By Peter Cochrane, 8 October 2009 10:00
COMMENT
Written in a coffee shop on the corner of 1st and 71st Street in New York on bright autumn day. Dispatched to silicon.com via a free wi-fi node.
For more than 20 years now I have worked on artificial life and intelligence systems. Much of the time, efforts in this area have been confounded by a lack of common definitions and descriptions, compounded by questionable performance measures.
In fact I think I can confidently state that we lack any meaningful description, definition, measure, quantification or understanding of intelligence, to the point where we are almost flying blind.
As our species is clearly intelligent, this lack of understanding presents something of a paradox, and a major barrier to scientific study.
In general, we can't even converse productively about this topic without descending into comparisons with carbon life and intelligence, and worse, belief systems. It seems that most humans feel really threatened by machines that outperform, or challenge them mentally. Witness the 'hoopla' surrounding Gary Kasperov, IBM Deep Blue and a game of chess.
Looking at this with the cold eye of reason, we ought not to be upset by the fact that machines beat us at anything. We should be asking how they did it, and how we might exploit that capability to the full.
The reality is our brains aren't going to get a whole lot bigger, and we are not going to get any smarter, but the problems we face as a species will multiply - and we will need all the intellectual help we can get.
So now to business. One of my hobbies is the study of obtuse and difficult problems that present roadblocks to our continued progress, such as the quantification and understanding of AI. Recently I had a bit of a 'huh' (the most important expressions in science) moment when a mathematical analysis of a 'minimally intelligent system' produced the following:
Where:
I = Intelligence (comparative ability to solve problems)
S = Sensor facility
A = Actuator or some output device
P = Processor power
M = Memory capacity
And:
K = A constant related to the system type
ks = A constant related to the system configuration
kp = A constant related to the processor
km = A constant related to the memory
If you are not a mathematician, scientist or engineer, don't panic. Just focus on the implications detailed below.
If I am right in my analysis the implications are profound as this formula says:
- You can have intelligence without memory and processing power (in the discrete sense). All you need is a sensory and actuator system (S and A) that affords a reactive output from an input stimulus. Is this a reasonable outcome? I reckon. There are many examples in nature - slime mould and jelly fish, for example. In the field of robotics this quality has also been demonstrated many times.
- More importantly, this formula says that intelligence grows as the logarithm of the sensor, actuator, processor, memory (SAPM) product. So provided the complex product is far greater than unity, if we increase processing power tenfold, then intelligence is bounded by a log(10) increase, and if I increase memory by 100-fold it is bounded by a log(100) increase, and so on.
To make this more explicit let's assume a 'base 10' log system to simplify the enumeration. And let us say that the product of the SAPM terms increases from 1 in steps 100, 1000, 10,000; then the comparative intelligence increase would increase as 2, 3, 4.
And so to increase a system's intelligence tenfold, the SAPM term would have to be increased by a factor of 10,000,000,000.
An axiomatic condition that the formula satisfies is that if either the sensor (S) or actuator (A) go to zero, then so does the intelligence. Obviously, if there is no input, or no means to output, then to all intents and purposes the system is dead to the world. At best it would be some gibbering or twitching entity incapable of coherence.
This description of intelligence signifies quite a slowdown in the assumed rate of AI progress, and offsets the fears of the 'singularity community' somewhat. It also explains why all intelligence measures to date, based on IQ tests and/or neural count and interconnects, are out of kilter with our real-life experiences of intelligent systems.
Just a word of warning: The system model I used to derive the above was of the simplest and most fundamental kind. Even a modest increase in the number of elements, loops and nested processes quickly renders a full analysis impossible with the mathematical tools and abilities at our disposal. And I don't see this situation improving anytime soon - if ever!
So it might just be that we have to build and evolve our AI systems much further before we have a tool set capable of proving, or otherwise, the above formula and the conclusions for a more complex, or general case.
What is going to be interesting is whether we have to pose the question - or will our systems just become curious enough to do so themselves?
Comments
There are 13 comments. Join the discussion
1. Simon Dufour
I don't understand your article. How do you define intelligence?
The intelligence itself is not something we can quantify like that. Oh, we can qualify an intelligence by validating its output. However, even then, it all depend on the software and not the memory nor the processing power.
When we successfully create an AI using a model of the humain brain, if we double the computation, we'll double the intelligence since the AI would "think" 2 times faster.
Anyway.. I just wanted to point that I don't understand your point and how it prove anything or how you came up with that. Especially against Ray Kurzweil's arguments.
2. David Hughes
I would go along with the outcomes of your formula as you express them. I too studied artificial intelligence - in the 1970's. My conclusion was that intelligence was the ability to form hypotheses that could be subsequently tested or used from an incomplete set of premises. This form of reasoning already has a name = abductive reasoning - see Wikipedia. It relies on having a codified knowledge base (memory) and a means of identifying patterns. Two nice things about this characterisation of intelligence are that it is related to humour and it is the basis of a metaphor. Both of these we would think of as examples of the use of intelligence. Lots of forms of humour from puns to satire rely on a 'mistake' in abductive reasoning. Metaphors are a manifestation of abductive reasoning.
3. Radical Meldrew
Intelligence? In my book it's the ability to recognise situations, react appropriately and adapt and refine the overall approach gradually by a process of learning how to avoid basic errors. The things that make a massive difference to the customer and staff experience in any business is hard to define and almost impossible to appreciate if senior management are not connected with the core values. This is certainly something a machine cannot do....not yet anyway?
Modern businesses however are anything but intelligent, they are almost robotic in their approach. Things tick along slowly….then suddenly….the board buy into a crusading new business mantra spearheaded by a guru who promises that he will totally transform everything overnight into a roaring success.
The board wearily retreat back into the safety zone when it inevitably doesn't work and they do nothing new for a while. They are fully aware that that no progress is being made but they do not wish to repeat the last nasty experience. This unfortunately makes them vulnerable to the next ‘flavour of the month’ campaign that comes their way, they realise they are seen a stale and reticent so they willingly fall prey to something new when they are assured that this will work. Definitely, no doubt, etc, etc.
You may well wonder what this has to do with the discussion of intelligence…..Well I seriously think that robots would be valid replacements for some board members. They’d be just as effective and a darn sight cheaper to run!
4. Peter Cochrane
Simon = Apologies for the lack of clarity - but space limits what I can fit in. Let me take it from the top:
We lack any meaningful description, definition, measure, quantification or understanding of intelligence.
So I have done a bit of a "Dr Samuel Johnson" and defined a measure of intelligence to be: The difference between the information input and the efficacy of the output weighted by time to resolve.
Throwing more processing power at a problem can mean two things - a faster clock - or finer parsing if the problem will parse.
I'm pretty sure my approach holds for both!
PLEASE NOTE THE LINE: If I am right in my analysis the implications are...
I have purposely elected to promote a debate because I have yet to fully test this across a wide set of cases. BUT where I have it seems to fit.
If we wait for the theorists/purists we may never get there - and right now I need a tool I can use for a project I am working on.
For sure I do know the memory and processing power applied to AI has increase as per Moore's Law. BUT the intelligence certainly hasn't.
BTW - IQ tests and machine comparisons with animals and humans has been totally discredited.
So this is my torch in our dark night!!
I'll publish more as I move this along.
Thanks for the input - it all helps.
Peter
5. Peter Cochrane
David = Thanks for you comment and nice one. There have been so many attempts to define intelligence with words, abstractions and analogies. But it is like trying to nail a jelly to a tree! Peter
6. Peter Cochrane
Radical = Well I'm empathic to all that! BUT managers often find themselves in a Catch 22 situation pressured from all sides and with no business modelling, decision support or suitably visualisation technology. NOT to mention that many of their problems now have 100s of dimensions. In the face of this scale of problem we as a species are badly equipped!
In my view we need a combination of human and machine intelligence in order to survive.
Thanks for the input - and whatever you do - do not give in to bad management practices, emulate the poor thinkers, or cease pushing for +ve change.
Thanks for the input, and all the best, Peter
7. Lovebug
As someone once said about AI and computers: "The goal of Artificial Intelligence seems as far off today as it always has. However, the interim point of Artificial Stupidity was reached some time ago"
8. Philip Needham
In subterranean lakes, creatures have evolved and lost the power of sight, reducing the sensors from 5 to 4. Does this lead to less intelligence or more?
9. Adam the Amoeba
Am I missing something, or have we ignored the fact that intelligence evolved? Apologies to the creationists out there, but scientific evidence suggests that intelligence in individual organisms is the sum of multiple collaborating/competing internal systems, and continues to be shaped by the environment, based on sensory inputs and processing of them. It is true we do not fully understand these mechanisms. Yet. As someone still involved in computational intelligence based on biological modelling at various levels, I note that as computers get more powerful, so does our ability to use them as tools to help understand ourselves. Can we reduce everything to simple equations? Don't know. We will have to for now while we use current computational hardware platforms in parallel as abstractions for biological systems. Our brains are not fully utilised anyway, so why would they need to be bigger if they are not working to full capacity? And let's face it, intelligence is knowing that trying to nail jelly to a tree is not going to work, either because this was learned directly from experience, or because that knowledge was passed on somehow either genetically or by some other mechanism.
10. Peter Cochrane
Lovebug = It is interesting isn't it - I have watched and waited too! And that is why I have set a different agenda. I'm not trying to build a human or anything resembling a human. We have too many of them already! I'm far more interested in what alternative intelligences and life forms can do. Peter
11. Peter Cochrane
Pilip = I would say that a different intelligence would result! Peter
12. Peter Cochrane
Adam = I would say that a powerful intelligence would solve the problem of nailing a jelly to a tree by keeping the jelly at a low enough temperature and thereby increasing its viscosity!
I have had so many emails on this topic I have determined to write at least one more blog soon - explaining the ideas further and including some entropic aspects.
Standby, Peter
13. Peter Cochrane
Pilip = I would say that a different intelligence would result! Peter