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Picking Arbitrary Values and Numberline Subtraction

Kids are learning subtraction with the numberline, and how their arbitrary value choices reflect the trends of society.

Society has a plethora of arbitrary values. I was inspired to see that kids are learning subtraction using the concepts of distance and the number line (LearnZillion: Solve subtraction problems using a number line). I’ll give an example if you didn’t check out the link.

  1. Pick two numbers x, y (given: 273, 834).
  2. Construct a number line with the given numbers as points:
  3. Step up or down from the numbers in hops:
  4. Add up the hop distances:
    500 + 60 + 1 = 561

So 834 - 273 = 561.

But the neat thing is that it gives children the chance to learn about making choices of where to hop. Given 105 - 35 they might hop to 55 and then to 105 or they might hop (bidirectionally) to 40 and 100.

The best choices for this sort of subtraction is, as far as I can tell, the following:

  1. For each common column, from smallest to largest, hop from the low number until that column is normalized.
  2. If the last hop increased the column count, include that column as a common column.
  3. Add the remaining uncommon amount of the larger number.

So for 123,456 - 789:

120,000 + 2,000 + 600 + 60 + 7 = 122,667

At each step we only focus on matching the single column. If we overrun the default number of columns for the smaller number (eg, 856 + 600 = 1,456), we may take more steps. But we will never add more than nine of whatever unit size we’re focused on.

So in this case we probably have a good algorithm for picking what would otherwise be arbitrary hops. Kids can still learn the method without this algorithm, and they can play around with finding their own hops.

But we find arbitrary numbers throughout the law and in our daily lives. They have economic, social, and psychological ramifications. Tax brackets tend to be based on arbitrary income levels, for example. Inflation and other factors (such as the number of people with incomes previously considered outliers increase) may invalidate those existing, arbitrary values.

We should tend to avoid arbitrary values in the law. Fines should be based on an individual’s income, as is done in some European countries. Fining a poor person the same as a rich person for a minor infraction such as speeding makes zero sense. Either the fine will be excessive for the poor person, or it will be meaningless to the rich person.

We may again face problems with arbitrary values as new technologies come along. Autonomous vehicles may be able to safely exceed speed limits, but will undoubtedly be forced to comply with limits that make little sense for years beyond the widespread adoption of such vehicles.

And yes, the federal budget. What amount should the budget be? We have endless scoring of laws and regulations from the Congressional Budget Office and Office of Management and Budget. But when we actually formulate the budget, it is entirely arbitrary. It is based on whims and beggings of special interests, or on emotional appeals for the social welfare.

I favor social welfare, but just as prison sentences should be chosen for their effect and not out of emotional reflexes, so should social welfare programs budgets.

But at least young kids will become acquainted with picking arbitrary values using the number line. Maybe they will find algorithms for picking other values that have profound repercussions on society. Or maybe they’ll just get better at picking the arbitrary ones.

Why Information Matters

A short post on the value of information to our way of life.

If you look at the history of any major problem, the solution has involved the freeing of information in some manner. For diseases it involved understanding the transmission, immunity patterns, and eventually understanding the actual bacteria and viruses. World War II was largely an information war, with mathematical feats used to free information and hide it, to gain the upper hand in the conflict.

Is hiding information okay? It depends on the information being hidden. For example, for a military campaign in the aforementioned war, a certain amount of hiding was necessary. But that sort of information has a short half-life (the time until the sensitivity of the information is halved).

Other information is private. That means the information may be necessary to the person’s well-being. It’s up to the person (or organization) to determine when and if to share that information, and who to share it with.

But, all things being equal, the more information that is known about a problem, the easier it is to solve the problem. That means systems that try to tie up what is really public information, like scientific and artistic works that have been published (from the same general origin as public) are failures from their inception. They are confusing control with revenue.

It makes sense for people that create works have a decent quality of life. But that’s different than what’s being done. What’s being done is you have people afraid to share their works because they don’t want someone else stealing their works. You have people who are doing everything in their power to lock down a perpetual copyright law enforced under penalty of death. You have people fighting for the right to share art and scientific knowledge with each other. And you have people missing crucial pieces of information in their endeavors to become better scientists, artists, citizens, because access is blocked.

That’s all bad enough, but the same tools being sold to the Copyright Armada are also turned against people fighting oppressive regimes the world over. You have the same information blocks leading to huge recessions because the traders are naive enough to think an information gap is their best way to make money.

Information is the critical element that makes us more than mere animals, just as when a crow picks up a piece of bent wire and uses it as a tool it is something greater than a crow with a piece of wire. Information is what allows us to do something other than forage and hunt all our days, without shelter.

It is critical that we improve our flows of information. It is information alone that can prevent our worst acts and enable our best acts.

Doodles 4 Google

Google let kids design their logo to express their own answers to the question, “What if?” The results are almost as wonderful as the dreams that spawned them.

Doodles 4 Google:

Doodle 4 Google is a competition where we invite K-12 students to reinvent Google’s homepage logo. This year we asked U.S. kids to doodle around the theme “What if…?”

You can now vote on the finalists in the four age ranges: K-3, 4-6, 7-9, and 10-12.

You get to vote once per age group.

If you’ve got the time, go look over all of the finalists; they’re all amazing and I can only imagine the ones that didn’t make the finals were just as great. This is why Google is more different than Apple and more professional than Microsoft.

But that’s beside the point. The point is that this gave all these kids a bit of time to create and also to recognize the possibility that any one of them could be the future designers that get their work shown to hundreds of millions of people. The project itself, as much as the question it posed, is truly inspirational.