There are very profound ways in which “2+2=5”, but modulo 3 is not one of them. There “2+2=1” or “2+2=-5”. All three of these statements have mathematical truth, as does “2+2=4”, and even more literary and philosophical depth.

There is a perceptual truth to the color of socks that begs the contingent fact as well.

Math as a metaphor for nature is deceptively accurate. Einstein and Tagore had a bout about this. Eugene Wigner was troubled by it. Arezoo had much more to say and misspoke a bit or would say more herself. Math is a hammer.

I liked this show and the topic, but as usual, there wasn’t enough time. That Islami thinks about time is prophetic of perhaps a future blog or show where she could shed light on time and math grazed and left wanting here.

Thanks, Ray, for the recommendation on Yackel’s book. I will attempt to figure that out over winter break.

2 + 2 = X, 3+1, #, or anything else, even a blank space. But there is one equation that is absolute, that unites everything, making everything just One. It is the equation that Einstein died searching for. And it was simply time that stood in his way, imagine that. = is the solution to his quest. = is the light at the end of the tunnel, the promised land, the truth.

What do we fight for? What did MLK, Gandhi, and Lincoln die for? Equal is the definition of justice. And what about our Democracy, it is based on equality. Yet for some reason, whilst we focus mathematically on the left and right side of an equation, = the truth or absolute is over-looked.

Has anyone had a class called Equal 101, anyone? We are taught mathematics but not equality. What is up with that? Maybe that is why we struggle with it so.

To answer the above question: equal is the Universal Truth.
Thanks, =

That is what Einstein's first wife said!

I kid, somewhat, but Einstein struggled with family/social norms, social justice, anti-semitism, and equality his entire life. Equality there did not match the equality of the unified theory that he pursued late in life. The devil is in the details.

Einstein was a complicated man and cultural figure. He lost his first child to potential parental neglect without ever meeting her (it seems) despite being a long but doable train ride away. She died at 21 months, the details of which are not clear. Walter Isaacson's biography is fairer to this than I am here.

It is funny that mathematics and Einstein run together so often, probably due to the visual simplicity of e=mc^2. Alfred was no natural mathematician (very few people are), and his first wife did help him with it. Einstein excelled at thought experiments that were not based on math for much of his lauded work.

Equality in math is vital, as is symmetry. However, that supersymmetry was not demonstrated at the large hadron collider points back to the still excellent standard model. I doubt time held back Einstein or the world. We have sunk many billions of dollars and brain hours looking for that equality sign. This may be due to a philosophical bias toward an a priori mathematical reality. That this reality is not necessarily present is reflected in some of Arezoo Islami's work. Not an "=", but a "?".

Math has never been as strong as it is today. Linear Algebra is running computational roughshod over previously intractable practical problems. Absolute top intellect is engaged and publishing preprints and communicating in a collegial environment that very much aims toward equality. Shinichi Mochizuki's proof of Szpiro's conjecture was published just this year in a mind-bending fashion that will take experts years to validate. We all should be celebrating co-existence with Terence Tao, Ed Frenkel, and Kiran Kedlaya et al. My personal favorite is Steven Strogatz. He has written many books for non-math and math types to explain the wonder and practicalities.

Math research is cheap. When we support it properly, it can be fantastically rewarding. When we philosophically call it a prescriptive reality, that calls for a rebalancing of the scales. These are human beings using human tools to look at and describe their own thoughts and nature.

I would prefer to talk to The Professor, but alas he is gone and you will have to do. There is some jest here too.
I feel better now.
As for time keeping Einstein from the truth he died searching for, it is true. He said it was Maxwell that taught him the universal constant of the speed of light. A constant that is probable at best. Had he understood that nature including light is truly immeasurable, as science itself has proven, QM or probability at best, he would have removed it from his famous equation. God does not play dice! Oh, now we are back to Copenhagen, from whence science has never left, nor resolved. For shame.
The flaw in science is in its very foundation, measure. "Man is the measure of all things," Protagoras said. The flaw in the scientific method of measure is spelled out in Heisenberg's Uncertainty Principle. Ye must have faith in science too!

What I am getting at here is the resolution of the QM problem, the solution to the Unified Field Theory, the answer to Einstein's quest, And, the proof of God! Truth is

If energy equal mass times the speed of light squared, but light is truly immeasurable, then his equation can be reduced by removing the uncertainty, leaving energy equals mass. And if energy equals mass then absolutely = is all that remains. In fact it is the only certainty in an equation. It is also the ultimate solution.
The mathematical equation for everything is =. = is the single truth.

As Einstein knew, simplification was the path to the solution. It was "C" that stood in his way.

How important is it you ask? it is what mankind has been fighting and dying for. MLK, Gandhi, Lincoln, Justice, Democracy, Civil War, BLM, uh everything. And science can't find the equation that unites everything, WOW!

Oh and I am so glad you mentioned the collider, my favorite. The solution is not dividing minute particles to find the God particle, the solution was in the unity of all particles, including space, science went the wrong way. Oneness anyone. What is more powerful than everything, another name for God?

Can One teach the blind to see, or must One learn to see Oneself? I think the answer here is the later, but then One can only TRY!

Be One, =

MJA,

There is no replacement for The Professor. I will not due, or do, for that matter. If that makes you feel better, you are a better person than I am. Knowing myself, that is a shallow bar. I make mistakes, change my philosophy, and rewrite my life with every word and learning.

As you say, one must learn to see oneself. It is good to understand the multiple meaning and import in that statement.

Math is a human device, as are algorithms. When we look with math to see, is it any wonder that we end up in Nick Bostrom’s simulation hypothesis. How do we refer to the world? That is a question left to us by others.

Though symmetry is fundamental to math, equality is not nor even to human culture. Equality is a tool that allows insight. The majority of humans show positive bias/affect/valence for those who look like them, not their equals. As you say, it is a struggle and a worthy one.

The majority of scientists, technologists, and capitalists, who drive our world, philosophically misunderstand mathematics and algorithms as separate from human tools. Elon Musk is one. Getting philosophical issues wrong is never good, always wasteful, and rarely serves the greater good.

I am confident we both aspire to the greater good, though I am not your equal.

Thanks for this get back. I respect your view and insight and give it greater weight than my own. It is a better world than I see. It is one I seek as well.

Tim

Equal is =, as you is I, as 1 is One.
I can't thank you enough,
Be One. =

I don't think math was timeless in its' humble beginnings. I may have implied this notion before, but don't recall when or in relation to which post. I think I said something about finger counting; the abacus; etc. That these methods of using number developed over time and IN time is given. They were not timeLESS, however. I recall mentioning something about the calculus, Newton and Leibnitz...that they allegedly developed it independently, around the same time...and Newton did not like being upstaged. That both men had this idea is not remarkable. Newton probably did not reach an epiphany after being struck by a falling apple. Leibnitz may have, but it remains that the idea happened in time, not timelessly.
If the feature of timelessness is fitting at all, it is fitting now; after most of what is known and useful in mathematics is, in fact, known and useful. If it will be argued that math, in its' usefulness, has enabled us to do things, impossible without it, there will be no argument from me: the passage of time and human innovation helped identify needs and wants; mathematics became algorithmic, and, things got done. Sometimes, propositional attitude is the father of progress, while laziness, the mother of invention, started it all. Remember you heard it here (just kidding!)

Timelessness is a quaint;. romantic metaphor. Why? Because the passing of time allows everything that can happen to happen. But time is inanimate---it does not cause anything to happen.

With the second paragraph of my 1/20/22 remarks, I was trying to get to a more fundamental, origin-based reason for the usefulness of math: a more, uh, pragmatic notion of an answer. There had to be a long view timeline on the entire project. When they developed a substantial ability to think, people also acquired the desire to DO. Doing necessitated a capacity to recognize and use relationships: primitively, if such-and-such, then, such-and-such, and so on. That sort of deductive reasoning 'grew up' in the stew of experience. In its' infancy, this mainly experiential means of doing must have been hit-or-miss, often as not. The next step, sans a sophisticated use of number, would have been replication-if we do this once and the outcome is favorable, will it be so if we do it again? Without a long history and dissertative discussion (which has already been done several ways), it is readily apparent all of this took a long time. And, at bottom, this is why math is so useful: once it was gotten right, then further refined and perfected, the sky was the only limit. So to speak. Then, it was discovered, that was not necessarily so...