Knowledge Creation through Multimodal Communication
Marcus Berliant and Masahisa Fujita
Washington University in St. Louis and Kyoto University
May 17, 2024
There are now   2 papers completed in this project:
 Dynamics of Knowledge Creation and Transfer: The Two Person Case
(Elementary, in International Journal of Economic Theory) Knowledge Creation as a Square Dance on the Hilbert Cube (Main, in theInternational Economic Review) The Dynamics of Knowledge Diversity and Economic Growth (Application, in
the Southern Economic Journal)
 Culture and Diversity in Knowledge Creation (Application with cites to religious
texts, Regional Science and Urban Economics)
 This paper
 AI paper? Now over 200 pages.
Copies of the papers are available, e.g. from my web page.
There will be lots of pictures today.

Expositional Note
The papers are long and have quite a bit of algebra in them. That is because
we prove everything analytically. This paper is 86 pages short.
 In contrast, it is easy to present this work quickly using only pictures, including
both the statement of results and idea of proofs. You just have to get the hangof it.
 There will be a minimum of notation and lots of pictures and hand waving.


Abstract from First Paper:

FACING
COUPLEBACK TOBACK DANCERSMINI-WAVE(LEFT HAND)

FACING COUPLESBACK TO BACK OCEAN WAVE
(RIGHT HAND)
COUPLESOCEAN WAVE(LEFT HAND)

RIGHT HAND BOX
CIRCULATELEFT HAND BOX
CIRCULATETWO FACE LINE
(RIGHT HAND) STATIC SQUARECIRCLESINGLE FILEPROMENADE

ALAMO STYLE

COUPLE 1

Source: http://www.penrod-sq-dancing.com/fasr1.html

What do you know about square dancing? It’s a metaphor...
 This was the abstract, until Masa decided that we had to get serious. (Me,serious?)
 I’m not Masa, so you will have to settle for second best.
 The first line describes the process of writing these papers.
Outline of this Talk
I. Motivation and related literature
II.
The model basics for all of the papers
Short Rest
III.
The Model with 2 persons in the stationary stateIV.
Effect of F2F lead time on the mode of communication and joint
knowledge productivity
V.
Knowledge composition, productivity, and choice of work mode
VI.
Dynamics of the two-person system
VII.
Summary, correcting inefficiencies, extensions
Don’t worry, each section is short!

Motivation and Related Literature
Motivation
Motivation: Questions About Knowledge Creation
How should the process of knowledge creation be modeled?
 How does the knowledge creation process function when there are multiple
ways for people to communicate, for example face to face or using theinternet?
 Relative to the one communication channel case, what different patterns ofjoint research among knowledge workers emerge, and how is the productivityof research work affected?
 Under what conditions are the conceptual and technical phases of knowledge
production best accomplished through each of the communication channels?


Motivation: Tacit Knowledge
When analyzing the dynamics of knowledge creation, as we do here, theconcept of tacit knowledge among the people creating new knowledge arisesorganically.
 As tacit knowledge is the part of knowledge that is not manifested in the final
product, readers will recognize it as what is learned by authors in the academic
research setting that is not explicitly embedded in a published paper, including
this one.
 What are the efficiency consequences of tacit knowledge?
 What kind of innovation policy is appropriate in the presence of tacitknowledge?
 Can artificial intelligence have tacit knowledge?
 To address these questions, we must first build a model that incorporates tacitknowledge.
 We are not aware of any formal models of either multimodal communication ortacit knowledge in the prior literature.
Essential Features:History matters, agents change
Too much in common → not enough originality, low productivity
Too little in common → communication difficult, low productivity
Endogenous Agent Heterogeneity - Horizontal

On the one hand:
Whether working alone or with others, a person’s accumulated knowledge basemight not be compatible with that of another person with whom they’ve had nocontact.
On the other hand:
If two people have been working together for a long time, their base ofknowledge in common increases, and their partnership eventually becomes lessproductive.
We investigate the permanent effects of knowledge creation and growth.

Useful Analogy
Working jointly to share ideas and create new onesPartner dancing(For now, 3 or 4 cannot dance together, though couples can dance
simultaneously.)
People can work or dance alone.

Macro Mode


↙↘




↙↘

↙↘

   ↓↓ ↓↓True Microfoundations(We Are Trying to Get Here)A Robot Economist?

Preview of the Results
Preview of the Results

Deterministic Framework

Our WorkMyopic Agents
 In contrast with our previous work, here we separate the knowledge creation
process into conceptual and technical phases, and allow researchers tochoose the mode of communication, F2F or the net, that suits them best ineach phase.
Preview: Modes of Communication

Figure 1. Knowledge creation through multiple modes of communication

Preview: Main Results
1. First, we find that a crucial parameter in the model is the lead time for F2F
communication. What we mean by lead time is the fixed cost forcommunicating F2F, such as the cost of commuting to the office.
2. Second, in contrast with our previous work, the steady state will not, ingeneral, be the state with highest productivity. The net effect is that
achieving and maintaining the highest productivity profile of knowledge incommon and differential knowledge requires more heterogeneity or larger
research groups than we found in our previous work.
3. Third, the effect of tacit knowledge on knowledge productivity is notinternalized by the knowledge workers.
4. Fourth, as net and transport technology improves, knowledge composition
becomes more important than geographical distance in the choice of
research partners.

Preview: Application to Covid Restrictions (Appendix A)
Applying this framework to pandemic restrictions, we show, for example, how
the productivity of knowledge workers with longer commutes to work is
affected less than those with shorter commutes when pandemic restrictions on
face to face work are implemented.
 This application requires the introduction of multimodal communication to ourmodel.


Related Literature
Related Literature
Covid, etc.
 See paper for literature review
 Part of our framework here is based on the insightful empirical paper by Lin etal (2022).
 They break down the knowledge creation process into conceptual andtechnical phases.
 The early conceptual phase involves tacit knowledge deployment, whereas thelater technical phase involves explicit knowledge.
 Using a large data set, they find that face to face communication is more
effective in the conceptual phase, whereas remote teams can be effective inthe technical phase.


The Model Basics for All of the Papers
The Basic Model - Previous Papers: What is an Idea?
This Paper

Recipe for Udon Noodles... 

Everyone can read the labels, but it takes time to learn the contents (it takes
no time to read the labels).
 Ideas are ordered (k) Time is continuous (  )

x ki t 

1 if person i knows idea k at time t
0 otherwise

Knowledge of person i at time t : K i t  x 1i t, x 2i t, . . .  ∈ 0, 1  (Specifies
set of ideas known by person i at time t.)

Knowledge Creation
Creation of new ideas alone - dancing alone: Opening a box not opened
previously by anyone.
 Joint creation of new ideas: Opening a box not opened previously by anyone
together. Becomes knowledge in common.
 All take time. Opportunity cost is time in this model.


The Hilbert Cube  0, 1 H where H  1, 2, 3, . . . 
So for all i, for all t, K i t is a vertex of the Hilbert cube.
For our analysis today, we treat ideas symmetrically, so we don’t need to know
K i t, but only some statistics about K i t:
 # of ideas known by i at t:

n i t  ∑ x ki tk1# of ideas known by both i and j at t:

n cij t ∑ x ki t  x kj tk1# of ideas known by i but not by j at t:
n dij t  n i t − n cij t

The 2 Person Model: ChoicesConsider 2 agents.
If either does not want to meet, then no meeting occurs.
If both want to meet, then there is a meeting. Myopic core.

Framework above is useful for explaining the model. What follows are the realassumptions. All rates are per unit of time: Individual Production:y i t  n i t  felicity New ideas created alone at t:
  n i t New ideas created jointly with a meeting at t:
1

n cij t  n dij t  n dji t 3Best  Even Split - % common ideas, % ideas exclusive to i, % ideas
exclusive to j. Overlap for communication, but agents are different.
Originality. Like Masa and Marcus, they know different stuff. Functional form
more general in many of the papers.



Agents are myopic. Their only choice is meeting or not. Choose option withhigher increase in rate of output:
dy/dt
max y
If tied:
dy/dt
max d
y
dt



The perfect foresight version of the model is difficult, but we have some resultswith it.



Divide all endogenous variables (“n”) by the total # of ideas (for both) to obtainnormalized variables “m”, interpreted as percentages.
m c  m dij  m dji  1Know m dij , m dji  know m c
We are now within  of having all the notation. Most everything else will bepictures.
   0  No meeting   1  Meeting

The Model with 2 Persons in the Stationary State
The Model with 2 Persons in the Stationary State

Figure 2. The activity tree for knowledge creation by person i in Isolation.

Figure 3. The activity tree for joint knowledge creation

The Structure of One Period - JOINT Work
Conceptual

Independent

Technical

Lead Time CF  Time spent in Conceptual work Face to face CN  Time spent in Conceptual work on the Net
 The two persons can jointly choose  CF and  CN freely, subject to the following
constraint:1   F    CF   CN  1,  CF ≥ 0,  CN ≥ 0
where  F  0 represents the lead time of joint thinking for conceptual
development F2F.
 In practice,  F reflects the time cost of preparing for a F2F meeting, such ascommuting time to the common CBD office (or common university), or travel
time between two cities or two countries where each of the two persons resideseparately.
 Lead time for Net is normalized to zero.
Lead Time

Face 2 Face

RemoteConceptual Sub-PeriodLead Time

Face 2 Face

RemoteTechnical Sub-Period
Workers can choose % mode of communication in each Sub-Period: F2F (atwork) and Remote (at home) Covid restrictions limit the sum total of F2F across Conceptual and Technicalsub-periods.


Effect of F2F lead time on the mode of communicationand joint knowledge productivity
Effect of F2F lead time on the mode of communication and joint
knowledge productivity
Assumption 1. In both the phase of conceptual development and the phase oftechnical development, thinking jointly F2F is more effective than thinking
jointly through the Net. Furthermore, the effectiveness of F2F relative to the
Net is greater in conceptual development than in technical development.
 This assumption is based on two ideas. First, tacit knowledge is bestdeveloped and exploited face to face. Nonaka and Takeuchi (1995) provide
case studies, including the invention of the first automatic home bakery
machine by Matsushita and the development of the City car model by Honda.
Both involved the exploitation of tacit knowledge. Second, empirical evidence
developed by Lin et al (2022) is consistent with this assumption.
Figure 4. The parameter value of F2F lead-time and the three ranges ofcommunication mode  F when  CF / CN  2 and  F / N  1. 5.

Figure 5. h F  is the relative productivity of joint work at  F in comparison with the
productivity of joint work at  F  0 over the three ranges of parameter  F .

No Net Technology
Figure 5 can be interpreted as representing the impact of the development of
net-communication technology, where the broken curve represents the relative
productivity at each  F when no net-technology is available, whereas the real
curve represents the relative productivity under the effective use of modern
net-technology.
 The case where no net-technology is available is studied by Inoue et al (2022),
since the internet didn’t exist during the Spanish flu epidemic.
 Without this substitute for F2F, the effect on knowledge creation was severe.
Figure 6. The impact of the advancement of net-technology on the relative
productivity curve

Knowledge composition, productivity, and choice ofwork mode
Knowledge composition, productivity, and choice of work mode
To understand stuff graphically, it’s useful to look at the symmetric states:
m dij  m dji  m d
Once symmetric, always symmetric.

Figure 7. The knowledge growth rate curve g J m d  and the Bliss Point m B .

Figure 8. Knowledge growth rate curves g J m d ;  F  for  F  0   F   CF , sharing thesame Bliss Point m B , and the share of differential knowledge for each of threepotential partners.

Dynamics of the two-person system
Dynamics of the two-person system̃  mB.
Figure 9. The dynamics of two-person system when m E  m

Tacit Knowledge
Next we shall define tacit knowledge and then explain how it arises in ourcontext. The the ideas behind “tacit knowledge” originate with Polanyi (1958).
Polanyi (1966, p.4) famously states, “We can know more than we can tell.”Tacit Knowledge“...we classify human knowledge into two kinds. One is explicit
knowledge, which can be articulated in formal language including
grammatical statements, mathematical expressions, specifications,manuals, and so forth. This kind of knowledge can be transmittedacross individuals formally and easily. This has been the dominantmode of knowledge in the Western philosophical tradition. However,
we shall argue, a more important type of knowledge is tacitknowledge, which is hard to articulate with formal language. It is
personal knowledge embedded in individual experience and involves
intangible factors such as personal belief, perspective, and the value
system. Tacit knowledge has been overlooked as a criticalcomponent of collective human behavior.” Nonaka and Takeuchi(1995, p. viii)

Figure 10. Dual dynamics of formal-K and total-K for the two-person system.

Inefficiency in Switch Point
The presence of tacit knowledge causes this.
 The difference between the two switching rules becomes clear when we
consider this situation in the context of the academic world.
 An evaluation committee always faces the difficult problem of how to evaluate
the contribution of each author when papers are written jointly.
 A simple, drastic rule would be that when a paper is written by 2 authors, thecontribution of each author just equals one half of the contribution of the paper.
Inefficiency in Switch Point
In the actual academic world, however, an evaluation committee tends toadopt a more generous rule.
 That is, if we consider efficient growth of the total knowledge of each (young)researcher in the long-run, when a paper is written by 2 persons, theevaluation committee is justified to allocate much more than one half of thepaper’s contribution to each author.
 That is because tacit knowledge accumulates during the knowledge
production process; such knowledge is invisible in the final product, namely the
paper itself.
Inefficiency in Sink Point
There is only one other potential partner, and the partners become too similar(m d is too small).
 This happens even if there is no tacit knowledge.
 Need a Square Dance.


Summary, correcting inefficiencies, extensions
Summary
Building on our earlier work, we have developed a model of knowledge
creation in the context of two persons when multiple modes of communication
are available, and knowledge workers can independently use the internet forthe purpose of search.
 Departing from our earlier model based on modeling knowledge creation as asingle activity, we have elaborated the entire process of joint knowledge
creation as an activity tree.
 It has been shown that with the advancement of net technology, joint
knowledge creation can be conducted over a wide range of geographical area
without losing much productivity.
 Tacit knowledge, missing from earlier models, plays a huge role in our
analysis of the dynamics of the system.


Correcting Inefficiencies
2 sources of inefficiency in the model Efficient growth of total knowledge requires that the switch from working in
isolation to joint work should occur much earlier, where the growth rate of total
knowledge per person in joint work is equal to the growth rate of total
knowledge in isolated work.
 To remedy the inefficiency caused by a myopic switching rule based on percapita output of patent production, a public agent may subsidize a significant
portion of the revenue from patent-sales.


Correcting Inefficiencies
Second, a more interesting and more important inefficiency is that the growthrate of formal-K at the sink point is significantly lower than at the Bliss Point.
 When the research partners are in a low-productivity sink point trap, what
possible mechanism could enable the partners to escape from this trap andattain much higher productivity?
 Answer: A modified square danceExtensions


It is our hope, more generally, that the model of knowledge creation throughmultimodal communication developed in this paper can be extended andapplied in a broader context such as efficient development of international

academic societies in the age of rapidly developing ICT and AI.
 It would be of interest to allow other forms of agent heterogeneity, such aslarge and small city residents, or CBD and suburban residents.
 Intergenerational transmission of knowledge and improvements in internet
search productivity due to the increasing stock of knowledge over time should
be investigated.
 To sum up, there is much further work to be done to analyze themicroeconomic dynamics of knowledge creation in settings with tacitknowledge and multiple modes of communication.