There is a Last Number and also Infinity

InfinityI’ve decided while the concept of infinity exists so does a final number. Full disclosure: I’m not good at math and I’m hardly a mathematician. That being said, the subject of infinity and numbers proves to be an endlessly fascinating subject for me. I assert that infinity and a final number can coexist. Any mathematicians care to tell me the depths of my stupidity? I’ll be reading the comments.

It would seem at first glance the two concepts are incompatible. If there is a final, last number, then infinity cannot exist and vice versa. Here’s the factor that existing theory, in my opinion, fails to take into account. Neither numbers nor infinity are real. That is to say they are both incredibly useful constructs but they don’t actually exist. In the same way the words you are reading don’t really exist, that emotions like love and hate don’t have physical form.

Sure, we feel love. I’m not denying we have emotions. Nor do I pretend the words I have written and you are reading don’t have meaning. I’m just saying they only exist as constructs of the human mind that help us organize our world in convenient ways. Words are merely jots on a page approximating sounds. We give those sounds meaning in the same way we give letters and groupings of letters meaning they do not actually have.

Numbers are wholly constructed to make life easier to understand and move through. Time is likewise a human construct that simply does not actually exist in a physical way. You cannot weigh an emotion, a number, a word, or a unit of time. These things are all incredibly useful. We would not have the world we live in without these constructs but they are simply that, constructs.

If numbers don’t actually exist, which is my assertion, then the last number is simply the largest number we have so far named. Certainly, a larger number can be imagined but until that moment; it does not exist, even in a constructed fashion. Currently we can say that Graham’s Number is the largest number in the world. That being said, the concept of infinity is also a human construct and exists as such side by side with Graham’s Number.

Pi does not really exist and therefore the last digit of Pi, base 10, is the one we have most fully calculated. Thus, Pi has a last digit but is also infinite.

What are the practical implications of my hypothesis? Nothing, really. The world is the same whether or not we consider numbers to be real or simply constructs. My life does not change nor does yours. However, once I accepted this idea, that time, numbers, words, and emotions are merely names we associate with constructs in order to make our world more orderly, the less importance they have. They are tools to be used to achieve results but I need not worry about their bounds or origins.

Who created the numeric constants of the universe? Us, simply because they don’t actually exist.

Tom Liberman

Science Rocks

Science Week – Engineering

ScienceMy third day of Science Week pays tribute to the engineers of the world, both past and present. If it wasn’t for them we wouldn’t be able to get to work in the morning, or at least it would not be nearly as easy. So, stick around and learn all about engineering!

Engineers have been an integral part of improving society since people began to write down their achievements and likely long before that!

Engineering has fascinated the world since early times with the ancients making spectacular structures like the Pyramids of Egypt, the Lighthouse of Alexandria, the Parthenon, the Great Wall of China, and the list goes on. I could easily wax poetic about my favorite subject, history, until your eyes bleed but I’ll refrain, you can thank me later in the comments.

My goal today is talk about how engineering and engineers have changed your life for the better and how important it is that we continue to encourage people to take up this noble field. Math and science are the backbone of all technological achievements and we do well as a society to tell children exactly that and reward them when they show an interest in those fields.

Modern engineering began in the Renaissance with men like William Gilbert and Thomas Savery A look at the biographies of those men is well worth a perusal for anyone with a casual interest in engineering.

The modern era traces its roots to Allesandro Voltra, Michael Faraday, and George Ohm among others. Gosh, I really could write a blog about each of these amazing men but as I sit here at my computer I cannot help but think about how much my life depends on modern engineering.

At its most basic engineers apply the principals of Physics and Mathematics to improve the status quo.

My alarm clock wakes me up in the morning and without the ability to tell exact time modern life ceases to exist as we know it. Thank you, John Harrison.

Of course, the alarm clock wouldn’t work without electricity, so thank you again, Allesandro!

I’m about to drive thirty miles to work. That’s a distance that would have been impossible until automobiles were invented and then roads for them to traverse. We take roads for granted but without them life is very different. I’m tempted to talk about the Via Appia and Appius Cladius Caecus but must refrain, stay on topic!

Concrete. There’s a story. I don’t have time to tell it all but suffice it say that the Roman engineers so valued it they kept their formulations as tightly held secrets. When the Empire fell concrete was lost until likely the 16th Century. Old Roman ruins still stand today!

My work today is in Granite City, Illinois and my drive takes me past the home of the St. Louis Cardinals, Busch Stadium. Thank you, Jim Chibnall. I might be tempted to mention that this ballfield is where I get to see Adam Wainwright apply the principals of aerodynamics to the curveball.

Today I teach steelworkers how to use computers but as long as we’re talking about steel we need to think about all the products that use it. Did I mention that after I pass the stadium I get to see the most beautiful monument in the world? Thank you, Eero Saarinen and Hannskarl Bandel for the Gateway Arch. Made of steel.

Steel is in virtually every building, every car, and certainly in the Eades Bridge on which I drive over the Mississippi River. Thank you, James B. Eades.

Gosh, this post could go on forever and I haven’t even gotten out of the car! So, take a few seconds to appreciate all the work of engineers the world over and how it effects your life at almost every moment.

It seems like we want to emphasize business, and medicine, and law when it comes to educating our children these days and there is nothing wrong with those fields but without the engineers of the world … well … the world wouldn’t be what we know it.

So to all you future engineers out there, including my niece Tess, who are studying hard, keep up the good work! You will change the world.

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Tom Liberman
Sword and Sorcery fantasy with a Libertarian Twist