Search Results for “math”

Thoughts on 9/11 and its Aftermath

Posted on 13 September 2021 by David Merkel

Picture Credit: Jackie || Though the idea for the lights bringing back the twin towers is beautiful, for me, someone who travelled to the PATH station beneath them many times, I miss the twin towers.

For those that don’t know my blog well, I described what happened to me during 9/11 in two places:

My 9/11 Experience
The Education of a Corporate Bond Manager, Part I (and a little bit in part VI, but that’s mostly on bond management)

There’s one small thing I left out. I was planning to go to a conference at the World Trade Center on 9/12, if things were in good enough order at my work. I had to leave it flexible, because I did not know what would come of my client meeting planned for 9/11 — the client was rarely reasonable, and I might have to jump on a bunch of projects, and not go to NYC. As it was, I never had to make that choice. The events that unfolded made it for me.

One of the things that surprised me at the time was all the people who said, “Why did they attack us? What did we ever do to them?” in the US. I remember an email that came to me saying that, and I came up with seven reasons why they would do it. Now, I don’t have that email, so I am guessing at what I said, and I may not be able to come up with all seven, but I will try to do it here.

The US supports Israel.
Our entertainment dominates the globe, and poisons their culture, as many in Islamic countries like the entertainment, and become lukewarm to serious Islam.
We support “moderate” Islamic governments, which keeps serious Islamists out of power.
We kept bases in Saudi Arabia, desecrating their Holy Land.
The Saudi Monarchy talks a good game with respect to Islam, but they oppose radicalism, and the US supports them.
They hate the US because it is so morally degenerate, and yet so rich, which gnaws at them because the more consistent a nation is with Islam (excluding the accident of crude oil), the poorer they tend to be.
The US invaded Iraq for less than significant reasons in Gulf War I. The US & Israel make military and pseudo-military actions with impunity in the Middle East. Think of Reagan bombing Ghaddafi.

Okay, I got to seven, and I suspect at least six of these were in my original email. My statement to those I ran across in 2001 was that the attack was not irrational. They had genuine reasons to hate the US government.

I think we didn’t learn anything from 9/11. Or, we didn’t care that we offended them. We essentially doubled down.

We fought Gulf War II.
We invaded Afghanistan, a nation that is not a nation, and tried to change it, blowing a lot of money on a hopeless cause. Cultural change is almost impossible to achieve, and certainly will not happen when pushed by outsiders.
The O-bomber used drone strikes with impunity to eliminate enemies, and occasionally innocent people by mistake. Now Biden follows in his footsteps.
Seal team six eliminated Osama Bin Laden in Pakistan. (Do we really want a world where those who are technologically powerful can assassinate with impunity? How should we feel about Salvador Allende of Chile?)

I believe that war is legitimate if there are legitimate reasons. I believe in Just War Theory. Aside from that, I tend to be a pacifist. One of the few things I liked about Trump was that he was probably the least hawkish President that we had in a long time. I don’t think the US has had a legitimate war over the last 70 years. It is our job to defend our nation, not the world as a whole.

I think we have created more problems in the Middle East over the last 20 years, and to the degree we feel we have to continue to interfere there, those problems will increase still more. If you think of George Washington warning about “entangling alliances,” I think we have fallen into the dangers that he described. And if you think of Eisenhower warning us about the “military-industrial complex,” that has come to dominate us as well.

We may have beaten back serious Islam for a time, but it will come back. We have offended them too much. The US has to understand that the hatred that exists in the Middle East can’t be solved. Let them fight, and let us stay out of it. Protect our nation? Yes. Protect the world? No. Offensive wars are almost never just.

Part of being a strong nation is controlling that strength, and only using it in the most severe situations that affect us directly. If you waste that strength on lesser matters, you weaken you own nation, and your reputation abroad.

So no, I don’t think we did the right things as a nation post-9/11, and I haven’t even touched on the loss of freedom here. The US needs to be more humble, and not impose its will on the rest of the world.

Math Drill for Your Children (and Grandchildren)

Posted on 25 September 2019 by David Merkel

Every now and then I do something off-topic with Aleph Blog. This is one of those times.

I’ve talked about math pedagogy perhaps half a dozen times since starting this blog back in 2007, and if you are a long-term reader, you know that I think the powers that be DON’T HAVE A CLUE AS TO WHAT THEY ARE DOING!

What, am I flustered? No, no. I am being perfectly serious, and in my opinion moderate. One of my daughters, my wife and I are all good math tutors. We can take on the hard cases and make them learn. In my opinion, the height of good math education in the US occurred in the 1950s, before I was born. I remember as a kid reading the older textbooks and thinking how wonderful it would be if these were the textbooks at my school.

But that’s not my main reason for writing this evening. I want to explain that students need a firm grounding in their math facts if they want to succeed with math. Otherwise, they will feel dumb, hate math, and not want to study it.

All of my children, with varying degrees of intelligence, were able to work through the 100 math facts for addition, subtraction, multiplication and division… getting them to get all of them right in five minutes by third grade, and three minutes by fifth grade.

Is memorization the highest expression of math skill? No. But it enables other skills that won’t emerge unless basic calculations are easily done. It is a mercy to children to drill them until the facts are lodged in their heads for easy retrieval.

To give a different example, my daughter who was our best math student came to me and said that the work I had done with her on precalculus was far better than what public schooled students had received.

Oddly, the public schooled students had proceeded far beyond my daughter in terms of titles of courses taken. But they lacked the ability to actually DO the calculations when they got to college. My daughter became a TA. MAny of them did not.

Part of what I did in teaching her, and other children of mine was always go back to first principles. As an example, with Trigonometry — the unit circle. I would show how everything is derived from the unit circle. The ability to work things out from basic principles is fundamentally different from the seemingly bright children who focus on learning the algorithm to solve problems, but don’t really get the concept as a whole.

Now, don’t get me wrong, problem solving was the main driver of math in our home school, but not to pass tests — it was to promote understanding.

Okay, back to the basics. Do you want your younger children to have a firm foundation in math? I have a spreadsheet that many people have used for drill. You can download it here.

It’s pretty simple. It gives the basic 100 math facts randomized for addition, subtraction, multiplication and division, and a new one my skilled daughter asked for, one that mixes all four, so the student has to think extra hard as the student tries to solve it.

95% of children with repetition and encouragement can memorize their math facts and become more confident to absorb higher level math. Take the opportunity to genuinely improve your child’s math ability, and get them to learn their math facts. After that, they can move on to higher aspects of mathematical reasoning. (Ignore the math ideologues in the public schools, it is as if they want children to do doctoral work before the finish elementary schools. The ideologues are sophomores in the truest sense — wise fools who try to tell you the mankind is different than what it genuinely is, without any real proof for their veracity. They hide behind the shelter of the government, even though they should be fired for incompetence.

In summary, with math, go back to basics. Your child will do far better than his peers.

PS — This is true of the basics across subjects. (Insecure school districts fake progress by having students take so-called college level courses that truly are not such, as my daughter saw amidst her “peers.)

On Learning Compound Interest Math

Posted on 19 July 201420 July 2014 by David Merkel

When I read articles like?this where people get scammed borrowing money, I say to myself, “we need to teach children the compound interest math.”

Even my dear wife does not get it, and she sends the children to me when they don’t get it. ?But beyond learning the math, a healthy skepticism of borrowing needs to be encouraged, especially for depreciating items like autos.

The compound interest math is really one of the more simple items of Algebra 2. ?Everyone should be able to calculate the value of a non-contingent annuity at a given interest rate.

Once people learn that, they might have more skepticism regarding the long-dated pension-like promises that the government makes, because they can look at the future payment stream, and say, “I can’t see how we fund that.”

All for now.

On Math Education

Posted on 28 November 2012 by David Merkel

When I was a kid, my life was mathematics.? When I was little, my mom would hand me sheets of addition and subtraction problems that did not involve carrying or borrowing, and I would fill them out for her, and she would give me more.? That’s my earliest memory.? Second earliest is the procession for President Kennedy after his death.? Third earliest might be my Dad changing my brother’s diaper.? My mother once said, “You must have remembered it because of uniqueness.”

Anyway, when I was a kid, before I went into first grade, my mom taught me multiplication and division.? My Dad taught me some heuristic rules around percentages.

So when I came into first grade at age six, I was shocked that no one else could do math.? I was good enough with math and reading that the special education teacher took note of me, and helped give me my unusual education 1967-1969.? Though I was in a normal classroom, I was a “group of one.”? I had my own special reading and math books.? The teachers pushed a variety of enrichment materials to me, but it was like subpar homeschooling.? I was on my own, and no one would correct my work.? For a little kid, I was pretty motivated, but it would have helped a lot to have more adult interaction.

SRA helped on the reading side, and there were later SRA attempts at math though I don’t think that did much.

In third grade, they gave me a programmed instruction curriculum in math, in addition to the ordinary class.? At some points, I acted as a tutor to other students.? The programmed instruction was modeled after the “new math” fad.? I could get it, but at the time, I realized that I was so different from my peers, that I knew that if I could get it, that did not mean that others my age could get it.

Then in fourth grade, they mainstreamed me.? I spent time playing around with how to do square and cube roots by hand.? Tedious, but not that hard to do.

In fifth grade, my Father brought me an algebra book that used programmed instruction.? I puzzled over it, and didn’t get it until I talked to an older friend about it who told that “x’ is a number that we do not know, but are trying to calculate.

There’s more to this story, but I will drop it, lest I bore you…

What I experienced as a child affected me.? I could see the abstraction of math while young, and it amazed me.? But now look through my eyes as I find out that I am unusual.? There is a normal track for math, and a normal way to teach it.? As I tried to tutor my classmates, I realized math was not intuitive for almost everyone else as it was for me.

I became a good math tutor.? Parents would hire me , and ask me what my rates were.? I don’t know how I thought of this, but I said, “Five dollars per sitting.? A sitting could be five minutes or two hours. If I lose their attention span the sitting ends.”? That motivated the parents to motivate the kid.? After one short sitting, future sittings got longer.

As an adult, I married a math teacher.? She admits that I am the better with math, and that I often come up with creative ways to teach concepts that she could not.? She is still quite good with teaching math such that all of our biological and adopted children made progress in their percentile scores in math and other topics as they grew.

I think that I know math, and how to teach math.? I have done it while young, and older with my older children.? I have never taken a course in education, and thus my views of pedagogy have never been sabotaged by what is taught in most colleges regarding teaching children.

Some may think this assessment too harsh, but remember, we had the “New Math” in the Sixties.? It was a disaster.? For me, a math prodigy, thinking about math through the lens of set theory, it was challenging and interesting.? To most students, it was deadening.

So now we have the evil “Common Core Math Standards.” [CCMS] When I was a kid we joked about Communist plots to destroy America.? Well, I think the Communists are pretty weak in general — they don’t understand the nature of man.? But here we are trying to make kids try to make adult judgments regarding math.? That’s just plain stupid, because it doesn’t get the way children develop.

The Holy Grail of Critical Thinking

I don’t think critical thinking can be taught.? If you are smart enough, you will think critically. If not, no.

I say this as one where my wife and I have homeschooled our eight children for 18 years, and as my children get older they disagree with us to varying degrees.? We taught them well.? Sadly, some disagree with our premises.? But, they are all smart and the seven that have gone through standardized testing have all shown significant progress, moving 25% or more in the percentile rankings from elementary school to high school.? My wife teaches very well, and I support her. Please also note that five of the children were adopted, and the same effects happened with them.

But the CCMS flips things on its head.? Children need to learn facts.? They can absorb facts because they are easy for the young? to absorb.? Drill on math facts is a very good thing because it eliminates a hurdle to learning more in math.? Once you know the basics, the mind is capable of absorbing more abstract reasoning.

It is the opposite of what the experts say.? Math should focus on the concrete with young children, and as they get wiser, on to things that are more abstract.? They should not begin with abstraction, and try to move to the concrete.

Think about it for a moment: would you rather hire a guy who understood the basics of your business, or hire a guy who had a theory about your business, but did not understand the basics?? You would hire the former if you were smart.

Understanding the basics is important, and sadly, we have gotten away from it in the last 60+ years in math.? We did much better in the past, and we paid teachers less in real terms back then.? The colleges that teach teachers should be dismantled, and teacher accreditation should be eliminated, because there is no clear value created by accreditation.

We need education to be more like home schools, where teachers train students for many years in elementary grades K-8, where tutoring plays a large role. Understanding the student, and consistent mentoring makes a far brighter student.? Eliminating credentialing would being in brighter, more motivated teachers that ignore the idiocy to the teaching colleges.

Now maybe there is a home and private-schooling cabal, pushing CCMS in an? effort to destroy the public schools, or at minimum, assure that those who go to public schools will be peons to those who don’t go there.? I really doubt that, because those who don’t send their kids to public schools are more upright than those that don’t.? They are putting forth extra effort for their kids, versus people who don’t care.

Practical Advice

I live in Howard County, one of the richest counties in America.? Unique to Maryland, the counties are the school districts.? We homeschool in a county that is one of the best around.? We are evangelical Christians, but most homeschoolers here are secular. Why?

The school districts adopt a variety of dumb ideas like CCMS that hinder reading and math.? If I could vote to eliminate the public schools I would do so not out of ideology, but raw incompetence.

Most parents that we interact with are either hiring a tutor in math, or doing it themselves.? If that is the case, why not homeschool? It’s a lot easier than it looks, and it doesn’t take a lot of effort to outperform the public schools.

The main reason is the two-earner household.? Most could tighten their belts, and have one parent stay at home to teach the kids.? The second trouble is child control/discipline — my comment is if you are firm with them as parents were prior to 1950, you should have no problem, but consult your local statutes to figure what you have to hide from.

With CCMS many families will have to do one of the following:

Tutor their children in math
Pay someone to tutor their children in math
Homeschool
Start a war against those that set the public educational standards

Summary

Children are not capable of absorbing abstraction.? Every real parent knows that.? Fight the educated idiots who are trying to ruin math education with their misbegotten theories that do not understand math or kids.

Book Review: Bond Math

Posted on 29 July 201129 July 2011 by David Merkel

This book is the opposite of the book Interest Rate Markets, where bond markets were described, but there was no math.? This book was written by an academic who has done many seminars for bond professionals so that they could understand the math behind bonds.

The math rarely transcends algebra, except where he used calculus to briefly explain duration and convexity.? Perhaps he could have consulted with actuaries who use discrete approximations.

One more virtue of the book is that if you use Bloomberg, which is common for bond professionals, the book explains the nuances of how Bloomberg does many of its detailed bond calculations.? It even explains why you have to interpret some of what you get from Bloomberg with caution, because it may use different assumptions than you would expect.

So if you want to learn the bond math, this book is a congenial way to do so.? I recommend it highly.

Quibbles

Now, the writer is an academic who has never managed bonds.? As such, he can’t help a great deal with bond selection or portfolio management issues.? But that’s not the main goal of the book… he’s here to teach us the math, and nothing more.

Who would benefit from this book:

Anyone who wants to learn the bond math would benefit from this book.? Go learn and conquer.

If you want to, you can buy it here: Bond Math: The Theory Behind the Formulas (Wiley Finance).

Full disclosure: I asked the publisher for the book and he sent me a copy.

If you enter Amazon through my site, and you buy anything, I get a small commission.? This is my main source of blog revenue.? I prefer this to a ?tip jar? because I want you to get something you want, rather than merely giving me a tip.? Book reviews take time, particularly with the reading, which most book reviewers don?t do in full, and I typically do. (When I don?t, I mention that I scanned the book.? Also, I never use the data that the PR flacks send out.)

Most people buying at Amazon do not enter via a referring website.? Thus Amazon builds an extra 1-3% into the prices to all buyers to compensate for the commissions given to the minority that come through referring sites.? Whether you buy at Amazon directly or enter via my site, your prices don?t change.

Where Can I Learn the Investment Math? The Bond Math?

Posted on 25 December 2009 by David Merkel

I was recently asked where to look for how to understand quantitative investing, fixed income, etc.? Let me try to explain.

I have reviewed in the past Investing by the Numbers (Frank J. Fabozzi Series).? This is a good book that covers a wide number of areas in quantitative investing without getting too technical.? I learned a lot from it, and I don’t think the lessons there are out of date.

As for Fixed Income, the main book is Handbook of Fixed Income Securities 7th Edition, edited by Frank Fabozzi.? Fabozzi gets practical experts to write for him and he edits the book so that it reads well.? The result is a readable book that gives all of the qualitative information about the market, but does not deliver the math.? That’s a good thing.? Most people don’t want the math.

But… what if you are a misfit like me who does want the math.? Where do you go? Buy the Theory of Interest.? And, don’t buy it new.? Buy it used, or get it through interlibrary loan.? Same for Fabozzi’s book.? Don’t overpay.? And, if you can understand it well, maybe you would like to become an actuary.? The actuarial profession has done many good things for me; maybe it will do so for you also.

I have learned a lot from all three of these books.? You can too.

Beating the Mogul Game — An Exercise in Applied Mathematics

Posted on 10 December 200920 June 2017 by David Merkel

I have often wondered about how to rank sports teams.? This goes way back to when I was 10 years old, when I ran across a magazine at summer camp that purported to do this for NFL football.? And so I wondered for many years, looking at similar problems and wondering how a ranking of teams could be generated from a win-loss history.? I finally came to a conclusion when I played the Mogul Game.

The Mogul Game has 148 rich people, and they vary from the super-rich (Gates, Buffett, Ellison) to the not-so-rich (I think they got a kick out of putting Donald Trump at/near the bottom of the list, much as he boasts to Forbes that he is much wealthier than they calculate).

After playing the game idly for a little while, I concluded that if I wanted to win, I would have to capture and analyze data from the game in order to win it.? And so I did, recording who was richer than whom.? I went through four phases:

Doing qualitative comparisons when I wasn’t certain of who was richer.? Who had the two parties beaten and lost to?
Comparing the trial ranks when the difference was greater than 10.
Looking at the highest ranked persons that a given set of contestants had won against, and the lowest ranked that they had lost to.
Looking at the average of the highest rank won against and the lowest rank lost to as the best proxy for a contestant’s own rank, unless it violated the results of an actual contest.? In hindsight, I should have adopted that rule much earlier.

It took three days of off-and-on playing to master the game.? Not all that important, but as I mentioned above, the method can be applied with some modifications for ranking sports teams in an unbiased way.? The same could be applied to any competitive activity where there is a win/loss result.? There are two changes for other activities, though.? Games are not necessarily transitive.? Rich person A is richer than B.? B is richer than C.? A will always be richer than C.? In competitions, Team A can beat team B one day, and lose the next.? Also, Team A can beat team B, which can beat Team C, but C can beat A.? So, if I were doing this for baseball teams, my ranks would drive probabilities of one team beating another.

Why would this be necessary when one can simply inspect the win-loss percentages?? Teams with good records may have weak schedules, and this takes account of the strength of the teams played in assessing the strength of a team.? I’m not sure what they do with ranking College Football or Basketball teams, but this would be a more bloodless way of making the comparison.? Granted, it takes a certain number of contests before there is enough density of information to create a ranking, but given a list of wins and losses from an entire season, this method should be capable of ranking an entire league.

I know this is an odd post for me, but I found it to be an interesting project, and it does have other applications.? Thoughts?

If You Want to Do Well, Study Math, Science, or Business, and Work Hard

Posted on 13 June 200813 June 2008 by David Merkel

I read the coverage of this academic paper with some amusement. Something not mentioned by the reviewers is that the data set came from just one college. Should that then be applicable everywhere? I don’t know.

Also, the idea of correcting for brightness of students strikes me as misguided. Smart students know to apply themselves to majors that will pay off. Also, the concept that high-paying careers require more hours is also misguided. Most of the graduates in lower earning professions can’t work more hours, even if they want to; there is no demand for that.

The paper was written to deal with how one statistically deals with non-responses in surveying. That it deals with education is a happy accident. I would be careful generalizing from this paper. To me, it is another example of advanced research that is highly intelligent, but may lack common sense.

For Wonks Only — The Math of Volatility Mean-Reversion

Posted on 1 August 20071 August 2007 by David Merkel

I’ve estimated a number of mean-reverting models in my time. I had one of the best dynamic full yield curve models around in the mid-90s. The investment department at Provident Mutual said it was the first model that was not artificially constrained that behaved like the yield curve that they knew.

In yesterday’s article, I mentioned that I could give math behind estimating mean-reversion of volatility. In order to do the regression to estimate mean-reversion, we use a lognormal process, because volatility can’t be negative.

Taking the logs of both sides:

Alpha is the drift term, that will help us calculate the mean reversion level, beta is the daily mean reversion speed, and epsilon is a standard normal disturbance term. Assume that there are no more random shocks, so that the volatility returns to its equilibrium level, which implies:

Substituting into the log-transformed equation, we get:

where V-bar is the mean reversion level for volatility. From there, the solution is straightforward:

From my regression, alpha equals 0.046000, and beta is 0.98436. That implies a mean reversion target of 18.937, and that volatility moves 1.564% toward the mean reversion target. One last note: the standard deviation of the error term was 6.3383%, which helps show that in the short run, the volatility of implied volatility is a larger effect than mean-reversion. But in the long-run, mean-reversion is more powerful, because with the law of large numbers, the average of all the disturbances gets closer to zero.

Something Free For Parents Who Want To Help Young Children With Math

Posted on 10 March 20073 May 2007 by David Merkel

This is a little out of the ordinary for those who frequent my blog, but here is something that my wonderful wife and I use to help our children learn math. If you did not already know, we homeschool our eight children. We are not big on math drill; we think word problems teach reasoning far better. But to do word problems effectively, the ability to have instant recall of the 100 math facts in addition, subtraction, multiplication and division is crucial.

We have our children work at it until they can get it perfect in five minutes in third grade, and three minutes in fifth grade.

To use the spreadsheet (right-click and use “save link as” to download), select the tab that you want to work on. “little add, and “little subt” are the 64 math facts with no number greater than 10. To use the sheet, hit the F9 key to recalculate the sheet, which places all the problems in a new random order. (You’ll never get 2 sheets the same.) Then hit the print icon. F9, print, F9, print, etc… pretty soon you’ll have a lot of unique sheets for drill purposes.

Use and distribute as you see fit. I just want to see children who are good with their math. And, if it works for you, let me know.