Is math an invention of the human brain? Or does math exist in some abstract world, with humans merely discovering its truths? The debate has been raging since the time of the ancient Greeks.
Predictably, one of the answers seems to be: it depends on whom you ask. While most physicists are more or less evenly split, an overwhelming majority of engineers believe Mathematics is invented, while most mathematicians, along with Plato, view Math as an fundamental truth, independent of mankind, which we slowly uncover as we go.
Edward Frenkel is no exception to the statistics. Indeed it is with a rare enthusiasm that he defends the Platonist conviction:
He is not alone. Godfrey Harold Hardy, Roger Penrose, Kurt Gödel and many others have sided with Plato, while David Hilbert, Georg Cantor, the group known as Nicolas Bourbaki, and even Einstein held the opposite view.
Even if you have chosen a camp, however, the mystery remains intact. If you believe mathematics is invented by humans just like cars and operas, then, why does the world seem to obey its laws? As Einstein famously asked “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?” Or as Eugene Wigner wrote in his 1960 article The Unreasonable Effectiveness of Mathematics in the Natural Sciences “The miracle of the appropriateness of the language of mathematics to the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.”
On the other hand, if, like Frenkel, you believe mathematics exists independent of humans, that it was here before we evolved and will continue on long after we’re extinct, if you are, in short, a Platonist then you will ask: why are we humans able to grasp these concepts, to understand, in the words of Galileo, the language of God? And you will exclaim, with Einstein again: “The most incomprehensible thing about the universe is that it is comprehensible.”
So far, no one has any good answer. Some would see it as a problem. I regard it as an gift. Every time our thought process leads us to an apparently unsolvable conundrum, there is the invitation to recognize the limitations of thought itself, and to access Truth beyond the world of ideas. There is the opportunity to see that we have been trying to box reality in an either-or proposition of our own creation, and that it does not fit!
Take, as an analogy, the age-old debate between free will and destiny. Both of these are concepts. The idea that something could have happened any different than it did only exists in my head; so does the idea that it was predetermined to happen the way it did. Since we cannot rewind time, there is no conceivable experiment that can decide between these two statements. Therefore, the question itself is non-scientific, irrelevant, ill-conceived. It isn’t a question about Reality, it is a question about the model we’ve constructed about it, and it shows, exquisitely, the limitations of that model.
Another great opportunity to practice this ancient tantric meditation from Kashmir Shaivism: picture holding these two opposite ideas, one in each hand. First let one penetrate you, then let the other. When you feel ready, hold both together in your mind, as long as needed. When the illusion of linear thought is revealed, suddenly drop them both. You will feel like a heavy weight just lifted off your shoulders.
One step further, know the ineffable…
SAND co-founder Zaya Benazzo interviews Turiya Hanover, co-founder of The Path of Love
Aisha Salem talks of being willing to let go of our limitations, of keeping ourselves small, and of living our individuality
The universe is dreaming us up and we are all dreaming our lives into being.
"It is not a person that is waking up, it is consciousness."
Richard Rohr, as a Catholic priest and Franciscan Friar, will offer a concise history of how Western Christianity once had, soon lost, tried to retrieve, and now is roundly rediscovering its own traditional understanding of unitive consciousness
When even the sense of being collapses into the utter simplicity of what is.
Can you live "IN" the Dream world with absolute integrity and authenticity
What may or may not be appropriate behavior for a spiritual teacher?
In most spiritual traditions, love is seen only as universal or cosmic love.
Nonduality and Healing from Trauma - The Realization Process
Ever wonder how we try to predict the unpredictable? Supercomputers use the power of chaos theory.
Discover the esoteric relationship between form and formlessness embedded within the Shema
Performing at the opening night of the 2019 SAND gathering in Italy, Parvathy Baul sings and dances
In this inspiring talk, the mathematician Edward Frenkel speaks about the beauty and elegance of mathematics
To think of the human stage as simply for enlightenment shortchanges the potential of humanity.
The Yamabushi in northern Japan practice a once forbidden ancient religion. While their tradition is at risk of disappearing, it offers a way for those seeking a different path in Japan‘s society.
Lama Tsomo teaches us the ancient Tibetan compassion practice of Tonglen, one of the Four Boundless Qualities
Is it possible to live a life of activity while holding the perception of unity and fulfillment?
It's not only a big deal; it's the biggest deal of all.
While we have unlocked the potential of a single atom we have yet to unlock the full potential of wise, loving and compassionate action
This video is about Bell's Theorem, one of the most fascinating results in 20th century physics.
In this interview with Zaya Benazzo from SAND Italy, Ellen Emmet talks about the relationship between self-enquiry and the exploration of the body through tantra.
Dzogchen, the bardo, sleep and the yoga of dreams
Yoga does not bring us to truth, truth expresses itself through yoga.
There are many things that affect our mental health, from work-related stress to past traumas to whether or not we meditate each day.
In a rare meeting of minds, and a rare exploration of whether there is a predilection for spirituality, Gabor Mate asks Adyashanti to expand on passages from his recent book My Secret Is Silence.
Silent awareness is mostly drawn to light, sound, color, beauty, movement, patterns and contrast.
Ever since the tender age, I’ve had this passionate love affair with the aspen trees
Please enter your email and we’ll send you instructions to reset your password