A Quote by Thomas Banchoff

The slicing technique from Flatland still remains one of the most powerful tools for dealing with aggregates in higher dimensions. — © Thomas Banchoff
The slicing technique from Flatland still remains one of the most powerful tools for dealing with aggregates in higher dimensions.
The pop-music video is one of the most powerful communication tools we have. Most people have access to a phone, and you can click a video and absorb it in three minutes. If it's potent enough, you can take in the message or have some sort of experience in multiple dimensions, the music with the image.
Higher dimensions of Awareness means Higher dimensions of energy.
Although most informed balletomanes would place artistry above technique, artistry without a strong technique is a flaccid, bloodless thing indeed, whereas technique without much artistry can still dazzle us in the manner of the circus or sports arena translated to a higher plane. Though the perfect blend of the two elements is the consummation devoutly to be wished, the real enemy of good ballet is not the slight preponderance of one or the other but the prevalence of pantomime--the turning of dance into second-rate theater.
For what is important when we give children a theorem to use is not that they should memorize it. What matters most is that by growing up with a few very powerful theorems one comes to appreciate how certain ideas can be used as tools to think with over a lifetime. One learns to enjoy and to respect the power of powerful ideas. One learns that the most powerful idea of all is the idea of powerful ideas.
There are still psychologists who, in a basic misunderstanding, think that gestalt theory tends to underestimate the role of past experience. Gestalt theory tries to differentiate between and-summative aggregates, on the one hand, and gestalten, structures, on the other, both in sub-wholes and in the total field, and to develop appropriate scientific tools for investigating the latter.
PowerPoint is like being trapped in the style of early Egyptian flatland cartoons rather than using the more effective tools of Renaissance visual representation.
Whether you're dealing with your allies in Europe or you're dealing with a resurgent Russia, whether you're dealing with Iran or North Korea, you have to use the whole panoply of national tools of power to deal with the challenges the world faces.
Humor is one of the most serious tools we have for dealing with impossible situations.
Do you think it's possible that things that seem to be discrete in three dimensions might all be part of the same bigger object in four dimensions? ...What if humanity- that collective noun we so often employ- really is, at a higher level, a singular noun? What it what we perceive in three dimensions as seven billion individual human beings are really all just aspects of one giant being?
For the most part you are dealing with jealousy, you are dealing with love, you're dealing with hatred, you are dealing with revenge and all of these sort of classic things.
If you want to do evil, science provides the most powerful weapons to do evil; but equally, if you want to do good, science puts into your hands the most powerful tools to do so
Technique itself springs from play, because we can acquire technique only by the practice of practice, by persistently experimenting and playing with our tools and testing their limits and resistances.
The most powerful tools you can have are information and knowledge.
Reflection is one of the most underused yet powerful tools for success.
The most powerful people in my town were the doctors and the lawyers. I didn't really have any experience dealing with really powerful people until I started practicing law.
One of the most powerful scientific tools ever invented is the telephone.
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