quite a few years, and did nice work on rule 110. What happened with him in the late 1990s was unfortunate, and certainly the single worst experience I’ve ever had with the large number of talented people who I’ve worked with over the years. The good news is that it all got resolved satisfactorily a long time ago … and if it’s still being brought up, there must be some other agenda at work.

As it happens, some of the people who worked on the NKS book are thinking of putting together a collection of reminiscences about the making of the book (yes, there were lots of weird stories [finding photos of animals with “appropriate” expressions is one that immediately comes to mind]), and I know they’ve been in contact with Matthew recently.

Q: What other scientists or researchers, if any, do you admire most? Can be past or present. —AcesupZ

SW: Well, one might think this was a very subjective question … but perhaps there’s a way to answer it, at least in part, by pure data mining…

Let’s look at the list of people referenced in the NKS book: http://www.wolframscience.com/nks/index/names/

Now just count the mentions (with Mathematica of course) … and here are the winners: Alan Turing (19); Emil Post (14); John von Neumann (12); Gottfried Leibniz (12); Isaac Newton (11); Marvin Minsky (10); David Hilbert (10); Kurt Godel (10); Aristotle (10); Benoit Mandelbrot (9); Carl Friedrich Gauss (9); Leonhard Euler (9); Euclid (9); Georg Cantor (9); Claude Shannon (8); John Conway (8); James Clerk Maxwell (7); Johannes Kepler (7); Albert Einstein (7); Rene Descartes (7); …

Some of this I’m not surprised by; some is pretty surprising. I think Emil Post does so well because of a bunch of technical results that I used.

I’m not surprised Alan Turing “wins”; the things I’ve done seem remarkably aligned with his interests, e.g. http://blog.wolframalpha.com/2010/06/23/happy-birthday-alan-turing/

There are, I suppose, two main dimensions in terms of deciding who one might admire: first, what they did and how they thought, and second, how they lived their lives. There’s also a different standard for people one’s personally known, as opposed to historical figures.

Among historical people, I think I’ve been most impressed by the work and thought of Turing, Leibniz, Newton, Gödel, Einstein, Euclid, Darwin (and maybe others I’m now forgetting). Though I wouldn’t emulate many of the ways these people lived their lives…

Of famous people I’ve personally known, I’ve probably been most impressed by Richard Feynman and Steve Jobs.

Q: What can be done to improve natural language search algorithms?

wolframalpha often has a hard time parsing searches I try to do, so I often spend five minutes trying to rephrase things in a way it’ll understand.

For example, this morning I tried:

• “Time it takes to walk 500km” and it searched “time it”.

• “Time to walk 500km” and it searched for “walk”.

• “How long does it take to walk 500km” and it searched “how long does it take”.

• “time taken to walk 500km at average human walking speed” and it searched “average human walking speed”

—pseudolobster

SW: An interesting question… very related to a blog post I recently wrote about “artificial stupidity”: http://blog.stephenwolfram.com/2012/04/overcoming-artificial-stupidity/

If we change your input e.g. to “Time it takes to go 500km at 2mph” then it works just fine.

And in fact I think the problem Wolfram|Alpha is having with your input is not so much to do with natural language understanding as such, but rather with having enough knowledge, and handling it correctly.

Wolfram|Alpha has a value for “average human walking speed”, and indeed “500km at average human walking speed” works just fine. The problem is with the “linguistic compression” to e.g. “Time to walk 500km” … which requires extra knowledge.

We’re always working on upgrades to the linguistics/knowledge frameworks of Wolfram|Alpha … and there’s one particular upgrade that I think might make your examples here work … though I’m not sure.

We’ve been steadily working through different kinds of inputs and domains … and in areas like math where the system is quite mature, I’m very pleased at the level of query success we’re seeing.

Your examples here are exactly the kind of thing we spend a long time analyzing to improve things. You might think that it will get mired in specifics … but one of the achievements has been to develop frameworks that allow good generalization.

If you have other examples, please send them! (You can use the feedback form at the bottom of any Wolfram|Alpha page; yes, actual humans look at those…) It’s particularly nice to have the kind of “reformulation sequence” that you give here. The way we anonymize our query logs happens to make it difficult for us to piece together such sequences right now.

Q: If you were to write a Chapter 13 to the NKS book, what would it be about? —jv1967

SW: Funny you should ask… I had forgotten until recently … but actually I did start writing a “Chapter 13” … though I called it the Epilog. Its title was “The Future of the Science in This Book”.

I looked through it as I was writing my blog post today: http://blog.stephenwolfram.com/2012/05/looking-to-the-future-of-a-new-kind-of-science/

And actually … as I look through it now, it has some fairly interesting things to say :-)

Note that these were never finished or polished, but here are a couple of excerpts.

Principles: – Always try to address the most obvious questions and find the simplest examples; – Try to understand the root causes of things; do not be satisfied with technical explanations; – Do not be bound by what has been done before, but try to understand it as fully as possible; – Explain what you have done as clearly as possible, and with as little infrastructure as possible

Phases of the new science (when they begin): [these are my expectations] – Absorption: try to understand what I have done in this book (first absorption completes in 2 years; more in 5 years) – Make the first round of extensions: (2–3 years; finished in 10–15 years) – Build major new directions (15–30 years) – Small early stage technological applications (4–10 years) – Major technological applications (10–25 years) – Become a part of everyday thought (4–10 years) – Become a standard part of basic science education (15–20 years)

Q: Hi Stephen, thanks for doing an AMA! I have a few questions about NKS as I just recently read the book.

• I may have missed it, but how exactly do you define a program to be “simple”? We learn how everything is accomplished by simple programs, but I’m confused as to what counts as simple.

• I’m a little confused about something in chapter 11; we see that there are simple universal programs of very little complexity such as rule 110, however, as you also point out, a two color Turing tape is also universal. Isn’t this already enough evidence that simple programs can be universal?

• Can you give a brief summary of the NKS summer school program you have every year? What traditionally gets done by students and how does it work in general?

I have learned a ton from NKS already and hope to continue learning more. —srinilab

SW:

1. The operational definition of “simple” tends to be: small enough that you’d reasonably find in an enumeration of all possible programs of a certain type. For elementary cellular automata, it’s made very clear that they’re “simple” by the fact that they have names like “rule 30” or “rule 110”.

2. You have to specify not only what symbols can occur on the tape, but also what the rule for the Turing machine is. Among Turing machines, we now know, thanks to Alex Smith winning our prize for this, that there’s a 2-state 3-color Turing machine that’s universal. In the numbering scheme used in the NKS book and in the Mathematica TuringMachine function it’s Turing machine 596440. (Try it in Wolfram|Alpha too: http://www.wolframalpha.com/input/?i=2%2C3+universal+turing+machine)

3. The core of the program is doing an original project. There are lectures and hands-on workshops throughout, and I typically open the summer school by doing a live NKS experiment. But the real focus is on each student doing their own original project. And my own most important role seems to be helping to pick each project (which is a lot of fun, because I get to learn about all sorts of things). Click on names in the archives to find out about some previous projects: https://education.wolfram.com/summer-school/alumni/ There’s also a blog post about one student’s experiences at last year’s summer school and afterwards at: http://blog.wolfram.com/2012/05/01/from-the-wolfram-science-summer-school-to-wolframalpha-pro/

Personally I think the summer school works really well. And I’m viewing it as a possible model for a much larger scale experiment in education. By the way, I think we’re still accepting (sufficiently good) applications for this year’s summer school: https://education.wolfram.com/summer-school/

Q: I feel way too dumb to ask questions about physics so in no way of insulting you, what is your favorite fruit? :-) —Mumrik

SW: You really want to know? :-)

Actually, right at this moment I have a little tub of raspberries that I am consuming.

I happen to be quite a fruit enthusiast … in fact, every day I end up eating some raspberries, pineapple, strawberries, grapes and usually an apple. (OK, that’s surely more than you wanted to know :-) )

And one more thing: I don’t end up going into grocery stores very often (modern times; assistants; etc.) But when I do, I have this little running amusement going with my children: we always try to pick up one bizarre or rare fruit or vegetable. We’ve ended up with some weird stuff … that tasted really weird….

Q: If you had to fight a dinosaur to the death in a Dinosaur Death Match using only primitive weapons and not allowed to set traps, what’s the biggest dinosaur you think you win against? You don’t have to name a specific dinosaur, just give us a size reference. —funfungiguy

SW: Sadly, I think I would probably lose against anything with serious teeth…

Q: Hi thank you for doing this. I was wondering, you went to high school at Eton. What do you remember most about your time there? Do you have any favorite moments? Least favorite? —isAccount

SW: I learned all these “useless” subjects, like Latin and Greek … and the bizarre thing is that (a) I still remember most of what I learned, and (b) I’ve actually ended up using a fair fraction of what I learned! (Think: naming products etc.)

I was a “King’s Scholar” at Eton … I think the king in question was Henry VI, who lived before Columbus discovered America. The “allowance” for King’s Scholar had been 3d (3 old British pennies) and when I was at Eton they still ceremonially gave out 3d pieces once a year. There had been a choice of 3d or a pig, but apparently the pig option was discontinued some time before I was there.

Perhaps my quintessential British moment came on one of the few occasions when I actually ended up playing a sport. I was supposed to be bowling in cricket. Which I did by rolling the ball along the ground (“underarm”). It was rather successful, and I got someone out … who was quite upset. I pointed out that my scheme was not against the rules. But he responded that while that might be so, “it’s just not cricket”.

I suppose I learned some negative lessons at Eton too. The first term I was there I worked very hard so I would come top in the end-of-year exams for my class … which I succeeded in doing. But it turned out not to be very exciting … so that was the last time I was anything like that diligent.

I happened to go through the whole system quite young … and continually got the feedback that there would eventually be some “social” problem with that. That gave me a self-image of being a kind of pure academic kid. Which if one had looked more carefully wasn’t correct. I was always organizing stuff, though usually outside of the usual tracks … and doing things that were pretty obviously (in retrospect) the kind of things one would expect any entrepreneur-type to do.

Being a scholarship kid at Eton (the scholarship part was more about honorifics than about money, though there was money too) I ended up being with some pretty interesting other kids. And it’s been quite fascinating to me to see how they’ve all turned out (given that we’re all middle-aged now)…

Q: If somebody proved P=NP, what do you think your reaction would be? —Parthide

SW: I’d be surprised!

And then I’d ask just what axiom system (Peano arithmetic, set theory, … ?) was used to do it.

I have a suspicion that P?=NP ultimately isn’t a well-defined decidable question. But hopefully we’ll eventually see.

Q: Mathematica, NKS, Wolfram Alpha, what comes next? How are they all related and what is your criteria for choosing a project? —fxzvdn

SW: First, lots of combinations of those. There are some really interesting things emerging there.

I’m hoping one day to make a serious assault on finding the fundamental theory of physics. Perhaps that will be my next “very different” project.

How are all my projects connected? Well they all have in common that they involve taking some big hairy area and trying to break it down to find what’s essential, and then building up from there.

And each project required the previous one in order to be possible. NKS relied on Mathematica as a tool. Wolfram|Alpha I only realized was possible after what I discovered in NKS. And of course Wolfram|Alpha is all built in Mathematica.

About picking projects: I always have a supply of projects that I’m thinking about. Typically I gradually accumulate ideas about them. And wait for the right time—given ambient technology, the state of the world, my situation, etc.—to do them.

One feature of all my projects is that they’re never really done. They’re infinite projects (well, with NKS at least the book got simply “done” … 10 years ago today). And an important thing for me is to develop an organization that can keep moving each project forward, without me having to spend all my time on it. Because without that, I’d never be able to do a new project, ever.

What are my criteria for a “good” project? It must be something that I find intellectually really interesting and that I expect to make use of for the rest of my life. It must be something that I think nobody else will do, and that for some reason I and our organization are uniquely positioned to do. Oh, and it mustn’t take too long (as in, there should be something to show for it within a few years). For many projects, it also has to have some way to make business sense, so I can afford to build up a team around it, etc.

Q: What are some of your important life lessons? I saw this thing a while aago where you kept track of all of your emails and stuff, it looked like you stay up pretty late, do you find the late night to be a productive time to learn and develop ideas? —R0FLS

SW: I’ve been thinking of compiling some of my “best practices for life” :-) It’s a long list…

I tend to like to figure things out for myself. Sometimes I come to the same conclusion as everyone else; sometimes it’s completely different.

I really don’t know how I first got into the “staying up late” thing … but I’ve been doing it for 30 years now, and I suppose I have adapted everything else in my life to it … so it works well for me.

Q: Do you think intelligence has ‘normalized’? Basically, with more people alive than ever before and college education available to a large percentage of the world’s population, do you think we are seeing fewer break-out intellects because the playing field is more level? For instance, no more Maxwells, Newtons, Einsteins, etc. Or is it just that we are unable to see the current visionaries while still living in the same generation as their bodies of work?

Also, what affect do you think monetization of intelligence has had on scientific pursuit? For instance, your own private efforts have been much more lucrative than any research work alone would have done. Extending on that, do you think your decision to delve into private enterprise has lessened your potential contribution to scientific fields?

Thanks. —anexanhume

SW: It definitely is easier to see “break-out intellects” in retrospect than at the time. It’s also worth realizing that the domains of greatest creativity have shifted over the years. Sometimes they’ve involved science, sometimes not.

Also, it’s usually harder to have something “break-out” happen when there’s an area that’s more institutionalized. So having more people can hurt, rather than help. Because it pretty much forces there to be more structure in place, and that makes “breaking out” harder.

In education, there’s been a tremendous trend towards intense “mass production”, which certainly doesn’t help in having “break-out” things happen.

As far as the relationship between money and intellectual work. I’ve gone to a lot of trouble to set my life up so that I can really work on things that I think are worthwhile. And to create an organization that’s good at stimulating me, and taking ideas I have and turning them into reality. It’s great, and I’m certain I’ve been incredibly much more productive than if I’d for example stayed a professor or something.

I’ve also found that working on practical problems very often leads to me to new kinds of thinking that I don’t think would ever have occurred to me if I’d just been pursuing pure science.

Q: What kind of skills would one need to work on the wolfram alpha answer engine? —TheOtherSideOfThings

SW: What’s interesting about building Wolfram|Alpha is how many very different kinds of skills it needs.

I talked about this a bit before:

The main teams we have are: content areas (e.g. socioeconomic; geographic; scientific/medical; math; cultural/consumer; “miscellaneous”); frameworks; parsing; data curation; linguistic curation; user experience/design; web development; quality assurance; operations; [who am I forgetting?]

In aggregate the content areas are the biggest group.

We also have an “advanced R&D group”, that works on major new directions (e.g. recently many of the features in Wolfram|Alpha Pro).

In terms of peoples’ backgrounds: we’ve got quite a spectrum, including PhDs in lots of different areas. A remarkable number of people working on core parts of Wolfram|Alpha happen to have worked on NKS—which given some of the methods we’re using, may not be a coincidence :-)

For the content areas, we have people with specific expertise and background in those areas (and we’re also continually calling on outside experts for help). In other areas, I don’t have a precise inventory, but my impression is that we’re roughly equally split among physics, computer science and math in terms of educational background.

Q: I just want to say thank you. You are brilliant. Random question time: What is your favorite movie? If you had to recommend one that everyone in the world had to watch, what would you recommend?

When you were young, what did you want to grow up to be? Are you pleased with what you ended up doing? :-) that’s all. Thank you again! —anonymous

SW: In an effort to stay in touch with general culture, I’ve tried to see one new movie every week or so for many years. So I’ve seen lots of movies by now.

When I was a kid I was really excited about “2001”, and I would have called that my favorite movie. Now … I don’t know; there are lots of interesting ones (and also lots of terrible ones).

By the time I was about 12 I wanted to grow up to be a physicist. (Note that at the time, physics was the most “happening” area of science.) The good thing was that by the time I was 20, I was a physicist. So then I got to figure out what else I wanted to do. And I was lucky enough that computers were at about the right stage for me to start using them to do interesting things.

Yes I’m quite happy with the things I’ve ended up doing. Each successive project has built on the others. I wish they’d taken less than 30 years … but they’ve been big projects. And I’ve definitely had a good time doing them…

Q: My friend thinks he saw you at the Joint Mathematics meetings in Boston- were you actually there last January or were my friend’s eyes deceiving him? —dasseth

SW: I was there for a few hours. (I live near Boston.)

Q: Thanks for this AMA. I’d like to ask you:

1. What will be the most promising topics of research in computational science in the near future?

2. What are, in your opinion, the most important skills (mental and practical) for being able to hold a job at Wolfram Research?

3. I assume that Wolfram Research, having launched WolframAlpha, is trying to expand their customer base to casual users. Is the professional/academic market already saturated?

Also, thanks for your products. They help me more than I want to admit. —miramarco

SW:

1. There are lots. Including many based on NKS … some of which I touched on in a blog post I did today: http://blog.stephenwolfram.com/2012/05/looking-to-the-future-of-a-new-kind-of-science/ It’d be fun to make an organized list, though. Perhaps something for our annual summer school: https://education.wolfram.com/summer-school/

2. Being smart, and being able to apply your intelligence with good common sense to a range of different issues. Communicating clearly, and interacting well with people. Being able to understand things quickly, get started quickly … but get things finished, at very high quality with great attention to details.

3. No, it’s definitely not saturated. Far from it. There are huge areas where Mathematica (and Wolfram|Alpha) technology should be used, but aren’t. In fact, in a couple of weeks we’ll be opening up yet another professional market direction…

Q: Could you tell us a bit of your personal experience of doing a PhD at such an early age and how it happened? Did you have an advisor? Did you take any coursework or took lectures? I’ve heard you were kind of close to Feynman, was he your profesor while at Caltech? —BeingDigital

SW: I did a PhD early because I started doing science early. I guess I realized that even in the early 1970s one could perfectly well teach oneself from books … so I did. I wrote my first physics research paper when I was 14. I went to college briefly (at Oxford) when I was 16, but left pretty soon to go to graduate school. By the time I went to Caltech, I’d published a decent number of physics papers. (There’s more detail in: http://blog.stephenwolfram.com/2011/06/a-precociousness-record-almost-broken/)

I didn’t do any lectures or coursework in graduate school (well, actually, I did start going to one course by Feynman, but after the first homework he told me I shouldn’t bother to come any more … so I didn’t). I did interact quite a bit with Feynman. I wrote about some of my experiences a few years ago: https://www.stephenwolfram.com/publications/short-talk-about-richard-feynman/

The story of my thesis advisor is a bit odd. I was finishing my thesis, and about to become a faculty member, and it seemed that in some bizarre way I could be my own advisor (which sort of appealed to me). I also thought maybe Feynman should be my advisor. But he said two things to me. The first was that he thought he had some kind of curse with respect to graduate students, because he’d never had a successful PhD student (later I met a couple of his former students, who really had done rather well, as it turned out). The second was that he said: “you don’t want to be known as so-so’s student; pick someone less famous as an advisor”. So we brainstormed about whom. There was a young person at Caltech named Rick Field, who both Feynman and I liked. And Rick had not yet had any graduate students. So I said: “sure, I’ll be his first student”. Rick is still a physics professor today (in Florida). [A piece of trivia is that he is the older brother of the actress Sally Field … and the claim that she said she thought her brother had invented “field theory” is false :-) ]

Q: When will CDF be available on the iPad? —rkirchne

SW: Soon! (And, yes, the software engineering is highly nontrivial.)

Q: Are you still following/doing current research in physics? Can you summarize in no less than one sentence the “secret” of managing yourself and your resources to do all these projects? —tarek_me

SW: I haven’t done much physics as such in about 4 years; I’ve been “distracted” by Wolfram|Alpha and all the things it makes possible. I’m hoping to get back to it soon, though. I do follow general things in physics, both by reading and by talking to people in the field. And typically I don’t have trouble reading the latest physics papers if I need to.

I guess I manage to do lots of projects because (a) I’m fairly efficient and organized, and (b) I have a terrific people to work with at our company…

Q: In your most recent blog post you predicted that conventions and principles for computer experiments will become established. One obvious convention is the language specifying the computation, and Mathematica is an obvious candidate for that language.

Do you see Mathematica able to both fill that role and remain a proprietary system? —nswanberg

SW: We’ve already opened things up a lot with CDF. But we’re still trying to figure out the best ways to make Mathematica as a language be as fully open as possible, while maintaining the design integrity we’ve worked so hard to ensure—and making sure that we continue to be able to operate our business and go on energetically developing things. I’m hoping we’ll be ready for some interesting new announcements about all this later this year.

And, yes, Mathematica is a language and as a system is extremely well optimized for computer experiments. And certainly very few of the experiments I’ve ever done would ever have been realistic were it not for Mathematica.

Q: If I was tasked with demonstrating the power and versatility of modern technology to someone from 20 years ago, I’d show them my iPhone with its Wolfram application. It’s truly staggering to think about the contributions to knowledge and science made by folks like you. I don’t have a question, but you do have my sincere admiration. Keep doing what you’re doing. —patefacio

SW: Thanks!

Q: Hello Dr. Wolfram, thank you for taking the time to do this AMA.

Has there ever been periods of time where you’ve been burnt out or pessimistic about science and/or the way people react to science, and if so how did you rationalize and overcome those frustrations? —knotswag

SW: I wrote last week about reactions to the NKS book: http://blog.stephenwolfram.com/2012/05/living-a-paradigm-shift-looking-back-on-reactions-to-a-new-kind-of-science/

For years, I’ve tended to do things much more for myself than for the sake of other people’s opinions. Opinions also get pretty statistical after a while: there’ll be people who are very positive, and people who are very negative. Sometimes the negative people are interesting to interact with; sometimes they’re just negative, and don’t seem to add much.

I suppose it helps to be confident about what one’s doing. For me it also helps that I really like doing what I’m doing. And generally my experience is that when people tell me it’s a silly thing to do … well, that’s when it’s a really good idea!

Q: This is an important question:

Imagine you are a director. You are filming a scene that depicts the end of the world – say, for example, the Earth is being swallowed by a rapidly expanding sun.

You have to pick a song to play in the background of this scene. This song has to sum up, in your mind, all of humanity. It has to be a fitting tribute to human kind and to planet earth – a perfect goodbye for the planet that has so much history.

You can pick any song. Which one do you pick?

Really interested to see your answer! —anonymous

SW: Wow … I know about all kinds of things … but not songs. So really I have nothing to say here. Though for some reason I’m thinking of the music at the end of Dr. Strangelove, and at the end of Dark Star. Oh … and what about transmitting the few terabytes of systematic knowledge that the civilization has accumulated? I wonder if we could turn the Wolfram|Alpha knowledgebase into music; I’m not optimistic….

Q: Hey Stephen can you tell what the future of Wolfram Alpha is and how did you get the idea to make it? —VictorSavage

SW: We’ve got lots of things planned. Some of them relate to uploading data from users, as we do in Wolfram|Alpha Pro. Handling more with images and other kinds of data. Having more knowledge and content in general. Being able to do “invention” and modeling on the fly. Lots of things.

I’d been thinking about making something like Wolfram|Alpha since I was a kid. But I didn’t think it was possible until after I’d written the NKS book, which suggested some important principles.

Q: How do you see integration of computational thinking into general math education working? Is it something that every student should be exposed to? How deep does the integration go? —dandersod

SW: My brother Conrad has an initiative related to this, called Computer-Based Math: http://www.computerbasedmath.org/

I think there are also things to do directly with computation and NKS, without any direct connection to traditional “math”. And yes, I think these are great for all students. Both because it’s a foundation for a lot of things in the world. And also because it’s engaging in many different ways (e.g. one can make discoveries easily; there are interesting visual/artistic forms to generate; etc.)

It’s interesting to me that one can successfully teach Mathematica even to quite young students. It’s a very satisfying thing for them: type a small amount in correctly, and all kinds of things can happen.

Q: If you were forced to pick a 5 year period from history to be sent back to, what period would you pick? Your arrival date will be randomly picked from the 5 year period, meaning that you will arrive somewhere in the 5 year period. Also this is a one way trip, and there will be no return to the present. You can only bring with you what you can carry and already have access to, meaning anything you already own or can buy within one hour (budget limited to your current holdings) that you can carry. —MadMan2012

SW: Well … I’m not sure how well I’d do before modern candy and other comforts :-)

I guess I’d want to bring a computer and everything needed to repair it. Not sure I could fit a generator. So it’d have to be some time after electricity…

Heck … this is a weird hypothetical question. It would surely be fun to be telling people all the stuff we know now. But too far back and they really wouldn’t comprehend it.

I think the late 1800s might have been intellectually interesting—that was a time when the formalization of lots of things was happening, and with a different push it might have gone “all the way” to ideas of computing, but didn’t.

Where do I get to go in the world in your setup? Victorian England might have amusing in some ways.

Oh … perhaps I should go after 1959, so I could influence “myself” … and change my answer to this question.

Heck … I give up…

Q: Thanks for this opportunity—here are a few questions; responses to any/all would be appreciated =)

• I can’t seem to escape mentions of you and your work which, at most charitable, amount to, “He’s awfully bright, but can be quite an ass.” (referring to your egotism, tendency to take credit for others’ work, crank-iness, etc.) I don’t resonate with them, but I wonder—given the cost your personality and public persona (caricature?) have incurred on your work—whether you might comment on those dynamics and whether you’d like to have a different public persona, if you could flip a switch tomorrow. e.g. I’d love to know how or whether you think about stuff like that in considering how to get NKS/Mathematica/the ideas you care about ‘out there.’

• I often find myself disappointed by the Wolfram Demonstrations project. Basically, it makes Mathematica out to be nothing more than a cool applet generator instead of the powerful, transformative computational thinking aid I actually find it to be. Why is this? I don’t know what your internal definition of success for the Demonstrations project is, but I know that I would find something like the following far more demonstrative of Mathematica’s power: Say once a week or once a month, you sat down for an hour or two and did some real science and math in Mathematica, maybe screencasting it, maybe writing it up in a blog post, whatever. The range and depth of your knowledge and your deep familiarity with Mathematica and long term vision for it seem to put you in a pretty unique position to . I’m sure you’re very busy, but in the course even of a year you’d have a book that I think would do far more to persuade people of Mathematica’s value than NKS (though I understand that might not be a priority for you).

• Seymour Papert’s work is near and dear to me. LOGO is a bit of a relic, and the revolutionary potential of LOGO and Papert’s ideas have been shelved by detractors and proponents alike. Many would say that the immune system of traditional school neutralized the transformative potential of technology. Do you worry that Mathematica will fare similarly (ignored or marginal compared to your ambitions for it)?

• If you had to sum up your managerial/executive philosophy in a couple sentences, how would you? —aresnick

SW:

1. I always think I’m a pretty reasonable guy … and certainly there are lots of people who’ve been working with me for years who (usually) tell me the same thing. Actually, it’s rather nice in many ways having a reputation for being somehow difficult. Because when I actually meet people, they’re all excited about how nice and reasonable I seem to them :-) [I might mention that my friend Richard Feynman had the opposite situation, which wasn’t always so good. He had a reputation for being a super nice guy. In actually, he was a perfectly reasonable guy, but not “super nice”. So when people met him, they were often upset that he seemed to be a lot less nice than they expected.] Having said all this, I was probably brasher when I was a teenager than I am now … but that was a very long time ago (sadly), and one might think people would have updated their views a bit since then… (And of course I had the feature that I was “visible” when I was a teenager, interacting with professional scientists etc.—rather than just being off being a kid…)

2. That’s a good idea! I really enjoy doing “live experiments” with Mathematica. I do them at our summer school, and sometimes I get a chance to do them elsewhere as well. Many years ago we tried to figure out how to screencast live experiments, and make them generally interesting. We didn’t quite figure out the production scheme back then … but we really should think about it again. Thanks for the suggestion! (If you have more ideas about specifics, I’d love to hear them…)

3. I had a very nice dinner with Seymour Papert a few years ago, and was asking him very much the question you’re asking me. I don’t think he had a clear answer, and I don’t know the history well enough myself. The world has of course changed a lot since LOGO’s heyday, and I am hopeful that—especially with some new technology coming soon—Mathematica will be able to be delivered in ways that avoid the problems I think LOGO encountered. I have to say I view it as a hopeful sign that in less than 3 years, Wolfram|Alpha has become surprisingly widely accepted in schools. Clearly that started with students, but teachers seem to be getting on board very well too. And of course there are very interesting ways to use Wolfram|Alpha to do math etc. in true real-world settings, etc.

4. “Let’s do great things; we can!” I like to define ambitious goals, then help people achieve them. And of course I try hard to get the best people, and put them in the places that are the best fits for them.

Q: What is your favorite color? —sircmpwn

SW: Usually nobody would care about the answer to this question. But if you have an art department that designs your corporate identity, it can matter. Back when Mathematica was young, I said purple was my favorite color … so then all things Wolfram Research ended up being purple! I got quite fed up with purple, and was gradually led (I think) to some kind of light orange color that we now use a lot. We also have a lot of red in our corporate color palette, but that’s not because it’s a favorite color of mine…

Q: Any chance of Mathematica for iPad? I remember using it on NeXT, and that’s probably less powerful than an iPad 2 or above… —RiczWest

SW: Stay tuned…

Q: In a recent public email you mentioned existence of a model for galaxy formation being in the NKS domain. What other cosmological applications are you aware of in this vein, either published or being pursued? —unbusyb

SW: I worked on cosmology and its relations to particle physics back in the late 1970s, long before that was fashionable… With my friend Rocky Kolb, I even mentioned inflation in a footnote to a paper before it had officially been invented, saying that I thought it was implausible…

There are some really interesting cosmological implications of the kinds of network-based models of physics that I discuss in the NKS book. For example, one gets around needing inflation to explain homogeneity, in effect because the universe starts much higher dimensional than it ends up.

See e.g. http://www.wolframscience.com/nksonline/page-1055a-text

Q: What is your opinion on this quote: “And yet, even though useful quantum computers might still be decades away, many of their payoffs are already arriving. For example, the mere possibility of quantum computers has all but overthrown a conception of the universe that scientists like Stephen Wolfram have championed. That conception holds that, as in the “Matrix” movies, the universe itself is basically a giant computer, twiddling an array of 1’s and 0’s in essentially the same way any desktop PC does. Quantum computing has challenged that vision by showing that if “the universe is a computer,” then even at a hard-nosed theoretical level, it’s a vastly more powerful kind of computer than any yet constructed by humankind. Indeed, the only ways to evade that conclusion seem even crazier than quantum computing itself: One would have to overturn quantum mechanics, or else find a fast way to simulate quantum mechanics using today’s computers.” http://www.nytimes.com/2011/12/06/science/scott-aaronson-quantum-computing-promises-new-insights.html?_r=1&ref=science&pagewanted=all Vs. “I have my next big project picked out: trying to find the fundamental theory of physics.” https://www.stephenwolfram.com/publications/computation-future-human-condition/ —mazsa

SW: My basic opinion is “huh?”

Yes, there’s a formalism that’s been invented for quantum computing (I actually worked on an early version of such things around 1981 with Richard Feynman). But it’s still—even after a lot of years—completely unclear how that formalism relates to things that actually happen in the physical universe. And my own guess is that in fact there are some nasty gotchas connected with measurement processes, which aren’t directly handled in the formalism of quantum mechanics.

It’s a complete logical muddle to say that the existence of a theory of quantum computing implies that it’s proved that certain implications of the theory must be correct.

Now, in addition, there’s absolutely nothing about the kinds of NKS-based models of physics that I’ve worked on that’s inconsistent with quantum mechanics. In fact, there are some nice indications of quantum phenomena emerging in very elegant ways.

I’ve never met Scott Aaronson, though I did talk to him once on the phone around the time the NKS book was coming out. He had some argument “proving” that the NKS approach to physics was inconsistent with certain aspects of quantum mechanics. But as one of my colleagues patiently explained to him … his argument was mathematically incorrect. I think he published it anyway … which is certainly odd … and I guess people still quote it.

Q: What is the air-speed velocity of an unladen swallow? EDIT: Just checking if you knew it off the top of your head. —kablunk

SW: I don’t. I’d ask Wolfram|Alpha….

Q: What would you tell to those that claim that it was already known that simple programs were capable of great complexity? They put as examples things such as the mathematical constant pi, which has a simple (or many) formula but which output looks very random. Or chaotic systems (e.g. the logistic map).

I find fascinating that you managed to find rule 30 though, it seems to me that by all means it is the simplest possible program I can think of and still is capable of such behavior. —BeingDigital

SW: It’s absolutely correct that things like the digits of pi were known for a long time to look random, even though they came from simple rules. The point was that there wasn’t a conceptual framework for thinking about such things. (So, for example, when people studied primes, they looked for regularities in their distribution, rather than asking what the origin of the apparent randomness was.)

I discuss this history at considerable length in the NKS book and its notes: e.g. http://www.wolframscience.com/nksonline/section-2.3

Personally, I find it really interesting that these phenomena were seen even a long time ago … but the ambient intellectual structure just didn’t exist to understand their significance. It makes me wonder what things we see now need new structures to be understood…

Q: You earned a Ph.D. at 20, yet many students of that age struggle with basic calculus. What is your advice to students who rely on programs like your Wolfram Alpha engine to get themselves through math courses? Do you think it’s ethical for students to rely on such programs to pass their courses? —eponymoususername

SW: I’ve been using computers to do math for more than 30 years now. For me, the important thing is that by using computers I was always able to do many more examples … from which I could get an intuition about how the math should work out. And once one can guess from intuition how a problem should work out, it’s much easier to get the right answer when one does it by hand. Nowadays I find it pretty cool when I see people working out math by hand … it’s like “can humans really do that stuff?”

Q: What’s the most complex thing that I can get WolframAlpha to do? What’s the most amazing thing that I can get WolframAlpha to do? —soybean

SW: I don’t know! That’s the neat thing about programs like Wolfram|Alpha (and it’s something emphasized by computational irreducibility in NKS). Just because you know how the program is set doesn’t mean you can predict or imagine what it’ll be able to do…

Q: What are your thoughts on genetic algorithms? Some researchers are looking into automated research and design, Hod Lipson being a great example. Do you think this idea has a future? Is it even advisable to let inquiry become automated? —anonymous

SW: I’m definitely interested in “automated discovery”. In fact, we have a bunch of experiments going around Wolfram|Alpha Pro—being able to “tell people something interesting” about whatever data they upload.

My experience with NKS has been that incremental (e.g. genetic) algorithms don’t allow one to find the really surprising results that one can get to with exhaustive search.

One issue that I’m still grappling with is this. If one uses a method like symbolic regression, one can often find relations between things. But they’re just weird. Like say (and I’m making up the details) that the length of railways in a country is proportional to the cube of the number of radio stations divided by the number of doctors. Well, you look at relations like that and you say “that has to be nonsense”. But of course it might work just fine, and even go on working for new cases.

In some fields (like medicine) there are “nonsense” formulas (where units don’t match, etc. etc.) that actually work. I just don’t know quite how to think about such things. And I worry that if we output them for users, the users will either think our system is nuts, or they’ll blindly use the formulas and come up with silly results…

Q: I would be very interested to hear if you’ve ever worked with APL or J or the K/Q programming languages, and what your opinion of J especially is. It’s usefulness in research, mathematics, and industry and perhaps how it compares with Mathematica. Thanks for the opportunity and happy anniversary! —desparadacido

SW: I haven’t personally used APL or J for production purposes, though I studied APL in detail when I was designing SMP, the forerunner of Mathematica. I thought APL had some really interesting ideas, some of which have shown up in Mathematica.

I actually gave the keynote at the APL annual conference in 1989. I think they had some kind of conference song there, and there was a terrible moment where it said something about how APL had died and been reborn as Mathematica. From my point of view, I’d really like to see good ideas from APL propagate, and if Mathematica can help that, it’s great.

I got to know Ken Iverson at that conference, and talked to him quite a bit over the years. He explained to me his concept of APL being a notation for algorithms, analogous to mathematical notation for math. I said I’d ended up just leveraging people’s knowledge of English, and making the core of Mathematica notation be plain English words.

I talked to Ken Iverson, particularly late in his life, about why he thought people hadn’t understood functional languages better. His main conclusion seemed to be that somehow most people just weren’t smart enough (being an optimist about such things, I of course disputed this). I suppose it’s then really encouraging all around that in recent years it seems that functional programming is finally beginning to be widely understood.

Q: What’s your favorite NKS rule and why? —sortuo

SW: Rule 30. I even have it on my business cards :-)

Because it was when I absorbed what was going on in that rule that I began to understand that there needed to be an NKS…

Q: A few times now, I’ve found outright inaccurate information on Wolfram|Alpha. One that specifically comes to mind is that it says tuition at Cal Poly SLO is free for California residents. How should I report these errors to your site? (I sent feedback about four months ago and again I think two months ago but it still isn’t changed.) —OffhandOnion

SW: Please report errors using the feedback form at the bottom of each page. It’s read by real humans. You should have gotten a response. If you didn’t, complain!

[OK … I’m finally off now. This was a great way to spend part of the NKS 10th anniversary. Thanks everyone!]