Monsters Among Us

In order to fully understand ourselves, we have to open our minds to the fact that everything we do that is “unnatural” is an aspect of our behavior.

If I let my computer fall into the tub, I have witnessed a natural event; gravity working its magic on my computer, on the moon, planets and stars.

However, what could I have been thinking in order to drop my computation box into the tub?  That question is “unnatural” and in the realm of behavior.

Math is the same thing.  Much of what mathematicians do is solidly in the realm of the unnatural, saying more about our behavior than Nature herself.  Many times the very things mathematicians learn can be applied to our lives in very helpful ways.  Counting sheep comes to mind.  So does complex prime numbers for encryption.

There are many instances where mathematicians discover something that doesn’t seem to have any relationship to Nature.  Then after a century or two some genius comes along and figures out what that discovery can be used for in our daily lives.

John Horton Conway is such a brilliant mathematician of the first kind.  Among his many discoveries is something called the Monster Group.  It’s a place where objects exist within higher dimensions.  He was born in 1937, and he’s afraid that he won’t live long enough to learn what that Monster can be applied to in our reality.

As one who solidly believes that the study of higher math is also the study of an aspect of behavior, I would like to humbly submit this to Professor Conway.

The “Monster” is among us.

The key is to understand (which I don’t, by the way) that the monster lives within a dimensional space that is the product of 47 times 59 times 71.  That’s a lot of dimensions.  But the fact that this dimensional number is the product of three primes might be revealing in itself.  Here’s why.

In the simplest behavioral theory, we still have to accommodate Nature as a component.  The easiest way to do that is to collapse everything we understand in the natural sciences into their most basic “atoms.”  Like the Ancient Greeks, our atoms of behavior can be Energy, Space, Matter, and Time.  Collectively we can call these Resources, but there are no more than these four atoms in any behavioral question.  Time only goes one way at the macroscopic level, so let’s ignore it.

The other three behavioral atoms are more than complex enough such that they may be represented by 47, 59, and 71 different states.  The possible interplay between each of their “dimensions” with all of the others could give rise to your Monster.

I propose your Monster Group as a better representation of real atoms, from Hydrogen to Plutonium.  Every atom in the universe becomes one of your Monsters.

There you have it.  Crazy idea, no doubt.  But wasn’t it Hilbert who described one of his former students as not having enough imagination to be a mathematician?

Thank you for everything you have given humanity.

Sincerely,

Tusok

 

Numbers are Real Plus

The great mathematician, John Conway, discovered a very simple way to create all the numbers we will ever need using very simple rules.

Why is a mathematician being featured on a blog that’s dedicated to studying behavior?

Because math is an aspect of behavior.

Yes, you heard it here first.  Math is part of our behavior.

Math doesn’t feel like behavior when we’re in class, dreading the next quiz.  However, the whole concept of numbers, shapes, curves, areas and dimensions are all concepts that only live in our mind.

The fact that we can use these concepts to make our lives easier is extremely convenient, but not because we are directly connected to Nature.

We are INDIRECTLY connected to Nature.  That’s why it’s so important to study math, and to encourage mathematicians to research all sorts of new math.

Conway’s Surreal Numbers are a better way to construct all the numbers we currently know about.  It’s better because it’s simpler and more complete.

Do I understand what he’s created?  Hardly.  There’s a good chance almost no one alive fully understands what he’s given the rest of us.

But studying history reminds us that many great discoveries can take hundreds of years before SOMEONE figures out a way to use them.

This is where behavior kicks in.  As students of behavior we have to study history in general, history of science in particular, and also many aspects of today’s behaviors in order to get an idea as to what will happen in the future.

After all, when all is said and done, isn’t that the real purpose of studying any subject?  The ability to predict.

If you don’t think so, let me know.  If you’re on board with the idea, stick around.  This year is going to be fun, because there are a whole lot of predictions about to be made.

Thanks for sticking around.  I knew I could “count” on you.

And Happy New Year everyone!

Tusok

 

John Conway on Surreal Numbers

Don Knuth talking about Surreal Numbers and the book he wrote about them.

 

Numbers are Fake News

How fake is fake?

Can you fake a cake?

How fake can a fact be faked, before it becomes an alternative fact?

A fake fact?

Can there be such a thing as a fake fact?

So many questions, so little time.

So I thought I’d have some fun playing with our minds in a totally different direction.

Numbers.

Are numbers real?

No, not real numbers, as in 1, 2, 3 and 4.  But are they in fact, real things within nature?

Spoiler alert…  they aren’t real!

How’s that for a brain bender?  Want to know why?  Check this out.

Go ahead and count something.  Jumping sheep? as you try to go to sleep?

Fine.  One sheep.  Two sheep.  That seems easy enough.

But wait.  Let’s sheer those sheep.  After all, you might like to have a nice woolly blanket to keep you warm while you sleep.

Now I have naked sheep.  Are they still two sheep?

Fine.  Two sheep.  Now, what if I cut their toenails?  Do I still have two sheep?

Yes?  Alright.  Now, let’s get gory.  Except that these are phantom sheep that only jump through my dreams.  So all of you sleep-sheep-lovers, please don’t get angry.

If I take the legs off the sheep, do I still have two sheep?  No?  Now we’re getting somewhere.

What if I only take off a bit of leg?  Better yet, how much leg will you let me remove from my sleep-sheep before it is no longer a sheep?

Forget sheep.  Let’s try a rock.

One rock.  Two rock.

What if my rocks hit each other and become three or four rocks?  How is this possible?

What if they bang about so much that they become a million rocks.  Are they still the same two rocks?

That’s my point.  Anything you choose is a thing only because we want it to be that thing.  Nature doesn’t work that way.  One sheep.  One rock.  One country.  One planet.  One star.  These are all made up in our minds.

The numbers that we use in math class are concepts that enable us to live better, understand Nature better.  But they are concepts, not real things you might find lying in the street.

Believe it or not, this is important.  It’s important because there is now a way to create numbers that is much more “natural” than our current method.  And I’m going to do my best to share that with you next time.

Until then, keep counting those sheep.

Have a great New Year’s everyone.