T&L Publications

Brains mediate between sensors and motor.
Let S be the number of sensors.
Let M be the number of motors.
F is the number of functions.
F = S/M ;is a measure of complexity.
Size = S or M depending on how you measure.
Example:
You have a robot with 4 sensors and two motors.
F = 4/2 = 2
size = 2
Computing input complexity.
Sensors read nature and write a data stream.
The possible actions of the sensor depend on the number base. (Base 2 can have two actions, base 4 can have 4 actions, etc.)
Each sensor is a digit in the input number.
Add a sensor and you add a digit.
Let b be the number of sensor actions.
Let d be the number of sensors.
C = b^d ; Complexity is b to the d power.
Plug in some numbers and you will see why IF-THEN logic blows up when you add another sensor.<p> [email protected]

Where's the logic?

Brains, including those needed by robots are far beyond logic. To make a decent brain you cannot use computer design rules. Logic was invented to use on binary data. Boolean logic is below the level of arithmetic, that is more primative. For example a simple 8 bit subtraction is 256 exclusive or operations, all done in parallel. This is why you see only small robots.

you've brought op an interesting point,Harold, but instead of larger brains,I thought faster clocks were the answer.Prehaps combining the old style analogue math like op amps for course movements and using the digital stuff to finish the job might be applicable.

Thanks for the comment. I got interested in AI in 1958. I gave up on it in 1990. Since brains are different in size, there must be a least brain. If there is a least brain it must have a function.
I have an algebra and a complete system of tools to build brains of any size. I will be glad to send you a free paper on this if you will give me your email address.
[email protected]

I'm sorry that I can't provide the resource to find it but I read of a kind of sea snail that has very few neurons. The number twenty something comes to mind but I can't be sure. The reason it was mentioned in the article was that they are almost large enough to see without magnification. Their large size and limited number makes them a target for neural experiments. I suppose this would be a "least brain".

Thanks. The least possible brain function is simple negation. Neurons are a mathematical function although neither neurologists or mathematicions know that. My assumption is, since most of nature is, brains are mathematical functions. I have about 16 functions so far. The main thing is, all the functions must connect. Make synapes on the neurons headerss, and make the cable from the axon a plug, then plugs plug into headers.

<blockquote><font size="1" face="Verdana, Helvetica, sans-serif">quote:</font><hr>Originally posted by Harold:
Brains mediate between sensors and motor.
Let S be the number of sensors.
Let M be the number of motors.
F is the number of functions.
F = S/M ;is a measure of complexity.
Size = S or M depending on how you measure.
Example:
You have a robot with 4 sensors and two motors.
F = 4/2 = 2
size = 2
Computing input complexity.
Sensors read nature and write a data stream.
The possible actions of the sensor depend on the number base. (Base 2 can have two actions, base 4 can have 4 actions, etc.)
Each sensor is a digit in the input number.
Add a sensor and you add a digit.
Let b be the number of sensor actions.
Let d be the number of sensors.
C = b^d ; Complexity is b to the d power.
Plug in some numbers and you will see why IF-THEN logic blows up when you add another sensor.<p> [email protected] <hr></blockquote>

Ah, Harold--I see you're a mathematician! That explains the interesting prose.
But there are flaws in your logic--you yourself point out that "sensors read nature" (they don't necessarily "write a data stream")--but then you confuse your sensors with actuators! Sensors do not cause actions, so your formulas are what "blows up!"
I suppose if you have a hardwired logic gate system, then I can see how the complexity can be overwhelming as you add more sensors and decision trees. Actually, what you decribe is, in a loose way, what happens in the translation of a microprocesor's "opcodes" of the program code into register actions.
Maybe you can factor the program logic into your equations--it's there, even in nature in the lowest organisms that show any behavior.
For instance, arthropods have behaviors that are considered "reflex," and are mediated by what are known as "identified neurons," but even they show signs of plasticity, or ability to change/adapt.

Thanks for the comment.
Data flow for any live machine is:
Nature -> Sensors -> Brain -> Motors ->Nature
Note the feedback loop. My sensors write data streams. My motors read data streams. My HalTrees can match any neuron in form.
A neuron is Axon = f(all synapses)
A HalTree is Output = f(all inputs)
There are permutational problems all over the brain. You can think of every sensor as a digit, and every axon as a digit. The entire brain can be written as a number.

Suppose that I wanted to build arobot with a simple brain, oh let's say 6 neurons, that can learn/adapt based upon feedback from its sensors. Can your algebra system help me in designing and building such a system, or is it more of a theoretical construct? As an ex-mathematician I can appreciate the inherent structural beauty of an algebraic system, but right now I wanna build 'bots. A system that can learn and adapt would be very powerful, but it seems that most digital AI systems are highly computationally intensive. Do you have any experience or insights on building a simple brain?<p>Brett

Brett, with Hal algebra you can build a brain of any size. Here is the simplest. Motor = n(sensor)
To make this algebra from a standard algebra, let the variables be sockets. Let cables carry the data. Cables have plugs that plug into sockets.
Each operator in the language is a computer node.
There are single input and two input nodes. Two input nodes combine to form trees. There are no trees like this in standard mathematics, so I call them HalTrees.
Neurons are functions: axon = f(all synapses)
HalTrees are functions: Out = g(all inputs)
Generally Doing = Do - Don't ; where Do and Don't are HalTrees of any size.
I would be glad to send you Hal algebra as a language if you will provide your email.
[email protected]

what exactally duz a neuron do? Does it have any kind of residuial memory?What a bout frequency response decay rate according to fatigue(power limiting)Response to outside chemical changes.Response to electrical intensity and polarity changes.temp,sound intensity ect.

Toejam,
I don't think anyone knows what a neuron does. All I know is that it is in the form of a mathematical function. Axon = f(all synapses). Everyone is measuring like mad but the poor neuron only works properly when connected to others, so I think most people are measuring nonsense.
When I invented the CNode I gave no thought to neurons. Well not much thought. I knew two input devices would make trees, but there are no such trees in mathematics. So I had to invent HalTrees. It happens that HalTrees form a function and that they can match any neuron form since HalTrees can be any size. That does not mean my functions match neuron functions, but when you get down to basics, there are only so many function available. Nature has to choose from a limited set. So I am betting my functions are closer to neuron functions than anything else.
I think, inside the neuron is a brain. You can build a brain to match any cell. The neuron is a cell, so it has a brain.
Does that bother you that brains are made of brains? Tis the new world of complexity.
Thanks for the comment.

Hello,
I've been interested in this type of robotics for a long time now, since the 70's.
However, one bottleneck that remains is the practicality of building a artificial brain .
The fact remains that Neurons found in nature have more processing performance in a square mm than any computer technology today.
At this time is very difficult to replicate a artificial neuron on the same size and with the same performace.
Although, there have been strides in the analog technology recently where programmable analog circuits can be designed on one chip, albiet , low density, not comparable yet to even a Frog's brain.<p>This is one of the major reasons why you see mostly emulations of artifical brains using software running on a traditional computer hardware.
This is the most economical method at this time.
With the ever increasing speed of Processors, siginificant achievments have been made in this area.
Such as Intellegent Cars which can drive by themselves at normal speeds, using standard video cameras [stereo vision].<p>I think this will continue to be the avenue for progress until the next generation of computer technolgy becomes practical, such as , molecular computing or quantum computing.<p>Daniel