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Geometry

Geometry

Search complete. 120 mentions across 30 episodes found for "Geometry".

Sep 13, 2026

David WalesNARRATOR
201:09
But it is not without good reason that some of the greatest men have devoted special attention to this science.
David WalesNARRATOR
201:16
Geometry has two divisions; one is concerned with numbers, the other with figures.
David WalesNARRATOR
201:21
Now, knowledge of the former is a necessity, not merely to the orator, but to any one who has had even an elementary education.
David WalesNARRATOR
201:30
Such knowledge is frequently required in actual cases, in which a speaker is regarded as deficient in education, I will not say if he hesitates in making a calculation, but even if he contradicts the calculation which he states in words by making an uncertain or inappropriate gesture with his fingers.
David WalesNARRATOR
201:58
But geometry and oratory are related in a yet more important way than this.
David WalesNARRATOR
202:04
In the first place, logical development is one of the necessities of geometry.
David WalesNARRATOR
202:10
And is it not equally a necessity for oratory? Geometry arrives at its conclusions from definite premises, and by arguing from what is certain proves what was previously uncertain.
David WalesNARRATOR
202:23
Is not this just what we do in speaking? Again, are not the problems of geometry almost entirely solved by the syllogistic method, a fact which makes the majority assert that geometry bears a closer resemblance to logic than to rhetoric? But even the orator will sometimes, though rarely, prove his point by formal logic.
King BachPANELIST
18:38
In.
OliviaGUEST
18:38
Geometric.
King BachPANELIST
18:39
What's geometric? Isn't that math?
OliviaGUEST
18:41
Yeah.
Kelly BeshearNARRATOR
4:43
But perhaps this feeling of proud certainty would leave you immediately if someone were to ask you, What then do you mean by the assertion that these propositions are true? Let us proceed to give this question a little consideration.
Kelly BeshearNARRATOR
4:57
Geometry sets out from certain conceptions such as plane, point, and straight line with which we are able to associate more or less definite ideas, and from certain simple propositions or axioms which, in virtue of these ideas, we are inclined to accept as true.
Kelly BeshearNARRATOR
5:14
Then on the basis of a logical process, the justification of which we feel ourselves compelled to admit, all remaining propositions are shown to follow from those axioms, i.e. they are proven.
Kelly BeshearNARRATOR
5:26
A proposition is then correct or true when it has been derived in the recognized manner from the axioms.
Kelly BeshearNARRATOR
5:54
We can only say that Euclidean geometry deals with things called straight lines, to each of which is ascribed the property of being uniquely determined by two points situated on it.
Kelly BeshearNARRATOR
6:06
The concept true does not tally with the assertions of pure geometry, because by the word true we are eventually in the habit of designating always the correspondence with a real object.
Kelly BeshearNARRATOR
6:18
Geometry, however, is not concerned with the relation of the ideas involved in it to objects of experience, but only with the logical connection of these ideas among themselves.
Kelly BeshearNARRATOR
6:28
It is not difficult to understand why, in spite of this, we feel constrained to call the propositions of geometry true.
Landon D. C. ElkindNARRATOR
158:11
It was formerly supposed that pure reason could decide, in some respects, as to the nature of the actual world.
Landon D. C. ElkindNARRATOR
158:18
Geometry, at least, was thought to deal with the space in which we live.
Landon D. C. ElkindNARRATOR
158:22
But we now know that pure mathematics can never pronounce upon questions of actual existence.
Landon D. C. ElkindNARRATOR
158:28
The world of reason, in a sense, controls the world of fact, but it is not at any point creative of fact, and in the application of its results to the world in time and space, its certainty and precision are lost among approximations and working hypotheses.

50 MINS LATER

Landon D. C. ElkindNARRATOR
209:07
The study of different types of series is a general subject of which the study of ordinal numbers mentioned above is a special and very interesting branch.
Landon D. C. ElkindNARRATOR
209:17
But the unavoidable technicalities of this subject render it impossible to explain to any but professed mathematicians.
Landon D. C. ElkindNARRATOR
209:25
Geometry, like arithmetic, has been subsumed in recent times under the general study of order.
Landon D. C. ElkindNARRATOR
209:32
It was formerly supposed that geometry was the study of the nature of the space in which we live.
Steve PattersonHOST
19:14
It's just states of geometry in relation to one another.
Steve PattersonHOST
19:19
The problem with that view is it doesn't explain behavior at all.
Steve PattersonHOST
19:23
Geometry doesn't get us to physics.
Steve PattersonHOST
19:27
even if you have some fundamental, whatever the geometric construction of that fundamental subunit is, even if we understand how, you know, you use the term enchained, I think, in there, however it's enchained geometrically, it doesn't actually give us any explanation for why the universe would proceed to the next state the way that it does.
Steve PattersonHOST
19:49
without some additional stuff.

28 MINS LATER

Steve PattersonHOST
48:08
So this is sort of the same thing.
Steve PattersonHOST
48:10
What I'm saying is there is no...
Steve PattersonHOST
48:14
Geometry does not give us an explanation for why there is pushing or pulling.
WilkinHOST
17:45
"It's a growth axis," Raphael whispered.
WilkinHOST
17:48
"Geometric, biological.
WilkinHOST
17:49
If we overlaid this on cellular mitosis..." Caspar interrupted, agitated.
WilkinHOST
17:54
"Or it's a marker of something moving down there, using us to track it, or us as part of it." Safe's hand shook.
Kelly BeshearNARRATOR
4:41
Physical Meaning of Geometrical Propositions.
Kelly BeshearNARRATOR
4:45
in your school days most of you who read this book made acquaintance with the noble building of euclid's geometry and you remember perhaps with more respect than love the magnificent structure on the lofty staircase of which you were chased about for uncounted hours by conscientious teachers by reason of our past experience you would certainly regard every one with disdain who should pronounce even the most out-of-the-way proposition of this science to be untrue but perhaps this feeling of proud certainty would leave you immediately if some one were to ask you what then do you mean by the assertion that these propositions are true let us proceed to give this question a little consideration Geometry sets out from certain conceptions such as plane, point, and straight line with which we are able to associate more or less definite ideas, and from certain simple propositions or axioms which, in virtue of these ideas, we are inclined to accept as true.
Kelly BeshearNARRATOR
5:45
Then, on the basis of a logical process, the justification of which we feel ourselves compelled to admit, all remaining propositions are shown to follow from those axioms.
Kelly BeshearNARRATOR
5:56
i e they are proven a proposition is then correct or true when it has been derived in the recognized manner from the axioms the question of truth of the individual geometrical propositions is thus reduced to one of the truth of the axioms Now it has long been known that the last question is not only unanswerable by the methods of geometry, but that it is in itself entirely without meaning.

7 MINS LATER

Kelly BeshearNARRATOR
13:21
We speak of the height of the cloud, even when the pole which reaches the cloud has not been erected.
Kelly BeshearNARRATOR
13:27
By means of optical observations of the cloud from different positions on the ground, and taking into account the properties of the propagation of light, we determine the length of the pole we should have required in order to reach the cloud.
Kelly BeshearNARRATOR
13:38
From this consideration we see that it will be advantageous if, in the description of position, it should be possible by means of numerical measure to make ourselves independent of the existence of marked positions, those possessing names, on the rigid body of reference.
Kelly BeshearNARRATOR
13:55
In the physics of measurement, this is attained by the application of the Cartesian system of coordinates.
NickHOST
4:15
Mathematical demonstrations could be preserved even when the cosmologies surrounding them were challenged or abandoned.
NickHOST
4:22
Geometry could therefore cross religious boundaries more easily than many other elements of classical culture.
NickHOST
4:29
Christian theologians could reject the eternity of the cosmos while accepting the mathematical disciplines used to describe it.
NickHOST
4:36
They could deny the stars were gods while continuing to calculate their motions, oppose divination while preserving astronomy, and criticize pagan metaphysics while retaining the conviction that creation possessed order, proportion, and intelligibility.

6 MINS LATER

NickHOST
11:11
The world can function as a book because its author is also the author of scripture.
NickHOST
11:15
Natural forms, numerical patterns, animals, plants, colors, stones, and celestial motions might carry meanings when interpreted within the structure of Christian teaching.
NickHOST
11:27
Geometry, therefore, occupied an unusual position between nature and theology.
NickHOST
11:32
The geometric form was created by human hands, yet the relationships governing it were not invented arbitrarily.
speaker_2NARRATOR
50:52
Let us grant that the pursuit of mathematics is a Divine madness of the human spirit,—a refuge from the goading urgency of contingent happenings.
speaker_2NARRATOR
51:02
When we think of Mathematics we have in our mind a Science devoted to the exploration of Number, Quantity, Geometry, and in modern times also including investigation into yet more abstract concepts of order, and into analogous types of purely logical Relations.
speaker_2NARRATOR
51:17
The point of Mathematics is that in it we have always got rid of the Particular Instance, and even of any particular Sorts of Entities.
speaker_2NARRATOR
51:24
So that e.g., no Mathematical truths apply merely to fish, or merely to stones, or merely to colours.

18 MINS LATER

speaker_2NARRATOR
69:52
Between the epoch which stretches from Pythagoras to Plato and the epoch comprised in the seventeenth century of the Modern World nearly two thousand years elapsed.
speaker_2NARRATOR
70:00
In this long interval mathematics had made immense strides.
speaker_2NARRATOR
70:04
Geometry had gained the study of conic sections and trigonometry; the method of exhaustion had almost anticipated the integral calculus; and above all the Arabic arithmetical notation and algebra had been contributed by Asiatic thought.
speaker_2NARRATOR
70:18
But the progress was on technical lines.
Eric RankinHOST
33:27
My hypothesis and theory is that the Schumann resonance once was 9.
Eric RankinHOST
33:33
And then all geometry, man-made, extraterrestrial-made, or nature-made, is in literal harmony with this 9.
Eric RankinHOST
33:44
Because they all subtotal to nine.
Eric RankinHOST
33:46
So there's people that believe that things like the pyramids were like harmonic balancers or harmonic creators to somehow affect and hold this nine resonance where all of nature, including us, just nestles underneath it, inside of it, through it.
Eric RankinHOST
34:12
It only sounds like a difference from eight to nine hertz, one vibration cycle per second.
Eric RankinHOST
34:18
But to achieve that would be difficult in our understanding of light, speed of light in the ionosphere.
Eric RankinHOST
34:24
But to me, it makes a whole lot of sense that somebody – When extraterrestrials gave us a 360-degree circle, giving us launching all geometry, totaling nine, it would make a lot of sense to me that the Schumann Resonance was actually supposed to be or once was or could be again a perfect nine and everything just hums right inside of it then.
Susan ManewichGUEST
34:46
Mic drop.

20 more episodes mention Geometry.

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