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@njwildberger

Insights into Mathematics | Trying to sidestep the SAT problem | MathFoundations268 | N J Wildberger @njwildberger | Uploaded 4 years ago | Updated 2 hours ago
The SAT, or Satisfiability, problem is a major issue for the Boolean algebra approach to logic gate circuit analysis. In this video we explain this central problem, and then discuss how the alternative Algebra of Boole approach to logic gates helps us to circumvent it, at least for smaller circuits that can be analysed by hand. But even for larger circuits that arise in modern Integrated Circuit design, the Algebra of Boole allows an alternative exploration of this issue.

Along the way we will talk about Conjunctive Normal Form (CNF) and also more briefly about Disjunctive Normal Form (DNF). The importance of both of these categories diminishes markedly with the Algebra of Boole orientation!

The issue of NP-complete problems in computer science is also mentioned, as the SAT problem was the first such to be identified by Cook in 1971.

Video Content:
00:00 Introduction
2:31 The SAT Problem ,the first NP - complete problem
04:31 Conjunctive normal form (product of sums )
12:11 Simplifying CNF with Algebra of Boole
20:08 Proposition
24:32 Sidestepping the SAT Problem

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youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB
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Trying to sidestep the SAT problem | MathFoundations268 | N J Wildberger

$Pure mathematics relies on a fake arithmetic | Sociology and Pure Mathematics | N J Wildberger Number systems are at the heart of mathematics and have been for at least 4000 years. The Egyptians had a base 10 system that used fractions, albeit not in the way we do, while the Sumerians remarkably developed a base 60 floating point system. What systems do we teach in schools? What about scientists, engineers and computer scientists these days? What about modern pure mathematics? The answers might surprise you. Pure mathematics needs a bit of a serious shake-up. Sociologists ... please come to our rescue! Help us understand how we got into this mess, and what forces conspire to keep us in it. In this video we explain how we (modern pure mathematicians) currently rely on a demonstrably fake arithmetic. Of course people will want to kick and scream at this claim, so we present some level-headed challenges that will clarify if my bold claim has merit or not. And we also connect with two important aims from classical calculus finding the slope of a tangent, and finding the area under a curve. I assert that both of these important tasks can actually be done without infinite processes/limits and to find out how you can simply join the online Algebraic Calculus One courses (see below) currently for free. ;) This video is in the Sociology and Pure Mathematics series, where we attempt to bring some human social/cultural analysis to modern mathematics: or at least outline some broad directions that such an investigation could take. If you would like more discussion on the difficulties with real numbers, check out my paper Set Theory: Should you believe? at https://www.researchgate.net/publication/280387313_Set_theory_Should_you_believe. You can also look at the MathFoundations playlist found for example here courtesy of Cosmo Learning: https://cosmolearning.org/courses/math-foundations-with-norman-wildberger/video-lectures/ In particular look at the videos from about MF 84 to MF 123. **** Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated. ***** Here are all the Insights into Mathematics Playlists: Elementary Mathematics (K-6) Explained: https://www.youtube.com/playlist? list=PL8403C2F0C89B1333 Year 9 Maths: https://www.youtube.com/playlist?list=PLIljB45xT85CcGpZpO542YLPeDIf1jqXK Ancient Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e Wild West Banking: https://www.youtube.com/playlist?list=PLIljB45xT85DB7CzoFWvA920NES3g8tJH Sociology and Pure Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua Old Babylonian Mathematics (with Daniel Mansfield): https://www.youtube.com/playlist? list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov Math History: https://www.youtube.com/playlist?list=PL55C7C83781CF4316 Wild Trig: Intro to Rational Trigonometry: https://www.youtube.com/playlist?list=PL3C58498718451C47 MathFoundations: https://www.youtube.com/playlist?list=PL5A714C94D40392AB Wild Linear Algebra: https://www.youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp Famous Math Problems: https://www.youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf Probability and Statistics: An Introduction: https://www.youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf daeklnLse Booles Logic and Circuit Analysis: https://www.youtube.com/playlist?list=PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb Universal Hyperbolic Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI Differential Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP Algebraic Topology: https://www.youtube.com/playlist?list=PL6763F57A61FE6FE8 Math Seminars: https://www.youtube.com/playlist?list=PLBF39AFBBC3FB30AF *** And here are the Wild Egg Maths Playlists: Triangle Centres: https://www.youtube.com/watch?v=iLBGXDSUohM&list=PLzdiPTrEWyz6VcJQ5xcuqY6g4DWjvpmjM Six: An elementary course in pure mathematics: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS Algebraic Calculus One: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB Algebraic Calculus Two: https://www.youtube.com/playlist?list=PLzdiPTrEWyz5VLVr-0LPPgm4T1mtU_DG-$

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