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.

爱因斯坦是一个复杂的人物和文化人物。他失去了他的第一个孩子，可能是父母的忽视，从来没有见过她(似乎)，尽管有一个很长但可行的火车车程。她在21个月大的时候去世，具体细节尚不清楚。沃尔特·艾萨克森(Walter Isaacson)的传记在这一点上比我在这里说的更公平。

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.

数学研究很便宜。当我们适当地支持它时，它可以是非常值得的。当我们在哲学上称之为规范性现实时，这就需要重新平衡尺度。这些是人类使用人类的工具来观察和描述他们自己的思想和自然。

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.

正如爱因斯坦所知，简化是解决问题的途径。是C挡了他的路。

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,

没有人能替代教授。我不应该那样做，也不应该那样做。如果这能让你感觉好点，你比我强多了。认识自己，那是一种浅吧。我犯错误，改变我的哲学，用每一句话和每一个学习重写我的生活。

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.

谢谢你回来。我尊重你的观点和见解，并认为它比我自己的更重要。这个世界比我看到的要美好。这也是我所寻求的。

Tim

就像你是我，就像1是一。
I can't thank you enough,
Be One. =

我不认为数学在它卑微的开端是永恒的。我以前可能暗示过这个概念，但不记得是什么时候或者与哪个帖子有关。我想我说过手指计数;算盘;等。这些使用数字的方法是随着时间和时间发展的。然而，它们不是永恒的。我记得我提到过微积分，牛顿和莱布尼茨……他们据称是独立开发的，大约在同一时间…牛顿不喜欢被抢风头这两个人都有这个想法并不奇怪。牛顿可能不是在被掉落的苹果击中后才顿悟的。 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!)

永恒是一个古怪的东西;浪漫的比喻。为什么?因为时间的流逝让一切可能发生的事情发生。但时间是无生命的——它不会引起任何事情的发生。

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...