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+[0.000 --> 2.000]  I'm going to have to go.
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+[586.000 --> 588.000]  I'm going to have to go.
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+[594.000 --> 596.000]  I'm going to have to go.
+[596.000 --> 598.000]  ..
+[598.000 --> 600.000]  I see a couple of people joining in.
+[600.000 --> 602.000]  I think we are good to go.
+[602.000 --> 604.000]  Welcome everybody back to your second session.
+[604.000 --> 606.000]  In a special speciality.
+[606.000 --> 608.000]  My pleasure to introduce Varvrath Sp Warsky.
+[608.000 --> 612.000]  She's a Professor ofòngirieta Psychology at Stanford University.
+[612.000 --> 616.000]  Professor of Psychology and Education at the Columbia Teacher's College.
+[616.000 --> 619.840]  research career has spanned many topics including memory, knowledge representation,
+[619.840 --> 624.160]  language, special language and thinking, event perception and cognition,
+[624.160 --> 629.120]  gesture, diagrammatic reasoning and creativity. And this is led her to work with
+[629.120 --> 632.160]  an ample spectrum of collaborators including linguists, philosophers,
+[632.160 --> 636.320]  computer scientists, both in graphics and AI, biologists, chemists, engineers,
+[636.320 --> 640.400]  designers and artists. So as you can see, Barbara's profile is a clear example of
+[640.400 --> 645.040]  the multidisciplinary values that we appreciate so much at SEMF and we are
+[645.040 --> 650.080]  delighted to receive her reply to our invitation to speak at Special Speciality.
+[650.960 --> 656.800]  As myself, as a very strongly visually-minded person, I find Barbara's title,
+[656.800 --> 661.520]  Special Thinking, is the foundation of thought as a very intuitive statement.
+[661.520 --> 665.840]  But I'm looking forward to hearing the whole story. So the viewership floor is yours, Barbara,
+[665.840 --> 674.000]  please go ahead. Thank you, thank you for that generous introduction and for inviting me to this
+[674.640 --> 681.760]  very exciting meeting. I'm sorry we can't all be there to exchange our perspectives on space.
+[682.960 --> 691.040]  It's hard to use special terms without punning. So I think I'll share a screen. I have way too much
+[691.040 --> 700.720]  to tell you and I've cut it down but I'm still telling you way too much. You can stop me with questions.
+[704.720 --> 709.920]  I'm not finding the PowerPoint. Here it is.
+[712.640 --> 723.760]  Okay, so I assume I'm on screen. Everything's good. Yeah, okay, this is an example of Special Thinking
+[723.760 --> 733.440]  Steinberg, one of my favorite visual artists. So all things must move and act in space,
+[733.760 --> 742.640]  to survive. All living things again must move and act in space to survive. Even plants need to move
+[742.640 --> 751.040]  toward the sun away from the wind. So this is why I claim that all thought begins the special thought.
+[751.680 --> 760.800]  I'm happy to have people contest that view. So special, what do I mean by special thought? It's
+[760.800 --> 771.520]  moving in space and interacting with the things in space. And it's using in humans, it's thinking how
+[771.520 --> 779.520]  we think about space and how we use think is space to think and I'll touch on each of those.
+[780.320 --> 786.960]  So special thinking is the foundation of thought, not the entire edifice, but the foundation.
+[787.280 --> 796.000]  Some of the evidence comes from work that won the Nobel Prize, I think in 2014, by the Mosheurs
+[796.000 --> 804.000]  working in John O'Keefe's lab at UCL. And they, John O'Keefe's group had already found cells in
+[804.000 --> 815.040]  hippocampus that respond when the rant or other mammal wanders freely. There are cells in hippocampus
+[815.040 --> 822.400]  that fire whenever the animal is in a particular place. The firing is indicated by the red
+[822.960 --> 829.520]  the neural network. And these place cells gather information from all over the cortex,
+[829.520 --> 836.080]  simple as single cell. It's in my mind quite remarkable. So it's information about sight,
+[836.080 --> 842.960]  about smell, about reinforcement history, I think, about the motion of the rant.
+[844.160 --> 851.040]  And in fact, these place cells are established by motion. But in hippocampus, the place cells
+[851.040 --> 858.080]  aren't arrayed, especially. And this was a mystery for a long time in spite of the fact that
+[858.080 --> 865.280]  O'Keefe and Nadel called their book the hippocampus is a cognitive map. There was no map there.
+[865.840 --> 875.680]  And the map was discovered by the Mosheurs working in O'Keefe's lab, grid cells, one synapse away
+[875.680 --> 883.200]  in entorino cortex. And you can see the firing pattern on the right in the grid cells. And it's
+[883.920 --> 892.800]  exogonal approximate spatial array. So that was terribly exciting, finding that work. And what made
+[892.800 --> 901.920]  it even more exciting to me in human beings is very recent work showing that the same brain
+[901.920 --> 910.080]  structures, hippocampus and entorino cortex, that represent places in spatial relations,
+[910.080 --> 918.960]  also represent events in time, people, and ideas in temporal, social, and conceptual spaces.
+[919.040 --> 928.400]  So that again is quite strong evidence, I think, for the spatial foundation of abstract thought.
+[929.120 --> 937.520]  So the metaphor I've used or the analogy I've used is that the hippocampus creates checkers for ideas
+[937.520 --> 945.920]  and the grid cells are like a checkerboard only they're representing the relations among ideas.
+[946.720 --> 957.200]  So people like most creatures, our most animate creatures, move from place to place in the world.
+[957.760 --> 965.360]  And as they move, as we move, we leave traces on the ground and in the brain creating paths and
+[965.360 --> 974.800]  places. And the hippocampus also records roots, strings of places and paths. And you can think of
+[975.680 --> 984.240]  a minimal thought or a minimal diagram as a line linking two points to ideas by a relationship,
+[984.240 --> 992.480]  two places, by the path between them. And you can string together, can catnate these networks
+[992.480 --> 1001.760]  into paths in the world. Social networks, this is a social network drawn by one of our participants.
+[1001.760 --> 1011.840]  A phylogenetic trees, family trees, this is from the Museum of Modern Art illustrating the
+[1011.840 --> 1018.720]  major art movements in the early part of the 20th century. So we have networks representing
+[1018.720 --> 1028.240]  just a huge variety of things. Again, there are ideas linked by relations. So thought comes from
+[1028.240 --> 1035.360]  actions in space, our feet go from place to place along paths, just as our minds go from thought to
+[1035.360 --> 1043.760]  thought along conceptual relations. But our hands do something else. Human beings have very
+[1043.760 --> 1050.480]  active hands, very skillful hands. They do huge numbers of different things. And our hands act
+[1050.480 --> 1060.560]  on things, just as our mind acts on ideas. So paths create spatial schemas for thoughts,
+[1060.560 --> 1067.680]  dots, lines, networks. We talked about they can inscribe boxes or areas, they can go in circles,
+[1067.680 --> 1075.040]  spirals, zigzags. And these lines that are created in the ground, you can take different perspectives
+[1075.680 --> 1085.600]  will come back to that. So the first part of the talk will be putting the world in the mind.
+[1085.600 --> 1092.320]  How does the mind represent the different spaces that we inhabit? The second part will be using the
+[1092.320 --> 1102.000]  world. How the mind is put into the world. Something probably will not completely, you make the
+[1102.000 --> 1112.480]  human, but it certainly blossoms in humanity. So the major way, the major spaces that we need to
+[1112.480 --> 1119.120]  represent to function in the world, other spaces about a per se, the space around the body and
+[1119.120 --> 1127.920]  reach of hand or eye, and the larger space of exploration that we navigate and that has to be
+[1127.920 --> 1135.360]  put together from different views or different experiences, often different kinds of experiences.
+[1135.360 --> 1144.400]  And each of these spaces, the representations of each of these spaces are distorted by
+[1144.400 --> 1152.560]  perception and action and these are intertwined. So I'm going to go really briefly on the ways
+[1152.560 --> 1159.760]  that these spaces are distorted. I won't give you all the evidence. There is evidence.
+[1161.600 --> 1169.120]  So then there are the spaces that we create, putting the mind in the world, maps and other visualisation,
+[1169.120 --> 1176.000]  social spaces to accomplish the different tests we do together. We make sketches for design
+[1176.800 --> 1185.360]  and we create large urban spaces. There's a whole lot to be said about that and not nearly enough time.
+[1186.800 --> 1193.360]  So when thoughts overwhelm the mind, the mind puts thought into the world again, something
+[1194.080 --> 1200.080]  slightly uniquely human. And putting the mind, we can put the mind in the world, in the world,
+[1200.080 --> 1208.160]  using words as I'm doing now, using gestures as I'm doing at this moment. It's hard to do on zoom
+[1209.360 --> 1216.240]  and using graphics of various kinds. I'll concentrate a little bit. I'll only say a little bit
+[1216.240 --> 1224.080]  about words but concentrate on gestures and graphics which have a way of representing and
+[1224.080 --> 1229.920]  communicating information that's very different from the way language does it.
+[1230.720 --> 1238.240]  So these are cognitive tools to augment thought, communicate thought. So cognitive tools expand
+[1238.240 --> 1244.640]  the mind. They offload memory and information processing and enlarging the mind hugely.
+[1245.200 --> 1252.240]  They use space to represent literal and metaphoric space and action because they're in front of
+[1252.240 --> 1259.920]  the eyes and can be inspected in the overloading working memory. They promote infants and discovery
+[1259.920 --> 1266.800]  because they're public. They allow creation, revision and inference by a community. And again,
+[1266.800 --> 1276.080]  I think I say this as a challenge that they're uniquely human. Nobody has ever seen a gorilla
+[1277.040 --> 1286.880]  draw a map in the air or in the sand. So here we're going on language, actions and ideas are
+[1287.840 --> 1295.200]  like actions on objects. We raise ideas. We pull them together. We tear them apart. We turn them
+[1295.200 --> 1302.000]  upside down. We toss them around. We line them up. And we say that in language and many times
+[1302.000 --> 1311.600]  we gesture indicating those sorts of actions. But there are actions on ideas. There's no object there.
+[1311.600 --> 1320.960]  That's what makes them gestures. So space has meaning. A proximity in space indicates proximity
+[1320.960 --> 1329.440]  on any dimension. The vertical dimension is loaded because of gravity going up takes resources,
+[1330.400 --> 1342.320]  health, wealth and strength. So everything goes up in general. The horizontal is pretty much neutral,
+[1342.320 --> 1350.880]  but it's affected by cultural factors in particular reading order. And there's the whole cottage
+[1350.880 --> 1358.320]  industry looking at the effects of cultural reading order on cognition. Very interesting.
+[1359.280 --> 1369.920]  And perhaps surprising set of findings. And handiness has some sort of effect as well. Left-handed
+[1369.920 --> 1376.400]  people tend to indicate value with their left hand, right-handed people tend to indicate
+[1376.400 --> 1384.480]  valuable things with their right hands. But the effective handiness is limited and limited
+[1384.480 --> 1394.080]  probably to value. Okay, so space has meaning. We also have figurative spaces. Again, they're
+[1394.080 --> 1400.640]  spatial. We say we're out of depth. We say somebody's at the top of the class or feeling up.
+[1401.280 --> 1407.440]  Somebody fell in an depression. We got closer, thinking out of the box. Again, there are these
+[1407.440 --> 1416.720]  figurative spaces for thoughts. And we have them in language and in gesture. I'm going to skip that.
+[1417.280 --> 1424.560]  So space, now I'm going to go back to the spaces that we inhabit. Space is special. It's
+[1424.560 --> 1432.160]  supermodal. Not just we know about space, not just from vision. Blind people can have very good
+[1432.160 --> 1437.920]  senses of space and use blind people use gesture without ever having seen it.
+[1439.360 --> 1445.360]  So their gestures are for their own thinking. We know about space, not just from vision. We know
+[1445.360 --> 1453.360]  about it from hearing, from smell. Blind people use the texture under their feet. Sounds. So
+[1453.360 --> 1461.520]  that in many of these we might not be consciously aware of, but they're all important in navigation
+[1461.520 --> 1472.160]  and important in other spatial tasks. And so that each of these modalities contributes. They
+[1472.160 --> 1481.280]  contribute unique things, but they're overlapping and can be used to orient ourselves in space.
+[1481.920 --> 1487.040]  Spaces essential to survival. If we didn't know how to get home at night or food in our
+[1487.040 --> 1494.720]  mouths, we'd be in real trouble. As I've indicated space, spatial knowledge is the basis for other
+[1494.720 --> 1501.040]  knowledge. Our knowledge of space isn't like geometry or physical measurement. We don't have those
+[1501.040 --> 1508.960]  measuring instruments in our head. It's again comes from perception and action and it's
+[1509.520 --> 1517.200]  their systematic distortions due to perception and action. So let's start with a space around the
+[1517.200 --> 1526.880]  body. And bodies are experienced from the inside as well as the outside, unlike objects. From the
+[1526.880 --> 1533.040]  outside we have information, the same information we have for objects, perceptual information
+[1533.280 --> 1540.320]  primarily and contour the borders of objects are particularly important in recognizing them.
+[1541.760 --> 1550.000]  Insider information is can come from is can the septic proprioceptive. It's especially important
+[1550.000 --> 1559.760]  in function in what bodies can do. And the functional importance isn't correlated with body size.
+[1559.760 --> 1568.320]  It is correlated with how large the different parts of the body appear in kids drawings. These
+[1568.320 --> 1575.040]  are drawings that kids make all over the world. Although usually they have two legs, not one,
+[1575.040 --> 1581.360]  but the head is enlarged. The hands are enlarged and the legs and back are smaller.
+[1582.320 --> 1589.520]  And this is similar to our cortical representations of bodies where again the hands, the head
+[1590.640 --> 1600.320]  and other organs are relatively large legs and back relatively small. We did a series of tasks
+[1600.880 --> 1612.080]  that queried how people judge parts of the body and their judgments reaction times tube,
+[1613.840 --> 1621.920]  to name or identify different parts of the body functional importance ratings and so forth,
+[1621.920 --> 1632.880]  all correlate with function as indicated on the homunculus rather than with size. So size
+[1634.160 --> 1641.920]  of body is less important than functional significance in our representations of the body.
+[1641.920 --> 1649.920]  This is what we would look like if the size were correlated with if actual size was correlated with
+[1649.920 --> 1658.960]  cortical size. So that's the body, the space around the body. We can think of in terms of the
+[1658.960 --> 1669.760]  major axis of the body, the head foot axis, the front back axis, the left right axis, and also gravity,
+[1669.760 --> 1676.800]  the relationship of the body to the world. And we did a large set of studies looking at how people
+[1676.800 --> 1685.600]  keep track of the things immediately around the body as they navigate space and found that the
+[1687.440 --> 1695.760]  axis that was fastest, most accessible is the head foot axis, both because it's a symmetric and
+[1695.760 --> 1703.600]  correlated with gravity. The next fastest axis was the front back, our perceptual and motor
+[1704.320 --> 1713.680]  apparatus, our oriented frontwards, not backwards. And still the asymmetries are extremely important.
+[1713.680 --> 1721.840]  And that's the next fastest axis, axis for accessing things around it or keeping track of things
+[1721.840 --> 1729.200]  around it. And the left right has a symmetries, but they're far less salient and important and that
+[1729.200 --> 1740.400]  ends up being or discernible and that ends up being the least the worst or slowest axis for
+[1740.400 --> 1747.520]  keeping track of things around us. And in fact, many people confuse left and right and their cultures,
+[1748.480 --> 1756.640]  language cultures that don't distinguish left and right, a longer story. So bodies live in the world
+[1757.600 --> 1764.480]  and now we get to the world of exploration, which is the world that's too large to see from a single
+[1764.480 --> 1770.720]  point and it's put together from any sources, not just actually experiencing the world, but from
+[1770.720 --> 1777.280]  maps of the world, descriptions of the world, and how we integrate those different sources
+[1778.080 --> 1785.360]  is a real challenge both for people and for models. So there are a number of distortions, some
+[1786.240 --> 1794.720]  the first ones are research of other people. It's an interesting distortion of hierarchical grouping
+[1794.720 --> 1801.840]  of space. So even those spaces flat, we group it hierarchically. We don't remember the
+[1801.840 --> 1810.000]  directions amongst all the cities in the world. Instead, we use the higher order elements
+[1810.480 --> 1818.960]  to as acute to where the cities are. So in America, we use states to infer low
+[1819.680 --> 1827.680]  locations of cities and students in San Diego here at the bottom almost on the Mexican border
+[1827.680 --> 1835.520]  were asked what's the direction between San Diego and Reno and most of them put it put Reno
+[1835.680 --> 1845.200]  east of San Diego instead of west of San Diego as is the case and that's presumably because
+[1846.400 --> 1852.320]  people know that Reno is in Nevada, San Diego is in California and on the whole
+[1853.680 --> 1860.720]  California is west of Nevada. So they use the the orientations of the states to infer
+[1860.800 --> 1867.600]  the orientations of the city. So once this study was done, everybody did it in their own state or
+[1867.600 --> 1876.400]  country and hierarchical organization distorts not just directions but distances and so it's a
+[1876.400 --> 1889.600]  strong effect and there doesn't correspond to reality. Another distortion is Steinberg again caught
+[1890.560 --> 1897.680]  on to and that's that we judge distances that are close to us as larger than distances that are far
+[1897.680 --> 1906.400]  from us. That's again been shown in many, many experiments. At the perspective, we take influences
+[1906.400 --> 1914.080]  our distance judgment and farther distances get telescope as if we were on top of a mountain and
+[1914.080 --> 1923.440]  they seem smaller than the distances close to us. This distortion also happens in time as does
+[1923.440 --> 1930.800]  the hierarchical organization. So many of these distortions that I'm describing in space have
+[1930.800 --> 1938.320]  analogs in time in social relations in political judgments and so forth. Again,
+[1938.400 --> 1946.720]  bit of evidence that spatial thinking is foundational. So we have a major asymmetry in distance
+[1946.720 --> 1954.240]  estimations. People think that Pierce House is closer to the Eiffel Tower than the Eiffel Tower to
+[1954.960 --> 1962.960]  Pierce House. It's again a distortion that people have done all over the world on college campuses
+[1963.440 --> 1971.040]  in cities picking major landmarks. People know and asking for distances between from an ordinary building
+[1971.040 --> 1978.240]  to a landmark or from a landmark to an ordinary building and again the distance from a landmark
+[1979.440 --> 1986.320]  to an ordinary building is just to be smaller than the distance from an ordinary building to a
+[1986.320 --> 1993.600]  landmark and landmarks again describe neighborhoods. So they seem to encompass things that are
+[1994.320 --> 2002.160]  more than they are. People think magenta is more similar to red than magenta because red
+[2003.280 --> 2014.560]  seems to include all reds and magenta only includes itself. So again, these judgments happen in
+[2014.640 --> 2023.200]  other areas as well as spatial. We looked at a couple of other distortions that are analogous
+[2023.200 --> 2034.640]  to gistored grouping effects. People tend to group large bodies together. So people are participants
+[2034.640 --> 2039.440]  who are more likely to pick the incorrect map of the world, which is the one on the left,
+[2040.000 --> 2048.240]  than the correct one and the one on the left we've moved south America to be slightly more
+[2048.240 --> 2056.720]  under North America. And this distortion works on blobs that are even interpreted as countries.
+[2056.720 --> 2067.600]  It works on cities. It's it's pretty substantial. Another distortion we looked at is one we
+[2067.600 --> 2073.840]  called rotation. So the Bay Area, which you have depicted in front of you runs at an angle.
+[2074.480 --> 2081.920]  And we asked students at Stanford for the direction between Stanford and which is
+[2083.120 --> 2092.240]  sort of down here. Palo Alto and Berkeley, which is up here and you can see that actually Berkeley
+[2092.240 --> 2100.400]  is west of Stanford. But people tend to line up the Bay Area with the external coordinates.
+[2100.880 --> 2107.440]  So a significant majority of people think that Berkeley is actually east of
+[2109.280 --> 2119.200]  is west of Stanford and rather than east. And again, we find these distortions with artificial
+[2119.200 --> 2127.440]  stimuli. Italy, the boot of Italy gets straightened out. Japan gets put more horizontal. You can find
+[2127.440 --> 2136.400]  it everywhere. Okay, so the perceptual organization factors are we remember shapes is more aligned
+[2136.400 --> 2144.400]  with each other and we remember shapes is rotated to their reference frames. So cognitive maps
+[2144.400 --> 2151.200]  seem to be impossible figures. There's no way to put all those errors together in a coherent map
+[2151.920 --> 2158.960]  and representation. Cognitive maps seem to be created on the fly. It's not that we have a
+[2158.960 --> 2166.000]  file for them and pull them up when we need to make a judgment. We simply take whatever information
+[2166.000 --> 2173.920]  we have to make that judgment and that information can be approximate and in fact distorted.
+[2174.560 --> 2182.800]  So cognitive maps are closer to cognitive collages. There are multi-modal incoherent and maybe more
+[2182.800 --> 2192.800]  beautiful. So describing space needs a perspective. I'm going to say two words on describing space
+[2192.800 --> 2200.560]  on language. It's again something that's been studied quite a bit. And there are seem to be two
+[2200.560 --> 2208.400]  major ways of describing space and one is analogous to the way we experience it. It's a
+[2208.400 --> 2216.240]  route walking through it and that perspective has been called route, egocentric, embedded,
+[2216.320 --> 2222.800]  intrinsic. There are a number of different names for it. It's been distinguished in linguistics
+[2222.800 --> 2231.520]  in geography, in psychology and with different terms. This is quite common. I find it in research.
+[2232.240 --> 2240.880]  The other view is more map like it's been called survey or allocentric or overview. And we've
+[2240.880 --> 2248.400]  done a number of studies looking at how people describe space and they often promiscuously
+[2249.200 --> 2258.880]  mix the descriptions. They switch perspective without signaling and without even really realizing it
+[2258.880 --> 2265.360]  and people understand it. So despite the fact that linguists in geographers and even some
+[2265.600 --> 2273.120]  psychologists prefer a single perspective, people mix them. We'll see in a minute they mix them in
+[2273.120 --> 2282.800]  maps as well. So here this is an overview map of Stanford and embedded views Stanford and a
+[2282.800 --> 2290.400]  view and people switch and mix. As there's another view we can take on perspective. Again,
+[2290.400 --> 2296.720]  I won't have time to talk too much about it. And that's when I'm talking to you or when I'm talking
+[2296.720 --> 2305.360]  to somebody else but looking at a third person, we have a choice of perspective should we use our own
+[2306.240 --> 2314.000]  or somebody else's, the person we're talking to. In general when that person is in the conversation,
+[2314.000 --> 2324.880]  we use their perspective. Not our own. It's not just politeness because it's we did a series of
+[2324.880 --> 2331.360]  experiments on that. It has to do with relative cognitive load. If I'm telling you something,
+[2331.680 --> 2338.320]  your cognitive load is higher, you have to understand me. I know what I'm talking about presumably.
+[2338.960 --> 2345.280]  And so it's easier for me to take your perspective than for you to take mine.
+[2345.600 --> 2352.000]  In interesting cases when both of us are looking at Patrick here and he's reaching for a book.
+[2352.640 --> 2359.360]  And we ask people with respect to the bottle, the water bottle, where is the book?
+[2360.800 --> 2366.080]  Now you and I are talking together from our perspective the book is done the right.
+[2366.880 --> 2373.920]  From Patrick's perspective, the book is on the left. When Patrick is reaching is performing an
+[2373.920 --> 2383.120]  action, we talking to each other, facing Patrick, take his perspective. So this was surprising to us
+[2383.120 --> 2390.480]  and to various other people who replicated that, that it's easier to take the other person's
+[2390.480 --> 2397.360]  perspective than our own when action is involved. And I think it's a way of understanding the
+[2397.360 --> 2404.320]  action is by taking the other's perspective. So that's a couple of words on perspective.
+[2405.360 --> 2413.600]  Let me switch now and I know I'm throwing a huge amount at you to go back to graphics and
+[2413.600 --> 2422.000]  gesture, ways of externalizing saw. And they seem to have a very different semantic syntax and
+[2422.000 --> 2429.280]  pragmatics from language. They do seem to have their own semantic syntax and pragmatics. It's
+[2429.280 --> 2438.560]  looser than syntax semantics and pragmatics in language. But it's a more direct route to meaning
+[2439.200 --> 2448.560]  using elements or and spatial relations in the case of in both cases. Again, a longer story and
+[2448.560 --> 2457.280]  I'll only tell you part of it. I'd like to show you now some videos of people thinking. So these are
+[2457.280 --> 2464.800]  people alone in a room. They're reading very complicated descriptions and they're going to be
+[2464.800 --> 2474.480]  tested. So one set of descriptions were describing environments that either had four or eight landmarks.
+[2475.120 --> 2482.320]  We wrote that in our descriptions either from a survey perspective or a route perspective.
+[2482.320 --> 2489.680]  And the questions came from both perspectives. So this is part of a description. Edna is a charming
+[2489.680 --> 2496.560]  town nestled in an attractive highway and her done river highway river highway runs east west at the
+[2496.560 --> 2503.840]  southern edge of Edna toward the eastern border river highway under sex with mountain road which runs
+[2503.840 --> 2512.480]  north of it and so on. It will locate the four or eight landmarks and I'll show you someone who's
+[2512.480 --> 2521.360]  reading this again alone on the room with the doors closed and the instructions told her to learn
+[2521.360 --> 2532.480]  it for a test. They said nothing about gesturing. So, so watch her hands. She's not watching her hands.
+[2533.120 --> 2544.320]  She's essentially drawing a map. She's making a diagram on the table with pez for the streets
+[2545.360 --> 2554.320]  and dots for the landmarks and she's often repeating it, rehearsing with her hands.
+[2554.480 --> 2562.480]  And when I watch her and our other participants, we've run hundreds by now. I get the feeling that
+[2562.480 --> 2569.120]  their hands are translating the language into thought. You saw that the language is hard.
+[2570.160 --> 2580.400]  So 70% of our participants do this at least once. They read four descriptions. They perform better
+[2581.200 --> 2587.520]  the descriptions that they gesture on and if we take another group of participants and make
+[2587.520 --> 2595.280]  them sit in their hands, they perform worse and some of them say, I can't think without my hands.
+[2596.240 --> 2602.800]  So let me this person next person is reading a description of how a car break works. It's again
+[2602.880 --> 2611.120]  quite difficult. I won't test you or even read it. Let me show you him.
+[2618.880 --> 2627.040]  So he's going to do that again bigger. So again, he's rehearsing it. He's looking very carefully
+[2627.120 --> 2633.520]  at the language, translating the language and the actions of that's not a gesture, translating
+[2633.520 --> 2641.680]  the language into the actions of his body and not looking at his body. He's looking at the screen.
+[2643.280 --> 2650.320]  Okay, one more. This is a woman reading a description of parallel events in time. She's essentially
+[2650.320 --> 2656.000]  going to form a matrix on the top of the desk. She does look at her hands, but that's unusual.
+[2657.200 --> 2660.160]  Sorry. There.
+[2666.560 --> 2673.920]  So some people draw matrices on the top of the desk or in the air. Some people use the knuckles
+[2673.920 --> 2681.760]  of their hands as a matrix and put things there. So people model what they're reading differently,
+[2682.560 --> 2691.840]  but they all model. They're creating these structures in space. We call them visual motor or
+[2691.840 --> 2700.400]  spatial motor. They aren't visual. Blind people gesture, as I said, we were planning to do these
+[2700.400 --> 2708.080]  same studies on blind participants, but the the graduate student took a computer with all the
+[2708.080 --> 2716.000]  descriptions, went off to run the blind and I haven't seen her since. So those days are still in
+[2716.000 --> 2723.040]  the air and I hope someone does it. So the gestures model the situation in the text, the models are
+[2723.040 --> 2730.080]  spatial motor, not visual, preventing gesture, reduces comprehension. And again, I think gesture
+[2730.080 --> 2737.280]  translates language into thought. Gestures also promote collaboration. These two people are trying
+[2737.280 --> 2744.640]  to find a route after an earthquake to rescue people when roads are blocked off and they're
+[2744.640 --> 2751.920]  negotiating it. And you can see they're not looking at each other. They're only looking at their
+[2751.920 --> 2762.640]  gestures on the map. And they you can see sometimes they like to get into them. They take turns,
+[2762.640 --> 2771.520]  sometimes they're interested in getting there. And when they can gesture at the over the same map,
+[2771.520 --> 2778.000]  they're much happier with the collaboration than when a shower curtain intervenes between them.
+[2778.000 --> 2784.000]  So they can speak clearly, but they can't gesture on the same map. The gestures are far more
+[2784.000 --> 2791.920]  precise than the words. In fact, the people who can't gesture on the same maps have to rely on
+[2791.920 --> 2802.960]  spatial description. Their maps differ 30% of their time. Okay. So talking about nonverbal
+[2802.960 --> 2810.320]  communication, that's very quick. Spatial communication, that's very quick. In basketball games,
+[2810.320 --> 2817.440]  it's how people have to somehow communicate to their teammates, bluff the people on the opposite
+[2818.160 --> 2825.040]  team, manage the ball, follow the ball, shoot for it, own rapid fire succession, and it's all
+[2825.040 --> 2833.120]  implicit. Okay. A gestures for others, and I'm going to quickly go through this because I've
+[2833.120 --> 2840.800]  already overloaded you. I showed that gestures are important for our own thinking, but they're
+[2840.880 --> 2848.160]  also important for others. We study this in a situation where people watched a video of an
+[2848.160 --> 2858.480]  explanation of how a gen, gen, gen works, have saw action gestures, have saw structure gestures,
+[2858.480 --> 2864.960]  then they were given true false tests of both structure and action. And the most interesting
+[2864.960 --> 2873.840]  data were visual explanations of how the engine worked and videoed explanations of how the engine
+[2873.840 --> 2882.800]  worked. So remember, have saw gestures that indicated action, like the combustion of the engine
+[2882.800 --> 2890.400]  or the carburetor goes up and down, and have saw gestures that indicated the shape of the carburetor
+[2890.400 --> 2896.160]  or the shape of the engine. So they were structure gestures. So I'm not going to show you those
+[2896.160 --> 2909.040]  videos. I'm going to go this law to the results. So viewing action gestures made enable the participants
+[2909.040 --> 2916.640]  to answer more actions correctly. The actions could be answered on the basis of the script. You didn't
+[2916.720 --> 2924.640]  need the gestures to answer the questions. Nevertheless, people who saw action gestures answered more
+[2924.640 --> 2930.960]  action questions correctly. There was no difference for the structure gestures because structure
+[2930.960 --> 2938.320]  is easy for people. Action is hard. Notably, there was more action expressed in the visual
+[2938.320 --> 2947.840]  explanations. There were more gestures, action gestures in the videoed explanations.
+[2948.560 --> 2957.440]  Gestures were invented. They weren't imitated. And so that they saw the same number of gestures,
+[2957.440 --> 2968.160]  but invented extra ones to express actions. The people who saw actions also used more action
+[2968.160 --> 2978.400]  words in their explanations. And they didn't hear more action words, but they described it with more
+[2978.400 --> 2984.320]  action words. So I'm going to show you a couple of their visual explanations. This is someone who saw
+[2984.320 --> 2993.120]  structure gestures, another person who saw structure gestures, here's someone who saw action gestures.
+[2993.120 --> 3001.520]  And we counted the number of errors many more in the people who saw action gestures. We counted
+[3001.520 --> 3009.120]  these explosions and the bubbles and the carburetor, the action elements, many more in those who saw
+[3009.120 --> 3021.920]  action gestures. So seeing action gestures gave people a far deeper understanding of the action
+[3021.920 --> 3029.440]  than seeing structure gestures. The action gestures communicated a huge amount of information.
+[3029.440 --> 3037.440]  They internalized the action from seeing the action gestures, another person who saw action gestures.
+[3038.240 --> 3049.840]  So we found similar results asking people to learn how chemical bonding went. And then they were
+[3049.840 --> 3058.880]  asked to either make a verbal explanation of chemical bonding or of a visual explanation. These are some
+[3058.880 --> 3068.080]  of the visual explanations. So they're very different. They aren't the sorts of things they saw in the
+[3068.080 --> 3075.920]  unit. The people who made visual explanations performed far better on the test than the people that
+[3075.920 --> 3083.440]  made verbal explanation, another visual explanation, verbal explanation. It's just one word after another.
+[3084.640 --> 3094.640]  So this is a medium not used, usually used in teaching. The visual explanations also help teachers.
+[3094.640 --> 3101.200]  They help teachers know what are the misconceptions of the students. And I think it's something that
+[3101.200 --> 3108.400]  can be used for lots of different content, not just chemistry. So why are the visual explanations
+[3108.400 --> 3116.080]  better? There are natural mapping of meaning to space. They abstract the essentials, so do words,
+[3116.080 --> 3125.280]  but I think visual explanations for you to do it more. We did find more of the critical functional
+[3125.360 --> 3131.440]  and action information represented in the visual explanations than in the verbal ones.
+[3132.320 --> 3139.280]  Importantly, the visual explanations give you a check for completeness. Is everything I need there?
+[3140.160 --> 3147.040]  They also give you a check for coherence. Does it make sense? Have I described, have I visualized the
+[3147.040 --> 3156.240]  processes appropriately or inappropriately? So is my explanation complete? Is it coherent?
+[3156.240 --> 3163.840]  Making it visual gives me creates a model and lets me check for completeness and coherence.
+[3163.840 --> 3170.160]  It also provides a platform for inferring function from structure.
+[3170.640 --> 3185.040]  So good graphics abstract. They distort. They omit a lot of information and they add information
+[3185.040 --> 3192.960]  in particular multi-modal information and symbolic information. On the whole, they don't add sentences.
+[3193.040 --> 3200.000]  They add words and symbols here and there. But they do distort as the famous London
+[3200.000 --> 3208.080]  on Pube map, which is a classic in graphic design. By the way, the designer who was doing this had
+[3208.080 --> 3216.880]  just finished doing designs of circuit diagrams. And I think that influenced the way he visualized
+[3217.600 --> 3226.240]  the two. So ingredients of graphics are spatial relations and marks. And as I said, I think these
+[3226.240 --> 3234.000]  convey meaning directly. We've already done that. The marks and elements can be iconic. They can
+[3234.720 --> 3241.120]  iconic in a different sense than the philosophical. They can resemble what they're representing.
+[3241.120 --> 3247.200]  They can have figurative relations to what they're representing like scales of justice. They
+[3247.200 --> 3254.800]  can be schematic like a dot. And then in a network, they can be symbolic like words or plus and
+[3254.800 --> 3263.440]  equal signs. Meaningful schematic marks can be points and lines forming networks. Errors,
+[3263.440 --> 3271.920]  we have a whole set of research on how arrows convey meaning boxes or containers. And again,
+[3271.920 --> 3279.520]  there are parallels in gesture. So now I'm going to jump to ancient graphics and I'm really almost done.
+[3281.200 --> 3290.000]  So this is a, and people made graphic representations all over the world, more and more of being
+[3290.000 --> 3298.160]  found each day and are extremely exciting. We're not the only species that left graphic marks
+[3298.160 --> 3305.040]  where they could be seen by future generations. The undertiles apparently did, although
+[3305.840 --> 3315.120]  no one's yet found representative marks by the undertiles, they may. So this is the previous
+[3315.680 --> 3323.200]  oldest map when there was written writing, you can see that it mixes perspective has an overview
+[3323.840 --> 3333.520]  of the paths and frontal views of the landmarks. It's in stone, which is probably why it survived
+[3333.520 --> 3342.560]  6,000 years. This one also stone, it's twinches by one inch. It's a very small stone was found in
+[3342.720 --> 3352.560]  cave in Spain, probably 10 years ago. It's 14,000 years old. And the inscription on it is the area
+[3352.560 --> 3360.240]  surrounding the cave where the stone was found. So was portable? Maybe people took it under way
+[3360.240 --> 3367.600]  to know how to come back. Can you imagine the excitement of the archaeologists who walked into a cave
+[3367.600 --> 3374.400]  picked up in an archaeo's looking stone and saw that it represented the environment around it. I
+[3374.400 --> 3383.760]  mean, that's a thrill of a lifetime. Other kinds of maps, coastal escomones, again, this is pre-literate,
+[3383.760 --> 3391.920]  use these carved pieces of wood to negotiate the coastline of Greenland. The coastline is carved
+[3391.920 --> 3399.120]  into these pieces of wood. They're small, they fit inside a mitten. They're very cold.
+[3399.120 --> 3405.600]  They're in, it's cold area, they're explored tactically, manually. And if they fall in the water,
+[3405.600 --> 3414.720]  they float. Another kind of map, South Sea Islanders use these maps. The bambles tend to go in the ocean,
+[3415.680 --> 3423.520]  the open ocean, thousands of miles with the help of stars and training. The bambles strips are
+[3423.520 --> 3430.560]  the ocean currents. You can recognize them by the flotsam and jetsam on the surface of the sea.
+[3431.760 --> 3438.080]  The currents are like the highways of the ocean. They're the paths that take you easily from
+[3438.160 --> 3446.320]  Island to Island. The islands are indicated by those shells. And you can't see one island from the
+[3446.320 --> 3455.520]  other. So it must have been pretty scary getting in a boat, going on the open ocean to an unseen
+[3455.520 --> 3466.880]  place. At least some of them came home. So again, this is a valley in Italy, but we know that has
+[3466.880 --> 3472.960]  many of these petroglyphs. This is a drawing of a petroglyph. Again, you can see two perspectives
+[3472.960 --> 3482.160]  going back 4,000 years. These sorts of petroglyphs are again inscribed in rocks all over the world.
+[3483.120 --> 3490.080]  Another way of indicating a map is holding up your hand. And in North Coast Indians in the United
+[3490.080 --> 3499.600]  States use this to show the locations of various cities around them. So we have maps. We also have
+[3500.240 --> 3507.840]  ancient representations of time. This looks like a stampede. It's from Shovekave going back
+[3509.200 --> 3518.400]  33,000 years. There are even older cave drawings. I think there were some found 40, 45,000 years now
+[3518.880 --> 3526.400]  in Sulawesi in Indonesia, which are quite depicting animals. They're again quite beautiful.
+[3526.960 --> 3533.760]  This is from the United States. It's called newspaper rock petroglyphs that told the news of the day,
+[3534.480 --> 3542.800]  events. So again, we have a stampede. We have people with bozden arrows. This could be anywhere.
+[3543.360 --> 3548.000]  The same sort of drawings could be found anywhere in the world.
+[3550.400 --> 3558.240]  More on time events. This is making bread, Egyptian tomb, far later in civilization,
+[3558.240 --> 3566.720]  but it's showing step by step from sewing wheat to baking the loaves. And it's in a tomb.
+[3567.040 --> 3578.080]  This is particularly exciting. This is a petroglyph that was found in Kashmir. It goes back
+[3578.080 --> 3585.440]  4,000 years. And you see on the left the pet the stone on the right, the drawing from the stone.
+[3585.440 --> 3591.680]  You can see a man with the bow and arrow, a horned creature, and another man pointing upwards.
+[3592.160 --> 3600.400]  And he's pointing upwards to what looks like two sons. So an astronomer, an Indian astronomer
+[3601.360 --> 3611.280]  determined that from the age of the rock, which could be determined, that that 4,000 years ago,
+[3611.280 --> 3619.040]  then there was a supernova. So again, can you imagine the excitement of seeing a supernova in
+[3619.440 --> 3627.200]  the brightness of day, two sons suddenly. And that single event was striking enough that it was
+[3627.200 --> 3636.000]  inscribed in a stone. So we've got space, we've got time, more time, more time calendars,
+[3636.640 --> 3644.640]  sometimes circular, sometimes tabular. We find people representing time on lines, again,
+[3644.640 --> 3654.480]  a longer story. So we have space, time, number. These again go back, these are a stone,
+[3656.400 --> 3664.640]  also unbones, some sort of tally, we don't know what for, going back 70 to 100,000 years,
+[3664.640 --> 3671.440]  but tallys again are found all over the world. They're very primitive representations of number,
+[3672.160 --> 3680.480]  one to one correspondences, which is what babies get quite early. And number names and number symbols
+[3680.480 --> 3689.440]  took a long time for civilization to develop. And there are still cultures that thrive today with no
+[3689.440 --> 3697.680]  number words. And I asked, how will they answer if you asked them how many children they have?
+[3697.680 --> 3704.080]  And I was told they would give the list of names of their children. They don't use their hands,
+[3704.800 --> 3714.400]  and they don't count, past three. Okay, more tallys, other ways of representing number, we just use
+[3714.400 --> 3719.840]  our fingers, but they're the cultures that use other parts of their body can come far,
+[3720.560 --> 3729.600]  higher with their body than we can. Eboncuses, so ancient graphics show people animals things,
+[3730.160 --> 3740.240]  they show place and space, they show time and events, they show number. And there are, for many of
+[3740.240 --> 3748.880]  these, dedicated places in the brain for representing these things, so in certainly names, not for numbers,
+[3748.880 --> 3757.760]  but one to one correspondences. So that these are important things than our lives. And in fact,
+[3757.760 --> 3766.160]  if you look at contemporary newspapers and so forth, the graphics will be often people,
+[3767.280 --> 3775.200]  things, animals, place, space, time, events, and number. So ancient graphics are quite similar
+[3775.280 --> 3786.160]  to modern ones. So clear graphics are great for clear thinking and clear guidance,
+[3786.160 --> 3794.080]  messy for discovery. So this is actually clear for discovery, but was used for inference,
+[3794.080 --> 3802.720]  the cholera epidemic in the early 1800s in London before the germ theory of disease,
+[3802.720 --> 3810.560]  and the city official John Snow asked people to make a map of the cholera cases,
+[3810.560 --> 3817.360]  the cluster around the Broad Street pump, and he said without knowing anything about how
+[3817.360 --> 3826.480]  disease is transmitted, but on a hunch, had them remove the handle from the pump and the epidemic
+[3826.720 --> 3835.760]  updated. It would be wonderful if COVID had been so easily. Special patterns of forward conceptual
+[3835.760 --> 3844.000]  inferences archaeologists can use site maps to infer the organization of society was at hierarchical,
+[3844.880 --> 3851.360]  are there big houses and small houses, are there special purpose houses or just dwellings,
+[3851.360 --> 3857.840]  so they can tell a great deal about the society, the culture, the economics just from the spatial
+[3858.400 --> 3867.200]  patterns. This is another set of inferences World War II. There were bombers going from England
+[3868.160 --> 3875.360]  to bomb sites in Germany, some were coming back, some were not coming back. The question,
+[3875.360 --> 3880.720]  there was a bit of money to reinforce the bombers, so where do you reinforce?
+[3881.520 --> 3891.440]  And people make a diagram with a landmark for the bombers that returned, so that's the one on
+[3891.440 --> 3898.880]  the right, and where you reinforce in those white places where the bombers didn't return.
+[3899.840 --> 3904.400]  Okay, and of course that's where the pilot and the co-pilot were.
+[3906.880 --> 3915.200]  Here are some cases that are more concerned with art and design where ambiguity is important.
+[3915.200 --> 3923.760]  You don't want clear diagrams or architects don't want clear diagrams of what they're designing.
+[3923.760 --> 3932.640]  They don't like CAD-CAM programs because they make everything to order. Instead they make sketches,
+[3933.200 --> 3939.040]  and their sketches, they look at their sketches, they make the sketches for one reason,
+[3939.040 --> 3943.760]  they look at their sketches, and they get new ideas from the sketches.
+[3944.560 --> 3951.360]  So beginning architects can see this pattern here and say that I can use that triangle,
+[3951.360 --> 3958.640]  elongated triangles, a motif, and I can use it repeatedly. They didn't intend them,
+[3958.640 --> 3966.080]  but they see it when they look, but it's in the diagram. And novices can see things in the
+[3966.080 --> 3973.600]  diagram, whether they're musicians or chess players, they can see things that are in the diagram,
+[3973.600 --> 3981.040]  seeing things that aren't in the diagram, extrapolating from a takes expertise in music and chess,
+[3981.040 --> 3986.720]  and in design. So experienced architects can see that traffic is going to be a mess,
+[3986.720 --> 3993.680]  or they can see the light is going to fall badly in the winter. But it's ambiguity that allows
+[3993.680 --> 4001.680]  the re-interpretation. Again, we've brought that into the lab. So it promotes creativity.
+[4002.400 --> 4012.640]  It works in artists, in artists who is does beautiful work, did a dissertation partly with me,
+[4012.640 --> 4019.600]  studying other artists whose practice is growing. She studied a great many of them,
+[4019.600 --> 4025.840]  and again, videotaped them as they drew and asked what they were thinking about afterward.
+[4025.840 --> 4033.600]  She also coded how they drew, which turned out to be extremely interesting in terms of style,
+[4034.240 --> 4042.720]  and characterizing each of them. But the artists say they explore. It's a safe place to explore.
+[4042.720 --> 4049.520]  They deliberately make mistakes, and they make discoveries. They draw for one instance,
+[4050.240 --> 4057.360]  they see other things. They say the sketch talks to me. The ideas emerge from the page.
+[4058.400 --> 4065.840]  They talk about it as a conversation between the eye, the hand, and the page. If they talk,
+[4065.840 --> 4073.680]  it interferes. Language gets in the way. This is extremely intelligent, but non-verbal.
+[4073.760 --> 4080.240]  And I think musicians will say the same architects say the same. They're having this kind of
+[4080.240 --> 4087.040]  conversation between what their hands do, or what their mouth does if they're playing clarinet,
+[4088.240 --> 4096.880]  and what they create in the world, and then back again, and that guides their creativity.
+[4097.040 --> 4105.440]  Okay, this is the world as nature gave us, minus the concrete. This is the world that we create.
+[4106.640 --> 4113.040]  We make order in the world. We make categories, hierarchies, and orders. In our bookshelves,
+[4113.040 --> 4120.640]  we line up books by size or topic. The same thing happens in a supermarket. We put things in
+[4120.640 --> 4130.240]  categories and some categories on our shelves. We also organize by themes. And we can see that
+[4130.240 --> 4137.120]  in our houses. We put everything that has to do with cooking and eating in the kitchen. They come
+[4137.120 --> 4143.840]  from different categories. I'm not finding the kitchen. I guess that's the kitchen.
+[4145.120 --> 4150.400]  Everything to do with cleaning in the bathroom, again, coming from different categories,
+[4150.720 --> 4158.240]  for leisure in the living room, again, different categories. So we also organize by themes around
+[4158.240 --> 4168.800]  things that areas or that serve the same function. So other ways we put our mind in the world. We
+[4168.800 --> 4175.840]  make one-to-one correspondences, repetition cycles, embeddings in our place settings.
+[4176.480 --> 4183.680]  In our buildings, we have a balcony for each room and each apartment. And then presumably each
+[4183.680 --> 4193.440]  apartment has the same set of things in it. We do these organizations of rows and columns and
+[4193.440 --> 4201.280]  categories and themes in the three-dimensional world. And imagine, I mean, just think how
+[4201.360 --> 4208.880]  different our world is from the world of our hunter-gather ancestors. For most of the world was
+[4208.880 --> 4216.640]  the world that nature gave us and not the world we designed. And how much the design world communicates
+[4216.640 --> 4224.720]  to us tells us what kind of building this is, how to find our way within a building, what a set
+[4224.720 --> 4232.240]  table means as opposed to a pile of dishes somewhere and so forth. So babies growing up in this
+[4232.240 --> 4241.200]  design world receive a great deal of intelligence from this design world. We then use the designs that
+[4241.200 --> 4251.200]  we create deliberately to create diagrams like the periodic table, time tables, bar graphs. This
+[4251.280 --> 4258.080]  is the likelihood of a computer issue being solved by reconfiguring, re-imaging, antivirus,
+[4258.080 --> 4266.960]  uninstalling, or turning it on and off. And this is how long it took me to draw and color each of
+[4266.960 --> 4276.640]  these bars. So if we use those organizations to organize knowledge and communicate deliberately.
+[4277.200 --> 4286.960]  So I developed a term. It's a Latinate word and Latinate words in English are ugly. Sorry for
+[4286.960 --> 4293.680]  that. If someone comes up with a better one, I'll be really happy. It's a contraction of spaced
+[4293.680 --> 4302.480]  action and abstraction. And the concept is the actions in space create abstractions. The actions
+[4302.480 --> 4311.120]  on objects in space could turn into gestures on thoughts in our mind. And the abstractions that we
+[4311.120 --> 4318.480]  create in space, the rows and columns, and one-to-one correspondences, could turn into diagrams that we
+[4318.480 --> 4326.560]  use to communicate abstractions. And then we go one step further. We diagram the world.
+[4327.280 --> 4335.520]  So this is an airport from the top. It says where the service trucks can go, where the buses
+[4335.520 --> 4342.400]  carrying people can go, where the planes can go, where they must stop. Every inch of the of the
+[4342.400 --> 4350.640]  ground of an airport is diagrammed. And it controls the behavior of all the things moving on it.
+[4351.600 --> 4359.280]  And we're not allowed there. We would mess everything up. But we are allowed here. And again,
+[4359.280 --> 4365.920]  our world is diagrammed. It tells where bikes can go, where buses can go, where cars can go,
+[4365.920 --> 4372.640]  what direction cars can go, where they can park, where they must stop, when they must go,
+[4372.640 --> 4379.520]  where they can turn, where they can't turn, where people can walk, and so forth. And these are
+[4379.600 --> 4388.640]  there to enable behavior and to control behavior, organize our behavior. So we'd not only design the
+[4388.640 --> 4399.680]  world, we've diagrammed it. And that's my end. And I'm open for questions or comments and
+[4400.320 --> 4405.840]  apologies for throwing too much at you. So I think I'll stop sharing.
+[4406.240 --> 4415.040]  Yes, many thanks Barbara. That was fascinating. It was a very broad overview. So indeed taking the
+[4415.040 --> 4422.560]  overview point of view for that part. So please, any questions, any comments? Raise your hands.
+[4423.040 --> 4426.240]  Okay, see some run of virtual applause. Of course, very well deserved.
+[4426.880 --> 4429.440]  I'm going to make the counter here.
+[4434.800 --> 4444.480]  You're muted, I think. Can you hear me? No, no. Yes. Okay. So Peter, you have your hand.
+[4445.200 --> 4455.760]  Please go ahead. Yeah, hi, Barbara. It was a bit of a overlap between our talks.
+[4455.760 --> 4462.080]  We're talking about. Yeah, that's very interesting. I don't have a question, but I have two comments.
+[4462.800 --> 4468.960]  The one person's this use of gesture in describing the function of an engine. I found that extremely
+[4468.960 --> 4476.560]  interesting. Yeah. So there was people functioned much better when you use the action action gestures.
+[4476.560 --> 4483.360]  And for me, that's the case of a pantomime. I mean, you are using your body to mimic the forces of
+[4483.760 --> 4490.480]  what's going on in the engine. And to me, that's very interesting because the forces are
+[4490.480 --> 4495.280]  a rather abstract, but you can use your hands. And that fits very nicely with my description of
+[4495.280 --> 4501.920]  how we understand verbs. So this kind of pantomime, the forces, I mean, that's my definition of
+[4502.960 --> 4510.000]  of a pantomime really helps people. And for me, pantomime is a very good instrument in teaching.
+[4510.000 --> 4515.440]  It was very nice to see that you find so big differences between using a pantomime and not using
+[4515.440 --> 4522.720]  a pantomime. So that's my first comment. My second comment is you gave it this very nice
+[4523.600 --> 4530.800]  outline or overview of all kinds of old pictures, all kinds of old diagrams. And then you summarize
+[4530.800 --> 4537.360]  it by saying that we show people elements and things. We show places. We show time and events.
+[4537.360 --> 4545.760]  We show numbers. And this maps very nicely on to work on basic categories in children that's been
+[4545.760 --> 4554.560]  done by Elizabeth Spelken and Susan Carey. They talk about objects, places, actions and numbers as
+[4554.560 --> 4559.600]  the basic categories. And it's so nice to see that there's a parallel between the categories
+[4559.600 --> 4565.760]  of a child and the categories that you find in these old drawings. I found that really amazing.
+[4566.320 --> 4568.800]  So these are just two comments and no question.
+[4570.160 --> 4580.720]  Okay, I think I'll respond. Susan Carey and Ms. Spelken are talk a lot. So yeah, it's no accident.
+[4580.720 --> 4591.120]  But I think we got to those core ideas a bit separately and then Liz did then. But who knows,
+[4591.200 --> 4599.200]  ideas echo and and reverberate and and are in the air. There's a side case.
+[4600.560 --> 4607.360]  Yes. And it is for pantomime. The gestures go beyond that. I mean, I'll agree with you on pantomime.
+[4607.360 --> 4614.720]  And our mutual friend, Herb Clark, has written a great deal of that again, great minds and all of that.
+[4615.360 --> 4622.880]  But gestures do far more than pantomime. They really have their own logic, strings of gestures,
+[4622.880 --> 4630.880]  tell a story, and they're right. So we've looked at people describing from memory spaces and the
+[4630.880 --> 4639.440]  gestures and we could find 21, 30 gestures in a row that are diagramming a space and putting things
+[4640.080 --> 4645.840]  in it. So they're creating a diagram as well, which is is an abstraction of an environment.
+[4646.880 --> 4654.160]  Gestures can set up spatial schemas in a way that's hard for language. So I can say in the one hand
+[4654.160 --> 4662.240]  on the other and then or set up arguments. You know, this person said this and this person said that.
+[4662.320 --> 4671.840]  Then I can pile up their their arguments in the separate spaces because I've created those spaces.
+[4671.840 --> 4680.960]  I can create a line and put things on a line. So I can do a great deal with gestures in structuring
+[4680.960 --> 4687.200]  thought and structuring a space and indicating actions. And I do it in a direct way.
+[4688.080 --> 4697.040]  And it's much harder to do that in language to set up these general spatial schemas.
+[4697.040 --> 4706.240]  Set up a hierarchy. People have studied how non-literate people describe their familiar
+[4706.240 --> 4714.480]  relations and they set up a family tree with their hands and describe the generations by going
+[4714.480 --> 4723.520]  back and forth. So gestures can do a really rich set of conceptual communication.
+[4724.400 --> 4729.200]  I totally agree with that. My point was that the difference in the two conditions you had was
+[4729.200 --> 4734.240]  whether you used action, action gestures or not. I mean, there are lots of others action, but just
+[4734.240 --> 4739.840]  the action gestures helped in understanding the function of the of the engine because you
+[4739.840 --> 4745.920]  represented the forces by the by the actions. That was my only point. Of course, there are all kinds
+[4745.920 --> 4753.440]  of other gestures. Forces or things go in a circle or they move down here in the car break.
+[4754.320 --> 4761.040]  Right. They can they write. Absolutely. And we've done other studies and other people have too
+[4761.040 --> 4769.440]  that when students learn complex systems, it's the action that's hard. The even low spatial people
+[4769.440 --> 4779.360]  and half the world is low spatial. It can get the spatial structure, but getting the the action is hard.
+[4781.920 --> 4786.800]  Okay, I see other questions. Do you want to call on people or should I?
+[4786.800 --> 4790.400]  No, I can give them way. I'm worried. I think I'll meet guys next.
+[4791.600 --> 4792.000]  Okay.
+[4792.400 --> 4799.600]  Hey, hey, thanks. I really loved listening to all these different connections and things.
+[4800.240 --> 4806.560]  I have one comment and then a question. So my comment real briefly is just that I once went to a
+[4806.560 --> 4813.600]  dance performance that was about people's connection across space and time, like relationships and
+[4813.680 --> 4822.720]  memory and how we can can sometimes be together and then also apart but still be connected through
+[4823.840 --> 4828.800]  through our experiences that we had together. And I just remember having this visceral
+[4828.800 --> 4835.600]  realization of how effectively the like the gestural communication of the dance along with the
+[4835.600 --> 4841.840]  music communicated things that I really can't even articulate, but that I felt that I understood.
+[4842.080 --> 4849.760]  It was just really a moving experience. So that's my comment. And then my question is I'm just
+[4849.760 --> 4858.880]  curious to hear a little more about how you think of or what you've observed about how people
+[4859.440 --> 4868.320]  understand scale and size and like maybe some cultural aspects of that or things that are more
+[4869.200 --> 4874.880]  embodied in our experience as humans. I'd love to hear more about that if you have any thoughts.
+[4876.480 --> 4882.880]  Thank you for the questions and the comments. Can you give me a pointer to the dance? Sounds great.
+[4884.000 --> 4887.520]  I'll try to remember. It was a long time ago. I'll try to find it.
+[4887.520 --> 4896.400]  Yeah, no, that's... And dancing is another one of those highly intelligent, nonverbal
+[4897.200 --> 4904.400]  activity where dancers are communicating with each other and with you, right, in very expressive
+[4904.400 --> 4912.400]  ways, acting too. Size and scale are complicated and it's not something I've studied directly,
+[4912.400 --> 4924.560]  but I know if you know the aims, what's it called, their scale visualization, you can find it on
+[4924.560 --> 4933.520]  the web. It's nearly a hundred years old of looking at scales from the microstoplet to the
+[4934.480 --> 4943.920]  enormous and trying to get people to understand it, but that's having people understand scale.
+[4943.920 --> 4951.280]  Either very small or very large is not easy and I know people in science work on it and I don't
+[4951.280 --> 4960.080]  think there are any easy tricks on that, but there are ways of conveying it. Cultural, the only
+[4960.160 --> 4968.400]  cultural difference is a story and that somebody was... This is a story probably true, maybe not,
+[4968.400 --> 4976.640]  of being in Africa years ago and teaching tribal chiefs about mosquitoes and malaria and that you
+[4976.640 --> 4985.120]  had to be careful of mosquitoes because they could transmit malaria and the diagram of the mosquito
+[4985.120 --> 4993.520]  showed a highly enlarged mosquito with all the parts and where the mosquito drew blood and infected
+[4993.520 --> 5001.040]  the person the mosquito was drawing blood from and the story is that after leaving that the tribal
+[5001.040 --> 5006.640]  chief said, well, maybe in America your mosquitoes are like this, but here they're like this.
+[5007.440 --> 5017.120]  And there I think size does deceive and I think it's deceive science forever, scientists study big things
+[5018.240 --> 5027.680]  and the assumption is big things are important and little things can't be important because they're
+[5027.680 --> 5035.280]  little. They don't exercise much force. So I think if a philosopher or science went through the study
+[5035.360 --> 5045.760]  of many different sciences and what was studied first, it would be big things and little things get...
+[5045.760 --> 5053.200]  I mean, some things are too liver to be seen so that being able to see makes the difference, but
+[5053.200 --> 5058.640]  I think size, we make this inference that if it's bigger, it must be important.
+[5058.880 --> 5066.240]  Yeah, that's really what I was curious if you saw it that way too because I see it that way and I
+[5067.600 --> 5073.120]  think about that I wonder where that comes from and what we're missing out on
+[5074.400 --> 5082.080]  by carrying that assumption around. Yeah, it's a great topic to study.
+[5082.720 --> 5086.000]  All right, thanks, Mika. Max.
+[5089.120 --> 5094.960]  I think you're beauty. Yes, hello. I hope you're... Yes.
+[5096.400 --> 5101.280]  So yes, this was very, very, very fascinating and I think it's particularly interesting for a
+[5101.280 --> 5106.800]  multidisciplinary group like this because figures have become the little franca of multidisciplinary
+[5106.800 --> 5113.520]  research. So drawing thinkers in the tradition of, you know, livenants and other people are sort of,
+[5114.400 --> 5120.880]  you know, sort of a kind of common crowd, it was kind of interface, but what I particularly liked
+[5120.880 --> 5129.520]  about your talk was this separation of diagramming and gesturing because one thing we do a lot is
+[5129.520 --> 5134.800]  like, you know, we talk about data positivization, we try to learn network diagrams, diagramming
+[5134.880 --> 5143.360]  and whatever, but as people in practice tacitly, it's a no-text book. We will encounter gesturing,
+[5143.360 --> 5149.280]  like when we draw by hand and there is two challenges I think which are seem to me
+[5149.280 --> 5156.240]  to brag me as the same challenge and I would love to hear your opinion of where this comes from.
+[5156.240 --> 5161.120]  So you said ambiguity is something architects like these kind of drawings. Now one of the
+[5161.120 --> 5173.760]  interesting thing is this is not the next one. Sorry, I mean, random is one of the hardest things
+[5173.760 --> 5179.200]  one can do. So you need to train for really long times to actually move your hand in a sort of
+[5179.680 --> 5185.840]  random way that is not just, you know, some suggest you would make casually because you will have
+[5185.840 --> 5191.200]  a style. And now this is, you know, in music, the source of uncertainty and electronic music
+[5191.200 --> 5197.440]  would be similar. Then on the other hand, to draw a circle with a brush has the exact same problem.
+[5198.240 --> 5203.440]  Now the interesting thing is a circle, you know, is a two-dimensional thing, but if you have a
+[5203.440 --> 5208.800]  brush, two dimensions is not enough because as you do this, you're, you're a brushable curl and
+[5208.800 --> 5213.600]  stuff like that. That the artist Mario Klingerman a couple of weeks ago actually when he tried to
+[5213.600 --> 5219.600]  teach us AI robot to draw a circle with a brush, he said, I had to get the quaternions up because
+[5219.600 --> 5225.280]  he had to sort of like make these things. So the weird thing is even the simplest most control
+[5225.280 --> 5233.440]  things in gesture need sort of a more complicated math than the resulting figure. And getting out of
+[5233.440 --> 5241.120]  that, out of the control is equally hard. And so my question is, is there something, why is
+[5241.120 --> 5247.360]  gestures so good? Why is sense of motoric action so good to understand the world? Is there
+[5247.360 --> 5253.840]  something that goes beyond the representation that Peter Gerdinford and you sort of like focused
+[5253.840 --> 5259.760]  on other than gestures? So is there something in gesture that is a gap in neural science and
+[5259.760 --> 5268.880]  cognitive science that we should really focus on? So you asked a bunch of questions in your comments,
+[5268.880 --> 5277.680]  and I'm not sure I can address all of them. In my mind it's a bit of a mystery why the gestures
+[5277.680 --> 5286.000]  that we make help our own thinking? Because there are movements of the body. And the moments of
+[5286.000 --> 5293.120]  the body correspond our conglue and to our thinking. They're modeling what we're thinking about.
+[5294.080 --> 5301.520]  So they're creating another channel other than say a diagram or a verbal description for
+[5302.640 --> 5309.360]  understanding. So we know that having more than one channel, more than one kind of representation
+[5309.360 --> 5319.920]  helps memory and thinking. But it's still a bit of a mystery to me why the spatial motor actions
+[5319.920 --> 5327.520]  that are representing, they're not doing anything, they're representing some information again in
+[5327.520 --> 5336.720]  this, in the way that language represents. And it's, I suppose you could say the same thing about
+[5336.720 --> 5345.360]  language. Why does describing how something a process happens? Why does that help our thinking
+[5345.360 --> 5353.120]  about the process? And there we could say well the thinking preceded it, but so suppose we're
+[5353.120 --> 5361.120]  reading about a process and understanding it. How does that understanding happen? I don't think we
+[5361.120 --> 5372.480]  really know how that understanding happens even from reading. And so it just is more familiar.
+[5372.880 --> 5380.240]  Understanding things from either from reading or from somebody's explanation of it. It's a
+[5380.240 --> 5387.280]  little less familiar realizing that we understand from gestures. But I think it's a bit of a mystery.
+[5387.280 --> 5395.760]  How language can lead to understanding? And suddenly how this spatial motor can lead to understanding?
+[5395.760 --> 5402.400]  I don't know if Peter has or if somebody doing brain has some ideas on that.
+[5402.400 --> 5410.480]  Can I just continue on this? I mean, you mentioned that architects don't like CAD and CAM programs
+[5410.480 --> 5415.680]  because they give too much detail. What's an architect that's what they rectify?
+[5417.200 --> 5422.640]  They're rectified. But also in a sketch you can eliminate all the irrelevant things. You can focus
+[5422.640 --> 5428.000]  on what's the important part of the thinking and the designing and so on. And I would say that
+[5428.000 --> 5433.520]  the similar thing happens with gesture. A gesture is also eliminating a lot of things happening
+[5433.520 --> 5438.080]  in the event or something. You're abstracting away and this abstracting away
+[5438.800 --> 5444.480]  hatred on focusing on the most relevant things. I think that's the common thing between a sketch
+[5444.480 --> 5449.840]  and a gesture that it's an abstraction that brings out the most important parts of the information
+[5449.840 --> 5456.480]  you want to think about. No, no, that's a point I've made many times and a brief with
+[5456.480 --> 5464.880]  and gestures necessarily abstract even more than drawings. But I think the question was a little
+[5464.880 --> 5475.760]  deeper than that. But maybe Max, you have more thoughts. Maybe I can put it in another sentence.
+[5475.760 --> 5480.080]  Could it be that the gesture itself is a deeper understanding than whatever you do with the
+[5480.080 --> 5485.520]  gesture? In other words, like Gajarichta said painting can only be understood by more painting or
+[5485.520 --> 5490.480]  a ballet dancer doing a pirouette. The perfect understanding of a pirouette is being capable of
+[5490.480 --> 5495.920]  doing a pirouette. And you can write down whatever you want. It will never be a pirouette.
+[5495.920 --> 5501.840]  So the question is, if there is something like should we record gestures?
+[5502.000 --> 5508.000]  No, it's not. Because there are really good representations, not only representations, but
+[5508.480 --> 5513.280]  if they are sort of easily repeatable, they are understanding. I don't know whatever the
+[5513.280 --> 5522.080]  description links in gestures. So the kind of... I'm going to agree with you. I'm just, you know,
+[5522.080 --> 5531.360]  I'm trained as a cognitive psychologist. So I need evidence that shows that. And we have
+[5531.360 --> 5538.960]  some. I mean, the idea that seeing action gestures gives people a far deeper understanding of
+[5538.960 --> 5549.600]  action. They've internalized it. But so that does give some evidence that gestures induce either
+[5549.600 --> 5554.960]  ones you make or ones you see induce a deeper understanding. But it doesn't show how.
+[5555.360 --> 5567.680]  But I think we don't know how language leads to good understanding either. So it's, or diagrams for
+[5567.680 --> 5574.160]  that manner. And what I like about diagrams and gestures is they communicate more directly.
+[5576.320 --> 5582.000]  You can write. Yeah. Right. Yeah. I think there's another
+[5582.000 --> 5587.760]  couple of questions. Yes. Yes. So thanks Max for that. Be now. I think you're next.
+[5589.440 --> 5598.240]  I hope you all can hear me. Yes. Okay. Thank you. That was really a wonderful presentation.
+[5599.200 --> 5608.160]  And there was too much for me to sort of grasp. So I just wanted to check with you, whether I
+[5608.160 --> 5616.000]  could probably sub of the very fundamental things correctly. Because I was wondering like you begin
+[5616.000 --> 5624.240]  by saying that all things must move to survive and things would move in space and things would
+[5624.240 --> 5630.720]  interaction. There will be interactions in space. And then there was a point when you mentioned
+[5631.440 --> 5639.360]  that the representations of things or space is distorted by perceptions and actions and
+[5640.320 --> 5650.080]  and I'm under the impression that the motion and the space or let me put it in there. I was
+[5650.080 --> 5655.200]  trying to understand the relation between the motion and the space. And I'm under the impression
+[5655.280 --> 5663.840]  that there is a space out there in which motion happens. And it is a representation of that space,
+[5663.840 --> 5673.840]  which is which probably is the elementary or the fundamentals of thought in that sense.
+[5674.800 --> 5677.120]  Did I get it correctly or I'm totally wrong?
+[5677.120 --> 5689.920]  Okay. I mean, what you say, if I understand what you said, it makes sense. But I didn't know
+[5689.920 --> 5702.560]  if there was a question there. The question is that, so the, is there a space out there?
+[5703.200 --> 5714.320]  And is there a separation which is a space between space and mind in that sense? Or the motion
+[5714.320 --> 5721.680]  happens in a space and that space has nothing to do. That space is a pre-existing space in which
+[5721.680 --> 5731.040]  the motion happens. And then the representations and interactions which gets generated through that
+[5731.040 --> 5736.400]  motion is what are distorted in our mind and then that that's what probably constitutes the thought.
+[5737.360 --> 5743.360]  Is that what you're trying to say? It's part of what I'm trying to say, but it's not just the
+[5743.360 --> 5752.320]  motion, it's the perception as well. Okay. It's both of those and people who study perception
+[5752.320 --> 5759.760]  and action in more details than I do. They study it directly. Talk about perception action coupling.
+[5760.480 --> 5770.720]  Okay. And it's an old literature. If you, if you have one kitten going in the circle in an
+[5770.720 --> 5777.040]  environment, carrying another kitten. So one kitten is moving and acting in that environment,
+[5777.040 --> 5783.280]  but the kitten whose passive who's just being carried, they develop different perceptions.
+[5783.280 --> 5789.120]  The action is needed for the perception, for the correct perception. So the kitten that
+[5789.120 --> 5801.520]  just sees doesn't get, it doesn't, it doesn't get as much new vision as the kitten that actually
+[5801.520 --> 5810.320]  moved in the environment. So perception and action are deeply coupled. I mean, we need perception
+[5810.320 --> 5821.200]  to move accurately, right? Yeah. Yeah. So they're deeply separate. And again, sorry for putting
+[5821.200 --> 5831.440]  so much on you. The initial slides showed a book I wrote that encompasses what I said in way more.
+[5832.400 --> 5843.760]  And so there's depth there in the book and it's cheap on Amazon. So I don't mind recommending it.
+[5843.760 --> 5850.480]  If it were one of those El Sivir publications that cost several hundred dollars. But this I think
+[5850.480 --> 5858.560]  is the last I looked at was 17. So it's not. Yeah, we have, we have, we have the link on our website. So
+[5858.560 --> 5864.000]  it's under under your talk. Yes. You can find it. I find it there. Indeed.
+[5865.760 --> 5873.200]  Thank you. And again, I don't think I breast all your questions, but that might take another talk.
+[5873.840 --> 5880.320]  Yes. Yeah. Most likely. I'd rather not thank you very much. Shea Heade.
+[5881.120 --> 5888.880]  Thank you very much for your very interesting presentation. I just wanted to go back. I'm sorry, my
+[5888.880 --> 5896.880]  voices got a terrible flu. So very bad voice. Sorry about that. I just wanted to go back to the
+[5896.880 --> 5904.080]  discussion on gesture. And everyone was portraying gesture as always being good. And I wanted to give
+[5904.080 --> 5912.320]  an example of how gesture can go wrong. My field is mass education. And this was from research
+[5912.320 --> 5918.960]  project. We a teacher was trying to teach a children the concept of halving. And what she did
+[5918.960 --> 5926.400]  was she had dots on a page and they were spaced apart if you can can think about the domino in
+[5926.400 --> 5933.200]  the way in which dots are spaced on the domino. And then she was explaining halving by cutting
+[5933.200 --> 5939.440]  through the piece of paper. And she went through several of these. So the half of two is one,
+[5939.440 --> 5946.400]  the half of four is two. And then she gave the child the number two, the symbol two. And the child
+[5946.400 --> 5954.000]  picked up the the scissor and cut the two in half. So that was a case where gesture was giving the
+[5954.000 --> 5962.880]  incorrect information about what halving entailed. So thank you for the example. You know,
+[5962.880 --> 5970.240]  there are good ways of explaining and poor ways of explaining. There are good textbooks that
+[5970.240 --> 5978.080]  explain well and ones that are unreadable or overly complicated. And the same goes for diagrams
+[5978.080 --> 5990.240]  and gestures. There are effective ones and less effective ones. And you pointed to one that's
+[5990.240 --> 5999.760]  ineffective and maybe came from the teacher's own misunderstanding. I can't tell from without
+[5999.760 --> 6009.280]  seeing it in more detail. But sure, they're going to... I'm the whole gestures are quite informative
+[6009.280 --> 6018.480]  above speech. Because speech articulating speech, explaining processes, explaining what things
+[6018.480 --> 6025.600]  look like, explaining giving directions can often be very hard to put in words. So there are...
+[6026.560 --> 6034.080]  Some nice cases come from looking at children. This is work of Susan Golden Metal. So she studied
+[6034.080 --> 6043.600]  children who are on the cost of understanding conservation. So there is fat glass and a tall
+[6043.600 --> 6053.200]  thin glass and there is water in each of them. And the kids are asked, is it the same amount of
+[6053.200 --> 6060.320]  water or not? And very young kids are fooled by the perception of the height of the water or the
+[6060.320 --> 6067.200]  width of the water. But children who are just in the verge of saying the same, the water is the
+[6067.280 --> 6076.000]  same because they've seen it pour or it can't explain why it's the same or they say it's different.
+[6076.000 --> 6083.280]  But they do a pouring action. And when they do that pouring action, which indicates that they
+[6083.280 --> 6090.240]  understood conservation that the amount of water can't be changed by pouring it from one container
+[6090.720 --> 6096.720]  to another. Even though they can't explain it in words and say it's different quantities,
+[6096.720 --> 6102.160]  because this is... they hear the water is higher. But if they do this within a couple of weeks,
+[6102.160 --> 6113.440]  they're going to get conservation. So they have a rudimentary idea, a concept that they're
+[6113.520 --> 6122.080]  exhibiting in their gesture, but they can't articulate in words. And again because that
+[6123.360 --> 6133.360]  operation of pouring is closely connected to what conservation means, but saying it in words
+[6133.360 --> 6141.120]  is much harder for child. So the similar thing happens with giving directions. People often say
+[6141.200 --> 6149.440]  right, but they point left and you should go the way they point. Okay, the gestures more likely to
+[6149.440 --> 6161.600]  be correct than the words. But sure, they're condemning gestures and just as they're condemning words,
+[6162.240 --> 6169.360]  gestures that indicate lack of understanding, just as words can indicate lack of understanding.
+[6169.840 --> 6175.680]  So thank you for pointing that out. Right, thanks very much to Sehita for your question.
+[6176.240 --> 6180.320]  So I'll give you a couple more minutes to think of questions. I have one. I don't want to miss
+[6180.320 --> 6186.160]  the opportunity to ask. So you did mention arrows in your studies and counting arrows in drawings
+[6186.160 --> 6189.760]  and things like that. So as the representative mathematician in the audience, I guess,
+[6190.480 --> 6194.960]  obviously we use arrows in all manners of ways. And in fact, in very important ways,
+[6194.960 --> 6199.280]  they are very deeply ingrained in the formalisms that we actually use every day.
+[6201.440 --> 6205.440]  It's likely that at some point category theory would be mentioned and it's theory about arrows,
+[6205.440 --> 6210.480]  everything is an arrow and we do operations with arrows. And indeed, the power of this theory is
+[6210.480 --> 6217.680]  the fact that you draw drawings that are just immediately graspable. I mean, you just ride your
+[6217.680 --> 6221.840]  statement in a diagram that effectively, I mean, if you've never seen it, you've never heard the
+[6221.840 --> 6226.160]  terrible category theory. Basically, you have a graph with arrows. You have letters and arrows
+[6226.160 --> 6230.720]  between the letters. That's the most typical. Maybe there are couple of symbols between the letters
+[6230.720 --> 6235.280]  sometimes, but mostly is a set of letters, sort of a field of letters in a page and then arrows
+[6235.280 --> 6240.800]  between them. That's basically, and some diehard category theory fans would say that all mathematics
+[6240.800 --> 6244.880]  is encoded in that way. I am more reluctant to say that it's just arrows. I think they're missing
+[6244.880 --> 6249.920]  higher order structure, but certainly arrows are extremely, extremely prevalent in mathematics.
+[6249.920 --> 6256.160]  So I'm very curious. So I wanted to ask a couple of things. One is that, do you think there is
+[6256.160 --> 6262.560]  a reason that arrows have become, I mean, arguably the symbol of an arrow comes from the actual
+[6262.560 --> 6268.160]  arrow that we use to hunt, I guess. But do you think there's a reason why this symbol, in particular,
+[6268.160 --> 6275.360]  is, you know, especially relevant or especially evocative to humans? And the other question,
+[6275.360 --> 6280.720]  and then maybe we can advertise the talk on Thursday from currently over, Manantan Winn,
+[6280.720 --> 6286.160]  about the origins of this spatial representations, which is, what do you think are the prehistoric
+[6286.160 --> 6289.920]  origins of such a thing? But I think first is the question of, do you think there's something
+[6289.920 --> 6293.200]  in the symbol itself that makes it particularly powerful?
+[6295.520 --> 6301.760]  Yeah, we actually have done a fair amount of work on arrows, not in the context of math,
+[6301.760 --> 6307.840]  but you see, if you look theoretically, I mean, we talk, I mentioned that we talk about points
+[6307.840 --> 6313.760]  and lines and boxes. I didn't include arrows this time, but I usually do.
+[6313.760 --> 6322.320]  Eros are asymmetric lines. So they indicate an asymmetric relationship. Eros have lots more
+[6322.320 --> 6330.640]  meanings, and I have a colleague who distinguished 107, but I think that's too many. I think
+[6330.640 --> 6339.920]  around 7 and 8 will do. And again, I have a big part of a talk on arrows and our work on arrows,
+[6339.920 --> 6347.600]  but they do indicate implication as in math. They an asymmetric relationship, they indicate
+[6347.600 --> 6358.080]  temple order, and they can then indicate causality. They can be used to indicate invisible forces,
+[6358.080 --> 6366.800]  like wind or gravity. So there are 7 or 8, I think, core uses of arrows. We studied them only
+[6366.800 --> 6374.640]  in prosthesis diagrams. So we presented people with diagrams of how a bike pump works or how
+[6374.640 --> 6383.840]  their pulley system goes, and we presented them either with arrows or without arrows. And we
+[6383.920 --> 6391.280]  asked people to interpret the diagrams. And when there are no arrows, people write us structural
+[6391.280 --> 6398.800]  descriptions. They tell us where the parts are in relationship to other parts. When we have arrows,
+[6398.800 --> 6405.440]  they give us a process from beginning to end. So they start at the beginning, it's a bike pump,
+[6405.440 --> 6412.880]  you push down, and the arrow goes into the cylinder and out the tube and then face the tire,
+[6412.880 --> 6422.320]  but they give us a step-by-step causal explanation just from the arrows. That arrow flips the
+[6422.320 --> 6429.120]  meaning of the diagram. And we did the opposite study. We call this empirical semantics,
+[6429.120 --> 6435.280]  and we've done it for bar graphs and line graphs, and we've done it for arrows, and for a number
+[6435.280 --> 6448.560]  of other visual symbols like them, sketch maps, where we ask people to produce a diagram from
+[6448.560 --> 6456.880]  a description, and then we also ask people to produce a description from a diagram. And if we get
+[6456.880 --> 6463.280]  the same thing back, it's like translating from Chinese to English and back to Chinese,
+[6464.240 --> 6472.640]  then we think the semantics are clear. So the arrows are just told you the descriptions
+[6472.640 --> 6480.080]  from the diagrams. We've also given people descriptions of either the structure of a carburet
+[6480.080 --> 6488.160]  or a bicycle pump or a police system, or the process and ask people to produce a diagram.
+[6488.880 --> 6495.520]  And if we give the process, we get arrows. And if we don't, if we give the structure, we don't get
+[6495.520 --> 6505.280]  arrows. So arrows change the meaning completely. Now, we did one study with four year olds and
+[6505.280 --> 6512.160]  arrows, and some of the different meanings like temporal or motion going up, going down, and our
+[6512.160 --> 6520.480]  four year olds, who were probably, they were upper middle class four year olds, not, and they
+[6520.480 --> 6527.760]  did grasp those meanings of arrows, but I don't know what would happen if you would go to a culture
+[6527.760 --> 6534.880]  that's never been in school. I do know maps can be produced by cultures that haven't been in
+[6534.880 --> 6547.520]  school, and they abstracted many of the ways that maps I showed you. But arrows, yeah. So on
+[6547.520 --> 6556.000]  math, I have a colleague who came from math into cognitive science, and what he and loves math,
+[6556.080 --> 6565.120]  and what he argues is that equations are stories, which I thought was a really sweet way of looking
+[6565.120 --> 6573.600]  at an equation. They're going from beginning to end, and they tell a story, and they tell a story
+[6573.600 --> 6579.920]  of functions or elements or whatever of something happening, and arrows are part of the story.
+[6580.400 --> 6588.320]  Yeah, I mean, yes please go. Your arrows are pretty much implications.
+[6592.720 --> 6597.520]  Yeah, and that's also so interested about arrows, because you pointed to what was my
+[6598.240 --> 6603.040]  focal interest of curiosity, which was the inevitability of arriving at something that looks like an
+[6603.040 --> 6609.760]  arrow, because obviously, if I mean, it'd be interesting to see, I mean, the asymmetric line,
+[6609.760 --> 6616.560]  or asymmetric segment, perhaps, is quite a unique shape. I mean, there are many degrees of freedom
+[6616.560 --> 6621.600]  to think of an asymmetric segment, because you can put a dot on the end or a point at the end of
+[6621.600 --> 6627.440]  like triangle in the end, but it doesn't really change that much. So yeah, it's very interesting.
+[6627.840 --> 6633.600]  I guess we can discuss this again on Thursday. We have the sort of cognitive archaeology
+[6633.600 --> 6638.640]  perspective on all these questions that I think it will tie very nicely with, especially the
+[6638.640 --> 6645.120]  latter part of your talk, when you describe the sort of extent of old evidence of spatial
+[6645.120 --> 6650.480]  thinking and representations. So let me say we have a couple more things to bow to arrows.
+[6650.480 --> 6650.880]  Yes please.
+[6650.880 --> 6659.200]  A Gumbrich looked at them at some point. They are really an art historian, and he couldn't
+[6659.200 --> 6668.000]  find examples of arrows before the 20th century. There are a few, and I have them, and the old
+[6668.000 --> 6674.240]  one or I have diagrams of them, the oldest ones indicated the direction of flows of a river,
+[6675.200 --> 6681.920]  or a water wheel. And I haven't found, but I don't know how to even search this systematically.
+[6682.400 --> 6690.960]  Examples older than that. What you have older than that are hands. So you have in ancient manuscripts
+[6690.960 --> 6700.320]  depictions of hands, not ancient, but because they're written, but say medieval manuscripts,
+[6700.320 --> 6706.800]  you'll find depictions of hands pointing at things. And when children are asked to invent
+[6706.800 --> 6716.240]  mathematical symbols, they use hands. They also use feet. And some use arrows, these are five and six
+[6716.240 --> 6724.720]  year olds. So hands do something pointing fingers and pointing in the world. Do some of what arrows
+[6725.440 --> 6732.720]  do. They point at something and they have that asymmetry. I mean we have arrows in the natural world,
+[6732.720 --> 6742.160]  in the form of the arrows that are shot in the air, but also in the form of rivers pointing
+[6742.160 --> 6751.520]  downward, of erosion in sand, and convergence in arrows. But I don't know if that led to depictions
+[6751.520 --> 6760.640]  of arrows. So it's really a bit of a mystery or unsolved problem of where when arrows first began
+[6760.640 --> 6769.440]  in, it would be mostly in Western or maybe even Eastern mathematics. From what I've looked at
+[6769.440 --> 6777.760]  in Chinese and Japanese diagrams, for the most part they're not abstract. In fact, Western diagrams
+[6777.760 --> 6789.360]  don't get abstract until the late 18th century. And that's a bit of a mystery, the age of enlightenment.
+[6790.400 --> 6799.840]  So a lot of mysteries left to be solved. Max, these are arrows as well. They're very short common.
+[6800.800 --> 6808.480]  Pointing is the most frequent static gesture in Baroque painting. And it's probably true
+[6808.480 --> 6813.440]  also for earlier paintings. And so probably has to do with fact that Gumbrich didn't have to write
+[6813.440 --> 6823.840]  corpus to check. So he had to borrow institute, but even that is limited. So I think there is this,
+[6823.840 --> 6832.720]  yeah. Beyond the hand at the side of the manuscript, which Tupaclis cut off here.
+[6836.000 --> 6844.240]  The pointing of individuals, Baroque painting is interesting because the people typically point
+[6844.240 --> 6852.480]  to something which might find other references. You can also see this, the chaffle of Sant'Arisa
+[6852.480 --> 6860.400]  of Bernini, the people of King of the, if you start looking at a person who's guided around.
+[6861.040 --> 6868.000]  And it has a very similar effect as if there were actual arrows. And so that is, I think, an interesting
+[6868.000 --> 6873.680]  thing because arrows early on probably would find on street signs and stuff like that. So there may
+[6873.680 --> 6882.320]  be something like that. So this pointing thing, as we should not flate the fact that we draw
+[6882.320 --> 6891.200]  line with a tip as that not being there as an absence of an arrow. There may just be a different
+[6891.200 --> 6898.640]  convention just like cross walls were denoted by an X, while barrel walls were denoted by a
+[6898.640 --> 6905.920]  semi-circle, which later on were interpreted as being a niche in a rectangular room. So there may
+[6906.080 --> 6912.880]  be different conventions for arrows and pointing is indeed probably the one. So yes, I mean, there are
+[6912.880 --> 6922.960]  arrows and paintings and manuscripts. And a baby's point before they speak and so pointing is an
+[6922.960 --> 6932.400]  early gesture to draw attention. And other babies will look where you're pointing. Monkeys won't,
+[6932.400 --> 6937.680]  don't guerrillas won't, guerrillas point, but other guerrillas don't look where they're
+[6937.680 --> 6945.520]  pointing. And we can point not just with our hands or fingers in some situations pointing is in
+[6945.520 --> 6953.040]  polite. It's the we but we can point with our eyes. So if we're at a party and we want to go and
+[6953.840 --> 6960.960]  or significant other, we signal the significant other by pointing with our eyes toward the door
+[6960.960 --> 6973.280]  and hoping no one else will see. So yeah, and when people are counting, they need to point and if
+[6973.280 --> 6981.120]  you make seven tie their hands behind the back, they point with their eyes or their head. So there
+[6981.920 --> 6990.800]  humans have no worse ways of pointing. Okay, thanks for those comments on ours. I'm particularly
+[6990.800 --> 6996.080]  interested. So there was one final question I think a comment on the chat. I think,
+[6996.720 --> 7001.760]  Shahida was asking for the reference on the equations of stories of narratives.
+[7002.720 --> 7012.160]  I think it's David Landy, but it would take me quite a bit of time to find it. Sure. I think
+[7012.160 --> 7019.040]  the name good. Yeah, and I see Francine has said that the guerrillas don't point, but chimpanzees and
+[7019.040 --> 7026.800]  binobles do. I'm not sure that Tomasello doesn't have evidence about guerrillas, but the point is
+[7027.040 --> 7036.640]  that the point is that other come species don't look and dogs are an interesting case because they
+[7036.640 --> 7044.800]  co-evolved with humans and do all kinds of things that other species that aren't interacting that
+[7044.800 --> 7056.160]  much with humans do. The recent work on dogs is fascinating. So anything else? Yeah, and the
+[7057.200 --> 7063.920]  equation is David Landy and it would really take me a long time. Yes, I think the name will be
+[7063.920 --> 7071.360]  enough. Much more than it wasn't just something he said. Yes, yes. All right, so I think that's
+[7071.840 --> 7079.360]  a good point to end our first day of speciality. I would like to thank Barbara and Peter so much
+[7079.360 --> 7086.320]  for their contributions. I think they were an excellent starting point for the mood of the week.
+[7086.320 --> 7091.200]  And I hope to see many of you during the possible times that you can make it because I know
+[7091.200 --> 7097.040]  everyone has a busy schedule, but we'll be looking forward to that. We reminded of the different
+[7097.040 --> 7101.600]  social spaces on Discord if you want to continue with the conversations. As you saw on the emails,
+[7101.600 --> 7108.800]  I want to bore you more. Thank you very much. I'll see you tomorrow. Thank you. Thank you. Goodbye.