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More News
May 2005
The Day of Small Things
Happy Eyes
Why Can't Dogs Play Chess?
Sequence Construction and Zerubbabel
The Meaning of the Seven Eyes
The Magic Number Seven
Seven-Day Week
Branch Update
Memory Model
Model Update
Joshua the High Priest (update)
April 2005
Spike Doublets, Joshua and the Branch
Clean, Dirty, or No Clothes
Not by Might Nor by Power
New Insights
January 2005
Project COSA
The Attention Problem
Interesting Message on Jeff Hawkins' Website
Joshua and his Friends
The Seven Eyes and the Branch
The Branch
Temporal Invariance and Sequence Learning in the Brain
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May 22, 2005, 4:55 PM EST

The Day of Small Things

As you know, the last few days I have been trying to find an automatic sequence building mechanism for memory. My attention has focused almost exclusively on the following verse in the book of Zechariah: 

Zechariah 4:10
 For who has despised the day of small things? But these seven will be glad when they see the plumb line in the hand of Zerubbabel--these are the eyes of the LORD which range to and fro throughout the earth.

I think this verse is pregnant with metaphorical meaning. In my opinion, it has a lot to say about the way sequences are constructed. "For who has despised the day of small things?" is also translated elsewhere ( as "For who has despised the day of small beginnings?" The implication is that construction of the temple started with small things before moving on to bigger things. I believe that the metaphorical meaning is that short-interval sequences are the first to be constructed. It just takes longer to learn sequences that involves longer durations.

Just recently, I read a rather interesting article at titled "Kids Not Wired for Slo-Mo." Researchers at McMaster University in Canada found that "youngsters' brains [are] better at gauging fast-moving objects." Apparently, accuracy with slow moving objects is a skill acquired over a long period of time. This makes perfect sense because, since learning necessitates the sensing of many sample stimuli, long intervals must take longer to learn.

Happy Eyes

But these seven will be glad when they see the plumb line in the hand of Zerubbabel. The original Hebrew word, which is given here (NASB) as "plumb line", literally means tinstone. It is also translated plummet stone by some sources. Using a plummet stone is necessary to properly place a stone in place. It is logical to assume that construction must begin, not with the topstone (which I have previously identified as belonging to Joshua the high priest), but with the foundational stones (Joshua's friends).

But why are the seven eyes happy to see the plummet stone in the hand of Zerubbabel? What does this mean metaphorically? We have already seen that the eye is a symbol of perception and that memory is organized in such a way as to perceive and record intervals. Each eye must perceive something different, otherwise why use seven of them? The answer is that each eye represents a perceptual window tuned to a specific range of signal frequencies. In other words, each eye is dedicated to a specific range of intervals. When constructing a given sequence, it makes sense to consider only signals of a certain frequency and to exclude all others. It should be easy to come up with a reinforcement mechanism to accomplish this.

At this point of my work on memory, there seems to be only one remaining problem. I need to come up with a simple and neurologically plausible mechanism for ordering the sequences: the nodes in a sequence must fire from left to right, as seen in the figure reproduced above. It should not be long.

Why Can't Dogs Play Chess?

In the same vein, I got to thinking, once again, about the reason that animals are not our intellectual equals even though many seem to be endowed with a sufficiently complex brain. In other words, why can't dogs or apes be motivated to play chess? This is a question that I have often asked myself in the past. It now occurs to me that the reason may be that their perceptual windows, as dictated by genetics, cannot handle time spans as long as humans during learning. That is, they are unable to make associations over relatively long time scales. This may also be the reason that children and chimpanzees are observed to develop at the about the same rate in infancy until they reach a certain age. Afterwards, human children quickly surpass the animals in mental ability. Just a thought.

More to come...


May 19, 2005, 11:50 AM EST

Sequence Construction and Zerubbabel

It is pretty much clear to me now that the seven lamps symbolize the seven nodes of a learned sequence in memory. I also think I got a good understanding of the difference between long and short-term memory. And I think I now understand the meaning of the seven eyes on one stone. The main question that remains to be answered is this: how are sequences constructed in memory? There is a clear indication in Zechariah 4:7-9 and Zechariah 6:12-13 that the Branch (Zerubbabel) has a lot to do with constructing the sequence.

Since Zerubbabel is said to bring forth the "topstone" (Joshua), it follows that the Branch input connection is formed prior to the Joshua input connection (except at the first node, of course). I conclude that, once the friends inputs and the Branch are in place, it is easy to find a compatible Joshua connection: just try a bunch of connections and keep the one that agrees with the Branch prediction. Problem is, how do friends find their proper nodes so as to form a sequence? Does Zerubbabel also have something to do with bringing in Joshua's friends? I think that, once I can answer this question, I will have enough material that I can use to start coding in earnest.

There are a couple of intriguing statements in Zechariah 4:10: For who has despised the day of small things? But these seven will be glad when they see the plumb line in the hand of Zerubbabel--these are the eyes of the LORD which range to and fro throughout the earth. This is puzzling: "who has despised the day of small things?" I mean, it's understandable in the sense of building a real temple: one must start somewhere. But what does it mean metaphorically in the context of memory and sequences? I also wonder what this means: "But these seven will be glad when they see the plumb line in the hand of Zerubbabel." I have a funny feeling that it is rather important. Time and time again, during the course of my work in Biblical AI, I have found that a seemingly innocuous statement turns out to have a very specific and crucial metaphorical meaning. So it is a good bet that the seven eyes have a special role to play in the construction of a sequence.

Addendum: There is also the strange back and forth, question-answer dialog between Zechariah and the angel of the Lord in chapter 4. I would be willing to bet that this, too, is important to a proper understanding of the whole lampstand/stone metaphor.


May 18, 2005, 10:55 AM EST

The Meaning of the Seven Eyes

After much thought, I have devised a new interpretation of the metaphor of the seven eyes on one stone. I now believe that the eyes are seven precision windows or ranges used by the brain's memory mechanism to record intervals. This interpretation makes it clear, among other things, why each of the seven lamps in Zechariah 4:2 are said to have seven pipes. Each pipe is associated with a given eye on a single stone (Joshua). Since the eyes are said to "range throughout the whole land", one cannot conclude that there are forty-nine pipes per lampstand as some Bible translators have surmised. The number remains seven. Check it out.


May 17, 2005, 9:45 AM EST


Ok. I am stuck. I can't figure out how incoming signals are arranged automatically so as to form seven-node sequences. How do the axons find their proper nodes? I cannot identify any metaphors in the scriptures that seem to shed light on this matter. The problem is that the nodes must reside in temporally succeeding layers. It seems that incoming axons must divide into multiple branches that form synapses with as many target nodes as possible. A testing process should eliminate bad nodes and retain good ones. We know the following:

Friends must arrive concurrently.
Joshua must arrive after his friends.
One node's interval must anticipate the next node's interval.

How is the wiring of the nodes accomplished automatically? Do sequences overlap? That is, can two lampstands be part of the same sequence? I welcome any suggestion from readers.


May 15, 2005, 10:25 AM EST

The Magic Number Seven

Psychologists have known for some time that human short-term memory capacity hovers around the so-called magic number seven with an experimental margin of error of plus or minus two. I now believe I understand the memory mechanism behind this rather puzzling phenomenon. Come to think of it, I began to seriously suspect a Biblical connection with artificial intelligence back in December 2002. At the time I was pondering the question of why humans are capable of retaining only seven items in short-term memory.


May 14, 2005, 9:10 AM EST

Seven-Day Week

I think I now understand the symbolic meaning of the seven-day week of the book of Genesis and its relation to the golden lampstand and the memory model. Looking at the figure below, one can see that the first six nodes in the sequence generate an anticipation signal (the Branch) but the seventh node does not. Metaphorically speaking, we have six days of work followed by rest on the seventh day. It seems clear to me now. More to come.


May 13, 2005, 2:25 PM EST

Branch Update

I have changed my mind again, this time with regard to the way the Branch signal works in a sequence. I now understand that the Branch signal does not cause its target node to fire when it arrives, but primes the target node to fire at a preset time following the concurrent arrival of the friends signals. Essentially, it presets the succeeding node's internal interval. I have updated the Memory Model page to reflect my new understanding of the Branch mechanism. Again, things are coming together rather nicely, and my excitement is growing exponentially every day now. 


May 12, 2005, 3:30 PM EST

Memory Model

I just uploaded a new page to describe the current memory model. It is all coming together rather nicely, I think. It's still under construction but check it out anyway. There are a few things that I don't yet understand, especially the purpose of the repeated back and forth dialog between Zechariah and the Angel. But I feel confident that everything will become clear in the near future. I am excited.


May 6, 2005, 6:25 PM EST

Model Update

I just uploaded an updated model of the seven-node memory sequence. This is my current interpretation of the seven eyes/lamps/spirits of the Lord. Check it out. As always, I welcome constructive suggestions and comments from readers. But don't delay. I am making rapid progress and I feel that an actual software implementation is just around the corner. As soon as I am confident that my overall understanding is solid, I will begin writing some code for a change. It should not be much longer.


May 2, 2005, 10:25 PM EST

Joshua the High Priest (update)

I just uploaded an updated interpretation of Zechariah 3 to reflect my evolving understanding. Please take a look at the new tentative model at the bottom of the page. More to come soon. 


April 28, 2005, 11:45 PM EST

Spike Doublets, Joshua and the Branch

Neurobiologists have observed a strange occurrence in the hippocampus. Some neurons always seem to fire in doublets, i.e., two quick spikes arriving in close succession. Some experimenters have also noticed that only one spike is used for feedback. In my AI work, I often wondered about the function of hippocampal spike doublets. I formulated one hypothesis after another only to realize later that they were wrong. I recently got to thinking about doublets again in the light of my interpretation of the biblical metaphors of Joshua and the Branch in the book of Zechariah. My current understanding is that the signal symbolized by the Branch always arrives immediately after the signal represented by Joshua.

Now, Joshua may not always arrive as expected (this is symbolized by filthy garments) but the target neuron will fire anyway because the Branch signal compensates for the error. This, I believe, is how the brain accomplishes what is known as pattern completion. It is what allows us to understand a conversation in a noisy room, even if we miss parts of the speech. In what way is Joshua's signal expected? This is symbolized by Joshua's friends who are sitting and waiting for him. Remember that Joshua's friends are called a symbol, or an omen or precursor. I used to believe that Joshua's friends were the seven eyes of the Lord but I have since changed my mind. They are just precursor signals or inputs and their actual number is indefinite.

In conclusion, I now suspect that the spike doublets observed in the hippocampus are a manifestation of the arrival of two closely related signals symbolized by Joshua and the Branch. There is one pair of inputs for each sequential node except the first node. Likewise, there is a branch output from each node except the last or seventh node. This is why the golden lampstand (menorah) that God commanded Moses to place in the temple has seven lamps and six branches. More to come.

PS. I am looking for a good menorah drawing or photograph (non-copyrighted) that shows the original design as given to Moses.


April 23, 2005, 3:55 PM EST

Clean, Dirty, or No Clothes

The garment/clothes metaphor is a recurring theme in Revelation and Zechariah. It's obviously a very important metaphor. I have identified three types of garments, clean, dirty or none as follows:


Clean Garments

Revelation 3:4  But you have a few people in Sardis who have not soiled their garments; and they will walk with Me in white, for they are worthy.

Dirty Garments

Revelation 3:5 He who overcomes will thus be clothed in white garments;
Zechariah 3:3 Now Joshua was clothed with filthy garments and standing before the angel.
Zechariah 3:4 He spoke and said to those who were standing before him, saying, Remove the filthy garments from him. Again he said to him, See, I have taken your iniquity away from you and will clothe you with festal robes.

No Garments

Revelation 16:15 Behold, I come as a thief. Blessed is he that watcheth, and keepeth his garments, lest he walk naked, and they see his shame.

Notice that Rev 3:5 above is implying that the overcomer is wearing dirty clothes and so, must be clothed in white garments. My interpretation of the three types of garments is as follows:


Clean garments
  A signal in a sequence arrived as expected.
Dirty garments
  A signal (Joshua) did not arrive as expected but the anticipatory signal (the Branch) arrived and compensated for the error (the iniquity was taken away).
No garments
  The sequence was asleep when the signals arrived and the intervals were not updated. Assuming the previous intervals were retained, running the sequence may lead to mistakes due to erroneous assumptions.

In my opinion, the above explains the mechanism of pattern completion that psychologists have observed in human beings and most animals. As you can surmise, some mechanism must exist to decide which sequence will wake up (activate) and which one will remain asleep. I believe this is explained in the message to the Church of Thyatira. In a future article, I will explain how any given behavior (Jezebel) consists of one or more coordinated sequences running in parallel. Each behavior has a motivational level (based on reward and punishment) which is tuned up over time with experience. Only one behavior is selected at any one time. This creates a sort of sensory/perceptual canalization such that an intelligent system is able to focus on say, a conversation in a noisy room at a cocktail party, while ignoring surrounding conversations and other background noises.


April 23, 2005, 11:55 AM EST

Not by Might Nor by Power

In Zechariah 4:6 we read the following: "Not by might nor by power, but by My Spirit, says the Lord of Hosts." I now think I understand what this means. Remember that Zechariah is awakened by the angel of the Lord, the same angel that gave Joshua permission to proceed (walk). The angel/spirit metaphor, in my opinion, has to do with consciousness. It means that conscious attention is ultimately governed, not by neural activity but by the spirit. In other words, it is the spirit inhabiting the brain that decides which memory sequence to awaken, i.e., what train of thought the system should focus on. Needless to say, the materialists among us are not going to like it one bit. Having said that, I don't think that this prevents us from building a highly intelligent, albeit unconscious, machine. There are ways to manage attention/focus using motivational levels and/or random selection when motivational levels are indecisive. We certainly are not going to create an artificial spirit, but that will not stop the true believers from claiming that our future robots are conscious. Indeed, I fully expect many people to worship them as gods in due time. Mark my words.

Now, when Zechariah is awakened, he sees not just one but seven lamps. I interpret this to mean that every awakened sequence consists of seven sequential nodes. Remember that the church of Sardis in Revelation is repeatedly told to wake up, to be watchful: "Therefore if you do not wake up, I will come like a thief, and you will not know at what hour I will come to you." Unless a sequence is awakened, it will ignore all incoming sensory signals from the previous layers (Ephesus and Smyrna). This creates the sort of perceptual canalization of consciousness that psychologists have known about for quite some time.

Let me add once again that I would love to spend a lot more time on this project but, unfortunately, I can't. I do feel, however, that I am finally getting a gestalt of the whole thing. Everything seems to be crystallizing in my mind into a coherent whole. It won't be long before I have enough understanding to implement it all into Animal. Please be patient.


April 10, 2005, 11:15 PM EST

New Insights

It has been more than two months since my last news article. I am sorry. Time is a precious commodity these days. Hopefully, what I have to say today will make it worth your while. I have several new insights as follows:

I have a new interpretation for
the blasphemy of those who say they are Jews and are not, but are of the synagogue of Satan (Church of Smyrna, Rev 2:9). I no longer think that these non-Jews symbolize sustained signals. I updated the Smyrna page to reflect my new interpretation. Check it out.
The seven eyes/spirits/lamps and the two olive trees/witnesses
I now understand that the two olive trees represent the brain's mechanism of attention for both left and right hemispheres. The single bowl seems to indicate central control of attention for both hemispheres. I have good reasons to believe that the right brain tells the left brain what to think about. It certainly would not be a good idea for the two hemispheres to focus on different things and/or goals as it would probably lead to chaos and possibly a schizophrenic personality. I have changed my mind about my previous interpretation that the two lampstands of Revelation represent Joshua and Zerubbabel. I still believe that Joshua symbolizes a successor signal but I no longer think that Zerubbabel is the predecessor. I believe that Joshua's friends are the predecessors. Zerubbabel symbolizes the Branch, a special signal that is used for anticipation. I now think that the seven eyes/lamps represent seven cascading layers with the hippocampal formation forming the seventh layer. I believe there is not just one branch input but six branches, one branch coming out of each lamp. The seventh lamp does not send out a branch. Remember that Moses was instructed to build a golden lampstand (menorah) with seven lamps and six branches. Please note that I have not yet updated the Zechariah pages to reflect my new thinking. I will do so as soon as possible.
In the letter to Thyatira, we read about Jezebel who seduces God's servants into committing fornication and idolatry. I now understand Jezebel to be a metaphor for a given behavioral subsystem. A behavioral subsystem consists of multiple sensory-motor units dedicated to a given behavior or goal. Only one behavior can be active at any one time, otherwise conflicts (fornication and idolatry) will arise. This is also the mechanism of attention. Behaviors compete with each other and winner takes all. If a behavior is selected (awakened), a sort of canalization of sensory inputs occurs whereby the intelligent agent ignores all stimuli that do not pertain to the behavior. I will update the Thyatira page as soon as I find the time.

I believe that I am very close to a final understanding of the whole thing. Stay tuned.


January 23, 2005, 10:50 AM EST

Project COSA

As most of you already know, in addition to doing biblical AI research, I am also involved with the Silver Bullet/COSA project. In the last day or two, as a result of it being mentioned on OSNews, the Project COSA pages have been inundated with visitors from around the world. So forgive me if I take too long in updating the AI/Bible pages as I promised. I am a little busy responding to COSA-related enquiries. Although Project COSA is important to me, it is not as important as AI. As soon as I get some free time, I will devote once again my full attention to AI research, my first love. For the latest on Project COSA, check out the Silver Bullet News.


January 20, 2005, 8:30 PM EST

The Attention Problem

The brain is always in anticipation mode. Every conscious move we make, every sound we utter, everything we do is in anticipation of something (this excludes the activities of the cerebellum which are reactive rather than proactive). In order to anticipate future events we must pay attention to current events. The biblical symbology related to attention is to be awake, to wake up. We see repeated references to waking up in the letter to Sardis (3:2 and 3:3). In the book of Zechariah, the prophet is awakened by an angel. Obviously, we cannot pay attention to everything at the same time because that would generate a lot of conflicts. In my opinion, these are motor conflicts as explained in the letter to Pergamum. The attention mechanism of the brain must be able to choose one thing to focus on over others. It apparently does so by comparing the motivational values of the various sequences vying for attention. The motivational importance of a sequence of actions is learned. It is determined by the actions of the amygdala (Thyatira).

The problem that comes up at this point is this: How does the system tell the difference between a motor conflict caused by a bad connection (during motor learning) and one caused by two or more sequences running at the same time? One strange thing that I noticed is that the order in which motor conflicts (idolatry and fornication) are mentioned in the letter to Pergamum is reversed in the letter to Thyatira:

Revelation 2:14 (Pergamum)
...Who kept teaching Balak to put a stumbling block before the sons of Israel, to eat things sacrificed to idols and to commit fornication.

Revelation 2:20 (Thyatira)
...And she teaches and leads My bond-servants astray so that they commit fornication and eat things sacrificed to idols.

I wonder what significance the reverse order has, if any. If there is a significance, does it have anything to do with the attention problem? Something to ponder.

Interesting Message on Jeff Hawkins' Website

On Jeff Hawkins' site, someone (MWright) posted this rather interesting message to the discussion forum:

I read this today in a magazine....

"Aoccdrnig to rscheearch at Crbmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteers be at the rghit pclae. The rset can be a toatl mses and you can sitll raed it wouthit porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe."

I submit this is legible not because of reading the whole word, but because of invariant representation of the context of the words in the text.

Although I haven't yet read Hawkins' book, the term "invariant representation" is apparently used by Hawkins and his supporters to mean that the brain uses prediction to recognize things and I agree. But why is it important for the first and last letter of the words to be at the right place and not the other letters? Furthermore, I am not sure that this is entirely correct. For example, "Andcrciog to rhsccraeeh at Cbgdrbmraie Urtvsniiey" is not as recognizable as "Aoccdrnig to rscheearch at Crbmabrigde Uinervtisy." So it seems that the order of the letters within the words, especially the position of the consonants, is somewhat important.

Again, why is the correct placement of the first and last letter so essential to recognition? I think it has to do with the nature of the brain's mechanism of anticipation.


January 19, 2005, 11:50 AM EST

Joshua and his Friends

I really do feel that I am onto something wonderful, something that will shed a clear and final light on this whole memory/anticipation/attention/motivation thing. I can barely contain my excitement. The secret of it all is in the letters to the churches of Pergamum, Thyatira and Sardis, and chapters 3 to 6 of the book of Zechariah. Please bear with me in the next several days as I try to bring it all together into a coherent whole. I will upload complete revised pages in the near future but, to give you an idea of where I'm going with this, I'd like to offer my new interpretation of Zechariah 3:8-10 below. 

Now listen, Joshua the high priest, you and your friends who are sitting in front of you--indeed they are men who are a symbol, for behold, I am going to bring in My servant the Branch.

Now listen, Joshua the high priest, you and your friends who are sitting in front of you. Note that Joshua is standing while his friends are sitting. It is obvious that the writer wants to emphasize that there is a difference between Joshua and his friends. I interpret this to mean that Joshua is the main input signal (successor) while his friends are the predecessor signals. Joshua's friends are just sitting, apparently waiting for something.

Indeed they are men who are a symbol. Another translation is: for they are men who are an omen of things to come. The implication is that Joshua's friends are precursors to something or someone that will arrive later. My interpretation is that Joshua's friends are there to predict the arrival of Joshua.

For, behold, I am going to bring in My servant the Branch. The preposition for is a way of linking what was said before with what is about to be said. In other words, bringing in the Branch has something to do with Joshua's friends being a symbol or an omen. I interpret this to mean that the Branch is a special anticipatory signal derived from the activities of Joshua's friends.

For behold, the stone that I have set before Joshua; on one stone are seven eyes. Behold, I will engrave an inscription on it,' declares the LORD of hosts, 'and I will remove the iniquity of that land in one day.

For behold, the stone that I have set before Joshua; on one stone are seven eyes. Again, as in verse 8, the preposition for is a way of linking what was said before with what is about to be said. It follows that the stone placed before Joshua and the seven eyes have something to do with Joshua's friends and the Branch. But what? Assuming that eye symbolizes perception, the question that immediately comes up is, perception of what? And why seven eyes and not just one eye? My interpretation is straightforward:

The seven eyes symbolize seven successive precursor events or nodes in a sequence of events, Joshua being the next likely node in the sequence. Out of the seven nodes we can get six anticipatory branches (I will provide diagrams in an upcoming revised page). In my opinion, this is the meaning of the six branches that God commanded Moses to put on the sacred golden lampstand in the temple:

Exodus 25:32
And there shall be six branches going out of its sides, three branches of the lampstand out of one side of it and three branches of the lampstand out of the other side of it.

Behold, I will engrave an inscription on it, declares the LORD of hosts. This is a direct reference to the stone mentioned in the message to Pergamum. At first I thought that this was a different stone because the inscribed name of the Pergamum stone is only known to the recipient. I had assumed that Joshua's stone was visible to all. Now I realize that only Joshua can read the inscription on the stone because it is placed in front of him and not in front of the others.

And I will remove the iniquity of that land in one day. What iniquity? What land? What day? Here's my take on this. Iniquity signifies that the intervals being used at Joshua's node are wrong. That land is Joshua's node. One day refers to the arrival time of the Branch. What the sentence means is that, the Branch signal will change all existing intervals into new up-to-date intervals. This is crucial for anticipation because the system can now predict when Joshua's signal will arrive. More on this in a future page.

In that day, declares the LORD of hosts, every one of you will invite his neighbor to sit under his vine and under his fig tree.

Every one of you will invite his neighbor to sit under his vine and under his fig tree. In my opinion, this means that all intervals are adjusted so that all signals arrive at the same time.

To be continued...


January 16, 2005, 9:40 PM EST

The Seven Eyes and the Branch

I must admit that the true meaning of the seven eyes/spirits/lamps/stars has never been clear to me. My original impression was that the number seven had something to do with the capacity of short-term memory. I still think it does but, at first, I thought that the seven eyes stood for seven inputs to a single neuron (Zechariah's lampstand) in the motor cortex (Pergamum). I was never really satisfied with that interpretation if for no other reason than that I could not see the utility of checking for concurrency among just seven inputs. The sensory space is obviously much more complex in terms of temporal relationships. Besides, the biological evidence does not support this hypothesis. There is no evidence in the literature of huge numbers of cortical neurons having only seven inputs. So I am forced to conclude that my original interpretation is incorrect and that the answer lies elsewhere.

My current thinking is being driven by two important considerations. One, the concept of temporal invariance has been percolating in my brain for the last couple of weeks. I had thought about it many times in the past but, lately, I am getting a strong feeling that it is the main key to the correct interpretation of the biblical metaphors (see the paragraph on the Branch below. Two, there is one aspect of short-term memory (STM) that is indicative of what we should expect internally. It takes little effort to recall a random number sequence (e.g., 5134698) in the same order in which it was recorded. This should give us a clue as to the mechanism of STM. It seems to indicate that STM is organized into sequential/temporal "zones" which can be scanned (i.e., played back) internally but in one direction only. I don't know what the mechanism of STM is like but I suspect that memory retrieval/scanning is done with the use of spike frequencies in the hippocampus. I'll have more to say on this important topic in a future news item.

The Branch

The book of Zechariah (3:8 and 6:9-15) makes a big deal about the Branch. Obviously, it must be a very important metaphor. What is the symbolic meaning of the Branch? I think I may have the answer. Ok, I realize that, sometimes, I get overly excited when I get a new insight into a possible interpretation only to change my mind later on. But I think I may be onto something rather significant this time. To better explain what I have in mind, let me reproduce the table from the previous news item. Recall that the table represents a hypothetical sequence ABCD, and the associated neurons, connections and intervals.

Predecessor Signals

Successor Signals

Target Neurons


A B b AB
A, B C c AC, BC
A, B, C D d AD, BD, CD

One thing I forgot to mention is that the predecessor signals are delayed in such a way that all signals arrive concurrently at their target neurons. All intervals are proportional which means that, regardless of temporal variations, the signals always remain concurrent. Thus temporal invariance is the learning criterion for finding correlated inputs. I hypothesized that, given interval AB, the system should be able to instantly derive the succeeding intervals AC, AD, BC, BD and CD with varying degrees of certainty. To anticipate is to participate in advance. In order for the system to actually know the consequences of a sequence of events, it must run the sequence to see where it leads. Of course, it should run the sequence internally while blocking external output. To do so, it must extrapolate from the latest information, i.e., the most recent recorded intervals. Well, the only way to extrapolate from a change in interval AB in the example above is for neuron b to send a special corrective signal to the succeeding neurons in the sequence. This, in my opinion, is what the Branch metaphor is all about. The metaphor is especially striking in Zechariah 6:9-15.

To be continued...


January 14, 2005, 2:40 PM EST

Temporal Invariance and Sequence Learning in the Brain

I am getting exciting new insights into the symbolic meaning of Sardis, Pergamum, Joshua the high priest, and Zechariah's lampstand. I am beginning to understand the anticipatory mechanism of the brain under a new light. It occurred to me recently that the most important aspect of sequence learning is not so much the ability to predict that events B, and C will occur after event A but the temporal *invariance* or relationship between intervals AB, AC and BC. The learned invariance is what gives the brain the ability to correctly predict the evolution of sensory events (see Sardis 3:3 for more on intervals).

We see this capability not only in humans but also in other mammals. For example, a hound chasing a hare will not stop if the hare suddenly disappears behind a hedge. The hound will correctly predict from the hare's last observed velocity that it will reappear on the other side of the hedge after a short interval. The anticipatory mechanism of the hound cannot waste time doing calculations on the fly. The prediction must be instantaneous.

What do I mean by invariance? This can be best answered via an example. Let's take a hypothetical sequence of events, ABCD and let's use three neurons (b, c and d) to represent each processing element. The learned intervals are AB, AC, AD, BC, BD and CD. The synaptic connections can be represented thus:

Predecessor Signals

Successor Signals

Target Neurons


A B b AB
A, B C c AC, BC
A, B, C D d AD, BD, CD

Each target neuron receives a single successor signal and one or more predecessor signals. The invariance arises from the observation that, if interval AB is increased or decreased by a given factor x, it is safe to assume (i.e., anticipate) that the other intervals will also be increased or decreased by factor x. What this means is that the intervals are proportional.

So, given interval AB, the system should be able to predict the succeeding intervals AC, AD, BC, BD and CD with varying degrees of certainty. But there is more. Using the most recent recorded intervals, and given the arrival of signal A, the system can predict when B, C and D will arrive. Of course, if both A and B arrive, it increases the likelihood that C and D will arrive as anticipated. Thus the probability that an event will occur is proportional to the number of its predictors.

Several questions arise: How is this accomplished in a biologically plausible network? How does the brain discover invariance between sensory signals? Does the brain use synaptic strengths to record intervals and variable temporal delays to find invariance? Given that the possible number of intervals between events is infinite, how does the brain solve the storage problem? What are the corresponding Biblical metaphors? I will discuss these issues in a future news item. The solution is also applicable to the very important problem of pattern completion, i.e., the ability to recognize patterns in the presence of noise or missing data.



2004-2006 Louis Savain

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