Dear Dr. Bosco, why not try the grid cells? http://en.wikipedia.org/wiki/Grid_cell

Hope this helps,

Rutger.

The Parietal area, is the basis for the organism centric view of location, but to map a geometric model, the hippocampus needs to become involved. Recent research seems to suggest that not only does it map but that also it is sensitive to relationships within the map. However, I have begun to wonder if the abstraction is not stored in the parahippocampus.

The ballance between hippocampus/parahippocampus might be programmed by nurture, but also dependent on age, and hippocampus function. This is because the strategy for which area to look in for the data, is variable.

A study on inborn geometry

http://www.eurekalert.org/pub_releases/2006-01/hu-iad011706.php

http://www.sciencemag.org/content/311/5759/381.abstract

Representation of space in the brain

http://phys.org/news205587824.html

http://phys.org/news121536271.html

http://english.people.com.cn/90001/90781/90879/6333458.html

http://www.eurekalert.org/pub_releases/2010-03/uop-vdl031910.php

http://www.eurekalert.org/pub_releases/2010-01/ucl-thb012010.php

The navigation system of the brain

http://www.pnas.org/content/early/2012/03/30/1109599109.short

http://www.kurzweilai.net/like-gps-the-brains-navigation-system-for-the-external-world-requires-precisely-timed-pulses

http://medicalxpress.com/news/2011-11-cerebellum-cognitive-enables.html

http://medicalxpress.com/news/2011-09-gps-rhythmic-neurons-code-position.html

http://www.ntnu.edu/news/another-link-in-mapping

http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.1000992

http://www.eurekalert.org/pub_releases/2007-06/cp-bin061507.php

http://www.newscientist.com/article/dn16751-brain-scan-reveals-memories-of-where-youve-been.html

Ant navigation

https://www.researchgate.net/publication/8126513_Trail_geometry_gives_polarity_to_ant_foraging_networks

http://www.eurekalert.org/pub_releases/2006-10/babs-haf101606.php

http://www.eurekalert.org/pub_releases/2006-04/sfeb-hlc033106.php

http://www.eurekalert.org/pub_releases/2006-04/sfeb-npl033106.php

Representation of numbers in the brain

http://www.eurekalert.org/pub_releases/2009-09/cp-ctb091709.php

http://www.eurekalert.org/pub_releases/2010-03/uom-oep032210.php

http://web.mit.edu/press/2012/thinking-logarithmically.html

http://www.newscientist.com/article/dn9198-pigeonbrained-birds-can-think-in-logarithms.html

Representation of tool manipulation

http://www.psychologicalscience.org/media/releases/2010/mahon.cfm

Slime mold navigation

http://arstechnica.com/science/2012/10/organism-without-a-brain-creates-external-memories-for-navigation/

Other:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427547/

Regards,

Joachim

Article Trail Geometry Gives Polarity to Ant Foraging Networks

Joachim, that is a rather indigestable lump of references. Would it be possible to limit yourself to 5 or 6 at a time, please.

I think you have mistaken the question by the way, covering navigation more than geometry. Most of the articles I have read out of the great load you dropped, are about place cells, which are important to location, but not to geometry except in that mapping location and direction gives us some basis on which to study the orientation of the geometric primitives that were suggested in the first two articles.

Of interest to me would be articles showing a link between path cells, and Orienting Network activation allowing abstract dimensions to be detected.

I want to thank all the scholars who have contributed, I will read all the suggested references (some of whose new for me) and I hope to find the "holy grail" to finish writing a paper on the relationship between two dichotomies geometry / landmark and implicit / explicit memory ... Thanks again guys!

Graeme, thank you for commenting my style.

I should have put the links into attached lists.

My own opinion on how the brain encodes geometry

is totally different from neural research. I don't

like the notion of specialized cells.

There is the limited capacity of the working memory,

be it seven or only four items. It has the status

of an axiom.

We have only one working memory, that is able

to store items (I prefer the term symbols) of

any kind.

We don't have a separate working memory for

sounds, for smells, for numbers, for geometric

representation. Would it be otherwise, a person

could increase the capacity of his WM by

combining different storages and so be able

to store 20, 30, or more items. That is of

course not possible, it hasn't been observed.

The conclusion is: geometric objects or concepts

are encoded as tuples of symbols, and mental

manipulation of them takes place in the one

and only working memory.

Regards,

Joachim

@Joachim: It is much more complex than that. We now know that the Ventro-Lateral PFC has an area of about 1/3 that is made up of an echo of other areas of the cerebral cortex. While Millers 7 +/- 2 is still paid lip service we know that the digit span test as used to determine that size, is Language specific and that Chinese Students at their prime can memorize 13 digits even though other languages are more limited.

Utilizing special techniques such as the technique used to make telephone numbers, we can expand the effective length of the string of numbers to 7 clusters of 3 or 4 digits each. But in essence to do so we are no longer memorizing digits.

The reason that researchers thought that there were different memories for sounds smells, etc, is that the Working Memory echoes the cortex which is separated into sensory modalities, and the relative size of the memory needed to store each different type of sense is different yet the number of elements that can be memorized seems consistently low. Current wisdom is that it is determined by the number of clusters of storage locations that can be rehearsed in 3 seconds.

The main limitation is, in fact the bottleneck, which creates a serial dependency in any attempt to rehearse any memory. My theory is that that bottleneck is created by a mapping function necessary to turn context based implicit memory into Place-code addressable implicit memory, so that it can be rehearsed.

In any case, the specialized cells, are part of a much more complex system, that needs to be dealt with as a whole, and the signals of these cells, should be interpreted into the larger system I agree, the difference is that these specialized cells are in a separate memory system that operates in parallel to the cerebral cortex, and impacts indirectly on the cerebral cortex, possibly affecting which clusters of information get stored in Working Memory AFTER the bottleneck. We should not throw the knowledge they offer away simply because we can't work with single cells with any great accuracy without embedded contacts.

I found interesting both Graeme and Joachim's points of view. Sincerely, the reference to the working memory for the reorientation paradigm does not seem entirely relevant. After all, the basic task uses only two cues (therefore under the wm span) layout and one landmark (in our approach, the landmark may be close (positional) or distant (directional) with respect to the target). Despite this simplicity there are errors in working memory task and some healthy individuals (elderly) are struggling to reach a learning criterium in a reference memory task when the layout only is available, and when the landmark is not directly associated with the target (directional). It is relatively easy to explain the latter result by resorting to a probable deficit of the medial lobe, less clear is why the geometry does not work. Unfortunately I can not completely rule out the involvement of the occipital lobe and the first visual pathways. I hope that my English has not affected the understanding of my doubts.

All the best

Andrea

I don't think you should be trying to rule out the Occipital Lobe, there are shape sensors that allow the brain to recognize the underlying shapes/angles/etc. there. My earlier suggestion was about the "Abstract" representation, which is not made from the primitives so much as symbolizes the particular combination of primitives. For instance a square is made from 4 right angles and 4 equal straight edges. but once you have seen one square you have seen them all.

You can recognize the square nearly as fast as you can recognize the right angles. That make it up.

Thank you again Graeme to keep the debate alive. With regard to the occipital lobe I meant that I can not exclude that the lack of recognition of the rectangular layout is a perception matter rather than memory / representation. Surely I cannot exclude the occipital contribution. What do you think about "spatial cue awareness"? Why do people recognize the use of landmarks while layout remains neglected from the cognitive interview at the end of tasks?

I think it has something to do with the organization of the hippocampus, in that recognition of locations is easier than recognition of layout at the hippocampus level.

Layout is more oriented towards placement within a location and the hippocampus is not really sensitive to that since the place codes only fire when you are "In the right place" and associations to that place make the landmarks important.

I was able to know more about the neurobiological point of view. It seems to me that

the interaction between grid cells and border cells (so scattered among others) may be a good, rather basic, explanation for the imperfect encoding of geometry. Now I need a good cognitive model explaining the lack of awareness for the geometrical information. Thanks again to everyone.