Continuous version of the Fourier series.
Can be used to represent functions that are not periodic: math.stackexchange.com/questions/221137/what-is-the-difference-between-fourier-series-and-fourier-transformation while the Fourier series is only for periodic functions.
Therefore, the Fourier transform can be seen as a generalization of the Fourier series that can also decompose functions defined on the entire real line.
As a more concrete example, just like the Fourier series is how you solve the heat equation on a line segment with Dirichlet boundary conditions as shown at: Section "Solving partial differential equations with the Fourier series", the Fourier transform is what you need to solve the problem when the domain is the entire real line.
A conjecture is an open problem in mathematics for which some famous dude gave heuristic arguments which indicate if the theorem is true or false.
Ideally can be thought of as a one-way ticket gate that only lets electrons go in one direction with zero resistance! Real devices do have imperfections however, so there is some resistance.
First they were made out of vacuum tubes, but later semiconductor diodes were invented and became much more widespread.
It sees and moves individual atoms!!!
Once Ciro was at a University course practical session, and a graduate was around helping out. Ciro asked if what the graduate did anything specifically related to the course, and they replied they didn't. And they added that:Even though Ciro was already completely disillusioned by then, that still made an impression on him. Something is really wrong with this shit.
One has to put the bread on the table.
Other people that think that the educational system is currently bullshit as of 2020:
- Einstein, quoted in The New York Times, March 13 1949, p. 34:[ref]
- Ron Maimon
- Xavier Niel: fortune.com/2018/11/30/billionaire-xavier-niel/ "Want This Billionaire's Attention? Drop Out of School" (2018). He also created 42.
- Year On
- by Zach Caceres
- Anand Raja submission "Students and Universities": publications.parliament.uk/pa/cm200809/cmselect/cmdius/170/170ii.pdf, www.linkedin.com/in/anandraja/.
- xsrus.com/life-school-and-the-80-20-rule. Also GPA 2.0 linked from xsrus.com/ to xsrus.com/gpa-2.0 but down now
- A Mathematician's Lament by Paul Lockhart www.maa.org/external_archive/devlin/LockhartsLament.pdf
- www.learningforreal.org/quotes/ quotes Elbert Hubbard:She's somewhat focused on the performing arts, but what she says applies basically equally well to the natural sciences. A talk: www.youtube.com/watch?v=ggYL9gQeVEk She talks about authentic learning.
- www.youtube.com/watch?v=iG9CE55wbtY Do schools kill creativity? by Sir Ken Robinson (2017)
- Erik Finman thinks school is broken
- sociable.co/technology/silicon-valley-education-students-entrepreneurs/ Bringing Silicon Valley into Schools: How to Make Students Entrepreneurs of Their Own Education (2016)
- hackeducation.com/2015/04/25/factory-model The Invented History of 'The Factory Model of Education' by Audrey Watters (2015)
- www.forbes.com/councils/forbescoachescouncil/2025/04/17/the-ai-fear-factor-why-leaders-resist-and-how-to-move-forward/ The Single Best Idea for Reforming K-12 Education by Steve Denning (2011)
The true value of snake oil is intangible as well.
David Deutsch on Education interviewed by Aidan McCullen (2019)
Source. Key quote that hits the nail:
So right... the purpose of education is not to teach facts. The purpose of education is to propose ways of thinking, which students themselves must try to apply and decide if it suits them! And use the patterns of thinking that are useful to reach their goals.
Like Noam Chomsky, he proposes education has been a system of indoctrination more than anything else e.g. twitter.com/daviddeutschoxf/status/1406374921748496386:At twitter.com/DavidDeutschOxf/status/1051475227476185089 another good quote by Churchill:
All compulsory education, "tough" or not, "love" or not, in camps or not, and whether it "traumatises" or not, is a violation of human rights.
Headmasters have powers at their disposal with which Prime Ministers have never yet been invested.
Quote selection by Charles Bukowski (2016)
Source. Generally speaking, you're free until you're about 4 years old. Then you go to grammar school and then you start becoming... oriented and shoved into areas. You lose what individualism you have, if you have enough of course, you retain some of it... Then you work the 8 hour job with almost a feeling of goodness, like you're doing something. Then you get married like marriage is a victory, and you have children like children is a victory... Marriage, birth, children. It's something they have to do because there's nothing else to do. There's no glory in it, there's no steam, there's no fire. It's very, very flat... You get caught into the stricture of what you're supposed to be and you have no other choice. You're finally molded and melded into what you're supposed to be. I didn't like this.
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