Category Archives: Creativity

Lovelace’s Creativity Test

Source:  Motherboard, Jul 2014

The Lovelace Test is designed to be more rigorous, testing for true machine cognition. It was designed in the early 2000s by Bringsjord and a team of computer scientists that included David Ferrucci, who later went on to develop Jeopardy-winning Watsoncomputer for IBM. They named it after Ada Lovelace, often described as the world’s first computer programmer.

The Lovelace Test removes the potential for manipulation on the part of the program or its designers and tests for genuine autonomous intelligence—human-like creativity and origination—instead of simply manipulating syntax.

An artificial agent, designed by a human, passes the test only if it originates a “program” that it was not engineered to produce. The outputting of the new program—it could be an idea, a novel, a piece of music, anything—can’t be a hardware fluke, and it must be the result of processes the artificial agent can reproduce. Now here’s the kicker: The agent’s designers must not be able to explain how their original code led to this new program.

In short, to pass the Lovelace Test a computer has to create something original, all by itself.

Even the most advanced self-learning neural network can only perform tasks that are first mathematized and turned into code. So far, essentially human functions like creativity, empathy and shared understanding—what is known as social cognition—have proved resistant to mathematical formalization.

Related Resource:
“The Lovelace 2.0 Test of Artificial Creativity and Intelligence”, Oct 2014


Falling Price of Light (500,000X)

Source: BBC, Feb 2017

The labour that had once produced the equivalent of 54 minutes of quality light now produced 52 years.  And modern LED lights continue to get cheaper and cheaper. Switch off a light bulb for an hour and you are saving illumination that would have cost our ancestors all week to create.

It would have taken Benjamin Franklin’s contemporaries all afternoon.

But someone in a rich industrial economy today could earn the money to buy that illumination in a fraction of a second. 

Related Resource: Quora, date indeterminate

Imagining New Possibilities for Math (i.e. Crypto)

S0urce: HackerNoon, Dec 2017

There are four additional problems with a blockchain-driven approach.

  1. First, you’re relying on single-point encryption — your own private keys — rather than a more sophisticated system that might involve two-factor authorization, intrusion detection, volume limits, firewalls, remote IP tracking, and the ability to disconnect the system in an emergency.
  2. Second, price tradeoffs are entirely implausible — the bitcoin blockchain has consumed almost a billion dollars worth of electricity to hash an amount of data equivalent to about a sixth of what I get for my ten dollar a month dropbox subscription.
  3. Fourth, systematically choosing where and how much to replicate data is an advantage in the long run — the blockchain’s defaults on data replication just aren’t that smart.
  4. And finally, Dropbox and and Google and Microsoft and Apple and Amazon and everyone else provide a set of valuable other features that you don’t actually want to go develop on your own. Analogous to Visa, the problem isn’t storing data, it’s managing permissions, un-sharing what you shared before, getting an easy-to-view document history, syncing it on multiple devices, and so on.

The same argument holds for proposed distributed computing and secure messaging applications. Encrypting it, storing it forever, and replicating it across the entire network is just a ton of overhead relative to what you’re actually trying to accomplish. There are excellent computing, messaging, and storage solutions out there that have all the encryption and replication anyone needs — actually better than blockchain based solutions — and have plenty of other great features in addition.

Straight A-students != Best Innovators

Source: The Conversation, date indeterminate

where do innovators come from? And how do they acquire their skills?

One place – perhaps among the best – is college. Over the past seven years, my research has explored the influence of college on preparing students with the capacity, desire and intention to innovate.

In this time we’ve learned that many academic and social experiences matter quite a bit; grades, however, do not matter as much.

as GPAs went down, innovation tended to go up. Even after considering a student’s major, personality traits and features of the learning environment, students with lower GPAs reported innovation intentions that were, on average, greater than their higher-GPA counterparts.

Additionally, findings elsewhere strongly suggest that innovators tend to be intrinsically motivated – that is, they are interested in engaging pursuits that are personally meaningful, but might not be immediately rewarded by others.

We see this work as confirmation of our findings – grades, by their very nature, tend to reflect the abilities of individuals motivated by receiving external validation for the quality of their efforts.

Perhaps, for these reasons, the head of people operations at Google has noted:

GPAs are worthless as a criteria for hiring.

Here is what our analyses have revealed so far:

  • Classroom practices make a difference: students who indicated that their college assessments encouraged problem-solving and argument development were more likely to want to innovate. Such an assessment frequently involves evaluating students in their abilities to create and answer their own questions; to develop case studies based on readings as opposed to responding to hypothetical cases; and/or to make and defend arguments. Creating a classroom conducive to innovation was particularly important for undergraduate students when compared to graduate students.
  • Faculty matters – a lot: students who formed a close relationship with a faculty member or had meaningful interactions (i.e., experiences that had a positive influence on one’s personal growth, attitudes and values) with faculty outside of class demonstrated a higher likelihood to be innovative. When a faculty member is able to serve as a mentor and sounding board for student ideas, exciting innovations may follow.

Interestingly, we saw the influence of faculty on innovation outcomes in our analyses even after accounting for a student’s field of study, suggesting that promoting innovation can happen across disciplines and curricula. Additionally, when we ran our statistical models using a sample of students from outside the United States, we found that faculty relationships were still very important. So, getting to know a faculty member might be a key factor for promoting innovation among college students, regardless of where the education takes place or how it is delivered.

  • Peer networking is effective: outside the classroom, students who connected course learning with social issues and career plans were also more innovative. For example, students who initiated informal discussions about how to combine the ideas they were learning in their classes to solve common problems and address global concerns were the ones who most likely recognized opportunities for creating new businesses or nonprofit social ventures.

Being innovative was consistently associated with the college providing students with space and opportunities for networking, even after considering personality type, such as being extroverted.

Networking remained salient when we analyzed a sample of graduate students – in this instance, those pursuing M.B.A. degrees in the United States. We take these findings as a positive indication that students are spending their “out-of-class” time learning to recognize opportunities and discussing new ideas with peers.


From our findings, we speculate that this relationship may have to do with what innovators prioritize in their college environment: taking on new challenges, developing strategies in response to new opportunities and brainstorming new ideas with classmates.

Time spent in these areas might really benefit innovation, but not necessarily GPA.

Are Mathematicians Creative?

Source: Quora, date indeterminate

Theorem 1. Mathematics is the most creative human activity.

I refer especially to research, although other activities which apparently involve simple calculations, such as taxes, may be creative too. Especially taxes.

In order to prove the theorem, let’s prove some lemmas first.

Lemma 1. The length in bits of any creative work is smaller than a finite fixed number N.

Proof. The universe may be infinite, but to us, in our lifespan, only a finite part is accessible. The possible configurations of matter in this region may be infinite, but we can distinguish only among a finite number of states. You may think that you can distinguish an infinite number of colors, or of sound frequencies, or of music timbres, but you can’t, so we can digitize them. The proof is in the fact that you can listen music CDs, watch movies on DVDs, read books which contain strings of letter of a finite size. This goes for mathematics too. Add to this the limitation of the maximum quantity of information provided by the Bekenstein bound and you will see that this is true.

Corollary 1. Any human activity, no matter how creative, consists in moving among a finite number of distinguishable states.

Proof. For example, the state when a composer has created a piece of musical composition, or a writer wrote a piece of literature or poetry. Take a one page poem. There is a finite number of strings of letters which can fill a page. A finite number of them are poems. Take a 10000 pages book. There is also a finite number of strings that can fill that book, and a smaller number even make sense. Similarly, the musical notes and instruments available are finite. You can say countable if you don’t limit the length, but in practice, they are all finite, as seen in Lemma 1.

Lemma 2. Any human activity, no matter how creative, is like solving a labyrinth.

Proof. The number of available states, though large, is finite. The number of changes from one state to another is therefore also finite. The number of chains of changes from one state to another is also finite, the length of such chains being limited by N. These possible states and changes between them form a graph, which is a labyrinth. You may object that the labyrinth is not fixed, and that there are places of it where you are allowed to push the walls. It is true, but there is a finite number of configurations in which you can rearrange the walls. By including all possible configurations, you will eventually get a finite length fixed labyrinth.

From the above Lemmas follows:

Corollary 2. All human activities, no matter how creative may seem, are the same, being like solving a labyrinth.

However, Theorem 1 claims that mathematics requires more creativity. To see why is this, let us first define creativity.

Definition 1. The “is more creative” is a relation of partial order between human activities, defined by the following. Everything else being equal among two or more activities, the more creative one is the one in which:

1. It impacts more positively the creativity of the other activities.

2. The proportion of the admissible paths joining a start point and an end point of the labyrinth among which you have to choose is smallest. Equivalently, the constraints are greater.

3. You get to break fundamental rules more often.

4. You can create more worlds and create them more completely, in particular the world in which the labyrinth itself exists.

Proof of Theorem 1.

Let us examine the criteria in Definition 1, and compare how they hold on mathematics as compared to other activities.

1. Mathematics impacts physics, chemistry, engineering, IT, technology more than anything else. You may say that physics, but mathematics impacts physics, while physics is merely inspiration for mathematics. By its impact on technology, mathematics allows more creativity in all other activities, including in arts.

2. One may think that having more freedom means more creativity. But what creativity would someone need to solve a labyrinth, when he is able to walk through the walls? Yet, you will see in literature and movies how often the characters succeed in their tasks, and not necessarily by having superpowers, but by conceiving unrealistic plans that turn out to work, or in general by being extremely lucky. Well, some may object that the better art is in dramas, so in this case the art relies on character’s bad luck. Anyway, the point in arts is to induce feelings and thoughts in the reader, so this is a difficult task. Or at least it was until Hollywood realized that there are success recipes for the scripts, which will always make the viewer laugh or cry. Even in this case, truly creative screenwriters and directors find not only ways to induce the feelings, but also create new feelings. At this point, mathematics may look very bad, I mean, come on, what feelings can you have when you read a theorem. In fact, solving math problems or following the proof of results in which you are interested induces a deal of positive feelings, when everything falls in place and makes sense, like a big Aha.

Mathematics has only one constraint: be (logically) consistent. In arts you have to be consistent too, but you can get away with inconsistencies, and if they are big, you can simply say that you revolutionize the field. In mathematics, being inconsistent can’t pass as being the Picasso of mathematics.

3. If you think that the logical consistency requirement of mathematics makes impossible creating anything new, think more. Take the notion of number. Everybody uses numbers in their creations, they appear in music, literature, and anywhere else. But only mathematicians realized you can subtract a bigger number from a smaller one, or divide by two an odd number, or take the square root of a negative number, and they found how to do it in a consistent way. So they are able to break the rules. In fact, they broke every rule, for instance commutativity and associativity, the postulate of parallels, or anything you may consider. For any property, no matter how cherished may have been once, there are mathematical structures in which that property doesn’t hold. I said that the only requirement is logical consistency, but mathematical logicians also study weaker forms of consistency.

4. A writer can create an entire universe, and I don’t mean here only the Harry Potter universe, or the Dune universe, or the Star Wars universe. Even a room where there are only twelve angry men is a universe. However, you will not know what happens when you get out the door of that room. The fact in any fictional universe which are not in the book can be anything. So in fact they create parts of a universe. But in mathematics, once you give the axioms, you give the entire universe. Other mathematicians can explore it. Or think at the Mandelbrot set. A simple formula like

z(n+1) = z(n)^2 + c

gives infinitely diverse beautiful forms. An infinite universe out of a few letters. Mathematicians are godlike beings who can create infinite universes with so few symbols.

Curiosity Drives Creativity & Innovation

Source: IdeaToValue website, Jun 2017

the world’s greatest innovators are passionately curious and even nosy or annoying.

They approach situations and problems from an open, childlike, mind unconfined by rigidity or preconceived notions.

Fueled by curiosity, they ask crazy questions.

Their expertise grows as they actualize their curiosity by developing a love of learning. Their curiosity impulse and prior knowledge alert them to invisible gaps or details others miss, fueling even more questioning. Their curiosity drives them to become persistent. Their wide interests and curiosity enable them to apply ideas across divergent fields, improving upon the ideas of others,

Their wide interests and curiosity enable them to apply ideas across divergent fields, improving upon the ideas of others, synthesizing ideas, and discovering patterns from disparate fields to generate new ideas. Curiosity reveals new options even at dead ends and inspires a sense of purpose and meaning. Continuously rewarded and renewed curiosity becomes a lifelong passion.

How to nurture the curious attitude?

  1. Find and remove what gets in the way of your curious mind
  2. Never be too shy to ask questions, and ask questions even when you think you know everything you need to know. 
  3. Become more a interesting person and live a more interesting life by reconnecting with your inner child, sense of wonder, and mindset 
  4. Turn away from the familiar, and open your mind to new ideas, interests,experiences, and adventures 
  5. Dig deeper and understand the context, origin, and history of things
  6. Forge deep and quality relationships by showing your sincere and genuine interests in people around you, across all levels
  7. Build your own lab with full of experimental tools as your sandbox to tinker or try out new things; enjoy mistakes and failures 
  8. Finally, work with inquisitive minds, rather than just qualified and experienced people

Claude Shannon on Creativity

Source: The Creativity Post, Aug 2017

A very small percentage of the population produces the greatest proportion of the important ideas.

This is akin to an idea presented by an English mathematician, Turing, that the human brain is something like a piece of uranium. The human brain, if it is below the critical lap and you shoot one neutron into it, additional more would be produced by impact. It leads to an extremely explosive of the issue, increase the size of the uranium.

Turing says this is something like ideas in the human brain. There are some people if you shoot one idea into the brain, you will get a half an idea out. There are other people who are beyond this point at which they produce two ideas for each idea sent in.

Those are the people beyond the knee of the curve. I don’t want to sound egotistical here, I don’t think that I am beyond the knee of this curve and I don’t know anyone who is. I do know some people that were. I think, for example, that anyone will agree that Isaac Newton would be well on the top of this curve. When you think that at the age of 25 he had produced enough science, physics and mathematics to make 10 or 20 men famous — he produced binomial theorem, differential and integral calculus, laws of gravitation, laws of motion, decomposition of white light, and so on.

Now, what is it that shoots one up to this part of the curve? What are the basic requirements? I think we could set down three things that are fairly necessary for scientific research or for any sort of inventing or mathematics or physics or anything along that line. I don’t think a person can get along without any one of these three.

The first one is obvious — training and experience. You don’t expect a lawyer, however bright he may be, to give you a new theory of physics these days or mathematics or engineering.

The second thing is a certain amount of intelligence or talent. In other words, you have to have an IQ that is fairly high to do good research work. I don’t think that there is any good engineer or scientist that can get along on an IQ of 100, which is the average for human beings. In other words, he has to have an IQ higher than that. Everyone in this room is considerably above that. This, we might say, is a matter of environment; intelligence is a matter of heredity.

Those two I don’t think are sufficient. I think there is a third constituent here, a third component which is the one that makes an Einstein or an Isaac Newton. For want of a better word, we will call it motivation.

In other words, you have to have some kind of a drive, some kind of a desire to find out the answer, a desire to find out what makes things tick. If you don’t have that, you may have all the training and intelligence in the world, you don’t have questions and you won’t just find answers.

This is a hard thing to put your finger on. It is a matter of temperament probably; that is, a matter of probably early training, early childhood experiences, whether you will motivate in the direction of scientific research. I think that at a superficial level, it is blended use of several things.

This is not any attempt at a deep analysis at all, but my feeling is that a good scientist has a great deal of what we can call curiosity. I won’t go any deeper into it than that. He wants to know the answers. He’s just curious how things tick and he wants to know the answers to questions; and if he sees thinks, he wants to raise questions and he wants to know the answers to those.

another thing I’d put down here is the pleasure in seeing net results or methods of arriving at results needed, designs of engineers, equipment, and so on. I get a big bang myself out of providing a theorem. If I’ve been trying to prove a mathematical theorem for a week or so and I finally find the solution, I get a big bang out of it. 

The first one that I might speak of is the idea of simplification. Suppose that you are given a problem to solve, I don’t care what kind of a problem — a machine to design, or a physical theory to develop, or a mathematical theorem to prove, or something of that kind — probably a very powerful approach to this is to attempt to eliminate everything from the problem except the essentials; that is, cut it down to size.

Almost every problem that you come across is befuddled with all kinds of extraneous data of one sort or another; and if you can bring this problem down into the main issues, you can see more clearly what you’re trying to do and perhaps find a solution. Now, in so doing, you may have stripped away the problem that you’re after. You may have simplified it to a point that it doesn’t even resemble the problem that you started with; but very often if you can solve this simple problem, you can add refinements to the solution of this until you get back to the solution of the one you started with.

A very similar device is seeking similar known problems. I think I could illustrate this schematically in this way. You have a problem P here and there is a solution S which you do not know yet perhaps over here. If you have experience in the field represented, that you are working in, you may perhaps know of a somewhat similar problem, call it P’, which has already been solved and which has a solution, S’, all you need to do — all you may have to do is find the analogy from P’ here to P and the same analogy from S’ to S in order to get back to the solution of the given problem.

This is the reason why experience in a field is so important that if you are experienced in a field, you will know thousands of problems that have been solved. Your mental matrix will be filled with P’s and S’s unconnected here and you can find one which is tolerably close to the P that you are trying to solve and go over to the corresponding S’ in order to go back to the S you’re after. It seems to be much easier to make two small jumps than the one big jump in any kind of mental thinking.

Another approach for a given problem is to try to restate it in just as many different forms as you can. Change the words. Change the viewpoint. Look at it from every possible angle. After you’ve done that, you can try to look at it from several angles at the same time and perhaps you can get an insight into the real basic issues of the problem, so that you can correlate the important factors and come out with the solution.

It’s difficult really to do this, but it is important that you do. If you don’t, it is very easy to get into ruts of mental thinking. You start with a problem here and you go around a circle here and if you could only get over to this point, perhaps you would see your way clear; but you can’t break loose from certain mental blocks which are holding you in certain ways of looking at a problem. That is the reason why very frequently someone who is quite green to a problem will sometimes come in and look at it and find the solution like that, while you have been laboring for months over it. You’ve got set into some ruts here of mental thinking and someone else comes in and sees it from a fresh viewpoint.

Another mental gimmick for aid in research work, I think, is the idea of generalization. This is very powerful in mathematical research. The typical mathematical theory developed in the following way to prove a very isolated, special result, particular theorem — someone always will come along and start generalization it. He will leave it where it was in two dimensions before he will do it in N dimensions; or if it was in some kind of algebra, he will work in a general algebraic field; if it was in the field of real numbers, he will change it to a general algebraic field or something of that sort.

This is actually quite easy to do if you only remember to do it. If the minute you’ve found an answer to something, the next thing to do is to ask yourself if you can generalize this anymore — can I make the same, make a broader statement which includes more — there, I think, in terms of engineering, the same thing should be kept in mind. As you see, if somebody comes along with a clever way of doing something, one should ask oneself “Can I apply the same principle in more general ways? Can I use this same clever idea represented here to solve a larger class of problems? Is there any place else that I can use this particular thing?”

Next one I might mention is the idea of structural analysis of a problem. Suppose you have your problem here and a solution here. You may have two big a jump to take. What you can try to do is to break down that jump into a large number of small jumps.

If this were a set of mathematical axioms and this was a theorem or conclusion that you were trying to prove, it might be too much for me try to prove this thing in one fell swoop. But perhaps I can visualize a number of subsidiary theorems or propositions such that if I could prove those, in turn I would eventually arrive at this solution.

In other words, I set up some path through this domain with a set of subsidiary solutions, 1, 2, 3, 4, and so on, and attempt to prove this on the basis of that and then this one the basis of these which I have proved until eventually I arrive at the path S.

Many proofs in mathematics have been actually found by extremely roundabout processes. A man starts to prove this theorem and he finds that he wanders all over the map. He starts off and prove a good many results which don’t seem to be leading anywhere and then eventually ends up by the back door on the solution of the given problem; and very often when that’s done, when you’ve found your solution, it may be very easy to simplify; that is, to see at one stage that you may have short-cutted across here and you could see that you might have short-cutted across there.

The same thing is true in design work. If you can design a way of doing something which is obviously clumsy and cumbersome, uses too much equipment; but after you’ve really got something you can get a grip on, something you can hang on to, you can start cutting out components and seeing some parts were really superfluous. You really didn’t need them in the first place.

Now one other thing I would like to bring out which I run across quite frequently in mathematical work is the idea of inversion of the problem. You are trying to obtain the solution S on the basis of the premises P and then you can’t do it.

Well, turn the problem over supposing that S were the given proposition, the given axioms, or the given numbers in the problem and what you are trying to obtain is P. Just imagine that that was the case. Then you will find that it is relatively easy to solve the problem in that direction. You find a fairly direct route. If so, it’s often possible to invent it in small batches.

In other words, you’ve got a path marked out here — there you got relays you sent this way. You can see how to invert these things in small stages and perhaps three or four only difficult steps in the proof.