Calculus Made Easy and Memorable

I made a website to help people learn calculus. I have taken a 1910 book Calculus Made Easy by Silvanus P. Thompson that has already been digitized and put on the web in a nice format at https://calculusmadeeasy.org/. This was created by nadvornix and other volunteers. This edition has added some memorisation reminders to the text.

The book is famous for being accessible to teenagers. Some of the text has dated in the century since. Martin Gardner created a new edition in the 1980s with some of the text deolded and some extra background chapters. Making similar updates might improve this book some more.

Orbit is a tool that tests your knowledge of text you just read. And then retests you on a regular basis. This vastly increases the amount you remember for very little extra time or effort. Some of the evidence that timed repetition aids recall is given in this essay 

Calculus made Easy and Memorable is on the web at http://calculusmadememorable.org/ and the code is here. 

Why put a new more memorable calculus book online? ‘1 million students take a college-level Calculus 1 course in the United States, at an average cost of $2,500. And then 40% of them fail.’ That is 1 billion loss a year in one country from failing one course. Anything that helps reduce that rate could be a boon.

A Patreon for Materials

Prizes are a really good way of funding science but are not used enough. All sorts of prizes from longitude to private space have speed up technological development in their area.

Kaggle is an interesting example of current innovation incentivised using prizes. Kaggle defines a metric over a dataset and people try an build models that predict that well. This is then tested over another dataset to prove your predictions are the best. For not very much money a large number of very skilled people work on a defined problem for fun, kudos and the possibility of profit.

1. Typical Kaggle competition lasts 3 months, offers $25,000-100,000 in prize fund and attracts around 1000 specialists

2. At least top 10% of those specialists, ~100 persons are of prime quality, many others 'just' good.
   

Could a similar thing be done for discovering materials with properties we want? There are all sorts of problems that could be solved with materials with new properties. There are commercial incentives to develop many useful materials already. A more efficient solar panel or energy dense battery could have such commercial value lots of people are working on making them already. But some properties of materials are known to be useful but not commercialised yet to have huge competition or budgets trying to create them.

If we agree prizes are a useful incentive. And that we need new materials with useful properties how might a kaggle for such prizes work?

Kaggle has test datasets unknown to competitors held out to prove later which prediction model is best. For a materials version proving specific qualities in the lab would, initially, be too expensive. Relying on the scientific peer review process, of quality journals, would probably be enough initially. Occasionally issues in published materials research comes to light. But that happens in kaggle competitions too. And with prizes fairly low the incentives for shenanigans are not huge. Use a paper being published by a high quality journal as proof that a material has the defined property.

How long would the competitions be open for? The millenium prize for solving known big hard maths problems are open ended. Kaggle competitions are shorter a few month time periods. The time needed for journal papers to be approved and the difficulty of making materials means a year is probably more practical. Having a year competition timeline makes it more open to tinkerers than big grand ambitious challenges. I think 'A prize to someone who makes a wire room temperature superconductor at atmospheric pressure' is too ambitious. 'A prize to someone who publishes the warmest superconductor in a substance that can be turned into a wire by December 2022' is more practical. Competitions for improvements of a defined characteristic over a period of a year or two seem to be the best prize incentives to me.

How much would the prizes be for? Using journals keeps the cost of running the competitions low. But also means huge amounts of money cannot be involved. Also unlike kaggle a company putting up a dataset is not paying the prizes. The prizes would just be donated by people who can see that creating a product with these properties would be useful for improving our lives. As such a Patreon like model where donations are collected would probably be best. Stripe lets foundations setup as non profits set up these sorts of donations. Prizes would probably be in the 100K to -> 1 million range but initially to prove the concept would be much lower. 

What would be a good initial material quality to test this Patreoned Kaggle for materials idea on?

Assurance Contracts to Provide Ireland with the Grid Scale Battery Storage?

My last post was 

€100 off Electricity Bills or an Investment in Batteries?

where I argued that it was better to invest much of this money given back by the government in the electricity grid in the form of utility scale batteries.

These batteries would be a public good making island of Ireland electricity cheaper, greener and more reliable. They would improve things for everyone in Ireland. Batteries are non rival in that everyone benefits if we build them. They are non excludable as anyone who uses the grid is helped. And battery storage is currently not provided nearly enough of. There isn't any in Ireland yet and even if quite a large amount of battery storage added to the grid extra storage would still help.

Making electricity cheaper would also be fairly progressive as on lower incomes a bigger proportion of your income tends to be spent on electricity. But many have argued that this €200 million should be spent on other public goods like welfare payments rather than electricity. I am arguing here if we spend the money on electricity batteries is a better way to spend it on infrastructure rather than on an electricity bill. 

The Hornsdale Power Reserve cost €57m in 2017 and now would be much cheaper per kwh as the price of batteries keeps dropping. Let us say we need to get €57m from this grant to build a battery system for Ireland. How could we collect this money? The government could have not given out the cheques, except to those in receipt of social welfare, but the government have already said they will.

One way is an assurance contract. Kickstarter is this, where the money is collected from people but it is held until the €57m is gathered, so if not enough money is gathered to build the battery no money is taken. We would need to trust the collector will keep our money safe until the needed amount is gathered. And that the organiser will actually build the battery with the money if the required pledge level is reached. 

The free rider problem is the largest issue though. Why would I pay if someone else is going to pay for me and I get the cheaper green energy anyway?

In this case the government (or another grid battery organiser) have to get the money voluntarily. One way to do this is a Dominant Assurance Contract (DAC). They would create a website saying

Give us your €100 electricity rebate and we will create a battery storage device that will make electricity in Ireland greener, cheaper and more reliable by adding battery capacity to the grid. The minimum we need €57m and that will add 129 MWh and 100 MW* but a stretch goal is adding more capacity if we get more money. If we do not get €57m in pledges everyone who did pledge will get €120 for their €100 pledge back.

*this is the 2017 Hornsdale value we would get more now.

There are some issues here. Governments don't offer dominant assurance contracts like this. They don't like the risk of having to pay back money. Though the paper linked to calculates how low this risk is. I do not know who other than the government people would trust enough to give money back if the pledge was not met and to actually create the battery if it was.

Secondly a public good like a bridge people don't make money from (unless it is a toll bridge). This battery would generate income. I think people pledging that this income would in a large part be reinvested in another system to making electricity cheaper, greener and more reliable again. 

Who else would pay into such a scheme? The large tech companies are building large data centers here and have promised to add to the grid to make up for the extra electricity. They haven't actually protected the grid but by expanding battery storage they could do this. Also they don't want an unreliable grid so it is in their interest to expand battery storage use in Ireland. 

People want to reduce their carbon usage. Home batteries to supply electricity are one way to do this. But grid scale solutions are a lot more efficient per euro spent. Also many who want to reduce carbon output dont have the €4000ish needed for a home system but will be able to spend the €100 or slightly more.

An assurance contract to gather up peoples €100 to spend on a grid scale solution. What do you think?

 

€100 off Electricity Bills or an Investment in Batteries?

 

€200 Million spent on utility scale battery storage could make electricity cheaper and more environmentally friendly in Ireland for the future.

Australia and California have installed battery storage recently, so the technology is not unproved. They allow energy to be stored from wind, solar and hydro sources and used later. This means that the most polluting forms of electricity never have to be turned on. Offices and homes do not use much electricity at night. If we can store energy at night to use when demand is high it means wind can be a greater proportion of the grid and we don't have to use as much non green energy.

Also because the energy is stored when it is plentiful and cheap and used when it is rare and expensive the costs of producing energy overall drops. These batteries pay for themselves pretty quickly. In 2017 they "built the Hornsdale Power Reserve, for a capital cost of A$90 million" but since then it "saved South Australian consumers over $150 million." 

Based on a cost of 'The 2020 starting point of $345/kWh' this €200m would provide about 2/3 of the 666 megawatts. That is about 2/3 of Moneypoint. Or over twice Turlough Hill. Batteries supply energy for about 4 hours. But it will be clean energy from Ireland growing renewable energy production.

These are also very fast to build. '63 days between grid contract and completion'. So it is not like it would take years to bring this extra energy into the grid as it would with new power stations or even wind farms. 

Instead of giving everyone €100 off their electricity bill using that money to improve our grid to have greener and cheaper electricity is a better use of that money.