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JMIR Medical Informatics
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Theme Issue 2020:National NLP Clinical Challenges/Open Health Natural Language Processing 2019 Challenge Selected Papers (17) Natural Language Processing (470) Ontologies, Classifications, and Coding (158)
Published on 14.1.2021 in Vol 9 , No 1 (2021) :January
Preprints (earlier versions) of this paper are available at https://preprints.jmir.org/preprint/23104, first published August 01, 2020 .
Clinical Term Normalization Using Learned Edit Patterns and Subconcept Matching: System Development and Evaluation
Rohit J Kate 1
Rohit J Kate, PhD
Department of Computer Science, University of Wisconsin-Milwaukee, Milwaukee, WI, United States
3200 N Cramer St
Milwaukee, WI, 53211
Phone: 1 4142294264
Email: katerj@uwm.edu
Background: Clinical terms mentioned in clinical text are often not in their standardized forms as listed in clinical terminologies because of linguistic and stylistic variations. However, many automated downstream applications require clinical terms mapped to their corresponding concepts in clinical terminologies, thus necessitating the task of clinical term normalization.
Objective: In this paper, a system for clinical term normalization is presented that utilizes edit patterns to convert clinical terms into their normalized forms.
Methods: The edit patterns are automatically learned from the Unified Medical Language System (UMLS) Metathesaurus as well as from the given training data. The edit patterns are generalized sequences of edits that are derived from edit distance computations. The edit patterns are both character based as well as word based and are learned separately for different semantic types. In addition to these edit patterns, the system also normalizes clinical terms through the subconcepts mentioned within them.
Results: The system was evaluated as part of the 2019 n2c2 Track 3 shared task of clinical term normalization. It obtained 80.79% accuracy on the standard test data. This paper includes ablation studies to evaluate the contributions of different components of the system. A challenging part of the task was disambiguation when a clinical term could be normalized to multiple concepts.
Conclusions: The learned edit patterns led the system to perform well on the normalization task. Given that the system is based on patterns, it is human interpretable and is also capable of giving insights about common variations of clinical terms mentioned in clinical text that are different from their standardized forms.
JMIR Med Inform 2021;9(1):e23104
clinical term normalization; edit distance; machine learning; natural language processing
Clinical terms mentioned in clinical notes are not always in their standard forms as listed in standardized terminologies or ontologies. The use of synonymous words, abbreviations, syntactic variations, morphological alternations, and spelling variations are some common reasons clinical terms may be mentioned differently in clinical notes [1]. For example, a clinical note may mention "diffuse inflammatory reaction", but a standard terminology resource such as Unified Medical Language System (UMLS) [2] may list the same clinical concept as "diffuse inflammation" or "inflammation diffuse". As another example, a clinical note may mention "allergy to ferrous sulphate", but the terminology may mention "allergy to ferrous sulfate". Although a resource such as UMLS includes many synonyms for clinical terms, it does not exhaustively cover them. For example, neither of the 2 example mentions is listed in UMLS. In addition to the type of variations indicated earlier, mentions of clinical terms in clinical notes may have variations because of the writing conventions, or style of the medical center or simply because of typographical errors.
It is important, however, to map clinical terms mentioned in clinical notes to their corresponding concepts in a standard terminology for automated downstream applications, such as coding, biosurveillance, or clinical decision support, as well as for enabling portability of information across different medical centers. This task of mapping a clinical term mention to a standard terminology is called clinical term normalization. It is not trivial to automate this task because of all the possible variations of clinical terms mentioned earlier. For example, we found that in the test data set of the Medical Concept Normalization (MCN) corpus [3], only 62.37% of clinical terms matched exactly to the clinical terms listed in UMLS. There have been several approaches developed to automatically normalize clinical terms. Some of them use string-matching rules or approximations [4,5]. Other approaches cast clinical term normalization as an information retrieval [6] task and match clinical terms based on measures such as cosine similarity between their words [7,8]. More recently, machine learning methods have been employed for the clinical term normalization task [9,10], including deep learning–based methods [11-13]. Machine learning–based approaches for normalization have been shown to be more robust and accurate.
Previously, most clinical term normalization systems were evaluated on the benchmark data set of SemEval 2014 Task 7 [14], which had been previously used for the shared task of ShARe/CLEF eHealth Evaluation Lab 2013 [15]. However, this data set was designed for the combined task of information extraction [16] and clinical term normalization. In addition, it was restricted to clinical terms of only "disease and disorder" semantic type. Recently, a new corpus, called MCN [3], was created exclusively for the clinical term normalization task, which also includes clinical terms of other semantic types. This corpus was provided as the data set for 2019 n2c2 Track 3 [17], a shared task for clinical term normalization. In this paper, we describe our system that we had submitted for this shared task. This system is based on our earlier work [9,18] in which edit patterns to normalize clinical terms were automatically learned from the synonyms from UMLS. In this study, we extended that approach to also learn word-based edit patterns in addition to character-based edit patterns. We also extended it to learn patterns from the training data besides learning from UMLS. Previously, the approach had been evaluated only for the "disease and disorder" semantic type using the SemEval 2014 Task 7 data set. In this study, we evaluated it on other semantic types using the MCN data set. Besides the learned edit pattern–based component, our system includes a new subconcept matching–based component for normalization. Our system also includes a disambiguation component to choose the best concept for normalization in case there are multiple potential concepts.
Our system, UWM, achieved an accuracy of 80.79% on the test data set of the MCN corpus, which ranked sixth among the 33 system submissions and was behind by only 1.15% (absolute) to the second ranked system (81.94%) and was well above the mean (74.26%) and the median (77.33%) of all the participating systems [17]. The top system scored 85.26% and used a massive end-to-end deep learning architecture. An advantage of our method, however, is that because it is pattern based, it is easy to interpret how the system does normalization and it also provides insights into common variational patterns found in clinical terms. It also does not require heavy computational resources that are typically required for deep learning–based methods.
The objectives of this study are (1) to develop a clinical term normalization system using edit patterns learned automatically from synonyms of clinical terms and improve it further through subconcept matching and (2) to evaluate the system and its components on the MCN data set of clinical term normalization.
This section describes our system for clinical term normalization and the data set used for its evaluation.
We used the MCN corpus [3], which was provided to the participants of the 2019 n2c2 Track 3 shared task. This data set consists of 100 discharge summaries, which is a subset of the clinical notes that were originally used for the fourth i2b2/VA shared task [19] and has now become a benchmark data set for clinical named entity recognition. These clinical notes were obtained from the Partners HealthCare and Beth Israel Deaconess Medical Center. In the MCN corpus of 100 discharge summaries, the spans of the concept mentions were manually annotated with their concept unique identifiers (CUIs) from UMLS (2017 AB version). The CUIs were restricted only to the 2 vocabularies of SNOMED CT (US version) and RxNorm (for medications), as present in the UMLS Metathesaurus. The concepts were medical problems, treatments, and tests. The data set was divided into training and test sets, each with 50 discharge summaries; the training data set had 6684 mentions, and the test data set had 6925 mentions. There were a total of 3792 unique CUIs. For the normalization task, the character spans of the mentions in the discharge summaries were provided, and the systems were required to identify their CUIs.
A few guidelines that were used for the annotation process of this data set are worth mentioning. If a mention span could not be mapped to any CUI, the annotators assigned multiple CUIs to that mention whenever possible. For example, "left breast biopsy" could not be normalized to any existing concept in SNOMED CT; hence, the annotators instead annotated "left" and "breast biopsy" to their respective 2 CUIs by identifying the largest span that could be normalized [3]. For the normalization task, the character spans of "left" and "breast biopsy" were separately provided to be normalized independently. Ties were resolved during the adjudication stage for consistency; for example, alternatively, one could have annotated "left breast" and "biopsy". Theoretically as well as ideally, one could convert such compositional mentions into their postcoordinated concepts in SNOMED CT [20,21], but this was not done for this data set. The mentions for which the above compositional concept annotation strategy did not help were annotated as CUI-less. There were 2.70% (368/13,609) CUI-less mentions in the entire corpus.
A mention could be over multiple spans, which was indicated in the data set through multiple character spans but was assigned a single CUI. For example, for the mention "left atrium is moderately dilated", there will be two separate character spans—one for "left atrium" and one for "dilated"—and hence the clinical term to be normalized will be "left atrium dilated" that will be assigned a single CUI, given that the concept exists in SNOMED CT.
We want to point out that although the MCN corpus as well as the 2019 n2c2 task has been called "concept normalization", the task is, in fact, "term normalization" because the terms are being normalized and not the concepts. In the context of SNOMED CT, concept normalization means normalizing a concept to its standard form in SNOMED CT [22]. In SNOMED CT, a concept is represented in terms of its relations with other concepts, and there is often more than one way to represent a concept. Thus, concept normalization is a task in which a SNOMED CT concept is represented in terms of its relations in a standardized, unique way [23]. Concept normalization is, in fact, independent of any clinical term used to express the concept. On the other hand, term normalization means normalizing a clinical term to its standardized form in a terminology. Hence, in this paper, we will call the task "clinical term normalization" instead of "clinical concept normalization".
Clinical Term Normalization System
Given a mention of a clinical term in a clinical text, the task of clinical term normalization is to map it to its corresponding concept in the terminologies of SNOMED CT or RxNorm by assigning it the UMLS CUI or assigning it CUI-less if there is no such corresponding concept in the terminologies. This section describes our system for clinical term normalization. Figure 1 gives an overview of this system.
Figure 1. Overview of the clinical term normalization system. CUI: concept unique identifier; UMLS: Unified Medical Language System.
An input clinical term is first lowercased because our entire system works only with lowercased characters. Next, some common words are removed which were known to have been included in the mention spans because of the i2b2 complete noun/adjective phrase annotation policy [19]. These common words included "a", "an", "the", "his", "her", "patient", "patient's", any", "your", "this", "that", and "these". In addition, characters "'s", "'d", "-", "'", ">", and "<" were also removed from the mentions.
Exact Matching
Most mentions of clinical terms found in clinical text often exactly match the clinical terms already listed in UMLS. In addition, many clinical terms in the test data of the MCN corpus are common enough that they have already been mentioned and annotated in its training data. Hence, as a first step, our system tries to exactly match the input clinical term with the already annotated terms in the MCN training data as well as in UMLS. To match in UMLS, all the English language synonyms of the concepts that are present in SNOMED CT and RxNorm are checked for equality match. In the implementation, this is done efficiently using a hash table. In the Results section, we report the accuracy of exact matching in only the training data, in only UMLS, and together in both of these.
Although exact matching seems straightforward and one would expect it to always lead to the correct answer, sometimes the same clinical term exactly matches with more than one concept. For example, "atrial fibrillation" is listed as a term for a "disease and syndrome" concept with CUI C0004238, and it is also listed as a term for "laboratory result or test" concept with CUI C0344434. The latter is in the sense of a finding of electrocardiogram. Hence, the exact matching process would match both the concepts, thus leading to 2 possible CUIs as output. This type of ambiguity of multiple possible output CUIs commonly occurred in this data set, not just in the exact matching step but also in the subsequent steps of the system. Hence, we included a disambiguation component in our system that is described later.
Automatically Learned Edit Patterns
If the input clinical term does not exactly match either in the training data or in UMLS, then our system tries to normalize it by editing it based on the common patterns of variations of clinical terms that are learned automatically from known synonyms of clinical terms. This method for normalization was introduced in our previous work [9], in which it was tested only for the clinical terms of "disease and disorder" semantic type for the SemEval 2014 Task 7 data set [14]. For 2019 n2c2 Track 3, we adapted this method in 3 ways—first, in addition to "disease and disorder" semantic type, now it also learns patterns for all other remaining semantic types present in these data; second, in addition to character-based patterns, now it also learns word-based patterns; and third, in addition to UMLS, now it also learns patterns from the training data to learn variations that are specific to the given corpus. In the following section, we describe this method and the adaptations.
Edit Patterns
This method is based on the observation that often the clinical terms expressed in clinical notes have common variations from their mentions in standard terminologies; for example, they may not mention "nos" (not specified) at the end, they may mention "neoplasm" instead of "tumor", or they may have an extra "s" for plural, or have a spelling variation such as "tumour" instead of "tumor", etc. Often, exact matching fails because of such variations. The method is designed to automatically learn such common variations from the synonyms of clinical terms from a resource such as UMLS. Given a list of clinical terms and their synonyms, for every pair of synonyms, the method computes the Levenshtein edit distance [24] between them, which is the minimum number of edit operations of insertions, deletions, and substitutions that will convert one term into another. For example, converting "glycemic" to "glycemias" requires minimum of 2 edits—insert "a" after "i" and substitute "s" for "c". It is not the edit distance but the sequence of edits that is important for our method. The sequence of edits can also be obtained through the Levenshtein edit distance computation. We call the sequence of edits along with the characters that remain unchanged as an edit pattern. For example, the edit pattern that changes "glycemic" to "glycemias" will be "BEGIN SAME g SAME l SAME y SAME e SAME m SAME i INSERT a SUBSTITUTE c|s END". The pattern essentially says, "keep the characters same till 'i' then insert 'a' and substitute 's' for 'c'". The "BEGIN" and "END" signify that the edit pattern is applied from the beginning of the term and ends at the end of the term. However, this edit pattern can only convert "glycemic" to "glycemias" that were already known to be synonyms and hence is not useful unless it is generalized to match other clinical terms. The method next generalizes the edit patterns.
Generalization of Edit Patterns
Given 2 edit patterns, their generalization is defined as the longest contiguous common pattern that includes all the edit operations. Thus, the generalization process generalizes over "SAME", "BEGIN", and "END" symbols. For example, given the edit pattern from the previous paragraph and the edit pattern "SAME a SAME n SAME e SAME m SAME i INSERT a SUBSTITUTE c|s END", which converts anemic to anemias, the generalization will be the pattern "SAME e SAME m SAME i INSERT a SUBSTITUTE c|s END", which says, "if 'emic' is at the end of a clinical term then convert it to 'emias'". This is shown in the top part of Figure 2. This generalized pattern can now apply to other clinical terms, for example, it can convert "ishemic" to "ishemias". However, it will not convert "arrhythmic" to "arrhythmias" because the pattern expects an "e" before "mic". The generalized patterns can be further generalized with other patterns using the same process of determining the longest contiguous common pattern. For example, once further generalized with "SAME t SAME h SAME m SAME i INSERT a SUBSTITUTE c|s END", the new further generalized pattern will be "SAME m SAME i INSERT a SUBSTITUTE c|s END", which will convert arrhythmic to arrhythmias. This is illustrated in Figure 2.
Figure 2. An illustrative example of how the method generalizes edit patterns by finding the longest contiguous common pattern that includes all the edit operations. In this example, it learns the edit pattern to convert clinical terms ending with "mic" to "mias".
However, thus continuing to generalize will lead to overly general edit patterns, such as "SUBSTITUTE c|s" that says, "change every 'c' to 's'" that can change the meaning of a clinical term. Hence, there needs to be a way to gauge how good an edit pattern is and whether it is useful or overly general. In our method, this is done by counting the number of positives and negatives corresponding to every edit pattern. To compute these, the edit pattern is applied to the given list of clinical terms and their synonyms (eg, from UMLS). The number of times a clinical term is converted into one of its synonyms is counted as the number of positives. On the other hand, the number of times a clinical term is converted into another clinical term that is not its synonym (eg, a different concept in UMLS) is counted as the number of negatives. If the converted term is not a clinical term or it does not match in the list of clinical terms, then it is not included in the count of either positives or negatives. After computing the number of positives (p) and negatives (n), a score of p/(p+n+1) is assigned to the edit pattern, which is a simple form of m-estimate formula [25]. This score captures how accurate and how broadly applicable an edit pattern is in converting a clinical term into its synonym. Adding one in the denominator ensures that a pattern with a higher p will have a higher score even when n is zero. The patterns that are overly general will have a low score because they will have a high value of n. Good patterns will have a very high p value but a very low n value. Its score is used as the confidence of a learned edit pattern for normalizing a clinical term. We used a high threshold of 0.9 for the score, and only edit patterns with scores higher than 0.9 were included in the normalization system. We found through cross-validation within the training data that the method was not very sensitive to this threshold value, but it needed to be high for a good performance. An efficient algorithm to generate edit patterns using the method described above is given in a study by Kate [9].
We point out that the method to obtain edit patterns described earlier will always also generate a reverse pattern for each pattern. For example, if it generates a pattern to insert "s" in the end, then it will also generate a pattern to delete "s" in the end. This is because the synonyms are not considered in any order when generating the edit patterns; hence, each pair will be considered in both directions—generate the second from the first and generate the first from the second. As a result, the reverse of every edit pattern is also generated.
Applying Edit Patterns for Normalization
Given an input clinical term, an edit pattern is applied as follows. First, the system checks if the edit pattern matches the clinical term, that is, the clinical term is consistent with the presence of all the "SAME", "SUBSTITUTE", and "DELETE" characters as well as with the "BEGIN" and "END" symbols. For example, the edit pattern "SAME m SAME i INSERT a SUBSTITUTE c|s END" matches the clinical term "arrhythmic" because it has "mic" in the end. This is illustrated in Figure 3. If the edit pattern matches, then all its edit operations are applied at the matched location (in case an edit pattern matches at multiple locations within the clinical term, then each case is treated separately, although this rarely happens for a good edit pattern). In the previous example, "mic" will be changed to "mias", hence converting the original clinical term "arrhythmic" to "arrhythmias". Next, the system checks whether the resulting term is present in UMLS (or in its relevant portion, eg, within concepts of SNOMED CT and RxNorm) as one of the synonyms of the concepts. If so, the CUI of the corresponding concept is returned as the output of normalization. If the resulting clinical term does not match any synonym in UMLS, then the system moves on to match the next edit pattern. If multiple edit patterns match the clinical term, then all the corresponding CUIs are returned as the output; out of these, the best CUI is later selected by the disambiguation component. Given that our system only retains the edit patterns that have high scores, all the CUIs obtained by them are good potential candidates.
Figure 3. An illustration of how the edit pattern "SAME m SAME i INSERT a SUBSTITUTE c|s END" converts the clinical term "arrhythmic" to "arrhythmias".
It should be noted that in this method, edit distance computation is used to generate edit patterns and not simply to find the closest term by edit distance because a close term by edit distance could often mean an entirely different concept. For example, the edit distance between "typical angina" and "atypical angina" is only one, yet the 2 clinical terms refer to 2 very different and, in fact, exactly opposite concepts. On the other hand, the edit distance between "cardiac sarcoidosis" and "heart sarcoid disease" is 12, yet they are synonyms. In our method, the edit pattern of "BEGIN INSERT a", which inserts "a" in the beginning, will have many negatives and hence will receive a poor score. On the other hand, the edit pattern that changes "cardiac" to "heart" removes "osis" and adds "disease" will have many positives and very few or no negatives and hence will receive a high score. This shows that our method does not really depend on edit distance but only uses edit distance computation to generate edit patterns that are then generalized and judged for their goodness based on their numbers of positives and negatives.
Character-Based and Word-Based Edit Patterns
We described the method of learning edit patterns using examples in which characters were inserted, deleted, and substituted. However, sometimes, variations in clinical terms are simply due to the use of different words, such as "heart" instead of "cardiac". Although these edits can also be expressed in terms of edits of characters, the generalization process over multiple patterns may lose such a pattern. Hence, in addition to character-based patterns, our method also directly learns word-based patterns such as "SUBSTITUTE cardiac|heart". The method works in exactly the same way as described earlier, except that words instead of characters are treated as units of edits. In our method, words are tokens separated by whitespaces. In our results, we show the contribution of both types of patterns.
Edit Patterns From UMLS for Different Semantic Types
The clinical terms of different semantic types often exhibit different variations. For example, substituting "assay" for "measurement" is very common in clinical terms of "laboratory procedure" semantic type, whereas substituting "subcutaneous" for "intradermal" is very common in clinical terms of "clinical drug" semantic type. Hence, to capture such patterns efficiently, we applied our method of learning patterns separately to each of the 35 different semantic types of UMLS, which were the major semantic types of the clinical terms present in the MCN data set determined using its training set. For example, the top 5 semantic types in the training set were "disease or syndrome", "pharmacologic substance", "laboratory procedure", "finding", and "therapeutic or preventive procedure". For each of the 35 semantic types, the method considers the concepts of that semantic type in UMLS and their listed synonyms and generates edit patterns. The patterns are both character based and word based, which are separately generated. We found that a maximum of 5000 concepts for each semantic type were sufficient to generate good patterns. Using more concepts did not help because the common variational patterns are easily learned from within that many concepts, and adding more concepts would only lead to additional learning of rare patterns that would not apply in the test set. Table 1 shows a few illustrative examples of learned edit patterns for 4 different semantic types. As the semantic types of test clinical terms are not given in the data set, edit patterns of all the semantic types are applied during normalization.
Table 1. Illustrative examples of edit patterns automatically learned from UMLS for a few semantic types and automatically learned from the training data. The first 4 and the last 2 edit patterns are word-based, whereas the remaining 4 edit patterns are character-based. The number of positives and negatives of each pattern are also shown.
Learned edit pattern Positives Negatives Comment
Clinical drug
SUBSTITUTE intradermal|subcutaneous 133 0 Change "intradermal" to "subcutaneous"
DELETE oral SUBSTITUTE tablet|tab 26 0 Change "oral tablet" to "tab"
Diagnostic procedure
SUBSTITUTE fibreoptic|fiberoptic 41 0 Spelling variation
DELETE magnetic DELETE resonance SUBSTITUTE imaging|mri SAME of SUBSTITUTE both|bilateral 23 0 Change "magnetic resonance imaging of both" to "mri of bilateral"
Laboratory procedure
SUBSTITUTE k|c SAME o SAME c SAME y SAME t SAME e 54 0 Change "kocyte" to "cocyte"
BEGIN SAME h DELETE a SAME e SAME m SAME o 52 0 Change "haemo" to "hemo" at the beginning of the clinical term
Neoplastic process
INSERT u SAME r SAME _space_ 1148 2 Example: "tumor of"→"tumour of"
SAME a SAME r SAME c SAME i SAME n SAME o SAME m SAME a DELETE s END 26 0 Delete "s" if the clinical term ends with "arcinomas"
Training data
SUBSTITUTE obs|finding 5 0 Change "obs" to "finding"
INSERT on SUBSTITUTE o/e|examination 13 0 Change "o/e" to "on examination"
Edit Patterns From Training Data
The edit patterns learned from UMLS, as just described, capture the common universal patterns of variations in clinical terms. However, there are often patterns of variations in clinical terms that are unique to the genre of clinical notes or to the particular medical center from where the clinical notes were obtained. To learn these variational patterns, our method is also applied to the supplied training data of the MCN data set. To do this, the mentions of the clinical terms in the training data are added as additional synonyms of the UMLS concepts they were normalized to. These concepts (total 2311 unique) along with additional 3000 random UMLS concepts to drive the generalization process were used to learn edit patterns by the process described previously. In this case, we did not distinguish between different semantic types because there were not sufficient examples of each semantic type in the training data for the learning process. In the results, we separately evaluate the contribution of the edit patterns obtained from the training data. The last 2 rows of Table 1 show 2 illustrative edit patterns learned from the training data.
Of all the edit patterns thus obtained, only those with a score above the 0.9 threshold were retained as mentioned earlier. These were a total of 63,726 character-based and 22,832 word-based patterns. For a given input clinical term, each of the patterns is then applied as described earlier. If more than one CUI is obtained through this process, then the disambiguation component of the system (described later) is used to select the best CUI to output.
Subconcept Matching
In case neither exact matching nor learned edit patterns could normalize a clinical term, then our system tries to normalize it using the subconcepts present in it. First, the method determines all the subconcepts present in the clinical term. This is done by considering all the subterms of the clinical term, which are all the contiguous word subsequences in the clinical term (ie, all n-grams), including of length one (ie, individual words). For each subterm, the method then checks if it matches in UMLS. The matched concepts are deemed to be the subconcepts of the clinical term and are represented in terms of their CUIs. For example, for the clinical term "nasal o2", the method will find 2 subconcepts corresponding to the subterms "nasal" (CUI: C1522019) and "o2" (CUI: C4541402). Next, the method looks if there is any concept in UMLS that has exactly these subconcepts present. The subconcepts of a concept in UMLS are determined by finding the union of the subconcepts in each of its listed clinical terms in the same way by considering all its subterms. The UMLS concept of "oxygen administration by nasal cannula" has exactly the same 2 subconcepts corresponding to the subterms "nasal" (CUI: C1522019) and "oxygen" (CUI: C4541402). Hence, the clinical term "nasal o2" will be normalized to the UMLS concept of "oxygen administration by nasal cannula". Note that in this case, exact matching would not have worked, and it is unlikely that an edit pattern would have captured this variation because it is not very common. Additionally, note that the method overlooks other subterms such as "administration by" and "cannula", which do not correspond to any concepts in UMLS. If the clinical term cannot be normalized even after this method is applied, then the system outputs CUI-less.
Please note that this method is not the same as simple subterm matching, otherwise "o2" will not match "oxygen". Instead, this method performs subconcept matching, which automatically considers the synonyms through the CUIs. One complication in this approach is that there could be multiple subconcepts (ie, multiple CUIs) corresponding to a subterm. For example, "o2" in addition to matching the concept with CUI C0030054 (the element oxygen) also matches the concept with CUI C4541402 (a military officer position). Hence, in our method, at least one match between the 2 sets of CUIs is deemed as a match of subconcept. In the abovementioned example, "oxygen" matches the CUI C0030054 (although it does not match the CUI C4541402), and hence, there is a match of the subconcept.
Each of the 3 normalization components described previously—exact matching, learned edit patterns, and subconcept matching—can lead to normalization to multiple concepts in UMLS. However, the normalization task, as set up for the MCN data set, is expected to output only one concept. Hence, the normalization system needs to disambiguate the concept whenever a clinical term is normalized to multiple concepts. We built a disambiguation component in our system, which is based on patterns of semantic types of the concepts to be disambiguated. We observed that it was often the case that when a clinical term was normalized to multiple concepts of a few semantic types, then the correct concept was frequently of one particular semantic type among them. Hence, we developed a method to automatically learn such rules from the training data. For all the clinical terms in the training data for which the system normalizes to multiple CUIs, it considers all combinations of different semantic types of those sets of CUIs. It then determines the combinations out of these for which the correct CUI is always of a particular semantic type. For example, it learned that whenever the multiple CUIs have semantic types of "finding", "health care activity", and "organism function", the semantic type of the correct CUI was always "health care activity". A total of 56 such patterns were automatically learned and were used during testing to resolve ambiguities. In case the ambiguity could not be resolved (ie, none of the patterns matched), then the first matched concept (effectively random) was output by default.
We experimentally evaluated the contributions of various components of our system on the task of clinical term normalization. All the results were obtained on the test data of the MCN corpus as provided for the 2019 n2c2 Track 3. As in the shared task, the performance was measured in terms of accuracy, that is, percentage of clinical terms that were normalized correctly—either to the correct CUI or correctly to CUI-less. There were a total of 6925 clinical terms to be normalized in the test data, of which 217 (3.13%) were CUI-less. In the following, we first show all the results obtained while using the disambiguation component. We later show how the results are affected if this component is not used.
Table 2 shows the results for the first component of our system that does exact matching. It achieved an accuracy of 76%. This shows that a large number of clinical terms can be normalized simply by exact matching. The next 2 rows of Table 2 show the contributions of exactly matching clinical terms only in the training data and only in UMLS. A large drop in accuracy can be seen in both cases. This shows that both the resources greatly contribute toward the combined accuracy and that neither is sufficient on its own to achieve good accuracy. Among the 2 resources, UMLS was found to be more important. However, it is clear that there are sufficient variations in clinical terms that are specific to this corpus and not present in UMLS. This could also be partly because of the conventions adopted by the creators of the MCN corpus for marking mentions in the clinical notes.
Table 2. Performance evaluation on the clinical term normalization task using only exact matching.
System Accuracy (%)
Exact matching (training data+UMLSa) 76.00
Exact matching (training data only) 57.91
Exact matching (UMLS only) 62.37
aUMLS: Unified Medical Language System.
In Table 3, we show the results of adding the normalization component to the system that uses learned edit patterns. The results when only character-based patterns and when only word-based patterns are used are shown in the next 2 rows. In the last 2 rows, the results are shown when the edit patterns are learned only from UMLS and when learned from the training data (the latter also includes some terms from UMLS as described before). All these results include exact matching results (with both UMLS and the training data).
Table 3. Results of the ablation study for the method using different types of learned edit patterns.
System (includes exact matching) Accuracy (%)
All edit patterns 79.93
Character-based edit patterns 79.6
Word-based edit patterns 78.28
Edit patterns from UMLSa 79.88
Edit patterns from training data 78.56
It can be observed from the table that learned edit patterns helped in increasing the accuracy from 76% to 79.93%. This also shows that the method of learned edit pattern generalizes beyond "disease and disorder" semantic type, for which it was originally developed and evaluated [9], and works for other semantic types. From the next 2 rows of the table, one can see that character-based patterns were more important than word-based patterns. However, on its own, each type of pattern also did well. This indicates that character-based patterns can often express what word-based patterns can express and vice versa. For example, deleting the word "nos" can also be expressed as deleting those 3 characters; and changing characters "mic" to "mias" can be directly expressed as changing the word "arrhythmic" to "arrhythmias" (although its number of positives and negatives will be different). However, character-based patterns can exhibit better generalization in some cases; for example, deleting "s" at the end to convert plurals to singulars can be learned easily in a character-based pattern, but word-based patterns will have to learn that separately for each word.
The last 2 rows of Table 3 show how the performance changed when patterns learned only from UMLS were used and when patterns learned from training data were used. The results indicate that patterns learned from training data add to the accuracy but only marginally (from 79.88 to 79.93). The 2 illustrative edit patterns shown in the last 2 rows of Table 1 were learned only from the training data and could not be learned from UMLS alone. However, patterns learned without a large part of UMLS led to a larger drop in accuracy (78.56%).
The results in Table 4 show the contribution of the subconcept matching component of the system. Each result includes the exact matching results. Subconcept matching by itself obtains 77.79% accuracy and in combination with edit patterns, it increases the accuracy from 79.93% to 80.79%. This shows that this component is helpful, although not as important as edit patterns. The accuracy of our full system was 80.79%, which was the official accuracy of our system in the 2019 n2c2 Track 3 as evaluated and reported by the organizers.
Table 4. Results showing the impact of the subconcept matching component of the system.
Subconcept matching 77.79
Edit patterns 79.93
Edit patterns+subconcept matching 80.79
In Table 5, we show the performance gain obtained by leveraging the training data. The result shown in the first row was obtained when training data were not used either for exact matching or for learning edit patterns. The second row shows the results of the full system in which training data are used for both the purposes. It can be observed that using training data greatly helps. This indicates that the clinical terms mentioned in real-world clinical notes frequently differ from how they are listed in UMLS. This could be because of linguistic variations used in writing free text as well as because of conventions or the style of writing clinical notes specific to a genre or a medical center. The large drop in accuracy was mostly because of not doing exact matching in the training data as was already observed in Table 2. Not learning edit patterns from the training data reduced accuracy by only a small amount, as was previously seen in Table 3.
Table 5. Results obtained with and without using the training data.
Without using training data 68.01
With using training data 80.79
All the results reported so far were obtained while using the disambiguation component of the system. The difference in performance because of this component is shown in Table 6 for different normalization components and their combinations. It can be observed that disambiguation consistently helps in each case but not by a large amount. The results obtained by incrementally adding the normalization components with and without the disambiguation step are graphically shown in Figure 4. To determine the upper limit for the disambiguation component, the results obtained using oracle disambiguation are shown in the last column of Table 6. In oracle disambiguation, the system's normalization for a clinical term is considered correct if any one of the multiple CUIs it outputs is correct. One can see that the gap between accuracies of the system's disambiguation and oracle disambiguation is very large (from 80.79% to 85.5%). This shows that when the system normalizes a term to multiple CUIs, then one of them is frequently correct, but it is not easy to determine which is the correct one. We also found that if semantic types of all input clinical terms are given, then the system achieves an accuracy of 83.64% without oracle disambiguation (in this case, the system ensures that the output CUI corresponds to the relevant semantic type). This shows that most of the ambiguity is between CUIs of different semantic types. For example, the name of a substance (eg, sodium) may correspond to the concept of the substance as well as to the concept of its measurement, and both will be of different semantic types. Similarly, many clinical terms could be normalized to a concept of "disease and syndrome" semantic type as well as to a concept of "laboratory or test result" semantic type that is used to determine that disease.
Table 6. Performance evaluation measured in terms of percent accuracy with and without the disambiguation componenta.
System Without disambiguation With disambiguation Oracle disambiguation
Exact matching 75.81 76.0 78.93
Edit patterns+exact matching 79.7 79.93 83.65
Subconcept matching+exact matching 77.62 77.79 83.31
Edit patterns+subconcept matching+exact matching 80.56 80.79 85.5
aThe results of oracle disambiguation are also included in the last column for comparison.
Figure 4. Accuracy (%) of the system on the Medical Concept Normalization data set evaluated by incrementally adding the normalization components with and without the disambiguation step.
We experimentally found that a majority of clinical terms can be normalized simply by exact matching in the training data and in UMLS. Both these resources contribute significantly when normalizing using exact matching. Beyond exact matching, we found that there are certain patterns common among synonymous clinical terms. These patterns are both character based and word based. We presented a method that learns such patterns automatically and uses them to edit clinical terms to match their known synonyms. Finally, we found that a few more clinical terms can be normalized by extracting their subconcepts and then matching these subconcepts.
The availability of training data was found to be critical in obtaining good accuracy thus indicating that variations of clinical terms found in clinical text could be specific to the type and source of clinical notes that may not have been captured in a general resource such as UMLS. We also found that many clinical terms in clinical text normalize to multiple clinical concepts. Although there are certain patterns based on semantic types that can help, in general, it is difficult to determine the correct concept when a clinical term normalizes to multiple concepts. This was a major source of error for our system. We note that the postadjudication interannotator agreement of the MCN data set was low (74.2%) [3], which also indicates that human annotators also faced the problem of multiple possible CUIs. It also shows that this data set is far from perfect, and automated systems will always have a certain amount of errors when evaluated on this corpus.
Besides ambiguity, we found a few more common sources of errors. Sometimes a clinical term mentioned in text would be in an implicit shortened form whose complete form would be inferable from its medical context to domain experts. For example, the text would mention "balloon" and mean (and thus normalize to) "balloon pump device"; similarly, it would mention "rhythm" and mean "finding of heart rhythm" or mention "alveolar" and mean "alveolar duct of lung". However, our system would normalize only the shortened forms to their respective clinical concepts, thus leading to errors. Another source of error was the use of related words inside clinical terms that are not exactly synonyms; for example, the text would mention "upper lung field", but it would normalize to "upper lobe of lung" or mention "airway protection" but normalize to "airway management". Some errors were caused by subtle differences between concepts in SNOMED CT; for example, our system would normalize "left lower abdomen" to "entire left lower quadrant of abdomen". but the correct answer was the concept "structure of left lower quadrant of abdomen".
Limitations and Future Work
As noticed earlier, the disambiguation component of our system has room for improvement. One limitation of our system is that it does not look at the surrounding context of the clinical term in the clinical note and treats the task of normalization independent of this context. Potentially, the context of a clinical term can help in determining its semantic type, which can then help in disambiguation. However, we also note that determining the semantic type of clinical terms is traditionally considered as part of the information extraction task and not the normalization task. For example, SemEval 2014 Task 7 required both information extraction and normalization in which the entities to be normalized were to be first extracted from clinical notes and were restricted to "disease and disorder" semantic type. Hence, the semantic type of the clinical terms to be normalized was already known, which reduced potential ambiguities. We also note that one could also modify the evaluation process to allow multiple CUIs for clinical terms when the corresponding concepts are equivalent or closely related. Another possibility is to provide rules for preferring one type of concepts over other types based on their semantic types or hierarchies in SNOMED CT or based on other criteria.
The learned edit patterns were found to be good at capturing sequential edits, but they could not capture if the edits were of a different kind. For example, to normalize "asthma–cardiac" to "cardiac asthma", one needs to jumble the words, something that our edit patterns cannot capture (they will capture substituting each word with the other but that will not generalize to a pattern for jumbling the words that could match other clinical terms). In the future, patterns that capture such transformations could be learned from the data. Alternatively, a word-based similarity measure could also be used as is done in information retrieval [6]; however, it could also lead to incorrect normalization in other cases. Our method did not handle abbreviations of clinical terms separately. It either handled them through exact matching, if the abbreviations were mentioned as synonyms in UMLS or the training data, or through edit patterns that automatically learned abbreviations (eg, the edit pattern shown in the last row of Table 1). Given the prevalence of abbreviations in clinical text, in the future, using a dedicated component for abbreviation identification and disambiguation is likely to improve results [26].
Although our method may learn when a word can be substituted by another word, it does not consider word similarity which could potentially help in normalization. Incorporating word similarity in our method as captured through a suitable word embedding [27] will be an avenue for future work. The ontological structure of SNOMED CT in terms of its hierarchies and relations could also be leveraged for the normalization task in the future. For example, if the related concepts could be identified from the clinical term, then this can lead to finding the correct concept in SNOMED CT [21]. Edit patterns are used in our method to represent when 2 clinical terms can be normalized to the same concept. Another possibility for future work is to use a deep learning architecture to represent when 2 clinical terms could mean the same concept. For example, the neural network could take the edit pattern between 2 terms as input and learn to output whether the 2 clinical terms are synonymous or not. The network could be trained with the same examples from within the UMLS and training data as done in our approach.
We presented a system for the clinical term normalization task. It uses edit patterns of both characters and words that are automatically learned from UMLS and the training data. The edit patterns capture how clinical terms can be edited to convert them into their synonyms to normalize them. These edit patterns are human interpretable and depict the common variations of clinical terms used in clinical notes. Our system also used the matching of subconcepts to normalize clinical terms. Our system achieved 80.79% accuracy on the MCN test data set. Whenever our system found multiple possible concepts to normalize a clinical term, often one of them was correct, but it was not easy to determine the correct concept as annotated in the data, which accounted for some loss in accuracy. Through ablation studies, we found that many clinical terms in the data set could be normalized by exact matching in UMLS and the training data, and normalization using learned edit patterns was the most important component for normalizing the rest of the clinical terms.
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CUI: concept unique identifier
MCN: Medical Concept Normalization
UMLS: Unified Medical Language System
Edited by Y Wang; submitted 01.08.20; peer-reviewed by L Chen, S Matos, S Madani; comments to author 22.09.20; revised version received 31.10.20; accepted 18.11.20; published 14.01.21
©Rohit J Kate. Originally published in JMIR Medical Informatics (http://medinform.jmir.org), 14.01.2021.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work, first published in JMIR Medical Informatics, is properly cited. The complete bibliographic information, a link to the original publication on http://medinform.jmir.org/, as well as this copyright and license information must be included.
Kate RJ
JMIR Medical Informatics ISSN 2291-9694


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Da dove viene la matematica: Come la mente situata porta in essere la matematica è un libro del linguista cognitivista George Lakoff e dello psicologo Rafael E. Núñez. Il libro si propone di fondare una scienza cognitiva della matematica, o una teoria della matematica incorporata.  È notevole soprattutto per il dialogo che ha originato fra matematici, linguisti e psicologi a proposito del radicamento delle dimostrazioni matematiche.

Il libro propone e tenta di intraprendere un'analisi cognitiva della matematica che analizzi le idee matematiche in termini delle esperienze umane, metafore,  generalizzazioni ed altri meccanismi cognitivi che ad esse danno luogo. In definitiva, sostiene il libro, la matematica è un risultato dell'apparato cognitivo umano e deve pertanto essere compresa in termini cognitivi.  Questa analisi è distinta dalla pratica matematica di per sé e non può essere intrapresa da matematici non formati nelle scienze cognitive.

Il platonismo nella filosofia della matematica viene respinto: tutto ciò che conosciamo e potremo mai conoscere è la matematica umana, la matematica scaturita dai nostri cervelli, e la questione se esista oggettivamente una "matematica trascendente" è pertanto irrefutabile e quasi senza senso.

La matematica non è un'opinione.  Che me ne importa di linguisti o psicologi?

Tra i tecnici, c'è un consenso che la matematica sia un punto di vista neutrale, in effetti che se la logica di per sé è un valido mezzo investigativo, la matematica debba egualmente esserlo. La matematica è in qualche senso "utile", e nella misura in cui è egualmente utile a due esseri umani, è "neutrale".  Tuttavia, nei primi decenni del Novecento, l'ontologia fondamentale dell'algebra era in dubbio: Alfred North Whitehead, Bertrand Russell, e Kurt Gödel avevano stabilito che la logica e la teoria degli insiemi erano in qualche senso radicate in qualcos'altro, qualcosa di geometrico e di molto "reale".

Nel tardo Novecento, iniziò a crescere una letteratura della matematica e dei suoi fondamenti nel campo delle scienze cognitive: Amos Tversky, Daniel Kahneman ed altri misero alla prova la rigida prospettiva dualista/occidentale delle relazioni soggetto-oggetto che aveva dominato la matematica dai tempi di Cartesio, con un consenso crescente che la cognizione umana condividesse molti condizionamenti.

In parallelo, George Lakoff e Mark Johnson svilupparono una critica delle metafore, ed un modello soggetto/relazione/oggetto più generalizzato basato sulla metafora concettuale.

Nel frattempo, i postmodernisti, soprattutto Michel Foucault, svilupparono una critica profonda all'etica, alla teologia ed alla filosofia occidentale, centrata sull'assenza di qualsiasi modello del corpo umano vivente ed agente.  Come se il "cogito ergo sum" di Cartesio fosse una prospettiva letterale e divina del cosiddetto "mondo reale", e la matematica stessa fosse oggettiva ed immutabile: sempre scoperta, mai inventata. Ciò era contrario ad un insieme crescente di riprove nella fisica quantistica, che dimostrarono che gli osservatori in realtà alterano ciò che osservano, e che il processo stesso della cognizione umana cambia la "realtà".

Una teoria situata?

Il termine "situato" venne gradualmente a riflettere prospettive che assumevano un corpo osservatore, e che tenevano conto dei limiti imposti dalla sua fragilità e (in alcune analisi) dalla sua moralità. Il pensiero postmoderno divergé aspramente dal pensiero matematico, ed i filosofi del corpo quali Marilyn Waring e John Zerzan iniziarono a mettere in dubbio senza mezzi termini lo stesso concetto di Numero come guida alle scelte umane.

Una "scienza cognitiva della matematica" avrebbe dovuto unificare queste svariate critiche, e superare gravi lacune professionali e culturali - non soltanto dentro il mondo occidentale, ma anche fra i popoli indigeni ed altri la cui visione del mondo fosse guidata da qualcosa di molto diverso dalla matematica. Alcune di queste società erano persistite e prosperate per millenni senza alcuna idea sofisticata dell'algebra moderna, benché tipicamente avessero la geometria elementare. Questa era una delle tante anomalie che i presupposti occidentali sulla cultura non riuscivano a spiegare: ad esempio, come sofisticati progetti edili fossero stati condotti senza la maggior parte dei metodi algebrici usati dagli ingegneri moderni.

Il corpo e i sensi creano la matematica?

La "scienza cognitiva della matematica" come definita da George Lakoff e Rafael E. Núñez è "una teoria situata delle idee matematiche derivata dalle scienze cognitive contemporanee e coerente con esse".  Sostiene che "la matematica è radicata nell'attività cognitiva quotidiana degli esseri umani anziché in qualche aldilà platonico trascendente." In altre parole, che il corpo umano ed i sensi sono ciò che crea la matematica, e che questa può essere condivisa con altri esseri umani, solo perché sono così simili a noi. "La matematica potrebbe esserci oppure no nel mondo, ma non c'è modo per noi di affermarlo scientificamente," sostiene il Dott. Lakoff.  La matematica ha successo nella scienza, sostengono i Dott. Lakoff e Nunez nel loro libro, soltanto perché gli scienziati la costringono a funzionare. "Tutta l'"aderenza" tra la matematica e le regolarità del mondo fisico avviene nelle menti dei fisici che comprendono entrambe le cose."

Alcuni definiscono ciò un rifiuto postmoderno di accettare un universo radicalmente autonomo a cui noi non interessiamo affatto.  Ma obiezioni del genere sembrano molto modeste.

Cervelli in natura

Alcuni critici, tra cui Tom Seigfried, affermano che i sostenitori della scienza cognitiva della matematica "ignorano il fatto che i cervelli non soltanto osservano la natura, ma ne sono anche parte.... [e non riescono a spiegare come la matematica possa] parlare di fenomeni mai sospettati prima." Come altri sostenitori della controversa ontologia fondamentale della fisica delle particelle—che alcuni considerano il modo migliore di comprendere "il livello fondamentale della realtà"—Seigfried argomenta che il potere della matematica di prevedere ciò che gli esseri umani percepiranno è una dimostrazione della sua obiettività:

"Molti scienziati sospettano che il successo della matematica comunichi una profonda verità sull'universo, rivelando una inerente struttura matematica che domina il cosmo, o almeno lo rende comprensibile." ...agli scienziati.  "Se la matematica è una invenzione umana, sembra che la natura sapesse cosa sarebbe stato inventato."

Questa argomentazione è ben nota, e fu riassunta al meglio dal fisico Eugene Wigner in L'irragionevole efficacia della matematica nelle scienze naturali ("The Unreasonable Effectiveness of Mathematics in the Natural Sciences"), 1960: "L'enorme utilità della matematica nelle scienze naturali è qualcosa che rasenta il misterioso di cui non c'è alcuna spiegazione razionale."

Qual è l'agenda?

Il Santa Fe Institute dà a George Lakoff e Rafael E. Núñez il merito per
 Il radicamento dell'aritmetica, della teoria degli insiemi e della logica formale nel cervello e nel corpo.
 La struttura cognitiva dell'infinito attuale (l'infinito come una "cosa") per un'ampia varietà di casi: l'insieme infinito dei numeri naturali, i punti all'infinito, l'induzione matematica, i decimali infiniti e i reali, i limiti ed i minimi estremi superiori, gli infinitesimali e gli iperreali, ed i numeri transfiniti.
 La struttura concettuale caratterizzante il significato di , che ci consente di caratterizzare in termini cognitivi ciò che l'identità di Eulero  significa realmente e perché è vera sulla base di ciò che significa.

Ciò tenta di rispondere ad una domanda che ha tormentato i filosofi della matematica da quando Bertrand Russell ed Alfred North Whitehead fallirono nell'intento di radicare l'aritmetica nella teoria degli insiemi e nella logica formale, nel 1912. Su cosa si basa la matematica?

L'ambizioso programma dei cognitivisti è di permettere di far risalire tutte le dimostrazioni della matematica ai "quattro processi distinti ma correlati [che] strutturano metaforicamente l'aritmetica di base: la raccolta di oggetti, la costruzione di oggetti, l'uso di una canna metrica e lo spostarsi lungo un percorso." O, per quelle dimostrazioni che non possano essere così rintracciate, di metterle da parte come numerologia.

Matematica e politica

Questo non è il primo tentativo di mettere alla prova la matematica e la fisica come arbitri primari della realtà condivisa dagli esseri umani. Almeno dai primi anni '60, alcuni hanno sostenuto che le scienze militari segrete, la fabbricazione di armi nucleari, e la loro supposta "utilità" sono la prova che gli esseri umani continuano a costruire ed estendere i loro modelli anche dopo che questi si sono ormai dimostrati controproducenti per le vite umane, se non per l'intero pianeta. Alcuni critici postmoderni (compreso John Zerzan) e femministi (compresa Marilyn Waring) sostengono che la prospettiva radicalmente autonoma del Numero manipola il mondo con efficacia soltanto da un certo punto di vista - quello di una "cultura dominante".  E che in tempi recenti questa prospettiva si è dimostrata tutt'altro che "utile".

Naturalmente, questo è un argomento politico, ma la scienza non è immune alla politica.  E neanche ai rimpianti.  Dopo che la sua rivoluzionaria teoria della relatività fu sfruttata per costruire la prima arma nucleare, Albert Einstein lamentò:

"Se solo lo avessi saputo, avrei fatto l'orologiaio."

Matematica del fare, matematica del sentire

Il lamento di Einstein evidenzia il problema delle scelte etiche negli esperimenti - una questione di vecchia data che mette alla prova la falsificabilità come prova di verità - se non osate testare una teoria, come fate ad affermare che è vera? Se la sperimentate mettendo in pericolo persone di cui voi od altri si preoccupano, state guadagnando consensi per la teoria attraverso la "sperimentazione" o attraverso la "paura", cioè, il consenso dipende dal terrore di spingere lo scienziato ad un esperimento? Se è così, come fa lo scienziato a conoscere cosa è reale?

Quando i primi osservatori di una esplosione nucleare videro la nube a forma di fungo, e si accorsero che l'atmosfera non si era incendiata (cosa che non poteva essere prevista fino a quel momento), si guardarono forse l'un l'altro accennando felicemente che la matematica era stata convalidata? Oppure, come preferirebbero i filosofi del corpo, calcolarono il probabile impatto della loro azione sui corpi, empatizzandolo, e si ritirarono con orrore?

"La matematica potrebbe esserci oppure no nel mondo," ma noi certamente ne sentiamo l'impatto sui nostri corpi, p.es. come proiettili che obbediscono a f = ma, o come freddo dovuto ad uno sfratto invernale per mancanza di una certa quantità di credito. La cosa più sicura che possiamo dire sulla matematica è che descrive qualcosa che facciamo e che ciò è correlato ad altre cose che sentiamo. Ma è reale per le piante come lo è per gli animali? Per le ecologie come per le infrastrutture?

Se noi esseri umani non la mettessimo per iscritto, quanta matematica esisterebbe?

La matematica si applica ad altre forme di vita?

Alcuni mettono in dubbio l'affermazione di Lakoff secondo cui "non c'è modo per noi di affermarlo scientificamente," e fanno notare che la storia delle scienze cognitive sta trovando modi di sperimentare tesi precedentemente fondate solo sull'autodescrizione.

Nelle note a piè di pagina della sua analisi sull'"irragionevole efficacia" della matematica, Wigner abbozza una diversa prospettiva del problema, sostenendo che "è utile, nelle discussioni epistemologiche, abbandonare l'idealizzazione che il livello dell'intelligenza umana abbia una posizione singolare su una scala assoluta. In alcuni casi può anche essere utile considerare la realizzazione possibile al livello dell'intelligenza di qualche altra specie." Questo argomento rimase inesplorato per molti decenni, mentre la psicologia cognitiva, l'antropologia, la primatologia ed altre scienze investigavano "il livello dell'intelligenza di qualche altra specie."

Quando si fa ricerca "sul ruolo dell'embodiment e sui suoi vincoli biologici e cognitivi", un'importante ricerca empirica è in quale misura gli specifici fenomeni cognitivi su cui si fonda la matematica siano condivisi con gli altri ominidi, con le grandi scimmie, con tutti i primati e con altri animali.  O, se per questo, con i robot ed altre entità che potremmo accettare come attori radicalmente autonomi.

Qualunque sia il risultato di tale "sperimentazione sui primati" sembra certo che scopriremo che alcuni aspetti della matematica sono limitati agli esseri umani:

Gli esseri umani impongono la matematica al mondo?

Eticamente, quindi, potremmo anche chiederci, se i nostri modelli matematici si dimostrano "reali" solo da un certo punto di vista umano addestrato, quali sono i limiti etici e ragionevoli della loro sperimentazione? È giusto creare inverni nucleari o buchi neri o acceleratori di particelle sempre più grandi per determinare se una data teoria prevede correttamente il risultato di atti pericolosi, o di enormi stanziamenti di preziose risorse? E se alcuni concetti non sono ampiamente sperimentati, per preoccupazioni etiche o di costi, fino a che punto si possono apprezzare i modelli matematici corrispondenti?

Simili argomentazioni hanno dato vita al principio precauzionale - i progressi nella scienza cognitiva della matematica potrebbero essere dovuti all'ampia adesione a tale principio.

Oppure, potrebbero essere una commedia postmoderna per spostare risorse dalle scienze naturali ad una serie di progetti preferiti dai vari linguisti e primatologi:

Questa teoria si potrà mai dimostrare?

Sembra esservi qualche polemica sulla possibile rigorosità di queste dimostrazioni. In una risposta lunga e dettagliata al recensore Bonnie Gold, Lakoff rivendicò "un lavoro diverso da quello dei matematici professionisti.  Noi dobbiamo rispondere a domande del genere: Come può un numero esprimere un concetto? Come possono le formule e le equazioni matematiche esprimere idee generali che si ritrovano al di fuori della matematica, idee quali la ricorrenza, il cambiamento, la proporzione, i processi autoregolanti, e così via? Come differiscono le idee nell'ambito matematico da idee simili (ma non identiche) al di fuori della matematica (p.es. l'idea di "spazio" o "continuità")? Come si può capire la matematica "astratta"? Quali meccanismi cognitivi sono usati nella comprensione matematica?"

Ciò è naturalmente incompatibile col desiderio dei matematici di dimostrare nuova matematica in termini della matematica più vecchia, piuttosto che trovare metafore comuni alla matematica vecchia ed al corpo umano.

Il "cogito ergo sum" di Cartesio sembra messo seriamente alla prova - una teoria situata partirebbe necessariamente da spiro, audio, video... E attendo, la decisione più fondamentale su dove dirigere la propria attenzione.  Cosa è importante?

Ciò come cambierebbe la scienza?

Questa linea di ricerca sembra appiccicare alla matematica molte tendenze categoriali considerate precedentemente il dominio delle scienze politiche, della teologia e di altri campi che si fondano su ontologie complesse piuttosto che su assiomi nitidi.

Unitamente all'accettazione dei limiti etici, una caratteristica importante delle scienze del XX secolo è stata la scoperta di limiti alle capacità percettive e cognitive umane. Se anche la matematica avesse limiti del genere, ciò non sorprenderebbe, sia che tali limiti riguardino la fattibilità investigativa in senso stretto (p.es. il principio di indeterminazione, il teorema di Gödel, ecc.) o che siano eticamente imposti dal principio di precauzione: la religione, infatti, sostiene da tempo che i principi etici e morali siano una guida essenziale per le concezioni umane.  La fede e la ragione, come la teologia e la filosofia, si sono alternate per millenni come arbitro finale delle dispute nelle scienze naturali:

Papa Giovanni Paolo II riassunse il dibattito nella sua enciclica Fides et ratio (1995), ricordando che "anche la ragione ha bisogno di essere sostenuta nella sua ricerca da un dialogo fiducioso e da un'amicizia sincera. Il clima di sospetto e di diffidenza, che a volte circonda la ricerca speculativa, dimentica l'insegnamento dei filosofi antichi, i quali ponevano l'amicizia come uno dei contesti più adeguati per il retto filosofare" (n. 33).  Nella stessa enciclica, esortò filosofi e scienziati a indirizzare con cura le proprie ricerche: "non posso non incoraggiare i filosofi, cristiani o meno, ad avere fiducia nelle capacità della ragione umana e a non prefiggersi mete troppo modeste nel loro filosofare. La lezione della storia di questo millennio, che stiamo per concludere, testimonia che questa è la strada da seguire: bisogna non perdere la passione per la verità ultima e l'ansia per la ricerca, unite all'audacia di scoprire nuovi percorsi" (n. 56).

Un'argomentazione analoga si ritrova nell'articolo di Wigner, che intravede nell'analisi della cognizione umana la possibilità di giungere a "stabilire una teoria dei fenomeni della coscienza, ... coerente e completa tanto quanto le nostre attuali teorie del mondo inanimato." Tale condizione sarebbe in grado di "sottoporre a grande tensione la nostra fede nelle nostre teorie e nella nostra concezione della realtà dei concetti da noi formati. Ciò ci causerebbe un profondo senso di frustrazione nella nostra ricerca per ciò che ho chiamato 'la verità ultima'. Il motivo per cui una situazione del genere è concepibile è che, fondamentalmente, non sappiamo perché le nostre teorie funzionano così bene. Perciò, la loro accuratezza potrebbe non dimostrare la loro verità e consistenza."

Esortazioni simili si ritrovano in altre confessioni religiose: La tradizione buddhista, ad esempio, incoraggia all'investigazione imparziale della natura, denominata dhamma-vicaya, con l'avvertenza che il principale oggetto di studio deve essere la coscienza di sé.  Anche l'attuale Dalai Lama, Tenzin Gyatso, ha espresso grande interesse nell'esplorare la connessione tra il buddhismo, la psicologia e le altre scienze.

Se le scelte etiche influenzassero le nostre convinzioni fondamentali sulla scienza modellando gli esperimenti che intraprendiamo, e se ciò a sua volta influenzasse i nostri modelli matematici e la nostra accoglienza di alcune idee come "reali", allora le teorie che accettiamo sarebbero in effetti le nostre stesse scelte etiche.

Ciò implica che certe scienze sono "finite"?

Ora sono diventato Shiva, il distruttore di mondi. Robert Oppenheimer

Considerare la scelta emotiva tra le reazioni "situate" alla prima esplosione nucleare aiuta a mettere in evidenza il fatto che gli esseri umani definiscono i loro stessi esperimenti per cosa "funziona", e pertanto che la loro fede condivisa nella matematica non è necessariamente una fede in altro che la loro stessa cognizione e cultura. Se esistessero scienze dove la falsificabilità o la casistica non potessero essere comprese o finalizzate in qualche metodo ragionevole di cui si possa dire che tutti gli esseri umani ne fanno esperienza in modo simile, ciò suggerirebbe che si potrebbero abbandonare alcune indagini.

Le "due possibilità, di unione e di conflitto, menzionate prima, entrambe concepibili" di Eugene Wigner, la sua porta aperta all'abbandono di una teoria del campo unificato che comprenda la relatività generale e la meccanica quantistica, potrebbero anche aprire la porta all'abbandono della stessa previsione. Almeno, nella misura in cui si applica a noi stessi e ad altri esseri cognitivi. Accettare ed ampliare una scienza cognitiva della matematica ha implicazioni etiche che sembrano inevitabili: Se inventiamo la matematica e la scienza e la imponiamo ad altri che la inventano di meno, allora la stessa scienza potrebbe non essere nulla di più che una forma di colonialismo mentale:

Modellare o non modellare?

Come hanno a lungo sostenuto i popoli indigeni soggetti al colonialismo, la dipendenza del mondo occidentale dalla matematica e dalla previsione dove la scelta etica è necessaria ha conseguenze - una delle quali potrebbe essere l'accettazione di una matematica che conduce alla distruzione, in alternativa ad una matematica egualmente valida che conduce altrove. Matematica come punto di vista neutrale, semplice previsione, o dominio? La scelta è vostra...

È semplicemente una questione di scelte vedere qualcosa come aperto a diverse possibilità o determinato da fattori radicalmente autonomi? Che scelta abbiamo sulle strutture matematiche che concepiamo?  La scienza cognitiva della matematica riduce la certezza, compresa forse la certezza del conflitto.

Se la matematica è soggettiva, tutta la scienza è "cognitiva"?

L'embodiment di tutta l'astrazione matematica è un progetto grandioso, che con ogni possibilità non sarà mai completato.  Tra le altre questioni, esistono non pochi interessi che traggono vantaggio dalla presunzione che si possa costruire in sicurezza matematica su matematica, senza fare attenzione ai corpi o alla loro etica disordinata:

Le simulazioni numeriche, gli esperimenti di fisica delle particelle, o altre attività umane che poggiano su un concetto di cognizione relativamente oggettivo, potrebbero apparire in pericolo di essere sacrificate ad un obiettivo politico - una matematica completamente situata imporrebbe un onere irragionevole di oggettività su qualsiasi processo scientifico che impiegasse per consuetudine l'analisi reale o complessa.  Dimostrare semplicemente che un modello non ne contraddice altri potrebbe non bastare più per convincere i finanziatori che ogni passo della derivazione è stato "situato" - che si fonda su assiomi e dimostrazioni che sono essi stessi completamente radicati.

Se gli scienziati accetteranno questa subordinazione radicale all'etica ed alle scelte, ed una riclassificazione della loro opera come sottoinsieme delle scienze cognitive, è forse una questione più politica che scientifica.

Critiche

Una risposta all'obiezione di Lakoff al platonismo è la prospettiva che qualsiasi mondo contenente esseri cognitivi capaci di escogitare concetti matematici deve operare secondo i principi della logica formale.

Inoltre, se si accetta il logicismo nella sua unica forma coerente, si deve respingere la negazione completa di una matematica trascendentale da parte di Lakoff, anche se si accettano i risultati della sua ricerca.

Bibliografia

 G. Lakoff, R. Núñez: Where Mathematics Comes From, Basic Books, 2000 traduzione italiana Da dove viene la matematica. Come la mente embodied dà origine alla matematica, Bollati Boringhieri, 2005

Voci correlate

 Scienza cognitiva della matematica
 Filosofia della matematica
 Filosofia del corpo

Collegamenti esterni

Filosofia della matematica

redpajama_set_name: RedPajamaWikipedia


text:
Isolation in the Unknown
January 14, 2020 by bnbeaman
By Jo Ladner
*contains ending spoilers for "Over the Garden Wall*
"Over the Garden Wall" has been a Halloween tradition for me ever since it first released in 2013. A short mini-cartoon series Cartoon Network did specifically for Halloween, it's plenty spooky and full of Halloween tropes, with living skeletons, ghosts, singing frogs, two brothers—Wirt and Greg— trying to find their way home, becoming lost and isolated in the woods, and The Beast.
image via Bing Images
The Beast is a hulking shadow that lives in the woods of The Unknown (the place where Wirt and Greg find themselves lost), collecting spirits of lost children to use as fuel for his lantern. He remains elusive through most of the show, although all the people Wirt and Greg bump into warn them of The Beast and his spirit-snatching tendencies. What exactly is The Beast, though?
The Beast himself is a spirit—much like the ones he collects—and like most ghosts and spirits he relies on the energy of others to keep himself aflame, as he says, since The Beast is not capable of doing this himself. He needs someone else to fill of role of the lantern bearer and keep him alive, which plays into the common tropes that ghosts and spirits are not able to completely function by themselves and that they need a vessel in order to stay manifested (the lantern, in The Beast's case). They require assistance, however willingly —or unwillingly— given, and that is what the lantern bearer does. They collect the edelwood to grind into the oil for the lantern, keeping it lit for The Beast, who isn't capable of doing it for himself.
The Woodsman is the one who holds The Beast's lantern though most of the show, and in the last episode Wirt is given responsibility for it for a moment when it's accidently knocked from the Woodsman's hands and Wirt picks it up. The Beast is a master manipulator, another common trope of ghosts, and in order to keep and motivate the current lantern bearer, he lies to them and tells them that a spirit of a loved one is the one in the lantern. He plays off their guilt of losing that loved one to get them to keep fueling the lantern. The Beast tells the Woodsman that the light is the spirit of his daughter, and for Wirt, he says it is the spirit of his brother, Greg. The Beast keeps the Woodsman isolated in the woods to keep him from learning the truth, and the action of this isolation accomplishes two things. It keeps the Woodsman in the dark about the state of his daughter (who, despite The Beast's word, is home alive and well), and it alienates him from the other townsfolk. The townsfolk fear The Beast, and they hold the belief that "he who carries the lantern must be The Beast." This belief immediately pegs the Woodsman as someone dangerous, and so the townsfolk stay away from him and he stays away from them. So, a cycle starts: isolation, alienation, then self-imposed isolation. The Beast is about to do the same to Wirt before Wirt questions who exactly the spirit in the lantern is. This is where we learn that it is really The Beast's spirit, and Wirt blows it out and sends it back to the world of the dead.
The idea of spirits keeping people in isolation to feed them in seen in a few other characters in "Over the Garden Wall." Lorna is possessed by a violent and murderous ghost, and Lorna's aunt keeps her in a secluded house to keep the ghost from harming others. Quincy Endecott, while not haunted by a literal ghost, is haunted by the idea of one, and he barricades himself in his manor while his fear drives him halfway to madness. These two characters aren't nearly as terrifying as The Beast, although, at first glance, they appear to be more terrifying. They are given physical bodies and appearances, while The Beast is nothing more than a shadow —the shadow in the corner of your eye, if you will. The Beast is given only a passing glance at first, but the longer Wirt and Greg, and by extension the audience, are left to think on The Beast, the scarier he becomes. He plays on the parental fears of losing one's child, either to kidnapping or death, which you can see with the Woodsman. He uses the children's fears of "The Scary Thing In The Dark," the thing that can take them away (another thing we're warned about). That's what makes The Beast so terrifying: his ability to evoke fear in both children and adults through very similar means.
The Beast is not a traditional ghost in this sense, but he is still using the tactic of isolation to keep himself alive. And do we not see this in other ghost stories and in other haunted houses and locations? What about Jack Torrance in Stephen King's The Shining? Elenore Vance in The Haunting of Hill House? Or even your local ghost story, warning you to never go into the woods just on the edge of town on your own?
Over the Garden Wall, created by Katie Krentz and Patrick McHale, with Elijah Wood, Collin Dean, Melanie Lynskey and Christopher Lloyd, Cartoon Network, 2013.


text:
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OSL_NAMESPACE_EXIT

#ifdef OSL_HOST_RS_BITCODE
extern "C" {
#    define STRDECL(str, var_name) \
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// Prefix for OSL shade op declarations.
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/// Get the 4x4 matrix that transforms by the specified
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/// Get the 4x4 matrix that transforms points from the named
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/// Get the 4x4 matrix that transforms points from "common" space to
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OSL_RSOP bool
rs_get_inverse_matrix_space_time(OSL::ShaderGlobals* sg, OSL::Matrix44& result,
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/// Get the 4x4 matrix that transforms by the specified
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OSL_RSOP bool
rs_get_matrix_xform(OSL::ShaderGlobals* sg, OSL::Matrix44& result,
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/// Get the 4x4 matrix that transforms by the specified
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/// rs_get_matrix_xform and invert it, but a particular renderer may have a
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OSL_RSOP bool
rs_get_inverse_matrix_xform(OSL::ShaderGlobals* sg, OSL::Matrix44& result,
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/// Get the 4x4 matrix that transforms 'from' to "common" space.
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OSL_RSOP bool
rs_get_matrix_space(OSL::ShaderGlobals* sg, OSL::Matrix44& result,
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/// Get the 4x4 matrix that transforms points from "common" space to
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OSL_RSOP bool
rs_get_inverse_matrix_space(OSL::ShaderGlobals* sg, OSL::Matrix44& result,
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/// Transform points Pin[0..npoints-1] in named coordinate system
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///
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/// Note to implementations: just return 'false'
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OSL_RSOP bool
rs_transform_points(OSL::ShaderGlobals* sg, OSL::StringParam from,
                    OSL::StringParam to, float time, const OSL::Vec3* Pin,
                    OSL::Vec3* Pout, int npoints,
                    OSL::TypeDesc::VECSEMANTICS vectype);

redpajama_set_name: RedPajamaGithub


On the end of August 2018, a US federal court finalized a $245 million penalty against Pinnacle Ultimate metal-on-metal hip implants made by Johnson & Johnson and its affiliate DePuy Orthopaedics. The hip-implant devices were defective and it was alleged that the patients had serious injuries due to the implants. As far as I have heard, the company is not going for an appeal it seems.
There are lawsuits against DePuy Pinnacle hip happening in many other counties outside the US like in Canada, United Kingdom, Australia, Ireland, Germany and Italy.
These lawsuits made me wonder why there is no nationwide ban of the against the hip implants offered by the DePuy Pinnacle or why there was no action taken against them for breaching the quality mark. As far as I know, the penalty amount is because of the personal injury caused by their faulty devices not due to their misconduct.
Can someone please help me to understand why the court has taken no action against the company for breaching the medical standards?


Hello, I have recently moved to the area and I am looking for a cleaner once a week for a couple of hours. Does anyone have any recommendations?
Hi I have a Tues or Weds free. Please call or text me 07799 796963. References supplied.