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vol I chap 3 sect 2

Volume I: Motion

Previous: 3.1. Understanding the mechanisms of vision.

3.2. Generation of a mental Global Positioning System (GPS).

Maps are useful for describing positions and directions with the purpose of understanding where are we and in what directions could we move. Maps are schematic graphical bidimensional representations of three-dimensional environments that might include positions, places, distances, paths, structures, orientations, borders and tracks of motions. Maps are useful tools where objects are located and oriented trajectories are represented.

Ancient sailors used the constellations in the night sky to figure out theirs positions and directions. Nowadays, instead of stars we use satellites. All we need for map navigation is a simple hand-held GPS receiver as a component or segment of a Global Positioning System.

A GPS is a system for making measurements of distances and times by producing, detecting, measuring and interpreting electromagnetic signals. A typical GPS system, like the one used for communications in cellular phones, consists of three major segments: the space segment, the control segment, and the user segment.

The space segment is a set of satellites surrounding Earth where signals are generated to indicate positions as well as times measured in atomic clocks located in the satellites. The control segment is a ground station collection of radars on Earth serving for localization and orientation of the satellites as well as for the registration of their orbits. The user segment corresponds to the cellular phones of the users who capture the signals from the satellites looking for visualizations of places and trajectories.

Distances can be measured directly by sending a short laser pulse and measuring how it takes to travel between two points: a transmitter source of the electromagnetic signal in a satellite and a receiver in a ground station on Earth. The full time between emission in a satellite, its reflection on one receiver and the reception on the original satellite is two times the distance between transmitter and receiver divided by the constant speed of light.

Although the speed of light signals is independent of the positions and velocities of the satellites, the times required to travel the distances between transmitter and receiver must consider the motions of the satellites surrounding Earth and the ground stations on Earth because our planet turs around the Sun. The frequencies of the clocks aboard the satellites are corrected regularly from the reference time maintained on the ground stations.

Each GPS satellite carries an accurate record of its own position and time. A minimum of four satellites must be in view of the receiver for it to compute four unknown quantities: three position coordinates with origin at the Earth's center (latitude, longitude, and altitude) and the measured delay of the received signal corresponding to the time spent by the signal for traveling between the satellite and the receiver. Data defining for each satellite their own four-dimensional positions in space-time are computed simultaneously and continuously broadcasted. These coordinates may be displayed, such as on a moving map display, or recorded or used by some other system, like a vehicle guidance system.

Two relativistic corrections must be done to the oscillatory frequency of the atomic clocks located inside the satellites:

Velocity time correction: the clock in the satellite moves at high velocities with respect to the observer on Earth, then according to the special theory of relativity the faster an object moves, the slower its time passes (as measured by the frame's clocks).

Gravitational time correction: the satellites are located at higher altitudes with respect the Earth´ surface, then according to general relativity the presence of gravitating bodies like Earth curves spacetime and therefore there is a relativistic time delay in radar signal travel time near Earth.

The combined effect of previous corrections of time dilation causes the clocks on the satellites to gain nearly 38.6 microseconds per day relative to the clocks on the ground. When these corrections are neglected, errors in the determination of GPS positions are produced: range errors are up to 13 meters and vertical errors are over 20 meters.

Existence of a mental GPS in animals and humans.

A concept of a cognitive map as a conceptual representation of place in the brain was proposed in 1948 by Edward Tolman (1886 - 1959) who studied how animals learn to navigate by exploring their environment. More recently, John O´Keefe, May-Britt Moser and Edvard I. Moser received the 2014 Nobel Prize in Physiology or Medicine. Their experiments demonstrated that inside the brain a sort of inner Global Positioning System (GPS) functions as a neurological network of interconnected nervous cells for the operation of higher cognitive functions like visualization, memorization, and learning. They identified four types of neural cells whose functions were the following: to detect localizations in space (place cells), to sense orientation possibilities for moving (direction cells), to organize a framework of patterns (grid cells) and to signal obstacles and appropriates paths for moving (border cells).

In what follows, we quote the document WORK describing the main contributions of each one of the laureates and indicate the content of his or her Nobel Lecture and their corresponding subtitles. We present in three Appendices more detailed descriptions of their Nobel Lectures: Appendix 2A contains two parts: the first one is related to the Accepted knowledge or questions under discussion in O´Keefe´s time, and the second one concerns O´Keefe main contributions or explanations reported in his Lecture. Next two Appendices contain excerpts of the other two Nobel Lectures: Appendix 2B corresponds to May-Britt Moser and Appendix 2C to Edvard I. Moser.

2014 Medicine Nobel Prize awarded to O’Keefe.

WORK: "The awareness of one’s location and how to find the way to other places is crucial for both humans and animals. To understand the ability to orient ourselves in space, John O’Keefe (1939) studied the movements of rats and signals from nerve cells in the hippocampus, an area located in the center of the brain. In 1971 he discovered that when a rat was at a certain location in a room, certain cells were activated, and that when the rat moved to another location, other cells became activated. That is to say, the cells form a kind of internal map of the room."

MLA style: John O'Keefe – Facts. NobelPrize.org. Nobel Prize Outreach AB 2023. Thu. 16 Mar 2023. https://www.nobelprize.org/prizes/medicine/2014/okeefe/facts/

NOBEL LECTURE: Spatial Cells in the Hippocampal Formation by O’Keefe.

  • Introduction
  • What about the other cell types required by the theory?

MLA style: John O’Keefe – Nobel Lecture. NobelPrize.org. Nobel Prize Outreach AB 2023. Thu. 16 Mar 2023. https://www.nobelprize.org/prizes/medicine/2014/okeefe/lecture/

2014 Medicine Nobel Prize awarded to May-Britt Moser.

WORK: "The awareness of one’s location and how to find the way to other places is crucial for both humans and animals. In 2005 May-Britt Moser (1963) and Edvard I. Moser discovered a type of cell that is important for determining position close to the hippocampus, an area located in the center of the brain. They found that when a rat passed certain points arranged in a hexagonal grid in space, nerve cells that form a kind of coordinate system for navigation were activated. They then went on to demonstrate how these different cell types cooperate."

MLA style: May-Britt Moser – Facts. NobelPrize.org. Nobel Prize Outreach AB 2023. Thu. 16 Mar 2023. https://www.nobelprize.org/prizes/medicine/2014/may-britt-moser/facts/

NOBEL LECTURE: Grid Cells, Place Cells and Memory by May-Britt Moser.

  • The relationship between grid cells and place cells.
  • Entorhinal speed cells.
  • The hippocampus—memory or space?
  • Mechanisms for associating events with place—odours as a gateway.
  • Remapping keeps memories apart.
  • From spatial mapping to navigation

MLA style: May-Britt Moser – Nobel Lecture. NobelPrize.org. Nobel Prize Outreach AB 2023. Thu. 16 Mar 2023. https://www.nobelprize.org/prizes/medicine/2014/may-britt-moser/lecture/

2014 Medicine Nobel Prize awarded to Edvard I. Moser.

WORK: "The awareness of one’s location and how to find the way to other places is crucial for both humans and animals. In 2005 May-Britt Moser and Edvard I. Moser (1962) discovered a type of cell that is important for determining position close to the hippocampus, an area located in the center of the brain. They found that when a rat passed certain points arranged in a hexagonal grid in space, nerve cells that form a kind of coordinate system for navigation were activated. They then went on to demonstrate how these different cell types cooperate."

MLA style: Edvard I. Moser – Facts. NobelPrize.org. Nobel Prize Outreach AB 2023. Thu. 16 Mar 2023. https://www.nobelprize.org/prizes/medicine/2014/edvard-moser/facts/

NOBEL LECTURE: Grid Cells and the Enthorinal Map of Space by Edvard I. Moser.

  • From psychology to neurophysiology—and back
  • Moving into unknown territory—the entorhinal cortex
  • Grid cells and their functional organization
  • A universal map
  • Grid cells and the geometry of the environment
  • Fine-scale topography of the grid-cell network
  • How is the grid pattern generated?
  • General principles of network function

MLA style: Edvard I. Moser – Nobel Lecture. NobelPrize.org. Nobel Prize Outreach AB 2023. Thu. 16 Mar 2023. https://www.nobelprize.org/prizes/medicine/2014/edvard-moser/lecture/

It is quite informative to consider the learning and research personal trajectories of these 2014 Nobel laureates. See their documents called Biographical:

MLA style: John O’Keefe – Biographical. NobelPrize.org. Nobel Prize Outreach AB 2023. Sun. 17 Dec 2023. https://www.nobelprize.org/prizes/medicine/2014/okeefe/biographical/

MLA style: May-Britt Moser – Biographical. NobelPrize.org. Nobel Prize Outreach AB 2023. Sun. 17 Dec 2023. https://www.nobelprize.org/prizes/medicine/2014/may-britt-moser/biographical/

MLA style: Edvard Moser – Biographical. NobelPrize.org. Nobel Prize Outreach AB 2023. Sun. 17 Dec 2023. https://www.nobelprize.org/prizes/medicine/2014/edvard-moser/biographical/

Next: 3.3. Cognitive procedures for creating scientific knowledge.