The Mathematics of the Ethereum Hack

I was a lazy student. College and graduate school offered seductive alternatives to “studying” and I took full advantage of them.

I began as a physics major, but soon discovered that the amount of math required for a degree in physics was, in itself, sufficient to gain a degree just in mathematics. I therefore switched to math.

Math was easy for me. In spite of never studying and seldom showing up for class, I graduated with honors and a Bachelor of Science degree in mathematics from Roanoke College. That same college gave me an Honorary Doctor Of Science degree many years later.

My grades were sufficient to get a graduate teaching assistant-ship from Northeast Louisiana State University. While there I chose the sub-field of point-set-topology as my main focus. There was absolutely no practical use for this field at the time, but the underlying math was so trivial that a ten year old could master it in a matter of weeks. My laziness, again got the better of me.

I got thrown out of Northeast Louisiana state before the end of my first year for sleeping with my students – nearly all of them, if I remember correctly. At least the female students.

I transferred to Virginia Polytechnic the following quarter and began anew. By now, however, my talents in math had grown to the point that my impatience could no longer tolerate the stagnant, formulated condition of my professors.

I would jump up in class, impatiently snatch the chalk out of my professor’s hand and complete a theorem in, what I considered, a more elegant and beautiful manner than the approach my professor was taking, as an example.

I was thrown out before the end of my second quarter.

What I have learned of math, from that point on, I learned on my own.

What I learned from my chosen field – the study of the collection of things into sets and the relationships between sets, in the universe of possible sets – changed my life.

All of reality can be defined in terms of point-set-topology. The known elements constitutes a set. The world of molecules creates various sets that all intersect, at a different dimension, with the set of elements. If sets of molecules become large enough then the world of physical matter that we can see, touch and interact with, is created, and within this world are ever larger possibilities to create sets.

And underlying and empowering all of these sets is the world of quantum particles, creating ephemeral sets that appear, from who knows where, and just as quickly disappear into who knows what, or when.

It is a field filled with exquisite mysteries that can be solved with agonizingly beautiful precision.

Which brings us to the Ethereum Hack. (For more background, see this article.)

The weakness exploited by the DAO hackers was not a weakness in the math of the blockchain or in the math of any part of the DAO structure. The math is sound. However, the math used by by the hackers was equally sound. Mathematics cares little for the concepts of “loss”, “hurt” or any other principles of human perspective.

Without boring the reader with unnecessary detail, the technique used by the hackers was equivalent to a trivial, but powerful technique used for dozens of years by programmers called a “recursive subroutine”. In layman’s terms it is a routine that calls itself as its own subroutine. Trivial to construct but sometimes difficult to conceptualize.

The DAO hackers used an equivalent technique called a “recursive child DAO creation scheme”. Suffice to say that it worked.

Leaders in the Ethereum community are now discussing a solution to this hack using two concepts: soft forks and hard forks.

It is the hard fork that horrifies everyone who fully understands the math of the blockchain and it’s transaction processes. It basically involves changing a past rule in a manner that allows all the people who lost assets to recover those assets.

This sounds good. But to do this requires, in effect, reversing time for a moment.

Mathematics is comfortable with the concept of time reversal. The simple addition of a minus sign to a formula is all that is needed.

However, doing so forever alters the reality of whatever the formula is being applied to.

The blockchain and its transaction processes did not include this minus sign for a reason. Doing so would create chaos in the real world to which the blockchain is being applied. As humans, we have never experienced a condition where time runs backwards and we are incapable of dealing with a reality in which this is allowed.

If the leaders within the Ethereum community decide on a hard fork course, then the ultimate result, at some point, will be chaos within a system designed from the ground up to bring order.

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