I turn off the sound, turn on the captions, set the speed to one quarter, and don’t look at you gesturing. Plenty of time and fewer distractions. Highly recommend using screen videos. Work out your presentation on the computer, record as you go. Explain the steps and move the pieces around yourself in real time. It takes some preparation and you can do it by editing too.
But I find talking heads mostly useless and distracting. You are putting your face between the people and the material. Metaphorically sit beside them and let them see the same screen that you do. Whisper in their ear or write your explanation. If the caption is well written the Google translate can convert the whole (taken is pieces because they have a size limit) caption listing and translate it to other languages. They are getting better and anything in the other languages is better than none. The chance of your spoken English to text and the translated to other languages — coming out even close — is small.
You could do these same exercises, demonstrations, walk-throughs, verifications, checks, proofs, examples — on a web page that supports symbolic mathematics with integrated simulations and visualizations (more than simple graphs). Numerics are not bad. You used that mentally when you said every term (1/(1+x)) would be smaller than the corresponding 1/x. But you could have showed the actual values.
In real problems in engineering, sciences, economics, finance, budgeting, planning, project and device design and myriad other places, you will have to also do the quantitative demonstrations – for yourself and others. I am looking at all mathematics on the Internet – all of the tools, people, uses. This video presentation has to go into human eyes and minds. And in the minds find matching resonances (memories that are close).
But with you in between, the people are not doing it themselves, except those who know how to do it by paper and pencil. Or rarely who have a symbolic math tool they can afford and is not so bloated it takes forever to learn or afford or use. Don’t tell people how to fish, or show them pictures of fish and fishing – give them a fishing poles, some hooks and bait, directions to where to fish, and give them a community of others doing the same thing.
YouTube only has this clunky blog thing. No index, no faqs, no collaboration, no building something together. There are horrific problems in the world, and people are only sharing words about the problems, not sharing the data and tools and organizations to map ans solve the problems. You know some of them. And truthfully, most of the posed mathematical problems only have value in the real world when the insights and more efficient methods help save lives, assure the survival of the human species, teach not hundreds or thousands – but billions of people who need better skills, better tools, and efficient project management for the really large, hard, but not impossible problems of the world.
I am working on “covid” which has 7.5 billion entries on the Internet. That is mostly massive duplicates and variations on a core of a few hundred pages of knowledge and essential guidelines.
Think about the problem of 4.8 Billion people who have some access to the Internet. They search for “covid” related things and get 7.5 Billions starting points and an almost infinite number of pathways. None of the material is traceable (much of it). Now you or I might spend hours or days or months tracing out tiny pieces, and sometimes we can find the author and tools and data and check things. But that level of diligence, and that amount of time and effort and skill – must be multiplied by the number of potential views (4.8 Billion) to get an estimate of the cost of our current messy Internet on society.
“mathematics” on the Internet has 320 Million entry points. Many mouths shouting — “I can tell you about mathematics”.
It is not good for society as a whole when all the mathematicians in the world are not working together – not to create a monopoly on tools and methods, jobs and applications – but to document what is known, what is being worked on, and share it – in the form of tools that new generations can use.
I am working on “atomic fuels”, “faster than light communication”, “global climate change”, “solar system colonization” and many thousands of similar topics. 7.8 Billion people is a lot of people and human time. The basic human brain is capable of much more than we ever require of it. And it can grow and stretch with good training data sets and tools for exploring and visualizing. You show symbolic mathematical steps. But your could have the computer do it, and let people step though the formal symbolic substitutions and operations to see how they are done. The processes of the steps are the product of some human learning of what is important to do when comparing quantities, structures and patterns. We should not make billions of people learn by rote listening to talking heads, but give them real tools and real data.
The vast streams of raw data about the world, and the mass of collected data that has been processed by humans into words and many representations is mostly on paper. PDF is paper. The whole Internet is mostly paper. It all requires humans to read the pages, recognize the words and things, and then mentally manipulate the pieces. But the computer can do that for us, and we control and guide what it does. Making every person working on covid, for instance, is forcing massive delays in dissimination of knowledge. It impede sharing and progress. Because only a few people have enough memory of the pieces discussed to do anything. And the tens of millions who could help, are prevented because they have to build every equation, ever dataset, every program, ever bit of logic again.
If a paper is good, then millions might read it. But if it is poorly written, and it takes hours or days or weeks to understand just the pieces, then it is a burden on all those reader that has quantifiable economic and social impact. For covid, the delays mean 200,000 deaths each month. Just because the world is playing that game of “whisper” or “telephone” where a child whispers something in the ear of the next, and it gets repeated many times, – coming out garbled at the end. It always is garbled. For children at a birthday party it is a big laugh. But when millions of lives depend on something and the people involved all over the earth persist in sending “papers” to each other, rather than putting tools and data and models and active communities online — it is just sad.
Thank you, I like your skills and efforts, but I think you could also help with problems in the world. Training, not entertaining, people to use math for serious problems would help. Not memorizing steps, but finding and using good tools that can be used for global scale problems
Richard K Collins, Director, The Internet Foundation