ಪರಿಕಲ್ಪನೆಯ ಅಧ್ಯಯನ | భావన అధ్యయనము
-
-
Bikes can readily beat the fastest human(s) at speed, which in no way suggests that a study of automobiles can inform the mechanics of human locomotion or the workings of human brain! If anything, the obvious superiority [vis-a-vis human experts] of the so-called Artificial Intelligence (AI) programs at games is a resounding declaration of the categorical difference between AI and the human brain.
More broadly, but for the reality underlying appearances, the extreme empiricism extolled in “What does AI’s success playing complex board games tell brain scientists?” would have been sensible and reasonable. It is impossible to make sense of the “blooming buzzing confusion” that we all are suspended in by rolling dice. Truth is not a statistical notion. Science is not a miracle machine. Stated differently, trail-and-error alone is inadequate to account for our scientific understanding of reality (Fodor, 2006, p. 93). Then, what else do we need?
Reason, experience, and the alignment of reason with experience sustain the evermore proper science—the hallmark of human intelligence. Thus, we need to study science to gain insights into intelligence. The carefully reasoned mathematical understanding of the reconstruction of reality from its appearances (Lawvere and Rosebrugh, 2003, pp. 125-126, 149-152) and of the functorial semantics of mathematical theories (Lawvere, 1963, 2004) underwriting science is particularly relevant for our present purposes. Lawvere’s functorial semantics of scientific theories [and not the successes at simple–relative to scientific advances–games] can help us develop a proper understanding of the workings of human brains and minds (Posina, Ghista, and Roy, 2017).
References
Fodor, J. A. (2006) How the mind works: What we still don’t know. Daedalus 135: 86-94.
-
The characterization of artificial intelligence (AI) as alchemy, albeit emotive, is merely an acknowledgment of the lack of understanding of the workings of the underlying algorithms (1, see also 2). In developing an explicit theoretical understanding of intelligence, following in the footsteps of physics makes perfect sense. However, the toy problem (black-and-white images instead of color photos) prescribed for gaining insights into recognition algorithms appears to be diagnostic of a deeper problem with contemporary AI, which is getting lost in the here & now of immediate solutions and losing sight of the big picture: development of the science of intelligence (3). Here we suggest a different approach: mathematical knowing as a Bohr atom of knowing, which can serve as a solid foundation to build the science of human intelligence (subsuming reasoning, perception, and cognition, among others).
But how, and why?
First, science is a hallmark of human intelligence. As such, a scientific account of science constitutes the science of intelligence. Although we do not have the science of the development of scientific theories and models, we have functorial semantics: a mathematical account of abstracting theories and building models of various categories of mathematical objects (4, 5). Taking a cue from Galileo’s investigation of a simple motion—motion of falling bodies—that served as a foundation for the science of motion, we suggest investigating the functorial semantics of mathematical knowing as an elementary form of the more elaborate scientific knowing in particular and ordinary cognition in general (6). Functorial semantics spells out the mathematics of going from [categories of] mathematical objects to their measured properties, abstract theories, and concrete models; and this functorial calculus can provide an overarching mathematical framework needed for the advancement of AI, somewhat analogous to way calculus provided the mathematical framework needed for the advancement of physics (7).
References
- M. Hutson, Science 360, 478 (2018).
- M. Buchanan, Nature Physics 14, 326 (2018).
- S.J. Russell, P. Norvig, Artificial Intelligence: A Modern Approach (Pearson Education Limited, 2016), pp. 1-31.
- F.W. Lawvere, Reprints in Theory and Applications of Categories 5, 1 (2004).
- F.W. Lawvere, in The Logical Foundations of Cognition, J. Macnamara, G.E. Reyes, Eds. (Oxford University Press, 1994), pp. 43-56.
- V.R. Posina, D.N. Ghista, S. Roy, Mind & Matter 15, 161 (2017).
- F.W. Lawvere, in Language, Logic, and Concepts, P. Bloom, R. Jackendoff, K. Wynn, Eds. (MIT Press, 1999), pp. 411-425.
-
Individuals do not set the course of events; it is the social force.
The singular purpose of education is to nurture the universal yearning for understanding. Here we show how a nurturing pedagogy naturally resolves the “learning crisis”, with the solution manifesting as human development (alluded to in Muralidharan and Singh, 2021). In doing so, we spell out–for further discussion–how the historic Indian education reforms embodied in the National Education Policy 2020 (NEP) can be implemented. Furthermore, the nurturing pedagogy that we advocate invariably results in the culture of research excellence that the national education policy calls for (NEP, pp. 45-46).
First, what is understanding? Understanding is organized knowledge, wherein bits and pieces of knowledge are organized into a cohesive body of understanding “so that the new ideas and methods collected and developed as one goes through life can find their appropriate places” (Lawvere and Schanuel, 1997, p…
View original post 3,235 more words
-
Grassmann’s theory of pedagogy is at least as deserving of trial as the pragmatist theory of teaching only skills, which as we have seen did not achieve its goal (F. William Lawvere, 1991, p. 12).
The philosophical preamble of Grassmann orients a student towards applications of pure mathematics that the student should seek.
Grassmann helps students develop for themselves the proper estimation of the relation between general and particular at every stage of the learning process (F. William Lawvere, 2005, p. 3).
Grassmann describes the two-fold division of the science of thinking: Mathematics and Dialectics. Dialectics seeks the unity in all things, and mathematics is the art and practice of taking each thought in its particularity and pursuing it to the end. Students need a guide to follow in a unified way both of these activities: passing from the general to the particular and from the particular to the general (F. William Lawvere, 1996, p. 256).
A universal instrument—category theory/theory of naturality—for guiding the learning, development, and use of advanced mathematics does not fail to have its indications also in areas of school mathematics (F. William Lawvere, 2005, p. 1).
Upcoming (related) attractions:
Knowledge vis-à-vis Understanding
Understanding: Clear vs. Proper
Learning vis-à-vis Teaching (Ideal Student Experience)
Description: Viewshape and Universe of Discourse
Reasonable effectiveness of mathematics in natural sciences (to be contrasted with miracles)
Education: Practice and Theory (F. William Lawvere, 2003, p. 213)
Development of Understanding: Slow, imperceptibly slow (The rising sea, 2003, p. 1).
-
The ‘I’ is an abstract general; not a particular I.
-
With all due respect, I find that:
“The Indian National Curriculum Framework for Foundational Stage 2022 (NCF) is based on cutting-edge research from across the world in multiple disciplines, which includes among other things better understanding in the fields of neurosciences, brain study, and cognitive sciences” (NCF 2022, p. 5)
to put it very mildly, my worst fear manifesting as a lucid nightmare (maybe I need to take more melatonin 😉
Here’s why?
Just in case you are like me and thinking that’s way back in the 90s; surely, things must have gotten better. Sadly, it got worse: graduating from the aforementioned mess to a failed enterprise (“What happened” in the title is an intended pun on Hillary Clinton’s book-length wailing after she lost to Trump 😉
Did the dark night of the soul break into, if not bright daylight, at least a cloudy and/or sunless morning? No, it continues to compound confusion with added attractions following failed academic distractions aka debates, all in the name of sincere soul-searching.
Here’s my understanding of the continuing failure of cognitive science to mature:
The High Priests of CogSci can’t tell the difference:
Mind vs. Consciousness
which laypeople have no trouble telling apart:
thinking about a cat is not the same as seeing a cat.
Even more disturbing:
The cogsci priesthood don’t know and/or doesn’t care to learn a corresponding—60-year old—scientific difference:
which is:
a theory is a theory of a universe of discourse (consisting of objects, which, in turn, are geometric objectifcation of concepts/abstract generals, and their mutual relations), while models are models of objects of the universe (of discourse obtained by interpreting the theory of the given universe into a background such as intuition; see my unabashed self-promotion 😉
Speaking of concepts, which is where cogsci went wrong (cf. Fodor), here’s our scientific understanding of concept formation. Given my impression that many cognitive scientists think that the concepts making rounds in the hallowed hallways ensconced under ivory towers are a class apart from those that laypeople use to think—quite effectively everyday—here’s a familiar physicist Einstein recruited for the much needed re-education, a not so famous mathematician Schapira, along with the science that cognitive scientists need to learn, for a simple reason: the kinship between the exalted science and everyday experience (see also Lawvere and Rosebrugh (2003) Sets for Mathematics, pp. 235-236).
The really sad aspect of all dis is the ‘you kno who’ aren’t even original in making a mess of cognitive science:
Here’s Marvin Minsky, the founding father of artificial intelligence (AI), on the progress made:
“We found that little of significance had changed since 1969. One reason why progress has been so slow in this field is that researchers unfamiliar with its history have continued to make many of the same mistakes that others have made before them” (Minsky and Papert, Perceptrons, p. vii; my Minsky number is 3, for those dat are into those things 😉
Then there is Gian-Carlo Rota (Head of the Dept. of Math @ MIT) on AI:
Pattern recognition? Image processing? Filtering through noise? Big words in the world of big bucks, problems clamoring for fast solution. The know-nothings will be surprised to learn that the solutions to these “practical” problems are more likely to come from the work of Harish-Chandra: a monument aere perennius, than from the Mickey Mouse animations on which the Federal Government wastes millions (Indiscrete Thoughts, p. 249).
How about the contemporary AI: Google’s DeepMind, Meta’s whatever et al. seem to be marching ahead on breakthrough-after-breakthrough-laden scientific pathway?
As you might have guessed, I have been busy trying to beat some sense
and/or reason into boneheaded AI as is my wont, albeit to no avail 😉Advancing Artificial Intelligence
Universal yearning for understanding
Thankfully, I’m not all alone:
Summing it all, what we need is a sincere audit of the practice of science:
In closing, Amma Saraswati, please save science and education from corporate “scientists” (science has been through a lot already in the academia) /\/\/\
P.S. I’d like to question the self-congratulatory leftists in Indian academia: What is your scholarly contribution to ensuring that there is the prerequisite literature review by your fellow academicians investigating the mind: Buddhism has articulated particularly well the benefits of expanding the scope of the conscious mind (Kandel et al. (2013) Principles of Neural Science, p. 1016), not to mention the profound recognition that there are concepts underlying language (ibid, pp. 1347-1348). The non-trivial nature of this distinction—concepts vs. words—and the failure to recognize the distinction has hindered scientific progress (please see Lawvere and Rosebrugh (2003) Sets for Mathematics, pp. 194-195, 239-240). A related note to da (unconscious 😉 leftists in Indian academia, Indians believe in education (more so than in any god of any religion they were born into): to see for yourself, plz stop by Malabar Café, Mathikere, Bengaluru, Karnataka, ~9AM!
P.P.S. I’d like to humbly and publicly (having gotten no response to my private emails) request His Holiness Professor Peter Johnstone to think about the ethics of misappropriating/muddling others’ intellectual inheritance: the moral of our Elephant story. Thank you Sir! Speaking of the British, as an admirer of John Maddox, who inspired me to take up the challenge of answering his editorial question, I’d like to request Nature to refrain from selling fake news and magical thinking, unless, of course, you are itching to meet the fate of your British empire 😉 In a similar spirit, being an admirer of the first editor George Croom Robertson of the journal MIND, as much as I appreciate the generosity of your spirit in highlighting the philosophy around the world, I find the absence of late Professor Sarvepalli Radhakrishnan’s papers on Indian philosophy and its problems published in your own journal MIND little puzzling. Be that as it may, I am truly grateful for drawing attention to seminal and longstanding thorough investigations of Buddhist philosophy by Professor Graham Priest (cf. Catuṣkoṭi; see also late Professor Linton’s Localic take on Catuṣkoṭi, which is what got me into it 🙂 The journal MIND may have conveniently forgotten the publications of Professor Sarvepalli Radhakrishnan in its pages, but we still fondly remember Sarvepalli Radhakrishnan and celebrate his birthday as our Indian National Teachers’ Day 🙂
P.P.P.S. Lest anybody entertains the thought that all or any of this might bring about the desired change in the practice of education and/or science, I have to admit that my ventures—THE SOCIETY FOR THEORETICAL NEUROSCIENCE—dedicated to the express purpose of drawing cognitive neuroscientists’ attention to the distinction—THEORY vs. MODELS—didn’t go anywhere.
-
In questioning,
Ground of the given
Affirmed in the ordinary
Destined to a distant negation
Making room for space
Addressed as commonplace
With access denied,I learn,
Everyday experience dismembers into
A L P H A B E T
Left of the imploding
I of consciousness,To be without being
aka
Conscious experience.