2. John Doyle Control and Dynamical Systems Caltech

3. Research interests Complex networks applications –Ubiquitous, pervasive, embedded control, computing, and communication networks –Biological regulatory networks New mathematics and algorithms –robustness analysis –systematic design –multiscale physics

4. Collaborators and contributors (partial list) Biology: Csete,Yi, Borisuk, Bolouri, Kitano, Kurata, Khammash, El- Samad, … Alliance for Cellular Signaling: Gilman, Simon, Sternberg, Arkin,… HOT: Carlson, Zhou,… Theory: Lall, Parrilo, Paganini, Barahona, D’Andrea, … Web/Internet: Low, Effros, Zhu,Yu, Chandy, Willinger, … Turbulence: Bamieh, Dahleh, Gharib, Marsden, Bobba,… Physics: Mabuchi, Doherty, Marsden, Asimakapoulos,… Engineering CAD: Ortiz, Murray, Schroder, Burdick, Barr, … Disturbance ecology: Moritz, Carlson, Robert, … Power systems: Verghese, Lesieutre,… Finance: Primbs, Yamada, Giannelli,… …and casts of thousands…

5. Background reading online On website accessible from SFI talk abstract Papers with minimal math –HOT and power laws –Chemotaxis, Heat shock in E. Coli –Web & Internet traffic, protocols, future issues Thesis: Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization Recommended books –A course in Robust Control Theory, Dullerud and Paganini, Springer –Essentials of Robust Control, Zhou, Prentice-Hall –Cells, Embryos, and Evolution, Gerhart and Kirschner

6. + Regulatory Interactions Mass Transfer in Metabolism * Biochemical Network: E. Coli Metabolism * from: EcoCYC by Peter Karp From Adam Arkin Supplies Materials & Energy Supplies Materials & Energy Supplies Robustness Supplies Robustness Complexity  Robustness

7. Complexity Robustness

8. Transcription/ translation Microtubules Neurogenesis Angiogenesis Immune/pathogen Chemotaxis …. Regulatory feedback control An apparent paradox Component behavior seems to be gratuitously uncertain, yet the systems have robust performance. Mutation Selection Darwinian evolution uses selection on random mutations to create complexity.

9. Transcription/ translation Microtubules Neurogenesis Angiogenesis Immune/pathogen Chemotaxis …. Regulatory feedback control Such feedback strategies appear throughout biology (and advanced technology). Gerhart and Kirschner (correctly) emphasis that this “exploratory” behavior is ubiquitous in biology… …but claim it is rare in our machines. This is true of primitive, but not advanced, technologies. Robust control theory provides a clear explanation. Component behavior seems to be gratuitously uncertain, yet the systems have robust performance.

10. Overview Without extensive engineering theory and math, even reverse engineering complex engineering systems would be hopeless. (Let alone actual design.) Why should biology be much easier? With respect to robustness and complexity, there is too much theory, not too little.

11. Overview Two great abstractions of the 20 th Century: –Separate systems engineering into control, communications, and computing Theory Applications –Separate systems from physical substrate Facilitated massive, wildly successful, and explosive growth in both mathematical theory and technology… …but creating a new Tower of Babel where even the experts do not read papers or understand systems outside their subspecialty.

13. “Any sufficiently advanced technology is indistinguishable from magic.” Arthur C. Clarke

14. “Those who say do not know, those who know do not say.” Zen saying “Any sufficiently advanced technology is indistinguishable from magic.” Arthur C. Clarke

15. Today’s goal Introduce basic ideas about robustness and complexity Minimal math Hopefully familiar (but unconventional) example systems Caveat: the “real thing” is much more complicated Perhaps any such “story” is necessarily misleading Hopefully less misleading than existing popular accounts of complexity and robustness

16. Complexity and robustness Complexity phenotype : robust, yet fragile Complexity genotype: internally complicated New theoretical framework: HOT (Highly optimized tolerance, with Jean Carlson, Physics, UCSB) Applies to biological and technological systems –Pre-technology: simple tools –Primitive technologies use simple strategies to build fragile machines from precision parts. –Advanced technologies use complicated architectures to create robust systems from sloppy components… –… but are also vulnerable to cascading failures…

17. Robust, yet fragile phenotype Robust to large variations in environment and component parts (reliable, insensitive, resilient, evolvable, simple, scaleable, verifiable,...) Fragile, often catastrophically so, to cascading failures events (sensitive, brittle,...) Cascading failures can be initiated by small perturbations (Cryptic mutations,viruses and other infectious agents, exotic species, …) There is a tradeoff between –ideal or nominal performance (no uncertainty) –robust performance (with uncertainty) Greater “pheno-complexity”= more extreme robust, yet fragile

18. Robust, yet fragile phenotype Cascading failures can be initiated by small perturbations (Cryptic mutations,viruses and other infectious agents, exotic species, …) In many complex systems, the size of cascading failure events are often unrelated to the size of the initiating perturbations Fragility is interesting when it does not arise because of large perturbations, but catastrophic responses to small variations

19. Complicated genotype Robustness is achieved by building barriers to cascading failures This often requires complicated internal structure, hierarchies, self-dissimilarity, layers of feedback, signaling, regulation, computation, protocols,... Greater “geno-complexity” = more parts, more structure Molecular biology is about biological simplicity, what are the parts and how do they interact. If the complexity phenotypes and genotypes are linked, then robustness is the key to biological complexity. “Nominal function” may tell little.

20. Transcription/ translation Microtubules Neurogenesis Angiogenesis Immune/pathogen Chemotaxis …. Regulatory feedback control An apparent paradox Component behavior seems to be gratuitously uncertain, yet the systems have robust performance. Mutation Selection Darwinian evolution uses selection on random mutations to create complexity.

21. Temp environ Temp cell Folded Proteins Unfolded Proteins Aggregates Loss of Protein Function Network failure Death Cell

22. Temp environ Temp cell Folded Proteins Unfolded Proteins Aggregates Loss of Protein Function Network failure Death Cell How does the cell build “barriers” (in state space) to stop this cascading failure event?

23. Temp environ Folded Proteins Temp cell Insulate & Regulate Temp

24. environ Folded Proteins Temp cell Thermo- tax

25. Temp environ Temp cell Folded Proteins Unfolded Proteins Aggregates More robust ( Temp stable) proteins

26. Temp environ Temp cell Folded Proteins Unfolded Proteins Aggregates Key proteins can have multiple (allelic or paralogous) variants Allelic variants allow populations to adapt Regulated multiple gene loci allow individuals to adapt

27. -1/T 21 o Log of E. Coli Growth Rate 37 o 46 o Heat Shock Response 42 o

28. -1/T 21 o Log of E. Coli Growth Rate 37 o 42 o 46 o Robustness/performance tradeoff?

29. Temp environ Temp cell Folded Proteins Unfolded Proteins Refold denatured proteins Heat shock response involves complex feedback and feedforward control.

30. Alternative strategies Robust proteins –Temperature stability –Allelic variants –Paralogous isozymes Regulate temperature Thermotax Heat shock response –Up regulate chaperones and proteases –Refold or degraded denatured proteins Why does biology (and advanced technology) overwhelmingly opt for the complex control systems instead of just robust components?

31. E. Coli Heat Shock (with Kurata, El-Samad, Khammash, Yi) rpoHgene Transcription 32  mRNA hsp1hsp2 Transcription & Translation FtsH Lon DnaK GroL GroS Chaperones Proteases - - Translation 32  Heat stabilizes 32  Heat Outer Feedback Loop Local Loop Feedforward

32. Heater Thermostat

33. Added mass Moves the center of mass forward. Tail Moves the center of pressure aft. Thus stabilizing forward flight. At the expense of extra weight and drag.

34. For minimum weight & drag, (and other performance issues) eliminate fuselage and tail.

39. Why do we love building robust systems from highly uncertain and unstable components?

40. P - + Assumptions on components: Everything just numbers Uncertainty in P Higher gain = more uncertain

41. G - K + P - + Negative feedback

42. G - K + Results for y  (1/K )r: high gain low uncertainty d attenuated S = sensitivity function Design recipe: 1 >> K >> 1/G G >> 1/K >> 1 G maximally uncertain! K small, low uncertainty

43. Results for y  (1/K )r: high gain low uncertainty d attenuated Extensions to: Dynamics Multivariable Nonlinear Structured uncertainty All cost more computationally. G - K + Design recipe: 1 >> K >> 1/G G >> 1/K >> 1 G maximally uncertain! K small, low uncertainty

44. G - K Transcription/translation Microtubule formation Neurogenesis Angiogenesis Antibody production Chemotaxis …. Regulatory feedback control Uncertain high gain

45. Summary Primitive technologies build fragile systems from precision components. Advanced technologies build robust systems from sloppy components. There are many other examples of regulator strategies deliberately employing uncertain and stochastic components… …to create robust systems. High gain negative feedback is the most powerful mechanism, and also the most dangerous. In addition to the added complexity, what can go wrong?

46. G - K + F +

47. F + If y, d and F are just numbers: S = sensitivity function S measures disturbance rejection. It’s convenient to study ln(S).

48. ln(S) F F < 0 ln(S) < 0 attenuation F > 0 ln(S) > 0 amplification ln( |S| )

49. ln(S) F   ln(S)   extreme robustness extreme robustness F  1 ln(S)   extreme sensitivity extreme sensitivity F

50. Assume: 1. F (and S) random variables 2.Prob( F = -1 ) > 0 ln(S) F Increase F  = 1 F +

51. If these model physical processes, then d and y are signals and F is an operator. We can still define S(  = | Y(  /D(  | where E and D are the Fourier transforms of y and d. ( If F is linear, then S is independent of D.) Under assumptions that are consistent with F and d modeling physical systems (in particular, causality), it is possible to prove that: (Bode, ~1940) F +  log|S |  he amplification (F>0) must at least balance the attenuation (F<0).

52. log|S | ln|S| F Negative feedback  Positive feedback

53.  log|S | ln|S| F Negative feedback Robust  Positive feedback …yet fragile

54. Robustness of HOT systems Robust Fragile Robust (to known and designed-for uncertainties) Fragile (to unknown or rare perturbations) Uncertainties

55. Feedback and robustness Negative feedback is both the most powerful and most dangerous mechanism for robustness. It is everywhere in engineering, but appears hidden as long as it works. Biology seems to use it even more aggressively, but also uses other familiar engineering strategies: –Positive feedback to create switches (digital systems) –Protocol stacks –Feedforward control –Randomized strategies –Coding

56. Complexity Robustness

57. Current research So far, this is all undergraduate level material Current research involves lots of math not traditionally thought of as “applied” New theoretical connections between robustness, evolvability, and verifiability Beginnings of a more integrated theory of control, communications and computing Both biology and the future of ubiquitous, embedded networking will drive the development of new mathematics.

58. Robustness of HOT systems Robust Fragile Robust (to known and designed-for uncertainties) Fragile (to unknown or rare perturbations) Uncertainties

59. Robustness of HOT systems Robust Fragile ChessMeteors Humans Archaea

60. Robustness of HOT systems Robust Fragile ChessMeteors Humans Archaea Humans + machines? Machines

61. Robust Fragile Uncertainty Diseases of complexity Cancer Epidemics Viral infections Auto-immune disease

62. Robust Fragile Sources of uncertainty In a system –Environmental perturbations –Component variations In a model –Parameter variations –Unmodeled dynamics –Assumptions –Noise

63. Robust Fragile Sources of uncertainty 

64.  Typically NP hard. If true, there is always a short proof. Which may be hard to find.

65.  Typically coNP hard. More important problem. Short proofs may not exist. Fundamental asymmetries* Between P and NP Between NP and coNP Fundamental asymmetries* Between P and NP Between NP and coNP * Unless they’re the same…

66. Standard techniques include relaxations, Grobner bases, resultants, numerical homotopy, etc… Powerful new method based on real algebraic geometry and semidefinite programming (Parrilo, Shor, …) Nested series of polynomial time relaxations search for polynomial sized certificates Exhausts coNP (but no uniform bound) Relaxations have both computational and physical interpretations Beats gold standard algorithms (eg MAX CUT) handcrafted for special cases Completely changes the P/NP/coNP picture How do we prove that

67. Bacterial chemotaxis

68. Random walk Ligand MotionMotor Bacterial chemotaxis (Yi, Huang, Simon, Doyle)

69. Ligand Signal Transduction gradient Biased random walk MotionMotor

70. Signal Transduction Motor Ligand Motion High gain (cooperativity) “ultrasensitivity” References: Cluzel, Surette, Leibler

71. Signal Transduction Motor References: Cluzel, Surette, Leibler + Alon, Barkai, Bray, Simon, Spiro, Stock, Berg, …

72. +CH 3 R ATPADP P ~ flagellar motor Z Y P Y ~ P i B B ~ P P i CW -CH 3 ATP W A MCPs W A +ATT -ATT MCPs SLOW FAST ligand binding moto r

73. ATPADP P ~ flagellar motor Z Y P Y ~ P i CW ATP W A MCPs W A +ATT -ATT MCPs FAST ligand binding moto r Fast (ligand and phosphorylation)

74. 0123456 0 1 0123456 Time (seconds) No methylation Barkai, et al Short time Y p response Che Yp Ligand Extend run (more ligand)

75. +CH 3 R ATPADP P ~ B B ~ P P i -CH 3 ATP W A MCPs W A SLOW Slow (de-) methylation dynamics

76. +CH 3 R ATPADP P ~ flagellar motor Z Y P Y ~ P i B B ~ P P i CW -CH 3 ATP W A MCPs W A +ATT -ATT MCPs SLOW FAST ligand binding moto r

77. 01000200030004000500060007000 0 1 3 5 01000200030004000500060007000 Time (seconds) No methylation B-L Long time Yp response

78. No methylation Extend run (more ligand) Tumble (less ligand) Ligand

79. Biologists call this “perfect adaptation” Methylation produces “perfect adaptation” by integral feedback. Integral feedback is ubiquitous in both engineering systems and biological systems. Integral feedback is necessary for robust perfect adaptation.

80. Tumbling bias Signal Transduction Motor Perfect adaptation is necessary … ligand

81. Tumbling bias ligand Perfect adaptation is necessary … …to keep CheYp in the responsive range of the motor.

82. Fine tuned or robust ? Maybe just not the right question. Fine tuned for robustness… …with resource costs and new fragilities as the price.

83. + Regulatory Interactions Mass Transfer in Metabolism * Biochemical Network: E. Coli Metabolism * from: EcoCYC by Peter Karp From Adam Arkin Supplies Materials & Energy Supplies Materials & Energy Supplies Robustness Supplies Robustness Complexity  Robustness

84. What about ? Information & entropy Fractals & self-similarity Chaos Criticality and power laws Undecidability Fuzzy logic, neural nets, genetic algorithms Emergence Self-organization Complex adaptive systems New science of complexity Not really about complexity These concepts themselves are “robust, yet fragile” Powerful in their niche Brittle (break easily) when moved or extended Some are relevant to biology and engineering systems Comfortably reductionist Remarkably useful in getting published

85. Criticality and power laws Tuning 1-2 parameters  critical point In certain model systems (percolation, Ising, …) power laws and universality iff at criticality. Physics: power laws are suggestive of criticality Engineers/mathematicians have opposite interpretation: –Power laws arise from tuning and optimization. –Criticality is a very rare and extreme special case. –What if many parameters are optimized? –Are evolution and engineering design different? How? Which perspective has greater explanatory power for power laws in natural and man-made systems?

86. -6-5-4-3-2012 0 1 2 3 4 5 6 Size of events Frequency Decimated data Log (base 10) Forest fires 1000 km 2 (Malamud) WWW files Mbytes (Crovella) Data compression (Huffman) Los Alamos fire Cumulative

87. Size of events x vs. frequency log(size) log(probability) log(Prob > size) log(rank)

88. -6-5-4-3-2012 0 1 2 3 4 5 6 Size of events Frequency Fires Web files Codewords Cumulative Log (base 10) -1/2

89. The HOT view of power laws Engineers design (and evolution selects) for systems with certain typical properties: Optimized for average (mean) behavior Optimizing the mean often (but not always) yields high variance and heavy tails Power laws arise from heavy tails when there is enough aggregate data One symptom of “robust, yet fragile”

90. Source coding for data compression Based on frequencies of source word occurrences, Select code words. To minimize message length.

91. Shannon coding Ignore value of information, consider only “surprise” Compress average codeword length (over stochastic ensembles of source words rather than actual files) Constraint on codewords of unique decodability Equivalent to building barriers in a zero dimensional tree Optimal distribution (exponential) and optimal cost are: Data Compression

92. 012 0 1 2 3 4 5 6 DC Data How well does the model predict the data?

93. 012 0 1 2 3 4 5 6 DC Data + Model How well does the model predict the data? Not surprising, because the file was compressed using Shannon theory. Small discrepancy due to integer lengths.

94. Web layout as generalized “source coding” Keep parts of Shannon abstraction: –Minimize downloaded file size –Averaged over an ensemble of user access But add in feedback and topology, which completely breaks standard Shannon theory Logical and aesthetic structure determines topology Navigation involves dynamic user feedback Breaks standard theory, but extensions are possible Equivalent to building 0-dimensional barriers in a 1- dimensional tree of content

95. document split into N files to minimize download time A toy website model (= 1-d grid HOT design)

96. # links = # files split into N files to minimize download time

97. Forest fires dynamics Intensity Frequency Extent Weather Spark sources Flora and fauna Topography Soil type Climate/season

98. A HOT forest fire abstraction… Burnt regions are 2-d Fire suppression mechanisms must stop a 1-d front. Optimal strategies must tradeoff resources with risk.

99. Generalized “coding” problems Fires Web Data compression Optimizing d-1 dimensional cuts in d dimensional spaces… To minimize average size of files or fires, subject to resource constraint. Models of greatly varying detail all give a consistent story. Power laws have   1/d. Completely unlike criticality.

100. d = 0data compression d = 1web layout d = 2forest fires Theory

101. -6-5-4-3-2012 0 1 2 3 4 5 6 FF WWW DC Data

102. -6-5-4-3-2012 0 1 2 3 4 5 6 FF WWW DC Data + Model/Theory

103. Forest fires? Burnt regions are 2-d Fire suppression mechanisms must stop a 1-d front.

104. Forest fires? Geography could make d <2.

105. California geography: further irresponsible speculation Rugged terrain, mountains, deserts Fractal dimension d  1? Dry Santa Ana winds drive large (  1-d) fires

106. -6-5-4-3-2012 0 1 2 3 4 5 6 FF (national) d = 2 Data + HOT Model/Theory d = 1 California brushfires

107. -6-5-4-3-2012 0 1 2 3 4 5 6 Data + HOT+SOC d = 1 SOC FF d = 2  .15

108. Critical/SOC exponents are way off SOC  <.15 Data:  >.5

109. Forest Fires: An Example of Self-Organized Critical Behavior Bruce D. Malamud, Gleb Morein, Donald L. Turcotte 18 Sep 1998 4 data sets

110. 10 -2 10 10 0 1 2 3 4 0 1 2 SOC FF HOT FF d = 2 Additional 3 data sets

112. Fires 1991-1995 Fires 1930-1990

113. HOT SOC d=1 dd dd HOT  decreases with dimension. SOC  increases with dimension. SOC and HOT have very different power laws.

114. HOT yields compact events of nontrivial size. SOC has infinitesimal, fractal events. HOT SOC size infinitesimal large

115. HOT SOC HOTData Max event sizeInfinitesimalLarge Large event shapeFractalCompact Slope  SmallLarge Dimension d  d-1  1/d SOC and HOT are extremely different.

116. SOC HOT & Data Max event sizeInfinitesimal Large Large event shapeFractal Compact Slope  Small Large Dimension d  d-1  1/d SOC and HOT are extremely different. HOT SOC

117. yet fragile Robust Gaussian, Exponential Log(event sizes) Log(freq.) cumulative

118. Gaussian log(size) log(prob>size) Power laws are inevitable. Improved design, more resources

119. Power laws summary Power laws are ubiquitous HOT may be a unifying perspective for many Criticality, SOC is an interesting and extreme special case… … but very rare in the lab, and even much rarer still outside it. Viewing a complex system as HOT is just the beginning of study. The real work is in new Internet protocol design, forest fire suppression strategies, etc…

120. Universal network behavior? demand throughput Congestion induced “phase transition.” Similar for: Power grid? Freeway traffic? Gene regulation? Ecosystems? Finance?

121. Web/Internet? demand throughput Congestion induced “phase transition.” Power laws log(file size) log(P>)

122. random networks log(thru-put) log(demand) Networks Making a “random network:” Remove protocols –No IP routing –No TCP congestion control Broadcast everything  Many orders of magnitude slower Broadcast Network

123. Networks random networks real networks HOT log(thru-put) log(demand) Broadcast Network

124. HOT Turbulence flow pressure drop random pipes streamlined pipes

125. HOT turbulence? Robust, yet fragile? Through streamlined design High throughput Robust to bifurcation transition (Reynolds number) Yet fragile to small perturbations Which are irrelevant for more “generic” flows HOT flow pressure drop random pipes streamlined pipes

126. Shear flow turbulence summary Shear flows are ubiquitous and important HOT may be a unifying perspective Chaos is interesting, but may not be very important for many important flows Viewing a turbulent or transitioning flow as HOT is just the beginning of study

127. random designed HOT Yield, flow, … Densities, pressure,… The yield/density curve predicted using random ensembles is way off. Similar for: Power grid Freeway traffic Gene regulation Ecosystems Finance?

128. pipes channels wings Turbulence in shear flows Turbulence is the graveyard of theories. Hans Liepmann Caltech Kumar Bobba, Bassam Bamieh

129. Chaos and turbulence The orthodox view: Adjusting 1 parameter (Reynolds number) leads to a bifurcation cascade to chaos Turbulence transition is a bifurcation Turbulent flows are chaotic, intrinsically nonlinear There are certainly many situations where this view is useful.

130. velocity low high equilibrium periodic chaotic

131. pressure drop average flow speed “random” pipe

132. pressure (drop) flow (average speed) laminar turbulent bifurcation

133. Random pipes are like bluff bodies.

134. pressure flow Typical flow

135. pipes channels wings Streamline

136. log(pressure) log(flow) laminar turbulent “theory” experiment Random pipe streamlined pipe

137. log(Re) log(flow) Random pipe streamlined pipe

138. log(Re) Random pipe streamlined pipe It can be promoted (or delayed!) with tiny perturbations. This transition is extremely delicate (and controversial).

139. Transition to turbulence is promoted (occurs at lower speeds) by Surface roughness Inlet distortions Vibrations Thermodynamic fluctuations? Non-Newtonian effects?

140. None of which makes much difference for “random” pipes. Random pipe

141. Shark skin delays transition to turbulence

142. log(pressure) log(flow) water 80 ppm Guar It can be reduced with small amounts of polymers.

143. HOT turbulence? Robust, yet fragile? Through streamlined design High throughput Robust to bifurcation transition (Reynolds number) Yet fragile to small perturbations Which are irrelevant for more “generic” flows HOT flow pressure drop random pipes streamlined pipes

145. streamwise Couette flow

146. upflow high-speed region downflow low speed streaks From Kline

148. Streamwise constant perturbation Spanwise periodic

149. Streamwise constant perturbation Spanwise periodic

150. w v u flow velocity z y x flow position z y x flow position flow w v u velocity

151. z y x flow w v u velocity position

152. z y x flow w v u velocity position

153. 2d NS

154. 2d-3c model z y x flow position 2 dimensions w v u flow velocity 3 components

155. 2d-3c model These equations are globally stable! Laminar flow is global attractor.

156. t energy Total energy (Bamieh and Dahleh)

157. 02004006008001000 10 -10 10 -5 10 0 5 t energy energyN=10R=1000t=1000alpha=2 Total energy vortices

158. What you’ll see next. Log-log plot of time response.

159. Random initial conditions on concentrated at lower boundary.

160. Exponential decay. Long range correlation. Streamwise streaks.

161. HOT turbulence? Robust, yet fragile? Through streamlined design High throughput Robust to bifurcation transition (Reynolds number) Yet fragile to small perturbations Which are irrelevant for more “generic” flows HOT flow pressure drop random pipes streamlined pipes

162. Complexity, chaos and criticality The orthodox view: –Power laws suggest criticality –Turbulence is chaos HOT view: –Robust design often leads to power laws –Just one symptom of “robust, yet fragile” –Shear flow turbulence is noise amplification Other orthodoxies: –Dissipation, time irreversibility, ergodicity and mixing –Quantum to classical transitions –Quantum measurement and decoherence

163. Epilogue HOT may make little difference for explaining much of traditional physics lab experiments, So if you’re happy with orthodox treatments of power laws, turbulence, dissipation, quantum measurement, etc then you can ignore HOT. Otherwise, the differences between the orthodox and HOT views are large and profound, particularly for… Forward or reverse (eg biology) engineering complex, highly designed or evolved systems, But perhaps also, surprisingly, for some foundational problems in physics