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Science at the Sabha - Session 2
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Megha Anilkumar Nair
6:10
Good evening and welcome to the second session of ‘Science at the Sabha 2023’ organized by the Institute of Mathematical Sciences (IMSc), Chennai. For this session, we have Prof. Siddhartha Gadgil from IISc, Bangalore and Prof. Hema A Murthy from IIT, Madras.
6:11
Meena Mahajan, Professor at IMSc introduces Prof. Gadgil.
6:13
Prof. Gadgil starts off with a quick survey on the advent of automation, starting with chess. He mentions the automation of the Chinese game of 'Go' in 2017, a notable milestone.
6:14
6:18
He begins with mathematical proofs and delves into what went into the constructions of those proofs. He refers to Daniel Kahneman's systems of thinking about proofs.
6:20
Stressing on the computational power of our brain, he poses a question, "If our brain is so fast, why aren't we supercomputers?" He compares the computational power of our brains to that of computers today.
6:22
6:23
While reflecting on the memory of laptops today, he stresses the fact that ideas must precede hardware.
6:24
Moving on to the ingredients of doing mathematics, he concludes the introductory part of his talk by putting some concrete numbers on the predictions for the future of computing.
6:28
Prof. Gadgil explores mathematical proofs starting with 'Robbins Conjecture', speculated in the 1930s and proven in 1956. Next, he touches upon the 'Boolean Pythagorean Triples Theorem' by Ronald Graham in 1980.
6:29
6:31
"What about math at large?" he asks. He suggests the automation of mathematics. It is improving, which also facilitates formalization. Programming helps in evading some human errors.
6:33
He cites the Lean theorem prover as a tool that checks proofs and says that a computer-verified proof is only as trustworthy as the system that verified the proof. He goes on to talk about the milestone of automation in mathematical proofs.
6:35
6:36
Reflecting on examples of how Lean verified a proof by German mathematician Scholze and another proof on the sum of proofs; Prof. Gadgil draws on how automation has enabled mathematicians and researchers to negate errors in proofs.
6:39
Interactive theorem provers are a boon for the mathematical research community, but the question remains, "Are these provers completely correct always?" He emphasizes his point by citing software like Intel that use such theorem provers.
6:42
Delving into Artificial Intelligence, he cites 'Deep Blue' which defeated the chess world champion Garry Kasparov in 1997. He draws parallels between tacit knowledge- that is difficult to transfer to another person via writing it down or verbalizing it- and 'deep learning'.
6:44
"Deep neural learning drives artificial intelligence. Starting in 2012, deep neural networks performed well in image processing tasks," says Prof. Gadgil.
6:49
He gives the example of the Go-playing system AlphaGo that defeated 18-time world champion Lee Sedol in March 2016. The deep neural network was cloned to reflect the moves of expert Go players. He compares the efficiency of AlphaGo and Deep Blue.
6:50
AlphaGo v/s Lee Sedol
6:53
Explaining the playing style of AlphaGo as "aggressive", he summarizes a revolutionary paper 'Attention is all you Need'. The efficiency of models increased as time passed. He classifies computer systems today as being highly capable in intuition and precise reasoning.
6:54
6:57
Answering a question from the audience, he says that language models don't have a good grip on reality. He stresses that these models tend to be wrong and need an independent authority to verify them.
6:58
As Prof. Gadgil concludes his talk and Meena Mahajan, Professor at IMSc introduces Prof. Hema A Murthy.
7:00
Prof. Murthy begins by emphasising that deep learning models need huge computer power and memory.
7:02
Music information retrieval is largely independent and customized today, with the existence of applications like YouTube. She questions whether the social media algorithm in play today enables users to independently exercise their choices.
7:04
Expanding on the example of listening to a Carnatic music concert she says that melody is a tune characterized by a sequence of distinct fundamental frequencies.
7:07
Prof. Murthy explores the distinction of various ragas by delving into the different scales of measurement of frequencies and pitches. She goes on to distinguish between Indian and Western music with respect to its scale, pitch, annotation, and extent of improvisation.
7:09
"The notes of western classical music are very sharp," she explains, while drawing comparisons between Hindustani and Carnatic music.
7:11
Prof. Murthy stresses the absence of a score in music and how it does not have absolute time. This is in contrast to Western music where timing is specified to beats.
7:19
She adds that pitch extraction and processing allow identification of the tone and visualize the tonic of various instruments accompanying the music being sung. Delving into the graphical interpretation of the motifs of the same raga in different 'Srutis', she explains different methods and tools used to process music.
7:23
Is the computational analysis of Carnatic music an area that would interest you?
Yes, very much (66.7% | 2 votes)
 
No, I don't think so (0% | 0 votes)
 
Maybe (33.3% | 1 vote)
 
Total Votes: 3
Prof. Murthy says that machine learning algorithms are widely used to process large sets of musical data to dissect the composition into Pallavi, Anupallavi, and Charanams.
7:24
Prof. Murthy asserts the point that Carnatic music is very composition based.
7:27
She goes on to talk about raga verification and reflects how the audience at a concert associates a piece of music to a particular raga moments after hearing it. She stresses on how this reduces the interpretation of the piece to a narrow scope.
7:28
Raga verification in Carnatic Music
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