https://www.menimagerie.com/manuscripts daily 0.75 2020-04-22 https://www.menimagerie.com/manuscripts/2018/6/7/the-final-metaphor monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528558438758-TE8L7B5NYZ3SMZSU9JF7/couple2.png The Manuscripts - The Final Metaphor https://www.menimagerie.com/manuscripts/2018/6/9/a-tantalising-possibility monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528559725137-GF97WCJBSJIK2UNB6YIW/tetris.PNG The Manuscripts - A Tantalising Possibility https://www.menimagerie.com/manuscripts/2018/6/9/the-poet-inside-all-of-us monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528557952045-37TKCRB0JL38FYM2LLUQ/MetaphorIllustration.jpg The Manuscripts - The Poet Inside All of Us https://www.menimagerie.com/manuscripts/2018/6/9/from-hierarchies-to-networks monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528559284087-JTTYS6XSQ95VZVNIUKA0/image-asset.png The Manuscripts - From Hierarchies to Networks https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528559215003-GSP5VI2CT1UQU5JGWQEI/image-asset.png The Manuscripts - From Hierarchies to Networks https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528559246046-H1OGOTXKK8KGLVGDKSO2/combinatorics.png The Manuscripts - From Hierarchies to Networks https://www.menimagerie.com/manuscripts/2018/6/9/the-redundant-scientometrician monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528556422056-C476N3AZTI9G07LSM4I9/scientometrician.png The Manuscripts - The Redundant Scientometrician https://www.menimagerie.com/manuscripts/2018/6/8/xiii-the-different-statistical-approaches monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528498767966-6W44ITSGCWO8ITLM20K6/image-asset.png The Manuscripts - XIII. The Different Statistical Approaches https://www.menimagerie.com/manuscripts/2018/6/8/xii-the-neyman-pearson-approach monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528497535605-OATCGB1ZBHGT3L6B7PJB/power.png The Manuscripts - XII. The Neyman-Pearson Approach Two ways of visualizing power: as a function of effect size, or as the relative area of the values in the alternative hypothesis' probability distribution that would qualify as significant. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528498112048-1DSB29FE853VT25XGJ96/phacking.png The Manuscripts - XII. The Neyman-Pearson Approach Statistical methods for detecting publishing bias and "p-hacking". https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528497715840-N7OQN62RIESF3YEE2Z7P/stoppingrule.png The Manuscripts - XII. The Neyman-Pearson Approach https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528497152423-6QKOL24B8B58SR6WV0UR/twotailed.png The Manuscripts - XII. The Neyman-Pearson Approach How we allocate the alpha-level's "extreme percentage constituting improbability" is up to us - either in only on or both directions. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528497267351-VZWGFFST369J0EIZ30TA/fishingnet.png The Manuscripts - XII. The Neyman-Pearson Approach The cost-benefit analysis of setting alpha and beta-levels may be compared to deciding about the mesh-width of a fishing net, where you wish to catch any small fish. The bigger mesh (lower beta), the greater chance of catching small fish, and not mistakenly conclude that from no caught fish that no small fish exist (false negative). However, it also increases risk of bigger fish being caught (false positive), which you could reduce by having smaller width (lower alpha). If small and big fish differ more in size (larger effect size), choosing levels becomes easier, because small width would catch small fish, with less risk of false negatives. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528496989679-RYSDUC9YFOG9XXTB2LCY/referenceclass.png The Manuscripts - XII. The Neyman-Pearson Approach The "reference class" represents a category of potential replications of the experiment, in which everything except the influence of chance is identical. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528497443079-V2LHHB6RFJX8F7PRP1H4/baseratefallacy.png The Manuscripts - XII. The Neyman-Pearson Approach The alpha and beta levels don't tell us how many of our findings are likely to be false. To know this, we must have an estimate of the base rate (Bayesian prior) proportion of true effects versus true null effects. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528497815428-2JW5XV9USESQF2ATY319/dependenttest.png The Manuscripts - XII. The Neyman-Pearson Approach https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528497860492-9K7VYH89YK77JCLBC6YH/confidenceinterval.png The Manuscripts - XII. The Neyman-Pearson Approach Confidence intervals is a highly informative way of summarising the results, representing the range that 95% of the time will include the true population value. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528497610745-TBH082SHNP9P9DQ01WQN/truthinflation.png The Manuscripts - XII. The Neyman-Pearson Approach "Truth inflation" occurs when underpowered experiments report their obtained effect size as the mean effect size. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528497978257-D9OTGRVIM9FRWGNU2FW7/publicationbias.png The Manuscripts - XII. The Neyman-Pearson Approach Researchers' and journals' preference for significant results may make theories seem more promising than they are. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528497696375-TP0X68L8PTYKWCECPV4A/familywise.png The Manuscripts - XII. The Neyman-Pearson Approach https://www.menimagerie.com/manuscripts/2018/6/8/xi-the-likelihood-analysis-approach monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528496676132-IQCSRPRYP4CC8W26O466/likelihoodratio.png The Manuscripts - XI. The Likelihood Analysis Approach The likelihood ratio gives relative strength of evidence, which is conceptually separated from the probability of obtaining such evidence. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528496767130-MFR59J0T1CLTKRW4BH25/likelihoodinterval.png The Manuscripts - XI. The Likelihood Analysis Approach The likelihood interval is defined so that no value has strong evidence over another - the included values are more or less equal in their evidential support. https://www.menimagerie.com/manuscripts/2018/6/8/the-bayesian-approach monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528496112811-PQXHY4PJ35KIJJACB369/bayes.png The Manuscripts - X. The Bayesian Approach To apply Bayes' theorem to a simple within-subjects design, we first make a prior distribution where we associate each possible effect-size with the hypothesized probability. Then, from the likelihood (sample mean distribution) we simply multiply the corresponding probabilities. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528496395713-BV98QI75KL8O45PJ1A19/credibilityinterval.png The Manuscripts - X. The Bayesian Approach As you collect more data, the posterior will approach the "true" distribution, and consequently the interval will shrink in width (precision). You may thus use this as a stopping rule, running until it excludes the alternative hypothesis. https://www.menimagerie.com/manuscripts/2018/6/8/ix-the-knobs-of-the-normal-distribution monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528495830583-CKOO00SPVWN4FFAMAIIK/onesample.png The Manuscripts - IX. The Knobs of the Normal Distribution https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528493747650-G6IUDNK3S4NKQL9UBES1/medianmean.png The Manuscripts - IX. The Knobs of the Normal Distribution In the normal distribution the mode, the median and the mean are the same, but for approximations the mean is usually used, because it takes the most information into account. If the median is a fulcrum that balances the number of values on either side, the mean balances the number of total "value-units" on either side. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528495702038-DKFKMFICF9HXJRPQA9EZ/zscores.png The Manuscripts - IX. The Knobs of the Normal Distribution Standard (z) scores allow us to associate the range below/above a value on any normal distribution with a probability via a single table, by expressing them in terms of standard deviations from the mean. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528495622630-4CGULEWEVYFHOM5TA5IE/standarddeviation.png The Manuscripts - IX. The Knobs of the Normal Distribution Standard deviation is the width-parameter of the normal distribution and can be understood as "average deviation", but it is not strictly a mean deviation, since its formula gives disproportionate emphasis to large deviations. https://www.menimagerie.com/manuscripts/2018/6/8/viii-additive-effects-and-linear-relationships monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528492789076-6NFCAJ9C723JSZG71W45/linearsystem.png The Manuscripts - VIII. Additive Effects A linear relationship can be seen in how deviations from the mid-line are normally distributed: there is a central tendency for change in X to be associated with a proportionate change in Y. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528493022436-QABXMXFYYO2IJGI09R5N/powerlaw.png The Manuscripts - VIII. Additive Effects The normal distribution and the power distribution https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528493309887-P7WQSQKG28EMMKY7DO8Z/clt.png The Manuscripts - VIII. Additive Effects https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528492892267-DZDPXCJAGTEWWZT7K97H/linearoverrange.png The Manuscripts - VIII. Additive Effects Relationships are typically linear only over restricted ranges. For example, the number of potatoes on this kitchen scale is related to the number of degrees rotated by its arm... until it has gone full circle. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528493420897-OFKMTW06Q458OH6JEQSZ/quincunx.png The Manuscripts - VIII. Additive Effects The Quincunx physically realizes the binomial distribution. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528493183996-BI9CSTXPQ3IMWMFAUAKR/binomial.png The Manuscripts - VIII. Additive Effects The binomial formula gives the relative height of a specific quincunx-stack (i.e. its probability) by adding the probabilities of all the possible paths whose left-right combinations lands the ball in that stack. More generally, it gives the distribution of n independent, binary, equally biased, random events whose outcomes have an additive effect on each other, which is why, as n approaches infinity, it approximates the normal distribution so ubiquitous in Nature. https://www.menimagerie.com/manuscripts/2018/6/8/vii-the-contrived-counter-factual monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528492292162-IUC3PRING3I8ZZAQRRVJ/betweenwithin.png The Manuscripts - VII. The Contrived Counter-Factual https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528492203044-LR0RQNYC6WSMV6FLZE6Z/causal_structure.png The Manuscripts - VII. The Contrived Counter-Factual A scientist's task to chart the causal structure of a system through experimentation can be compared to that of understanding the workings of a complex contraption by identifying things that change in its state (e.g. sound) and linking it to parameters (the settings). https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528492385060-2QSJ981BJNIQZJ4RXG34/randomization.png The Manuscripts - VII. The Contrived Counter-Factual The members of a population differ along an indefinite number of variables. By choosing members randomly we - on average, without guarantees - preserve the relative frequencies of different states in the sample without ever specifying the variables. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528491999340-J82YFISFQ65UHJXVRKSZ/populations.png The Manuscripts - VII. The Contrived Counter-Factual The brain categorizes objects and events into "populations". Each member's state of the population may differ on an indefinite number of dimensions, or "variables". The distribution of variable states in the population determines a certain state's long-term frequency - in other words, its probability. By probing a subset of the population (a sample) we hope to estimate this probability. https://www.menimagerie.com/manuscripts/2018/6/8/vi-confirmatory-and-exploratory monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528491162230-LGX5Z0OKTOOG98G0BLQI/parallel-terraced-scan.jpg The Manuscripts - VI. Confirmatory and Exploratory "Parallel terraced scan" describes a positive feedback-mechanism believed to play a role in human perception, in which a space of possible hypotheses is explored in parallel, but resources are allocated in proportion to how promising each seems. https://www.menimagerie.com/manuscripts/2018/6/8/v-maximizing-falsifiability monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528490552669-W2K8BZ5F7L5K83YVCYKG/opticalfibre.png The Manuscripts - V. Maximizing Falsifiability Science is like an optical fibre - some kinds of feedback allow it to progress faster than others https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528490912754-VGPWX5I6GFCNCAKJPA1J/duham.png The Manuscripts - V. Maximizing Falsifiability The interpretation of data depends on a basis of other, often more corroborated theories. Therefore, a theory's track record matters for how easy it is to falsify. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528490637473-B1E982NTA82ZTOKDSSUR/falsifiability.png The Manuscripts - V. Maximizing Falsifiability The more data patterns a theory excludes, and the more diverse range of domains it makes predictions for, the more falsifiable it is. https://www.menimagerie.com/manuscripts/2018/6/8/confirmation-bias-in-terms-of-bayes monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528490210949-TPDO7BO4INO3YSLASOEW/wason.png The Manuscripts - IV. Confirmation Bias in Terms of Bayes In Wason's classical paradigm, participants only look for confirmatory evidence, which prevents them from noticing more general generating rules. https://www.menimagerie.com/manuscripts/2018/6/8/the-hypothesis-set monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528489146040-IH3FW2O82MTN2GONMKPH/BayesianScience.png The Manuscripts - III. The Hypothesis Set Science is analogous to Bayesian inference, in which both our a priori confidence in a theory and how well it fits new data influence our belief in it. For example, if we have three theories about the bias of a coin (either a 0.6, 0.5, or a 0.4 bias for heads) and we observe five heads in sequence, then Bayes' theorem tells us how we optimally revise our certainty that the coin has a 0.6 head bias. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528489363584-3GJA2BLKLC2S1QHLK6R8/god.png The Manuscripts - III. The Hypothesis Set Theological arguments that are covertly Bayesian depend on what hypotheses they entertain in their prior. Because of the degree of arbitrariness in this selection, quantitative reasoning may in this case be meaningless. https://www.menimagerie.com/manuscripts/2018/6/8/the-ill-defined-possibility-space monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528480818534-8Z7GGKBSSQW5KWTP0C2C/everett.png The Manuscripts - II. The Ill-defined Possibility Space According to Everett's many-worlds interpretation, quantum randomness appears non-deterministic because we only have access to one of all logically conceivable universes. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528481014902-59AC4ZHCAMSK5BAX6BM3/anthropic.png The Manuscripts - II. The Ill-defined Possibility Space The Weak Anthropic Principle states that when physicists find some property of cosmos that appears fine-tuned to support sapient life, they should regard this not as a marvellous coincidence, but as a necessity since - in the space of possible universes - only universes with these properties would be compatible with the physical himself! https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528488573048-AY4UX1HK6I74YW77YQC7/statespace.png The Manuscripts - II. The Ill-defined Possibility Space https://www.menimagerie.com/manuscripts/2018/6/8/surface-tension monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528488006715-J1LT1LAXUQRJTL3ADTFH/scientistonice.png The Manuscripts - I. The Self-modifying Filter https://www.menimagerie.com/manuscripts/2018/6/9/ix-science-as-information-processing monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528552056179-FQ56XTLXKLASQ2G4OJWR/newton2.png The Manuscripts - IX. Science as Information-Processing. https://www.menimagerie.com/manuscripts/2018/6/9/viii-bayes-and-brains monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528551688161-UFT2INFGJI2NODO4GE16/predictivecoding.png The Manuscripts - VIII. Bayes and Brains According to the "predictive coding" approach, the brain learns by implementing Bayesina inference, in which predictions about sensory state are continually revised to minimize the mis-match with actual data. Revisions cascade upwards an analytical hierarchy, and the best high-level hypothesis determines perceptual content. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528551794158-92L2RT57FI4O7D5LCTOW/parallel-terraced-scan.jpg The Manuscripts - VIII. Bayes and Brains "Parallel terraced scan" describes a positive feedback-mechanism believed to play a role in human perception, in which a space of possible hypotheses is explored in parallel, but resources are allocated in proportion to how promising each seems. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528551586216-V74XB8FAAKHD7U7WZWS1/conditional.png The Manuscripts - VIII. Bayes and Brains https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528551627120-FR20ZZLH3XXSKB1H31QQ/image-asset.png The Manuscripts - VIII. Bayes and Brains https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528551885885-069FUKAI7UKZU2R54F3A/biases.png The Manuscripts - VIII. Bayes and Brains The brain has two systems - one for conscious and another for unconscious processing. Inconsistencies between their versions of Bayesian reasoning sometimes lead to biases and maladaptive decision-making. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528551555951-V498IZR33W161GY8AS6Q/independent.png The Manuscripts - VIII. Bayes and Brains https://www.menimagerie.com/manuscripts/2018/6/9/vii-randomness-probability-compression-and-redundancy monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528551063760-7JLY46DMKFR15VJMAXLY/statespace.png The Manuscripts - VII. Randomness, Probability, Compression and Redundancy According to the "frequentist" interpretation, probability is an objective property of reality. A more modern interpretation is that it reflects the dynamical organization of the system behind the random variable. It may have attractors, where randomly selected initial conditions converge on the same outcome, leading to a high relative frequency and probability. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528551171301-VASA07WGY7A5YPK1GLG3/brownian.png The Manuscripts - VII. Randomness, Probability, Compression and Redundancy The Brownian motion of pollen grains is due to random collisions with water molecules that sometimes become lop-sided. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528551241528-74BWVQ07ZGZGGLK7RN3S/kolmogorov.png The Manuscripts - VII. Randomness, Probability, Compression and Redundancy Kolmogorov complexity defines complexity as the size of the computer program that outputs it. A highly ordered system, like an origami figure, can be similarly compressed into its folding instructions. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528551392034-5THXAWA7D9M3LWLKV88V/dynamic.png The Manuscripts - VII. Randomness, Probability, Compression and Redundancy https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528550978287-YA95F3M11VEQZOLXN3GC/snowball.png The Manuscripts - VII. Randomness, Probability, Compression and Redundancy Like a paper snowball, randomly generated sequences are incompressible, but do not vary in any meaningful way https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528551319242-CSSWNG7HFRS7OIXGE6JV/redundancies.png The Manuscripts - VII. Randomness, Probability, Compression and Redundancy Natural language has information redundancies that act like padding to prevent the signal from deteriorating in noisy conditions. https://www.menimagerie.com/manuscripts/2018/6/9/vi-thermodynamic-entropy monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528550572525-5FMPVYUHG4A168GZ45QA/maxwell.png The Manuscripts - VI. Thermodynamic Entropy Maxwell's demon is impossible, for sorting requires computation, and computation is physical work, which increases entropy. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528549441690-FH0HE257TOE45YNW1A0J/thermodynamic.png The Manuscripts - VI. Thermodynamic Entropy Thermodynamic entropy corresponds to a system's "invisible information" - the bits that describe its micro-states. https://www.menimagerie.com/manuscripts/2018/6/9/v-basic-information-theory monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528549117979-AF2S1IQ0CSP4XJ8Z2BTA/differentinformation.png The Manuscripts - V. Basic Information Theory Confusion arises around the concept of information when we forget what system we refer to: the physical medium ("syntactic"), the recipient's understanding ("semantic"), or how it affects his decision-making ("pragmatic"). The latter ones are much harder to quantify. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528548942988-ZQROQJUHWN0GERZWVX1Z/gibson.png The Manuscripts - V. Basic Information Theory Time to collision may be simply estimated based on how fast the image of an object is expanding. According to Gibson's ecological approach, organisms are tuned to such invariant relations. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528549029354-6ZF6XKD65045Q58UWO12/bits.png The Manuscripts - V. Basic Information Theory For each independent physical distinction with two equiprobable micro-states, or "bit", the number of possible macro-states is multiplied by 2. The number of bits defines the information content. https://www.menimagerie.com/manuscripts/2018/6/9/iv-a-patchwork-of-metaphor monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528548257326-GHMJQTC87DWLM9G5U0XL/complicity.png The Manuscripts - IV. A Patchwork of Metaphor The dynamic of the Universe is nearly decomposable into systems. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528548335237-FB5NNYA4QZ641IOO52KV/homeostasis.png The Manuscripts - IV. A Patchwork of Metaphor Homeostasis may be compared to a tray of water that, in order to be stable on average, uses cues to predict future disturbances, so as to take pre-emptive actions that offset them. The system is therefore in constant non-equilibrium. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528548421154-7ZHQQLYVZV3NSH8SKDGL/categories.png The Manuscripts - IV. A Patchwork of Metaphor Categories are meaningful, for distinguishing between them has consequences for a system's survival. https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528548120791-NKFGPYEZS6RDHNLSG38Q/scientificmetaphor.png The Manuscripts - IV. A Patchwork of Metaphor Patchworks of scientific metaphor, asymptotically approaching reality by allowing us to comprehend abstract relations through comparison with concrete ones. https://www.menimagerie.com/manuscripts/2018/6/9/iii-umwelts-affordances-and-measurements monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528547613487-QJ7NZ6E3OUQ6S4BLVXT0/measurement.jpg The Manuscripts - III. Umwelts, Affordances and Measurements https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528547422943-YTR7Q1BXCX4VSVXFXAKV/holonfiltering.jpg The Manuscripts - III. Umwelts, Affordances and Measurements https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528547353593-R0PSLSBJ011JOEM5BH42/categoriesbystructure.jpg The Manuscripts - III. Umwelts, Affordances and Measurements https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528547541299-SQP0TVUFKA9EVV85MS17/catvisualattention.jpg The Manuscripts - III. Umwelts, Affordances and Measurements https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528547497382-LVEQ9O7G1FXQZ0Y3JAYK/basiclevelcategories-2.jpg The Manuscripts - III. Umwelts, Affordances and Measurements https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528547684827-DYGQ6XO823HAKV3JFMIS/statistics.jpg The Manuscripts - III. Umwelts, Affordances and Measurements https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528547741712-B9YOTBQ6WFKOTLI61ULR/grainandextent.jpg The Manuscripts - III. Umwelts, Affordances and Measurements https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528547281412-2D0QL9LEAJ21CA12VSY1/umwelt.png The Manuscripts - III. Umwelts, Affordances and Measurements https://www.menimagerie.com/manuscripts/2018/6/9/ii-back-to-hierarchy-theory monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528547052649-E65QL35HI7RCCLWP4PWG/non-nested.jpg The Manuscripts - II. Back to Hierarchy Theory Non-nested hierarchies https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528546832518-OKY2561USNID7IYD8MJ4/signal-boundary.jpg The Manuscripts - II. Back to Hierarchy Theory Signal-boundary hierarchy https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528546755593-RLE5CGTJWR1MT8Y6SJL7/hierarchy.jpg The Manuscripts - II. Back to Hierarchy Theory https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528546997010-PT9YXXXP9HHNJJ5WKC9M/nested.jpg The Manuscripts - II. Back to Hierarchy Theory Nested hierarchies https://www.menimagerie.com/manuscripts/2018/6/9/what-english-gardens-know-about-education monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528562988590-1KW9J1SNBRU3BRLWVOPT/hindsightbias.jpg The Manuscripts - What English Gardens Know About Education https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528562944358-NWQYKBUXOLMKYXNY8EUK/bottomupapproah.jpg The Manuscripts - What English Gardens Know About Education https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528563164294-EP4XGXMZY8A7TW5AJRJ8/preferentialencoding.jpg The Manuscripts - What English Gardens Know About Education https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528562702147-INQT7OZG96ZDQT9VK683/extendedpatterns.jpg The Manuscripts - What English Gardens Know About Education https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528562757493-RI9VNM3I5I9YH38OWB49/gardens.jpg The Manuscripts - What English Gardens Know About Education https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528562806574-EXUVHL6N5H4IWJC1LY0J/closure.jpg The Manuscripts - What English Gardens Know About Education https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528563049954-IWVKVQ4XN0KS77T1IG98/neardecomposable.jpg The Manuscripts - What English Gardens Know About Education https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528562862599-8EQ9BXJJDVFVR8GX4X7H/paradigmshift.jpg The Manuscripts - What English Gardens Know About Education https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528563110558-KJGIF60XZ6DIM47AWQZO/topdownapproach.jpg The Manuscripts - What English Gardens Know About Education https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528563611098-ZC1K7P5P15EUSQID09XU/landscape1-2.png The Manuscripts - What English Gardens Know About Education https://www.menimagerie.com/manuscripts/2018/6/9/i-profundities-worth-pondering monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528545975094-IC1V7R40ZH2KXA57PRVL/thinker.jpg The Manuscripts - I. Profundities Worth Pondering https://www.menimagerie.com/manuscripts/2018/6/9/it-from-bit-or-from-metaphor monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528560109278-ZFD8RPENASE70CS51AIQ/grotto.png The Manuscripts - It From Bit, Or From Metaphor https://www.menimagerie.com/manuscripts/2018/6/9/the-prison-steganographer monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528556263781-3Y9399R0Q59B4BIV9ZPC/steganographer1.png The Manuscripts - The Prison Steganographer https://www.menimagerie.com/manuscripts/2018/6/9/the-wastepaper-origamist monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528556038223-2RGG8748FFTKBNAWG98R/wastepaper-origamist1.jpg The Manuscripts - The Wastepaper Origamist https://www.menimagerie.com/manuscripts/2018/6/9/vii-hierarchy-theory-literature monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528554855032-D5MO36MLSQ8K7OKZG8EN/image-asset.png The Manuscripts - VII. Hierarchy Theory Literature https://www.menimagerie.com/manuscripts/2018/6/9/vi-clockwork-simulations monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528554615708-D1L2XY3EQL49NLNDC3E8/clockwork.jpg The Manuscripts - VI. Clockwork Simulations https://www.menimagerie.com/manuscripts/2018/6/9/v-douglas-hofstadter-and-parallel-terraced-scan monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528554375154-JBNDX7A60JA5JV0ER18W/parallel-terraced-scan.jpg The Manuscripts - V. Douglas Hofstadter and "Parallel Terraced Scan" https://www.menimagerie.com/manuscripts/2018/6/9/iv-ian-stewart-jack-cohen-and-complicity monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528554189354-1Z83NHXJ3THEL5JI6GRH/complicity.png The Manuscripts - IV. Ian Stewart & Jack Cohen and "Complicity" https://www.menimagerie.com/manuscripts/2018/6/9/iii-john-h-holland-and-the-multiplier-effect monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528553972469-ZNHI88W094JPVKXN5I6I/multiplier.png The Manuscripts - III. John H. Holland and the "Multiplier Effect" https://www.menimagerie.com/manuscripts/2018/6/9/ii-herbert-a-simon-and-near-decomposability monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528553746820-V8PNR8OFVPXJHDBZ9CSG/neardecomposability1.jpg The Manuscripts - II. Herbert A. Simon and "Near-Decomposability" https://www.menimagerie.com/manuscripts/2018/6/9/i-a-spectral-mosaic-poised-on-flux monthly 0.5 2018-06-09 https://images.squarespace-cdn.com/content/v1/5a2d26d980bd5ef5532fe2fa/1528553332854-EYNCM5KGHH0EUR8S4JII/poised-on-flux.png The Manuscripts - I. 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